Analytical Methods for Lawyers

 

v    Idea of the Course

¯    Brief survey of lots of areas useful to lawyers

¯    Many of which could be a full course--my L&E

¯    Enough so that you won't be lost when they come up, and É

¯    Can learn enough to deal with them if it becomes necessary.

v    Mechanics

¯    Reading is important

¯    Discussion in class

¯    Homework to be discussed but not graded--way of testing yourself

¤       Prefer handout hardcopy or on web page? URL on handout

¯    Midterm? First time.

v   Topics

¯    Decision Analysis

¯    Game Theory

¯    Contracting: Application of Ideas

¯    Accounting.

¯    Finance

¯    Microeconomics.

¯    Law and Economics.

¯    Statistics.

¯    Multivariate Statistics: Untangling one out of many causes. Death penalty

v    First Topic: Decision Analysis

¯    Way of formally setting up a problem to make it easier to decide   

¯    Typically

¤       Make a choice.

¤       Observe the outcome, depends partly on chance

¤       Make another choice.

¤       Continue till the end, get some cost or benefit

¤       Want to know how to make the choices to maximize benefit or minimize cost

¯    Simple Example: Settlement negotiations

¤       Accept settlement (known result) or go to trial

¤       If trial win with some probability and get some amount, or lose and have costs

¤       Compare settlement offer to average outcome at trial, including costs.

¯    Fancy example: Hazardous materials disposal firm

¤       You suspect employees may have cut some corners, violated disposal rules

¤       First choice: Investigate or don't.

á       If you don't, probably nothing happened (didn't violate or don't get caught)

á       If you do, some probability that you discover there is a problem. If so É

¤       Conceal or report to EPA

á       If you conceal, risk of discovery--greater than at previous stage (whistleblowers)

á       If you report, certain discovery but lower penalty

¯    In each case, how do you figure out what to do? Two parts:

¤       If you knew all the probabilities and payoffs, how would you decide (Decision Analysis)

¤       What are the probabilities and payoffs, and how do you find them?

¯    Simple case again: Assuming numbers

¤       First pass

á       Settlement offer is $70,000

á       Trial cost is $20,000

á       Sure to win

á       Tree diagram

á       Lop off inferior branch--easy answer

¤       Second pass: As above, but 60% chance of winning

á       Square for decision, circle for chance node

á       On average, trial gives you $40,000

á       Is that the right measure?

á       If so, inferior. Lop off that branch

á       Settle

¤       Risk aversion

á       If you are making similar decisions many times, expected value.

á       If once, depends on size of stakes.

¯    Where do the numbers come from?

¤       Alternatives: Think. Talk to client, colleagues, É  Think through alternatives.

á       Partly your professional expertise

á       Forces you to think through carefully what the alternatives are.

¤       Probabilities

á       Might have data--outcome of similar cases in the past. Audit rate.

á       Generate it--mock trial. Hire an expert.

á       By intuition, experience. Interrogate. What bets would I accept?

¤       Payoffs

á       Include money--costs, profits, fines, É Past cases, experts, É .

á       Reputational gains and losses

á       For an individual, moral gains and losses? Other nonpecuniary?

¯    Sensitivity analysis

¯    (Land Purchase Problem?)

¯    Is ethics relevant?

¤       Criminal trial--does it matter if you think your client is guilty?

¤       EPA--does it matter that concealing may be illegal. Immoral?

á       What if not looking for the problem isn't illegal, but É

á       Finding and concealing is?

v   Query re Becca

v    Mechanics

¯    Office Hours handout

¯    Everyone happy with doing stuff online?

v    Review: Points covered

¯    Basic approach

¤       Set up a problem as

á       Boxes for choices

á       Circles for chance outcomes

á       Lines joining them

á       Payoffs, + or -, and probabilities.

¤       Calculate the expected return from each choice, starting with the last ones

á       Since the payoff from one choice

á       May depend on the previous choice or chance.

¤       If one choice has a lower payoff than an alternative at the same point, lop that branch

¤       Work right to left until you are left with only one series of choices.

¯    Complications

¤       Expected return only if risk neutral

¤       You have to work out the structure, with help from the client and others

¤       Estimate the probabilities, and É

¤       Payoffs, not all of which are in  money.

¯    Sensitivity analysis to find out whether the answer changes if you change your estimates.

v    Handout problems

¯    Settle or go to trial

¯    Which contract to offer

¤       Easy answer for the team

¤       Note that we have implicitly solved the player's problem too.

á       Upper contract, if he has back pain, playing costs him $2 million, gets him nothing, not playing neither costs nor gets, so don't play

á       Lower contract, if he has back pain, playing costs him $2 million, gets him $10 million. Not playing gets and costs nothing. So he plays.

¤       Note also a third option, that we didn't mention--no contract.

á       Better than the first

á       Could change the numbers to make it better than the second

á       Demonstrating that one has to figure out the structure of the problem.

v    Questions?

v    More book problems

¯    Land purchase problem

v     

v    Game Theory Intro: Show puzzling nature by examples

¯    Bilateral monopoly

¤       Economic case--buyer/seller, union/employer

¤       Parent/child case

¤       Commitment strategies

á       In economic case

á       Aggressive personality.

 

1/17/06

 

v    Move to front of the room

v    Strategic Behavior: The Idea

¯    A lot of what we do involves optimizing against nature

¤       Should I take an umbrella?

¤       What crops should I plant?

¤       How do we treat this disease or injury?

¤       How do I fix this car?

¯    We sometimes imagine it as a game against a malevolent opponents

¤       Finagle's Law: If Something Can Go Wrong, It Will

¤       "The perversity of inanimate objects"

¤       Yet we know it isn't

¯    But consider a two person zero sum game, where what I win you lose.

¤       From my standpoint, your perversity is a fact not an illusion

¤       Because you are acting to maximize your winnings, hence minimize mine

¯    Consider a non-fixed sum game--such as bilateral  monopoly

¤       My apple is worth nothing to me (I'm allergic), one dollar to you (the only customer)

¤       If I sell it to you, the sum of our gains is É  ?

¤       If bargaining breaks down and I don't sell it, the sum of our gains is É  ?

¤       So we have both cooperation--to get a deal--and conflict over the terms.

¤       Giving us the paradox that

á       If I will not accept less than $.90, you should pay that, but É

á       If you will not offer more than $.10, I should accept that.

¤       Bringing in the possibility of bluffs, commitment strategies, and the like.

¯    Consider a many player game

¤       We now add to all the above a new element

¤       Coalitions

¤       Even if the game is fixed sum for all of us put together

¤       It can be positive sum for a group of players

¤       At the cost of those outside the group

v    Ways of representing a game

¯    Like a decision theory problem

¤       A sequence of choices, except that now some are made by player 1, some by player 2 (and perhaps 3, 4, É)

¤       May still be some random elements as well

¤       Can rapidly become unmanageably complicated, but É

¤       Useful for one purpose: Subgame Perfect Equilibrium

¤       Back to our basketball player--this time a two person game

 

¤       But É Tantrum/No Tantrum game

¤       So Subgame Perfect works only if commitment strategies are not available

 

 

 

 

 

¯    As a strategy matrix

¤       Works for all two player games

¤       A strategy is a complete description of what the player will do under any circumstances

¤       Think of it as a computer program to play the game

¤       Given two strategies, plug them both in, players sit back and watch.

¤       There may still be random factors, but É

¤       One can define the value of the game to each player as the average outcome for him.

¯    Dominant Solution: Prisoner's Dilemma as a matrix

¤       There is a dominant pair of strategies--confess/confess

á       Meaning that whatever Player 1 does, Player 2 is better off confessing, and

á       Whatever Player 2, does Player 1 is better off confessing

á       Even though both would be better off if neither confessed

 

 

Baxter

Confess

Deny

Chester

Confess

10,0

0,15

Deny

15,0

1,1

¤       How to get out of this?

á       Enforceable contract

¬     I won't confess if you won't

¬     In that case, using nonlegal mechanisms to enforce

á       Commitment strategy--you peach on me and when I get out É

¯    Von Neumann Solution

¤       Von Neumann proved that for any 2 player zero sum game

¤       There was a pair of strategies, one for player A, one for B,

¤       And a payoff P for A (-P for B)

¤       Such that if A played his strategy, he would (on average) get at least P whatever B did.

¤       And if B played his, A would get at most P whatever he did

¯    Nash Equilibrium

¤       Called that because it was invented by Cournot, in accordance with Stigler's Law

á       Which holds that scientific laws are never named after their real inventors

á       Puzzle: Who invented Stigler's Law?

¤       Consider a many player game.

á       Each player chooses a strategy

á       Given the choices of the other players, my strategy is best for me

á       And similarly for everyone else

á       Nash Equilibrium

¤       Driving on the right side of the road is a Nash Equilibrium

á       If everyone else drives on the right, I would be wise to do the same

á       Similarly if everyone else drives on the left

á       Multiple equilibria

¤       One problem: It assumes no coordinated changes

á       A crowd of prisoners are escaping from Death Row

á       Faced by a guard with one bullet in his gun

á       Guard will shoot the first one to charge him

á       Standing still until they are captured is a Nash Equilibrium

¬     If everyone else does it, I had better do it too.

¬     Are there any others?

á       But if I and my buddy jointly charge him, we are both better off.

¤       Second problem: Definition of Strategy is ambiguous. If you are really curious, see the game theory chapter in my webbed Price Theory

v    Solution Concepts

¯    Subgame Perfect equilibrium--if it exists and no commitment is possible

¯    Strict dominance--"whatever he does É" Prisoner's Dilemma

¯    Von Neumann solution to 2 player game

¯    Nash Equilibrium

¯    And there are more

1/19/06

 

v    A simple game theory problem as a lawyer might face it:

 

You represent the plaintiff, Robert Williams, in a personal injury case. Liability is fairly

clear, but there is a big dispute over damages. Your occupational expert puts the plaintiffÕs expected future losses at $1,000,000, and the defendantÕs expert estimates the loss at only $500,000. (Pursuant to a pretrial order, each side filed preliminary expert reports last month and each party has taken the deposition of the opposing partyÕs expert.) Your experience tells you that, in such a situation, the jury is likely to split the difference, awarding some figure near $750,000.

 

The deadline for submitting any further expert reports and final witness lists is rapidly

approaching. You contemplate hiring an additional expert, at a cost of $50,000. You suspect that your additional expert will confirm your initial expertÕs conclusion. With two experts supporting your higher figure and only one supporting theirs, the juryÕs award will probably be much closer to $1,000,000 — say, it would be $900,000.

 

You suspect, however, that the defendantÕs lawyer is thinking along the same lines. (That

is, they could find an additional expert, at a cost of about $50,000, who would confirm their initial expertÕs figure. If they have two experts and you have only one, the award will be much closer to $500,000 — say, it would be $600,000.)

 

If both sides hire and present their additional experts, in all likelihood their testimony will

cancel out, leaving you with a likely jury award of about $750,000. What should you advise your client with regard to hiring an additional expert?

 

Any other ideas?

 

Set it up as a payoff matrix

 

If neither hires an additional expert, plaintiff receives $750,000 and defendant pays $750,000?

 

If plaintiff hires an additional expert, plaintiff receives $850,000 and defendant pays $900,000

 

If defendant hires an additional expert, plaintiff receives $600,000 and defendant pays $650,000?

 

If both hire additional experts, plaintiff receives $700,000 and defendant pays $800,000?

 

 

 

Defendant:

Doesn't hire

Defendant:

Hires

Plaintiff:

Doesn't Hire

750, -750

600, -650

Plaintiff:

Hires

850, -900

700, -800

 

What does Plaintiff do?

 

What does Defendant do?

 

What is the outcome?

 

Can it be improved?

 

How?

 

v    Game Theory: Summary

¯    The idea: Strategic behavior.

¤       Looks like decision theory, but fundamentally different

¤       Because even with complete information, it is unclear

á       What the solution is or even

á       What a solution means

¤       With decision theory, there is one person seeking one objective, so we can figure out how he can best achieve it.

¤       With game theory, there are two or more people

á       seeking different objectives

á       Often in conflict with each other

¤       A solution could be

á       A description of how each person decides the best way to play for himself or

á       A description of the outcome

¯    Solution concepts

¤       Subgame perfect equilibrium

á       assumes no way of committing

á       No coalition formation

¬     In the real world, A might pay B not to take what would otherwise be his ideal choice--

¬     because that will change what C does in a way that benefits A.

¬     One criminal bribing another to keep his mouth shut, for instance

á       But it does provide a simple way of extending the decision theory approach

¬     To give an unambiguous answer

¬     In at least some situations

¬     Consider our basketball player problem

¤       Dominant strategy--better against everything. Might not exist in two senses

á       If I know you are doing X, I do Y—and if you know I am doing Y, you do X. Nash equilibrium. Driving on the right. The outcome may not be unique, but it is stable.

á       If I know you are doing X, I do Y—and if you know I am doing Y, you don't do X. Unstable. Scissors/paper/stone.

¤       Nash equilibrium

á       By freezing all the other players while you decide, we reduce it to decision theory for each player--given what the rest are doing

á       We then look for a collection of choices that are consistent with each other

¬     Meaning that each person is doing the best he can for himself

¬     Given what everyone else is doing

á       This assumes away all coalitions

¬     it doesn't allow for two ore more people simultaneously shifting their strategy in a way that benefits both

¬     Like my two escaping prisoners

á       It also ignores the problem of how to get to that solution

¬     One could imagine a real world situation where

¯    A adjusts to B and C

¯    Which changes B's best strategy, so he adjusts

¯    Which changes C and A's best strategies É

¯    Forever É

¬     A lot of economics is like this--find the equilibrium, ignore the dynamics that get you there

¤       Von Neumann solution aka minimax aka saddlepoint aka É.?

á       It tells each player how to figure out what to do, and É

á       Describes the outcome if each follows those instructions

á       But it applies only to two person fixed sum games.

¤       Von Neumann solution to multi-player game (new)

á       Outcome--how much each player ends up with

á       Dominance: Outcome A dominates B if there is some group of players, all of whom do better under A (end up with more) and who, by working together, can get A for themselves

á       A solution is a set of outcomes none of which dominates another, such that every outcome not in the solution is dominated by one in the solution

á       Consider, to get some flavor of this, É

¤       Three player majority vote

á       A dollar is to be divided among Ann, Bill and Charles by majority vote.

¬     Ann and Bill propose (.5,.5,0)--they split the dollar, leaving Charles with nothing

¬     Charles proposes (.6,0,.4). Ann and Charles both prefer it, to it beats the first proposal, but É

¬     Bill proposes (0, .5, .5), which beats that É

¬     And so around we go.

á       One Von Neumann solution is the set: (.5,.5,0), (0, .5, .5), (.5,0,.5) (check)

á       There are others--lots of others.

¤       Other approaches to many player games have been suggested, but this is enough to show two different elements of the problem

á       Coalition formation, and É

á       Indeterminacy, since one outcome can dominate other which dominates another which É .

¤       Almost enough to make you appreciate Nash equilibrium, where nobody can talk to anybody so there is no coalition formation.

v    Applied Schelling Points

¯    In a bargaining situation, people may end up with a solution because it is perceived as unique, hence better than continued (costly) bargaining

¤       We can go on forever as to whether I am entitled to 61% of the loot or 62%

¤       Whether to split 50/50 or keep bargaining is a simpler decision.

¯    But what solution is unique is a function of how people think about the problem

¤       The bank robbery was done by your family (you and your son) and mine (me and my wife and daughter)

¤       Is the Schelling point 50/50 between the families, or 20% to each person?

¤       Obviously the latter (obvious to me--not to you).

¯    It was only a two person job--but I was the one who bribed a clerk to get inside information

¤       Should we split the loot 50/50 or

¤       The profit 50/50--after paying me back for the bribe?

¯    In bargaining with a union, when everyone gets tired, the obvious suggestion is to "split the difference."

¤       But what the difference is depends on each party's previous offers

¤       Which gives each an incentive to make offers unrealistically favorable to itself.

¯    What is the strategic implication?

¤       If you are in a situation where the outcome is likely to be agreement on a Schelling point

¤       How might you improve the outcome for your side?

v    Odds and Ends

¯    Prisoner's dilemma examples?

¤       Athletes taking steroids. Is it a PD?

¤       Countries engaging in an arms race

¤       Students studying in order to get better grades?

¯    Is repeated prisoner's dilemma a prisoner's dilemma?

¤       Suppose we are going to play the same game ten times in succession

¤       If you betray me in round 1, I can punish you by betraying in round 2

¤       It seems as though that provides a way of getting us to our jointly preferred outcome—neither confesses.

¤       But É

¯    Experimental games

¤       Computers work cheap

¤       So Axelrod set up a tournament

á       Humans submit programs defining a strategy for many times repeated prisoner's dilemma

á       Programs are randomly paired with each other to play (say) 100 times

á       When it is over, which program wins?

¤       In the first experiment, the winner was "tit for tat"

á       Cooperate in the first round

á       If the other player betrays on any round, betray him the next round (punish), but cooperate thereafter if he does (forgive)

¤       In fancier versions, you have evolution

á       Strategies that are more successful have more copies of themselves in the next round

á       Which matters, since whether a strategy works depends in part on what everyone else is doing.

á       Some more complicated strategies have succeeded in later versions of the tournament,

á       but tit for tat does quite well

¤       His book is The Evolution of Cooperation

v    Threats, bluffs, commitment strategies:

¯    A nuisance suit.

¤       Plaintiff's cost is $100,000, as is defendant's cost

¤       1% chance that plaintiff wins and is awarded $5,000,000

¤       What happens?

¤       How might each side try to improve the outcome

¯    Airline hijacking, with hostages

¤       The hijackers want to be flown to Cuba (say)

¤       Clearly that costs less than any serious risk of having the plane wrecked and/or passengers killed

¤       Should the airline give in?

¯    When is a commitment strategy believable?

¤       Suppose a criminal tries to commit to never plea bargaining?

¤       On the theory that that makes convicting him more costly than convicting other criminals

¤       So he will be let go, or not arrested

v    Moral Hazard

¯    This is really economics, not game theory, but it's in the chapter

¯    I have a ten million dollar factory and am worried about fire

¤       If I can take ten thousand dollar precaution that reduces the risk by 1% this year, I will—(.01x$10,000,000=$100,000>$10,000)

¤       But if the precaution costs a million, I won't.

¯    insure my factory for $9,000,000

¤       It is still worth taking a precaution that reduces the chance of fire by %1

¤       But only if it costs less than É?

¯    Of course, the price of the insurance will take account of the fact that I can be expected to take fewer precautions:

¤       Before I was insured, the chance of the factory burning down was 5%

¤       So insurance should have cost me about $450,000/year, but É

¤       Insurance company knows that if insured I will be less careful

¤       Raising the probability to (say) 10%, and the price to $900,000

¯    There is a net loss here—precautions worth taking that are not getting taken, because I pay for them but the gain goes mostly to the insurance company.

¯    Possible solutions?

¤       Require precautions (signs in car repair shops—no customers allowed in, mandated sprinkler systems)

á       The insurance company gives you a lower rate if you take the precautions

á       Only works for observable precautions

¤       Make insurance only cover fires not due to your failure to take precautions (again, if observable)

¤       Coinsurance.

¤        

¯    Is moral hazard a bug or a feature?

¤       Big company, many factories, they insure

á       Why? They shouldn't be risk averse

á       Since they can spread the loss across their factories.

¤       Consider the employee running one factory without insurance

á       He can spend nothing, have 3% chance of a fire

á       Or  spend $100,000, have 1%--and make $100,000 less/year for the company

á       Which is it in his interest to do?

v    Adverse Selection—also not really game theory

¯    The problem: The market for lemons

¤       Assumptions

á       Used car in good condition worth $10,000 to buyer, $8000 to seller

á       Lemon worth $5,000, $4,000

á       Half the cars are creampuffs, half lemons

¤       First try:

á       Buyers figure average used car is worth $7,500 to them, $6,000 to seller, so offer something in between

á       What happens?

¤       What is the final result?

¯    How might you avoid this problem—due to asymmetric information

¤       Make the information symmetric—inspect the car. Or É

¤       Transfer the risk to the party with the information—seller insures the car

¯    What problems does the latter solution raise?

v    To think about:

¯    Genetic testing is making it increasingly possible to identify people at risk of various medical problems

¯    If you are probably going to get cancer, or have a heart attack, and the insurance company knows it, insurance will be very expensive, so É

¯    Some people propose that it be illegal for insurance companies to require testing.

¯    What problems would that proposal raise?

1/24/06

 

v    Genetic Testing:

¯    A. No Testing

¯    B. Customers can test; insurance companies cannot condition rates on results

¯    Customers can test, insurance companies can condition rates

¯    What happens?

v    Contracts

¯    Why they matter

¤       A large part of what lawyers do is drawing up and negotiating contracts

¤       In many different areas of the law

á       Employment

á       Partnerships

á       Sales contracts

á       Contracts between firms

á       Prenuptial agreements and Divorce settlements É 

¯    Why make a contract?

¤       Why deal with other people at all?

á       Because there are gains to trade

á       The same property may be worth more to buyer than seller

á       Different people have different abilities

á       Specialization and division of labor

á       Complementary abilities

á       Risk sharing

¬     An insurance contract not only transfers risk

¬     It reduces it--via the law of large numbers

á       Does a bet due to different opinions count as gains from trade?

¤       A spot sale isn't much of a contract--why anything else?

á       Because performance often takes place over time

á       And the dimensions of performance are more complicated than "seventeen bushels of wheat."

á       Even a spot contract might include details of quality--not immediately observable--and recourse.

¯    Two Objectives in negotiating a contract

¤       Maximize the size of the pie

¤       Get as much of it as possible for your client

¯    The second was covered in the previous chapter

¤       If there is some surplus from the exchange

á       Meaning that you can both be better off with a contract

á       Than without one

¤       Then you are in a bilateral monopoly bargaining game

á       You are both better off if you agree to a contract

á       But the terms will determine how much of the gain each of you gets

¤       Where commitment strategies or control of information might help

á       But at the risk of causing bargaining breakdown

¬     Each of us is committed to getting at least 60% of the gain, or É

¬     I have persuaded you that what you are selling is only worth $10 to me, and it is worth $11 to you.

á       And the pie goes into the trash

¯    This chapter is about the first--maximize the size of the pie

¤       Any time you see a way of increasing the size

¤       You can propose it, combined with a change in  other terms--such as price

¤       That makes both parties better off

¤       This point is central to the chapter—if you are not convinced, we should discuss it now.

v    Why incentives matter

¯    People often talk as if "more incentive" was unambiguously good

¤       Gordon Tullock's auto safety device

¤       There is such a thing as too much incentive

¤       What is the right incentive--for anything?

¯    Consider a fixed price contract to build a house

¤       Instead of spending $10,000 on roofing material that lasts 20 years

¤       The builder spends $5,000 on material that lasts 5 years

¤       After which the material must be replaced at a cost of $12,000

¯    What is the sense in which this is a bad thing?

¤       Compare to the case where the $5,000 material lasts 19 years.

¤       You want to set up the contract so he won't use the cheap material in the first case, but É

¤       What about the second?

¯    How about the incentive not to breach a contract?

¤       Should contracts ever be breached?

¤       When?

¤       How do you get that outcome?

¯    Enforceability and observeability

¤       Consider the marriage contract

á       Al-Tanukhi story

á       Lots of dimensions of performance are unobservable by an outside party

á       So a wife who wants a divorce É  .

á       You might want to think about the general problem of marriage contracts

¬     Traditional: Divorce hard, gender roles largely specified by custom

¬     Current: Divorce on demand, terms freely negotiable day by day, mostly not enforceable

¬     Alternatives?

¬     What are the problems in designing a marriage contract?

¬     We will return to that question

¤       Ideally, the contract specifies terms that are observable

¤       Not always a sharp distinction

á       Sometimes performance can be imperfectly observed--how well is this house built?

á       And one might specify how to observe it--name the expert body whose standards you are agreeing to.

¤       A second enforceability problem--what if a party breaches and can't pay the damages?

¯    Reputation

¤       In today's discussion, we implicitly assume that the only constraint on both parties is the contract itself

¤       In many cases that's not realistic. One or both parties is a repeat player, and wants not only to stay out of court but to keep customers and get more.

¤       We will return to that question later, since it is relevant to how to structure contracts.

v    Production Contracts—building a house.

¯    One party pays the cost, gets the house, the other builds it.

¯    Cost-plus or flat fee: Advantages and disadvantages

¤       Why is there a "plus" in cost plus?

á       If one contractor will do the job for cost+$10,000, why won't another do it for cost+$9,000?

á       Isn't the "plus" something for nothing? $9,000 is better than zero.

¤       Is it "plus" or "plus 10%?"

¤       Why?

¯    Incentive to get inputs at the lowest possible cost

¤       Flat fee: any savings goes to the contractor

á       So he wants to minimize cost--including both price and his time and trouble

á       Which is what you want him to do

á       Why do you care about his time and trouble?

á       What would happen if you set up the contract to force him to buy the input at the lowest possible price (holding quality fixed--same brand of windows, say)? Imagine he had to pay you a five thousand dollar penalty if you could show that, somewhere, it was possible to buy an input for less than he paid?

¤       Cost plus: savings on price goes to you

á       But any increase in time and trouble needed to get the lower price he pays

á       So he won't try very hard to find a lower price

á       Even if it would save you more than it costs him to do so

¤       Cost plus 10%?

á       Friedman's rule for finding the men's room

á       And why it sometimes doesn't work

¤       If you are using cost plus, how might you control the problem?

¤       What are the problems you will face?

¯    Incentive to get inputs of the right quality

¤       Do we always want the highest quality inputs?

á       Do you only eat at gourmet restaurants?

á       And buy the highest quality car you can afford?

¤       Flat fee contract: Incentive of the builder is É

á       To use the least expensive inputs, whatever their quality

á       Because a dollar saved is a dollar earned--for him

¤       Cost plus contract, he doesn't care--extra quality comes out of your pocket

¤       Cost plus 10%?

¤       With a flat fee contract, how might you try to control the problem?

¤       What problems arise in doing so?

¯    Uncertainty:

¤       Renegotiating the contract

á       Your client forgot something important--try to prevent that in advance

á       Something important changed.

á       You are stuck in a bilateral monopoly with the builder

¬     The bargaining range is bounded on one side by the terms of the initial contract--if he fulfills it he is in the clear

¬     And on the other side by the most you are willing to pay for the change

¬     Which might be expensive

á       You could include terms for changes in the contract

¬     Will that be easier with flat fee, cost plus, cost plus 10%?

¬     Think about it from the builder's standpoint.

¤       Risk bearing

á       What if something changes that greatly increases the cost?

¬     Under flat fee, the builder swallows the loss

¬     Under cost plus, you do

á       What if something changes that greatly lowers the value to you?

¬     You contract to have land cleared and a new factory built

¬     In 1929

¬     Risk allocation depends on the contractual terms for breach

¬     Or on negotiation--again, with a potential holdout problem

á       Why does risk bearing affect the size of the pie?

¬     Because different parties have different abilities to bear risk

¬     Because poor contract terms or bargaining breakdown might lead to a smaller pie--the land gets cleared, the factory built, and it sits empty until 1942.

 

 

Electronic Equipment Service Contract

 

Global Consolidated Industries (GCI) has for years had an in-house electronic equipment maintenance department. It has been responsible for providing maintenance (such as periodic cleaning and lubrication of moving parts) and repair (fixing machines when they break down) on thousands of printers, photocopy machines, FAX machines, scanners, and so forth. The experience, in a word, has been a disaster. On most days, secretaries can be seen running from floor to floor and pushing in line to use other machines when theirs are inoperative. Even the CEO is often heard screaming about memos being late, meetings having to be rescheduled, and other headaches caused by out-of-order equipment.

 

GCI has decided that it is time to contract out for these services. As a member of GCIÕs general counselÕs office, you have been called in to participate in the contract negotiations with the outside service provider, Reliable Response Repair (RRR).

 

RRR has offered two contracts for your consideration. Under one contract, RRR receives a flat rate per machine each contract year. (For example, there is a $200 per year charge for a standard, mid-size photocopy machine.) Under this arrangement, RRR is obligated to provide all necessary maintenance and to repair broken-down machines promptly.

 

Under the second contact, RRR is paid $75 per hour (plus parts) for all maintenance and repair services. Under this arrangement as well, RRR is obligated to provide all necessary maintenance and to repair broken-down machines promptly.

 

Explain the pros and cons of each of the two contracts. Which seems best? Can you think of additional terms that would improve it?

 

v    What is RRR's incentive to do a good job of maintaining and fixing the machines under either contract?

v    To do it promptly?

v    What are GCI's incentives under each contract? Why might RRR care about that?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

v    Flat rate:

¯    RRR incentives

¤       Incentive to maintain if it is cheaper than fixing

¤       Incentive to do a good job of fixing, since if not they have to come back

¤       Promptness? Only to the extent you can enforce that term

á       So you may want to define it more precisely

á       Must show up within 2 hours, fix within 4, or É

á       Penalty based on how many hours machines are down each year, or É

á       Bonus for less than 6 hours down time per machine

¤       Risk?

á       Very little risk to GCI—they know how much they will pay

á       All of the risk is on RRR—what if a machine has problems and keeps giving trouble?

á       But GCI is big enough so that such effects should average out

¯    GCI incentives:

¤       Why do you worry about those?

¤       GCI has little incentive to take good care of machines, train people well, control whatever inputs they provide that affect the chance of breakdown

¤       Little incentive to hold down RRR's cost by, say, not using machines heavily at two in the morning, or only asking for a technician to be sent when the problem is serious

¤       GCI has reduced incentive to buy good quality machines

á       So the contract might specify machines presently on site, which RRR can inspect in advance

á       Or specify what brands and models of new purchases are covered

v    Per hour:

¯    RRR incentives

¤       If per hour is more than their real cost, a serious problem

á       Why maintain when you get paid to fix?

á       Why fix well when you get paid to come back?

¤       If per hour is at their real cost, still have to monitor to make sure they are really working that many hours

¤       Promptness still a problem as above.

¯    GCI Incentives

¤       GCI now has an incentive to buy good machines

¤       To take good care of the machines

¤       Only to call a tech when really needed

¤       And RRR might charge more at 2 A.M. (modification of terms)

¯    Question: Does GCI have to use RRR under this contract?

¤       If not, they can use competition or the threat of it to control some of these problems, but É

¤       A problem if RRR is hiring extra maintenance personnel specifically to deal with GCI repairs.

v    What if quality of repair affects machine lifetime?

¯    Either way, RRR has little incentive to do a good job in that dimension

¯    Perhaps GCI should lease the machines from RRR, with repairs and maintenance included in the terms.

v    Perhaps what we want is some of the cost on each party

¯    Per hour payment low enough to give RRR an incentive to maintain machines, fix  them right, but É

¯    High enough to give GCI an incentive to do what it easily can to avoid breakdowns.

¯    The same principle as coinsurance.

¤       Neither party bears the full cost, so neither has as much incentive to prevent the problem as we would like, but É

¤       Each bears enough of the cost to make it in its interest to take most of the precautions that ought to be taken.

 

 

Musician and Nightclub Booking Arrangement

 

Your client, Jerry the Jazz musician, is becoming increasingly well-known in the region. He has recently been offered a booking arrangement by the Nightowl nightclub, the ritziest jazz bar in the city, for Tuesday nights. They propose paying him $500 per appearance plus 10% of house profits. Because they want to have the opportunity to use other musicians for variety, taking advantage of out-of-town players who pass through, they are only willing to guarantee Jerry 26 Tuesday night appearances over the course of the year. They would give him one weekÕs notice with regard to each Tuesday, and he would be obligated to appear when called.

 

Jerry tells you that he finds this offer attractive because it would give him some stability in his income, something he has never had before. On the other hand, he does not like the idea that the arrangement would preclude his doing any other gigs on a Tuesday night (or out-of town gigs on Mondays or Wednesdays); given his increasing reputation, he occasionally gets great one-shot offers.

 

How do you advise Jerry regarding his contract negotiations with Nightowl?

 

 

v    Gains from trade

¯    Jerry and Nightowl both reduce uncertainty

¯    Appearing regularly at Nightowl probably benefits both

v    Problems that might be fixable:

¯    Jerry wants flexibility for out of town gigs

¯    How to reduce the cost of that to Nightowl?

¤       If he gives them a month advance notice, might be able to fill in

á       They only plan to use him half the Tuesdays

á       Still some cost--there might not be anybody good in town

á       But perhaps less than the benefit to Jerry

¤       What if he can get off if he finds a substitute?

á       How do we define an adequate substitute?

á       Someone they have hired before?

á       Someone from a pre-agreed list?

¤       What if he agrees to play a different day when he isn't there Tuesday?

¤       What if he can take off a fixed number of Tuesdays by one month advance notice?

á       Hypothetical numbers

á       Jerry wants the right to block out 5 Tuesdays, a month in advance

á       Nightowl thinks it costs them $400/Tuesday

¬     Hassle of finding a replacement

¬     Risk of lower quality

¬     Disappointment of Tuesday customers who are fans of Jerry's.

á       Jerry offers to accept $400 instead of 500 per appearance in exchange

á       Saves Nightowl $100x26 Tuesdays=$2600, so they are better off

á       Jerry can make $1000 more for out of town gigs, so gains $5000, loses $2600, so he is better off too

v    Other issues

¯    If Jerry has the option, he might choose big nights--New Year's Eve--since he is getting the same fee for every night from Nightowl, could get more elsewhere.

¤       How might we solve that?

¤       Pay him more for specified big nights?

¤       Or specified big nights he doesn't have the option of taking off?

¤       Or, when he notifies them, they bargain with him?

¯    Breach: Under the initial contract, what if he accepts a Tuesday gig and then Nightowl wants him that Tuesday?

¤       Liquidated Damages? What does the contract say?

¤       What if he is sick and can't play?

¤       Can Nightowl tell the difference? Depends how far away the gig is?

¤       Breach terms another way of getting flexibility

á       Liquidated damages of $300 if be backs out with a month notice

á       $500 a week's nnotice

á       $2000 if he just doesn't show up

á       How should we set the damages?

á       How about calling in sick?

¤       Negotiation another way of getting flexibility

á       Gets an invitation for an out of town gig

á       Asks Nightowl if they need him that night

á       If they do, starts bargaining

á       Assymetric information? How is it in Nightowl's interest to act?

á       Can Jerry tell?

v    Incentive issues

¯    For Jerry: What are his incentives

¤       To do a good job?

¤       To come when he says he will?

¯    What are Nightowl's incentives?

¤       To advertise Jerry

¤       To run a good club (why does he care?)

¤       To use him often?

á       Should there be different terms for other nights?

á       He isn't committed--but doesn't get paid as much?

á       His time is probably worth much less than $500 if he doesn't have a gig

v    Verifiability:

¯    Jerry gets 10% of profits--how measured?

¤       You are an unscrupulous Nightowl owner--how do you hold down what you pay Jerry?

¤       Can he tell?

¯    Are there other ways of rewarding him related to how good a job he does?

¤       More easily observed? Revenue--but also a bit tricky

¤       More closely targetted on his contribution?

v    General issues here are:

¯    Enlarging the pie

¯    Via incentives

¯    Risk bearing?

¯    Verifiability of terms

 

State AG Litigation Contract

 

You are a lawyer in the consumer protection division of the state attorney generalÕs office. Preliminary investigations as well as some undercover stories in the press reveal the possibility of a major billing scandal involving the health care industry. Following the growing number of states who have recently pursued such claims and the recent huge success in tobacco litigation, it is proposed to bring suit against a number of firms. The total damages claim is for hundreds of millions of dollars, possibly more than a billion.

 

 Your office, however, has only four attorneys, many of whom are quite busy on other matters. Therefore, it is agreed to hire an outside firm that specializes in large-scale litigation, probably one of those super-successful plaintiffsÕ boutique firms. Many of them have already expressed interest and some have been interviewed.

 

Two further notes. First, although this novel litigation strategy has the potential to be extremely lucrative, it will also be expensive, requiring that millions of dollars worth of lawyersÕ and expertsÕ time be invested up front. Second, the office is worried about the possible political fallout of making fee payments to outside lawyers that prove embarrassingly large.

 

Advise your department head on the compensation scheme that should be used in the contract with the outside firm. Focus on the form of the compensation scheme and any closely related matters. In preparing your advice, be sure that you do each of the following:

 

Describe different ways that the firm could be compensated.

 

Identify the major pros and cons of each approach.

 

Discuss how, if at all, any negatives of a given approach may be mitigated.

 

 

Compensation Scheme

Incentives

Risk

Political, Other

Flat Fee

 

 

 

Hourly

 

 

 

Contingent Fee

 

 

 

 

 

 

 

 

v    Flat Fee

¯    Incentives

¤       No financial incentive for lawyers to win

¤       Possible reputational incentive

¤       How well can a small AG's office monitor the lawyers?

¤       Can you control how hard they try by contract?

¯    Risk

¤       None on payment for law firm

¤       But they bear all the risk of costs

¤       Who is more risk averse?

¯    Political

¤       No risk of stories on huge fee payment, but É

¤       If the case fails, agency looks bad--money for nothing

v    Cost-Plus (hourly)

¯    Incentives

¤       To spend too much time if rate is higher than real cost of time to firm

á       Too little if rate is lower, but É

á       Less of a problem than the previous case, where hourly rate is zero.

¤       Can you verify

á       Hours actually worked

á       Quality of work. Who do they assign, how hard does he try?

¤       Can you control by contract?

¯    Risk

¤       All of the revenue risk is born by the state

¤       And most of the cost risk

¯    Political

¤       No risk of huge payments for now work, but É

¤       Risk of huge payments for no return

v    Contingent Fee

¯    Incentives

¤       Firm wants to win.

¤       How large a fractional payout?

á       Higher percentage, better incentives, but É

á       Less left for the state

á       What about 100% and negative fixed fee?

¤       At anything less than 100%, incentive still imperfect. Assume 50%.

á       If it costs the firm $1000 to increase expected return by $1500, they won't do it.

á       So still want some oversight

á       And hope reputation helps.

¤       No incentive for the firm to get relief other than a damage payment

¯    Risk

¤       Is being shared between firm and state

¯    Political

¤       No risk of large payment for no result

¤       But very large amounts to lawyers if the suit is successful might be embarrassing

v    What is the maximand?

¯    Suppose the defendant is actually innocent

¯    The law firm still wants to win

¯    Does the state?

v    School Gymnasium: Applying what we have learned.

¯    Flat fee or Cost plus?

¤       The school probably doesn't know enough to monitor a cost-plus contract

¤       And is probably in a poor position to bear risk

¤       So flat fee is probably better, but É

¯    Problems with flat fee

¤       Maintaining quality

á       Have to specify a lot of details

á       School doesn't have the expertise to do that, but É

á       Their architect might.

á       Hire some sort of expert to write the specs

¤       Making changes

á       Question your client carefully to keep later changes from being necessary

á       Perhaps include in the contract that changes can be made on a cost plus basis

á       Or plan on negotiating changes.

v    Arguments in litigation

¯    The book sketches the law and econ argument for enforcing the quality terms in a flat fee contract

¤       Because otherwise the builder has an incentive to degrade quality

¤       Even when doing so costs you more than it saves him.

¯    Do you think a judge would find that more or less convincing

¯    Than the "good faith" sort of argument?

v    Principle/Agent Contracts

¯    Lots of varieties, including

¤       Construction contracts we have been discussing

¤       Employment contracts

¤       Lawyer/client contracts--you are the agent.

¤       Is the President the voters' agent?

¤       É

¯    Possible forms

¤       Pay by performance--did you sell a car? Win a case?

¤       Pay for inputs--how many billable hours?

¤       Fixed-fee

¤       Combinations.

á       Employees frequently get a fixed salary, plus É

á       Bonus for specified accomplishments, by them or their unit or the firm, or É

á       Optional bonus--Google example.

á       Your raise next year is to some extent a "by performance" for this year

¯    Incentives: How to make it in the interest of the agent to do what the principal wants

¤       What does the principal want?

á       "To win her lawsuit?"

á       At any cost?

¤       Performance based contracts give the agent an incentive

á       To achieve the objective

á       If the reward for doing so is greater than the cost of doing so

á       Suppose the reward is 10% of the value of success

á       Will the agent act as the principal would like?

á       What about 200%?

á       If all we are concerned about is the right incentive, the reward should be É?

á       What are the problems with this solution?

¬     It might pay the agent too much.

¬     Consider a store whose profit depends on ten different employees.

¬     How would we solve that problem?

¬     The solution might impose too much risk on the agents.

á       So there are costs to the rule that gives the right incentive.

á       A further problem is measuring output

¬     Consider the President of a publicly traded company

¬     Perhaps profits are low this year because of high research costs which will bear fruit in five or ten years

¬     Or because of problems facing the industry for which he is not responsible.

¬     Consider a secretary or janitor or É  . How do you measure output?

á       One reason to decentralize firms is to make this problem a little easier to solve

¬     We can judge the output of the Buick division of GM better if it is run like a separate company

¬     Of one partner in a law firm if we can keep track of his accounts

¯    Input based contract

¤       For instance, paying an hourly wage

¤       Or billable hours

¤       Gives the agent an incentive on the measurable dimension of input

¤       But not on other dimensions--how hard he works, for instance.

¯    Fixed fee contract

¤       No automatic incentive to do anything

¤       Make the fixed fee for some measurable result (show up in court, etc.)

¤       Or have some way of defining what inputs the fixed fee is buying, and monitoring them.

¤       May rely heavily on reputation.

v    Risk bearing

¯    Performance based, risk born largely by the agent

¯    Input based, principal bears risk of outcome, risk of wanting more inputs.

¯    Fixed fee, principal bears risk of outcome, agent risk of costs.

v    Coffee house manager employment contract

¯    Performance based

¤       Do we have to base it on the profits of the whole firm?

¤       Or is there a better solution?

¤       What about compromises to reduce the risk the manager bears?

¯    Input based

¤       Performance depends on manager's inputs, but É

¤       Much of it is qualitative, hard to measure, harder to prove to a court in case of dispute

¤       And the quantitative--hours put it in--requires someone monitoring the manager

á       Which means someone working in his coffee house

á       And so partly dependant on him for promotion etc.

¯    Fixed fee--flat salary

¤       Requires monitoring of inputs and performance

¤       If unsatisfactory, replace the manager

v    Joint undertakings

¯    Include

¤       Partnership--such as a law firm

¤       Joint project by two firms--Apple and IBM, say

á       IBM develops a new chip (G5, 60 nm)

¬     Apple makes plans and promises based on it

¬     And Steve Jobs eats crow when he still doesn't have his 3 Ghz desktop.

á       How might a contract deal with this (don't know if it did)

¬     IBM controls how hard they try

¬     And has more information on what they can do, risks (not enough information, as it turned out—everyone had more trouble with 60 nm than expected)

¬     So should IBM be liable for Apple's losses?

¬     But Apple is the one deciding what promises Steve makes, other decisions affecting amount of loss.

¤       É

¯    Incentives

¤       Horizontal division—between partners, allocating income by business brought in, billable hours, É

¤       Functional division—Apple and Motorola above.

¯    Risk sharing

¤       May modify "reward by output" within firm

¤       Partly output, partly input, partly fixed

¯    What is observable?

¤       Did IBM make best efforts to develop?

¤       Could Intel be used as benchmark?

¤       Did Apple act to minimize loss due to failure of IBM to deliver?

v    Sale or lease of property

¯    Quality dimension

¤       Of property as delivered

¤       And as returned

¤       Inspect?

¤       Contractual restrictions on use, subletting, É

¤       Security deposit

á       Saves court costs if property damaged,

á       Solves judgement proof problem, but É

á       How do you keep landlord from confiscating it if not damaged?

á       Raises the general issue of structuring a contract wrt what happens if nobody goes to court. Will return to that Thursday

¤       Damage in delivery

á       Make the party who has possession liable? Can best control

á       Or the party who chooses third party to deliver

¯    Information

¤       What are you obliged to tell?

¤       Treaty of Paris, war of 1812, case.

¤       Poltergeist case

¯    Who bears the risk of the rented building burning down?

¤       Incentive—tenant

¤       Risk spreading? Probably landlord.

v    Loan

¯    Risk of bankruptcy,

¤       deliberate or otherwise.

¤       "deliberate" might include taking risks—heads I win, tails you lose.

¤       Control by

á       Security interest in property—borrower can't sell it

á       Controls on what borrower can do.

v    Resolving disputes

¯    Some can be avoided by anticipation, but É.

¤       There isn't enough small print in the world to cover everything

¤       And events may occur that you hadn't thought of.

¯    Damages for breach

¤       Expectation damages lead to efficient breach, inefficient reliance

¤       Liquidated damages solve the problem—if damages can be estimated in advance.

v    Negotiating the contract

¯    Try to maximize the pie

¤       By offering to buy improvements that help your side at a cost to the other

¤       To sell improvements that help them at a cost to you

¤       To trade

¯    Try to maximize your share—typically in the price

¤       While remembering that if you ask for too much

¤       You risk bargaining breakthrough

¤       And getting nothing

v    China to Cyberspace: Contracts without court enforcement

¯    An issue for

¤       You—because part of an attorney's job is staying out of court

á       Which you do in part by designing contracts

á       Which it isn't in either party's interest to try to get out of

á       Look at how many contracts amount to the consumer signing away as many of his potential claims as possible

¬     One explanation is that it is that way to benefit the seller at the buyer's expense

¬     That seems inconsistent with our analysis—any expense to the buyer will reduce what he is willing to pay for the product

¬     Why might this arrangement be in the interest of both? (stay tuned)

¤       Imperial China—because legal system was almost entirely penal

á       You could complain you had been swindled, ask the district magistrate to act

á       But you couldn't actually sue and control the case

á       And the legal system said almost nothing about contract law

¤       Cyberspace, because

á       Hard to use the legal system when dealings routinely cross jurisdictions

á       The technology makes it possible to combine anonymity and reputation

¬     Public key encryption as a way of maintaining anonymity

¬     And digital signatures as a way of proving identity

¯    Either your realspace identity, or É

¯    Your cyberspace identity

¯    I.e. that you are the online persona with a particular reputation.

¯    My legal eagle business plan

á       For quite a lot of people, anonymity might be a plus

¬     Lets you opt out of the state legal system—which contracts often try to do.

¬     Protects you in places where security of property is low

¯    Do you want to be a programmer known to be making $50,000/year

¯    In China, or Burma, or Indonesia, or É

¯    You might be worried about either private seizures—kidnapping your kids, say

¯    Or public ones.

¬     Might let you evade taxes or regulations at home.

¯    One way of enforcing contracts without the courts is reputation

¤       Reputational enforcement depends on your being a repeat player, so your reputation matters to you.

¤       It also depends on interested third parties knowing whether you cheated someone

á       Since your "punishment" isn't designed to punish you

á       But to keep other people from letting you cheat them

¤       If it is hard to know which party to a dispute is telling the truth

á       Interested third parties will distrust both—either might be lying

á       So it isn't in your interest, when cheated, to complain

á       So reputational enforcement doesn't work

¤       Arbitration is a way of lowering the information cost to third parties

á       If we went to a respected arbitrator, or one we agreed on advance

á       And he ruled in my favor, and you didn't go along

á       You are probably the bad guy

¯    Another way is structuring the contract so that it is never in either party's interest to breach

¤       I hire you to build a house on my property

á       If I pay you at the beginning, it is in your interest to take the money and run, if you can get away with it.

á       If I pay you at the end, it is in my interest to keep the house and not pay

á       So I pay you in installments during the construction

á       Arranged so there is no point at which either of us gets a large benefit from breach

á       Sometimes doing this requires costly changes in the pattern of performance

¬     Lloyd Cohen's explanation of the consequences of no fault divorce

¯    In the traditional marriage, women performed early, men late

¯    Many men find younger women more attractive, so É

¯    Incentive for a husband at forty, with the kids in school and his wife finally getting a chance to rest

¯    To dump her for a younger replacement

¬     How did women change their behavior to control the problem?

¯    Postpone childbearing in order to bring performance more nearly in sync

¯    Shift household production to the market and get a job

¤       Which both gets performance in sync, and

¤       Reduces the degree to which the wife is specialized to being the wife of that man

¤       And so at risk if he breaches.

¤       Since there are gains from completing the contract, in a world of certainty we ought to be able to structure payment and performance to achieve this, but É

á       In an uncertain world, where costs and benefits may change, it's hard

á       We can always reduce my incentive to breach by my giving you a deposit at the beginning, which you hold and will keep if things break down

á       But that increases my incentive to breach

¤       One solution is to use a hostage instead of a deposit

á       I give you something—my son, my trade secret—that

¬     it costs me a lot to lose

¬     but benefits you only a little to keep

¬     so pushes down my benefit from breach a lot, yours up a little

¤       Another solution is to structure payments so that the incentive to breach is on the party who has reputational reasons not to

á       You are going to do some work for me online—write a program, say

á       If you are a repeat player with reputation, I pay in advance

á       If I am, I pay for the program when it is delivered

á       Arguably, these explains the feature of real contracts discussed above

¬     It is in the interest of both parties to avoid expensive litigation

¬     The seller is a repeat player with a reputation, the buyer is not

¬     So substitute reputational enforcement for court enforcement

¬     Which would you prefer

¯    To buy a product with a long warranty from Apple or Kitchen Aid—in a world where the warranty wasn't enforceable

¯    Or from a no-name seller, in a world where you could sue the seller for not carrying out the warranty?

v    Other ways of staying out of the court

¯    So far as possible, arrange the contract so that the result you want is the one that happens with no court intervention

¯    Caveat emptor is an example

v    General observations

¯    a bunch of simplifications

¤       cost rather than current value

¤       Assets:

á       must be linked to some past transaction or event

á       yield probable future benefits

á       be obtained or controlled by the entity

¤       assets donÕt include good will, corporate culture, É

¤       all probabilities are one or zero

¤       why?

¯    Compare to tort law

¤       All probabilities are one or zero

á       Someone sues you for ten million dollars

á       If probability of guilt is .4, you owe nothing

á       If .6, you owe ten million

¤       Damages tend to be limited to

á       pecuniary, medical costs, lost earnings

á       less willing to include pain and suffering and the llike

¯    in both cases, we have to make decisions with a very crude process

¤       making legal outcomes depend on things in complicated ways is likely to raise litigation costs, legal uncertainty. Easier to prove a doctorÕs bill than a pain.

¤       Accounting aims at sufficiently clear cut decision rules

á       So that firms canÕt easily manipulate the outcome

á       To make them look good

á       Or reduce their taxes.

á       At a considerable cost in accuracy

v    Understanding accounting

¯    First rule—ignore Òdebit/creditÓ or reverse their meaning

¤       Most of the time, a debit makes a firm richer

¤       A credit poorer

¤       One explanation: "Debit" is from Italian Debitare—what others owe you

¤       And what about credit?

¯    Second rule—()= -

¯    making sense of a balance sheet

¤       photograph of the firm at an instant—compare two dates

¤       show a list of assets, most liquid at the top, at two periods

á       group into current assets, total

á       and long term ("property, plant and equipment") and total

á       total the two totals for total assets

¤       similar list of liability and owner's equity

á       liability a negative asset

¬     probable sacrifice of economic benefit É

á       why do you put equity with liabilities?

á       How much wealth does the firm itself (as opposed to stockholders and others) have?

á       the fundamental equation

¯    making sense of an income statement

¤       designed to show the changes over a period of time

¤       money coming in: Sales revenue (or equivalent for other sorts of firms)

¤       costs

á       cost of goods sold—raw material, labor, etc.

á       operating expenses: Costs not attributable to particular output

á       interest expense

á       income tax expense

¤       at each stage, you have a net to that point

¤       and end up with net income

¯    making sense of a cash flow statement

¤       the one in the book

á       money comes in as net income, but É

á       if part of the "income" is accrued but not received É

¬     it goes into accounts receivable, not cash,

¬     so less cash

¬     reverse if some accounts from last year are paid, increasing cash

¬     so subtract from income the increase in accounts receivable

á       accounts payable the same thing in the other direction

¬     we subtracted out expenses in calculating income, but É

¬     if some expenses were accrued but not paid É

¬     we still have the cash

á       we subtracted out depreciation in calculating net income—but they didn't use up any cash. Add back in.

á       also cash flows from

¬     borrowing (increases cash)

¬     paying dividends (uses up cash)

¬     etc.

¯    making sense of T-accounts

¤       The T-account records a single transaction, not a balance or a total over time

¤       each transaction is entered twice

¤       if you buy something

á       that decreases cash, increases asset (land, factory, raw materials)

á       if you sell something, increases cash, decreases inventory

¤       what if you make money?

á       Buy something for $100

á       Sell it for $200

á       How do you make the accounts balance?

¯    Joyce James Case

 

Joyce James graduated from college in June 2002.   As was traditional in the James family,  JoyceÕs parents paid all of her expenses through college.  But, upon graduation, she was expected  to fend for herself financially.  On the date of her graduation, Joyce had neither financial resources  nor financial obligations.  Now that she is responsible for her own finances, one of her friends has  suggested that she might want to think about putting together a financial statement of some sort.  What sort of financial statement do you think would be useful for Joyce?  How would you propose  she  account for the following transactions?

 

1. At her graduation exercises, Joyce was awarded a prize of $5,000 her senior thesis on Day  Hiking in Ireland. The prize came in the form of five one thousand dollar bills.

 

2. She spent $2,000 of the prize money buying books she would need for graduate school,

which she was planning to attend in September.

 

3. She spent another $2,000 traveling through Europe over the summer and collecting memories  of a lifetime.

 

4. At the end of the summer, she took out a $4,000 loan to cover the costs of graduate school.

 

v    Why might she want to work out a financial statement?

¯    To keep track of her situation—decide if she is too much in debt, etc.

¯    For other people—to get a loan, É

v    What kind of information is most useful to her?

¯    Probably a balance sheet, showing her assets and liabilities

¯    But to get there we will use T-accounts—more for our information than hers.

v    How do we record the prize?

¯    She gets $5000 in cash—where does that go?

¯    What's the balancing item?

¯    Is there a reduction in some other asset?

¯    An increase in a liability?

¯    If not, what's left.

v    She spends $2000 on books for grad School

¯    Where does the expenditure go?

¯    What's the balancing item?

v    She spends $2000 traveling in Europe and collecting memories?

¯    Where does the expenditure go?

¯    Are the memories an asset?

¯    If not, what balances the expenditure?

v    She takes out a $4000 loan to cover the costs of graduate School

¯    Where does the loan go?

¯    What balances it?

v    She spends $5000 on living expenses in graduate school

¯    Where does the expenditure go?

¯    What balances it?

v    Now put this all together for a balance sheet

¯    What are her assets?

¯    What are her liabilities?

¯    What is her equity?

v    Is this an accurate account of her actual situation?

¯    For what purpose?

¯    Are you thinking about loaning her money?

¯    Or marrying her?

v    The matching principle

¯    So far as possible, we want to put revenue and the associated costs in the same period

¯    So that we can see how what we are doing is affecting us

¯    So we try to recognize income when it is earned, not when we get it

¤       By showing it as an increase in accounts receivable

¤       If it isn't actually going to get paid until the next period

¯    And defer costs to when they will generate income

¤       Depreciation is an attempt to do that

¤       Your computer isn't a cost for this year but a cost spread over several years

¤       What happens if you buy identical inputs at different prices?

á       What value to use to measure them when you sell them (or use them)?

á       FIFO or LIFO?

v    The lawyer's perspective—why does all this matter to you?

¯    Contracts may specify things in terms of accounting entities

¯    The decision to make a loan may depend on accounting figures on the borrower

¯    Firms have legal obligations with regard to accounting, especially publicly traded firms, and you may have to tell them if they are fulfilling them.

¯    Others?

 

Accounting for Lawyers: 

Upstage Theater Company Handout

The Upstage Theater Company (UTC) is a non-profit community theater group that puts on

several plays each year.  On December 31, 2001, the Company had the following balance sheet.

 

Assets

Cash

$2000

Costumes and Sets

$3000

Total Assets

$5000

Liabilities and Surplus

Bank Loan

$4000

Total Liabilities

$4000

Surplus

$1000

In the course of 2002, the following events occurred.  The company would like your advice on how to account for these transactions.

 

1.         At the beginning of the year, an anonymous donor makes an unrestricted gift of  $1,000 to UTC.

 

2.         The company spends $1,000 on costumes and sets for the coming season.

3.         Over the course of the year, the company sells $3,000 of tickets for the yearÕs performances.

4.         Over the course of the year, the company spends $1,000 on the rental of auditoriums and other costs associated with putting on the yearÕs productions.

 

5.         Towards the end of the year, the company launches a new initiative to make advance sales of tickets for the next yearÕs season. $1,000 in advance sales are made.

 

v    $1000 gift

¯    where does it go?

¯    What balances it?

v    $1000 spent on costumes and sets

v    Sell $3000

¯    $3000 to cash

¯    could be balanced by equity, but É

¤       we want to keep track of income and expenses

¤       so as to be able to write an income statement

¤       so put it there

¤       and plan to transfer to equity when we close the books, subtract expenses

¤       add net income to equity

v    Spent $1000 on rental etc.

¯    Subtract from cash

¯    Balance where?

v    Make $1000 in advance sales

¯    Add to cash

¯    Balance where?

¯    Is this income?

¯    Liability? Do we owe it to anyone?

¯    From the standpoint of an income statement, we owe it to next year's income

¯    Since we want to match up income with expenses

¯    So it goes to deferred income

v    Costumes don't last forever--how do we include depreciation in this?

¯    Suppose four year lifetime--25% depreciation each year

¯    Where does it go?

¤       Reduction of inventory, and É

¤       Could be reduction of equity, but É

¤       We are trying to keep track of expenses, so

¤       Goes to expenses

v    At the end of the year we close out the books

¯    Add up cash credits and debits, starting cash, gives final cash

¤       $2000 initial

¤       +$5000 debits

¤       -$2000 credits

¯    Add up costumes etc:

¤       $3000+$1000-$1000

¤       =$3000 final.

¯    Add up income and expenses, transfer to equity (Surplus)

¯    End up with a balance sheet

¤       $5000 cash + $3000 costumes and setsw = $8000 assets

¤       $1000 deferred income +$4000 loan+$3000 equity=$8000

v    using the information

¯    a potential donor wants to know if his money is

¤       needed

¤       going down the drain ("throwing good money after bad)

¯    a potential lender wants to know if the company will be able to pay him back

¯    a government agency that wanted to subsidize the arts might want to know if these are good people to subsidize.

v    Summary of what we have done

¯    Asset adding to equity (donation)

¯    Asset converted to another use (cash to costumes)

¯    Cash balanced with income (ticket sales, will go to equity after netting costs when books are closed)

¯    Expenditure balanced with expenses (rental etc.--will go to É)

¯    Asset balanced with a liability to the future (advance sales)

¯    Depreciation: Reduce an asset, balance with an expense, will go to É

v    Back to the matching principle

¯    Ambiguity

¤       Revenue should be allocated to the period during which effort is expended in generating it

¤       An expense should be allocated to the period in which the benefit from it will contribute to income generation

¤       So if expense is in year 1, revenue in year 2

¤       Do you move expense forward or revenue back?

¯    If "effort expended" has an unambiguous date, move it to that year?

¯    Otherwise, answer depends on when you have the information?

¤       If we have an expense this year for income next year

á       We probably don't yet know the amount of the income

á       So move the expense forward--"prepaid expenses"

á       Similarly for "Deferred Income"--we'll know more next year

¯    "accounts receivable" go the other way--moving income back

¤       because the amount is (hopefully) known

¤       as are the rest of the associated expenses and income

v    fixing the oil problem (Figure 4-6)

¯    what was left out of the story and the accounts?

¯    What happens when we put it back in?

¯    We are moving profits into equity--eventually

v    "Conservative bias"

¯    a misleading term if it means "err in the direction of underestimating income and equity"

¤       intangibles, after all, can go down as well as up

¤       as can the market value of assets

¤       and ignoring changes in overall prices actually overstates income--eventually

á       Buy something for $1000

á       All prices double

á       Sell it for $2000

á       Accounting profit: $1000

á       Actual profit: zero

¯    more nearly a sceptical bias

¯    Err in the direction of ignoring things hard to measure

¤       Count intangibles if they have actually been bought at a price

¤       Use market value for financial assets where it is easily determined

v    Defining an entity

¯    How to reduce your taxes

¤       Have a small business

¤       Treat expenses for things used in your business and for consumption as business expenses

¤       IRS rules try to prevent this--home office, automobile, etc.

¤       But you are the one structuring and monitoring things

¯    What is happening is that you are (deliberately) blurring the lines between two entities

¤       Your business and

¤       You

¯    How to run a law school at a profit (or loss)

¤       Some costs could be counted as costs of the Law School or of the whole university

á       Maintainance of our lovely campus

á       Some publicity costs

¤       Attribute them to the university, and the law school is making a profit

¤       To the law school, and it is making a loss

¤       Sometimes law schools or business schools have agreements with the university they are part of

á       Defining how costs are divided

á       And how much of the school's revenue the university is entitled to

á       Which might be based on profit rather than revenue

á       In which case the accounting matters

¤       Sometimes it might pay to move some activities into the law school to make those lines clearer

á       Suppose the Law School thinks the university charges it too much for keeping track of student records

á       Shift to the law school having its own people keep track of its students

á       Have lunches in the faculty lounge instead of  Benson

¤       Do you prefer a profit or a loss?

á       Depends who you are talking to

á       If you owe a percentage of your profit to the University, prefer a loss

á       If you are raising money, probably prefer a profit--but not too big a profit.

¯    Enron

¤       Create an entity whose books your firm's accountants won't see

¤       Shift losses to it

á       Sell something to the entity at much more than it is worth

á       Or buy something for much less

¤       Or shift gains to it before Enron goes bankrupt--and make sure you control the entity

¤       One reason lawyers worry about making sure transactions are "arm's length."

 

2/14/06

 

Snowplowing

 

Joe Landscaper and Gill Snowfall are both in the business of plowing driveways for a number of years.  Their only revenues are payments they receive for their plowing services.  Their only expenses are from the purchase of gasoline and the wear and tear on their trucks.

 

A. Joe plows driveways in December and is paid $500 in cash.

 

B. Gil also plows driveways in December and sends his clients bills for $ 600.

 

C. Joe gets $200 of gas in December and puts it on his credit card.

 

D.   Gill buys $250 of gas in December and pays cash.

 

Who had a better month?

 

E.  On January 1st, GillÕs old truck dies and he decides to purchase a new truck for

$10,000.

 

How would you account for this transaction?

 

v    Payments for Joe and Gil in December

¯    Joe gets $500 in cash, balanced by ?

¯    Gil gets $600 in ? balanced by ?

¯    When are we recognizing income?

v    Expenses for Joe and Gil in December

¯    Joe buys $200 of gas on his credit card

¤       $200 in expenses

¤       where does the matching $200 go?

¯    Gill buys $250 of gas, pays cash

¤       $250 in expenses

¤       and É?

¯    We want both expenditures to be in this period

v    Who had a better month?

¯    Compare their income statements

¯    Whose income minus expenses figure was larger?

¯    Whose cash has increased more?

¯    Which matters? When? To whom?

v    Gill buys a new truck

¯    Asset for asset swap

¯    At what point does the cost of the truck show up as an expense?

v    Does this fit the matching principle?

v    Stuff I'm leaving out

¯    The discussion of standards, boards, etc. matters

¯    But it isn't about analytical methods, although it is about accounting

¯    So you can probably make sense of it just as well without my help as with it.

v    How to use the information accounts provide?

¯    Who are you?

¤       Investor, interested in long term expectations of the firm

¤       Lender--wants to know if he will be paid back

¤       Supplier--wants to know if he will be paid. Lawyer, for instance.

¤       Employee

¯    Will the firm be able to meet its short term obligations?

¤       Compare short term assets (Cash, accounts receivable, inventory)

¤       To short term liabilities (bills payable, short term loans, É)

¤       Is "assets more than liabilities" enough?

¤       Depends how fast that is likely to change

á       Lender has some control over that via contract

á       Can require borrower to maintain some financial ratio

¤       Rule of thumb: current assets should be at leat 1.5 to 2 times current liabilities

¤       What if current assets almost all in inventory? In accounts receivable?

¤       How could a firm improve its short term situation?

á       Take out a long term loan

á       Increase its cash, or É

á       Reduce short term debts

á       Does not increase long term solvency, but É

¬     The fact that someone is willing to make a long term loan to them

¬     Is evidence that the lender thought they were solvent

¬     But É  might want to check on the interest rate.

¯    Is the firm solvent--long term obligations?

¤       Look at ratio of liabilities to

á       Assets, or É

á       Equity.

á       Are these really different measures?

á       Could a firm look good on one and bad on the other?

¤       Leverage

á       Consider a firm with $10 million in assets, $9 million in liabilities

á       What are the good things about that situation?

á       What are the bad things?

á       For whom?

¬     Stockholders

¬     Lenders

á       Why would much higher degree of leveraging be acceptable in some industries than in others?

¬     How predictable is the value of Apple's inventory of iPods vs

¬     Merrill Lynch's inventor of securities?

¤       Look at interest payments vs earnings available to pay them

á       Interest coverage

¬     Calculate from Figure 4-3

¬     Operating Earnings/Inerest expense

á       How close is the firm to being unable to pay interest on its debts?

¯    How well run is the firm?

¤       Accounts receivable/sales revenue--how long does it take the average customer to pay?

á       Depends on the industry as well as management

á       How long does it take MacDonald's average customer to pay?

¤       Turnover ratio: How fast does the firm turn over its inventory?

á       "Just in time production" is a limiting case

á       But a firm that is doing a bad job of estimating demand will have inventory build up, or É

á       Be short--high turnover ratio could be evidence of a mistake

á       But also success--high demand for their goods.

¤       What is the average interest rate the firm pays on its loans?

á       A high rate might be evidence of bad shopping for loans, or É

á       A high risk premium

¤       For all of these, one would want to compare to other firms in the same industry

¯    How profitable is the firm?

¤       Note that "profit" means a lot of different things

¤       Revenue minus cost

á       The supermarket pays a dollar for that box of cereal

á       Sells it for two dollars

á       So their profit is 100%!

á       If only we cut out the middle man É

¬     Set up a consumer's coop

¬     Get government to distribute food instead of the supermarket

á       But all of those alternatives require

¬     Salary to employees

¬     Rent, utilities, maintainance on the facilities

¬     Interest on the money used to buy the inventory

¬     Allowance for spoilage, unsold goods, theft, É

¤       Operating Earnings/Revenue

á       Operating Earnings: Revenue minus cost of goods sold and indirect expenses

á       What is available to pay interest, taxes, dividends, and increase equity

¤       Return on assets

á       Net income (after paying everything including interest and taxes)

á       Divided by total assets

á       If this company has a higher ROA than most, than either É

¬     It is unusually well run (or lucky), or É

¬     Someone else should get into the business too

¬     Duplicate its assets with an investment I, get higher than the usual return.

¤       Return on equity

á       Same as ROA if no liabilities

á       Think of equity as what the owners would get if they liquidated the firm--carefully.

á       If return on equity is more than the market interest rate, they are better off keeping the firm going

¯    Two qualifications

¤       Some of these will be different in different industries

¤       All of these are subject to the problems with accounting as a measure

¤       Consider a firm

á       whose chief asset is land bought long ago for a million dollars, now worth $100 million

á       no large liabilities

á       And currently making $1 million/year

¤       Making $1 million on assets of $1million is stellar performance

¤       So is $1 million on equity of $1 million

¤       Is the firm doing well? Should the owners keep going or sell out?

¯    Book value of a share

¤       Equity divided by number of shares

¤       A good measure--if equity really measures what the stockholders own.

¤       The usual problems

á       Historical costs

á       Neglect of intangibles

á       And contingencies

¯    Earnings per share

¤       Net income (after everything)

¤       divided by number of shares

¤       If an accurate measure

¤       And if likely to continue into the long future

¤       A good basis for what the share is worth, but É

¤       If it isn't worth that on the market, someone may know something you don't.

¯    Price/earnings ratio

2/26/06

 

v    Taking advantage of accounting flaws

¯    You are the CEO of a company, and want its balance sheet to look good

¤       Perhaps you are trying to get a loan

¤       Or issue some new stock

¤       Or justify your lavish retirement terms

¤       Or conceal the fact that you've been stealing from the company

¯    What perfectly legal steps might you take to increase equity

¤       As defined by accountants

¤       Other than increasing the real, long term value of the company.

¯    What if you want the balance sheet to look bad

¤       Because you want to drive down the stock price before your friend buys lots of it

¤       Or you are planning to take the company private, and want to pay the stockholders as little as possible

¤       How do you lower equity as measured by accountants, without actually hurting the company, at least very much?

¯    Why are the answers to these questions of interest to you as a lawyer?

¤       One reason is that you might want to advise a client as to legal ways of fooling people

¤       Is there another--perhaps more ethically attractive--reason?

v    Animal Rights league

¯    Shifting from cash to accrual

¯    How to account for pledges?

¤       Debit pledges Receivable, credit Revenue

á       Next year, $285,000 in pledges actually paid

á       Debit cash $285,000, debit revenues $15,000 (pledge write-off)

á       Credit pledges receivable $285,000 + $15,000 (two items)

á       Note that pledges paid are an asset for asset swap

á       Pledges written off reduce revenue

¤       orÉ

¤       Figure that pledges are payment for future services

á       Debit pledges receivable

á       Credit deferred income

á       Then next year

á       Debit deferred income

á       Credit revenues

¤       To decide, ask whether the revenue is from the telethon or advance payment for next year's work

¤       Third alternative—expected value

á       On average, $100 in pledges is only $95 in expected contributions

á       So debit pledges receivable this year at $285,00, credit revenue with same

á       Next year, credit pledges receivable, debit cash

á       More accurate, less of a hard number (probability), more of an economist's approach, less of an accountant's

¯    How to account for moving expenses and salary of new executive director

¤       Capitalized (an investment, to be depreciated) or expensed?

¤       Start by crediting cash $150,000, which is no longer in your account

¤       If you expense it, debit expenses by $150,000, easy

¤       If you capitalize it

á       A new asset—prepaid moving expenses, debit $150,000

á       Each year, credit that by that year's share, debit the same amount to expense (of having an executive director).

á       Amortize 1/5 each year

¤       What if you capitalize it, and she quits after a year

á       Remaining $120,000 is written off—investment that went bad

á       Credit prepaid moving expenses (an asset, now reduced to zero)

á       Debit expenses (which will get subtracted from revenue)

¤       Expensing easier, more common, but É

¤       For a small company, large expense, amortizing it may be more realistic

¤       Since otherwise you lose lots of money the first year.

¯    Note that both of these raise the question of allocating income and expenses to the right period

¯    In both cases, the way you do it depends on a guess about the future

¤       Pledges might not be honored

¤       Jane might quit

v    Energy Cooperative

¯     Basically buying and selling fuel, with a subsidy

¯    How to account for cost of fuel bought: LIFO or FIFO

¯    Should they write off the value of half the computers, now obsolete

¯    Constraint: In default of a loan if

¤       Return on Assets falls below 5% or

á       What is it now

á       Net Income=$31,000. Assets $300,000.

á       ROA>10%

á       No problem?

¤       Liabilities to Surplus ratio above 200% ("Surplus"="Equity"

á       What is it now?

á       200%. Oops.

¯    LIFO will raise the

¤       (accounting) cost of fuel sold (priced at higher current price)

á       So next net year's income will be less if we switch to LIFO

á       Lowering the ROA--but unless the effect is very big, still no problem

¤       what about the value of inventory?

á       Does not affect the left hand side of the accounts--total value of what you bought is what you paid for it

á       Affects the right hand side--LIFO means inventory value falls faster as you sell oil

á       Since you are "selling the more expensive (later) oil first"

¤       So assets will be lower at the end of next year if we use LIFO

á       Which raises ROA, reducing any problem from lower income. But

á       Lower assets mean lower surplus mean higher liabilities/surplus

á       Oops We are in default

¯    Writing off computers

¤       Credit (Reduce) inventory, hence assets

¤       Reduce net income by $20,000

¤       Reduce surplus by $20,000

¤       If we did it for this year, net income from $31,000 to $11,000

¤       Assets from $300,000 to $280,000

¤       Pushing ROA below 5%, in default

¯    In either case, there are arguments for the change so É

¤       Before making it

¤       See if you can negotiate a change in loan terms, or É

¤       Refinance

v    Review The course so far.

v    Decision Analysis

¯    Way of formally setting up a problem to help you decide what to do

¤       Does not provide the information:

á       Choices to be made and how they are related (the graph)

á       Probabilities

á       Payoffs to the various outcome

á       But it does point out to you what information you must obtain

¤       Set up a graph showing

á       alternatives you choose

á        alternatives chosen by chance, with their probabilities

á       outcomes, with their payoffs--how much better or worse are you (or your client) if it comes out that way.

¤       Start at the right end--final outcomes

á       At each point where you make a decision--the last one you will make--evaluate the expected value from each choice

á       The final choice leads either to an outcome, with a value, or É

á       To a further choice made by chance, and you can evaluate its expected value: the sum of probability times payoff

á       One of the alternative choices you can make gives the highest payoff--eliminate the others (cut off the graphs)

á       Now that decision point has a value, just like the payoff of an outcome--the expected value from making the right choice there.

á       Do this for all your final decision points

¤       Repeat the process at the next decision point left, repeat for all those.

¤       Continue until you know all decisions you will make

¯    How do you get the information to set up the problem?

¤       Not from decision theory

¤       From your expert knowledge of the situation

¤       Your client's expert knowledge

¤       Research you can do, such as looking at similar cases to see their outcome

¤       Consulting with other experts

¯    Sensitivity analysis

¤       Since the numbers are probably uncertain

¤       It's worth varying them a bit, and seeing if your decision changes

¤       If the decision is very sensitive to some payoff or probability, perhaps you should investigate further to make sure you have it right.

¯    Risk aversion

¤       So far I have assumed you are maximizing expected return--the sum of dollar payoff times probability over all alternatives of the decisions controlled by chance

¤       For gambles small relative to your assets, that is the right thing to do

¤       For large gambles, the fact that additional dollars are probably worth less to you the more you have comes into play

¤       You have to ask yourself which gamble you prefer, not merely which has the larger expected return.

v    Game Theory: Strategic behavior. My best moves depends on what he does, his best on what I do

¯    Bilateral monopoly bargaining

¤       Common interest in getting agreement

¤       Conflict over who gets how much

¤       Bluffs, threats, commitment strategies

¯    Many player game adds in the possibility of coalitions

¯    Can represent a game as

¤       A sequence of choices, like decision theory, but with two (or more) people plus chance making decisions

á       Useful for solving a game by finding a subgame perfect equilibrium

á       Very much like the decision theory approach

¬     start at the right, the last decision anyone makes

¬     figure out which choice at that point is in that chooser's interest, lop off all others

¬     do it for all the rightmost choices

¬     them move left and do it again

¬     I don't have to worry that if I do X he will do Y if I know that, once I do X, it will be in his interest to do Z instead.

¤       Note that this assumes away commitment strategies

á       "If you do X I will do Y, which hurts you

á       even though it hurts me too

á       because knowing that, you won't do X, and that benefits me."

¤       In some games--one time, no reputation--commitment strategies are unlikely, so subgame perfect is a sensible approach

¤       In other games that is not the case.

¯    Represent as a strategy matrix (two player games usually)

¤       A strategy is a full description of what I will do given any sequence of choices by you and by chance

¤       Given my strategy and yours, there is some outcome, or expected outcome, that results

¤       So we can imagine a matrix showing all my strategies down the left, all yours across, outcomes for both of us in the cells

¤       And this approach, for a zero sum game, gets us to the Von Neumann solution

¤       A pair of strategies, each optimal against the other.

¯    One can look for a dominant solution to such a matrix

¤       As in prisoner's dilemma

¤       One choice is best for me, whatever you do

¤       Another best for you, whatever I do

¤       So we will choose those two

¤       Of course, there may be no such solution.

¯    One can look for a Nash equilibrium to a many player game

¤       My strategy is optimal for me, given what everyone else is doing

¤       The same is true for everyone else

¤       But we might be all better off if we all changed together

¤       For instance, from driving on the left to driving on the right.

¤       Or even if two of us changed together

¤       For instance, both rushing the guard instead of going back to our cells.

¯    Von Neumann solution to many player game

¤       Not in the book, not responsible for

¤       But I sketched the idea briefly.

¯    Schelling points

¤       In a bargaining situation, people may converge on

¤       An outcome perceived as unique--50/50 split, or what we did last time, É .

¤       Because the alternative is to keep bargaining, and that is costly.

¯    Moral Hazard: Economics not game theory but in the chapter

¤       If part of the cost of my factory burning down is paid by the insurer

á       I will only take precautions whose benefit is enough larger than their cost so that they pay for me as well as for us

á       So some worthwhile precautions won't be taken

á       Applies to any situation where someone else bears some of the cost of my action.

¤       One solution is for the insurance company to require certain precautions

¤       Another is to reduce the problem by not insuring too large a fraction of the value

¤       But sometimes, moral hazard is a feature not a bug, because the insurance company now has an incentive to keep the factory from burning down, and might be better at it than you are.

¯    Adverse selection: Also economics not game theory

¤       Market for lemons--problem with used cars

¤       Might solve by guaranteeing the used car--but that raises moral hazard problems.

¤       Bryan Caplan on a blog: Why doesn't this destroy the adultery market?

á       Why do you want him to leave his wife and marry you if

á       He's the sort of bum who is first unfaithful to his wife and then dumps her?

á       http://econlog.econlib.org/archives/2006/02/lemons_for_vale.html

v    Contracting

¯    Basic idea: How to maximize the total gain from the contract. All the rest is bargaining over cutting the pie.

¯    Basic solution--give people the right incentives.

¤       Arrange it so that if something costs $10,000 and produces a combined benefit for the parties of more than that, it is done, if less than that, it isn't

¤       Where something might be

á       What materials you use to build a house

á       Searching for the best price

á       Deciding to breach the contract

á       É

¯    construction contracts: Two and a half basic forms

¤       fixed price

á       incentive to minimize cost

á       but also to do it by skimping on quality

¤       cost +

á       no incentive to minimize cost

á       or skimp on quality

¤       cost +percentage of cost

á       incentive to maximize cost

á       and build only gold plated cadillacs

¤       choose according to

á       which problems are hardest to control

á       who you want to allocate risk to

¤       ways of trying to limit the damage done by the wrong incentives in each case

á       remembering that what you can specify is limited by

á       what you know enough to specify (quality, for instance)

á       and what you can observe.

¯    Other sorts of contracts add another interesting option

¤       Pay by results

¤       For instance a contingency fee for a law firm.

¤       Or commissions for salesmen

¯    We discussed

¤       Principal/agent

¤       Joint undertaking

¤       Sale or lease of property

¤       Loan

v    Accounting

¯    Understand four things about the mechanics

¤       A balance sheet

¤       Cash flow

¤       Income statement

¤       T accounts

¯    And how they are related

¤       T accounts show each transaction

á       Twice

á       Once on the left side, once on the right

á       Either because a gain balances a loss or

á       Because a gain without a loss increases income and eventually equity

¤       Fundamental equation: Assets=liabilities+equity (assets-liabilities=equity)

á       To keep that true when a transaction occurs, either

á       Liabilities don't change (increase one, decrease one)

á       Assets don't change (increase one, decrease one)

á       Change in assets equals change in liabilities

á       Change in assets or liabilities is reflected in change in equity

á       Some combination of the above

¤       Complications

á       Allocating income and expenses to the right time period—not always when income received or expenses paid

á       Various simplifications of what is really happening, to reduce the influence of judgement calls and thus reduce the ability of the accountant or firm to manipulate results

¬     Purchase price rather than market value

¬     Ignore intangibles unless they were purchased

¬     Treat uncertain outcomes as zero probability (p<.5) or certain (p>.5)

 

 3/7/06

 

v    What is finance

¯    Analysis of decision problems involving the allocation of resources over time

¯    In a world of uncertainty

v    The nature of the firm

¯    Coase.

¯    Why is the capitalist beach made up of socialist grains of sand?

¯    The inside contracting system

¤       Firm A makes gun stocks

¤       Firm B makes the barrels

¤       Firm C makes the receivers

¤       Firm D assembles and sells the guns

¤       What happens to B, C, and D if A is shut down because its owner gets sick?

¯    More generally, think about an economy which was markets all the way down

¤       Some parts of ours come close

á       The one person law firm--but he probably hires a secretary

á       People who mow lawns

á       Free lance writers

¤       Markets work well for selling a well defined good at a time--mowing a lawn

¤       For performance over time, we need contracts

á       And we have seen some of the potential problems that contracts raise

á       And the problems with trying to control them

¤       So one solution is a firm instead

á       The contract is "you do what the boss tells you within the following limits"

á       And if you don't like it you quit

¤       But that solution raises its own problems

á       Instead of the costs of transacting in the market, you have

á       The costs of monitoring your employees to make sure they are serving their employer's interest, not just their own

á       Which gets harder and more expensive the more layers of control there are.

á       Also É

¯    Berle and Means (actually Adam Smith) problem

¤       If the firm needs a lot of capital it organizes as a joint stock company

¤       Each individual stockholder has little incentive to follow what the firm is doing or try to use his vote to affect it

¤       So management can do what it likes with the stockholders' money

¤       Are there mechanisms to control this problem?

á       Base rewards on performance--bonuses, options

á       Takeover bids and the threat thereof

á       Hedge fund vs Mutual fund story

¬     Mutual fund managers get a fixed percentage of funds they manage

¬     Hedge funds, a percentage of the increase in fund value

¬     Both are potentially large stockholders with an incentive to monitor management

¬     Some evidence that hedge funds do it better

¯    Because their managers rewarded directly for success

¯    Because mutual funds are judged by relative performance, and hold many of the same stocks as their competitors

¯    Also, a controlling group of stockholders might be able to benefit themselves at the cost of other stockholders

¤       Firm A owns a large chunk of firm B, gets B to agree to contracts favorable to A.

¤       "Empty voting" story.

¤       Majority stockholders might take firm private on terms favorable to themselves

¤       Are there mechanisms for controlling this problem?

v    Relevance to legal issues

¯    The size of the firm

¤       If firms want to merge, are there benefits?

á       Relevant to anti-trust law, where mergers are suspect

á       Stockholders might be injured if managers are empire building

á       So Coaseian arguments about what activities ought to be inside or outside the firm become relevant

á       Also relevant to a CEO simply trying to do his job, serve the stockholders.

¤       If a firm wants to spin off parts of it, are there benefits?

á       If the firm is worth more in pieces than as a whole

á       Stockholders will benefit by the breakup

á       Management might not

¯    Managerial discretion

¤       On the one hand, the reason the firm exists

¤       On the other, an opportunity for managers to benefit themselves at the cost of stockholders

¤       Parkinson story.

¤       Should "socially responsible" firms be suspect?

á       Donation to art museums, opera, É

á       Helping out local schools?

á       Treating employees better than the terms of the contract requires?

¯    Limits to majority stockholder control

v    Coase, Miller/Modigliani, and simplifying assumptions

¯    Coase analyzed externality problems in a world with zero transactions costs

¤       Not because he believed we are in such a world, but É

¤       To show that in such a world the conventional analysis would be wrong

¤       Hence that the problems in some sense came from the transaction costs

¤       Which is relevant to understanding their implications

¤       If sufficiently interested, see several chapters of my Law's Order or my "The World According to Coase" on my web page.

¯    Miller and Modigliani analyzed the equity/debt question in a world of perfect information etc.

¤       Because showing that the ratio doesn't matter in that world

¤       Shows that the reasons it does matter have to do with imperfect information and the like.

v    Miller/Modigliani Theorem

¯    A firm can finance itself with debt or with equity

¤       Debt means the obligation to pay a fixed amount

¤       Equity gives a fixed share of the income stream

á       Sort of

á       Since the firm gets to decide whether to pay out dividends or retain earnings

á       But the retained earnings go to the firm, which the equity holders own.

¤       Historically, equity pays a higher return than debt

á       If saving for the long term

á       You are almost always better off owning stock than bonds

á       But É

¤       The return on equity is less certain

¯    Using debt is cheaper, so why not?

¤       The larger the fraction of the firm is debt, the more highly leveraged it is

¤       All variation in firm income goes to the equity holders

¤       So the uncertainty in the stock goes up, raising the risk premium

¤       And at some point, the amount of equity is low enough so that the lenders suspect their loan might be at risk--and charge a higher interest rate.

¤       One of the points we looked at in the previous chapter

v    Jenson and Meckling

¯    Incentive of firm managers as a special case of agency theory

¯    If you are my agent, I want you to act in my interest

¤       But you will act in your interest

¤       So I try to make it in your interest to act in my interest

¯    The problem results in three costs

¤       The cost to me of making you act in my interest--monitoring

¤       The cost to you of doing things that will make you act in my interest, so that I will hire you--for example posting a bond that forfeits if you don't

¤       The net cost of your not acting in my interest in spite of the first two

¤       Note that it's a net cost

á       If we can predict that you will act in a way that benefits you by $2000

á       And costs me $3000

á       The net cost is only $1000

á       And that is also the maximum cost to me--because knowing that,

¬     I will offer you at least $2000 less than if you were not going to do that

¬     And you will accept at least $2000 less.

¤       So the total cost due to the agency problem is the sum of the three

¯    In the case of a firm manager

¤       If he owns the whole firm, it's in his interest to maximize profit

á       Taking account of not only pecuniary costs (money)

á       But anything else that matters to him

á       Such as being liked by his employees or respected by his neighbors

á       Or not working too hard.

¤       The more of the ownership goes to other people, the less that is true

á       Just as the factory owner who has insured against fire for 90% of the value will only take precautions whose benefit is much larger than their cost

á       So the CEO who only owns half the firm will only work harder if it produces at least $2 of firm income for each $1 worth of effort

á       Except that if other people own more than half, they might fire him if they see he isn't working hard, or in other ways is sacrificing their interest to his

á       Which requires monitoring by the stockholders

á       Which is hard if stock ownership is dispersed

¯    So there is a real advantage to the firm run by its 100% owner

¤       And in many cases that is what we see

¤       The problem arises mostly if the firm needs more capital than the owner's wealth

¤       Which could be borrowed--debt rather than equity

¤       But the highly leveraged firm is risky for the owner, and É

¤       The lenders

¯    There is also a real advantage to a firm with concentrated stock ownership

¤       Because the large stockholder has an incentive to monitor management

¤       And if necessary try to get together with other large stockholders to replace it

¤       Hedge fund/mutual fund/stockholder situation

¯    All of which explains part of why firms are sometimes taken private

3/9/06

 

v    Review

¯    Coase

¤       Firms exist because there are costs to organizing cooperation by exchange and contract on the market

¤       There are also costs associated with organizing cooperation by hierarchical authority

¤       A lot easier to buy paperclips and paper on the market than to produce them yourself

á       Your top management doesn't have to know how the production is organized

á       And competition will get you the lowest cost.

¤       But having a key employee outsourced could raise a lot of problems

á       You can't do without him, so he could jack up his price, claim costs

á       And you don't know and can't afford to turn him down.

v    Berle/Means/Smith

¯    With dispersed ownership, stockholders have little incentive to monitor the managers who are their agents for running "their" firm.

¤       So managers can serve their own objectives with the stockholders' money

¤       Which might mean being lazy or incompetent

¤       Or paying themselves lots of money

¤       Or buying status by contributing the firm's money to "worthy causes."

¯    Legal restrictions on such behavior are weak

¤       ("business judgement rule")

¤       perhaps have to be weak if the firm is to work as a hierarchical structure run by management

¯    Market restrictions exist via the threat of proxy fights, takeovers

¤       Ownership of shares doesn't have to be dispersed all the time

¤       Becomes concentrated if someone is buying stock to get control

¤       Or via large institutional stockholders--pension funds, mutual funds, hedge funds.

¤       What is a "junk bond" and why is it called that?

¯    But conflicts over stockholder control raise a new problem

¤       One group of stockholders, with an effective majority, might benefit themselves at the expense of other stockholders.

¤       Either by how the company is run, or É

¤       By taking the company private, or merging it, on terms favorable to themselves

¤       The law tries to prevent this by requiring equal treatment.

v    Miller/Modigliani Theorem

¯    A company can finance itself with either debt or equity

¯    Debt, historically, receives a lower interest rate than equity

¯    But the higher the fraction of the financing is via debt, the riskier the equity

¤       Why not a 100% debt?

¤       Who then is the residual claimant?

¤       And what happens to the risk of default

¯    It turns out that, if you make some simplifying assumptions, the value of the firm is the same whatever the mix of debt and equity it chooses

¯    Which suggests looking at the failure of those assumptions in deciding what mix to use.

v    The firm as a problem in agency theory

¯    How do principals control agents?

¤       By monitoring their behavior--at some cost

¤       And punishing or firing them if they are not acting in the interest of the principal

¤       My recent tire purchase as an example

¯    How much control should there be?

¤       The amount that minimizes the sum of

¤       Cost to the principal, cost to the agent, net cost due to insufficient control

v    Time value of money

¯    How do you compare a payment today with a larger payment in the future

¤       Or a stream of payments over time with a single sum today

¤       For instance the income from owning a share of stock vs its present market value

¯    How compound interest works

¤       Suppose the interest rate is 10%=.1

¤       $1000 this year gives you $1000x(1+.1) next year gives you $1000x(1+.1) x(1+.1) in two years, and so on

¤       if we call the interest rate r, then

¤       $1000 this year gives you $1000x(1+r) next year gives you $1000x(1+r) x(1+r) in two years, and so on

¤       if the interest rate is small and the number of years is small, adding works pretty well

á       1% compounded over 5 years is only a tiny bit more than 5%

á       but 10% compounded over 10 years is quite a lot more than 100%

¯    Suppose you are comparing $1000 today with $1100 a year from now

¤       If you have $1000 today you can

á       put it in the bank and get $1000(1+interest rate) in a year.

á       So the $1000 today is worth at least $1000(1+r) in a year

¤       If you will have $1100 in a year you can borrow against it.

á       If you borrow ($1100/(1+r)) today

á       In a year the debt will be ($1100/(1+r))x(1+r)=$1100

á       Which your $1100 exactly pays off

¤       So $1000 today is equivalent to $1000 (1+r) in a year, where r is the interest rate

¯    This assumes

¤       That the future payment is actually certain--future payments sometimes are not

¤       That you can borrow or lend at the same interest rate--which you might not be able to do

¤       If you can't, the argument shows the boundaries. $1000 is worth at least as much as $1000x(1+rl) in a year, where rl is what you can lend at

¤       At most as much as $1000x(1+rb) in a year, where rb is what you can borrow at

¯    Generalizing the argument, the present value of a stream of payments over time

¤       Meaning the fixed sum today equivalent to the stream

¤       Is the sum of the payments, each discounted back to the present

¤       Where a payment in one year is divided by (1+r), in two years by (1+r)x(1+r), É

v    One example: You have just won the lottery--prize is 15 million dollars

¯    Actually, half a million a year for thirty years

¯    They offer you five million today as an alternative

¯    And the market interest rate is 10%. Should you accept?

¯    Harder versions

¤       How low does the interest rate have to be to make you reject their offer

¤       Your interest rate is 10%, the state can borrow at 5%. How much should they offer you?

¯    A useful trick

¤       What is the present value of $1/year forever

¤       If the interest rate is r?

¤       There is, or at least was, a security that works this way--a British Consol

v    Another example: With risk

¯    The court has awarded you a million dollar settlement, payable in five years.

¯    Of course, the firm might be out of business in five years

¯    What is the lowest offer you ought to accept, given that

¤       The prime rate is 5%

¤       You can borrow at 10%

¤       The firm can borrow at 15%

¯    First question: Why the difference?

¯    Second: Which rate should you use?

¯    First answer: the difference probably reflects risk of default

¤       The market thinks that, each year, there is about a 10% chance of default

¤       So a lender who lends $100 needs to be promised $115 next year in order to get, on average, $105. (slightly simplified because the two effects ought to compound, not add)

¯    Second answer:

¤       So you can use the market to estimate the risk you won't be paid, assuming that the same conditions that lead to defaulting on a debt lead to defaulting on a damage payment

¤       So you too should use 15% to discount the payment in order to decide whether to accept an offer

¯    Alternative approaches

¤       You could make your own risk estimate

¤       And might have to if the conditions that lead to one default are different than those that lead to another

¤       You might also want to use a higher rate if you are risk averse, since banks probably are not.

v    Choosing the interest rate to discount at

¯    Easy case

¤       Insignificant risk--the two alternatives are really both certain

¤       You can lend or borrow at the same interest rate

¤       Use that interest rate

¯    Hard case one--still risk free

¤       You must pay a significantly higher interest rate than you can get

¤        If you have enough capital so that you can pay for present expenditures by reducing the amount you are lending out, then your lending rate is the relevant one

¤       if you have to borrow, then the borrowing rate is the relevant one if in fact you will borrow

¤       if accepting later income instead of earlier income means not borrowing but spending less this year, more in the future, then the right rate is between the two numbers.

¤       Why?

¯    Hard case two: Risk, but you are risk neutral

¤       Some risk that future payments won't be made

¤       Try to estimate that risk and discount accordingly

¤       Which can sometimes be made by seeing what interest rate the future payer has to pay to borrow money

¯    Hard case three: You are risk averse

¤       The payers borrowing rate is a lower bound to what you should use

¤       Try to estimate the risk and decide how risk averse you are

¤       Or your client is, if acting as an agent.

v    Why isn't the riskless interest rate zero?

v    How does the interest rate depend on risk?

¯    For a risk neutral lender

¤       Why a bank should be very nearly risk neutral

¤       Why a stockholder should be very nearly risk neutral

¤       Against what sort of risk should a stockholder not be risk neutral?

¯    Are there any special kinds of risk for which a bank or stockholder could be expected to be risk preferring?

v    Internal rate of return

¯    The same calculation we have been doing, from the other direction

¯    You are given the choice between a million dollars today and $100,000/year for eight years

¤       You calculate the interest rate at which the two alternatives are equivalent

¤       That is the rate of return they are offering you on your million

¤       So if it is more than the interest rate you can borrow or lend at, accept, if less, reject

¯    A firm is planning to build a million dollar factory

¤       Which will make the firm $100,000/year for eight years

¤       Then collapse into a pile of dust

¤       The internal rate of return is the interest rate at which it is just worth doing

¤       Or in other words, the rate of return the project gives the firm on its million

¤       Decide whether to build it according to what the firm's cost of capital is.

 

v    Predictable irrationality aka behavioral economics aka evolutionary psychology

¯    Economists generally assume individually rational behavior

¤       Meaning that individuals have objectives and tend to take the actions that best achieve them

¤       This makes sense to the degree that the rational actions are predictable

¤       The mistakes are not, so treat the as random error

¯    There is some evidence, however, for certain patterns of "irrational" behavior

¤       Endowment effect

¤       Not discounting the future the way economists think you should

á       Would you rather have $100 today or $110 in a week? Many choose today

á       Would you rather have $100 in a year or $110 in a year + a week?

á       Few choose the $100

¯    Evolutionary psychology as an alternative to economics

¤       Similar pattern—act as if making the best choices for an objective

¤       But in evolutionary biology, we know the objective—reproductive success

¤       And evolution is slow, so we are adapted not to our present environment but to the environment we spent most of our species history in

¤       I.e. as hunter/gatherers.

¯    The endowment effect and territorial behavior

¤       Territorial animals have a territory they treat as theirs

á       The farther into it a trespasser of their species comes, the more desperately they fight

á       A fight to the death is usually a losing game even for the winner, so É

á       On average, the "owner" wins—the trespasser retreats

á       A biological example of a commitment strategy in a bilateral monopoly game

¤       Think of the endowment effect as the equivalent for non-territorial property

á       This is mine, so I will fight harder for it than it is worth

á       Knowing that, you won't try to take it away from me

á       We thus get private property without courts and police

á       As long as inequalities of power are not too great

¯    Uncertainty and trading off future against present

¤       The environment we evolved in was risky and short of mechanisms for enforcing long term contracts

¤       So we are designed to heavily discount future benefits vs present benefits

¤       "A bird in the hand is worth two in the bush"

¤       but not to heavily discount a year plus a week over a year—both are future

¤       this also explains why we have to use tricks to get ourselves to sacrifice present pleasure for future benefits

á       Christmas club for savings

á       "I won't have ice cream for desert until I have lost five pounds"

á       think of it as a rational economic you trying to control a much more short sighted evolved you

á       and facing the usual agency problems in doing so

v    "If you're so smart, why aren't you rich?" The economist's answer

¯    Ways of making money on the stock market and why they don't work

¤       Suppose a stock has been going up recently.

á       Buy it—it will probably keep going up?

á       Sell it—it will go back down to its long term value?

á       If either method worked—it wouldn't.

¤       There are a variety of more elaborate strategies which involve analyzing how a stock has done over time, or how the market has done, and using that information to decide whether to buy or sell

¤       People who do this are called "chartists."

¤       The idea is reflected in accounts of what the market did

¤       If it goes up and then down, that is called "profit taking"—with the implication that when it goes up it will go down.

¤       People talk about "support levels" and "barriers" and similar stuff.

¯    Suppose lots of investors are superstitious, so sell stock on Thursday the 12th, expecting something bad to happen on Friday the 13th

¤       So the stock (particular firm or the whole market, as you prefer) drops on or just before Friday the 13th

¤       What should you do if you know this and are not superstitious?

¤       What will the consequences be

¤       Generalize the argument to any predictable pattern.

¤       And you have the efficient market hypothesis, weak form

¤       The argument also works for lines in the supermarket or lanes in the freeway

v    The efficient market hypothesis

¯    Is the formal version of my Friday the 13th story

¯    You cannot make money by using past information about stock prices to predict future prices

¤       For instance, by buying a stock when it is below its long run average, selling when above

á       Because lots of other people have that information

á       The fact that it is below or above means other investors have some reason to think it is doing worse or better than in the past

¤       This is the weak form of the hypothesis—limited to price information

¯    You cannot make money by using other publicly available information either

¤       Such as the information sent out to stockholders

¤       Or the fact that demand for heating oil goes up in the winter

á       Radio ads telling you to speculate in oil futures on that basis

á       But oil futures already incorporate that information in their price

¤       Or the fact that this is an unusually cold winter—other people know that too.

¤       This is the semi-strong form of the hypothesis—all public information is incorporated in the stock price

¯    All information is incorporated in the stock price

¤       Cannot include information that nobody knows—a meteor is going to take out the main factory next week.

¤       What about information only one person knows?

¤       A handful of people?

¤       Does it depend on who the handful are and what the legal rules are?

v    Why the hypothesis cannot be (perfectly) true

¯    If even the weak form were perfectly true, and individuals knew it

¤       There would be no incentive to look for patterns in stock movements

¤       And if nobody is looking, the mechanism that eliminates the patterns doesn't work

¯    Consider the analogous problem with grocery store checkout lanes

¤       You have an armful of groceries, are at one end of the store—should you search all lanes to find the shortest?

¤       No—because they will all be about the same length, because É

¤       If one is shorter than the next, people coming in between them will go to the shorter, evening them out.

¤       The efficient market hypothesis. But É

¯    Two limits to it

¤       If it were perfectly true, nobody would bother to pay attention to line length,

á       so it wouldn't work.

á       Especially since length includes how much stuff each person has in his cart

á       Which takes some trouble to look at and add up

á       So, if people are perfectly rational, the differences in length have to be just enough to provide enough reward to those who do check to make enough people check to keep the differences down to that level.

á       Who searches? Those for whom the cost of doing so is lowest

¬     Because they are good at mental arithmetic and

¬     Don't have an armful of groceries

¬     So you should go to the nearest lane.

¤       Not all information is public

á       If you know that one checkout clerk is very fast and other people don't

¬     You go to her lane even if the line is a little longer

¬     And benefit from your inside knowledge

¬     Until enough people know to bring her lane up to the same length in time as the others

¬     At which point only insiders are in her lane

á       What if you know one is very slow and other people don't

¯    These limits explain

¤       Hedge funds and the like

á       Very large amounts of money

á       Very smart people working for them

á       In the business of finding very small deviations from efficiency and eliminating them

á       At a profit.

á       "Statistical arbitrate"

¤       Explaining Warren Buffet

á       He claims to be proof that the efficient market hypothesis is false

á       Because he has done enough better than the market so that, by chance, not one such investor ought to exist.

á       But then, his ability to evaluate information might be extraordinarily good

á       Which points out some of the ambiguity in the idea of publicly available information.

¯    At the individual level, the argument for throwing darts at the Wall Street Journal doesn't work if either

¤       You have information nobody else has

á       The checkout clerk in lane 3 is very slow

á       There is construction coming up in the left hand lane of the freeway

á       The CEO of the firm is an old college acquaintance, and you know he is a clever and plausible crook

¤       You have an opinion you are willing to bet on and know many other people will bet the other way

á       When the first Macintosh came out, I told a colleague I was getting one

á       He asked why I didn't get a PC Jr.

á       So I bought stock in Apple

á       I have made four investments on that basis.

¬     Three made me money

¬     One lost it

¯    But at the time I thought it was more likely to lose money than make it

¯    But had a positive expected return.

¤       Which suggests two ways of making money in the stock market

á       Knowing enough about the firm to tell if it is over or underpriced—accounting+ or É

á       Depending on your special information

¬     And not bothering to know everything else relevant to the firm

¬     Because the market will already have incorporated all that into the stock price.

¤       The third way to profit isn't by making money

á       If my wife is an oil geologist, I should stay out of oil stocks

á       Or even sell them short

v    Exercise, which I will put on the syllabus for you to think about

á      What is economics?

á      A way of understanding behavior

á      Based on a simple assumption

á      Rationality:

á      Meaning that people have purposes and tend to take those actionsÉ

á      Not a statement about how people think

á      But about the consequences

á      True of cats and babies

á      Not entirely true, but É

á      A lot human behavior fits that pattern, and É

á      We don't have a good theory for the rest, so É

á      Treat it as random error.

á      In some contexts, truer than it ought to be

á      Firms maximizing profits

á      Large markets where random effects cancel out

á      What does it apply to?

á      All behavior in all times and places

á      My size of nations

á      Economic Analysis of Law:

á      Armed Robbery

á      Contracts under duress

á      Mugger--argument for enforcing

á      Parole system in warfare--argument against

á      Pinochet--argument in both directions.

á      Politics, marriage, war, É  .

á      Rational ignorance. Name of congressman?

á      Armies running away. Njalsaga.

á      Silent student problem

á      Divorce rate?

á      We find out by trying

á      Conventional area of applications

á      Explicit markets, prices, inflation, unemployment, etc.

á      Ideas best worked out in those areas, so we will spend most of our time there, but É

á      With detours to apply the ideas elsewhere.

v    The coordination problem

¯    Why our society cannot exist and we must all be dead

¤       In order to achieve almost anything—produce food, build houses, make clothes

á       We require the coordinated cooperation of millions of people

á       The house requires, among many other things, wood

¬     Which requires people growing trees and cutting them down

¬     Which requires people making chain saws

¬     Which require people making iron and steel and gasoline

¬     Which require É

¤       There are, broadly speaking, to solutions to the coordination problem

á       Central direction—someone tells everyone what to do

¬     Which works on a small scale\

¬     But becomes hopelessly unworkable at the scale of a national economy

á       Decentralized  coordination via prices, voluntary exchange, etc.

¯    How should we judge alternative solutions to the coordination problem

¤       As embodied in legal rules

¤       Government policies

¤       É

¯    one way is by their net effect on everyone, which we can think of as the "size of the pie."

v    Perfect competition

¯    A simplified model of how the exchange market works

¤       Infinite number of participants, so each participant ignores the effect of how much he buys, sells, produces, consumes on the market price.

¤       Complete information

á       So if you are willing to pay $2 for something

á       It must be worth at least $2 to you—or you wouldn't have.

¤       All transactions are voluntary

á       No theft, or É

á       Torts, or É

á       Involuntary interactions not covered by law or contract, such as my playing my car stereo so loudly that it bothers other drivers.

¤       In explaining perfect competition one often makes additional simplifying assumptions, then drops them later.

á       You can find a much more extensive version in my Price Theory text, webbed on my site

á       Or my _Hidden Order_, which I will put a copy of on reserve.

á       In both I work through the simplified version, then put the complications back in.

¯    A pretty good approximation for some but not all market settings

¤       One big advantage over more complicated models is that we can solve it

¤       Prove theorems about the outcome, in particular.

¤       One can prove that it maximizes the size of the pie in a useful although not perfect sense

¯    Which means that one can look for ways of increasing the size

¤       By seeing where the assumptions break down

¤       And how those breakdowns reduce net benefit to people.

v    Demand and supply curves

¯    A demand curve shows quantity demanded as a function of price

¤       In casual conversation, I "want" X amount of something

¤       But in fact, how much I want depends how much it costs

¤       Because what I am really choosing is not "an ice cream cone" but

á       + the pleasure from consuming an icecream cone

á       -the value to me of the money I have to pay for it

á       -the cost to me of the calories I get from it

¤       and whether that nets to plus or minus depends, among other things, on the price.

¯    As price changes, I move along my demand curve—choose to consume more if the price goes down, less if it goes up

¤       Adding up individual demand curves, we move along the market demand curve

¤       Which is the horizontal sum of individual demand curves

¤       Since the amount we buy is the sum of what I buy and you buy and É

¯    A shift in the demand curve changes the relation between price and quantity

¤       Something happens which makes me willing to buy more (shift right) at any price

¤       Or less (shift left)

¯    Economists distinguish between

¤       a change in demand (demand curve changes)

¤       and a change in quantity demanded (quantity changes, whether because the curve moved or because the price changed with the curve staying the same)

¤       and that distinction avoids a lot of verbal confusion.

v    How much is it worth to me to be able to buy all the apples I want at $1/apple?

¯    Suppose I am willing to pay $3 to have one apple instead of zero.

¤       I am paying $1 to get something I value at $3,

¤       so gaining $2

¤       my "consumer surplus" on the first apple

¯    suppose I am willing to pay $2.50 to have two apples instead of one

¤       My surplus on the second applie is $1.50

¤       So my total surplus on the two aplles is $3.50

¯    But "willing pay $3 to have one apple instead of zero"

¤       Means that at a price of $3 I would buy one apple

¤       So my demand curve shows a quantity of 1 at a price of $3

¯    Following out the argument, my consumer surplus on buying all the apples I wish to buy at $1/apple is the area

¤       Under my demand curve and

¤       Above a price line at $1/apple

v    The same argument applies to a supply curve

¯    It shows how much a producer will produce and sell

¯    If I would produce a unit for any price above $1

¯    And can sell it for $3

¯    My producer surplus, aka "profit," is $2.

¯    Generalizing that argument, producer surplus is

¤       The area above the supply curve

¤       And below the price.

v    So total surplus from a particular market is the area between supply and demand curves

v    And the net effect on individual welfare of a change is the change in that area.

¯    But note that this assumes the ordinary market setting

¯    And we are about to see some problems with that assumption

v    Suppose we have price control on gasoline

¯    The market price would be $2/gallon, at which quantity supplied equals quantity demanded

¯    Instead the law fixes it at $1/gallon

¯    The book's version of what happens

¯    What is wrong with this story?

¤       At the price, consumers want to buy more than producers want to sell

¤       What decides who gets the gasoline?

¯    Simple answer: whoever gets to the gas station and before they run out.

¯    So lines start to form at gas stations

¯    How long does the line have to be for quantity demanded—at a price that includes the time waiting in line—to equal quantity supplied?

¯    What is the overall effect on surplus.

v    Government regulation over professions

¯    The arguments that are given in the book all assume a philosopher king government

¤       The government is trying its best to do good, but doesn't always succeed

¤       Is there a more plausible model?

¯    Facts on medical licensing history

¤       During the five years after Hitler came to power, about the same number of foreign physicians were admitted to practice as during the five years before

¤       During the Great Depression, the AMA informed medical schools that they were graduating too many students

¤       Every school cut back

¤       Medical licensing normally requires graduation from an approved School

¤       Where do you think the states got their list of approved schools?

¯    Licensing vs certifying

¤       If the problem is that consumers don't have the information, certifying is sufficient

¤       The argument for licensing is that, even with information, the consumers will make the wrong choice.

¤       Or that a large part of the cost from using a low quality professional is born by someone other than the person making the decision

á       I have a building designed by an incompetent architect

¬     It falls down, injuring other people

¬     Whom I cannot compensate for their loss

¬     But—as in moral hazard in general, although I don't have the full incentive, I have a substantial incentive, since if the building falls down I lose a lot of money

¬     And my mortgage company has an incentive too

á       I use an incompetent physician

¬     Don't get cured

¬     Spread my (contagious) disease

¬     But again É

¤       The argument against is that licensing can be used to control consumers in someone else's interest, usually the profession

á       Not only physicians and lawyers are licensed, but also

á       Yacht salesmen and egg graders and barbers and É

v    Monopoly

¯    What?

¤       A single firm that produces almost the total output for a market

¤       And so can control price--at the cost of selling less the higher the price.

¤       Of course, a firm in a competitive market can ask any price it wants too--but above the market price, its sales drop to zero.

¯    Why?

¤       Only owner of a required input

á       A choke point--the only pass through the mountains

á       De Beers?

¬     Demand story--that DeBeers created the demand for diamonds for engagement rings. But É

¯    "In fact, in 1938 some three quarters of all the cartel's diamonds were sold for engagement rings in the United States." (Before the publicity campaign started)

¯    unclear how much it is a story of an ad campaign that sold diamonds, how much of one that sold itself.

¯    Competing explanation by Margaret Brinig

¬     Do they control production?

¯    1957, Soviet production 20-30% of world

¯    Australia, Angola, Canada, Zaire (<3%),

¯    DeBeers mines "represented about half of total supply"

¬     A monopoly on marketing, not production

¬     Cartel? Natural monopoly? Unclear.

á       Me. Or Apple. Or your corner grocery store.

¬     More generally, the sole producer of a particular variety of good

¬     Has some monopoly power wrt buyers who want that variety

¬     And that sort of monopoly is much more common, and probably more important, than the "giant firm controlling the X industry" type.

¯    Natural monopoly

¤       Economies of scale

á       Sometimes increasing quantity reduces cost per unit, because fixed costs such as design or tooling can be spread over more units

á       Sometimes it increases cost, because the larger firm has more layers between the president and the factory floor

á       So average cost typically first falls with output, then eventually comes up again.

¤       If it keeps falling out to the full extent of the market, you have a natural monopoly

á       Since it can make money selling at a price at which a smaller competitor would lose money

á       It ends up with the whole market

¤       The common case of this is the specialized producer mentioned above

á       Where the cause is not the large economies of scale, but É

á       The small size of the market

á       A small town general store, me as a speaker, your favorite author

¤       But it could also exist on a large scale if there are very large economies of scale.

¯    Artificial monopoly: Predatory Pricing and The Standard Oil Myth

¤       "Big firm has deep pockets, sells below cost to drive out smaller firms"

á       both firms are losing money, but the big firm has more money to lose, so lasts longer

á       what is wrong with this story?

¤       McGee article in JLE

á       He went through the many volume transcript of the Standard Oil antitrust hearing

á       And found no examples of predatory pricing, actual or claimed

á       The closest was a threat to Cornplanter oil to cut prices on them if they didn't stop expanding at Standard's expense

á       The manager of Cornplanter, by his testimony, told the Standard Oil man that if they cut prices on him he would cut prices over a much larger area, costing them a lot more money.

á       And that was the end of the matter.

¤       Hard to prove that predatory pricing is impossible

á       Given the nature of game theory and commitment strategies

á       But the big firm seems to have the weaker hand in the game

á       Cheaper to try to buy out competitors—which Rockefeller did. But that has a long run problem

v    State enforced monopoly

¯    The original meaning of the term--monopoly privilege sold to raise money or given to favored subjects.

¯    Still a common form of monopoly

¤       It is illegal to compete with the Post Office in the delivery of first class mail

¤       It is illegal to sell liquor in states with a state liquor monopoly

¤       Until deregulation, the airlines were a cartel enforced by the CAB

á       It was illegal to change fares in either direction without permission

á       Or to start flying a new route without permission

á       PSA story

¤       Professional licensing is a form of state monopoly

¤       As are patents and copyrights

v    What is wrong with monopoly?

¯    Consider a simple case

¤       Fixed cost of a million dollars a year to operate a factory

¤       Marginal cost of a dollar widget to produce widgets

¤       If you produce a million widgets/year, average cost = $2

¤       If you produce two million, $1.50

¤       And so on out to infinity É

¯    What price maximizes the firm's profits?

¤       The lower the price, the more units they can sell

¤       Suppose they sold widgets for a dollar/widget--their marginal cost

¤       They lose a million dollars a year

¤       Raising the price and cutting quantity has to be a win

¤       When do you stop raising the price?

¤       consider marginal revenue--increase in revenue by selling one more unit

á       If marginal revenue <marginal cost, you are losing money on the last unit sold

á       So should cut back until you reach the quantity where MR=MC

á       Any further cut costs you, since you are cutting a unit that brings in more than it costs.

á       Selling one more unit/year gets you the price it sells for

á       Costs you the reduction at the price at which all others units can be sold, since it takes a slightly lower price to increase sales

á       So marginal revenue is less than the price

¯    If we consider the combined effect on seller and buyer, what price "should" the seller sell at?

¤       As long as price is above marginal cost

¤       There are consumers who value the good at more than it would cost to produce one more unit for them

¤       But are not getting it

¤       Producing that extra unit and giving it to the consumer would benefit the consumer by more than it cost the producer

¤       So the efficient rule is to sell at a price equal to marginal cost

¯    So a monopoly maximizes its profit at a higher price than the price that maximizes net benefit to customer plus firm.

¤       This is the standard economic argument for why a monopoly is inefficient

¤       And evidence of the risk of assuming technical terms have their common meaning

¤       Since the hearer will imagine the statement is about how badly run a monopoly firm is

¤       When it is actually about how a well run monopoly firm will act

¯    A second inefficiency: Rent seeking

¤       My railroad story

¤       The exchange control version

¤       The tariff version

¤       The price control version

¤       What's wrong with theft

¤       Gordon Tullock, "The Welfare Costs of Tariffs, Monopolies and Theft"

v    Oligopoly and cartel

¯    An oligopoly exists when economies of scale are large enough so there are only a few firms in the industry

¯    They might compete, trying to take account of the effect each has on prices

¤       We could model this as a Nash equilibrium

¤       Where each takes the behavior of the others as given

¤       And decides what price and quantity maximizes its profits

¯    Or they might coordinate, act as a cartel, all agreeing to hold down output in order to drive up prices

¤       In the U.S. at present, this is illegal

¤       Even if legal, each member of the cartel has an incentive to chisel—cut prices a bit under the table in order to lure customers from the others

¤       Unless the agreement is not only legal but enforceable

v    Monopolistic competition

¯    Lots of firms, differing in location or characteristics of the product

¯    Each one has a partial monopoly wrt customers "close" to it

¯    Competes for customers who are near two or more firms

¯    And if the outcome is above market profits, additional firms can enter the market

¯    Driving profits down.

v    What to do about natural monopoly? Three alternatives, all bad.

¯    Government monopoly--the post office

¤       What is its incentive to charge marginal cost?

¤       Or to hold costs down

¤       When some "costs" can be used to buy political support

¤       For instance from employee unions

¤       Or other sellers of inputs

¯    Regulated monopoly: Public utilities and the like

¤       If forced to charge marginal cost they go broke, so require a subsidy

¤       In practice the usual attempt to force average cost--still inefficient, but not as inefficient as what the monopolist would do

¤       But how do you know what average cost is?

á       If you ask the accountants, the firm has no incentive to hold down cost

á       Since whatever it is, that's what they are allowed to charge

¤       And why is it in the interest of the regulator to try to maximize social benefit anyway

á       When he could be currying favor with the regulatee in exchange for a well paying job when he leaves government service

á       Or buying votes for his political patrons at the cost of either the regulatee's stockholders or its customers

¯    Private monopoly

¤       Has the inefficiencies already discussed, but two advantages

¤       It does have an incentive to minimize costs, and É

¤       It doesn't have the ability to use the government to prevent competition

¤       Which matters if change over time makes it no longer a natural monopoly

¤       Consider, in contrast, the history of the ICC

á       Set up to regulate the (somewhat) monopolistic railroads

á       Regulated the competitive barge industry, and later trucking industry

á       In part to protect the railroads from their competition.

v    Other forms of monopoly

¯    The standard argument shows that competition is superior to monopoly, where competition is possible—i.e. not a natural monopoly

¯    So is an argument against government enforced monopoly

¯    Or monopoly created by one firm buying out is competitors.

¤       But the antitrust division has to distinguish that case

¤       From one where firms merge to make a better firm

¤       So ask the other firms in the industry

¤       And do the opposite of what they tell you to.

v    Price discrimination

¯    The problem with inefficiency from the monopolist's point of view

¤       All those customers out there who would buy my additional units at more than it costs me to produce them, but not at my price

¤       How can I make money off them too?

¤       By finding some way of charging different prices to

á       Different customers, or É

á       The same customer for different units.

¯    Consider a cookie company with identical customers, MC = .10/cookie

¤       $1/cookie up to 10/week, then .50/cookie

¤       can do better with a much more complicated pricing system

¤       better still with the cookie club

¤       but É how do we prevent resale?

¤       Cookies can only be consumed on the premises???

¤       Works better for electric power, or transportation, or medical services

¯    Consider an author and his publisher, with two kinds of customers

¤       Fans will pay $20 for the book

¤       New readers will pay $10

¤       Solution?

¤       What if the two kinds are rich Americans and poor Englishmen?

¤       Other examples

¯    Is price discrimination a good or bad thing?

¤       Perfect price discrimination eliminates the classical inefficiency, but É

á       Increases monopoly profit and so

á       Expenditures on getting it

¤       Imperfect price discrimination may reduce the classical inefficiency

á       Also may make possible the production of goods that could not cover their cost if all sold at the same price

á       But if you divide your market (U.S./England) a book might go to an Englishman who values it at $11 instead of an American who values it at $19, which is inefficient

á       And there are costs to doing the price discrimination

¬     Which you pay because you get a benefit

¬     But it may come at the expense of the customer who you are getting to pay a higher price, in which case on net it makes the two of you worse off

¬     Or it may permit a customer to get it who otherwise wouldn't, in which case it makes the two of you better off

¤       So the net effect is indeterminate

á       Price discrimination might on net make us better off

á       Or worse

v    Externalities

¯    The simple solution to the coordination problem

¤       Everyone bears the costs of his own actions

¤       Pays enough for inputs (labor, raw materials) so that the sellers don't lose by selling them to him—otherwise they wouldn't.

¤       Charges a price for his output at which the buyers don't lose by buying—otherwise they wouldn't

¤       If his income minus his costs are positive then

á       He produces, and É

á       In terms of net effects, should produce

¤       So we have a whole lot of tiny decisions, coordinated through the price system

¤       For more details, read a price theory textbook, prefereably mine.

¯    Why it doesn't work with externalities

¤       My action imposes a cost on you which doesn't require your permission

¤       So I ignore that cost, take the action even if my gain is less than your loss (negative externality)

¤       Or my action produces a benefit I can't charge you for, and I might fail tot ake it even if your benefit was larger than my loss. (positive externality)

¤       Note that the problem isn't the existence of the external cost

á       Internal costs are costs too

á       The problem is that because the cost is external, it leads individuals acting rationally to make the wrong decision

á       And individual rational action is what we mostly rely on to get the right decision made.

¯    The Regulatory solution

¤       Have a government agency decide what I ought to do, taking into account all costs external and internal

¤       And order me to do it

¤       Filter my factory's smokestack, for example

¤       This has two problems

á       It requires information about the costs of alternatives that the regulator probably doesn't have and the firm has no incentive to tell the truth about

á       The regulater may find better things to do with his power than improve the world

¯    The Pigouvian solution

¤       Tax me the amount of my externality

¤       Now I will take account of it in my decisions

¤       Filter the smokestack if and only if doing that is the cheapest solution

¤       And costs less than the resulting reduction in pollution is worth

¤       Obvious problems

á       Whoever sets the tax needs to measure the damage done by the pollution—so it requires less information than direct regulation, but still some

á       Again, the incentive of those setting the tax

¯    Coase's criticism

¤       Nothing works

á       An externality isn't a cost I produce for you, but É

á       A cost of things both of us are doing that are incompatible

á       The physician and the candy factory.

á       Airport noise is only a problem because there are people living under the flight path

á       The lowest cost solution might be to reduce the noise, or to have something other than housing under the flight path

á       But if the airlines must pay a tax for the noise, they may reduce it at a high cost, when the alternative solution is less expensive—and would occur if the airlines were not being taxed.

á       More generally, the Pigouvian solution requires you to know which party is the lower cost avoider of the problem—or whether the best solution is for both parties to do some avoidance

¤       Everything works

á       If transaction costs are low, the physician wins the case, but moving his consulting room costs less than moving the machinery, É time to start bargaining

á       If the airlines are not taxed for the noise, but noise reduction is the less expensive solution

á       The airlines will contract with the owners of the land under the flight path to reduce the noise—at the owners' expense

á       Or buy the initially cheap and empty land, then reduce the noise, then resell.

á       More generally, if the outcome is inefficient, some change could produce benefits for all concerned, so if transaction costs are low they will bargain to that change

á       The right to do X moves to whomever values it most highly

¤       It all depends

á       On transaction costs

á       Organizing a contract by which everyone who lives in Los Angeles pays everyone who drives there to reduce his pollution would be hard

á       So where transaction costs are high, we are back with the Pigouvian problem.

v    Externalities and the law

¯    EPA style regulation is the first approach—give orders about outcomes

¤       Require all power plants to remove X% of the sulfur from what goes up the smokestack

¤       Giving no incentive to use low sulfur coal instead.

¤       There are states that produce high sulfur coal. They have senators.

¯    The tort system can be viewed as a version of Pigouvian taxes

¤       I impose an externality, you sue me

¤       I have to "make the damage whole," i.e. pay the amount of the damage

¯    Control of air pollution via tradable emission permits can be seen as

¤       Pigouvian approach, with the government deciding the amount of pollution, the market deciding the price

¤       The Coaseian approach, with the right to pollute moving to those who value it most highly

¤       But without any possibility of bargaining between polluters and breathers.

v    Public goods: Does not mean a good produced by government. Government produces some private goods, many public goods are privately produced.

¯    Two characteristics usually used to define a public good

¤       Non-excludability. If the good is produced, it will be available to all the members of a preexisting group of people

á       Consider an (unencrypted) radio broadcast

á       Or my repainting my shabby looking house

¤       Non-rival. One person's use of the good doesn't interfere with another person's

á       The cost of the radio broadcast does not depend on how many people choose to listen to it

á       My neighbor enjoying the improved appearance of the neighborhood doesn't keep passing drivers from admiring my handsome house

¤       In my view, it is the first characteristic that is responsible for the essential characteristics of a public good

á       A good that is only non-rivalrous is simply a natural monopoly with marginal cost of zero

á       A good that is non-excludable raises the problems we will discuss, even if my use does to some degree interfere with yours

¯    The public good problem: How to pay for producing it

¤       I propose to build a flood control dam, cost $1 million dollars

¤       The protection is worth $10,000 each to a thousand farmers downstream

¤       So the dam is worth building, but É

¤       How do I get them to pay for it?

á       Each farmer knows that his payment is unlikely to make the difference

á       And if the dam is built, he benefits even if he didn't contribute

v    Possible solutions

¯    private

¤       Consider radio and TV—an obviously insoluble public good problem that is routinely solved, since both are produced privately

á       The ingenious solution is to produce two public goods

¬     One with a positive production cost and positive value to consumer

¬     One negative and negative

¬     And tie them tightly together

á       The negative one pays the broadcaster's costs, the positive one gets the listeners

¤       Consider my dam story with ten farmers, and a $50,000 dam

á       I draw up a contract by which each farmer agrees to pay $5,000

á       If and only if every other farmer does

¤       Consider the story with 100 farmers, of which two are large farmers who gain by $40,000 each.

á       They might agree to pay for the dam, letting the rest free ride—it's still worth it to them.

á       Which is how my house gets painted—it's worth it to me, even if my neighbors get some of the benefit

á       The big farmers, or homeowner, are a "privileged minority."

¤       Technological solutions

á       Sometimes, whether a good is public depends on how you produce it

á       Radio or TV broadcasts could be encrypted, for instance

á       In a world without copyright, you could keep books in libraries chained to the desk, charge for access

¯    Legal

¤       To some degree, whether something is a public good depends on the law

á       Without copyright law, the author produces a public good

á       One could make it illegal to listen to a radio frequency without having paid the broadcaster

¬     Such a law would be costly to enforce, but É

¬     England actually has a version of it (I think one payment for all TV listening)

á       In open range, grazing land is a commons, so a public good

¬     Converting it to private property makes it a private good

¬     But again, there may be costs

¯    Government production

¤       How we produce national defense

á       Book's claim that it wouldn't be privately supplied is an exaggeration

á       The Commanche, with no government at all, blocked expansion across Texas for a couple of decades

á       But it clearly is a hard public good problem

¤       Problem with public production: Usual two

á       It's hard to do it right

¬     How do you find out what the optimal quantity and quality of the public good are? No market feedback. Ask the customers—they want lots of it, at someone else's expense.

¬     How do you find out if it is worth producing at all? Cost might be higher than benefit

á       It may not be in the interest of those making the decisions to do it right

v    Public goods as a problem in the political market

¯    Rational ignorance

¤       The simple model of democracy requires each voter to know what his representatives are doing, if they should do it, vote them out if not.

¤       That requires a lot of expensive information

¤       And acquiring that information means producing a public good for everyone in the country—a very large public

¤       So most of us don't

¯    The market for legislation

á       Legislation that benefits all members of an interest group is a public good for the members.

á       A concentrated interest group can do a better job of solving its internal public good problem than a dispersed interest group

á       So legislation tends to benefit concentrated groups at the expense of dispersed groups.

v    Again Transaction costs

¯    Some are the public good problem

¤       If homeowners pay the airline to reduce noise,

á       all homeowners benefit

á       Including those who didn't contribute

á       So why should I chip in?

¤       For a small public, such problems might be soluble via conditional contracts and the like

¤       So this problem becomes larger the larger the numbers involved

¯    Some are holdout problems

¤       Suppose the homeowners have the right, and the airline can be enjoined from making noise by any one of them

¤       Further suppose reducing noise costs $10 million, soundproofing 100 houses costs $1000 each

¤       What happens?

¯    Even with small numbers of people, there can still be problems associated with bilateral monopoly bargaining

¤       Actual mistakes about how much it is worth to the other party

¤       Or bargaining breakdown because both parties are trying for most of the gain

¯    In assigning rights via the legal system, there are at least two important questions

¤       Who has the right—airline to make noice, homeowners not to be bothered by noise

¤       Is the right injunctive or for damages?

¤       Think about how we might decide

¤       All of which is getting into law and econ stuff—more of which is coming up.

v    Welfare economics

¯    The problem: Questions economist get asked--"Should we do X?"

¤       "Is strict liability better than negligence?"

¤       "Are tariffs good for America?"

¤       "Should we restrict immigration?"

¯    we respond with "economic efficiency"

¤       a criterion of goodness that has two characteristics

á       it corresponds to a significant degree to what people are asking

á       and, if we rephrase questions in terms of it, we can often answer them

¤       but the correspondence is very imperfect

¯    defining efficiency

¤       This is my version, based on Alfred Marshall

á       It isn't how most textbooks put the argument

á       But it is what most economists actually do

¤       Measure all costs and benefits by willingness to pay, sum them

á       If I would pay up to a dollar to get an apple, the value of my getting it is $1

á       If you would pay up to fifty cents, É

á       So transferring the apple from you to me increases total benefit by $.50

¤       Anything that increases the total is an economic improvement, anything that decreases it is a worsening

¯    What is wrong with it:

¤       It accepts individual preferences as defining value—heroin is of value to a heroin addict, as shown by the price he will pay

¤       It does interpersonal comparisons as if a dollar represented the same happiness to everyone—rich and poor, materialist and ascetic

¤       It assumes that all that matter is something like human happiness

á       What if cutting down the oldest tree in the world benefited humans

á       Or eliminating a species

á       Or suppressing a great novel that made its readers sad

¯    On the other hand

¤       A lot of economic issues have a large and random group of beneficiaries, similarly of losers, so individual differences may average out

¤       If you believe that taking a dollar from Gates to give to a beggar is a good thing, perhaps an efficient legal system to maximize the pie combined with a straightforward tax and transfer system to redistribute it makes sense

¤       Dollar values are expressed in individual actions, so we actually have a way of maximizing them

¤       On a free market, the apple ends up with whomever values it most

¤       No mindreading required.

¯    Do read the book's discussion, since it is rather different from mine.

 

Law and Economics

 

v    What is it

¯    You are in a society where life imprisonment is the highest punishment

¤       Someone proposes life for armed robbery

¤       Is it cruel and unusual? Is it just?

¤       The economist asks

á       Do you really want armed robbers to kill their victims

á       Because if the punishment for armed robbery and armed robbery+murder are the same

á       The additional punishment for murder is zero

á       And a dead man can't identify you in a police lineup

¤       The economic approach assumes individuals are rational, deduces the effect of legal rules, and lets you decide if you like that effect or not.

¯    You take a particularly good opportunity to push your rich uncle off a cliff

¤       Unfortunately for you, a bird watcher has his camera pointed your way

¤       At the trial, you confess to the murder, but É

¤       Your attorney points out that

á       It was an unlikely opportunity

á       You only had one rich uncle

á       If you had another, he is unlikely now to go mountain climbing with you

á       So no need to punish you--it won't happen again.

¤       What is wrong with this argument?

¤       The economic approach as forward looking, not backward looking

á       Not primarily concerned with how to clean up this mess as an end in itself

á       But how the way we resolve this situation will affect acts that might lead to similar situations in the future

v    Property

¯    Why does the institution exist?

¤       To the non-economist, the obvious question is why anything should be property

á       Why not just let anyone use things when he needs them?

á       None of this "mine and thine" nonsense

¤       To the economist, why anything should not be.

á       Property solves two problems

¬     Getting the right things made

¯    If you make it, it is yours

¯    So if it is worth more than it costs to make, you gain by making it

¯    Which is the right rule for what ought to be made

¬     Getting things taken care of

¬     Allocating things to the right person

á       So why not use it for everything?

¬     How about the English language?

¬     The first inventor of a word owns it

¬     And anyone who wants to speak must get licenses for all the words

¤       The approximate optimality of aboriginal property rights

¤       There are advantages to treating things as property, as above, but also disadvantages

á       There are costs to defining, protecting, transacting over property

á       If the advantages are small and the costs substantial, we may be better off treating something as a commons

á       Putting up with some inefficient production and allocation

á       In exchange for saving those costs

á       For instance the English language

¤       Why we owe civilization to the dogs--a possibly true fable

¯    I.P. as an example

¤       Why are patent and copyright so different? The Constitution doesn't propose different rules

á       Copyright is given easily, for a long period of time

á       Patent grudgingly, for a short period of time

á       Why?

¤       Copyright protection (old style--not modern look and feel etc) protects things with clearly defined borders, where accidental trespass is unlikely and independent creation still more unlikely

á       Long terms don't over reward, because even after fifty years nobody else would have written your book

á       Enforcement isn't costly (but that is now changing with technology)

¤       Patent protection protects ideas--fuzzy boundaries, accidental trespass likely, independent invention likely

á       Various requirements try to limit protection

¬     to inventions not likely to be made tomorrow by someone else

¬     Such as novelty and nonobviousness

á       Costly to enforce--litigation over fuzzy boundaries, costs of checking everything you invent to make sure nobody else has patented it

á       Term should be and is short, because after a while someone else would probably have invented it

¤       So I.P. fits our sketch of why some things are more suitable for property protection than others

v    Property II: What's in the bundle

¯    Ownership of land gives you some rights wrt the land, but not all

¤       Can prohibit trespass, uses, but not overflights,

¤       May or may not control mining under

¤       Or pumping oil somewhere else that makes the oil under your land flow away to someone else's reservoir

¯    How might we decide what to include?

¯    Coasian analysis

¤       Minimize the sum of inefficiencies from the wrong person owning a right

¤       And transaction costs of moving rights to the right person

¤       By starting with a bundle containing rights that are likely to be most valuable to the owner of the other rights in the bundle

¤       The right to farm is worthless without the right to go on the land, of little value without the right to exclude trespassers

¤       The right to control high overflights, on the other hand

á       Is not of especial value to the land owner

á       And if each landowner has it for his land, rebundling to make airline flights possible is very costly

á       Similarly for the right to broadcast radio signals over the land

¯    Real world example: Pennsylvania

¤       A state made largely of coal

¤       Land consists of three estates

á       The surface estate

á       The mineral estate

á       The support estate

¤       They can be separately owned

á       Under some circumstances the support estate is most valuable to the surface owner

á       Under some to the mineral owner

á       So they can contract to move it to the one who values it more

v    Torts I

¯    Optimal level of precautions

¤       We want legal rules that induce people to take precautions against accidents

¤       Up to the point where an additional precaution costs as much as it saves

¤       So there is an "optimal level of auto accidents" above zero

¤       Given that preventing such accidents is costly

á       Might mean spending more on better cars

á       Driving more slowly

á       Driving less

á       É

¯    One sided injury

¤       A driver injures a pedestrian

á       Only the pedestrian is injured

á       And (assume) there is nothing he can do about it

á       So our objective is to get the driver to take the optimal level of precautions

¤       Strict liability

á       The driver must pay damages equal to the damage done

á       So he bears the entire cost

á       So it is in his interest to take all precautions that are worth taking

¤       Negligence (economist's version)

á       The driver pays the damages if and only if he did not take at least the optimal level of precaution

á       So either he takes the optimal level of precaution and is not liable

á       Or he doesn't, and is liable, and if he is liable, as we just saw

á       It is in his interest to take the optimal level of precautions

á       So the outcome is the same. Except É

¤       This assumes the court can judge what precautions he took and should have taken

á       Divide precautions into two categories

¬     Observable—how often does he have his brakes checked

¬     Unobservable—how attentive was he. Did he really need to take this trip?

á       In practice, the negligence rule can only apply to observable precautions

á       So a rational driver takes the optimal level of observable precautions, will not be liable, and has no incentive to take the unobservable precautions

á       In the literature, "unobservable precautions" are often called

¬     Activity level

¬     Since how much you drive might be observable, but É

¬     The court has no way of knowing how important trips are for you

¬     So in practice ignores the question of whether you are driving more than you ought, so increasing the risk of accidents more than you ought.

¯    Two sided injury

¤       Two sided in causation, not effect. Only the pedestrian is injured, but the risk depends on his precautions as well as the driver's

¤       Strict liability on the driver means that

á       The driver has an incentive to take the efficient level of precautions, but É

á       The pedestrian, who will be fully compensated, has no incentive to take precautions at all

¤       No liability gives the opposite result—incentive for the pedestrian, who bears the risk, none for the driver

¤       Negligence on driver, if all precautions are observable, however É

á       The driver has an incentive to take the optimal precautions, so É

á       If there is still an accident the driver is not liable, so É

á       The pedestrian has an incentive to take optimal precautions too

á       In effect, we are controlling the driver by a top down mechanism

¬     The court decides what he ought to do

¬     And punishes him by making him liable if he doesn't do it

á       And controlling the pedestrian by the standard decentralized mechanism

¬     He bears the cost, so

¬     It is in his interest to take it into account in his precautions

á       Works imperfectly if not all precautions are observable, courts make errors, etc.

¤       Another alternative—make each of them bear the full cost

á       Fine the driver the amount of the damage done—gives him the incentive

á       Don't give the fine to the pedestrian—he still has the incentive

á       Of course, in that system, neither has an incentive to report the accident

á       We have converted from a tort to a criminal solution to the problem

¤       Yet another—divide the cost between them

á       This is like coinsurance.

á       Driver bears (say) half the cost

¬     So he doesn't have an incentive to take all precautions worth taking

¬     But he does have an incentive to take the ones most worth taking

¬     I.e. the ones where the payoff is much larger than the cost

á       And similarly for the pedestrian

á       This may be how tort works in practice

¬     Most pedestrians would prefer not to be hit, even if they could sue

¬     Because the tort system, arguably, doesn't fully compensate

¯    Strict liability with a defense of contributory negligence

¤       Works just like negligence liability

¤       With the roles of driver and pedestrian exchanged

v    Torts II: What does causation mean anyway?

¯    You see a friend walking along, stop him to chat for a minute.

¯    He continues on. A barrel falls out of an upstairs window on him and kills him

¯    Did you cause his death? If you hadn't stopped him, he wouldn't have been under the barrel when it fell

¯    Should you be liable?

v    Torts III: Caveat emptor vs caveat venditor

¯    A coke bottle explodes, back when they were made of glass

¤       I was holding it and get injured

¤       Is coca cola liable? Should they be

¯    Under caveat emptor—"buyer beware"—I take the bottle as I find it, risk included

¤       Is it in Coke's interest to take optimal precautions to prevent defective bottles?

¤       Yes if the consumer is fully informed about the risk, since I will pay less for a bottle the more likely I think it is to explode on me

¤       No if the consumer doesn't have enough data to estimate the risk

¤       So the argument against caveat emptor is that making Coke liable will give them an incentive to take the right precautions

¯    Under caveat Venditor ("seller beware") Coke is liable

¤       Why did the bottle explode?

á       The bottle had been sitting on the table for three hours, and I was holding it when shaking my hand to emphasize a point in my 4th of July speech.

á       And wasn't wearing glasses

¤       More generally, the risk of accident depends on how the product is used, what precautions the user takes.

¤       And caveat Venditor eliminates the user's incentives to take precautions

¤       And it is far more difficult for coke to know how careful each user is, and charge a higher price to more careless users, than for the user to know how risk coke bottles, on average, are, and base the price he is willing to pay in part on that risk.

¯    A third alternative is freedom of contract

¤       If the default rule is caveat emptor the seller can include a guarantee. As many sellers do.

¤       If the default is caveat Venditor the buyer can sign a waiver of liability.

¤       And have it enforced by the courts.

¤       So now it is the opinion of buyer and seller of the costs and benefits to them of the alternative rules that determines what actually happens.

v    Contracts

¯    Much of this we have already done

¤       Why you want to design a contract to maximize the size of the pie

¤       How to do it

¤       By looking at the incentives that the contracts give the two parties

á       Ideally, to make decisions that maximize the combined benefit

á       For instance, a fixed price contract when quality isn't an issue

á       Which gives the builder an incentive to minimize cost--including his time and trouble as well as price paid.

¯    One interesting issue is punishment for breach of contract

¤       We want efficient breach--breach when completion costs more than it is worth

¤       But not opportunistic breach--breach that benefits the breaching party by less than it injures the victim

¤       And we can use damage rules to try to get that result

á       Expectation damages: The breaching party must make the other party whole

¬     Meaning as well off as if there had been no breach

¬     Again the Pigouvian solution: Breaching party bears all of the costs of breach, gets all the benefit

¬     So breaches only if net benefit is greater than net cost.

á       Reliance damages

¬     I must make you as well off as if the contract had not been signed

¬     But do not have to compensate you for the gain you would have made from the contract being carried through

¬     So may have too great an incentive to breach if there was a profit expected.

á       No damages?

¬     Still gets the efficient result in a fully Coasian world

¬     Because when you threaten a breach that benefits you by $1000 and hurts me by $2000

¬     I propose that I instead raise the price I am paying you by $1500

á       Specific performance?

¬     Still works in a fully Coasian world, because

¬     When I refuse to permit a breach that costs me $1000 and saves you $2000

¬     You offer to readjust the price by $1500 in my favor

á       The disadvantage of the latter rules is the potential for bargaining costs and bargaining breakdown

á       The disadvantage of expectation damages (and reliance damages) is that a court has to measure the costs    

¤       A further issue is inefficient reliance

á       You agree to buy a million customized widgets from me in six months

á       I can produce them in my current factory at a cost of $3 million, or

á       Retool at a cost of $1 million, then produce for an additional $1 million

á       My retooling is a reliance expenditure

¬     I am relying on your buying the widgets

¬     And the million dollars is down the drain if you don't

á       When should I customize? When shouldn't I?

á       When will I under expectation damages?

¤       A final alternative is liquidated damages

á       We agree in advance on what damages for breach will be

á       If we know enough when the contract is signed, we set them at expectation damages

á       What is the effect on the incentive for inefficient reliance?

á       Courts may refuse to enforce a liquidated damages agreement

¬     If they think it is a penalty clause

¬     I.e. that the amount is substantially more than damage done

¬     Are there good reasons parties might want a penalty clause?

¤       Consider (digression) the general issue of property rights vs liability rights

á       We allocate cars via property rights

¬     If you steal my car, we don't just bill you for two day's use

¬     We impose a punishment intended to stop you from doing it (but see more below)

¬     Perhaps on the theory that cars will then be allocated via the market

¬     If it was worth that much to you, you should have bought it from me.

á       We allocate accident risk via liability rights

¬     If I dent your car, I don't get hanged, I get sued

¬     And am supposed to pay enough to make up for the damage

á       Could imagine doing it the other way

¬     Thief must reimburse victim for actual cost imposed

¬     Driver must get permission from everyone he might dent before he pulls out of the driveway

á       Pretty clearly, that wouldn't work as well, because É

¬     Markets allocate better than courts for ordinary property, but É

¬     For imposing a low risk on many people, transaction costs of using the market are prohibitive, so use the court instead

á       Note that one version of property vs liability is the question of whether a tort verdict should result in an injunction or damages.

¤       Back to liquidated damages

á       A penalty clause is a privately agreed on property rule

á       "if you want to breach the contract, you have to buy the right from the other party."

á       The legal system sometimes uses property rules instead of liability rules

á       Why shouldn't parties sometimes find it in their interest to?

v    Crime

¯    What is wrong with crime anyway?

¤       I steal $100 from you, I am $100 better off, you are $100 worse off

¤       In terms of economic efficiency, why should the rest of us care?

¯    If I, or anyone, can steal $100 from you

¤       We compete to be the one who does it--you only have one wallet

¤       As long as the most energetic thief is spending less than $100 on the job

¤       It pays someone else to spend more

¤       The opportunity to steal is an incentive to rent seeking

¤       Which can dissipate the full amount stolen

¤       So the marginal thief abandons a $10/hour job to make $10.01/hour stealing, after allowing for all special costs and benefits of the job

¤       Some thieves are better than average, so benefit

¤       But there is an additional cost to precautions taken by potential victims

á       Also rent seeking, even though we approve of them.

á       Since the lock on my door is an expenditure made to make sure I, not you, end up with the $100

¯    Efficient crimes

¤       A hunter, lost in the woods and starving, finds a locked cabin with a telephone and food

¤       Breaks in, feeds himself, calls the coops

¤       His gain is larger than the owner's loss--an efficient crime

¤       Not true of most crime, because usually, if I value your property more than you do I don't have to steal it, I can buy it

¯    How might we arange to have efficient and only efficient crimes?

¤       One solution is to special case them--make them legal

á       The starving hunter gets off under the doctrine of necessity

á       The traffic cop notices your wife about to give birth in the back seat and doesn't give you a ticket

á       But this only works if the fact that it is efficient is observable from the outside

¤       The other solution is to punish them--but not too much

á       Set the punishment equal to the damage done to the crime's victim

á       So if my benefit is greater, I will still commit the crime

á       Pigou again

¤       Criminal punishment is usually probabilistic

á       So instead of setting punishment if convicted equal to damage

á       We set expected punishment--roughly, probability of conviction times punishment if convicted--equal to damage

¯    What is wrong with this (common in the L&E literature) story?

¤       Do we believe that the reason we don't raise the punishment for murder, or try harder to catch murderers, is that we are afraid there will not be enough murders?

¤       We have counted costs and benefit to criminal and victim, but ignored

¤       Costs and benefits of catching and punishing criminals to the rest of us

¯    The cost of deterring crime is

¤       The cost of catching criminals, plus

¤       The cost of punishing them

á       Economic efficiency counts everyone, so

á       A fine is costless--what the criminal loses the state gets

á       Execution is expensive--it costs one life (to the criminal) and we don't get a life

á       Imprisonment is even more expensive, relative to the amount of deterrence we get

¬     The criminal loses his freedom and

¬     We have to pay for the jail

¤       Costs of trials, administration, etc.--the hangman's wages.

¯    Suppose expected punishment is less than damage done

¤       The marginal crime--the one that is not quite deterred

¤       Does $1000 worth of damage, benefits the criminal by $900

¤       And happens--because the expected punishment is $899.

¯    We could raise expected punishment a little and deter that crime

¤       Thus saving $100 net cost, but É

¤       Increasing expected punishment might increase the cost of detterence by $200

¤       In which case we are better off not doing it.

¤       On the other hand

¯    The cost of deterring one more crime might be negative!

¤       Because if we deter a crime we don't have to punish it

¤       And punishment (and apprehension and É) is expensive

¯    So if the crime rate is very elastic

¤       A little extra punishment gets a big reduction in crime rate

¤       We want expected punishment more than damage done

¤       Because deterring crimes that are (slightly) efficient saves us more in enforcement costs than it loses us in gains from efficient crimes

¯    If the crime rate is very inelastic, on the other hand

¤       We want expected punishment less than damage done, because

¤       Crimes that are only slightly inefficient

¤       Cost more to deter than deterring them is worth

¯    Which might explain why we don't deter all murders, even if

¤       We think they are all inefficient crimes

¤       Or at least, we can't all agree on which people the world is better off without.

v    Law enforcement

¯    Police are rational too, and respond to incentives

¯    Consider civil forfeiture

¤       Property used in the commission of a crime--say a house where marijuana was sold--forfeits to the state

á       And since it is civil, the standard of proof is only "preponderance of the evidence."

á       No need to prove the owner of the house guilty of anything.

¤       If the property goes to the police department that seizes it, how are its incentives affected?

¤       Historical evidence (Bruce Benson article)

á       Many states had forfeiture statutes that turned over the property to some agency other than law enforcement, such as education funds

á       Federal forfeiture statute passed. Not much effect—most law enforcement is state and local

á       Federal statute amended

¬     Federal law enforcement could "adopt" a state or local seizure

¬     Share the proceeds with the police department responsible

¬     Thus evading the state rules on where the money went

á       Law enforcement resources shifted towards the War on Drugs

¤       My experience: Conference on money laundering in the Pacific Rim

á       One series of talks described a particular operation

á       Which brought in, if my memory is correct, more than a hundred million dollars

¯    This suggests the answer to an interesting puzzle:

¤       Why we use inefficient punishments

á       Fines are more efficient than imprisonment or execution

á       Execution with organs forfeiting for transplant is too

á       Why not a system designed to squeeze all it can out of convicted criminals?

¤       Perhaps because such a system creates an incentive to convict people

á       Larry Niven story about organ forfeiture

á       African colonialist version

á       Mencken's American version

á       Modern concern with punitive damages, class actions, É

v    Another puzzle for you to think about

¯    Why do we have both criminal law and tort law to do the same thing?

¤       Impose costs on people who do things that hurt others

¤       One system with private prosecution, one public

¯    Would a pure criminal or pure tort system do the job?

¤       Iceland managed for over 300 years with pure tort

¤       China for much longer with pure criminal

¯    Why do we treat certain things as torts, certain things as crimes?

¯    Why do we have one set of legal rules for tort, another for crimes

¤       Preponderance of the evidence vs beyond a reasonable doubt

¤       Intent not required for torts, is required for crimes

¤       É

 

Statistics: 4/4/06

 

v    In choosing how to present and look at data, there are two related issues

¯    How to actually learn things about the data

¯    How to convince other people of things you want them to believe

¤       Both how to do it, and É

¤       How not to be a victim of people doing it

v    Descriptive Statistics I: Mean vs median

¯    Summing up data

¤       Mean aka average

¤       Median

¯    Suppose you want to know about the average, cubical, cardboard box

¤       We have five boxes

¤       1Õx1Õx1Õ, 2Õx2Õx2Õ, É 5Õx5Õx5Õ

¤       What are the average height, width, and depth of a box?

¤       What is the average volume of a box?

¤       Do they correspond?

¤       What if we use median?

¯    The mean

¤       depends on how we measure the variable, the median does not

¤       is sensitive to large outliers, the median does not

¤       The median ignores how far anything is above or below the median

¯    Consider two income distributions

¤       A: $5000, $5001, $5002

¤       B: $4999, $5000, $10,000

¤       Which has the higher median? Mean? Which measure is more interesting?

¯    On the other hand—suppose you believe some of your numbers are wrong

¤       In case B, a typo converts $10,000 to $100,000

¤       Messes up the mean, doesnÕt affect the median

¯    Or suppose you have ordering, but no natural quantitative measure

¤       Comparing chess players, say

¤       You could use their rating, average it, but É

¤       Which player is average then depends on just how ratings are calculated

¤       Which player is median only depends on the rating getting the order right

v    Histogram

¯    Visual portrayal of frequency: the idea

¯    Again consider my cubic boxes

¤       This time lots of them—1Õ, 1.1Õ,1.2Õ É

¤       With different numbers of different sizes, so a histogram might be interesting. But É

¤       If we do it by edge size, we ask how many boxes of sizes 1Õ-1.5Õ, 1.5Õ-2Õ, etc. Get a histgram

¤       If we do it by volume we ask how man 1 cubic foot to 2 cubic feet, 2 to 3, É.

¤       How do the results differ?

á       Increasing from 1Õ to 1.5Õ increases volume from 1 cubic foot to 27/8=3.375

á       From 1.5 to 2 increases volume from 3.375 to 8.

á       So the relative sizes of the intervals is different for the different methods

á       Making the pattern of the frequency distribution different.

á       If it were uniform the first way, it would look like an increasing frequency the second way

¯    On the other hand É

¤       If there are lots and lots of 3Õ boxes relative to everything else

¤       That will show up as a spike either way

¤       So histogram is useful for spotting that kind of pattern

á       Is it double peaked

á       My usual student evaluations—tells me something, not clear what

á       Is it assymetrical? Depends in part on how you define your variable. Boxes.

á       What would you expect a U.S. income distribution to look like? Why?

¤       But somewhat ambiguous for Òfrequency is increasingÓ or decreasing  pattern

¤       And a clever lawyer could take advantage of that.

v    Other ways of fooling or being fooled

¯    Have the vertical axis start well above zero, to magnify changes

¯    U.S. vs Japanese CO2 growth—real example

v    Dispersion

¯    The mean or median does not tell us how wide the spread is—which might matter

¯    The usual definition is the standard deviation

¤       Defined as the square root of the average squared deviation!

¤       One reason to do it that way is that the average of the deviation is É.?

¤       Squaring means that both negative and positive deviations increase the average

¤       Other reasons we wonÕt go into

¯    ChebychevÕs rule—for any distribution, normal or not

¤       At least 75% of the points are within 2 standard deviations of the mean

¤       At least 89% within three standard deviations

¤       Can you see why this has to be true?

v    Normal distribution

¯    A particular family of distributions (Òbell curve)

¯    Where once you know the mean and the standard deviation you know the distribution

¯    Which many real world distributions approximate

¯    And which has characteristics that are known and useful

¯    About 68% within one stdev, 95% within two, 99.7% within three

¯    If you know the mean IQ is 100 and the stdev is 15, just how special is your IQ 150 kid?

¯    Z score table is the continuous version of that rule

¤       Z score is the number of standard deviations from the mean.

¤       Table tells you how likely it is that the Z score is that high or higher

v    Digression:

¯    How likely is it that a bridge deal will be 13 spades to one player, 13 hearts to another, É?

¤       How about any other deal?

¤       So why, in the first case, do we conclude that someone stacked the deck?

¯    Suppose you a coin is fair

¯    Flip it 100 times. Heads 53 times. What question do you ask?

¤       How likely is it that a fair coin will come up 53/47? Not very. Coin must not be fair?

¤       But you get the same answer for 52/48, É indeed any single outcome rather unlikely

¤       Ask instead, how likely is it that the evidence against a fair coin is at least this strong, i.e.

á       At least 53 heads or at least 53 tails

á       Pretty likely

¤       That is a two tailed test. The null hypothesis is a fair coin, and if unfair you donÕt know which way

¤       If you somehow knew the coin was either fair or weighted towards heads, use a one tailed test—how likely is it that I will get at least 53 heads out of 100.

v    Sample statistics vs population statistics

¯    You have statistics, such as mean or standard deviation, for your sample

¯    You want to estimate the statistics for the larger group the sample is drawn from

¯    Consider standard deviation—which I think the book gets wrong

¤       Suppose I have a sample of one

á       Population is the classroom

á       We want to know the distribution of heights

á       I happen to know my height 5Õ 3.5Ó

¤       What is the mean of that sample?

¤       What is the standard deviation?

¤       Do we conclude that the population has that mean with that standard deviation?

¯    Rule turns out to be that you estimate the standard deviation of the population dividing by N-1 not N

 

4/6/06

 

v    Review

¯    Different ways of summarizing a bunch of data

¤       Mean vs median

¤       Histogram

¤       Standard deviation: Chebychev's rule

¤       Some ways may be deceptive, deliberately or not

¯    Normal Distributions

¤       Bell curve shape

¤       All normal distributions are the same except for two parameters

á       Mean—where the center is

á       Standard Deviation—how much it is stretched out

¤       So if you know how many standard deviations from the mean an observation is

á       You can look up on a table how likely it is to be at least that far from the mean

á       Which information might be used in two ways

¬     If you are confident about your mean and standard deviation, tells how atypical this sample is

¬     Alternatively, if your observation is very unlikely, perhaps you are wrong about the mean and/or standard deviation

¬     Warren Buffet as a five sigma event

¬     Which will get us into hypothesis testing

¤       Lots of distributions aren't normal, but É

á       If we are looking at the average of a sample from a distribution

á       The Central Limit Theorem tells us that the distribution of averages

á       Approaches a normal distribution as the size of the sample increases

¯    Practically anything is wildly unlikely

¤       Any particular series of heads and tails with coins, any particular bridge deal

¤       But "some sequence that ends up 50/50" is more likely than a particular sequence

¤       And if your suspicion is a weighted coin, the question isn't

á       How likely is this result with a fair coin (very unlikely, whatever the result) but

á       How likely is a result at least this far from the mean with a fair coin

á       Since any result far from the mean inclines you to reject the "fair coin" hypothesis

á       And your real question is "how likely am I to reject that hypothesis if it is true?"

¯    Sample statistics vs population parameters.

¤       You want to know average height and standard deviation for law school students

¤       You measure the students in one class.

¤       What does that tell you about all the students at SCU? In the Country? The World?

v    Hypothesis testing

¯    The basic logic of confidence results

¯    You have a null hypothesis—this coin is fair

¯    You have a sample—say the result of flipping the coin ten times

¯    You want to decide whether the null hypothesis is true

¤       In the background there is an alternative hypothesis

¤       Which is relevant to how you test the null hypothesis

¤       For instance—this coin is not fair, but I don't know in which direction

¯    You ask: If the null hypothesis is true, how likely is a result at least this far from what it predicts in the direction the alternative predicts

¤       For example, if the coin is fair

¤       How likely is it that the result of my experiment would be this far from 50/50?

¯    Suppose the answer is that if the coin is fair, the chance of being this far off 50/50 is less than .05 (i.e. 5%)

¯    You can then say that the null hypothesis is rejected at the .05 level

¯    Does this mean that

¤       the null hypothesis has less than .05 chance of being true?

¤       The alternative hypothesis has at least 95% chance of being true?

¤       To see why neither is correct, consider a simple experiment:

¯    Experiment

¤       Null hypothesis: Coin in my pocket is an ordinary fair coin

¤       Alternative—coin is double headed

¤       Flip the coin once—comes up heads

¤       Probability of a result that far in that direction is .5

¤       Do we conclude that the probability that the coin is double headed is .5?

¯    What's wrong with the (common) misunderstanding

¤       .05 is the probability of our result if the null hypothesis is true

¤       not the probability it is true if we get that result

¤       is, as in my example, the null hypothesis is initially much more likely than the alternative—very few random coins are double headed

¤       then the combined chance that the coin is fair and it came up heads (about .5)

¤       is much higher than the combined chance that it is double headed (say one in a million) and came up heads (one in one—if it's double headed)

¤       so after one flip—even after three or four all heads—we still think the odds are it is a fair coin

¯    so a confidence interval is a simple way of reporting how strong this piece of evidence against the null hypothesis is, but not how likely the null hypothesis is to be true

¯    analogously, it might be that a witness identification has only one chance in four of being wrong by chance

¯    but if you also have an absolutely solid alibi, you still get acquitted

¯    "Statistically significant" doesn't mean "important" it means "unlikely to occur by chance

¤       suppose a take a random coin and flip it 10,000 times

¤       the result will prove it isn't a fair coin to a very high level of significance

¤       even if it is "unfair" only by .501 vs .499 probability

v    The validity problem vs sampling error vs bias

¯    One problem with samples, which we have been discussing, is sampling error

¤       When you select ten students,

¤       by chance they might be taller or shorter than average

¯    Another is bias.

¤       If you are measuring age, not height, and select students in this class

¤       Since it isn't taken by first years

¤       Your sample is biased towards older studentsÉalthough

¤       There may be a bias the other way because it isn't an evening class.

¤       Famous example—telephone pole that showed Dewey would win

¯    A third is validity

¤       If you test age by asking people their age when their friends are around

¤       In some populations people refer to exaggerate their age

¤       In others to make it look smaller

¤       Similarly for asking about adultery in the presence of a spouse

¤       Or drug use in any context where the questioner knows the name of the respondent

¯    Note that bias and invalidity may be either accidental or deliberate

v    Specification Search problem

¯    How to make a fortune giving investment advice

¯    How to prove that Diet Coke causes cancer

¯    How you get the problem without even trying

¯    But nowadays, there are programs designed to try

¯    Which is one reason why you should put your data on the web and let other people play with it

4/11/06

 

v    Using statistics

¯    Theory: The average height of LS students is 5'10"

¤       You measure one person's height. It is 5'7". How good evidence is this for or against?

á       With no additional information, you can't say

á       Because you have no idea what the standard deviation is

á       But if the theory include a standard deviation of 2" É how would you analyze the data?

¤       Suppose the theory is only of the mean

á       How do you go about estimating the standard deviation?

á       By measuring several students, calculating the standard deviation of the sample

á       It will be, on average, a little lower than the standard deviation of the population. Why?

á       You adjust for that by dividing by N-1 instead of N, get an estimate for the population

á       Suppose the heights were 6' 2", 6', 5'7", 5'10"

v    Correlation is not causation

¯    More generally, facts don't speak for themselves.

¯    Consider Peltzman's analysis of the effect of requiring seatbelts (and some other things)

¤       Before the requirement, say, 40% of crashes were fatal, after 30%

¤       After the requirement, 10,000 crashes/year.

¤       So the requirement saved 1000 lives/year

¤       What is the hidden assumption in this argument?

¤       Why might it be wrong?

¯    Suppose you want to know whether the death penalty deters murder

¤       How might you find out?

¤       Compare murder rates in states with and without? What is wrong with that approach?

¤       Is there a better way?

v    Statistics in the Law

¯    Are there enough blacks on the jury that convicted your black client?

¤       What is the probability, on a random draw from the population, of this many blacks or fewer?

¤       If you are the prosecutor, how do you respond?

¯    Does a firm discriminate against women in wages? Promotion?

¤       Look at average wage—lower.

¤       Look at average position—lower

¤       As the defense attorney, what issues might you raise?

¤       As the plaintiff's attorney, how might you answer them?

¯    Does this drug have dangerous side effects?

¤       Of people taking this heart medication who had heart attacks, what % died from them? 45%

¤       Of people not taking it, only 30%

¤       Sample size is 1000 people taking the drug who had heart attacks, 1000 not taking it who had heart attacks

¤       You are the defendant's attorney. What questions might you ask?

¯    Others?

v    Exploratory Statistics: Looking for patterns

¯    You are an enterprising torts attorney, wondering if electric transmission lines do anything actionable

¯    How might you look for effects?

¤       Start with a database showing rates for cancer and other things by county

¤       And a map showing transmission lines

¤       And access to the U.S. census data

á       Which give you data at the individual level

á       Including place of residence

á       Age, race, gender

á       Possibly cause of death for those that recently died?

v    Summary: More conceptual than mechanical

¯    Descriptive statistics

¤       You have a bunch of data and want to describe them

¤       Mean or median—advantages of each

¤       Some measure of spread—typically standard deviation

¤       Plot of the distribution—a histogram

¤       How you present the data can make a difference

á       Which is important both in fooling people and

á       Not getting fooled

¤       Note that not all data are quantitative

á       You might have categories: race, gender, nationality

¬     Note that race could be quantitative—percent of ancestry

¬     But in the available figures usually isn't

á       You might have an ordinal rather than cardinal ranking

¬     Which chess player is better than which, not by how much

¬     Individual preferences

á       As long as there is a ranking you have a median, but not a mean

á       And for categories you don't even have that.

¯    Hypothesis testing

¤       We conjecture that something is true: This coin is fair

¤       We do an experiment

¤       What do the results tell us about whether our conjecture is true?

¤       We can calculate how likely the result (HHTHTTHTTH) is if the coin is fair

á       The answer is (1/2)10 = 1/1024 = aprox .001 !

á       Same figure for any other series of ten results, however

á       But add them all together and we get a probability of 1

¤       We need some alternative hypothesis to tell us which results count as more or less evidence against

¤       We can then ask "how likely is it that the evidence will be at least this strongly against

¤       Alternative hypothesis: coin is weighted towards heads.

á       So the more heads, the stronger the evidence against the fair coin hypothesis

á       Our experiment gave five out of ten.

¬     Probability of at least that many heads if fair coin is É?

¬     Very very weak evidence against the conjecture, but É

¬     Better than if it came out 7 tails and 3 heads.

¤       Alternative hypothesis: unfair coin, direction unknown

á       Suppose it comes up 7 heads, 3 tails

á       Ask the combined likelihood of 7/3, 8/2, 9/1, 10/0. If the coin is fair

á       Double that to allow for 7 tails, 3 heads etc.

á       Since they are just as good evidence against

á       Suppose the total is .2

á       We can then say that there is a .2 probability that a fair coin would produce evidence this good that it isn't fair.

¤       Errors of the first and second sort

á       If we take .2 as adequate evidence (unlikely—but perhaps for a tort suit?)

á       We will judge 1/5 of all fair coins to be unfair. Type one error

á       What fraction of unfair coins will we judge to be fair? Type two error

¬     That depends how unfair the coins are

¬     If they are double headed, none of them.

¬     If they are .501/.499, about 4/5 of them

¤       My example was with coin tossing

á       Probabilities are easy to calculate, if you know probability theory

á       A more common example involves taking a sample, figuring out whether it is strong evidence about some assertion about the distribution it is from

á       Which usually involves setting it up so the distribution is approximately normal

á       Which we do by using the central limit theorem

á       Heights of students are nowhere close to a normal distribution

á       But the average of the heights of 100 students comes quite close to one

á       Brief explanation of what a probability distribution is.

¯    Inferential statistics

¤       We look at a sample, try to estimate the characteristics of the population it is drawn from

¤       First problem is getting a fair sample: Critique each

á       Gun control, letters from constituents

á       For percentage of motorists who drive drunk, breathalyzer test to the driver of every twentieth car passing a checkpoint

á       For value of environment, survey shoppers at a Wal-mart

á       Jury pool, home phone numbers between noon and 5 on weekdays

á       To determine % of rotten apples in a crate, check the ones at the top.

¤       If you know you can't get a fair sample

á       how might you adjust?

á       What is the risk in doing so?

¤       Second problem is measuring what you want

á       Law school questionnaire problem

á       How you frame a question matters to perceptions

á       And the self-interest of the person answering matters to incentives

¤       The usual report of error margins ignores both of these problems.

¤       It asks

á       If our estimate of the standard deviation is correct

á       How likely is it that the mean of our sample differs from the mean of the population by how much?

á       If you are using .05, you are asking

á       What is the deviation such that the probability our mean is farther from the population mean than that is .05?

á       Remembering that the distribution of means is close to normal.

v    Multivariate Statistics 1: Bivariate

¯    Each item (person, country, state, year) has two characteristics

¤       How are they related to each other?

¤       Why?

¯    Descriptive approach: Scatterplot

¤       Approximate linear relationship. But note

¤       The plot might show you more complicated things, that calculating the correlation coefficient would miss.

¤      

¤       The first one you would get a positive correlation coefficient—what would you miss?

¤       The second one, near zero correlation. But É

¤       Very useful if you are looking for patterns

¯    Correlation coefficient: Numerical description of the relationship

¤       Summary

á       Value from –1 to 1

á       Sign tells you whether larger than average values of one variable imply larger than average values of the other (+) or smaller (-)

á       The magnitude tells you how perfect the relation is, not the slope.

á      

á       Which of these has the higher correlation coefficient

á       This is the same point I made earlier about significance

¬     Statistically significant means we are sure the effect is there

¯    It says nothing about how large it is

¯    550 heads/450 tails is much more significant evidence of unfairness than

¯    3 heads/1 tail

¤       Mathematical definition

á       For each value of the first variable, calculate how many standard deviations it is from the mean--+ if greater than mean, - if less

á       For each observation (person, state, É) multiply that figure for the first variable times that figure for the second

á       Average over all observations

¬     (except you divide by n-1 instead of by n in averaging)

¬     for the same reason we did it earlier—sample slightly exaggerates the correlation for the population.

¬     I think

¤       Why this makes (some) sense

á       If above average values of X occur for the same observation as above average values of Y, the product is positive

á       If below go with below, the product is still positive—negative times negative is positive

á       So if the two variables move together, get a positive correlation coefficient

á       If they move in opposite directions, above average of one go with below average of the other, so + times – or – times +, which gives negative

á       Average lots of negative numbers, get a negative correlation coefficient

¯    Correlation is not (necessarily) causation

¤       The result might be entirely due to some third variable that causes both

á       Driving an expensive car has a negligible effect on life expectancy—probably negative if itÕs a sports car

á       But probably correlates with life expectancy. Why?

á       Height has little effect on having children, but É

á       Number of children one has born is probably negatively correlated with height of adults

á       Because?

¤       Or it might be partly due to such third factors, so you don't know how strong the causal effect is

¤       And third factors might push the other way, reducing, eliminating, or reversing the causation

á       Death penalty and murder rates

á       If factors that make murder rates high make death penalty more likely

á       Either because high murder rates create pressure for death penalty

á       Or because the social factors that make people more willing to kill illegally also make them more willing to kill legally.

á       You might have a positive correlation masking a negative causation

¯    And causation is not necessarily correlation either

v    Causation, correlation, and prediction

¯    Correlation can be used to predict

¯    "if the state has a death penalty, it probably has a high murder rate"

¤       doesn't depend on which causes which

¤       or whether there is a third factor causing both

¯    but if you have the causality wrong, you might get the prediction wrong

¤       because you are missing other relevant evidence

¤       taller adults are less likely to have born children than shorter

¤       but taller women aren't.

 

v    Review: Bivariate statistics

¯    We have two characters, each associated with individuals in a population

¤       Height and weight of people

¤       Rainfall and average temperature of years

¤       Income and Lsat score

á      Which could be parental income and student LSAT score or

á      Entering LSAT and later income as a lawyer

¯    We want to know how the two are related

¤       When height is above average, is weight above average? (Probably)

¤       Do cool years have more rainfall?

¯    Correlation coefficient is a measure of how consistently

¤       When one variable is above its average, the other is above its (positive correlation)

¤       Or when one is above, the other is below (negative)

¤       1 is perfect correlation--if you plot them they are on a straight line, slopes up

¤       -1 is perfect negative correlation--straight line, slopes down

¤       0 is no correlation

¯    It measures the consistency of the effect, not the strength

¤       If every inch above average height results in .001 lbs above average weight, the effect of height on weight is tiny

¤       But very consistent

¤       So correclation coefficienty is 1

¤       An example of the distinction between the statistical significance of a relation and its size.

¯    Scatter diagram might show patterns even if there were no correlation

¯    Correlation does not necessarily correspond to causation

¤       If probability of death penalty correlates positively with murder rate

¤       Might be because a death penalty causes people to commit murder

¤       Might be because high murder rates create political pressure for a death penalty

¤       Might be because certain cultural characteristics cause both death penalty and high murder rate

¯    Correlation does make possible (imperfect) prediction

¤       If A correlates positively with B, then

¤       If you observe an unusually high value of A, you can predict an unusually high value of B

¤       And be right more often than you would be by chance. But É

¯    If you get the causation wrong, you might be missing other relevant evidence

¤       Height correlates negatively with number of children an adult has born

¤       But not for women

v    linear regression

¯    instead of measuring how close to a line the points come (correlation coefficient)

¯    you try to estimate the line they come closest to

¯    which requires some definition of "close."

¤       You want to count both being too high and too low as errors

¤       So the difference between point and line wouldn't work

¤       Instead use the square of the difference—positive each way

¤       Find the line that minimizes the summed square deviation.

¯    Unlike the correlation coefficient, this one measures the size of the effect

¯    y= A+Bx

¤       A is the intercept—where the line crosses the vertical axis

¤       B is the slope—how much the line goes up for each unit it goes out

¤      

v    Goodness of fit

¯    By convention, X (horizontal) is the independent variable, Y (vertical) the dependent: Y=A + BX

¯    Simplest "prediction" is that Y always equals its average value

¯    How much of the departure from that does the regression explain?

¯   

¯     

¯    TSS is the sum of squared residuals from the average

¯   

¯    So R2 is a measure of how much of the variance about the mean is explained by the regression line. Total variation minus variation unexplained by regression divided by total variation

¯    So R2 of 0 means the regression line does no better than just assigning the mean value to every point

¯    R2 of 1 means the regression explains all of the variance.

¯    Like correlation, this is a measure of goodness of fit

¤       In fact, R2 is the square

¤       of the correlation coefficient r

¯    And B, the slope, is a measure of the strength of the relationship.

v    Residuals

¯    If you plot the residuals from a regression--distance above or below the line

¯    It will show you which points don't fit the pattern

¯    In exploratory statistics, you might want to color points in ways reflecting other characteristics

¤       Men/women

¤       Blacks/whites

¤       Northern states/Southern states

¤       CEO's relatives/non-relatives

¤       And see if any such coloring explained the pattern

¯    In the book's example, Mary Starchway is both an outlier and an influential observation

¤       Outlier because her wage is much higher than anybody else's

¤       Influential observation because she is far off the experience/wage regression line

¤       Does the first necessarily imply the second?

v    Limitation of linear regression

¯    There might be a close relationship that isn't linear

¯   

¯    there are procedure analogous to linear regression for dealing with the first case

¤       Instead of plotting Y=A+BX you might plot

¤       Y=A+BX+CX2 for example

¤       Giving something like that if B<0 and C>0

¯    The second case strongly suggests that we need more than two variables

¤       Y is determined by X, and also by

¤       Whatever it is that distinguishes the two lines

v    Multiple Regression

¯    Suppose you believe that the murder rate depends on

¤       The death penalty

¤       The fraction of the population that is males 18-26

¤       This year's unemployment rate

¯    You could express that as M=a+b1D+b2F+b3U

¤       Here M is the murder rate, by state

¤       D is the probability that a murderer will get the death penalty, by state

¤       F is the fraction of the state population that is male 18-26

¤       U is the state's unemployment rate

¯    The regression could be cross section

¤       All states

¤       In one year

¯    Or longitudinal

¤       One state

¤       In a series of years

¯    Or both

¯    And lots of more complicated versions are possible, for instance

¤       Perhaps the murder rate depends on the square of D, or

¤       Perhaps D should be treated as a binary variable instead of continuous

á      States with death penalty, D=1

á      States without, D=0

¤       Derhaps murder rate in one year depends on current unemployment rate but last year's death penalty probability

á      In which case you use current variables for everything else

á      But a lagged variable for D

á      Meaning that the value for NY in 1990 is the death penalty probability for NY in 1989

¯    In all of these cases, you are minimizing the sum of squared deviation from the regression's predictions

¤       Define  as the value of M predicted by the regression

¤      i= a+b1Di +b2Mi +b3Ui

 

¤       Here i labels the particular observation (state and year in this example)

¤       We are looking for the values of a, b1, b2 and b3 that minimize

¤       The sum of squared residuals,  i.e. the sum of squared values of

¤       (Mi-i)

¤       summed over all i, which is to say over all states, or years, or É

4/20/06

 

v    Review.

¤       What is a multiple regression

á      We have a dependent variable

¬     Murder rate

¬     Bar passage rate

¬     Cancer rate

á      We think it is partly determined by other things on which we have data, which will be our independent variables

¬     For the murder rate that might include

¯    Fraction of the population male 18-26

¯    Urban population

¯    Ratio of executions to murders

¬     For Bar passage rate, entering GPA, first year grades, É

¬     For cancer rate, smoking, age, É

á      Our data show us, for each observation, the value of the dependent and independent variables

¬     For each state, murder rate, demographics, É

¬     For each graduating law student, did or didn't pass bar first time, entering GPA, É

¬     For each person in our sample, did or did not get cancer, smoker/nonsmoker, É

á      We are using the data to figure out how the independent variables affect the dependent variable

á      By fitting the data to an equation of the form:

á      yi=a+b1x1i+b2x2i+É

á      Finding the values of  a,  b1, b2, É that minimize the summed square error—that get the predicted values for yi as close as possible to the actual values, given  the actual values of  x1i, x2i, É

¤       We hope to learn two things from this

á      How does each independent variable affect the dependent variable

á      How sure are we of the effect—whether it exists and how big it is.

v    Interpreting multiple regression results

¯    As usual, we distinguish between statistical significance and size

¤       R2 tells you how much of the variance has been explained, but É

¤       If you use a lot of variables, it isn't surprising that you can explain a lot of variance.

¤       "Give me ten parameters and I'll fit the skyline of New York."

¯    The regression coefficient tells you the size of the effect, not how sure you are it is there

¤       Suppose we define D more precisely as the probability that a convicted murderer will be executed

¤       And M as the number of murders/100,000 population

¤       If b1=10, that means that an increase of .1 in the probability a convicted murderer will be executed 

¤       Leads to one more murder per 100,000 of population

¤       For "how sure you are there" you  use a confidence measure

á      Typically a t statistic, which measures

á      The size of a coefficient, say b1, relative to its "standard error"

á      Where standard error is an estimate of the standard deviation of the coefficient calculated from a sample of a given size

á      "If we did this regression many times, drawing our sample at random from the same population, how much would b1 vary?"

á      The more standard errors the coefficient is from zero, the more confident we are that it is not zero, i.e. that the independent variable, say the probability of execution, affects the dependent variable, the murder rate.

á      To turn this into a confidence interval, you use the t table, as described in the book.

¤       Consider the Bazemore et. al. result

á      The size of the coefficient on race was $394.51—not very large

á      Standard error was 137.67, so t=coefficient/st error=2.87, lots of df

á      Makes it to the .01 level

á      If you are the defense, how do you explain this away?

 

¬     How many regressions did they do?

¯    Hispanic? Gender? Quadratic instead of linear?

¯    If they tried a hundred different versions, not so impressive

¬     Are there hidden variables that correlate with race and something relevant to salary? For example,

¯    where are those masters degrees from

¯    in what fields?

¯    More generally, what can go wrong in multiple regressions

¤       Omitting variables: On purpose, accidentally, or because you don't have the data

á      If you omit a variable that is an important influence on what you are explaining—wage in wage discrimination lawsuits, for instance

¬     If it doesn't correlate with the variables you include, the result is only to lower the R2—you aren't explaining as much of the variation in wages as if you included it. But É

¬     If it does correlate, you end up assigning the effect of the missing variable to the variables that correlate with it

¯    If height affects how good you are at basketball

¯    And correlates with weight

¯    And you do a regression including weight but not height

¯    You conclude that heavier people are better players.

á      So any confidence result however strong can be explained away

¬     If there is a plausible variable left out that

¬     Has a large effect on the dependent variable

¬     And correlates with the variable you got the confidence result for

á      If that plausible variable can be measured, do, include it, see what happens.

¤       Specification search

á      You do a lot of different regressions, looking for the important variables

á      And the right form for them to appear in

¬     If effect gets stronger and stronger with increasing size, perhaps quadratic

¬     If weaker and weaker, perhaps logarithmic

á      If you roll the dice enough times, you will get a double six.

¤       Multicollinearity

á      Suppose two of your included variables correlate closely with each other

á      Neither appears significant—because most of its effect could be due to the other

¤       Causation in both directions

á      Their police example

á      Their expenditure on education vs test score example

á      A better one would be money spent on medical care vs health

¤       Correlated errors

á      Suppose we are studying the death penalty, using cross sectional data—i.e. data by state.

á      Dependent variable is the murder rate.

á      One independent variable is the ratio of executions to murders

á      They are not really related, as it happens, but É

á      Different states differ in how they measure the murder rate

¬     Some are very willing to interpret a death as a murder

¬     Others are very skeptical

¯    If it might be suicide, it is suicide

¯    If it might be accident, it is accident

á      What will the regression show?

¤       There are lots of fancier statistical procedures designed to deal with such problems

v    Our law school problem

¯    How would you set up a multiple regression to figure out how to improve the bar passage rate?

¯    What variables would you include?

¯    In what form would they appear?

¯    What problems do you see with omitted variables?

¯    With multicollearity?

¯    With causation in the reverse direction?

 

Questions from the book's supplementary material

 

Here is the least squares  regression equation relating Ames graduatesÕ yearly income in dollars 10 years past graduation to Ames GPA.  (Scale F=0 to A=4). 

 

Income = 1,208,000 + 25 GPA

 

Does this equation offer a good reason for greedy students to work hard to improve their GPA?

 

 

 

The Boston Post reports, ÒResearchers at Ames Law School have discovered that law  school GPA has a correlation of minus .35 with the number of alcoholic drinks per month that a student imbibes.  The authors of the study, Professors Stern and Meaney speculate that alcohol has a negative effect on higher brain functions of the type required to do well in law school  examinations.Ó

 

Comment  insightfully based on your textbook readings about  correlation.

 

The following question is in a survey – what is the last digit of your telephone number? 

What would the histogram of responses look like?

 

Suppose instead it was "the last digit of the month of your birth?"

 

v    Course Evaluations

 

Review  Of the Semester

 

v    Decision Theory

¯    A way of formalizing how you make decisions

¯    In order to help you do it

¯    Via a decision diagram

¤       You make a choice

¤       Something happens

¤       You make another choice

¤       É

¤       some choices have costs

¤       at the end you get an outcome of some value to you

¤       what sequence of choices,  on average,   gives you the best result?

á      Best is most simply defined as maximum expected value, but ..

á      In some cases that's wrong—risk aversion

á      You might much prefer a certainty of $100,000 gain to a .1 probability of $1,000,000

¯    The formal approach requires you to know all of

¤       the alternatives, probabilities, costs and payoffs

¤       So trying to set up the diagram forces you to think about what they are

¤       And try to estimate, using what you know, what your client knows, whatever  else you can find out.

v    Game Theory

¯    Strategic behavior

¤       In decision theory, there was only one actor

¤       Now there are at least two, with their own objectives

¤       And each of them is watching the others, and conditioning his choices on theirs.

¯    We would like to know

¤       Given a game structure, how should you play, and É

¤       What will happen, given how everyone plays

¤       One perspective is of a player, the other that of someone analyzing the result games will produce—perhaps because he is creating games

á      For instance, someone making laws

á      Or writing a contract

á      Or structuring a business

¯    One approach is subgame perfect equilibrium

¤       Which is essentially a two person version of a decision theory diagram

¤       Without commitment strategies

¤       Meaning that when Anne gets to her final choice, she always makes the decision that is best for her

á      And Bill knows she will, so can make his previous choice taking Anne's final action for granted

á      And doing what is best for him, given that

á      And Anne knows that, so in her choice before Bill's final choice É

¤       With commitment strategies, it might make sense for Anne to "tie her hands"

á      Set things up so if Bill makes the choice she doesn't want him to make

á      She will be committed to a choice he doesn't want her to make

á      Even though it's bad for her too

á      Because that way Bill won't make the choice she doesn't want him to.

¯    For an example where commitment strategies are important, consider bilateral monopoly

¤       AKA bargaining

á      We both benefit if the transaction goes through, but É

á      The terms of the transaction determine how much of the benefit each of us gets.

á      Union/Management bargaining, diplomacy, parent/child, buying a house É

¤       You can try to get better turns either by

á      Somehow committing yourself not to accept otherwise, or É

á      By misleading the other party about what terms it is in your interest to accept

¤       The risk of either is bargaining breakdown—nobody gets anything

¯    Another is to think of a game in terms of a strategy matrix

¤       Each of my strategies is a full description of what I will do

á      Start by advancing my queen's pawn

á      If you respond by É  I will next do É

á      All the way to the end of the game, for all possibilities

á      Where, in order to make your responses less predictable, your strategy might include flipping a coin at some point and deciding accordingly.

¤       The matrix shows all my strategies, all yours, and the outcome for each of us given any pair of strategies—what I'm doing and what you are doing

¤       Von Neumann showed that in a two person fixed sum game described that way, there was always a "solution"

¤       Meaning a pair of strategies, each of which was best against the other.

¤       A simpler sort of solution, but one that may not exist, is a pair of dominant strategies

á      Meaning that each is the best strategy whatever the other person does

á      In Prisoner's Dilemma, confessing is the dominant strategy for each player

¯    One approach to a many player game is a Nash Equlibrium

¤       Meaning a set of strategies, one for each player, such that

¤       Each player's strategy is best for him, given what the others are doing

¤       Everyone driving on the right is a Nash equilibrium

¤       So is everyone driving on the left

¤       So is the prisoners, faced by a guard with one bullet, not rushing him.

¤       As these examples suggest, a Nash equilibrium need not be

á      Either unique, or É

á      Optimal for the players

¯    Moral Hazard: Doesn't belong in this chapter but that's where they put it

¤       If I bear only part of the cost of my action—because my factory is insured

á      I have an inadequate incentive to take the action

á      And won't take it if its cost is too close to the benefit, since then

á      Its cost is more than my share of the benefit

¤       Solutions include

á      Requiring certain actions (sprinklers in the factory)

á      Only insuring partially, so that at least I take the really valuable precautions—the ones worth considerably more than they cost.

¯    Adverse Selection: The Market for Lemons

¤       If the seller knows the quality of what is being sold and the buyer doesn't

á      Buyer offers a price based on his estimate of average quality

á      At that price selling is much more attractive if your goods are of low quality

á      So mostly low quality goods get sold, high don't

á      And buyers adjust their offer down accordingly

á      So all the lemons are sold, for lemon prices, and almost none of the creampuffs—which would also get lemon prices

¤       Life or health insurance raises a similar problem

á      If customers know much more about the risk than the insurance company

á      High risk customers find insurance a much better deal than low risk

á      So the insurance company correctly concludes that if you buy you are probably high risk

á      And prices accordingly.

¤       Solutions include

á      Seller provides a guarantee—but that rises moral hazard problems

á      Keep both parties ignorant—forbid genetic testing before buying insurance

á      Make both parties well informed—let insurance company require genetic testing.

v    Contracting

¯    Basic idea—design the contract to maximize total benefit, bargain over dividing it

¯    Maximize total benefit by getting the incentives right

¤       Minimizing costs due to things like moral hazard aka exteralities within the contract

á      Try to set it up so that each party bears the costs that depend on his actions

á      Which might include precautions, deciding whether to breach, É.

¤       And to minimize adverse selection problems

¤       Which means making each party bear the costs he is best informed about

á      So A knows the risk that a strike will halt his production

á      And B doesn't care, because the contract requires A to compensate him if it does

¤       But the ability to do this may be constrained by one party's limited ability to observe things

á      Such as the quality of materials used to build a house

á      Or whose fault something going wrong was

¯    And we ran through the logic of that in different contexts, such as

¤       Production contracts: Building a house

á      How is the contractor paid, and É

á      What choices does he get to make, what are restricted by contracts

¤       Service contracts

¤       Principle/Agent relations

¤       Joint Undertakings

¤       Sale or lease of property

¤       Loan

¯    Issues common to many of these are

¤       Incentives and observability

¤       Damages for breach

¤       Resolving conflicts, renegotiating

v    Accounting

¯    A way of keeping track of what is happening in a firm or other organization

¤       Has to be rigid enough so that interested parties can't easily make things look good when they are not

¤       And yet reliable enough to generate useful information

¯    Rigidity requires simplifications, such as

¤       Cost to measure value most of the time

¤       Intangible assets such as goodwill ignored, unless purchased for a known price

¤       Almost all probabilities treated as one or zero

¯    Balance sheet: Photo of firm at an instant

¯    Income statement

¯    Cash flow statement

¯    T-Accounts

¤       Which show individual transactions, each in two places

á      If you buy thing, decreases cash, increases assets

á      Sell something, the other way

á      If they don't balance—sell for more than book value—the difference

¬     Goes to income, and eventually to

¬     Firm equity

¤       And eventually feed into income and from there to balance sheet

¯    Matching principle: How to decide to what period an expenditure or outcome is allocated?

¯    Defining an entity—boundary lines between you and your business, law school and university.

¯    Using such information to figure out

¤       Is a firm really solvent

¤       How is it doing?

¤       Why? Emma Lathen: Accounting for Murder

v    Finance

¯    Theory of the firm. Coase. Berle and Means. Adam Smith

¤       Relevant to legal issues, such as whether merger violates antitrust laws

¤       And how much discretion managers should have

¤       And what the limits are on the majority stockholders

¯    Debt/Equity question—how should a firm finance itself?

¯    Firm as a problem in agency theory.

¯    Time value of money: Present value calculations

¯    Efficient market theory

v    Price Theory (aka microeconomics)

¯    Economics: An approach to behavior,

¤       starting with the rationality assumption

¤       potentially applicable to all behavior

¯    the coordination problem

¤       can be solved by top down hierarchy—you do that, he does that, the other guy É

¤       or by a decentralized system of private property and exchange

¤       a lot of legal issues are about how to make the second method work better.

¯    Perfect competition

¯    Demand and supply curves—their intersection gives price and quantity

¯    Monopoly

¤       What it is

¤       Why it happens

¤       How it is in the interest of a monopolist to behave

á      Sell too little at too high a price

á      And spend resources becoming a monopoly

¤       What, if anything, we can do about it.

¯    Externalities—one reason the decentralized solution doesn't work perfectly

¤       If you don't bear all the costs of your action, get all the benefits, the action that Moral hazard was another way of describing the same problem

¤       best serves your interests may not best serve ours.

¤       Possible solutions include

á      Regulation—make make me do the right thing

á      Pigouvian tax—force the internalization

¤       Coase's criticism of Pigou's analysis—externalities are really jointly produced

¤       Also, if no transaction cost, bargaining eliminates them

v    Economic Analysis of Law

¯    Making sense of legal rules as systems of incentives

¤       Given these rules, how will people act in their own interest

¤       Is that the outcome we want?

¯    Property: Why it exists. Why some things are property and some are not. What's included in the bundle

¯    Torts: How do we get only "efficient torts"

¤       Meaning only torts that cost more to avoid than its worth

¤       Strict liability, negligence, ???

¤       Worry about incentives of both parties, and about what the court can or cannot know

¤       Really the externality problem again.

¯    Crime: How do you get only efficient crimes? How do you include the cost of catching and punishing criminals in your definition of "efficient crimes?"

v    Fundamentals of Statistics

¯    Descriptive

¯    Hypothesis testing

¯    Deducing  things

v     Multivariate statistics