26 January 2010

The design, difficulties, and results of social science experiments, Part II.

Each part contains a brief introduction to experimental social science, and descriptions of some real experiments. The introduction is the same, but the experiments are different. You must attend two parts, and in the third you will be participating in a real experiment.

- In theory, we ask for logical and quantitative analysis.
- We use
*models*.

- We use
- We require that theory be verified by empirical (practical) tests.
- The tests must correspond to the models.

- In general, tests can based on history or experiment.

- Does historical data "fit" the model?
- Use statistics:
- Analysis of variance for qualitative models (psychology).
- Regression analysis for quantitative models (economics).

- Data sources:
- Collected for other purposes.
*E.g.*, census, trade and, income data are collected by the government to create election districts and levy taxes, internal corporate data for management information. - Designed surveys. Consumer behavior: Michigan Panel Survey, National Longitudinal Survey.
- Combinations.

- Collected for other purposes.

- Varying quality of data, especially over time.
- Measured variables do not correspond to theoretical variables.
- Utility can't be measured.
- There is no market for "automobiles" in the sense of the Law of
One Price and market clearing.
- Prices are averages over models and transactions (bargaining).
- Quantities are averages.
- Market clearing is achieved by inventory adjustment.

- Experiments are designed to fit theory.
- Extraneous variables are controlled.
- Relevant variables match theoretical definitions.
- Relevant variables are recorded.
- Equations are calibrated to match theory.

- Framing effects:
- Stakes are small. Real economic behavior is "you bet your life/company/country"; can't do that with experiments.
- Typical experimental subjects (college students) are not real decision-makers (housewives, company president, country Prime Minister).
- Experiments normally restricted to gains, but agents may view losses differently.

- Not all interesting variables can be measured (
*e.g.*, utility). - Basic assumptions needed for measurement may be violated (
*e.g.*, expected utility). - Nevertheless, experiments are useful. (Including an endless source of graduation research themes!)

- We suppose that you are offered a chance to win one of three prizes, A, B, or C. You get utility U(A), U(B), or U(C) depending on which prize you receive.
- A
*lottery*is a set of probabilities, p(A), p(B), and p(C) corresponding to each prize such that p(A) + p(B) + p(C) = 1. - If the probabilities are p(A) of winning A, p(B) of winning B, and
p(C) of winning C, your
*expected utility*of the lottery p is V(p) = p(A)*U(A) + p(B)*U(B) + p(C)*U(B).

- First, you are offered the choice between lotteries
- Option 1: you get A with probability p(A), or B with probability p(B). Of course p(A) + p(B) = 1.
- Option 2: you get A with probability q(A), or B with probability q(B). Of course q(A) + q(B) = 1.

- Second, you are offered the choice between the lotteries
- Option 3: you get A with probability rp(A), or B with probability rp(B), or C with probability 1 - r. Of course rp(A) + rp(B) + (1 - r) = 1.
- Option 4: you get A with probability rq(A), or B with probability rq(B), or C with probability 1 - r. Of course rq(A) + rq(B) + (1 - r) = 1.

- The p's, q's, and r's are the same in every option.
- According to expected utility theory, you will choose Option 1 in the first treatment if and only if you choose Option 3 in the second treatment.
**Homework:**Prove it using the expected utility formula.

- Suppose A = 10,000 yen, B = 12,000 yen, and C = 0 yen.
- Some people who
*definitely*prefer 1 to 2, will also insist they like 4 better than 3.- This "violates" expected utility, and so is called a "paradox". But expected utility is not a law, just an hypothesis, so "preference reversal" is more accurate.

- Quite rare. Maybe a very few people just don't understand, but the economy as a whole can be predicted by expected utility.

- p, q, and r given as before, all positive. r is "big".
- Treatment 1: A = 10,000 yen, B = 12,000 yen, and C = 0 yen.
- Option 1: you get A with probability rp(A), or B with probability rp(B), or C with probability 1 - r.
- Option 2: you get A with probability rq(A), or B with probability rq(B), or C with probability 1 - r.

- Treatment 2: A = 10,000, B = 12,000, and C = 8000 yen.
- Option 3: you get A with probability rp(A), or B with probability rp(B), or C with probability 1 - r.
- Option 4: you get A with probability rq(A), or B with probability rq(B), or C with probability 1 - r.

- Preference reversal is quite common.
- Logic: when C is big, base level is secure, avoid too much risk. When C is small, not much chance of positive prize, so choose best chance of getting B (the biggest prize).

- Economists A. Roth (US), M. Okuno-Fujiwara (Japan), M. Maschler (Israel)
- Ultimatum game:
- Total prize of 100 dollars (10,000 yen).
- Player 1 proposes his share, from 0% to 100% of prize.
- Player 2 responds "yes" or "no".
- If "yes", split according to Player 1's proposal; if "no", both players get zero.

- Equilibrium: Player 1 demands 99%, player 2 says "yes".
- Control conditions: players are in individual rooms, never meet other players, play only once.

- Japan: great majority propose 50%, Player 2 says "yes". Average demand about 55%, almost all player 2 role say "yes".
- US: near majority propose 50%, Player 2 says "yes". Average demand about 65%, most player 2 role say "yes", but disagreement is not uncommon.
- Israel: about 1/3 propose 50%, Player 2 says "yes". Average demand about 85%, demands over 90% almost always refused.

- Another ultimatum game. Differences:
- Multi-player: One player 1, many player 2 all with veto (if one "no", all get zero).
- Players are game theorists and mathematical economists (Roth experiment, college students).
- Controls poor (the participants know each other very well).

- Result: Player 1 demands $990, offering $1 to each of the others. 5 say yes, 5 say no.

- Market games are usually constructed on the
*reservation price*principle. - Each buyer may buy one unit per market. If he does, he sells it
to the experimenter for a fixed price, set in advance. Buyers
want to pay a lot less than the fixed price, but make some profit
as long as they do pay less. The fixed price is that
*buyer's reservation price*. - Each seller may sell one unit per market. If he does
*not*, the experimenter will pay a fixed price (the*seller's reservation price*) for the left over good. Sellers want to receive a higher price than their reservation price, of course.

- Controls: Demand and supply curve defined by number of buyers (respectively, sellers) with each reservation price.
- No inventory; market must clear.
- Need market price setting.

- Auctioneer controls.
- Either buyer or seller may speak with permission, to say "buy at <price>" or "sell at <price>", or "accept". Offers are publicly posted.
- "Buy at" and "sell at" are binding offers; if accepted you must trade.
- The offer accepted is the most advantageous for the trader who accepts.
- All offers are cleared after each trade, and the process continues in the same way until no traders will accept.

- What is (economically) special about oil?
- It is a
*pure exhaustible resource*. - Consumers are
*perfectly competitive*. - Producers are an
*oligopoly*.

- Cannot be produced (unlike cars) and are not self-reproducing (unlike tuna).
- Sustainable use is impossible.
- Well-developed theory of optimal use and market behavior because constraints are simple.

- Everybody needs energy, and uses oil energy in many forms: gasoline, heating oil, electricity, jet fuel.
- Also use in products as a base for many plastics and as a lubricant.
- Compared to market demand, consumers are small and many. These are
conditions that lead to
*perfect competition*(price-taking behavior). **We model consumers as a demand curve.**- For simplicity, we simply take the same demand curve in each period.

- Producers are few and large.
**We model producers as an oligopoly.**They behave*strategically*, that is- They take the effect of their own behavior on price into account.
- They take the effect of others' behavior on price into account, and furthermore know that others will behave strategically.

- Strategic behavior is studied in
*game theory*. Unlike the competitive market, economists and other social scientists still disagree about what the best theory of strategic behavior is.

- Sellers in the oil market must possess a
*stock*to be able to sell; it is not possible to produce new oil for sale. - Quantities of oil (or the right to extract that oil from the ground)
are bought and sold. Thus, sellers may
*invest*in purchasing stocks as well as*draw down*the existing stock to sell to consumers (or investors). - In our market, we allow traders to buy and sell. Of course, they buy in hope of selling at a higher price later.

- If we have a stock of
*X*barrels of oil (perhaps still in the ground), and we use*Q*barrels per year, then we will run out of oil in*T = X/Q*years. - But we will still need energy in
*T+1*years. There is always a "tomorrow" we must consider when planning to use a an exhaustible resource today. - In theoretical models,
**we assume that decision-makers plan for an infinite horizon.** - In an experiment, however, we can't wait for infinity, even if we pretend that a year passes every five minutes.

- An important aspect of long-term planning is
*discounting*: people give less weight to rewards received in the future. - In theory, we model this with
*discounted utility*:*V(c1,c2,c3...) = U(c1) + d x U(c2) + d x d x U(c3) + ...*, where*c1*is received today,*c2*is received next year,*c3*the year after that, and so on.*0 < d < 1*. - However, in an experiment,
*the reward is received all at once at the end*.

- Both problems can be solved in the same way: by
*randomly stopping the game*with probability*1 - d*(continuing with probability*d*). - Randomly stopping allows the game to end in finite time.
- If
*R*is revenue to the subject, the probability of getting the prize is proportional to the revenue at some factor*a*. - With random stopping by the above rule, the probability of getting
the prize is
*p(A) = a x (R1 + d x R2 + d x d x R3 + ...)*. - But with a lottery,
*p(A)*is equivalent to utility!