Economics 2010a Fall 2003 Ed Glaeser Lecture 1 Introduction General Observations about Economics Defining the Field The Use of Economic Theory Traditional Ideas in Economics Choice Theory Rationality Weak Axiom of Revealed Preference Application: Ultimatum Games Defining the Field—What do you think that economics is? Subject Matter Based Definitions Ultra-pragmatic definitions (“what economists do”) Methodology Based Definitions This much is certain: Economics pretty much includes all topics related to human society. Money supply, international trade, public finance, economic growth. But also, fertility, crime, the marriage market, hate, terrorism, riots …. This is a tremendous opportunity for us. Economists at least like to think that the discipline follows Popperian scientific methods Stylized Facts -> Hypothesis Formation -> Testing Hypotheses Remember that Popper would tell you that hypotheses can only be proven false empirically, not proven true. This should keep us humble. Hypothesis Formation— The Theory Step of this Process—In Economics this means using the language of Mathematics to formalize one’s assumptions. Why is this so valuable? Some critics of economics say that our models are too simplistic. We leave too many things out. That is true—we do leave many things out. But it’s better to be clear about an argument. Failing to formalize a theory does not mean that you have been more general and holistic, it just means that you have been less rigorous. Other social sciences have inevitably followed economics into formalization and the social scientists who have not, have had trouble. I think that early formalization gave economics a huge edge over sociology. Economics does not have an edge in generating stylized facts—almost surely we are bad at this. We also do not seem to have an edge at creativity. For these reasons—it makes sense to be more aware of other disciplines. d. Now things get more controversial. I would further say that any “economic” model of the world needs to start with a formal description of decision-making agents. These agents are usually people and sometimes firms— Although modern theory of the firm has brought itself down to the individual as the unit of analysis. Old style—Baumal and sales maximization of firms. New style—model the agency problems that can cause individual managers to be empire builders. This distinguishes economics from mathematical social sciences that start with assumptions about aggregates, e.g. city population growth=f(city income). For what it’s worth, this claim also disqualifies mid 20th century macro-economics, which often began with assumptions about the determinants of Y, C, I and G. The great triumph of post-Lucas macro-economics is in building macro on micro foundations. The “rational expectations” revolution was not really about expectations, and has much less policy content than is often thought. The important point is that it rests macro- economics on models that start with individuals. Now things get highly controversial. Does Economics need to assume that people maximize something , or that their preferences are stable, or that people think all that clearly. Opinions differ. Read the introduction to Becker’s Economic Approach to Human Behavior, where he makes a strong case for maximization lying at the core of economics. As I will discuss in a second, I agree with this statement as a historical fact, i.e. most economists do rely on maximization, and furthermore as a matter of good practice, maximization is much easier to work with than its alternatives. But philosophically—I don’t think that maximization is necessary for work to be economics. You will have to decide this on your own. A final point about the definition of the discipline— Neville Keynes’ (and Milton Friedman’s) distinction of the field into positive and normative economics is useful. Positive economics—why the world looks the way that it does. Normative economics—how the world can be improved. Both areas are necessary and sometimes merge perfectly, but I for one, see my job description as trying to understand the world around me. What I hope that you will get out of this course? The ability to craft formal descriptions of the world around you that can then serve as a basis for empirical work. As a theorist—ultimately theory tends only to be useful if it eventually leads downstream and helps us to craft hypotheses that can be tested (back to Popper). This doesn’t mean that for a lot of great theory is pretty far from applications, but in the long run, it should be judged on the extent to which it adds to the great enterprise of understanding the world around us. Arrow/Debreu, etc., may look like they are far from data, but their framework served as underpinnings for far more applied work. As an empiricist—every regression you run should ultimately be based on a formal model. Example # 1: Comparative Statics. Much of what economic theory does is to derive comparative statics. To show what a particular model implies about the relationship between X and Y, or more precisely, what exogenous changes in X do to the equilibrium level of Y. Why do we do this? Example # 2: Estimating Parameters. For example, estimating what is the elasticity of labor supply, or the discount factor. Again—estimating parameters only makes sense in the context of a model. As a matter of discipline, it makes sense to write down a model that justifies every regression that you run. I would say that it even makes sense for the model to be precise enough to justify the exact functional form that you use. A classic example—people are fond of regressing growth in income on initial characteristics (years of schooling, to estimate what causes productivity growth). Even the most simple model tells you that this makes much more sense at the country than at the city level. Why? What would make more sense to use at the city level? The point is that economic theory guides our empirics. One last aside before entering into the mainstream of the class. Over the past 225 years, economics has had three pillars. The Incentive Principle: People respond to incentives. All else equal hen the cost of an activity rises, people do less of it, when the benefit to an action increases people do it more. Our equilibrium concept: An equilibrium occurs when returns are equalized across activities. No opportunities for arbitrage. Those were positive—this one is normative—well- being rises with the size of one’s choice set, which tends to imply that wealth and freedom are good things. (Exceptions to this include self-control problems, strategic interactions). You don’t have to agree with those things, but at least you should recognize that they have been at the heart of our discipline. These principles can be derived from maximization (we will do some of that), but they don’t need to be. I think it is our equilibrium concept that is our most powerful contribution (Smith deserves credit—think of compensating differentials. Psychologists—because they study people in the lab often have a richer (and I would say better) idea of what individuals are like than we do. As such, we can learn much from them. But their discipline doesn’t have an equilibrium concept and as such they are not really able to explain aggregate phenomena. As an example—in the wake of World War II— psychologists showed that ordinary people are perfectly willing to apparently administer extreme pain to innocent subjects if they are told to do so by an authority figure. (The Milgram experiment). They also showed that human beings naturally form hostile groups (Smuggler’s Cove). They also showed that when some students were assigned to play the role of prison guards, and other students to play the role of prisoners, the prison guards began behaving brutally towards their prisoners. These experiments are fascinating, important social science. But they do nothing to explain to us why Nazism took over in Germany in the 1930s and not 50 years earlier (or later) and not in France. The psychological focus on the lab pulls them away from even thinking about the causes of aggregate phenomena in a sophisticated manner. Now back to the mainstream. Behavioral economics or economics and psychology has been one of the most exciting areas of research over the past 25 years, but first to challenge rationality we need to understand the basic framework. Choice Theory (MWG Chapters 1+2)—MWG 1.C Possible observations (choices that people make) denoted x,y,z are members of a space X. X is a set of possible (mutually exclusive) alternatives from which an individual can choose. If there are L commodities then . The space X (the consumption space) is determined by technological limits (MWG, pp.18-22). Budget sets will be subsets of X. Preferences will rank elements of X. Preference relations. One way to think about consumer choices is preference relations. We start with . We denote a preference relation . An aside on notation—being something of an idiot—I have never switched to tex/latex/etc., and as a result use word. This is a big problem as word has an equation editor, that has always served my needs, but cannot match MWG. We read  as x is at least as good as, or weakly preferred to, y. Strict preference relations  implies  but not  You read this one x is strongly preferred to y. Indifference relation  defined as  and  This is a big notation problem—this is supposed to be one line, not two (see MWG, p. 6). You read this one as x is indifferent to y. By rationality we mean: Definition 1.B.1: The preference relationship  is rational if it possesses the following two properties: (i) Completeness: for all , we have that  or  or both. (ii) Transitivity: for all  if  and  then . Rationality implies (proposition 1.B.1) that: (i)  is both irreflexive (i.e.  never holds) and transitive (i.e.  and  implies ) (ii)  (again squint so you only see one line) is reflexive (i.e.  for all x), transitive and symmetric (i.e.  implies ). (iii) if  and  then . These are some useful properties which you are going to want to prove on your own. B is a family of subsets, denoted B, of X, i.e. every element of B is a set B ( X. Another issue on notation. B is meant to represent that fancy curlicued B that is introduced on the top of page 10 in the text. C(.) is a correspondence mapping B to X, such that C(B) ( B. It is a choice rule that chooses a set C(B) for every set , such that C(B) ( B, for all B(B. In case you haven’t guessed B is supposed to stand for budget set, and that is the usual interpretation of this. A choice structure is the combination: (B , C(.)). MWG Example 1.C.1 X={x, y, z} B ={{x, y}, {x, y, z}}   x is the preferred option no matter what is in the budget set. Another rational possibility   Choose x when only x or y is available, but choose z when it is available. A less rational possibility   y had been available before, yet the individual chose x. When z is included into this, the person chooses y. A possible way to make sense of this — x, y, z are three pieces of cake that you are offered. You have two things that you care about (1) eating more cake, and (2) not looking gluttonous. As a result, you always take the second largest piece of cake. Your choice may be totally rational (back to what precisely that means in a second), but we don’t recognize it because we haven’t properly specific the problem. You don’t just care about eating cake (i.e. x, y, z, aren’t the only outcomes that matter in the choice set), you also care about the approval of the host. If approval is either zero (if you take the biggest piece) or one, then B ={{(x, 1), (y, 0)}, { (x, 1), (y, 1), (z, 0}} We are no longer surprised that (x, 1) is chosen over (y, 0) but that (y, 1) is chosen over (x, 1). Jerry Green calls this step 1 and step 2 errors, or the problem of mistakenly describing context. If you think about our problem as trying to figure out what people are trying to do based on pretty limited information. Then our method is to (1) describe the context in which people are operating, and (2) operationalize a quantitative description of their actions. Errors are made in both steps. Trying to accurately describe context as well as possible is important. The Weak Axiom of Revealed Preference MWG Definition 1.C.1 The choice structure (B , C(.)) satisfies the weak axiom of revealed preference if the following property holds: If for some  with  we have , then for any  with  and , we must also have . The choice function is allowed to have more than one Element (i.e. such that C(B) ( B, ( B(B) If  then the agent must either prefer x to any other element in C(B) or the agent must be indifferent between x and any other element in C(B). A new definition:  The elements in  are the agent’s preferred alternatives in B. Definition 1.D.1: The choice structure (B , C(.)) is rationalized by the preference relation  relative to B if  for all . In other words the choice structure (B , C(.)) is rationalized by the preference relation  relative to B if C(B) is a set of maximizers of  over all  for all . It is possible to satisfy the weak axiom and yet for there not to exist a preference relation that seems to be maximized by the observed choices. MWG Proposition 1.D.2: If (B , C(.)) satisfies: i. the weak axiom of revealed preference, ii. B includes all subsets of X with two or three elements, then there is a unique rationalizing preference relation, i.e.  for all . An application—the ultimatum game. Step 1: the first player puts forward an allocation of 10 dollars which can be any integer amount. Step 2: the second player either accepts the allocation, in which case both players get the allotted money, or rejects the allocation in which case, neither player gets any money. What would you predict should happen? What would “economics” predict should happen? What does happen is that: (1) most offers are either 4 or 5 dollars, and (2) those are accepted, and (3) offers that are three dollars or less, are rejected very frequently. How can we understand this? How can we think about ways to test our theories?