MODELING

1. MODELING

2. Before getting into the details of modeling, let’s talk about the readings some, especially Varian, and some of Thomson • Varian: What are some of his key ideas? • Look for ideas in the real world, not in journals • Use journals to • understand problems, what is being done, and how it is being done, but find the neat “new” ideas outside of the professional literature • But you still need to know the literature, before and after you start research.

3. In many cases your ideas can come from your own life and experiences. One of my favorite pieces of my own work is the paper I wrote on ‘‘A Model of Sales’’. … I noticed that the prices fluctuated quite a bit from week to week. It occurred to me that the challenge to economics was not why the prices were sometimes low (i.e., during sales) but why they were ever high. Who would be so foolish as to buy when the price was high since everyone knew that the item would be on sale in a few weeks? But there must be such people, otherwise the stores would never find it profitable to charge a high price. Armed with this insight, I was able to generate a model of sales. In my model there were two kinds of consumers: informed consumers who read the ads and uninformed consumers who didn’t read the ads. The stores had sales in order to price discriminate between the informed and uninformed consumers.

4. My “Are Cherries Lemons?” and “The Public Finance of Healthy Behavior” papers came the same way. • For the first, we observed how cherries were sometimes sold sorted, and sometimes by size, and we wondered why. • For the second, I started thinking about how most people get subsidized health insurance, either directly through programs like Medicare and Medicaid, and indirectly by tax benefits for taking compensation in health insurance. So you don’t need to be as smart as Varian for his idea to work.

5. Once you have a research idea, you now need to put it in the context of economics. • The best way to do this is to build an economic model. • Formal (mathematical) • Informal (descriptive or graphical) • Do this even if you will not include the model in the paper. • It gives you context • It gives you direction • It helps clarify the problem

6. All economic models look pretty much the same. There are some economic agents. They make choices in order to advance their objectives. The choices have to satisfy various constraints so there’s something that adjusts to make all these choices consistent. This basic structure suggests a plan of attack: Who are the people making the choices? What are the constraints they face? How do they interact? What adjusts if the choices aren’t mutually consistent?

7. What are the goals of a theoretical model? • Your first goal is to make your model simple, as simple as possible so it still reveals the essence of what is going on. • Your second goal is to generalize your model so it fits as many situations as possible.

8. How to build a theoretical model: • Start with a general statement of what you want to show. In words, not math • List the elements needed • Your ASSUMPTIONS • Agents, and their problems • What are they trying to optimize • What do they get to choose • How do the agents interact? • Specify institutional constraints • Specify information flows and asymmetries. • What constraints, institutional, informational, or market based, affect each agent, and how? • What adjusts if choices are not mutually consistent.

9. How to build a model (continued): • Now start putting math to the model • Even if you won’t use a formal mathematical model, state the assumptions, relationships, constraints, and adjustments in mathematical symbols • Don’t worry, yet, if it is solvable • Specify an argument for each choice variable, and why it matters • Write an equation for each constraint and interaction • Write an objective function for each agent • Model how things constraint if choices are not consistent • Start thinking about what is needed of all the equations, objectives and arguments you have down

10. How to build a model (continued): • Build a very simple example, giving specific, simple functional forms for all objectives and constraints. • See if the model is solvable in its current complexity • For the specific functional form, start simplifying • Reduce agents, markets & constraints as possible. • Reduce the model so it captures only one of the elements of interest. • Change the elements addressed, but keeping the model simple. Example: In a price-quality tradeoff problem, first hold quality constant and focus on price, then hold price constant and focus on quality.

11. How to build a model (continued): • Now start building a general model • Still in your specific example, start adding back in agents, arguments and constraints. • Change orders of incremental complexity • Notice what elements cause the most problem • Decide on a model, still with your specific functional form, that captures the elements of primary interest. • Notice what limitations your functional form impose. • For example, linear forms are very constraining • Does it have constant elasticity of demand, or constant returns to scale.

12. How to build a model (continued): • Now change your specific functional form so it is not as constraining as your first • If you assumed constant elasticity, change it so elasticity is variable with price, or if it was inelastic, make it elastic. • Move from constant returns to scale to decreasing returns to scale in production. • See how this changes • A the ability to solve the model and the results • The feasible space of application. • Note the importance of the characteristics of the specific functional forms to make the model solvable, and on the results.

13. How to build a model (continued): • Finally, state your model in general functional notation. • From what you learned with specific functional forms, indicate the constraints placed on the general functional forms • These are assumptions, like more is better and diminishing marginal utility • ie., U(x)>0, U(x)>0, U(x)<0. • Characterize how a solution is found (for example, a fixed point theorem) • Indicate what the solution looks like, and what it implies. • Understand the feasible space for application

14. How to build a model (review): • General rules • Start with a very simple example. • Start with specific functional forms rather than general notation. • Use as few agents, markets, constraints as possible. • Do not worry, at first, if it captures all of the elements you want to address; just make sure it captures at least one. • Change the elements addressed, but keeping the model simple.

15. Key things about modeling • At the heart of production is (usually) profit maximization. • At the heart of consumer demand is utility maximization. • At the heart of macro and public policy issues is welfare economics and microfoundations. • We start with (assumed) true premises, hence we end up with true conclusions if our assumptions are correct. It is deductive, not inductive. • Give it the context of economics.

16. Key Things (continued) • A model is hierarchal • If you are applying an existing theory • Don’t derive well-known results • Focus on how the question is an application of the existing knowledge. • If you are modifying an existing theory • Restate its known form; but don’t assume the reader knows previous work • Introduce changes • Explicitly explain how assumptions have changed • Be clear about manipulations

17. Thomson (citation on web page, not assigned for today but for later) focuses more on writing, and we will talk about much of it. When talking about writing papers, he says, • Good writing requires revising, revising, and revising again. • Good modeling also requires revising, revising, and revising again.

18. Example of a non formal theory, “The Public Finance of Healthy Behavior” (http://www.ses.wsu.edu/People/faculty/rosenman/econs529/PFHB.pdf) • Uses two period state-preference: This is a fairly standard model in economics so doesn’t need extensive introduction. But explain how it differs from the norm: “… individuals decide in the first period of life is how much of their income to devote to self-protection which lowers the probability of becoming ill in the second period of life. In the second period of life a person finds himself or herself either healthy or sick, the probability of each outcome depending on how much self-protection was taken in the first period.” (page 4)

19. 2. Clearly state the innovations in the model: “All individuals live two periods. All are healthy in the first period, but face a probability of sickness in period 2. For individual i the probability of being healthy in period 2 is ρ(hi) where hi is the amount of period 1 (endowed) income devoted to building health, and 0≤ ρ(hi) ≤1 for i=w,p and ρ′(hi)>0 and ρ′′(hi)<0. Thus, by investing in health the individual can lower her probability of illness in period 2.” (page 7)

20. 3. Explain the meaning of assumptions: “Often investing in one’s health costs less than not doing so. Eating less takes less income than eating more; bicycling for transportation costs less than using a car. In the context of this model, however, that would make investing in health a free good as they would have to give up no other consumption to do so, and we would expect people to invest in their health until the marginal utility was zero. Moreover, the high-incidence of behaviorally related health problems such as obesity indicates that this is not the case; that in fact, improving ones health in some way lowers ones utility. The characterization of the utility arguments used here captures this idea. We implicitly assume there is no “fast lane” effect (Phelps, 2003, p. 106) of higher income on health, that is, those with greater incomes do not necessarily consume a less healthy lifestyle. At the same time, the “health spa” effect is possible because of the greater ability to invest in a healthier lifestyle that the greater income affords the individual.” (page 7)

22. Describe the results: “From (6a) we find that

23. In an empirical paper your model or theory section provides a logical and deductive argument that starts with your research question and ends with your proposed hypotheses. • Sets up a proposed “cause and effect” • Goal is to provide a logical and compelling deductive argument to support you inductive empirical analysis.

24. Econometric Modeling • Understand your strategy • Relate your approach and model to your theory • What are the testable hypotheses that come out of your theory, whether your theory is formal or informal • Make sure you recognize the feasible space and implications of your theory. • Decide on the type of empirical analysis you will be doing (regression, principal component, mean comparison, correlation, CGE model etc.). • Say in words why it is appropriate. • Say in words the economic assumptions implicit in the approach

25. Econometric Modeling (continued) • Specify a functional form and why it is appropriate • Say in words why it is appropriate. • Say in words the economic assumptions implicit in the approach • Formalize the underlying assumptions • Make a chart of expected signs and/or magnitudes. • Make a list of possible specification errors. • Follow the approaches you learn in econometrics, but be rigorous on robustness checks, especially in specification.