MODELING
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.
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.
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.
• 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
• 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?
•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.
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.
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
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.
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.
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.
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
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.
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.
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
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.
Example of a non formal theory, “The Public Finance of
Healthy Behavior”
(http://www.ses.wsu.edu/People/faculty/rosenman/econs529/PFHB.pdf)
1. 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)
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)
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 highincidence 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)
Describe the results:
“From (6a) we find that
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.
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
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.