Econ 170 -- Spring 2005

Midterm 2 Notes

#9: On the answer sheet 0.568 should be 0.0568.

Discrete Dependent Variables

A linear model with a normally distributed error term does not logically explain a dependent variable that only takes on two values.

The logit and probit models are much more elegant.

Implementing 2SLS in Stata

Term Paper

Ways to present regressions:

1. As equations set off in text

2. As tables

Term Paper Specifications

Due: 5/3

How long does my term paper have to be?

]]> It has to have sections.

Cover Sheet (name, title, date)

1. Introduction (1 page)

Two approaches:
a) para 1 "___ is an interesting/important question."
para 2 "This paper is about that."
b) para 1 "This paper is about ..."
goal: to reach people who only read introductions.

2. The Model (2 pages)
justify lhs variables. justify rhs variables.

3. The Data (1 page and a table)

4. Empirical Results (2 pages text (3 with equations), n pages tables)
regressions in text as equations
regression in tables
regressions in Stata format (log file, using fixed pitch (courier))
(Pros watch the number of decimal digits.)
Tables on separate pages is fine.

5. Summary and Conclusions (1 page)
Restate goal more briefly that in the introduction.
What did we learn?
Goal: Catch people who flip to the conclusions.

Every paragraph has a topic sentence, which comes first unless you have a really good reason for breaking this rule.

Every sentence has a subject and a verb, in that order unless you have a really good reason for breaking this rule.

Decide whether "I" wrote the report, "We" wrote the report, or nobody wrote the report and then be consistent.

Try not to "run regressions".

Identification and Two-Stage Least Squares

Identification is required for parameter estimation to be possible. Two-stage least squares is a common method for estimating identified equations.

]]> We have already discussed the covariance between the right-hand side endogenous variable P and the two structural equation error terms.

Tw--stage least squars (2SLS) plugs in reducted form equation predictions for endogenous right-hand side variables and then, in stage two, estimates a structural equation with "hatted" variables. This works because the hatted variables are not functions of the structural equation error terms.

2SLS is possible only if an equation is identified. Otherwide, there is exact collinearity in the second stage.

The excluded variables that identify an equation shifts equations other than the one that is being identified.

Is a simple IS-LM model identified? It depends on whether you think that monetary and fiscal policy set the money supply and deficit without any concern for Y. This assumption would fly in the face of often stated objectives of these policies.

2SLS with Stata

To run two stage least squares with Stata, use the ivreg command. This is in the menu as Statistics | Linear regression and related | Multiple equation models | Instrumental variables and two-stage least squares.

Here is a log file with a 2SLS regression of rate on percapinc poverty and crimespendpc, where over64 is an instrumental variable.

Term Paper

The term paper is due at the final exam.

You can choose to use your own data or one of the following:

Bureau of Labor Statistics survey
BLS data
useful notes

St. Louis Federal Reserve Bank
FRED

Simultaneity

When the right-hand side regressors are correlated with the error term, the parameters estimates are not consistent. This problem arises with simultaneous equations systems, which includes most economics models.

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A graphical view of the model:

ch. 13 help

Hints for the homework: log file.

The Number of Equations

Supply and Demand involves two curves and two equations.

A regression model involves one curve and one equation. There is a fundamental mismatch.

Who Pays a Sales Tax?

We started our discussion of simultaneous equations models with a classic example.

]]> The basic diagram has two supply curves, one for the price paid by the consumer (with tax) and one for the price received by the supplier (without tax).

The supply curve comes from the Theory of the Firm. This analysis leads to Q on the horizontal axis.

Who pays the sales tax depends on the slopes of the supply and demand curves.

Heteroskedasticity

Plotting the data or, especially, the residuals vs. one of the regressors is an effective test for heteroskedasticity. The Goldfeld-Quandt test formalizes the concept by looking at the residual variance for the largest third and the smallest third of the values for x.

A simple model of the process generating the heteroskedasticity leads to a simple transformation to homoskedasticity.

Another pattern (not heteroskasticity) might also be apparent from a plot of the residuals. Here we see a classic case of the wrong functional form.

Heteroskeasticity is really important in financial market research when it takes the form of Autoregressive Conditional Heteroskedasticity (ARCH). The prices of assets vary with their risk, which can be viewed as their conditional variance.

HW

Due Tuesday 4/5: Chapter 12, #1-7.

Due Thursday 3/31: the following exercise that can be based largely on the do file mc2-rho.do
.

]]> Consider 3 models:

1) y = a + b*x + e

2) y = a + b*x + u

3) y = a + b*x + c*y[-1] + e,

where u = rho*u[-1] + e and e is an i.i.d. normally distributed error term. You could estimate four models:

A) y = a + b*x + e (ignore possible serial correlation)

B) y = a + b*x + u (Cochrane-Orcutt, estimate rho)

C) y = a + b*x + c*y[-1] + e

D) y = a + c*y[-1] + e.

For all combinations of data generating processes (1, 2, 3) and estimated models (A, B,C, D), run simulations sufficient to understand the properties of the estimated models given each DGP. Make a table of some sort to illustrate your results (including dwstat).

For serious students: How do your results depend on the values of rho and a, b, and c?

Serially Correlated Errors