Economics 421 - Econometrics

Material for Lecture 16 on Tuesday 3/1/11

Today:

• Finish Chapter 9 - Simultaneous Equations Estimation
• Begin Chapter 10 - Limited and Qualitative Dependent Variables

Next Time:

• Continue Chapter 10 - Limited and Qualitative Dependent Variables

Video:

Material for Lecture 15 on Thursday 2/24/11

Today:

• Continue Chapter 9 - Simultaneous Equations Estimation

Next Time:

• Finish Chapter 9 - Simultaneous Equations Estimation, perhaps start Chapter 10

Video:

Run, Run, Run Those Regressions Away...

Even if I could sing, I wouldn't do this:

Homework 7

1. Problem 9.3 on page 276 of the text.

2. For the model

Q_t = a₀ + a₁P_t + a₂Y_t + a₃X_t + a₄Z_t + u_t
P_t = b₀ + b₁Q_t + b₂Y_t + b₃W_t + v_t
Y_t = c₀ + c₁P_t + c₂W_t + w_t

Determine whether each equation is under, exactly, or over identified. Assume that Q, P, and Y are endogenous, and that the constant, X, Z, and W are exogenous.

3. Answer the following questions about your project:

(i) Do you expect any measurement problems, i.e. do you expect to have errors in variables problems? If so, what effect will that have on your estimates and test statistics (if you don't think this will be a problem, say that and explain why, and then say, but if I did have this problem it would cause the following difficulties and then describe the effect it would have on the estimates and test statistics). How can the problem be fixed?

(ii) Are there any important omitted variables? If so, what effect would the omitted variables have on the estimates and test statistics? (And again, even if you think you have every important variable, show that you understand this issue by explaining what types of problems it causes).

(iii) Do you expect problems with endogeneity bias (endogenous varaibles on the right-hand side of the equation that are correlated with the error term)?  Think hard about this one, and if you do have this problem, what is the solution?

Material for Lecture 14 on Tuesday 2/22/11

Today:

• Continue Chapter 9 - Simultaneous Equations Estimation

Next Time:

• Continue Chapter 9 - Simultaneous Equations Estimation

Video:

Material for Lecture 13 on Thursday 2/17/11

Today:

• Finish Chapter 8 - Stochastic Regressors and Measurement Errors
• Begin Chapter 9 - Simultaneous Equations Estimation

Next Time:

• Continue Chapter 9 - Simultaneous Equations Estimation

Video:

Homework 6

1. Problem 8.5 on page 253, part 1 only.

2. Consider the following simple Keynesian macroeconomic model of the U.S. economy.

Y_t = C_t + I_t + G_t + NX_t

C_t = β₀ + β₁YD_t + β₂C_t-1 + ε_1t

YD_t = Y_t – T_t

I_t = β₃ + β₄Y_t + β₅r_t-1 + ε_2t

r_t = β₆ + β₇Y_t + β₈M_t + ε_3t

where:

Y_t = gross domestic product (GDP) in year t
C_t = total personal consumption in year t
I_t = total gross private domestic investment in year t
G_t = government purchases of goods and services in year t
NX_t = net exports of goods and services (exports - imports) in year t
T_t = taxes in year t
r_t = the interest rate in year t
M_t = the money supply in year t
YD_t = disposable income in year t

The endogenous variables are Y_t, C_t, I_t, YD_t, and r_t. The exogenous and predetermined variables are G_t, NX_t, C_t-1, T_t, r_t-1, and M_t.  Find the reduced form equations for this model.

3. (a) For your project, what econometric model do you plan to estimate and what hypothesis or hypotheses do you plan to test? (b) Depending upon whether your data are time-series or cross-sectional, test the model for autocorrelation or heteroskedasticity. (c) If you find a problem with either, explain explicitly how you plan to correct for it. If the tests do not indicate a problem, explain how you would have corrected for the problem had the test come out the other way (that is, no matter how the test comes out, explain how to correct for the problem of heteroskedasticity or autocorrelation as appropriate for your model. You don't have to actually do the correction for this homework (though if it was present, you would do the correction for the project), just explain how to do it.).

Material for Lecture 12 on Tuesday 2/15/11

Today:

• Continue Chapter 8 - Stochastic Regressors and Measurement Errors
• Begin Chapter 9 - Simultaneous Equations Estimation

Next Time:

• Continue Chapter 9 - Simultaneous Equations Estimation

Video:

Material for Lecture 11 on Thursday 2/10/11

Today:

• Begin Chapter 8 - Stochastic Regressors and Measurement Errors

Next Time:

• Continue Chapter 8

Video:

The Cochrane-Orcutt Procedure

The Cochrane-Orcutt procedure:

One note: In step 5 when it says to use the estimated betas obtained in step 4 in equation  (9.5),  this means to go back to the origanal equation (9.5) and find u_t = Y_t - b₁ - b₂X_2t  - ... - b_kX_kt where the b's are the estimated betas using the transformed ("starred") variables in step 4. However, be careful about obtaining the value of b₁. Note from above in equation (9.9) that you have to divide the estimate of the constant from the regression involving the "starred" values by 1-ρ in order to obtain b₁.

Homework 5

1. Complete steps 1 through 3 of the Empirical Project Outline (as discussed in class).

2. Problem 8.3 on page 253.

3. What are the three requirements for a good instrumental variable? [We'll cover this on Tuesday.]

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[Note: The *next* homework will ask: (a) For your project, what econometric model do you plan to estimate and what hypothesis or hypotheses do you plan to test? (b) Depending upon whether your data are time-series or cross-sectional, test the model for autocorrelation or heteroskedasticity. (c) If you find a problem with either, explain explicitly how you plan to correct for it. If the tests do not indicate a problem, explain how you would have corrected for the problem had the test come out the other way (that is, no matter how the test comes out, explain how to correct for the problem of heteroskedasticity or autocorrelation as appropriate for your model).]

Material for Lecture 10 on Tuesday 2/8/11

Today:

• Finish Chapter 12 - Autocorrelation
• Discuss projects
• Begin Chapter 8 - Stochastic Regressors and Measurement Errors

Next Time:

• Continue Chapter 8

Video:

Empirical Project Outline

Here is a brief outline of the project. We will talk more about this in class:

1. Statement of theory and hypothesis

• What is the hypothesis or hypotheses that you are testing? Be explicit.
• What does theory say about each hypothesis you are interested in testing, i.e. what are the theoretical predictions?

2. Specification of the econometric model

• Specify the econometric model you will estimate. What variables will be in the model? Will you take logs, add squares of variables, or do any other transformations of the data?
• What sign do you expect each coefficient to have, and what is the interpretation of the coefficients?
• Do you expect to have any trouble with the error term such as serial correlation or heteroskedasticity?

3. Obtain data

• What would an ideal data set look like? What data are actually available? Where will you get the data. Be specific about data sources.

4. Estimation of the econometric model and diagnostic tests

• What estimation technique will you use?
• What problems will you test for? If you detect problems, how will you correct for them?

5. Test hypotheses

• What tests will you conduct and what significance level will you use to evaluate the outcome?

6. Forecasting or prediction

• How can you use the model you have estimated to make forecasts or predictions?

It will take longer than you think to do the estimation stage, so give yourself plenty of time. When the project is finished, it may or may not turn out the way you hoped. That's okay, you will not be graded on how clever you are at finding an interesting hypothesis to investigate, or on whether you find out anything particularly noteworthy when you are done, though you might. The goal is for you to illustrate that you know how to use the tools and techniques that we learn in class, and that is the basis for the evaluation of the projects.

Midterm

Midterm and Solution.