Economics 421 - Econometrics

Final Exam for Winter 2011

Final and  answer key.

Final Exam for Winter 2009

The final exam for Winter 2009 is here.

Final Exam for Winter 2009

Final and answer key.

Topics for Final

We covered the following topics in the course:

1. Assumption required for estimates to be BLUE

2. Hypothesis testing:

a. t- tests (both one-sided and two-sided)
b. Joint hypotheses (F-Tests, Chi-square tests, etc.)

i.  Exclusion restrictions
ii. Linear combinations of parameters

3. Heteroskedasticity

a. What is heteroskedasticity?
b. How heteroskedasticity occur?
c. The consequences of estimating a heteroskedastic model with OLS
d. Tests

i.   LaGrange Multiplier Tests (Models  1, 2, and 3)

Model 1:
Model 2:
Model 3:

ii.  Goldfeld-Quandt test
iii. White's test

e. Corrections/Estimation procedures

i.   Multiplicative:
ii.  Feasible GLS

Model 1:
Model 2:
Model 3:

iii. White’s correction

8. Autocorrelation

a. What is it and why might it occur?
b. Consequences of ignoring serial correlation and estimating with OLS

i.   Model including a lagged dependent variable
ii.  Model with serially correlated errors
iii. Model with both a lagged dependent variable and serial correlated errors.

c. Tests for serial correlation

i.   The Durbin-Watson test.
ii.  Durbin's h-test.
iii. The Breusch-Godfrey test for higher order serial correlation.

d. Corrections

i.  Non-linear estimation
ii. The CORC procedure

9. Testing for ARCH errors

10. Stochastic Regressors and Measurement Errors

a. Assessing the bias and consistency of an estimator
b. Errors in variables

i. Consequences of estimating with OLS (differences in mismeasurement. of  the dependent variable and the independent variables).
ii. Application of errors in variables: Friedman's Permanent Income Hypothesis.

c. Instrumental variable estimation

i. What is an instrument.
ii. How is IV performed?
iii. Show how IV estimation can solve the problem of correlation of the right-hand side variables with the error term.

11. Simultaneous equation models

a. Structural equations (behavioral, identities, equilibrium conditions, technical equations) and reduced form equations. Endogenous, exogenous, and predetermined variables.
b. Consequences of ignoring simultaneity, i.e. demonstrate simultaneity bias.
c. Underidentified models, exactly identified models, and overidentified models

d. Estimation by 2SLS

12. Multicollinearity

a. What is multicollinearity and how does it affect OLS estimates and standard errors?
b. Detection of multicollinearity
c. What to do for perfect and imperfect multicollinearity.

13. Specification tests

a. LM test for adding a variable to a model

14. Qualitative and limited dependent variables

a. Linear probability model

i. description of model, problems, and estimation

b. Probit model

i. description of model and estimation

c. Logit model

i. description of model, attractive properties, and estimation

d. Limited dependent variables

i. description of the model when the dependent variable is limited, problems with OLS, and estimation

15. Maximum likelihood

a. Brief description of what maximum likelihood estimation does.
b. properties of maximum likelihood estimators.

Material for Lecture 19 on Thursday 3/10/11

Today:

• Review for final

Next Time:

• There is no next time

Video:

Material for Lecture 18 on Tuesday 3/8/11

Today:

• Finish Chapter 10 - Limited and Qualitative Dependent Variables
• Maximum Likelihood Estimation

Next Time:

• Review

Video:

Material for Lecture 17 on Thursday 3/3/11

Today:

• Begin Chapter 10 - Limited and Qualitative Dependent Variables

Next Time:

• Continue Chapter 10 - Limited and Qualitative Dependent Variables

Video:

Homework 8

1. Consider the following simple Keynesian macroeconomic model of the U.S. economy. [Macro data set]

Y_t = CO_t + I_t + G_t + NX_t

COt = β₀ + β₁YD_t + β₂CO_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
CO_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

Endogenous variables: Y_t, YD_t, CO_t, I_t, r_t,
Exogenous and predetermined variables: G_t, NX_t, T_t, M_t, CO_t-1, and r_t-1

(a) Using OLS, estimate equations for CO_t and I_t.
(b) Using 2SLS, estimate equations for CO_t and I_t.

2. Finish your project. It is due at the beginning of class on Thursday, March 10.

Project Write-Up

Here's a few general guidelines to help with the write-up of your empirical project. Let me stress once again that your main goal for the project is to show that you understand how to use the tools and techniques we learned in class:

1. Introduction

Introduce the problem and discuss the question you are trying to answer with your empirical project.

2. Theory and Hypotheses

Discuss the theory underlying your model and state the hypotheses you are going to test. You should also state the significance levels you will use in your tests.

3. Empirical Model and Data

Present the empirical model you are using to test your hypotheses. This is where specification issues should be addressed. For example, did you log your data? Did you include squared terms or interactions? Are there any important omitted variables? If so, what are the consequences? Did you use tests to see if variables you weren’t sure about belong in the model? You should also discuss the data and data sources in this section.

4. Violations of Assumptions

At this point, you have the basic empirical model specified and you have discussed specification issues. You should now discuss potential violations of the Guass-Markov conditions. The goal is to test for heteroskedasticity or serial correlation, and then either correct your model for the problem if it exists, or describe how you would have corrected the model had you found a problem. There are direct tests for heteroskedasticity and autocorrelation, but you should also discuss any other notable violations of the assumptions that may be present in your model and how those will be handled or accounted for. For example, are measurement errors a problem? Do you need to use instrumental variables to solve any endogeneity problems?

5. Results

Now that you have described the specification of the model, and described how you checked and corrected for any problems that exist, you are now ready to present estimates of your final model. After presenting the final estimates, you should discuss the overall fit of the model, and interpret the coefficients. What do the coefficients tell you? This is also the section where you should present the test results for the hypotheses you are examining, and then discuss the results.

6. Conclusion

What did you learn? Did the data support your hypotheses? How could you improve the model? What could you do in a follow-up study to learn more about this topic?