Economics 421 - Econometrics

Video Lecture Files

Video Lectures for Winter 2008
Lecture 1 Media Player Google Video wmv MPEG4 mov	Lecture 7 Media Player Google Video wmv MPEG4 mov	Lecture 13 Media Player Google Video wmv MPEG4 mov
Lecture 2 Media Player Google Video wmv MPEG4 mov	Lecture 8 Media Player Google Video wmv MPEG4 mov	Lecture 14 Media Player Google Video wmv MPEG4 mov
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Lecture 4 Media Player Google Video wmv MPEG4 mov	Lecture 10 Media Player Google Video wmv MPEG4 mov	Lecture 16 Media Player Google Video wmv MPEG4 mov
Lecture 5 Media Player Google Video wmv MPEG4 mov	Lecture 11 Media Player Google Video wmv MPEG4 mov	Lecture 17 Media Player Google Video wmv MPEG4 mov
Lecture 6 Media Player Google Video wmv MPEG4 mov	Lecture 12 Media Player Google Video wmv MPEG4 mov	Lecture 18 Media Player Google Video wmv MPEG4 mov

[Link to videos from other classes]

The Media Player and Google Video links go to new pages with embedded video players. The other links are for downloads (right click). If you have any problems, please let me know.

Syllabus for Winter 2008

Introduction to Econometrics
Course: Economics 421/521
Professor: Mark Thoma
Office/Hours: PLC 471 on W/F 12:30-1:30 p.m.
Phone/Email: (541) 346-4673, mthoma@uoregon.edu
Web Page: http://economistsview.typepad.com/economics421/

Course Description: This course is a continuation of the econometrics sequence. The first course, EC 420/520, introduces the linear regression model and discusses estimation and testing under (mostly) ideal conditions. This course looks at what happens when the conditions are less than ideal due to departures from the assumptions necessary for ordinary least squares to be the best linear unbiased estimator, and provides alternative regression techniques that address  problems arising from the violations of the basic assumptions.

Text: Dougherty, Christopher, Introduction to Econometrics, 3rd ed. (Oxford: University Press, 2007)

Prerequisites: Economics 420 or the equivalent.

GTFs, Office Hours, Location, and Email Address:

Eric Gaus	T    1:00-2:00	PLC 516	egaus@uoregon.edu
Ania Aksan	M 12:30-1:30	PLC 516	aaksan@uoregon.edu

Lab Times:

Lab	21718	1600-1720	Wed	442 MCK
Lab	21719	1800-1920	Wed	442 MCK
Lab	25801	2000-2120	Wed	442 MCK

Tests and Grading: There will be two midterm exams and a final. The midterms will be given Thursday, January 31st and Thursday, February 28th. The final will be given on Thursday, March 20th at 1:00 p.m. No make-up exams will be given. Each midterm is worth 20% and the final is worth 30%. Grades will be assigned according to your relative standing in the class.

Empirical Project: There will be an empirical paper that will comprise 10% of your grade. The paper is due no later than Thursday, March 13 at the beginning of class. Details will be given during lecture.

Computer Labs: The statistical software package EViews will be used for estimation and testing. Labs will consist of instruction and examples helpful in completing the homework assignments, and other activities. The homework is worth 20% of your grade.

*Tentative* Course Outline:

We will cover the following chapters:
Specification of regression models	Ch. 6
Heteroscedasticity	Ch. 7
Autocorrelation	Ch.12
Stochastic regressors and measurement errors	Ch. 8
Simultaneous Equations Estimation	Ch. 9
And, as time permits:
Binary Choice Models and Maximum Likelihood Estimation	Ch. 10
Models Using Time Series Data	Ch. 11

More details on the readings, homework, homework due dates, etc. will be posted here on an ongoing basis, so please check back regularly.

Final Exam for Winter 2008

Final and answer key.

Topics for Final

We have covered the following topics in the course:

1. Uses of regression models

a. Hypothesis testing
b. Prediction

2. Assumptions required for OLS estimator to be BLUE

3. Hypothesis testing:

a. t- tests (both one-sided and two-sided)
b. F-Tests (tests that coefficients are jointly zero and tests involving linear combinations of the coefficients)
c.  Chi-Squared tests

4. The Types of Specification Error

5. Consequences of including an irrelevant variable

6. Consequences of excluding a relevant variable

7. Heteroskedasticity

a. How heteroskedasticity might arise
b. The consequences of estimating a heteroskedastic model with OLS
c. Tests

i. Goldfeld-Quandt
ii. White's
iii. LaGrange Multiplier Tests (Models  1, 2, and 3)

d. Corrections

i. Multiplicative:
ii. Model 1:
iii. Model 2:
iv. Model 3:
v. White’s (We didn’t give an explicit function for this one)

8. Autocorrelation

a. Assumptions required for estimators to be BLUE.
b. Assessing potential bias of an estimator.
c. Consequences of ignoring serial correlation and estimating with OLS.

Topics covered after Midterm 1:

d. Tests for serial correlation

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

e. The CORC procedure

f. Corrections for higher-order serial correlation and search procedures

i. Estimating a model with higher order serial correlation using a generalized CORC procedure.
ii. Hildreth-Lu search procedure.

9. 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.

10. 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

Topics covered after Midterm 2:

d. Estimation by 2SLS

11. 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.

12. Specification tests

a. LM test for adding a variable to a model (with and without endogeneity)

13. 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, OLS when the dependent variable is limited, and estimation

14. Maximum likelihood

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

 

Material for Thursday 3/13/08

Today:

• Finish chapter 10
  

Video:

Lecture 18 [Google video] - Winter 2008
Lecture 18 [Windows Media] - Winter 2008

Economics 421 Lecture 18

Material for Tuesday 3/11/08

Today:

• Discuss project, continue chapter 10
  

Next Time:

• Finish chapter 10
  

Video:

Lecture 17 [Google video] - Winter 2008
Lecture 17 [Windows Media] - Winter 2008

Economics 421 Lecture 17

Material for Thursday 3/6/08

Today:

• Discuss project, begin chapter 10
  

Next Time:

• Continue chapter 10
  

Video:

Lecture 16 [Google video] - Winter 2008
Lecture 16 [Windows Media] - Winter 2008

Economics 421 Lecture 16

Material for Tuesday 3/4/08

Today:

• Multicollinearity and other specification issues
  

Next Time:

• Finish specification tests, start chapter 10
  

Video:

Lecture 15 [Google video] - Winter 2008
Lecture 15 [Windows Media] - Winter 2008

Economics 421 Lecture 15

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 and turn it in on Wednesday, March 12 in lab.

Midterm 2

Midterm 2 and solution.

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 worry about violations of the Guass-Markov conditions. The goal is to test for, 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

After describing the specification of the model, describing how you checked for problems and corrected for those 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?

Scores, Distribution, and Grades for Midterm 2

The scores for midterm 2 are available in Blackboard, and the grades and distribution are discussed on this page.

Material for Tuesday 2/26/08

Today:

• Continue with chapter 9

Next Time:

• Midterm 2

Video:

Lecture 14 [Google video] - Winter 2008
Lecture 14 [Windows Media] - Winter 2008

Economics 421 Lecture 14

Topics for Exam 2

We have covered the following topics since the last midterm:

Serial Correlation (continued)

1. Tests for serial correlation

a. The Durbin-Watson test.
b. Durbin's h-test.
c. The Breusch-Godfrey test for higher order serial correlation.

2. The CORC procedure

3. Corrections for higher-order serial correlation and search procedures

a. Estimating a model with higher order serial correlation using a generalized CORC procedure.
b. Hildreth-Lu search procedure.

Stochastic Regressors and Measurement Errors

3. Assessing the bias and consistency of an estimator

4. Errors in variables

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

5. Instrumental variable estimation

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

Simultaneous equation models

6. Structural equations (behavioral, identities, equilibrium conditions, technical equations) and reduced form equations. Endogenous, exogenous, and predetermined variables

7. Consequences of ignoring simultaneity, i.e. demonstrate simultaneity bias

8. Underidentified models, exactly identified models, and overidentified models

Material for Thursday 2/21/08

Today:

• Continue with chapter 9

Next Time:

• Continue with chapter 9

Video:

Lecture 13 [Google video] - Winter 2008
Lecture 13 [Windows Media] - Winter 2008

Economics 421 Lecture 13

Homework 7

1. 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.

2. Problem 9.3 on page 276 of the text.

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).

Material for Tuesday 2/19/08

Today:

• Begin chapter 9

Next Time:

• Continue with chapter 9

Video:

Lecture 12 [Google video] - Winter 2008
Lecture 12 [Windows Media] - Winter 2008

Economics 421 Lecture 12

Material for Thursday 2/14/08

Today:

• Finish chapter 8 (through page 366).

Next Time:

• Begin chapter 9.

Video:

Lecture 11 [Google video] - Winter 2008
Lecture 11 [Windows Media] - Winter 2008

Economics 421 Lecture 11

Homework 6

1. Continuing with the model we used in problem 4 of  Homework 4, i.e. the regression of real consumption (C) on real disposable income (DI), use the CORC procedure to correct the model for the presence of first-order serial correlation. [List the values of rho at each step, and include the final estimates].

2. Problem 8.3 on page 253.

3. Problem 8.4 on page 253.

4. What are the three requirements for a good instrumental variable?

5. Problem 8.10 on page 268 (skip the Hausman-Wu test). Here is the data set. [Note: The variables are EARNINGS=earnings (be sure to take the log), S=years schooling, EXPER=work experience, ASVABC=composite standardized test score, SM=years mother in school, SF=years father in school, SIBLINGS=number of siblings, and LIBRARY=member of family had library card when respondent was 14.] There are eight data series and 540 observations. Also, the name of the variable EXP has been changed to EXPER since EXP is an illegal name.

Material for Tuesday 2/12/08

Today:

• Finish chapter 12 (through page 366), begin chapter 8.

Next Time:

• Continue chapter 8.

Video:

Lecture 10 [Google video] - Winter 2008
Lecture 10 [Windows Media] - Winter 2008

Economics 421 Lecture 10

Run, Run, Run Those Regressions Away...

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

Material for Thursday 2/7/08

Today:

• Finish chapter 12 (through page 366).

Next Time:

• Begin chapter 8.

Video:

Lecture 9 [Google video] - Winter 2008
Lecture 9 [Windows Media] - Winter 2008

Economics 421 Lecture 9

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. Also, equation (9.7) is the equation for the residuals, i.e. u_t = ρu_t-1 + e_t, or use the approximation ρ = 1 - .5d, where d is the Durbin-Watson statistic (see text).

Homework 5

[Due in lab on Wednesday 2/13. Homework 4 is also due on 2/13.]

1. Continuing with the model we used in problem 4 of  Homework 4, i.e. the regression of real consumption (C) on real disposable income (DI), test for the presence of fourth order serial correlation.

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

Material for Tuesday 2/5/08

Today:

• Continue chapter 12 on serial correlation.

Next Time:

• Finish chapter 12 (through page 366).

Video:

Lecture 8 [Google video] - Winter 2008
Lecture 8 [Windows Media] - Winter 2008

Economics 421 Lecture 8

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 1

Midterm 1 and solution.

Topics for Exam 1

We have covered the following topics

1. Uses of regression models

a. Hypothesis testing
b. Prediction

2. Assumptions required for OLS estimator to be BLUE

3. Hypothesis testing:

a. t- tests (both one-sided and two-sided)
b. F-Tests (tests that coefficients are jointly zero and tests involving linear combinations of the coefficients)
c.  Chi-Squared tests

4. The Types of Specification Error

5. Consequences of including an irrelevant variable

6. Consequences of excluding a relevant variable

7. Heteroskedasticity

a. How heteroskedasticity might arise
b. The consequences of estimating a heteroskedastic model with OLS
c. Tests

Goldfeld-Quandt
White
LaGrange Multiplier Tests (Models  1, 2, and 3)

d. Corrections

Multiplicative         
Model 1                     
Model 2                     
Model 3                     
White’s                       (We didn’t give an explicit function for this one)

8. Autocorrelation

a. Assumptions required for estimators to be BLUE.
b. Assessing potential bias of an estimator.
c. Consequences of ignoring serial correlation and estimating with OLS.

Material for Tuesday 1/29/08

Today:

• Begin chapter 12 on serial correlation.

Next Time:

• Midterm 1

Video:

Lecture 7 [Google video] - Winter 2008
Lecture 7 [Windows Media] - Winter 2008

Economics 421 Lecture 7

Homework 4

Economics 421/521
Winter 2008
Homework #4

1. What are the consequences of estimating an autoregressive model using OLS?

2. Perform a Durbin-Watson test at the 5% level of significance for positive first-order autocorrelation using the following regression output (standard errors in parentheses):

Y_t = 2.0 + 3.7*X_1t - 4.4*X_2t,    T = 42
       (.7)   (1.1)          (2.8)           DW = 1.22

3. Recall the model from homework 1:

Given data on M2, real GDP, and the T-bill rate, estimate the following regression...:

M_t = β₀ +   β₁RGDP_t +   β₂Tbill_t + e_t

Don't be surprised if the fit is very good - we'll explain why that may be misleading later in the course.

Does model suffer from serial correlation? Use a Durbin-Watson test to answer the question. Is the fit as good as the R² and t-statistics indicate?

4. Regress real consumption (C) on real disposable income (DI) and test for serial correlation using a Durbin-Watson test. The data are here (the data are quarterly, and span the time period 1947:Q1 - 2007:Q3).

5. Explain why the Durbin Watson statistic is always between 0 and 4. Also explain why the Durbin-Watson statistic is between 0 and 2 when there is positive serial correlation, between 2 and 4 when there is negative serial correlation, and equal to 2 when there is no correlation at all.

Material for Thursday 1/24/08

Today:

• Finish chapter 7 on heteroskedasticity.

Next Time:

• Begin chapter 12 on serial correlation.

Video:

Lecture 6 [Google video] - Winter 2008
Lecture 6 [Windows Media] - Winter 2008

Economics 421 Lecture 6

Homework 3

The assignment will be handed out in lab this week (1/23), and will be due in lab next week (1/30):

1. Problem 7.1 in the text.

2. Problem 7.2 in the text.

[Note: pdf of problems 7.1 and 7.2]

3. What are the consequences of heteroskedasticity, i.e. if you estimate a hetroeskedastic model with OLS, what problems will you encounter?

4. Using this data set, repeat the example from class, i.e. first regress the log of salary on a constant and the two variables proxying for experience, years and years squared (years²):

     log(salary) = β₀ + β₁*years + β₂*years² + u_t

Then, form either the residual squared (resid²), the absolute value of the residual (|resid|), or the log of the residual squared (log(resid²)) as appropriate and perform the three LM tests for heteroskedasticity (note: resid is the estimated value of u_t).

5. Using the second model of heteroskedasticity, i.e. that |resid| = α₀ + α₁*years + α₂*years², correct the salary model in problem 4 for hetroskedasticity and reestimate.

6. Test the salary model in problem 4 for heteroskedasticty using White's test. Correct the standard errors using White's correction. How do the coefficients and corrected standard errors compare to those obtained in problem 5?

Material for Tuesday 1/22/08

Today:

• Continue with chapter 7 on heteroskedasticity.

Next Time:

• Finish any remaining material from chapter 7, begin chapter 12 on serial correlation.

Video:

Lecture 5 [Google video] - Winter 2008
Lecture 5 [Windows Media] - Winter 2008

Economics 421 Lecture 5

Material for Thursday 1/17/08

Today:

• Continue with chapter 7 on heteroskedasticity.

Next Time:

• More chapter 7

Video:

Lecture 4 [Google video] - Winter 2008
Lecture4 [Windows Media] - Winter 2008

Economics 421 Lecture 4

Copies of Chapters 6, 7, and 12

Here are copies of the first three chapters we will cover in the textbook, chapters 6, 7, and 12:

PDF of Chapters 6, 7, and 12

Homework 2

Economics 421/521
Winter 2008
Homework #2

The assignment will be handed out in lab this week (1/16), and will be due in lab next week (1/23).

1. Assume that you’ve been hired by the surgeon general of the United States to study the determinants of smoking behavior and that you estimate the following cross-sectional model based on data for 1988 from all 50 states (standard errors in parentheses):

          Ĉi = 100 – 9.0Ei + 1.0Ii - 0.04Ti – 3.0Vi + 1.5Ri
                (36.)  (3.5)   (.75)   (0.05)   (.90)   (0.3)

          R2 = .57 n = 50 (states)

where C_i = the number of cigarettes consumed per day per person in the i^th state, E_i = the average years of education for persons over 21 in the i^th state, I_i = the average income in the i^th state (thousands of dollars), T_i = the tax per package of cigarettes in the i^th state (cents), V_i = the number of video ads against smoking aired on the three major networks in the i^th state, and R_i = the number of radio ads against smoking aired on the five largest radio networks in the i^th state. (a) Develop and test (at the 5% level) appropriate hypotheses for the coefficients of the variables in this equation. (b) Do you appear to have any irrelevant variables? Do you appear to have any omitted variables? Explain. (c) Assume your answer to part (b) was yes to both. Which problem is generally more troublesome, irrelevant variables or omitted variables? Why? (d) One of the purposes of estimating this equation was to determine the effectiveness of antismoking advertising on television and radio. What is your conclusion?

2. First, using the EAEF data set, take the natural log of EARNINGS to form the transformed variable LGEARN. Then do problem 6.2 on page 207 of the text, repeated here for convenience:

Using your EAEF data set, regress LGEARN

(1) on S and EXP,
(2) on S only, and
(3) on EXP only.

Compare the coefficients of S in regressions (1) and (2). Give both mathematical and intuitive explanations of the direction of the change. Also compare the coefficients of EXP in regressions (1) and (3) and explain the direction of change.

3. Using the EAEF data set, regress LGEARN on S, EXP, and ASVABC. Use an F-test to determine whether S and EXP are jointly significant.

4. Using the EAEF data set, regress LGEARN on S, EXP, and ASVABC. Use an F-test to determine whether the coefficients on S and EXP are equal. ________________________________________________________

Note: Variable definitions (see pages. 443-444 in Appendix B of the text):

EARNINGS = current hourly earnings in $ reported in 2002 interview.
S = Years of schooling (highest grade completed as of 2002).
EXP = Total out-of-school work experience (years) as of the 2002 interview.
ASVABC = Scaled standardized test score.

Material for Tuesday 1/15/08

Today:

• Continue with chapter 6
• Begin chapter 7 on heteroskedasticity.

Next Time:

• Continue with chapter 7

Video:

Lecture 3 [Google video] - Winter 2008
Lecture3 [Windows Media] - Winter 2008

Economics 421 Lecture 3

Material for Thursday 1/10/08

Today:

• Review of hypothesis testing
• Chapter 6
  

Next Time:

• Chapter 7 - Heteroskedasticity

Video:

Lecture 2 [Google video] - Winter 2008
Lecture2 [Windows Media] - Winter 2008

Note: The video operator did not show up, so I had to leave the camera in a stationary position during class. Thus, the quality of this video isn't is good as I'd hoped, but it should be good enough to suffice. I set the camera a bit low, so you will find yourself wishing that the camera could be tilted up just a little bit as it plays. But not much is missed.

Economics 421 Lecture 2

Material for Tuesday 1/8/08

Today:

• Review of regression models
• Assumptions required for estimates to be BLUE ( pgs. 68-71 and 127-128)
• Guass-Markov Theorem (pg. 90-93)

Next Time:

• Chapter 6

Video: 

Lecture 1 [Google video] - Winter 2008
Lecture 1 [Windows Media] - Winter 2008

Economics 421 Lecture 1

Homework 1

[Note: The assignment will be handed out in lab this week, and will be due in lab next week.]

Economics 421/521
Winter 2008
Homework #1

Part I. Hypothesis Testing

1. Suppose that you estimate a model of house prices to determine the impact of having beach frontage on the value of a house. After researching the problem, you decide to use the size of the lot instead of the size of the house as your explanatory variable for a number of theoretical and data availability reasons. The results (standard errors in parentheses) are:

PRICEi = 40 + 35.0 LOTi – 2.0 AGEi + 10.0 BEDi – 4.0 FIREi + 100 BEACHi
        (29) (5.0)       (1.1)      (10.0)      (3.0)       (9.0)

where n = 30, R2 = .63, and PRICE_i = the price of the i^th house (in thousands of dollars), LOT_i = the size of the lot of the i^th house (in thousands of square feet), AGE_i = the age of the i^th house in years, BED_i = the number of bedrooms in the i^th house, FIRE_i = a dummy variable for a fireplace (1 = yes for the ith house), and BEACH_i = a dummy for having beach frontage (1 = yes for the ith house).

a) You expect the variables LOT, BED, and BEACH to have positive coefficients. Test this hypothesis at the 5 percent level.

b) You expect AGE to have a negative coefficient. Test this hypothesis at the 10 percent level.

c) At first you expect FIRE to have a positive coefficient, but one of your friends says that fireplaces are messy and are a pain to keep clean, so you are not sure. Run a two-sided t-test around zero to test the two-sided hypothesis at the 5 percent level.

2. Consider the following regression:

log(Qci) = 921.6 – 1.3 log(Pci) + 0.7 log(Pai) + 11.4 log(Inci) 
           (121)  (0.3)          (0.05)          (2.8)

where n = 30, R2 = 0.82, and  where Qc_i = the total sales of CAMRY in the ith city in 2003, Pc_i = the price of a CAMRY in the i^th city in 2003 (in thousands), Pa_i = the price of an ACCORD in the i^th city in 2003 (in thousands), and Inc_i = the average income in the i^th city, the year of 2003 (in thousands). The numbers in the parentheses are standard errors.

a) How is the constant term interpreted?

b) How would you interpret the coefficient on log(Pc_i). Be explicit and explain, in terms of economic theory, the importance of its magnitude.

c) Get t-values for the coefficients in the regression. Are all of our coefficients statistically significant at the 5% level of significance? How about at the 1% level of significance?

d) Interpret R². Can we have a negative R²?

Part II. Short Answer

1. State the Gauss-Markov Theorem and explain the term BLUE.

Part III. Estimation

1. Given data on M2, real GDP, and the T-bill rate, estimate the following regression and test whether the coefficients differ from zero. Do the coefficinets have the expected signs?:

M_t = β₀ + β₁RGDP_t + β₂Tbill_t + e_t

Don't be surprised if the fit is very good - we'll explain why that may be misleading later in the course.