Economics 421 - Econometrics

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.

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
Lecture 3 Media Player Google Video wmv MPEG4 mov	Lecture 9 Media Player Google Video wmv MPEG4 mov	Lecture 15 Media Player Google Video wmv MPEG4 mov
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.

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

Homework 8 Solution

1. (a) After the data have been read in:

Do OLS on

COt = β₀ + β₁YD_t + β₂CO_t-1 + ε_1t

by running

with the result

Next, do OLS on

I_t = β₃ + β₄Y_t + β₅r_t-1 + ε_2t

by running

with the result

(b) Use 2SLS to estimate

COt = β₀ + β₁YD_t + β₂CO_t-1 + ε_1t

by running

with the result

Next, use 2SLS to estimate

I_t = β₃ + β₄Y_t + β₅r_t-1 + ε_2t

by running

with the result

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.

Homework 7 Solution

Solution to Homework 7 (homework is here).

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

Homework 6 - Solution

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].

The first step is to do an OLS regression of CONS (I renamed C as CONS since C is a constant in the program):

Next, save the residuals as UHAT1 (or a name of your choice) and regress UHAT1 on the lagged value of UHAT1:

we need the value of ρ from this regression so we can create the "star variables" CSTAR1 and DISTAR1 (or, again, a name of your choice). For example, CSTAR1 = CONS - .948630*CONS(-1) and DISTAR1 = DI - .948630*DI(-1).

Now, regress CSTAR1 on DISTAR1:

We are now ready to create the new set of residuals, UHAT2, and start a second iteration. Using the genr command, generate the new estimated residual series:

UHAT2 = CONS - (4.225818 /(1-.948630)) - .897377* DI

Find the new value of rho from a regression of UHAT2 on its lagged value:

Check to see if it is within .001 of the last rho. It isn't since |.948630-.987481|>.001, so transform to obtain the star variables as before, i.e. CSTAR2 = CONS - .987481*CONS(-1) and DISTAR2 = DI - .987481*DI(-1). Regress CSTAR2 on DISTAR2:

Find UHAT3 from:

UHAT3 = CONS - ( 25.84087/(1-.987481)) - .606430*DI

Find the new value of rho from a regression of UHAT3 on its lagged value:

Check to see if it is within .001 of the last rho. It isn't, so transform to obtain the star variables as before, i.e. CSTAR3 = CONS - .996529*CONS(-1) and DISTAR3 = DI - .996529*DI(-1). Regress CSTAR3 on DISTAR3:

Find UHAT4 from:

UHAT4 = CONS - ( 25.69932/(1-.996529)) - .371846*DI

Find the new value of rho from a regression of UHAT4 on its lagged value:

Check to see if it is within .001 of the last rho. It isn't, so transform to obtain the star variables as before, i.e. CSTAR4 = CONS - .997153*CONS(-1) and DISTAR4 = DI - .997153*DI(-1). Regress CSTAR4 on DISTAR4: 

Find UHAT5 from:

UHAT5 = CONS - ( 25.17282/(1-.997153)) - .353469*DI

Find the new value of rho from a regression of UHAT5 on its lagged value:

Check to see if it is within .001 of the last rho. It is since |.997556-.997153|<.001, so transform one last time to obtain the star variables, i.e. CSTAR5 = CONS - .997556*CONS(-1) and DISTAR5 = DI - .997556*DI(-1). Regress CSTAR5 on DISTAR5:

And the final estimates are:

BHAT0 = 24.78303/(1-.997556)

BHAT1 = .341632

2. Problem 8.3 on page 253.
3. Problem 8.4 on page 253.

The answers to both problem 8.3 and problem 8.4 are in this pdf file.

For problem 8.3: I didn't talk about how to check whether the constant is biased or not, so although this is discussed at the end of the solution, I was only looking for the answer that the slope coefficient is estimated inconsistently, and that it underestimates the true value.

Problem 8.4 is a bit trickier than it first appears. A complete answer is given, but for the part 1 where the expected value or r is non-zero, but r is independent of Q, I was only looking for the answer that the slope estimate is unbiased. The constant is biased in this case due to the non-zero mean in the error, but again we didn't cover how to check the bias/consistency of the constant term (though it isn't difficult). For part 2, which is a tricky problem, again I was only worried about the slope coefficient.

Problem 8.3 is probably more representative of what you might see on an exam.

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

An instrument should be (i) uncorrelated with the error term, (ii) correlated with the variable it is instrumenting for, and (iii) it should not be an explanatory variable itself.

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.

After taking the log of earnings and calling it LOGEARN, the OLS regression is:

to do the IV regression, use the 2SLS option in EViews:

which gives the following output:

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 5 - Solution

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.

[Note: This test is discussed beginning at minute 40 of lecture 8]

To do this problem, first regress m2 on a constant, rgdp, and tbillrate:

[Click on figure for larger version]

Save the residuals (I saved the resid series as uhat). Regress the estimated residual on four lags of the estimated residual and the other variables in the model (no constant), i.e. regress uhat_t on uhat_t-1, uhat_t-2, uhat_t-3, uhat_t-4, tbillrate, and rgdp:

[Click on figure for larger version]

Finally, form the test statistic (T-P)R², where T is the number of observations and P is the number of lags. This is distributed χ²(4). The critical value for this test at  5% level of significance is 9.49.

The test statistic is (191)(.972914) = 185.83, so reject that there is no serial correlation in the model.

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

Homework 4 - Solution

Economics 421/521
Winter 2008
Homework #4 - Solution

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

The coefficients remain unbiased, but OLS is inefficient, and OLS results in biased estimates of the standard errors (so the test statistics, e.g. t's and F's, are wrong)

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

At the 5% level of significance, the critical value of the DW statistic is (approximately, with interpolation) 1.41 at the lower end and 1.61 at the upper end. Since 1.22 is smaller than d_L = 1.41, we fail to reject that ρ=0.

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.

Here's the output:

[Click on figure for larger version]

Does model suffer from serial correlation? Use a Durbin-Watson test to answer the question.

Yes, definitely. The value of d_L (5%) is, approximately, 1.63. The test statistic of .02891 is far below this value, so we reject that ρ=0.

Is the fit as good as the R² and t-statistics indicate?

The t-statistics are biased upward so the fit is not nearly as good as the t-statistics might lead you to believe (which would be evident if we corrected for it). This is due to biased estimates of the residuals. So the the R² and t-statistics give a misleading picture of how well the model fits the data.

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).

Here is the regression output:

[Click on figure for larger version]

The critical value of the Durbin-Watson statistic is approximately d_L = 1.63 (there are tables that go beyond T=100, but the value doesn't change much after 100 observations. I used the value for 100 observations from the table in the text). Since the test statistic above is smaller than the critical value, the hypothesis that that ρ=0 is rejected.

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.

Start with the demonstration that d, the Durbin-Watson statistic, is approximately (2-2ρ) in large samples:

[Click on figure for larger version]

Now, since ρ must lie between -1 and 1, the Durbin-Watson statistic must lie between 0 and 4 [since 2-2(1)=0 and 2-2(-1)=4].

To see the last part, note that when ρ=0, d=2. Then, as ρ increases from 0 to 1, d moves from 2 to 0, and as ρ moves from 0 to -1, d moves from 2 to 4.

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.