Economics 421 - Econometrics

Material for Lecture 9 on Tuesday 2/1/11

Today:

• Finish Chapter 12 - Autocorrelation (Cochrane-Orcutt procedure, ARCH models)
• Answer questions on material for exam
• Begin Chapter 8 - Stochastic Regressors and Measurement Errors if there are not enough questions to fill the remaining time.

Next Time:

• Midterm Exam

Video:

Topics for Midterm

[Note: We will cover the last two items on the list, CORC and ARCH, on Tuesday. Previous midterms are here.]

1. Assumptions 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

Material for Lecture 8 on Thursday 1/27/11

Today:

• Continue Chapter 12 - Autocorrelation

Next Time:

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

Video:

Homework 4

Economics 421/521
Winter 2011
Homework #4
Due in lab next week

1. 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

2. 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?

3. Regress the change in the log of real consumption (C) on the change in the log of 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).

4. 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.

5. Continuing with the model we used in problem 2, test for the presence of fourth order serial correlation.

6. Continuing with the model we used in problem 3, use the AR(1) procedure in EViews to correct the model for the presence of first-order serial correlation.

Material for Lecture 7 on Tuesday 1/25/11

Today:

• Chapter 12 - Autocorrelation

Next Time:

• Continue Chapter 12 - Autocorrelation

Video:

Material for Lecture 6 on Thursday 1/20/11

Today:

• Finsih Heteroskedasticity
• Begin Chapter 12 - Autocorrelation

Next Time:

• Continue Chapter 12 - Autocorrelation

Video:

Homework 3

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

Economics 421/521
Winter 2011
Homework #3

1. Using the first model of heteroskedasticity, i.e. that resid² = α₀ + α₁*years + α₂*years², correct the salary model in problem 3 from Homework 2 for heteroskedasticity and reestimate.

2. Problem 7.2 in the text.

3. Test the salary model in problem 3 from Homework 2 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 3 of Homework 2?

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

[Note: pdf of problems 7.1 and 7.2, problem 7.1 was on the last homework.]

Material for Lecture 5 on Tuesday 1/18/11

Today:

• Continue Chapter 7 - Heteroskedasticity

Next Time:

• Chapter 12 - Autocorrelation

Video:

LM Tests for Heteroskedasticity

Here is an outline of the LM tests for Heteroskedasticity:

Material for Lecture 4 on Thursday 1/13/11

Today:

• Continue Chapter 7 - Heteroskedasticity

Next Time:

• Finish Chapter 7 - Heteroskedasticity, perhaps start Chapter 12 on Autocorrelation

Video:

Homework 2

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

Economics 421/521
Winter 2011
Homework #2

1. Using the EAEF data set, regress LGEARN on S, EXP, and ASVABC. Use F-tests to determine whether the coefficients on S and EXP are (a) jointly significant, and (b) equal. [Parts (a) and (b) are two separate tests.]

Note: Here are the 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.

2. Problem 7.1 in the text.

3. Using this data set, repeat the example from class for the first of the three cases we discussed, i.e. first regress the log of salary on a constant and the two variables proxying for experience, years and years²:

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

Then, form the estimated residual squared (resid²) and perform the LM test for heteroskedasticity (note: resid is the estimated value of u_t).

[Note: pdf of problems 7.1 and 7.2, problem 7.2 will be on the next homework.]

Material for Lecture 3 on Tuesday 1/11/11

Today:

• Chapter 7 - Heteroskedasticity

Next Time:

• Continue Chapter 7 - Heteroskedasticity

Video:

Homework 1

[Note: The assignment will be due next week in lab.]

Economics 421/521
Winter 2011
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 each of these hypotheses 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 coefficients 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 the good fit is misleading in this model later in the course.

Material for Lecture 2 on Thursday 1/6/11

Today:

• Review of hypothesis testing
• Chapter 7 - Heteroskedasticity

Next Time:

• Continue Chapter 7 - Heteroskedasticity

Video:

Material for Lecture 1 on Tuesday 1/4/11

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:

• Hypothesis Tests
• Heteroskedasticity (Chapter 7)

Video

Syllabus for Winter 2011

Introduction to Econometrics
Course: Economics 421/521
Professor: Mark Thoma
Office/Hours: PLC 471 on T/Th 1:30-2:30 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 then 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:

Sandy Tang	MW 12:30-1:30	PLC 533	htang2@uoregon.edu
Kris Holden	Hours: TBA	PLC 406	kholden@uoregon.edu
Jeff Allen	Hours: TBA	PLC 518	jca@uoregon.edu

Lab Times:

CRN	Time	Day	Room	Instructor
22171	1600-1720	W	442 MCK	Holden
22172	1730-1850	W	442 MCK	Holden
22173	1600-1720	Th	442 MCK	Tang
22174	1730-1850	Th	442 MCK	Tang

Tests and Grading: There will be a midterm exam and a final. The midterm will be given Thursday, February 3rd. The final will be given on Friday, March 18th at 8:00 a.m. No make-up exams will be given. The midterm is worth 30% and the final is worth 40%. Grades will be assigned according to your relative standing in the class.

Empirical Project: There will be an empirical paper that will comprise 15% of your grade. The paper is due no later than Thursday, March 10 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 15% of your grade.

*Tentative* Course Outline:

We will cover the following chapters:
Review of Multiple Regression and Hypothesis Testing
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.

Course Materials for Winter 2009

Here are the course materials for Winter 2009.