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Posted by Mark Thoma on Thursday, January 31, 2008 at 04:12 PM in Midterms, Winter 2008  Permalink  Comments (0)  TrackBack (0)
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 onesided and twosided)
b. FTests (tests that coefficients are jointly zero and tests involving linear combinations of the coefficients)
c. ChiSquared 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. TestsGoldfeldQuandt
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.
Posted by Mark Thoma on Wednesday, January 30, 2008 at 05:16 AM in Review, Winter 2008  Permalink  Comments (0)  TrackBack (0)
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Lecture 7 [Google video]  Winter 2008
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Economics 421 Lecture 7 
Posted by Mark Thoma on Wednesday, January 30, 2008 at 02:51 AM in Lectures, Winter 2008  Permalink  Comments (0)  TrackBack (0)
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Posted by Mark Thoma on Wednesday, January 30, 2008 at 02:51 AM  Permalink  Comments (0)  TrackBack (0)
Economics 421/521
Winter 2008
Homework #4
1. What are the consequences of estimating an autoregressive model using OLS?
2. Perform a DurbinWatson test at the 5% level of significance for positive firstorder 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 Tbill rate, estimate the following regression...:
M_{t} = β_{0} + β_{1}RGDP_{t} + β_{2}Tbill_{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 DurbinWatson test to answer the question. Is the fit as good as the R^{2} and tstatistics indicate?
4. Regress real consumption (C) on real disposable income (DI) and test for serial correlation using a DurbinWatson 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 DurbinWatson 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.
Posted by Mark Thoma on Tuesday, January 29, 2008 at 12:47 AM in Homework, Winter 2008  Permalink  Comments (0)  TrackBack (0)
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Lecture 6 [Google video]  Winter 2008
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Posted by Mark Thoma on Friday, January 25, 2008 at 03:04 PM in Lectures, Winter 2008  Permalink  Comments (0)  TrackBack (0)
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Posted by Mark Thoma on Friday, January 25, 2008 at 02:31 PM  Permalink  Comments (0)  TrackBack (0)
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Posted by Mark Thoma on Wednesday, January 23, 2008 at 10:26 AM  Permalink  Comments (0)  TrackBack (0)
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 (years^{2}):
log(salary) = β_{0} + β_{1}*years + β_{2}*years^{2} + u_{t}
Then, form either the residual squared (resid^{2}), the absolute value of the residual (resid), or the log of the residual squared (log(resid^{2})) 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 = α_{0} + α_{1}*years + α_{2}*years^{2}, 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?
Posted by Mark Thoma on Wednesday, January 23, 2008 at 03:00 AM in Homework, Winter 2008  Permalink  Comments (0)  TrackBack (0)
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Posted by Mark Thoma on Tuesday, January 22, 2008 at 02:32 AM in Lectures, Winter 2008  Permalink  Comments (0)  TrackBack (0)
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Lecture 4 [Google video]  Winter 2008
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Economics 421 Lecture 4 
Posted by Mark Thoma on Friday, January 18, 2008 at 02:40 PM in Lectures, Winter 2008  Permalink  Comments (0)  TrackBack (0)
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Posted by Mark Thoma on Friday, January 18, 2008 at 02:40 PM  Permalink  Comments (0)  TrackBack (0)
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
Posted by Mark Thoma on Wednesday, January 16, 2008 at 03:29 PM in Winter 2008  Permalink  Comments (0)  TrackBack (0)
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Posted by Mark Thoma on Wednesday, January 16, 2008 at 10:22 AM  Permalink  Comments (0)  TrackBack (0)
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 crosssectional model based on data for 1988 from all 50 states (standard errors in parentheses):
Ĉ_{i} = 100 – 9.0E_{i} + 1.0I_{i}  0.04T_{i} – 3.0V_{i} + 1.5R_{i }(36.) (3.5) (.75) (0.05) (.90) (0.3)
R^{2} = .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 Ftest to determine whether S and EXP are jointly significant.
4. Using the EAEF data set, regress LGEARN on S, EXP, and ASVABC. Use an Ftest to determine whether the coefficients on S and EXP are equal. ________________________________________________________
Note: Variable definitions (see pages. 443444 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 outofschool work experience (years) as of the 2002 interview.
ASVABC = Scaled standardized test score.
Posted by Mark Thoma on Wednesday, January 16, 2008 at 10:06 AM in Homework, Winter 2008  Permalink  Comments (0)  TrackBack (0)
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Posted by Mark Thoma on Tuesday, January 15, 2008 at 02:26 AM in Lectures, Winter 2008  Permalink  Comments (0)  TrackBack (0)
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Posted by Mark Thoma on Friday, January 11, 2008 at 07:32 AM  Permalink  Comments (0)  TrackBack (0)
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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 
Posted by Mark Thoma on Thursday, January 10, 2008 at 01:18 AM in Lectures, Winter 2008  Permalink  Comments (0)  TrackBack (0)
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Posted by Mark Thoma on Wednesday, January 09, 2008 at 01:00 PM  Permalink  Comments (0)  TrackBack (0)
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Posted by Mark Thoma on Monday, January 07, 2008 at 03:16 PM in Lectures, Winter 2008  Permalink  Comments (0)  TrackBack (0)
[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 LOT_{i} – 2.0 AGE_{i} + 10.0 BED_{i} – 4.0 FIRE_{i} + 100 BEACH_{i}
(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 twosided ttest around zero to test the twosided hypothesis at the 5 percent level.
2. Consider the following regression:
log(Qc_{i}) = 921.6 – 1.3 log(Pc_{i}) + 0.7 log(Pa_{i}) + 11.4 log(Inc_{i})
(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 tvalues 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 R^{2}. Can we have a negative R^{2}?
Part II. Short Answer
1. State the GaussMarkov Theorem and explain the term BLUE.
Part III. Estimation
1. Given data on M2, real GDP, and the Tbill rate, estimate the following regression and test whether the coefficients differ from zero. Do the coefficinets have the expected signs?:
M_{t} = β_{0} + β_{1}RGDP_{t} + β_{2}Tbill_{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.
Posted by Mark Thoma on Monday, January 07, 2008 at 02:59 PM in Homework, Winter 2008  Permalink  Comments (0)  TrackBack (0)