Final and answer key.
Final and answer key.
Posted by Mark Thoma on Friday, March 11, 2011 at 04:07 PM in Finals, Winter 2009  Permalink  Comments (0)
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Introduction to Econometrics
Course: Economics 421/521
Professor: Mark Thoma
Office/Hours: PLC 471 on M/W 3:304:30 p.m.
Phone/Email: (541) 3464673, 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:
Matt Cole  Hours: W 1011 
PLC 520  mcole@uoregon.edu 
Lab Times:
Lab  21820  16001720  Thu  442 MCK 
Lab  21821  18001920  Thu  442 MCK 
Tests and Grading: There will be a midterm exam and a final. The midterm will be given Monday, February 9th. The final will be given on Tuesday, March 17th at 3:15 p.m. No makeup 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 Wednesday, March 11 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.
Posted by Mark Thoma on Monday, March 23, 2009 at 01:26 PM in Syllabus, Winter 2009  Permalink  Comments (4)
[Use the arrows in the sides of the screen to scroll through the class videos.]
Posted by Mark Thoma on Saturday, March 21, 2009 at 12:33 PM in Lectures, Winter 2009  Permalink  Comments (2)
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Posted by Mark Thoma on Wednesday, March 11, 2009 at 03:36 PM in Lectures, Winter 2009  Permalink  Comments (0)
We covered the following topics in the course:
1. Assumption required for estimates to be BLUE
2. Hypothesis testing:
a. t tests (both onesided and twosided)
b. Joint hypotheses (FTests, Chisquare 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. Testsi. LaGrange Multiplier Tests (Models 1, 2, and 3)
Model 1:
Model 2:
Model 3:ii. GoldfeldQuandt test
iii. White's teste. Corrections/Estimation procedures
i. Multiplicative:
ii. Feasible GLSModel 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 OLSi. 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 DurbinWatson test.
ii. Durbin's htest.
iii. The BreuschGodfrey test for higher order serial correlation.d. Corrections
i. Nonlinear estimation
ii. The CORC procedure
9. Testing for ARCH errors
Material after Midterm
10. Stochastic Regressors and Measurement Errors
a. Assessing the bias and consistency of an estimator
b. Errors in variablesi. 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 righthand 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 (with and without endogeneity)
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.
Posted by Mark Thoma on Tuesday, March 10, 2009 at 11:25 AM in Review, Winter 2009  Permalink  Comments (0)
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Posted by Mark Thoma on Monday, March 09, 2009 at 03:29 PM in Lectures, Winter 2009  Permalink  Comments (0)
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 = β_{0} + β_{1}YD_{t} + β_{2}CO_{t1} + ε_{1t}
YD_{t} = Y_{t} – T_{t}
I_{t} = β_{3} + β_{4}Y_{t} + β_{5}r_{t1} + ε_{2t}
r_{t} = β_{6} + β_{7}Y_{t} + β_{8}M_{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_{t1}, and r_{t1}
(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 Thursday, March 12 in lab.
Posted by Mark Thoma on Thursday, March 05, 2009 at 04:23 PM in Empirical Project, Homework, Winter 2009  Permalink  Comments (0)
Here's a few general guidelines to help with the writeup 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 GuassMarkov 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 followup study to learn more about this topic?
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1. Problem 9.3 on page 276 of the text.
2. For the model
Q_{t} = a_{0} + a_{1}P_{t} + a_{2}Y_{t} + a_{3}X_{t} + a_{4}Z_{t} + u_{t}P_{t} = b_{0} + b_{1}Q_{t} + b_{2}Y_{t} + b_{3}W_{t} + v_{t}Y_{t} = c_{0} + c_{1}P_{t} + c_{2}W_{t} + w_{t}
Determine whether each equation is under, exactly, or over identified. Assume that Q, P, and Y are endogenous, and that the constant, X, Z, and W are exogenous.
3. Answer the following questions about your project:
(i) Do you expect any measurement problems, i.e. do you expect to have errors in variables problems? If so, what effect will that have on your estimates and test statistics (if you don't think this will be a problem, say that and explain why, and then say, but if I did have this problem it would cause the following difficulties and then describe the effect it would have on the estimates and test statistics). How can the problem be fixed?
(ii) Are there any important omitted variables? If so, what effect would the omitted variables have on the estimates and test statistics? (And again, even if you think you have every important variable, show that you understand this issue by explaining what types of problems it causes).
(iii) Do you expect problems with endogeneity bias (endogenous varaibles on the righthand side of the equation that are correlated with the error term)? Think hard about this one, and if you do have this problem, what is the solution?
Posted by Mark Thoma on Thursday, February 26, 2009 at 03:33 PM in Homework, Winter 2009  Permalink  Comments (0)
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Posted by Mark Thoma on Monday, February 23, 2009 at 03:27 PM in Lectures, Winter 2009  Permalink  Comments (0)
1. Problem 8.5 on page 253, part 1 only.
2. Consider the following simple Keynesian macroeconomic model of the U.S. economy.
Y_{t} = C_{t} + I_{t} + G_{t} + NX_{t}
C_{t} = β_{0} + β_{1}YD_{t} + β_{2}C_{t1} + ε_{1t}
YD_{t} = Y_{t} – T_{t}
I_{t} = β_{3} + β_{4}Y_{t} + β_{5}r_{t1} + ε_{2t}
r_{t} = β_{6} + β_{7}Y_{t} + β_{8}M_{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_{t1}, T_{t}, r_{t1}, and M_{t}. Find the reduced form equations for this model.
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 timeseries or crosssectional, 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. You don't have to actually do the correction for this homework (though if it was present, you would do the correction for the project), just explain how to do it.).
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Posted by Mark Thoma on Monday, February 16, 2009 at 02:14 PM in Lectures, Winter 2009  Permalink  Comments (0)
1. Complete steps 1 through 3 of the Empirical Project Outline (as discussed in class).
2. Problem 8.3 on page 253.
3. What are the three requirements for a good instrumental variable? [We'll cover this on Monday.]
[Note: The *next* homework will ask: (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 timeseries or crosssectional, 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).]
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Posted by Mark Thoma on Thursday, February 12, 2009 at 09:33 AM in Lectures, Winter 2009  Permalink  Comments (0)
1. Assumption required for estimates to be BLUE
2. Hypothesis testing:
a. t tests (both onesided and twosided)
b. Joint hypotheses (FTests, Chisquare 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. Testsi. LaGrange Multiplier Tests (Models 1, 2, and 3)
Model 1:
Model 2:
Model 3:ii. GoldfeldQuandt test
iii. White's teste. Corrections/Estimation procedures
i. Multiplicative:
ii. Feasible GLSModel 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 OLSi. 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 DurbinWatson test.
ii. Durbin's htest.
iii. The BreuschGodfrey test for higher order serial correlation.d. Corrections
i. Nonlinear estimation
ii. The CORC procedure
9. Testing for ARCH errors
Posted by Mark Thoma on Thursday, February 05, 2009 at 01:29 PM in Review, Winter 2009  Permalink  Comments (0)
The CochraneOrcutt 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}  b_{1}  b_{2}X_{2t}  ...  b_{k}X_{kt} where the b's are the estimated betas using the transformed ("starred") variables in step 4. However, be careful about obtaining the value of b_{1}. Note from above in equation (9.9) that you have to divide the estimate of the constant from the regression involving the "starred" values by 1ρ in order to obtain b_{1}.
Posted by Mark Thoma on Thursday, February 05, 2009 at 12:24 PM in Review, Winter 2009  Permalink  Comments (0)
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Posted by Mark Thoma on Thursday, February 05, 2009 at 10:00 AM in Lectures, Winter 2009  Permalink  Comments (0)
Here is a brief outline of the project. We will talk more about this in class:
1. Statement of theory and hypothesis
2. Specification of the econometric model
3. Obtain data
4. Estimation of the econometric model and diagnostic tests
5. Test hypotheses
6. Forecasting or prediction
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.
Posted by Mark Thoma on Monday, February 02, 2009 at 10:24 PM in Empirical Project, Winter 2009  Permalink  Comments (0)
This is from The Monkey Cage:
56% of women who consumed the most calories before conception gave birth to boys, compared with 45% of those who consumed the least. Of 132 individual foods tracked, breakfast cereal was the most significantly linked with baby boys.
That’s from a study by researchers at Exeter and Oxford, as per Melinda Beck’s writeup in the Wall Street Journal.
This made me wonder. After all, my brothers and I turned out to be, well, boys, and my mother never ever ate breakfast cereal. However, as a social scientist I recognize that correlational results admit of exceptions.
They also, as Beck notes, occasion doubt. One of the first things one is supposed to learn about “statistical significance” is that some results that appear to be real, aren’t. If you’re operating at the .05 significance level, then in the long run somewhere around 5% of the relationships that you accept as nonrandom should really be random. Those are “Type 1” errors — or are they “Type 2” errors? I could never keep those straight. (Andrew, though not not a frequentist, presumably can straighten me out here.) Anyway, these breakfast cereal results apparently have produced a minor kerfuffle among epidemiologists and statisticians, which you can read about in the Beck article. If nothing else, this episode provides a nice example for those who are teaching intro methods courses, and it also gives “Monkey Cage” readers an opportunity to admire the excellent pun I devised for the headline of this item. (Please hold your applause.)
Posted by Mark Thoma on Saturday, January 31, 2009 at 09:26 PM in Additional Reading, Winter 2009  Permalink  Comments (0)
Economics 421/521
Winter 2009
Homework #4
Due in lab on Thursday, Feb. 5
1. 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
2. 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?
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 DurbinWatson 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 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.
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 firstorder serial correlation.
Posted by Mark Thoma on Thursday, January 29, 2009 at 02:14 PM in Homework, Winter 2009  Permalink  Comments (0)
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[Note: The assignment will be discussed in lab on 1/22, and will be due in lab on 1/29.]
Economics 421/521
Winter 2009
Homework #3
1. Using the first model of heteroskedasticity, i.e. that resid^{2} = α_{0} + α_{1}*years + α_{2}*years^{2}, 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.]
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Posted by Mark Thoma on Wednesday, January 21, 2009 at 10:53 AM in Lectures, Winter 2009  Permalink  Comments (0)  TrackBack (0)
Here is an outline of the LM tests for Heteroskedasticity:
Posted by Mark Thoma on Wednesday, January 14, 2009 at 04:52 PM in Review, Winter 2009  Permalink  Comments (1)  TrackBack (0)
[Note: The assignment will be discussed in lab this week, and will be due in lab next week.]
Economics 421/521
Winter 2009
Homework #2
1. Using the EAEF data set, regress LGEARN on S, EXP, and ASVABC. Use Ftests 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. 443444 in Appendix B of the text):
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 years^{2}:
log(salary) = β_{0} + β_{1}*years + β_{2}*years^{2} + u_{t}
Then, form the estimated residual squared (resid^{2}) 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.]
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[Note: The assignment will be discussed in lab this week, and will be due in lab next week.]
Economics 421/521
Winter 2009
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 coefficients 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 the good fit is misleading in this model later in the course.
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