Econometrics
Spring 2011
Midterm Exam 2
Statement of Academic Honesty:
This exam entirely reflects my own work. I have not given assistance to anyone, nor have I received assistance from anyone. I am not aware that any other students have done so.
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Problem 1 (20 points)
State, with brief explanation, whether each of the following is true or false. Credit depends on the explanation.
a. When the regression error is heteroskedastic, OLS does not produce consistent estimates of the regression coefficients.
b. The p-value reported in regression output is the probability that the null hypothesis is true.
c. If a single-variable regression is estimated using only two observations, then R2 1.
A researcher has data on Y and X, and estimates the regression Yˆˆ0ˆ1X. Now let Q4X
and consider the regression Y 01Q. In other words, the dependent variable Y is the same for both regressions but the independent variable X is rescaled.
a. Prove that 1 1 ˆ1 4
.
b. What is the relationship between 0 and ˆ0? Prove your answer.
c. What is the relationship between yi and ˆyi for a particular observation i? Prove your
answer.
Problem 3 (30 points)
This problem refers to the regression output below. The researcher is investigating the consumption of organic apples. The data are a random sample of 660 households.
ORGLBS: Consumption of organic apples, in pounds ORGPRC: Price of a pound of organic apples, in US dollars FAMINC: Family income, in thousands of US dollars
REGPRC: Price of a pound of regular (non-organic) apples, in US dollars
EDUC: Years of education, in years
HHSIZE: Number of members in the household
Notice that the specification includes a quadratic in education. Also observe that the dependent variable and several of the independent variables are measured in logs.
Dependent Variable: LOG(ORGLBS) Method: Least Squares
Sample: 1 660
Included observations: 660
White Heteroskedasticity-Consistent Standard Errors & Covariance
Coefficient Std. Error t-Statistic Prob.
C -0.887864 0.787801 -1.127016 0.2601 LOG(ORGPRC) -1.024230 0.132333 -7.739778 0.0000 LOG(FAMINC) 0.047587 0.038626 1.231979 0.2184 LOG(REGPRC) 0.762013 0.143088 5.325491 0.0000 EDUC 0.182672 0.113637 1.607511 0.1084 EDUC^2 -0.005582 0.003844 -1.452033 0.1470 HHSIZE 0.033865 0.015161 2.233594 0.0258
a. Find the sum of squared residuals (SSR).
b. Test the hypothesis that the demand for organic apples is unit elastic1 (with respect to its own price). Show the hypotheses and test statistic. What is your conclusion?
c. Do regular apples substitute for organic apples? Is the relationship statistically significant? Explain.
d. What level of EDUC maximizes a person’s expected organic apple consumption?
e. A colleague of yours proposes to eliminate the quadratic term EDUC^2 from the regression. Briefly describe two ways you might evaluate your colleague’s suggestion.
A 401(k) is a special type of tax-preferred asset in the US, but not everyone is eligible. A major research question is whether eligibility for the 401(k) increases total asset accumulation, or whether it simply substitutes for other kinds of assets.
On the iLearn page, you will find a datafile entitled 401k.wf1. Define:
Y nettfa total financial assets, in thousands of US dollars
1 401
X e k dummy, =1 if eligible for a 401(k)
2
X age age, in years
3
X fsize family size, in persons
4
X inc family income, in thousands of US dollars
5
X marr dummy, =1 if individual is married
a. Estimate the model Yˆˆ0ˆ1X1ˆ2X2ˆ3X3ˆ4X4ˆ5X5. Enter the estimated coefficients and standard errors in the table below. Be sure to use White standard errors.
Estimated Coefficient Standard Error
0 ˆ 1 ˆ 2 ˆ 3 ˆ 4 ˆ 5 ˆ
c. Would there be omitted variables bias in estimating the impact of 401(k) eligibility on asset accumulation if inc were not included in the regression? Explain.
d. If inc were omitted from the regression, would the coefficient on e401k rise or fall? Explain intuitively without estimating the new model.
e. Give a 95% confidence interval for the impact of 401(k) eligibility on asset accumulation.
