Assignment:
1. Stata: The following questions use the data set "apples.dta". This data includes the results of a survey of households about the number of apples they buy in one week, the price per pound of apples in their area, and household characteristics (e.g. education level of the survey respondent, household size, family income in thousands, etc.).
a) How many households are there in the survey? How many states are represented in the survey? Which state has the most households in the survey?
b) What is the average number of pounds of apples purchased, price of apples, education level, household size, and family income?
c) Regress the pounds of apples purchased on the of apples while controlling for whether or not the respondent is male, education level, household size, family income, and age. Interpret the coefficient on the price of apples in a sentence. Is this coefficient statistically significant at the 95% level?
d) What is the average number of pounds of apples purchased by households in Florida? In Pennsylvania? Does this support the idea that there may be fixed differences in apple consumption across states?
e) Rerun the regression from part c) while controlling for a fixed effect for each state? How does the coefficient on price compare to the coefficient in part c)? Is the effect of price on pounds purchased still statistically significant at the 95% level? Explain what is achieved by including state fixed effects.
2. Stata: The following questions use the data set "construction_panel.dta". The data includes individual characteristics, natural log of wages, industry, and union membership status. We wish to estimate the effect of being a union member on wages, as unions may have greater bargaining power.
a) What type of data set is this? How many individuals are included in the data? How many years of data do we observe for each individual?
b) Run a regression with log wages as the outcome and union status as the explanatory variable. Interpret the coefficient on union in a sentence. Is it statistically significant at the 95% level?
c) You are concerned that the union effect may be overstated if union workers have better work ethics. Rerun the regression from part b) while controlling for individual fixed effects. How did adding individual fixed effects change the estimated effect of union membership? Does it appear that the concern was valid?
d) You are concerned that both union membership and wages may be increasing over time. Rerun the regression from part b) while controlling for a linear time trend. What effect did adding a time control have on the estimated effect of union membership? Does it appear that the concern was valid?
e) You wish to allow wages to vary from year-to-year. Rerun the regression from part b) while controlling for year fixed effects. What effect did adding year fixed effects have on the estimated effect of union membership?
3. You are interested in estimating how the number of days of work missed affects the size of an employee's annual raise:
Raisei = β0 + β1Missedi + ui
You collect data on the size of the raise ("raise") and the number of days of work missed ("missed") for 5 employees at a Santa Cruz convenience store. You are concerned that the estimated effect of days missed on the size of the raise may be biased by omitted variables. So, you gather data on the distance that each employee lives from the convenience store. You intend to use this as an instrumental variable for days of work missed.
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raise
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missed
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distance
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1
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8
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6
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6
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0
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2
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3
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3
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3
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1
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9
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8
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5
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2
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5
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a) Estimate Bo and βi using ordinary least squares and write the resulting equation.
b) Suppose that being "lazy" is an omitted variable. Carefully explain how omitting "lazy" from the regression is likely to bias the estimate of Bi.
c) You wish to use distance as an instrument for days missed. Explain the two restrictions distance must satisfy in order to be a valid instrument.
d) Compute the instrumental variables estimate for B1.
e) Compare the instrumental variables estimate to the ordinary least squares estimate of β1 in part a) and explain how and why they are different.
4. The country of Guilder has strict requirements for military service. Specifically, all those who are 5'8" (68 inches) or taller are drafted into the military at age 18. All those under 5'8" are not drafted into the military. You have been hired to estimate the effect of military service on employment. You gather data on whether or not somebody is employed at age 30 ("Employed") and height in inches ("h") for a sample of 12,000 residents of Guilder and estimate the following regression:
Employediˆ = 0.612+0.023(hi-68)-0.013(hi - 68)Militaryi +0.084Militaryi
(0.255) (0.011) (0.015) (0.033)
a) Interpret the coefficients on (hi - 66).
b) Interpret the coefficient on (hi -66) Military.
c) Interpret the coefficient on Military.
d) Test the hypothesis that being drafted into military service has no effect on being employed at the 95% confidence level.
e) Draw and label a graph of this regression line with employed on the vertical axis and height on the horizontal axis. Your graph should cover heights ranging from 60 to 76 inches.
f) What is the predicted employment rate for a person who is 5'7"? What is the predicted employment rate for someone who is 5'8"? How much of this difference is expected due to the difference in height and how much is due to crossing the military service height threshold?