Problem Set 1 Solved

Question 1 (25 points)

You are hired by the governor to study whether a tax on liquor has decreased average liquor consumption in your state. You are able to obtain, for a sample of individuals selected at random, the di erence in liquor consumption (in ounces) for the years before and after the tax. For person i who is sampled randomly from the population, Yi denotes the change in liquor consumption. Treat these as a random sample from a Normal( , 2) distribution.

    1) The null hypothesis is that there was no change in average liquor consumption. State this formally in terms of . The alternative is that there was a decline in liquor consumption; state the alternative in terms

of    . (5 points)

2) Now, suppose your sample size is n=900 and you obtain the estimates Y =-32.8 and s=466.4. Calculate the t statistic for testing H0 against H1. (Because of the large sample size, just use the standard normal distribution tabulated in Table G.1.) Do you reject H0 at the 5% level? At the 1% level? (10 points)

3) What has been implicitly assumed in your analysis about other determinants of liquor consumption over the two-year period in order to infer causality from the tax change to liquor consumption? (10 points)


Question 2 (15 points)

Using data from 1988 for houses sold in Andover, Massachusetts, from Kiel and McClain (1995), the following equation relates housing price (price) to the distance from a recently built garbage incinerator (dist):

\
log(price) = 9:40 + 0:312log(dist)


n == 135 and R2 = 0:162


1)Interpret the coe  cient on log(dist). Is the sign of this estimate what you expect it to be? (5 points)

    2) Do you think simple regression provides an unbiased estimator of the ceteris paribus elasticity of price with respect to dist? (Think about the city’s decision on where to put the incinerator.) (5 points)

    3) What other factors about a house a ect its price? Might these be correlated with distance from the incinerator? (5 points)










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Question 3 (15 points)

The data set in CEOSAL2.RAW contains information on chief executive o cers for U.S. corporations. The variable salary is annual compensation, in thousands of dollars, and ceoten is prior number of years as company CEO.

    1) Find the average salary and the average tenure in the sample. (5 points)

    2) How many CEOs are in their rst year as CEO (that is, ceoten = 0)? What is the longest tenure as a CEO? (5 points)

    3) Estimate the simple regression model

log(salary) =  0 +  1ceoten + u;


What is the (approximate) predicted percentage increase in salary given one more year as a CEO? (5 points)


Question 4 (20 points)

We used the data in MEAP93.RAW for Example 2.12 in the book. Now we want to explore the relationship between the math pass rate (math10) and spending per student (expend).

    1) Do you think each additional dollar spent has the same e ect on the pass rate, or does a diminishing e ect seem more appropriate? Explain. (10 points)

    2) Use the data in MEAP93.RAW to estimate the model:

math10 =  0 +  1log(expend) + u;


Report the estimated equation in the usual way, including the sample size and R-squared. What is the explanatory power of the model? Explain. (5 points)

    3) How big is the estimated spending e ect? Namely, if spending increases by 10%, what is the estimated percentage point increase in math10? (5 points)


Question 5 (25 points)

Use the data in WAGE2.RAW to estimate a simple regression explaining monthly salary (wage) in terms of IQ score (IQ).

    1) Find the average salary and average IQ in the sample. What is the sample standard deviation of IQ? (IQ scores are standardized so that the average in the population is 100 with a standard deviation equal to 15.) (5 points)

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    2) Estimate a simple regression model where a one-point increase in IQ changes wage by a constant dollar amount. Use this model to nd the predicted increase in wage for an increase in IQ of 15 points. Does IQ explain most of the variation in wage? (10 points)

    3) Now, estimate a model where each one-point increase in IQ has the same percentage e ect on wage. If

IQ increases by 15 points, what is the approximate percentage increase in predicted wage? (10 points)























































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