## [answered] A researcher obtains data on household annual expenditure o

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1. A researcher obtains data on household annual expenditure on books, B, and annual household

income, Y, for 100 US households in 2003. He hypothesizes that B is related to Y and the average

cognitive ability of adults in the household, IQ, by the relationship

log B = ?1 + ?2log Y + ?3log IQ + u (A) where u is a disturbance term that satisfies the regression model assumptions. He also considers the

possibility that log B may be determined by log Y alone:

log B = ?1 + ?2log Y + u (B) He does not have data on IQ and decides to use average years of schooling of the adults in the

household, S, as a proxy in specification (A). In the sample the correlation between log Y and log S is

0.86. He performs the following regressions: (1) log B on both log Y and log S, and (2) log B on log Y

only, with the results shown in the table (standard errors in parentheses): log Y

log S

constant

R2 (1)

1.1

(0.69)

0.59

(0.35)

-6.89

(2.28)

0.29 (2)

2.1

(0.35) -3.37

(0.89)

0.27 a.  Assuming that (A) is the correct specification, explain (and show the math), whether you

would expect the coefficient of log Y to be greater in regression (2).

b.  Assuming that (A) is the correct specification, describe the various benefits from using

log S as a proxy for log IQ, as in regression (1), if log S is a good proxy.

c.  Explain whether the low value of R2 in regression (1) implies that log S is not a good

proxy. 2. You wish to learn the e?ect of defense expenditure on other expenditures in the economy. You have

U.S. annual data for 1946 to 1975 on the following variables:

C

GNP

D =aggregate private consumption expenditure

=gross national product

=national defense expenditure a.  Why might you think there is heteroskedasticity present in an ordinary least squares

regression of C on a constant, GNP, and D?

b.  Assume a form for the heteroskedasticity (justify it brie?y) and suggest an estimator for

the e?ect of defense expenditure on private consumption expenditure.

c.  What are the properties of your estimator as compared to the o.l.s. estimator? 3.  Researchers Richard Fowles and Peter Loeb studied the effect of drinking and altitude on traffic

deaths. The authors hypothesized that drunk driving fatalities are more likely at high altitude than at

low altitude because higher altitudes the effect of alcohol is great since the intake of oxtgen is lower.

They had the following data: Fi - # of fatalities per motor vehicle mile driven in the ith state; Bi ? per

capita beer consumption in the ith state; Di ? a dummy variable equal to 1 if the state had a vehicle

safety program; and Ai the average altitude of metropolitan areas in the state.

a.  Write down a model that would allow a direct test of the authors? hypothesis. Explain the

expected signs of the coefficients in your model. What test(s) would you run? Be explicit. 4.  Explain what is meant by a ?Difference-in-Difference? model. What is it attempting to mimic?

What assumptions do you need to make for it to be valid? Write out a model that one would estimate

as a ?Difference-in-Difference?. 5. Comanor and Wilson (1967) specified the following regression in a study of advertising on profit

rates:

Profit Rate = ?0 + ?1(Advertising/Sales)+?2ln(Capital)+?3ln(Economy of Scale)

+?4ln(%Growth of Sales) + ?

Profit Rate

Sales

Capital

Economy of Scale = profit rate of ith firm

= advertising expenditures of ith firm

= gross sales of ith firm

= capital needed to enter ith firm?s market

= degree to which economies of scale exist in ith firm?s industry a. Hypothesize expected signs for each slope coefficient

b. Note there are two different nonlinear relationships in the equation. For each independent

variable, determine the shape that the chosen functional form implies and state whether you

agree or disagree with the shape. Explain your reasoning

c. Comanor and Wilson state that the simple correlation coefficient between (Advertising/Sales)

and each of the other independent variables is positive. If one of these remaining variables

were omitted in which direction would the estimate of ?1 likely be biased?

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