Homework1for Econometrics
(due March27,2013)
Spring2013
Instructor:Jihai Yu
TA:Kunyuan Qiao
1.Suppose that you are asked to conduct a study to determine whether smaller class sizes lead to improved student performance of fourth graders.
(i)If you could conduct any experiment you want,what would you do?Be speci…c.
(ii)More realistically,suppose you can collect observational data on several thousand fourth graders in a given state.You can obtain the size of their fourth-grade class and a standardized test score taken at the end of fourth grade.Why might you expect a negative correlation between class size and test score?
(iii)Would a negative correlation necessarily show that smaller class sizes cause better performance? Explain.
2.The data set BWGHT.DTA contains data on births to women in the United States.Two variables of interest are the dependent variable,infant birth weight in ounces(bwght),and an explanatory variable, average number of cigarettes the mother smoked per day during pregnancy(cigs).The following simple regression was estimated using data on n=1,388births:
\
bwght=119:77 0:514cigs
(i)What is the predicted birth weight when cigs0?What about when cigs20(one pack per day)? Comment on the di¤erence.
(ii)Does this simple regression necessarily capture a causal relationship between the child’s birth weight and the mother’s smoking habits?Explain.
(iii)To predict a birth weight of125ounces,what would cigs have to be?Comment.
(iv)The proportion of women in the sample who do not smoke while pregnant is about0.85.Does this help reconcile your…nding from part(iii)?
ing data from1988for 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)=0:94+0:312log(dist)
n=135;R2=0:162
(i)Interpret the coe¢cient on log(dist).Is the sign of this estimate what you expect it to be?
(ii)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.) (iii)What other factors about a house a¤ect its price?Might these be correlated with distance from the incinerator?
4.Let^ 0and^ 1be the OLS intercept and slope estimators,respectively,and let u be the sample average of the errors(not the residuals!).
(i)Show that^ 1can be written as^ 1= 1+P n i=1w i u i where w i=d i=SST x and d i=x i x. (ii)Use part(i),along with P n i=1w i=0,to show that^ 1and u are uncorrelated.[Hint:You are being asked to show that E[(^ 1 1) u]=0].
e the data in WAGE1.DTA for this exercise.
(i)Find the average education level in the sample.What are the lowest and highest years of education?
(ii)Find the average hourly wage in the sample.Does it seem high or low?
(iii)How many women are in the sample?How many men?
6.The data set in CEOSAL2.DTA 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.
(i)Find the average salary and the average tenure in the sample.
(ii)How many CEOs are in their…rst year as CEO(that is,ceoten=0)?What is the longest tenure as a CEO?
(iii)Estimate the simple regression model
log(salary)= 0+ 1ceoten+u;
and report your results in the usual form.What is the(approximate)predicted percentage increase in salary given one more year as a CEO?
2。