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Problem Set 2 Introduction to Econometrics

1. For many years, housing economists believed that households spend a constant fraction of income on housing, as in housing expenditure = (income) + u
The file housing.dta contains housing expenditures (housing) and total expenditures (total) for a sample of 19th century Belgian workers collected by Edouard Ducpetiaux1. The differences in housing expenditures from one observation to the next are in the variables dhousing; the differences in total expenditures are in variable dtotal.
1. (a)  Compute the means of total expenditure and housing expenditure in this sample
2. (b)  Estimate  using total expenditure for total income.
3. (c)  If income rises by 100 (it averages around 900 in this sample) what change in estimated expected housing expenditure results according to your estimate in (b)?
4. (d)  Interpret the R2
5. (e)  What economic argument would you make against housing absorbing a constant share of income?
6. (f)  What are some determinants of housing captured by u?
2. We will use data file called GPA4.dta to answer this question. Variables are defined on Table 1. Table 2 presents the results of four regressions, one in each column. Please use Table 2 to answer the following questions. Estimate the indicated regressions and fill in the values (you may either handwrite or type the entries in; if you choose to type up the table, an electronic copy of Table 2 in.doc format is available on the course Web site). For example, to fill in column (1), estimate the regression with colGPA as the dependent variable and hsGPA and skipped as the independent variables, using the “robust” option, and fill in the estimated coefficients
1. (a)  Fill out the table with necessary numbers, some will be on STATA output some you will need to calculate yourself.
2. (b)  Common sense predicts that your high school GPA (hsGPA) and the number of classes you skipped (skipped) are determinants of your college GPA (colGPA). Use regression (2) to test the hypothesis (at the 5% significance level) that the coefficients on these two economic variables are all zero, against the alternative that at least one coefficient is nonzero.
3. (c)  Find the F-statistic for regression (3) and explain what is it testing?
4. (d)  Find the F-statistic for regression (4) and explain what is it testing?
5. (e)  Are bgfriend (whether you have a boy/girlfriend) and campus (whether you live on campus) jointly significant determinants of college GPA? Use regression (2) and (4) to test your hypothesis. (i.e. use homoskedasticity-only F stat formula, eq.7.14 in the book, instead of directly testing with STATA)

1 Edouard Ducpetiaux, Budgets Economiques de Classes de Ouvrieres en Belgique (Brussels, Hayaz 1855)

Table 1
Definitions of Variables in GPA4.dta (data is from Wooldridge textbook)

Variable

colGPA

hsGP A skipped PC

bgfriend campus

Definition

Cumulative College Grade Point Average of a sample of 141 students at Michigan State University in 1994.
High School GPA of students.
Average number of classes skipped per week.

= 1 if the students owns a personal computer
= 0 otherwise.
= 1 if the student answered “yes” to having a boy/girl friend

= 0 otherwise.
= 1 if the student lives on campus. = 0 otherwise.

question

(3) (4)

Regressor

hsGPA skipped

Table 2
College GPA Results
Dependent variable: colGPA

(1) (2)

()()()() ()()()()

PC __

bgfriend campus Intercept

()()() __ __

() () __ __ __

()

()()()()

Fstatistics testing the hypothesis that the population coefficients on the indicated regressors are all zero:

hsGPA, skipped
hsGPA, skipped, PC
__

()()()()

hsGPA, skipped, PC, bgfriend, bgfriend, campus

Regression summary statistics

R2 R2

Regression RMSE n

()()() __ __

() () __ __ __

()

Notes: Heteroskedasticity-robust standard errors are given in parentheses under estimated coefficients, and p-values are given in parentheses under F– statistics. The F-statistics are heteroskedasticity-robust.

Following questions will not be graded, they are for you to practice and will be discussed at the recitation by your teaching assistant:

1. SW Empirical Exercise 6.1
2. SW Empirical Exercises 7.1