Econometrics 2023
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September 8, 2023
1 Econometrics
You are to turn in (i) a nicely formatted .pdf document containing your answers and any output (regressions, tests) needed to answer the questions, and (ii) separately, the code you used to generate the output (R or stata). If using R, the following packages will be helpful or necessary:
library（tidyverse）
library（vtable）
library（stargazer）
library（car）
library（AER）
1.1 Question 1:
This question uses data from leisure.csv, with a description of the variables included in leisure description.txt
.
The equation of interest is
leis1 =βo + β1 lhr山age + β2 lspsepag + β3 lothinc
+ β4 educ + β5 marr + β6 age + β7 age2 + u
a: create a summary statistics table that reports the mean, standard devi- ation, minimum, and maximum for onlg the variables in the regression above.
b: Run the multivariate regression listed above. In a table, report the coef- icient estimates, standard errors, and R2 value. Then interpret the coefficient estimates for β1 , β2 , and β3 in a way that a general audience of non-economists could understand.
c: Is there strong evidence that education afects leisure in a statistically signiicant way？ conduct a two-sided hypothesis test for whether the coefficient is zero and report the p-value. Interpret the p-value
d: Test the null hypothesis that β2 = β3. Report the results from this test and whether you can reject the null hypothesis. Discuss, in words, what this hypothesis is testing and what you conclude from the hypothesis test.
e: Test the joint null hypothesis that β6 = β7 = o. Report the test statistic and p-value for the test.
f: what is required for β1 to be an unbiased estimator for β1 . Evaluate whether this is likely to hold.
1.2 Question 2：
This question uses data from card.csv, with a description of the variables in- cluded in card description.txt
.
starting with the full card.csv dataset, create a new sample consisting only of individuals at least age 3o (age > 3o). Also, drop any observations that are missing data on motheduc. use this new sample to answer the questions below.
a: Report the mean and median hourly wage in dollaTS for individual in the sample.
b: Estimate the coefficients in the simple regression model below using or- dinary least squares estimation. Report the estimates in a table, along with the R2 and sample size.
log(山age) = βo + β1 educ + u (1)
c: Add controls for IQ and knowledge of the working world score (kw w). Report these results and discuss the change in the estimated coefficient on educ
d: Add an interaction term to the speciication in part (c) that tests whether the efect of education on wages difers between those living in the south and those not living in the south:
log(wage) = βo + β1 educ + β2 south + β3 educ x south + β4 IQ + β5 kw w + u
Test whether the efect of eduction in the south and non-south are statisti- cally diferent from each other at the 5% level.
e: In the regression from part (b), use the variable motheduc as an in- strumental variable for educ. Report these results, and discuss the necessary conditions for motheduc to be a valid instrumental variable.
2023-09-23