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ECON 7310:  ELEMENTS OF ECONOMETRICS

Tutorial 10:  Experiments and Quasi-Experiments, SW Ch13

E13.1 A prospective employer receives two resumes: a resume from a white job applicant and a similar resume from an African American applicant.  Is the employer more likely to call back the white  applicant to arrange an interview?  Marianne Bertrand and Sendhil Mullainathan carried out a  randomized controlled experiment to answer this question. Because race is not typically included  on a resume, they differentiated resumes on the basis of “white-sounding names” (such as Emily  Walsh or Gregory Baker) and “African American-sounding names” (such as Lakisha Washington  or Jamal Jones). A large collection of fictitious resumes was created, and the presupposed “race” (based on the “sound” of the name) was randomly assigned to each resume. These resumes were  sent to prospective employers to see which resumes generated a phone call (a “call back”) from  the prospective employer.  Use the data file Names .csv to answer the following questions.  See Names Description .pdf for more details about the data.

(a) Define the  “call-back rate” as the fraction of resumes that generate a phone call from the

prospective employer.   What was the call-back rate for whites?   For African Americans? Construct a 95% confidence interval for the difference in the call-back rates. Is the difference statistically significant? Is it large in a real-world sense?

(b) Is the African American/white call-back rate differential different for men than for women?

(c) What is the difference in call-back rates for high-quality versus low-quality resumes? What is the high-quality/low-quality difference for white applicants? For African American applicants? Is there a significant difference in this high-quality/low-quality difference for whites versus African Americans?

(d) The authors of the study claim that race was assigned randomly to the resumes. Is there any evidence of nonrandom assignment?

TSLS In this question, we fit the following regression model to the data tsls .csv

Y = β0 + β1 X1 + β2 X2 + u                                                     (1)

We are interested in studying the causal effect of X2  on Y , i.e., β2 .

(a) Estimate (1) using OLS. Write out the estimated regression equation along with standard errors and one measure of fit in a standard form.

(b) If X2  were endogenous, which least squares assumption would be violated?  What could be wrong with OLS if this assumption is indeed invalid?

(c) Estimate β2  using two-stage least squares (TSLS), instead of OLS. Z1  is one of our candidate instrumental variables (IV). What conditions must hold for Z1  to be a valid IV for X2 ?

(d) Suppose Z1  is a valid IV for X2 . Run a TSLS regression using Z1 . Write out the estimated regression equations for the second-stage estimation. Are (β0 ,β 1 ,β2 ) exactly identified, over- identified, or under-identified?  What could be wrong if we run TSLS “manually” (i.e., use the regress command twice to replicate the TSLS procedure)?

(f) Is Z1  is a weak IV? Test the relevance of Z1 .

(g) Suppose we have another candidate IV, Z2 . Test the exogeneity of Z2 .

(h) Now suppose both Z1  and Z2  are valid IV. Estimate (1) using both Z1  and Z2 .  How many IV do you want to use to estimate β2 ? Explain your answer.