Md Moshi Ul Alam
Md Moshi Ul Alam
Assistant Professor of Economics
Clark University
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Econometrics PS 4

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Prof Alam

Simplified Angrist and Krueger (1991) Replication

You will need libraries AER, ggplot2, and lmtest for this problem set.

Recall the context of our quiz on Instrumental Variables based on Angrist and Krueger (1991). Load iv_csl_dataset.csv in R using read.csv function. It contains a simplified simulated dataset based on Angrist and Krueger (1991). The variable qob indicates the quarter of birth of individual i (Q1, Q2, Q3, Q4). The rest should be self-explanatory.

We study the causal effect of education on earnings, controlling for a bunch of other included exogenous variables. \ln(Wage_i) = \beta_0 + \beta_1 Educ_i + \beta_3 Age_i + \beta_4 Region_i + u_i where Wage is the annual wage of individual i, Educ is years of education, Age is age in years, and Region is a categorical variable indicating the region of residence (representing region fixed effects) which includes the , and clearly E(u_i|Educ_i) \neq 0 so E(u_i | Educ_i, Age_i, Region_i) \neq 0 as well.

Question 1

Explore the dataset and report summary statistics of the variables

Question 2

Make two plots and describe what you see in each plot:

  1. mean years of education by quarter of birth
  2. mean log wage by quarter of birth

Question 3

Generate a dummy variable Z equal to 1 if an individual was born in Quarter 1, and 0 otherwise. Explain why Z is a valid instrument for Educ in the above regression.

Question 4

Estimate the 1st stage regression. Be careful to include the other exogenous variables in the regression. Report and interpret the results. See slide 39.

Question 5

Predict the values of Educ using the 1st stage regression and save them in a new variable called Educ_hat. Estimate the 2nd stage regression of ln(Wage) on Educ_hat and the other exogenous variables. Report and interpret the results. See slide 39 & 40.

Question 6

Now instead of manually doing the 2SLS procedure, use the ivreg function from the AER package to estimate the IV regression of ln(Wage) on Educ, using Z as an instrument for Educ, and including the other exogenous variables. Compare the results. What differs and why?

Use summary(yourivmodel, diagnostics = TRUE) to see the diagnostic tests and interpret whether the instrument is weak or not.

Question 7

Explain why your estimate is a Local Average Treatment Effect and for whom it is identified.