Econometric Problem Set

Econ 6896 Spring 2015 Problem Set 2 Due date: April 21th, 2015 before the class starts

The main objective of this problem set is to practice applications of Difference-in-Differences method which is a very common tool for empirical researchers.

In order to answer the questions, you should read Mastering ‘Metrics Chapter 5.

Please type your answers (12pt, double-spaced, save as pdf) and attached the STATA output including “.do” file.

You are welcome to collaborate on the problem set. You can share do/log files but please write up your own results.

This problem set is replication/extension of the Eissa and Liebman paper” Eissa and Lieb- man, Labor Supply Response and the Earned Income Tax Credit, QJE, 1996.

In EL (Eissa&Liebman) they use difference in differences techniques to examine the 1986 expansion of the Earned Income Tax Credit (EITC). In this exercise we apply their technique to analyze the 1993 expansion of the EITC.

We will estimate models like in EL for the 1993 expansion. In EL, the treatment group is single women with children, and the control is single women without children. We will estimate the same model. As an extension we will also estimate models where the treatment effect is allowed to differ between those with 1 vs 2+ children.

We have data for 1991-1996. We will assume that the before expansion years are 1991-1993 and the after expansion sample is 1994-1996.

We will use STATA for the problem set. You should have downloaded the STATA data set ps2.dta.

Data Set Overview: The data set consists of a sample of single women ages 20-54 with less than a high school education covering the years 1991-1996 from the Current Population Survey (CPS). (Note that EL estimates models separately for different education groups. We only have the lowest educational group. Ignore their results by educational group.) Start with “descibe” com- mand. All the dollar amounts are in 1997 dollars.

Questions:

1. Describe the 1993 expansion of the EITC. What does theory predict about the impact of this EITC expansion on the labor supply of single women with children? Discuss the predictions. Would you expect a difference by family size. Why or why not. Explain.

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2. Construct variables for difference-in-difference analysis as in EL equation 1. You will need a variable for the “treatment” (call it “anykids”) and for after the expansion (call it “post93”). Calculate the sample means by presence of children as in Table 1 of EL. Discuss the differences in the sample between single women with and without children. Calculate sample means separately for single women with 1 versus 2 or more children. How do the sample differ? (Don’t worry about the variables that are in EL that are not in the input data set. The variables in their Table I that you do not have: preschool children, weekly participation, and hours of work. You can create “filing unit size = number of children + 1 (for the woman)”. You can create earnings conditional on work from earnings.)

3. Estimate the impacts of the EITC on employment using a “single difference” model. In particular, take one after year (1996) and compare the employment of single women with kids to single women without kids. Estimate the unconditional “single difference” in a regression framework. What do you find? Given the information above, how might this estimate be biased?

4. Create a graph with plots mean annual employment rates by year (1991-1996) for single women with children (treatment) and single women without children (control). Discuss the differences that show up in the graph. Use this information to critique the validity of using single women without children as the control group. In particular, examine the “pre-treatment” trends and how they differ by group.

5. Calculate the unconditional difference-in-differences estimates of the effect of 1993 EITC expansion on employment of single women as in EL Table II. Also calculate the standard errors. Organize your table as in EL Table II. Explain your results. What is the estimated treatment effect? How does it compare to the magnitude of the treat- ment effect in EL? Do you expect the 1993 expansion to generate larger or smaller effects compared to the 1986 expansion? Why? (Use the specification in EL Table II, Panel B, Control group 1. Treatment group is less than high school single women with children; the control group is less than high school single women without children. Before is 91-93, after is 94-06.)

6. Recalculate the unconditional difference-in-differences estimates by allowing the treat- ment effects to vary for those with 1 and 2 or more children. Again organize your results as in EL Table II. This amounts to considering one treatment group at a time, the control group in both cases is single women without children. Which treatment effect is larger?

7. Estimate conditional difference-in-differences by running PROBIT regressions as in EL Table III. Estimate model labeled WITHOUT COVARIATES in column (1). What is the treatment effect? How does it compare to the unconditional treatment effect that you found in part (6). Is the what you expected? Why or why not? What is the interpretation of the coefficient on KIDS. What about POST93? (Please report dp/dx values for the probit.)

Reference:

1. Hilary Hoynes, Professor of Public Policy and Economics https://gspp.berkeley. edu/directories/faculty/hilary-hoynes#research.

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2. Eissa and Liebman, Labor Supply Response and the Earned Income Tax Credit, QJE, 1996

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