# DID estimator of the treatment effect

1. Repeated cross-sections and difference-in-difference.

Download “jtrain.dta” from Canvas. It contains data for 157 companies observed over two years (1987 and 1988). This dataset is originally from the Wooldridge website (http://fmwww.bc.edu/ec-p/data/wooldridge/jtrain.des), with 1989 observations dropped. All variable definitions can be found on the website. I have generated a variable “treatment” that equals one if the firm has received or will receive a government grant (it is the same for two years) for employee training.

1. If we treat this dataset as repeated cross-sectional data (ignore firm ID “fcode”), write down the DID regression equation that estimates the effect of the treatment (receiving the grant) on total training hours per trainee (hrsemp). Use “lemploy” as the control variable.
2. Estimate the above regression in Stata. Generate the necessary variables if they are not already in the dataset.

1. Which coefficient is the DID estimator of the treatment effect? Discuss the direction and magnitude of the treatment effect.

1. Panel data and difference in difference (continue with the previous analysis).

The same DID analysis can be conducted using the panel nature of this data. (Hint: You only need to replace the “treatment” fixed effect with the fixed effects for each firm, leaving the year fixed effect and the interaction term unchanged.)

1. Write down the regression equations for the three versions of the fixed effect regression: first-difference, demeaning, and dummy variables.
2. Carry out the estimation of the “demeaning” version of fixed-effect regression in Stata.

1. Which coefficient is the DID estimator of the treatment effect? Discuss the direction and magnitude of the treatment effect.
2. Do you expect results from the other two versions to be the same or different from the results above?
3. Estimate the random effect model for the regression you did in 2b. Conduct the Hausman test and discuss which model to choose.

1. Endogeneity and IV (continue with the analysis)
2. We want to estimate the effect of training hours (hrsemp) on reducing log scrap rate (lscrap). Estimate the first-difference regression using OLS. The first-differenced variables are chrsemp and clscrap, controlling for clemploy (the first-difference of log employment.)

1. A plausible omitted variable bias is from unskilled employees. Firms hiring unskilled employees have to train them longer. Other things equal, untrained employees also tend to create more scrap. Discuss the likely direction of this omitted variable bias using the formula, clearly define the terms in the formula.

1. The government grant can be used as an instrument for training hours. Since the OLS is in first-difference, the IV is also in first-difference (cgrant). Estimate the reduced form regression. Is the IV promising?

1. Carry out IV estimation using ivreg2 and interpret the results of training on scrap rate. (Hint: first-differencing estimates the coefficients of the original regression w/o differencing. So when interpreting coefficients, there is no need to consider the differencing.)

1. Discuss the results based on different components of an IV study that we learned in class.

(Note that the first-stage regression is the DID analysis in question 1. The “cgrant” variable is the same as the interaction term in DID. This is an example of IV with DID as the first stage. The reduced form regression is actually another DID analysis.)

1. Limited dependent variable models

In the following hypothetical studies, identified 1) the appropriate model(s) to be used; 2) what marginal effects should be reported; 3) the mathematical expression for the marginal effects on observation i; 4) the Stata command that produces each marginal effect.

1. You are analyzing whether graduate school applicants get admission from at least one school that they applied to.

1. You are studying the determinants of donation to charities (dollars) in a sample of US households

1. You are studying the drivers of fertility (number of children) in a sample of US households.

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