Use the data in JTRAIN98 to answer the following questions. See also Examples 3.7, 4.11, and 7.13 for linear model analysis. Here you will use a Tobit model because the outcome, earn98, sometimes is zero.

(i) How many observations (men) in the sample have earn98 = 0? Is it a large percentage of the sample?

(ii) Estimate a Tobit model for earn98, using train, earn96, educ, and married as the explanatory variables. Report the γ̂_train and its standard error. Is the sign what you expect? How statistically significant is it?

(iii) Does it make sense to compare the magnitude of the Tobit coefficient γ̂_train with the OLS coefficient from running a linear regression, say γ̂_train? Explain.

(iv) In part (ii), obtain the average partial effect—which is the average treatment effect—of train, and obtain its standard error. (Many econometrics packages have built-in commands to do this calculation.) How does it compare with the OLS coefficient, γ̂_train? What about statistical significance?

(v) To the Tobit estimation, include a full set of interactions of train with earn96, educ, and married. Now compute the APE (ATE) of train, along with a standard error. How does it compare with the linear model with full interactions in Example 7.13? [Incidentally, for getting the ATE it does not help to demean earn96, educ, and married before creating the interactions because of the nonlinear conditional mean function. Nevertheless, it will make the coefficients more comparable to those in the Tobit model without the interactions.]

(vi) Explain why the estimation in part (v) is not the same as estimating two separate Tobit models for the control and treatment groups and then obtaining the ATE as

where m̂(·) is the estimated mean function using the control (no training) group, m̂₁(·) is the estimated mean function using the treated (training) group, and x_i = (earn96_i, educ_i, married_i).

Transcribed Image Text:

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