The file JTRAIN2 contains data on a job training experiment for a group of men. Men could enter the
program starting in January 1976 through about mid-1977. The program ended in December $1977 .$ The idea is to test whether participation in the job training program had an effect on unemployment probabilities and earnings in $1978 .$
(i) The variable train is the job training indicator. How many men in the sample participated in the
job training program? What was the highest number of months a man actually participated in
the program?
(ii) Run a linear regression of train on several demographic and pretraining variables: unem 74
unem75, age, educ, black, hisp, and married. Are these variables jointly significant at the
5$\%$ level?
(iii) Estimate a probit version of the linear model in part (ii). Compute the likelihood ratio test for
joint significance of all variables. What do you conclude?
(iv) Based on your answers to parts (ii) and (iii), does it appear that participation in job training can
be treated as exogenous for explaining 1978 unemployment status? Explain.
(v) Run a simple regression of unem78 on train and report the results in equation form. What is
the estimated effect of participating in the job training program on the probability of being
(vi) Run a probit of unem 78 on train. Does it make sense to compare the probit coefficient on train
with the coefficient obtained from the linear model in part (v)?
(vii) Find the fitted probabilities from parts $(v)$ and (vi). Explain why they are identical. Which
approach would you use to measure the effect and statistical significance of the job training
program?
(viii) Add all of the variables from part (ii) as additional controls to the models from parts (v)
and (vi). Are the fitted probabilities now identical? What is the correlation between them?
(ix) Using the model from part (viii), estimate the average partial effect of train on the 1978
unemployment probability. Use $(17.17)$ with $c_{k}=0 .$ How does the estimate compare with the OLS estimate from part (viii)?

Answer

(i) 185, 24 months (ii) no (iii) same as in last part (iv) yes (v) (vi) see video (vii) two fitted values, exhaustive categories (viii) model is not saturated (ix) similar

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Introductory Econometrics

Chapter 17

Limited Dependent Variable Models and Sample Selection Corrections

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Video Transcript

Osborne Out of 445 observations. The number of those participating in their job training program is 185. The longest time in the experiment This 24 months. Part two. The F statistic for joint significance of the explanatory variables is 1.43 And the F Statistic has seven and 437 Degrees of Freedom. The p value is 0.19 Yeah, so the explanatory variables are jointly insignificant or three. We evaluate the same hypothesis, but we use a different regression approach. We estimate the model by Probert maximum likelihood and the likelihood ratio for joint significance is 10 points 18. This statistic follows a child square With 7° of freedom distribution. The p value for this likelihood ratio value is point 18. So we are unable to reject the null hypothesis. We come back to what we conclude in part two parts for. Yes, we can consider variable train to be independent of other observed factors because training ability training eligibility was randomly assigned among the participants. March five, this is there linear probability model result estimate coefficient on train is point 11 minus 0.11. That means participating in the training program is estimated to reduce unemployment chance by 11.1 point he says a large effect and its coefficient is highly significant. March 6th. We re estimate the equation with profit. We get the coefficient on train to be .121 and with a small standard error. Yeah, So although we have a different result for the coefficient of train, right? The T statistic is actually similar To what we get in part five, Part seven. The reason is we only have two fitted values, okay. In each case, and they are the same. The predicted value is .354 when the participants for the non participants. And the other value is 0.2 43 or the participants. This must be the case. Both models give us the self frequencies as the estimated probabilities. Part eight. We add more explanatory variables to The equation and now the results are not the same between two models. The reason is now the model. Um The models are not saturated, meaning the explanatory variables are not exhaustive and mutually exclusive. But because the other explanatory variables are insignificant, the fitted values are highly correlated between the LMP and property. Part nine. The estimated every partial effect of trend is about -11 two. It's very similar to the coefficient on train in the linear regression.

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