Consider the study of the effect of public-sponsored training programs. As argued in public programs of training and employment are designed to improve participant's productive skills, which in turn would affect their earnings and dependency on social welfare benefits.

We use the Job Training Partnership Act (JTPA), a public training program that has been extensively studied in the literature. For example, see The JTPA was a large publicly-funded training program in the United States that began funding in October 1983 and continued until late 1990's. We focus on the Title II subprogram, which was offered only to individuals with \barriers to employment" (long-term use of welfare, being a high-school drop-out, 15 or more recent weeks of unemployment, limited English proficiency, phsysical or mental disability, reading proficiency below 7th grade level or an arrest record). Individuals in the randomly assigned JTPA treatment group were offered training, while those in the control group were excluded for a period of 18 months.

Our interest lies in measuring the effect of training on participants' future earnings.

We use the database in ? that contains information about adult male and female JTPA participants and non-participants.

It has the following variables:

_ earnings: 30 months accumulated earnings

_ jtpa offer: JTPA offer: dummy variable for individuals that recived a JTPA offer;

_ jtpa training: JTPA training: dummy variable for individuals that took JTPA training;

_ sex: male dummy variable;

_ hsorged: dummy variable for individuals with completed high school or GSE;

_ black: race dummy variable;

_ hispanic: dummy variable for hispanic;

_ married: dummy variable for married individuals;

_ wkless13: dummy variable for individuals working less than 13 weeks in the past year;

_ age2225,age2629,age3035,age3644 and age4554: age range indicator variables.

Question 1.a The government is interested in whether JTPA training had an effect on future earnings after controlling for the effect of age, marital status, gender, race and education. Using OLS estimate this effect and comment on its sign, magnitude and statistical significance. Repeat the analysis for those with positive earnings only. Are there differences between these two estimations? Why? Also compute the same estimates in log earnings and comment.

Question 1.b The government is interested in knowing if training has a different effect on men than in women. Can you test for that using the first OLS model in

Q 1.a (in levels, including 0 earnings, controlling for covariates)?

Question 1.c Using the first model in Q 1.a., analyze if there are differences across the effect of training on wages on different quintiles of the distribution.

Comment on its differences using quantile regression models. Present a graph for

f0:1; 0:2; 0:3; 0:4; 0:5; 0:6; 0:7; 0:8; 0:9g containing the quantile regression coefficients of the effect of training on wages, together with its 95% con_dence interval.

Question 1.d Provide an elaborated argument to justify that the estimators of the effect of training in Q 1.a may be upward biased.

Question 1.e Use an instrumental variables strategy to find a consistent estimator of the effect of training on wages. You should argue that jtpa offer serves as a good instrument for jtpa training. Explain very carefully.