Consider a population of workers who live two periods. Each worker chooses between either working both periods or else participating in a government training program in the first period and working in the second. If the th i worker works both periods, his earnings in each period are

Wi=+i .

If he takes training, he has zero earnings in the first period, but his second-period earnings are

Wi=++i .

The parameter thus reflects the increase in second-period earnings that can be achieved through training. The error term i , which has the population mean zero, describes the distribution of earnings capacity across workers. Each worker knows his own i .

a) Assuming that workers maximize the present value of lifetime earnings and that the interest rate is r >0, what is the decision rule that determines whether a worker chooses to participate in the training program?

b) A research wants to estimate by the difference between mean second-period earnings of those who take training and mean second-period earnings of those who dont. Use the decision rule in part a) and the facts introduced in our lecture materials to derive the direction of this estimator's bias.