Problem 1

Consider the following one period problem of a person looking for a job. The pesrson has to decide about the amount of job search effort a, which causes disutility A per unit of search effort but increases the probability of finding a job Π(a). If the person finds a job he will work  h hours, receive wage per hour w, and pay fraction  of the earnings to the government. An unemployed person receives benefits b. In addition to earnings and benefits this person also receives non labor income d (regardless of the employment status). Utility function of the person if employed is U(c;  h) = log c e, utility function of the person if unemployed is U(c; 0) = log c.

(a) Write the problem of the consumer who is choosing optimal effort a to maximize the expected utility.

(b) Write the first order condition for optimal choice of effort a.

(c) Draw the diagram with a on horizontal axis showing the marginal benefit and the marginal cost of increasing a from the condition in part (b).

(d) Use diagram from part (c) to show and discuss the effects of following four changes (each of them separately in a new diagram)

(1) unemployment benefits become more generous

(2) person inherits money

(3) internet becomes available and makes search effort more productive (it increases the marginal probability Π0(a) for all a)

(4) economy is hit by a severe recession

Problem 2

The following problem will ask you to undertake an analysis of unemployment exit rates. Start by downloading CPS.dta which is a dataset containing an extract from Current Population Survey between January 2004 and December 2007. For each month in the sample, the dataset contains information on individuals who were unemployed, the description of variables is in CPS.pdf. If you plan to use R also dowload mlm.R.

(a) Estimate a multinomial logit model with unemployment (lfstatus equal to 1) as reference outcome, using age, gender, race, education, duration of unemployment, job openings rate and availability of extended unemployment benefits as explanatory variables.

Note 1: Since education and duration of unemployment are categorical variables you have to use i.deduc and i.ddur in Stata. In R, you first have to redefine these two as factor variables using the factor command: mydata$deduc.f <- factor(mydata$deduc) and then use deduc.f in the estimation instead of deduc.

Note 2: You can add the variable for availability of extended unemployment benefits dEB either directly as an extra variable, or by interacting it with duration of unemployment. In Stata this would be done using dEB#i.ddur. In R you would have to first create a new variable by multiplying dEB and ddur and them converting it into a factor variable as explained in Note 1.

(b) Comment briefly on the effects of age, gender and race on the likelihood of becoming employed ]and the likelihood of dropping out of labor force.

(c) What is the average marginal effect of having a college degree on probability of becoming employed? What is the average marginal effect of having a college degree on probability leaving labor force?

(d) Construct the data that shows how the average predicted probability of becoming employed changes with the unemployment duration and the availability of extended benefits. Repeat the same with the probability of leaving labor force. Plot a graph showing these four. Comment briefly on your results.

Attachment:- Files.rar