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4 Pages

Econ 339 Winter 2009 Midterm I - Solutions

Course: ECON 339, Spring 2012
School: Northwestern
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Word Count: 1136

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University Department Northwestern of Economics ECON 339 Labor Economics - Professor: Steffen Habermalz First Midterm Examination February 4th 2009 1. (5 pts. Each) Labor Force Participation Rate. Use the information in the table to answer the following questions. 2000 2050 popshare LFPR popshare LFPR Young 0.2 0.5 0.15 0.4 Middle 0.5 0.9 0.35 0.8 Old 0.3 0.65 0.5 0.55 a. Calculate the economy-wide...

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University Department Northwestern of Economics ECON 339 Labor Economics - Professor: Steffen Habermalz First Midterm Examination February 4th 2009 1. (5 pts. Each) Labor Force Participation Rate. Use the information in the table to answer the following questions. 2000 2050 popshare LFPR popshare LFPR Young 0.2 0.5 0.15 0.4 Middle 0.5 0.9 0.35 0.8 Old 0.3 0.65 0.5 0.55 a. Calculate the economy-wide labor force participation rate (LFPR) in both years. LFPR2000 = 0.2 0.5 + 0.5 0.9 + 0.3 0.65 = 0.745 LFPR2050 = 0.15 0.4 + 0.35 0.8 + 0.5 0.55 = 0.615 Hence, a change of -13% b. Calculate the contributions of the population composition and the group LFPRs to the change in the economy-wide LFPR LFPR2050 ( popshare = constant at 2000 level) = 0.2 0.4 + 0.5 0.8 + 0.3 0.55 = 0.645 LFPR2050 ( LF Pr = constant at 2000 level) = 0.15 0.5 + 0.35 0.9 + 0.5 0.65 = 0.715 This means that the change in population shares (population ageing) was responsible for 10% of the 13% change in the economy-wide LFPR. The change in group LFPRs explains the rest. c. A friend of yours suggests calculating the economy-wide LFPR in 2050 holding only the share of young people constant at the 2000 level and use it for further calculations. Comment. Not a good idea since the shares of all people necessarily need to add to one. Holding constant the share of young people means one would have distribute the extra 5% of people between middle-aged and old people in 2005. There is no obvious way of doing this. d. To what extent would old people need to work to achieve the same economy-wide LFPR in 2050 than in 2000? They would have to have a LFPR of 81% 1 2. Borjas (page 49, underlined by me) writes Finally, a researcher attempting to estimate the labor supply model quickly encounters the serious problem that the wage rate is not observed for people who are not working. However, a person who is out of the labor market does not have a zero wage rate. All that we really know is that this persons wage is below the reservation wage. Many empirical studies avoid the problem of calculating the wages non-workers by simply throwing the non-workers out to the sample that is used for calculating the labor supply elasticity. This procedure, however, is fundamentally flawed. The decision of whether to work depends on a comparison of market wages and reservation wages. Persons who do not work have either very low wages rates or very high reservation wages. a. (5 pts.) What is a reservation wage? The reservation wage is the market wage at which the person is indifferent between working and not working. The slope of the budget constraint equals the marginal rate of substitution of the indifference curve which goes through non-participation point. Picture would be nice here b. (15 pts.) Give a detailed explanation of why excluding non-working individuals when estimating the labor supply elasticity leads to biased estimates. Be sure to reference the underlined part above. Lets say we want to estimate the labor supply elasticity ln hoursi = 0 + 1 ln hourlywagei + u . By using this model we are usually implicitly assuming that the true population regression function is equal to E ( ln hoursi | ln hourlywagei ) = 0 + 1 ln hourlywagei which implies that E ( ui | ln hourlywagei ) = 0 . However, in this case we need to account for the fact that only working individuals will be included in the sample. Therefore we have to change the notation to E ( ln hoursi | ln hourlywagei , working ) = 0 + 1 ln hourlywagei + E ( ui | ln hourlywagei , working ) If the last term is NOT equal to zero we are estimating the wrong model!! How does to this relate our example? Lets incorporate the wage and the reservation wage into the equation. We get E ( ln hoursi | ln hourlywagei , w > wR ) = 0 + 1 ln hourlywagei + E ( ui | ln hourlywagei , w > wR ) Borjas states that people not working have either very low wages or very high reservation wages. This means that non-working are sufficiently different from the working unless people who work are also more likely to have low wages or high reservation wages. This 2 doesnt seem true. This means that some factor in the error term is related to the decision to ( ) participate in the labor force and E ui | ln hourlywagei , w > wR 0 and we are estimating the wrong model. This happens because our sample is selected and thus nonrandom. 3. (5 pts. each) Consider a firm with MPE = 100 0.1 ( E 20 ) that faces a constant price of P=10. 2 a. Assume that the labor market is competitive and the wage=804. What is the profitmaximizing short-run level of labor input? The VMPE = 1000 ( E 20 ) . Set this equal to the wage and solve for E=34. 2 b. Now assume that the firm faces an upward-sloping labor supply curve LS = 100 + 20 E . What is the profit-maximizing short-run level of labor input? Also calculate the wage that the firm will pay. Now we need to set VMPE=MCE. Derive as TC = w E = (100 + 20 E ) E = 100 E + 20 E 2 . Differentiate to get MCE = 100 + 40 E . Set VMPE=MCE and solve for E 1000 ( E 20 ) = 100 + 40 E 2 900 E 2 + 40 E 400 = +40 E E 2 = 500 E = 500 = 22.36 c. Which of the two firms in a) and b) makes higher short-run profits? (Assume that the firms are otherwise identical) The firm facing the upward-sloping labor supply curve could choose same wage/employment combination than the firm that operates in a competitive market but DOES NOT CHOOSE to do so. Since the firms are otherwise equal that must mean that the firm in b) makes higher profits. 4. Verschiedenes (5 pts. Each): a. Consider a firm in the long-run. You observe that, following a wage decrease, the firm uses more capital than before. Does this make sense in light of the fact that capital became more 3 expensive relative to labor? (10 pts.) This is not counterintuitive because of the existence of a substitution effect and scale effect. The decrease in wages lowers marginal cost, increases production and increases the demand for both inputs. The scale effect is (always) positive. The substitution effect leads to less demand for capital by the firm since capital became more expensive. The above situation just indicates that the scale effect was bigger than the substitution effect. b. Explain how Card/Krueger used high-wage and low-wage fast food employers in New Jersey to estimate the effect of the minimum wage on employment. CK use a DiD approach in which they used the increase in New Jerseys minimum wage to estimate the effect of a rise in the minimum wage on employment in the fast food industry. They use the low-wage (employers that paid part of their labor force less than the new minimum wage) employers in NJ as the treatment group since they are directly affected by the change in the minimum wage (they have to pay more). As a control group they used high wage employers in NJ because they should serve as a proxy for the changes in employment of low-wage establishments in the absence of the change in the minimum wage AND because these high-wage employers already paid their workers more than the minimum wage (the increase in the minimum wage for those employers is not binding). ( )( LowWage LowWage Highwage Highwage Emplbefore Emplafter Emplbefore They then calculated: Effect = Emplafter ) 4
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