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%
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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
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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.
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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.
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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
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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
)
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