Labor Economics

1. Static Labor Supply

Martin Halla

University of Innsbruck
Department of Public Finance

Last update: March 17, 2015

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Measuring the Labor Force I
I 3 types: employed (E), unemployed (U ), out of labor force
(OLF )
I Empirical definitions:
I E: Job with pay for at least 1 hour or worked at least 15 hours on a
non paid job (such as at a family farm)
I U : temporary layoff from a job or have no job an actively looking for
work in the past 4 weeks
I OLF : Residual group (i.e., house-man, retiree, student).

I Measured based on survey data:

I US: Based on Current Population Survey, which interviews about
50, 000 households per month. All individuals above 16 years of age
are considered.
I AUT: Based on Mikrozensus

I Alternative method/data: unemployment register

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Measuring the Labor Force II
I Labor force LF
LF = E + U
I Labor force participation rate:
LF
Labor force participation rate =
Population
I Employment rate:
E
Employment rate =
Population
I Unemployment rate:
U
Unemployment rate =
LF

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Measuring the Labor Force II

I Hidden unemployment: Calculation is based on a subjective

measure of unemployment
I What does it mean to actively looking for work in the past 4
weeks ?
I Persons who gave up looking for a job, are not considered as
unemployed
I In contrast, everyone claiming to be actively looking ? is
consider as unemployed
I Discouraged workers lead to an understatement of the true
unemployment rate
I Shall we prefer the employment rate?

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 As Table 2-2 shows, there also has been a huge increase in the labor force participation
rate of women. At the beginning of the century, only 21 percent of women were in the
Basic Facts about Male Labor Supply
labor force. As late as 1950, even after the social and economic disruptions caused by
two world wars and the Great Depression, only 29 percent of women were in the labor
force. During the past 50 years, however, the labor force participation rate of women has
increased dramatically. By 2009, almost 60 percent of all women were in the labor force.

TABLE 2-1 Labor Force Participation Rates of Men, 19002009

Sources: U.S. Bureau of the Census, Historical Statistics of the United States, Colonial Years to 1970, Washington, DC: Government Printing Office, 1975;
U.S. Bureau of the Census, Statistical Abstract of the United States, Washington, DC: Government Printing Office, various issues.

Year All Men Men Aged 2544 Men Aged 4564 Men Aged over 65
1900 80.0 94.7 90.3 63.1
1920 78.2 95.6 90.7 55.6
1930 76.2 95.8 91.0 54.0
1940 79.0 94.9 88.7 41.8
1950 86.8 97.1 92.0 45.8
1960 84.0 97.7 92.0 33.1
1970 80.6 96.8 89.3 26.8
1980 77.4 93.0 80.8 19.0
1990 76.4 93.3 79.8 16.3
2000 74.7 93.1 78.3 17.5
2009 72.0 91.0 80.8 21.9

3
For more detailed discussions of the trends in labor supply in the United States and in other coun-
tries, see John H. Pencavel, Labor Supply of Men: A Survey, in Orley C. Ashenfelter and Richard
Layard, editors, Handbook of Labor Economics, vol. 1, Amsterdam: Elsevier, 1986, pp. 3102; and Mark
R. Killingsworth and James J. Heckman, Female Labor Supply: A Survey, in ibid., pp. 103204.
See also Mark Halla
Martin R. Killingsworth, Labor Supply,
(U Innsbruck) Cambridge:
Labor Cambridge
Economics University
Static Press, 1983.
Labor Supply 5/33
 Confirming Pages
Basic Facts about Female Labor Supply

Labor Supply 25

TABLE 2-2 Labor Force Participation Rates of Women, 19002009

Sources: U.S. Bureau of the Census, Historical Statistics of the United States, Colonial Years to 1970, Washington, DC: Government Printing Office, 1975, p. 133;
and U.S. Department of Commerce, Statistical Abstract of the United States, 2011, Washington, DC: Government Printing Office, 2011, Table 596.

Year All Women Single Women Married Women Widowed, Divorced, or Separated
1900 20.6 43.5 5.6 32.5
1910 25.4 51.1 10.7 34.1
1930 24.8 50.5 11.7 34.4
1940 25.8 45.5 15.6 30.2
1950 29.0 46.3 23.0 32.7
1960 34.5 42.9 31.7 36.1
1970 41.6 50.9 40.2 36.8
1980 51.5 64.4 49.9 43.6
1990 57.5 66.7 58.4 47.2
2000 60.2 69.0 61.3 49.4
2009 59.2 64.2 61.4 49.3

It is worth noting that the increase in female labor force participation was particularly
steep among married women. Their labor force participation rate almost doubled in recent
decades, from 32 percent in 1960 to 61.4 percent in 2009.
These dramatic shifts in labor force participation rates were accompanied by a sizable decline
in average hours of work per week. Figure 2-1 shows that the typical person employed in pro-
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Av. Weekly Hours of Work of Production Workers,
1900-2010

Figure: Sources: The pre-1947 data are drawn from Ethel Jones, "New Estimates of Hours of Work
per Week and Hourly Earnings, 1900-1957," Review of Economics and Statistics 45 (November 1963):
374-385. Beginning in 1947, the data are drawn from U.S. Department of Labor, Bureau of Labor
Statistics, Employment, Hours, and Earnings from the Current Employment Statistics Survey, "Table B-7.
Average Weekly Hours of Production or Nonsupervisory Workers on Private Nonfarm Payrolls by Industry
Sector and Selected Industry Detail": www.bls.gov/ces/cesbtabs.htm.

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The Workers Preferences
Neoclassical model of labor-leisure choice:

I Consumption of goods: C
I Consumption of leisure: L
I Utility (measure of well-being) function:

U = f (C, L)

I Indifference curve:
I Indifference curves are downward sloping
I Higher indifference curves indicate higher levels of utility
I Indifference curves do not intersect
I Indifference curves are convex to the origin (implies diminishing
marginal rate of substitution; see below)

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Indifference Curves

Figure: Points X and Y lie on the same indifference curve and yield the same level of utility (25,000
utils); point Z lies on a higher indifference curve and yields more utility.

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Indifference Curves Do Not Intersect

Figure: Points X and Y yield the same utility because they are on the same indifference curve; points Y
and Z also should yield the same utility. Point Z, however, is clearly preferable to point X.

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The Slope of an Indifference Curve
What happens to a persons utility as she allocates one more hour to
leisure or buys an additional dollars worth of goods? :

I Marginal utility of leisure (M UL ): change in utility resulting

from an additional hour devoted to leisure activities, holding
constant the amount of goods consumed.
I Marginal utility of consumption (M UL ): change in utility
resulting from an dollar spent on goods, holding constant the
amount of leisure consumed.
I Slope is equal to the marginal rate of substitution
U ()
M UL L
M RSL,C = = U ()
M UC
C

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Differences in Preferences across Workers
Different workers will typically view this trade-off differently; thus
have different indifference curves

Figure: (a) Cindys indifference curves are relatively steep, indicating that she requires a substantial
bribe to give up an additional hour of leisure. (b) Mindys indifference curves are relatively flat, indicating
that she attaches a much lower value to her leisure time.

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The Budget Constraint

Consumption of goods and leisure constrained time and resources

I Non-labor income (such as property income or dividends) V
I Working hours h
I Hourly wage rate w
I Budget constraint
C =V +hw
I Thus, we abstract from saving
I Further, we assume that w is constant (across h)

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The Budget Constraint
Allocation of time:
I Person has two alternative uses for her time: work or leisure
I Working hours h (as defined above) and leisure hours L

I Time constraint:
T =L+h
I Combin(ed) constraints:

C =V +hw

C = V + (T L) w
C = (V + T w) L w
| {z } | {z }
Intercept Slope

I Each hour of L consumed has a price; which is w

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The Budget Line Is the Boundary of the Workers
Opportunity Set

Figure: Point E is the endowment point, telling the person how much she can consume if she does not
enter the labor market. The worker moves up the budget line as she trades off an hour of leisure for
additional consumption. The absolute value of the slope of the budget line is the wage rate.

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The Hours of Work Decision
I Agents choose bundle of goods & leisure that max. utility U
I Optimal bundle: budget line is tangent to indifference curve
I Slope of indifference curve (M RSL,C ) equal slope of budget line (w)
I M RSL,C : the rate at which the agent is willing to give up L in
exchange for additional C
I w: Rate at which the market allows to substitute L for C

I Tangency Condition
M UL
=w
M UC
I The marginal rate of substitution (subjective rate) equals the wage
rate (objective rate)
M UL
= M UC
w
I Last $ spent on L gives the same utility as the last $ spent on C

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An Interior Solution to the Labor-Leisure Decision

Figure: A utility-maximizing worker chooses the consumption-leisure bundle given by point P, where
the indifference curve is tangent to the budget line.

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Effect of a Change in Non-labor Income on Hours of Work
Income effect: Impact of the change in V (holding w constant) on h

Figure: An increase in nonlabor income leads to a parallel, upward shift in the budget line, moving the
worker from point P0 to point P1 . (a) If leisure is a normal good, hours of work fall. (b) If leisure is an
inferior good, hours of work increase.

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Effect of a Change in the Wage Rate on Hours of Work
A change in w has an income effect and a substitution effect

Figure: A change in the wage rate rotates the budget line around the endowment point E. A wage
increase moves the worker from point P to point R, and can either decrease or increase hours of work.

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Decomposing the Impact of a Wage Change

Figure: An increase in the wage rate generates both income and substitution effects. The income
effect (the move from point P to point Q) reduces hours of work; the substitution effect (the move from
Q to R) increases hours of work.

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Decomposing the Impact of a Wage Change

I The substitution effect always implies that an increase in w

(holding real income constant), increases h.
I The income effect is in principle ambiguous. Assuming leisure is
a normal good, the income effect implies that an increase in w
decreases h
I An increase in w increases h if the substitution effect dominates
the income effect.
I An increase in w decreasesh if the income effect dominates the
substitution effect.

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To Work or Not to Work?
What factors motivate a person to enter the labor force?
I Market wage: How much employers are willing to pay for an
hour of work
I Reservation wage: indicates how much the worker requires to be
bribed into working the first hour.
I Thus, our agent will enter the labor market if

market wage > reservation wage

I More precisely, the reservation wage is the minimum increase in

income that would make our agent indifferent between
remaining at the endowment point E and working that first
hour.
I Reservation wage will depend on a persons tastes for work

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The Reservation Wage

Figure: If the person chooses not to work, she can remain at the endowment point E and get U0 units
of utility. At a low wage (wlow ), the person is better off not working. At a high wage (whigh ), she is
better off working. The reservation wage is given by the slope of the indifference curve at the endowment
point.

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Labor Supply Curve

I Labor supply curve: (predicted) relation between h and the w

I See next slide
I Backward-bending labor supply curve

I Labor supply curve can be derived for all individuals

I Aggregate labor supply curve: adding up the hours that all
individuals in the economy are willing to work at a given wage
I Horizontal aggregation
I See two slides later

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Deriving a Labor Supply Curve for a Worker

Figure: The labor supply curve traces out the relationship between the wage rate and hours of work.
At wages below the reservation wage ($10), the person does not work. At wages higher than $10, the
person enters the labor market. The upward-sloping segment of the labor supply curve implies that
substitution effects are stronger initially; the backward-bending segment implies that income effects may
dominate eventually.

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Derivation of the Market Labor Supply Curve from the
Supply Curves of Individual Workers

Figure: The market labor supply curve "adds up" the supply curves of individual workers. When the
wage is below wA , no one works. As the wage rises, Alice enters the labor market. If the wage rises
above wB , Brenda enters the market

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Labor Supply Elasticity
I Labor supply elasticity: measurement for the responsiveness of
h to changes in w

Percent change in hours of work h/h h w

= = =
Percent change in wage rate w/w w h
I The labor supply elasticity gives the percentage change in h
associated with a 1 percent change in w
I Suppose that the workers wage is initially 10 per hour and that
she works 1,900 hours per year. The worker gets a raise to 20
per hour, and she decides to work 2,090 hours per year

((2090 1900)/1900) 100 10%

= = = 0.1
((20 10)/10) 100 100%
I can pos. or neg.; elastic if > |1|, inelastic if < |1|

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Estimation of the Labor Supply Elasticities
Regression model:

hi = wi + Vi + other variables

I hi number of hours that person i works

I wi wage rate
I Vi non-labor income.
I : impact of a one-dollar wage increase on hours of work (c.p.)
I > 1 substitution effects dominates income effect
I < 1 income effects dominates substitution effect
I : impact of a one-dollar increase in non-labor income
I < 1 leisure is a normal good
I > 1 leisure is an inferior good

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Empirical Estimates of the Male Labor Supply Elasticity

I Male labor supply is roughly around 0.1

I Thus, a 10 percent increase in the wage leads, on average, to a
1 percent decrease in hours of work for men
1. It is negative(!); i.e, income effects dominates substitution effect
2. It is inelastic; i.e, men are not very responsive to changes w

I Consensus on decomposition
I 10 percent increase in the wage
I Substitution effect increases h by about 1%
I Income effect decreases h by about 2%
I Note, substitution effect is positive (as predicted by the theory)
I Dominance of income effects could explain the decline in hours of
work between 1900 and 2000 (see above)

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Problems with the Estimated Elasticities
I Huge variation in estimates of across studies, why?
I Number of statistical and measurement problems
I Hours of work h
I Hours of work per day, per week, or per year?
I Labor supply curve more elastic the longer the time period
I Survey data is noisy
I Wage rate w
I Preferred measure is hourly wage rate
I Problems with noisy hours
I No wage rate for non-employed individuals
Non-random sample leads to selection bias
I Non-labor income V
I Correlated with (past) taste for work

I Pos. corr. between V and h may not imply that L is inferior

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 Theory at Work
Theory at Work: Work and Leisure in Europe and the USA
WORK AND LEISURE IN EUROPE AND THE UNITED STATES

In 1960, hours of work and labor force participation from the much higher European tax rates on earned
rates were roughly similar or higher in European coun- income. In Germany and Belgium, for example, the
tries than in the United States. The labor force participa- marginal tax rate on earned income is between 60 and
tion rate of men was around 92 percent in the United 70 percent, while in France and Italy, it is greater than
States, as compared to 92 to 95 percent in France, 50 percent. These tax rates contrast with the roughly
Germany, or Italy. Similarly, the typical employed per- 35 percent marginal tax rate in the United States. The
son worked around 2,000 hours per year in each of the higher tax rate generates substitution effects in Euro-
countries. pean countries that reduce the incentive to work.
By 2000, there was a huge gap in the work effort It turns out, however, that these tax rate differentials
of the typical person in Europe vis-a-vis the United may not be sufficiently large to explain the huge dif-
States. The male labor force participation rate was just ferences in labor supply. European labor market regula-
over 85 percent in the United States, as compared to tions, and particularly those policies advocated by labor
80 percent in Germany and 75 percent in France or Italy. unions in declining European industries to share work,
Similarly, annual hours of work per employed person seem to explain the bulk of the labor supply differences.
had fallen to 1,800 hours in the United States, but had Despite their stated objective of spreading out the avail-
fallen even further to about 1,400 hours in Germany, able work among a large number of potential workers,
1,500 hours in France, and 1,600 hours in Italy. these work-sharing policies did not increase employ-
Although it is now frequently alleged that European ment. Instead, they increased the returns to leisure as an
culture explains why Europeans work less than Ameri- ever-larger fraction of the population began taking lon-
cans, this hypothesis is not informative. After all, that same ger vacations. The social multiplier effect of a larger
culture led to a very different outcomeEuropeans work- return to leisure activity seems to have had a much
ing at least as much as Americansonly a few decades ago. wider social impact on the work decisions of potential
Recent research concludes that a small number of workers in many European countries.
observable factors tend to explain the differential work Source: Alberto Alesina, Edward Glaeser, and Bruce Sacerdote,
and leisure trends between the United States and west- Work and Leisure in the U.S. and Europe: Why So Different?
ern European countries. Part of these differences result NBER Macro Annual, 2005: 164.

To illustrate the problem introduced by these measurement errors, suppose that a worker
overreports her hours of work. Because of the way the wage rate is constructed (that is, as
theMartin
ratio of Halla
annual(Uearnings to annual hours
Innsbruck) of work),
Labor the denominator
Economics of this Supply
Static Labor ratio is too 31/33
 cular group of female workers and across cohorts of workers.24 In other words, th
participation rate of a given birth cohort of women increases as the women get old
Female Labor Force Participation (past the childbearing years). For example, the participation rate of women born aroun

TABLE 2-4 Country 1980 1990 2003

International
Differences Australia 52.7 62.1 66.4
in Female Canada 57.8 67.6 70.4
Labor Force France 54.4 57.8 62.0
Participation Germany 52.8 56.7 64.0
Rate (women Greece 33.0 43.6 50.2
aged 1564) Ireland 36.3 43.8 56.2
Italy 39.6 45.9 46.8
Source: U.S. Bureau
Japan 54.8 60.3 64.2
of the Census,
Statistical Abstract Korea, South 51.2 54.3
of the United States, Mexico 33.7 42.4
2006, Washington,
DC: Government New Zealand 44.6 63.0 67.6
Printing Office, Table Portugal 54.3 62.9 67.2
1343. Spain 32.2 41.2 50.7
Sweden 74.1 80.4 75.0
Turkey 36.7 26.9
United Kingdom 58.3 66.5 67.8
United States 59.7 68.5 71.7

I Common trend: Rising 23 female labor force participation

A survey of these international trends is given by Jacob Mincer, Intercountry Comparisons
I of Labor Force
Stronger trend in developed Trends and of Related Developments: An Overview, Journal of Labor Economics
countries
3 (January 1985 Supplement): S1S32.
I Increase with age and24across cohorts
James P. Smith and Michael P. Ward, Time-Series Growth in the Female Labor Force, Journal
I of Laboreconomic,
Differences due to varying Economics 3 (January 1985, Part
cultural, and2):institutional
S59S90; and Claudia Goldin, Life-Cycle Labor-Force
environments
Participation of Married Women: Historical Evidence and Implications, Journal of Labor Economics
I Increase in market wages (see next slide)
7 (January 1989): 2047. and/or decline in reservation wages;
what other other factors can you think of?

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Cross-Country Relationship between Growth in Female
Labor Force and the Wage, 1960-1980

Figure: Source: Jacob Mincer, "Intercountry Comparisons of Labor Force Trends and of Related
Developments: An Overview," Journal of Labor Economics 3 (January 1985, Part 2): S2, S6.

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