SHAPIRO–STIGLITZ THEORY

Introduction
Unemployment is
one of the most visible indicators of economic activity. The rate of
unemployment typically rises considerably during recessions then falls as the
economic recovers. People commonly view the typical unemployed worker as
suffering long-lasting despair and destitution, so the media publicize high
unemployment as a great social problem. We shall see that this view of the
unemployed worker is not an accurate depiction of the vast majority of those
out of work in the United States. In contrast, most of the unemployed find work
relatively quickly. While their income loss is significant, it is not
catastrophic for most workers who suffer an unemployment spell.
Some
degree of unemployment is socially and perhaps personally desirable. Much of
unemployment in the United States consists of new entrants to the labor market
seeking their first job, individuals who are voluntarily changing jobs or
occupations, and people in jobs for which periodic or seasonal layoffs are normal,
expected, and compensated for by higher wages during periods of employment. For
these individuals, unemployment is not a problem at all. It is merely part of
the natural functioning of a flexible and efficient labor market.
Economists
often view unemployment as one facet of an inevitable process of search in the
labor market. Jobs and workers are heterogeneous along many dimensions. Workers
differ (among other ways) by intelligence, creativity, education, training,
experience, physical size and strength, manual dexterity, ability to sustain
repetitive tasks, and preferences about their work environment. Jobs vary in
the abilities, education, and experience that are required to perform them, as
well as in working conditions, location, opportunities for advancement, and
many other characteristics. Since workers and jobs are so heterogeneous, the
process of matching the characteristics of a particular unemployed worker with
the most suitable vacant job often cannot be accomplished quickly. Instead
unemployed workers and employers having vacant jobs engage in a two-sided
search, seeking to achieve a good match as quickly as possible. The length of
this search process for a typical unemployed worker is a major factor in
determining the unemployment rate.
One
can imagine an economy in which this matching problem could be solved
trivially. If all workers and jobs were identical, for example, there would be
no gain to searching for a better match. Or if everyone had instantaneous and
perfect information about the characteristics of all workers and jobs, searches
could be accomplished in just a moment. However, in an economy in which the
matching problem cannot be solved trivially it is generally desirable to have
both a positive unemployment rate and a positive job vacancy rate. Successful
matching requires a pool of searching workers on one side of the market and a
pool of available jobs on the other. The socially optimal unemployment rate
depends on the size of the pool that is required in order for optimal matching
to occur. The optimal pool size, in turn, depends on the efficiency of the
“matching technology” in the economy as well as on a variety of social and
policy variables.
If
the costs and benefits of search are largely internal to the workers and firms
doing the searching, we might expect that a competitive market economy would
gravitate toward the socially optimal amount of search. However, the labor
markets of modern economies contain many distortions that might cause the long-run
equilibrium unemployment rate (the so-called natural rate of unemployment) to
be higher or lower than the optimal rate. In particular, a wide variety of
government policies influence the incentives of workers and employers to
continue searching, including unemployment insurance programs, job-protection
legislation, and “active” labormarket policies such as job-placement assistance
and training. 
Recent
analysis of unemployment has focused intensely on one particular empirical
problem: extremely high unemployment in continental Europe since 1980. From
1950 until 1970, the unemployment rate in most European countries averaged
about 2%, roughly half of the rate in the United States during that period.
Since 1980, Europe has suffered unemployment rates in the 8 to 12 percent
range, about twice the U.S. rate. Moreover, long-term unemployment (of more
than one year) is far more common in Europe than in America. Theories of
unemployment are able to explain some, but not all, aspects of the divergence
of unemployment behavior between Europe and America.
The
most interesting new tools that we employ in our analysis of unemployment is
dynamic programming, which is a common method of analysis of models involving
transition in continuous time between alternative discrete states. In the case
of unemployment models, the main states are employed and unemployed, with some
variations in selected models. Dynamic programming has a complicated side and a
simple intuition. We’ll focus on the latter here.

The statistical definition

In
order to measure unemployment, economists have adopted a statistical definition
that is only partially understood by the general public. Also, optimal matching
does not generally mean making the best matches that are conceivably possible.
Better matches involve costs (longer unemployment spells) as well as benefits
(better fit between jobs and workers). The optimal amount of matching balances
these marginal costs and benefits.
In
the United States are compiled by the Bureau of Labor Statistics (BLS) from the
monthly Current Population Survey (CPS) conducted by the Bureau of the Census.
This survey of approximately 64,000 households asks general questions about the
labor-market status of adult members of the household during the week prior to
the week in which the survey is taken.
Based
on the responses to the CPS questions, every adult is placed into one of three
categories: employed, unemployed, or not in the labor force.
Anyone who worked for pay at all during the reference week is considered to be
employed, including part time workers. Among those not employed, those who were
both actively seeking work and immediately available for work, plus those who
were awaiting recall from a temporary layoff from their previous job, are
classified as unemployed. Anyone else, i.e., those who did not work, were not
on layoff, and either were not actively seeking work or were not available for
work, are considered to be out of the labor force.
In
the United States, the extent of unemployment is commonly expressed as the unemployment
rate
, which is the number unemployed divided by the total labor force,
which consists of the sum of employment and unemployment. (In Europe, the
“headline number” is more likely to be the number of unemployed rather than the
rate.) The unemployment rate ignores completely those who are classified as out
of the labor force—they enter neither the numerator nor the denominator. To the
extent that it is difficult to distinguish between people who are unemployed
and those out of the labor force, this may cause ambiguity in the meaning of
the unemployment rate. To account for this potential problem, economists
sometimes use the employment/population ratio instead of the unemployment rate.
This ratio measures the share of the adult population that is employed and
treats unemployment and out of the labor force as equivalent states.

Problems with
the statistical measures

Apart
from the usual difficulties associated with surveys, such as inaccuracy in
responses, the categorization of the population by labor-market status poses
some particular difficulties. There are some “gray areas” between the three
categories that have led some economists (and politicians) to question the
relevance of published measures.
It
may seem like the least controversial boundary would be that between employment
and the other categories. There is an obvious benefit to basing unemployment
statistics on a survey such as the CPS rather than using such measures as
applications for unemployment insurance benefits. If eligibility for benefits
depends on their answer, then those out of work have a strong incentive to lie
about whether they are actively seeking work. The CPS approach is likely to
elicit more honest answers from respondents.
sification
seems easy. However, if there are individuals who are working part-time because
they have not been able to find a full-time job, then some degree of “problem
underemployment” is masked in the statistics. Part-time work accounts for a
large and growing share of employment in some OECD countries. Among countries
of the European Union, over 15 percent of workers in the Netherlands, Belgium,
the United Kingdom, Germany, Denmark, and Spain now work part-time, while less
than 10 percent of those in Greece, Portugal, Italy, Ireland, and France do. In
many cases, laws that treat part-time workers differently than full-time
workers help to explain these differences in rates.
In
a study of the working-hour preferences of EU workers in 1989, a large majority
in most countries indicated satisfaction with their working status. Among those
working full-time, 21 percent indicated that they would rather be working
part-time while 77 percent were happier with full-time work. (The remainder
responded “no reply.”) Among part-time workers, 66 percent were content with
part-time work while 30 percent would have preferred full-time employment.
Thus, it appears that for European countries about one-third of part-time
employment is involuntary, while about one-fifth of full-time workers would
prefer to work part-time.
This
result suggests that defining employment to include both part-time and fulltime
workers masks problems in both directions: workers working more hours than they
wish and workers working fewer hours than they want. Since there are somewhat
more workers who work less than their desired amount, there is probably on net
some degree of hidden underemployment in part-time employees. However, this may
be less than one might have expected from the raucous reactions of union
leaders and some politicians to the rise of part-time employment in recent
decades.
Another
difficult boundary is that between unemployed and out of the labor force. Many
countries have begun to collect data on discouraged workers, who are
officially classified as out of the labor force. Discouraged workers have given
up job search because they do not believe they can find a job. They are clearly
part of the unemployment problem if their
assumption is correct
. However, since they are not actively seeking work,
it is impossible to tell whether they would have, in fact, been able to find a
job had they continued their searches. As of 1991, the number of discouraged
workers as a percentage of the labor force ranged from virtually nil in number
was around one percent. The presence of discouraged workers suggests that the
measured unemployment rate may understate the true magnitude of unemployment.
However, there may be a counterbalancing bias due to “low-intensity searchers.”
Anyone without a job who answers affirmatively to the question “Are you looking
for work?” is classified as unemployed. Some individuals may answer yes to this
question even if their job search consists of sitting at home and waiting for
the phone to ring. (Or, in some countries, working at an unreported,
black-market job.) If some of the people counted as unemployed are actually, in
effect, either employed or out of the labor force, then unemployment may be
overstated.
Although
these problems may compromise the accuracy of unemployment statistics, it is
unlikely that the biases in the statistics change systematically from month to
month. Moreover, information about discouraged workers and involuntary
part-time workers are collected periodically to allow analysts to assess
whether the biases are changing over time. Interpreted with caution,
survey-based measures of unemployment are useful in measuring changes in
labor-market conditions over time.

Natural and
cyclical unemployment

We
often make a distinction theoretically among several categories of
unemployment, although it is difficult or impossible to decompose our empirical
measure in a corresponding way. The most fundamental distinction is between natural
unemployment
and cyclical unemployment. Milton
Friedman, in his famous presidential address to the American Economic
Association in 1967, coined the phrase “natural rate of unemployment” to refer
to the rate that results from the equilibrium operation of the microeconomy,
when macroeconomic conditions cause neither a general excess demand nor an
excess supply of labor.
At
any point in time, macroeconomic conditions can lead to a slack aggregate labor
market in which unemployment is above the natural rate or a tight labor market
with unemployment lower than the natural rate. The difference between the
actual rate and the natural rate of unemployment is often called cyclical
unemployment. Keynes emphasized the importance of cyclical unemployment during
the Great Depression, which he interpreted as a huge aggregate excess supply of
labor. 
When
unemployment changes, there is often disagreement among economists about
whether the causes are microeconomic or macroeconomic, in other words, whether
it is a change in natural or cyclical unemployment. In the early postwar period,
the natural rate of unemployment was widely regarded as being stable at about 4
percent in the United States and about half of that in Europe. Fluctuations in
un-employment during the 1950s and 1960s were believed to be changes in
cyclical unemployment. 
Changes
in the labor market and in the general level of unemployment in the 1970s and
1980s convinced most macroeconomists that the natural rate can fluctuate
considerably due to changes in the microeconomic structure of the labor market.
The natural rate in the United States was reckoned to be 5.5 to 6.5 percent in
the 1980s, but may be somewhat lower now. The causes of the current high
unemployment in Europe are regarded almost universally as microeconomic, which
means that they should be viewed as increases in the natural rate.
Macroeconomists
and labor economists have recently begun reexamining the sharp distinction
between natural and cyclical unemployment. Despite the inconvenience it imposes
on our theories, the microeconomy and macroeconomy are highly interdependent. A
period of recession or depression caused by strictly macroeconomic factors will
affect the microeconomic structure of the labor market in several ways. The
demand for durable goods is usually more sensitive to business cycles than
other goods, so these industries will shrink more than others in recessions,
which will affect the industry, regional, and occupational structure of the
demand for labor. On the supply side, workers who have been unemployed for a
long time often lose job skills or job-finding skills, making them less likely
to find a job.
Economists
have used the term hysteresis to refer to situations where prolonged increases in
cyclical unemployment raise the natural rate of unemployment. If hysteresis
occurs, then the unemployment rate may never return all the way to its original
natural rate after rising in a large and prolonged recession.
Within
the category of natural unemployment, economists sometimes distinguish frictional
and structural
unemployment. Frictional unemployment results from the natural frictions of the
labor-market matching process. You can think of the frictionally unemployed as
job searchers for whom suitable vacancies exist, but who have not yet found
these openings. Structural unemployment occurs when the skills and other
characteristics of the unemployed do not match the requirements of the
available jobs. Technological change and structural shifts in the economy often
cause changes in the skill composition of the job pool. If the labor force does
not keep up with these changes, then structural unemployment is likely to
result.
There is no
single unified model of unemployment. The Walrasian paradigm based on the
market for a homogeneous good predicts that there should be no unemployment, so
this workhorse benchmark model of neoclassical economics is not informative.
Instead, one must move beyond the Walrasian model in one way or another. Since
there are many ways in which actual labor markets differ from a Walrasian
market, there are many possible approaches that can be followed.
Introduction to Theories of Unemployment
While
employment and unemployment are clearly connected in important ways, a theory
of employment alone is not sufficient to explain the behavior of unemployment.
One fallacy that is often committed by uninformed members of the public and the
media is to assume that a decline in employment of, say, 1000 workers
necessarily means that unemployment will rise by 1000. If a firm lays off 1000
workers, only a fraction will enter the ranks of the unemployed, and many of
those are unlikely to remain there very long. Some of the laidoff workers will
find jobs right away, moving from one employment position to another rather
than into unemployment. Others will leave the labor force for retirement,
education, child-bearing, or other nonlabor activity. Similarly, when a firm
hires 1000 new workers, some will have been previously unemployed but many
others will come from other jobs or from outside the labor force as, for
example, with new graduates finding their first jobs.
 Rather than simply viewing unemployment as the
counter-state to employment, we model it as a process of search. The success
that individuals seeking new jobs will have in finding them depends on two
broad kinds of circumstances: (1) the general balance of demand and supply in
the labor market, and (2) the match between the searchers’ characteristics and
those of the available jobs. There are two broad categories of approaches to
explaining movements in unemployment that correspond to these two kinds of
circumstances.
  One approach emphasizes the heterogeneity of
workers and jobs. Because every worker and every job has unique
characteristics, matching them up through a search process is time consuming.
Search models examine the propensity of employers and job searchers to achieve
matches and how that propensity varies over time. This approach models the
flows of workers and jobs between states: a job match that results in a hire
transforms an unemployed worker into an employed worker and a vacant job into
an occupied one. To complete the model, one must examine the other labormarket
flows: job creation and destruction, entry to and exit from the labor force,
and the flow of separations of existing workers from their jobs.
In
the search approach, natural unemployment fluctuates when there are changes in
the efficiency of matching in the economy or in the other flows between
labormarket states. For example, if structural shifts in the economy
make it more difficult to match the characteristics of unemployed workers with
those of vacant jobs, then matching will be less efficient and the natural rate
of unemployment will increase.
It
should be emphasized that the kind of unemployment described by the search
theories does not require a general excess supply of labor. It stresses the
fact that even when the number of unemployed is equal to the number of job
vacancies, neither number is likely to be zero.
The
other major approach emphasizes microeconomic imperfections that lead to
imbalance between demand and supply in the aggregate labor market, especially
to excess labor supply. These imperfections can be associated with government
interference such as minimum wages and unemployment benefits, or with
deviations in the behavior of firms or workers from the assumptions of
price-taking competitive markets such as the presence of unions or
noncompetitive behavior by employers. This approach often tends to maintain the
assumption that labor is a homogeneous good and emphasizes the possibility of a
lasting imbalance between demand and supply in the unified labor market.
One
popular model that takes that approach is the efficiency-wage model.
This model is based on the notion that firms pay higher wages than would
normally be necessary in order to attract workers. Different versions of
efficiency-wage models stress different reasons why firms may do this. One is
that higher wages may prevent shirking by employees; another is that a higher
wage offer may attract a more qualified pool of applicants. While each firm in
an efficiency-wage model wants to pay more than other firms, that obviously
cannot happen. If all firms offer an efficiency wage, then aggregate wages in
the economy are bid up above the market-clearing level and a general excess
supply of labor results.
Contract
models

are based on the observation that labor contracts often forbid firms from
changing wages in the short run, but allow them to respond to variations in
their need for labor through layoffs and overtime. A rich literature exists
that examines the rationale for such contracts and their optimal structure.
Another
model that follows this approach is the insider-outsider model, where a
sharp distinction is drawn between the bargaining status of individuals who are
currently working (insiders) and those who are unemployed or out of the labor
force (outsiders). This model has been advanced as a promising explanation for
the poor performance of labor markets in continental Europe in recent decades.
Minimum Wages and
Unemployment
A
lengthy empirical literature has examined the impact of minimum-wage laws on
both employment and unemployment. Although there is a considerable range of
results, the consensus seems to be that minimum wages have relatively minor employment/unemployment
effects. Nonetheless, minimum-wage laws may have significant impacts in certain
time periods and on certain groups of workers, especially teenagers and
unskilled workers.

A simple
minimum-wage model

The
most basic analysis of the minimum wage proceeds in the way that we would
analyze any price floor. In Figure 1, labor is assumed to be homogeneous; all
workers participate in the same market and earn the same wage. If the market is
Walrasian, then the wage will be w*
and the economy will operate with full employment at the level L*. If a minimum wage is imposed at a
level higher than the equilibrium wage, say at w1, then the market cannot reach equilibrium. Only L
workers are
hired at w1 and L
″−Lworkers are
unemployed. 
Figure
1. Minimum wage in unified labor market
A
representative set of citations is Card and Krueger (1995), Deere, Murphy, and
Welch (1995),  Neumark and Wascher
(1995), Brown, Gilroy, and Kohnen (1982), and 
Brown (1988).
The
magnitude of unemployment arising out of the minimum wage in this model depends
on the elasticity of the labor-supply and labor-demand curves. If these curves
are highly inelastic (steep), then the unemployment gap is small and the main
impact of the minimum wage is to transfer income from consumers (through higher
prices of products) or producers (through lower profits, if the product market
is not competitive) to workers. If labor demand and supply are highly elastic
(flat) then there will be a large reduction in employment and a large increase
in unemployment.
Beyond
its simplistic representation of the labor market, the analysis depicted in
Figure 1 is flawed in one important respect: minimum wages are almost always
set well below the average wage in the economy, not above it. Suppose that the
minimum wage is set at w2
in Figure 1. In this case, the minimum is not binding since no one is paying
wages below w2 in
equilibrium. Thus, the minimum wage has no effect on the market at all. This is
obviously too simplistic an analysis to capture how a minimum wage affects the
market. Most workers, including virtually all skilled workers, earn more than
the minimum wage and are not directly impacted by its presence. Some workers,
mostly young and unskilled workers, may be affected, however. To capture this
kind of interaction, we need a segmented model of the labor market that
separates skilled from unskilled labor. 

Minimum-wage
effects on skilled and unskilled labor

A
two-sector labor market is shown in Figure 2. The left panel shows the
equilibrium of the market for skilled labor. In this market, the equilibrium
wage ws exceeds the
minimum wage wm, so there
is no direct effect of the minimum-wage law on unskilled labor. The right panel
shows the unskilled labor market in which the equilibrium wage wu is lower than the legal
minimum. The wage floor is effective in the unskilled market, preventing demand
from coming into equality with supply. As in our initial analysis of Figure 1,
employment is reduced and an unemployment gap exists.
This
would be the end of the story if there were no connections between the markets
for skilled and unskilled labor. However, there may be spillovers on either the
demand side or the supply side (or both). On the supply side, there would be no
immediate spillover of workers from one market to the other. Unskilled workers
cannot, presumably, become skilled immediately, while skilled workers earn a
higher wage in the skilled market and have no incentive to move. In the longer
run, supply flows in either direction are possible. Those who cannot find work
in the unskilled sector due to the excess supply situation may choose to
acquire skills and eventually move to the skilled sector. This would increase
the supply of skilled workers and drive their wage down. However, the gap
between skilled and unskilled wages has been reduced (for those unskilled who
have work), so there may be less incentive for workers to acquire skills if
they believe that they will be successful in getting an unskilled job at the
higher minimum wage. This spillover would tend to offset the previous one,
leaving the net effect on supply uncertain. 
On
the demand side, firms’ demand for skilled workers may be affected by the
increase in the wage for unskilled labor. If skilled and unskilled workers are
substitutes, the firm will increase its demand for skilled workers, which will
tend to push skilled wages upward. If they are complements, this will reduce
skilled-labor demand and lower skilled wages. Although the
substitute-complement relationship between skilled and unskilled labor is
likely to vary across industries, the most common assumption is that they tend
to be substitutes. If that assumption is true, then an increase in the minimum
wage will raise the wages of skilled workers. 
This
hypothesis is supported strongly by the intense political support for
minimum-wage legislation by labor unions. Most members of labor unions already
earn more than the minimum wage, so they have no direct interest in a higher
minimum wage. However, if a higher minimum wage for unskilled workers raises
the whole wage structure as firms substitute union workers for
now-more-expensive lower-skilled workers, then union members may gain as well.
Although union leaders may claim that their support of minimum-wage laws is
philanthropy toward or solidarity with unskilled workers, it is highly unlikely
that they would support these laws if they reduced
the wages of union members.
To
summarize, effective minimum-wage laws appear to benefit the fraction of
unskilled workers that are able to find jobs. They reduce the welfare of those
unskilled workers who cannot find employment. Skilled labor seems to gain from
higher minimum wages as substitution by firms pushes the entire wage structure
upward.
Of
course, higher general labor costs will eventually pass through to higher
product prices, which will most likely eat away much of the gain in wages that
skilled workers appear to get.
Figure
2. Minimum wage in a segmented labor market
A
final word about the effects of minimum wages. In a competitive market,
everyone who wants to work is able to find a job. But when jobs are rationed,
as in the minimum-wage model, then some unskilled workers will find jobs and
others will be unemployed. Who? What factors determine which unskilled workers
will be the lucky ones? Any time that jobs (or anything else) is rationed by
non-price means, the possibility of discrimination enters.
Unemployment Insurance and the Length of Job
Search
Under
competition, everyone finds a job and firms take what they can get. When there
is excess supply at the prevailing wage, employers can pick and choose. In
particular, teenage workers and members of recognizable minority groups may end
up getting fewer of the available jobs if employers on average prefer to hire
older and nonminority labor. Teens and racial minority groups often have high
unemployment rates; discrimination that arises under job rationing may provide
a partial explanation.
One determinant
of the rate of unemployment is the length of time that the average unemployed
job-searcher takes to accept a new job. If searchers find and accept new jobs
quickly, then unemployment is lower than if it takes a long time for people to
move from unemployed to employed. The length of job search is sometimes modeled
by considering the marginal costs and marginal benefits that a searcher expects
from continuing to search. The search terminates when the marginal benefit of
search no longer exceeds the marginal cost. 
The principal
cost of search is the wage income that is forgone by not having accepted the
best offer received to date. The longer a worker searches, the better the job
offers he or she accumulates, so the marginal cost of continuing becomes higher
the longer is the search. The benefit of additional search is that a better job
might be found. This marginal benefit is likely to decline as search continues,
since the incremental increase in job quality is likely to become smaller as
more jobs have been checked. 
The
declining marginal benefit curve in Figure 3 shows the falling marginal benefit
of search, while the rising marginal cost curve represents the increasing
marginal cost. Length of search is measured on the horizontal axis. Search
equilibrium occurs where marginal benefit equals marginal cost, with duration D*.
 Anything that changes the marginal cost or
marginal benefit of search will affect the chosen search duration, and thus
affect equilibrium unemployment. For example, if a person’s prospects for
improving on his or her best job offer suddenly appear to improve, then the
marginal benefit of search increases and the individual lengthens search time.
If a searcher’s spouse gets a better job, the marginal cost of search may fall,
increasing the length of search. One possible explanation for why unemployment
rose in the 1970s and 1980s when more and more married women entered the labor
force is that two-income families may have lower marginal search costs than
families with a single earner, allowing longer searches and raising the
equilibrium rate of unemployment.
It
may strike you as a big assumption to suppose that unemployed workers have job
offers to refuse. The mass media encourage us to think of unemployed workers as
having no choices, desperately in search of any
job. While there are undoubtedly some unemployed who fit this profile, it is
not typical. Most unemployed workers have the option of accepting a “poor
quality” job such as working at McDonald’s, even if they have received no
offers in their usual occupation or at their accustomed salary.
Cost/benefit of search
Figure 3.
Marginal costs and benefits of search

Unemployment
benefits and search duration

One
consideration that has a large effect on search cost is the availability of
unemployment-insurance benefits. If the government pays benefits to an
unemployed worker to “replace” a substantial share of his or her potential
salary, marginal search cost may be substantially reduced. In the United
States, workers who lose their job are entitled to a share of their previous
salary (usually about half, subject to an upper limit) for a limited period of
time (usually six months, though this is sometimes extended during recessions).
The presence of limited-time unemployment benefits would shift the left-hand
part of the marginal cost curve down as shown in Figure 4 assuming that
benefits run out after a period of time equal to D
. The presence of unemployment benefits
causes two potentially testable changes in unemployment. First, the duration of
search and the equilibrium rate of unemployment should both increase. Second,
because of the discontinuity in the marginal cost curve at the time limit for
benefits, there should be an unusually large share of the unemployed accepting
jobs at exactly that duration.
Figure
4. Equilibrium search with unemployment compensation
The
effect of benefits on unemployment is difficult to test because of the many
other factors that affect unemployment rates. In an empirical study of 1980s unemployment
rates in 20 countries, Layard, Nickell, and Jackman (1991) find that an
additional year of benefit eligibility cause unemployment to rise by 0.92
percentage points, and that an increase of one percentage point in the
“replacement ratio” raises unemployment by 0.17 points. Time-series studies for
the United States are less clear. The effect of unemployment benefits on search
can be seen more decisively from the effect of benefit duration on length of
unemployment spells. A study by Bruce Meyer found a remarkable tendency for the
length of unemployment spells to be exactly the maximum benefit duration. For
example, if unemployed workers are eligible for six months of benefits, then an
unusually large number of the unemployed would find jobs after exactly six
months. The replacement ratio is the percentage of previous income that the
worker receives in benefits.

Optimal search
duration

Although
there is considerable evidence that more generous unemployment benefits lead to
higher equilibrium unemployment, it is not clear that this is necessarily bad.
In order to assess the optimal duration
of unemployment from a social point of view, we need to examine the marginal social costs and benefits of search,
which may not be identical to marginal private
costs and benefits. 
Lengthening
the search of an unemployed worker may lead to a better match between the
skills of the worker and the requirements of the job. By using his or her
skills in a better way, the worker receives higher wages. Society gains from
this through improved productivity and efficiency—more output is available for
society from the worker’s effort. If wages reflect workers’ marginal product
accurately, then the social benefits of the increased search and improved
matching correspond to the individual or private benefits.
The
private cost to the worker of additional search is his or her forgone wages
from the best available offer. Likewise, society loses the output that the
worker would have produced had he or she not continued to search. If wages
reflect marginal products then social costs and private costs will be similar.
If
private benefits and costs of search match up with social benefits and costs,
then the individual’s choice of search duration will be socially optimal. If
the government then introduces unemployment benefits to this situation, private
search costs fall, but social costs do not change. Searchers will search longer
than the socially optimal duration and the equilibrium or natural unemployment
rate will be above the socially optimal rate.
However,
there are reasons why we may be skeptical about the optimality of searchers’
duration choices in the absence of unemployment benefits. One that is familiar
from our analysis of consumption and investment is the possibility of liquidity
constraints and imperfect capital markets. Households without substantial
nonhuman assets usually find it difficult, and often impossible, to borrow at
reasonable interest rates against future earnings. Consider the lone worker in
such a household. If he or she were to become unemployed, the cost of a lengthy
job search could be huge in terms of forgone utility (starving children come to
mind). However, from society’s point of view, the cost is merely the cash value
of the worker’s forgone wages. Whereas the worker cannot borrow against future
earnings, society does so easily. Thus, the effective cost of search to the
worker could be much larger than the social cost. In this case, the duration of
search in the absence of unemployment benefits could be too short and the
equilibrium unemployment rate too low. Introducing unemployment benefits may
serve to offset (more or less) this externality, leading to a more socially
efficient search decision.
The
presence of a labor union that engages in collective bargaining on behalf of
workers can alter the nature of the labor market in many ways. Several theories
of unemployment incorporate the behavior of unions. Romer analyzes the
insideroutsider model, which is often thought to represent union behavior. In
this section, we consider the direct effects of unions on employment and
unemployment.
Whole libraries
have been written about the goals, activities, and impacts of labor unions.
While union activities and styles of organization differ substantially from
country to country and over time, unions almost universally raise their
members’ wages through the process of collective bargaining. Unless unions also
raise the marginal product of labor, this will result in a lower level of
employment of union labor than would occur in a competitive market.
                    There
are several other models of theory of wages and employment in the labour market
equilibrium in the labour market equilibrium such as A two-Sector model of
unions and unemployment, Efficiency-wage models and Shapiro-Stiglitz model. The
focus of this paper is Shapiro Stiglitz model.     
In labour
economics
, Shapiro–Stiglitz theory of efficiency wages (or Shapiro–Stiglitz
efficiency wage model
) is an economic theory of wages and unemployment in
labour market equilibrium. It provides a technical description of why wages are
unlikely to fall and how involuntary unemployment appears. This theory was
first developed by
Carl Shapiro and Joseph
Stiglitz
.
When full employment is achieved, if a worker is sacked, he
automatically finds his next job soon. In the circumstances, he does not need
to exert his effort in his job, and thus full employment necessarily motivates
a worker to shirk provided that he is happy with loafing on the job. Since
shirking makes a firm’s productivity decline, the firm needs to offer its
workers higher wages to eliminate shirking. Then all firms try to eliminate
shirking, which pushes up average wages and decreases employment. Hence nominal
wages tend to display downward rigidity. In equilibrium, all firms pay the same
wage above market clearing, and unemployment makes job loss costly, and so
unemployment serves as a worker-discipline device. A jobless person cannot
convince an employer that he works at a wage lower than the equilibrium wage,
because the owner worries that shirking occurs after he is hired. As a result,
his unemployment becomes involuntary.
Unemployment is one of the most important subjects in
macroeconomics. Its constant presence in almost any economy raises a question
that many economists and researchers have tried to answer: why is there
unemployment? One of the simplest answers relies on the existence of a minimum
wage above market-clearing wage. However, what can be the explanation in the
absence of a minimum wage or when this is fixed below marketclearing wage?
Alfred Marshall proposed one of the most important ideas to answer these
questions: the efficiency wage hypothesis. Alfred Marshall argued that firms
could actually want to pay more than
market-clearing wage in order to increase the workers productivity or
efficiency. In this paper we focus our analyses on the ShapiroStiglitz model.
In this case, since firms cannot monitor their workers’ effort perfectly, they
have an incentive to pay more than market-clearing wage to induce workers not
to shirk.

 The Shapiro-Stiglitz Model

 Assumptions

There are four general assumptions:
§  The
economy is composed by a large number of workers,
, who maximize their
expected discounted utilities;
§  The
economy has also a large number of firms,
, who maximize their
expected discounted profits; 
§  Time
is continuous;
§  The
analysis focuses on the steady-state.
Shapiro
and Stiglitz (1984) entitled their paper “Equilibrium unemployment as a worker
discipline device.” This idea clearly fits in well with the model of the
previous section: high unemployment encourages greater effort. The
Shapiro-Stiglitz model is a specific application of efficiency wages in which
workers have an incentive to shirk (not work hard). Firms, obviously, would
like to assure that workers instead exert high effort and thus achieve high
productivity. If the firm can monitor worker performance at no cost, then it
can simply insist on its desired level of effort as a condition of employment
and fire workers who shirk. The level of performance required and the wage
would be set jointly at levels that would assure that the firm could attract
workers.
However,
the more interesting and realistic case is one in which firms cannot directly
observe individual workers’ effort. Instead, there is a given probability
(lessRecall from our study of real business cycles that the high degree of
observed fluctuation in employment was one aspect of the business cycle that
the Walrasian model failed to explain. Since workers get utility from higher
wages and lose utility from working hard, the combination of wages and work
requirements offered by the firm must give workers a level of utility as high
as that offered by other firms in order to attract workers.
Thus,
workers must decide whether to shirk or to work hard by balancing the increased
utility of shirking against the probability of being caught and fired. This is,
in itself, an interesting problem that warrants our attention. However, the
worker’s incentives depend in an important way on what happens to fired
workers. If they can simply move immediately to another firm and shirk, then
there is no real cost to being caught and no incentive to work hard. In order
to motivate hard work, the fired shirker must lose something by being fired. In
the spirit of the previous model, the fired worker either loses a wage premium
(efficiency wage) offered by the employer or faces the prospect of an
unemployment spell. Since all firms offer the same wage in equilibrium, it must
be the existence of unemployment that gives workers an incentive to work hard.
Hence the title “equilibrium unemployment as a worker discipline device.”
Solving the
Shapiro-Stiglitz model would be impossible without some simplification of our
usual macroeconomic framework. For example, the instantaneous utility function
(9.21) is obviously highly simplified. It neglects the tradeoff between
consumption and leisure, has no diminishing marginal utility, and does not
allow for variation in the marginal disutility of exerting effort relative to
the utility of wage income (the coefficients on w and e are the same).
However, for the purposes of the model, it is sufficient to focus attention on
the key tradeoffs for workers. Similarly, the assumption that effort is
discrete (taking on only the values 0 and e
) is obviously unrealistic, but introducing continuously varying degrees of
effort makes the model much more complicated without producing any new insights
   
As
Romer notes, workers in the model are in one of three states. They may be
employed and working hard (state E),
in which case they have instantaneous utility equal to w(t)
e . If they are in
state S, employed but shirking
(exerting zero effort), their utility is w(t). Unemployed workers (state U) get utility of zero. The highest
utility comes from being employed but shirking, but workers can remain in that
state only until their shirking behavior is discovered, at which point they are
fired and become unemployed.
The
formal analysis of the Shapiro-Stiglitz model introduces us to the concept of hazard
rates
, which have become a popular tool for analysis of economic
situations in which agents must predict when or if a particular event will
occur. Hazard-rate models first evolved from the actuarial literature of the
insurance industry (hence the name “hazard” that is attached). These models
represent the probability that a particular event will occur during a period of
time of given length by a hazard function such as the one shown in Romer’s
equation (9.22). The hazard rate b is
the instantaneous probability of changing from one state to another.
The
Shapiro-Stiglitz model has three hazard rates; b is the probability that the job of an employed worker who is not
shirking will end, q is the
probability that a shirking worker will be caught and fired, and a is the probability that an unemployed
24 worker will find a job. These probabilities govern the transition of workers
between states. The only decision that workers make in the model is whether to
work or to shirk when they are employed. As in other efficiency-wage models,
firms maximize profit by setting a wage level and employment level to maximize
profit. The key difference between this model and the simpler efficiency-wage
models is that the e(w, wa, u) function is
endogenously determined: workers decide whether to work hard or shirk as a
function of their wage and the unemployment rate. Similarly, the hiring rate a is determined endogenously by the
balance of demand and supply in the aggregate labor market.
To
solve the model, we first examine the decisions of firms and workers
individually, then we close the model by looking at how these individual decisions
interact in the labor market. Firms maximize profit at every moment as given by
Romer’s equation (9.23); workers maximize lifetime utility from equation (9.20)
and (9.21). The aggregate labor market enters because the job-finding rate a depends on the number unemployed.
We
begin by considering employed workers’ decisions about whether or not to shirk,
i.e., about whether to be in state E or state S. If workers considered only the present, they would always choose
to shirk, since that gives them the highest present utility. However, shirking
raises the probability of being fired and experiencing a period of
unemployment, which is the lowest-utility state. So workers must balance the
present utility gain from shirking against the expected future utility loss
from a greater probability of unemployment. Our basic decision rule is that
workers will choose the state that gives them higher lifetime expected utility.
Units
of measurement are a little tricky here. We usually think of probabilities as
pure numbers, but that is not the case for hazard rates because the time
dimension enters in an important way. For example, the probability that I will
die is 1; the probability that I will die in the next year is less than one;
the probability that I will die in the next week is less than that; and so on.
Hazard rates, which measure the probability that an uncertain event will occur,
must always be expressed per unit of time. In a discrete-time model, the
obvious temporal metric is to say there is a probability of a that the event will occur and (1
a) that the event
will not occur in the current period. In continuous time, we also measure the
probabilities on a perperiod basis, but since the event could happen at any
instant within the period, the probability compounds like compound interest.
That leads to the expression e
a for the
probability that the event does not occur at any moment during a period of
length one. This formula is directly analogous to the formula used for
continuously compounded interest in Chapter 4 of the coursebook.
an
individual over a short interval of time
Δt, then letting the length of the
interval go to zero to get continuous-time behavior.
Consider
Romer’s equation (9.24), which seems quite imposing upon initial inspection.
The equation below shows how each term in this expression can be interpreted.
hard,
broken down into the utility obtained over the interval from zero to
Δt and the utility
obtained after
Δt. The first term
(the integral) expresses the discounted utility that the worker gets between
time zero and time
Δt if she works
hard. The second term in (9.24) measures utility after time
Δt, given that she
works hard. 
 One key distinction in equation (9.24) is
between the V terms, which represent
the lifetime expected utility of a person in who is currently in a particular
state, and the terms (w
e ) and (0), which
represent the instantaneous utility one gets while in that state. The V terms are the capitalized lifetime
(stock) value of the flow utility earned in the various state one may move
through over one’s life. We integrate the instantaneous utilities in the first
term to get total utility earned between 0 and
Δt, then we add this to the lifetime
expected utility of the state she ends up in.
The
second term utilizes the V notation
to express the value (expected utility) of being in the two states in which a
hard worker might find herself. With probability e
bΔt, the worker
still has her job after
Δt and the value
at time 0 of being employed at
Δt is e−ρΔtVE. Note that we must discount this value
by e
−ρΔt in order to put
it in terms comparable to time-zero utility. The worker finds herself
unemployed at time
Δt due to layoff
with probability 1
ebΔt, and in that
state she has lifetime prospects with period-zero utility of e
−ρΔtVU. 
The
integral in (9.24) is easy to evaluate. Because the exponential function is its
own derivative (and integral), 
Bt   1   Bt
Aedt= A    e .
B
In
this case, A is (w
e ) and B is (ρ
+ b). That means that the definite
integral in (9.24) evaluates to
Δt
Δt−ρ+(      b)t     w e −ρ+(  b)t
0 e    (w e )dt= − ρ+b e       ⎥⎦t=
0
=⎢⎡w e   e−ρ+(        bt⎢⎡w e e−ρ+(      b)0
ρ+b     ⎦⎣ρ+b
=(1e−ρ+(     bt)
w e   .
ρ+b
Plugging
this expression into (9.24) gives equation (9.25), which has VE on both sides. Solving
yields equation (9.26). Taking the limit as
Δt approaches zero gives the instantaneous
value of being employed. This limit is somewhat tricky because the second term
involves
1ebΔt
−ρ+(bt.
1e
As
Δt
0, all of the exponentials with
Δt in the exponent approach one. That
means that the expressions on the top and bottom of this fraction both approach
zero. To find the limit, we use l’Hôpital’s Rule, which says that the limit of
such a fraction is the same as the limit of the derivative of the numerator
divided by the derivative of the denominator. The derivative of the numerator
with respect to
Δt is bebΔt and the
derivative of the denominator is (
ρ + b)e(ρ + b)Δt. Taking the
limit of this ratio as
Δt
0
gives b/(
ρ
+ b), which leads to Romer’s equation
(9.27).
Note
that (9.27) expresses the value of working hard as a function of the value of
being unemployed. Following a very similar sequence of steps gives equation
(9.29) as the lifetime expected utility of an employed person who shirks, and
(9.30) as the lifetime expected utility of an unemployed worker.
Romer
expresses these conditions in terms of the “return on a state,” which comprises
the “dividend” earned while in the state, and the expected “capital gain or
loss” from shifting from this state to another. The return is just the interest
rate (or rate of time discount in this model) times the capital value of being
in the state. The dividend is the utility yield from being in the state. The
expected capital gain or loss is the amount that one expects to gain or lose
from changing states in the future. Dynamic programming problems turn out to
have first-order conditions that imply that the return on the state equals the
sum of the dividend and the capital gain.
Since
all workers are the same, either all will shirk or all will work hard. In order
to get positive output, firms must pay a wage high enough to assure that no one
25
shirks. Workers will work rather than shirk if VE
VS. Since firms
want to pay the least that they can while still assuring that no shirking
occurs, they will pay a wage just high enough that VE = VS.
Romer’s equation (9.35) is the level of the wage that satisfies this
condition. 
Substituting
from the relationship between the job-finding rate a and the volume of employment L
yields equation (9.37), which is the no-shirking condition in terms of the
aggregate wage/employment locus. This is the upward-sloping curve in Romer’s
Figure 9.2. As one moves to the right along this curve, the unemployment rate
in the economy falls and the firms must pay a higher wage in order to prevent
shirking. At a very high unemployment rate (to the left), only a low wage is
required. If the firms in the economy offer a wage on or above the NSC curve,
there will be no shirking in the economy.
Equilibrium
in the labor market occurs where the no-shirking condition intersects the
demand for labor curve, which results from the usual condition that the
marginal product of labor equal the real wage. With this graphical apparatus,
we are able to do a variety of comparative-static experiments to analyze the
effects of changes in exogenous variables such as turnover and productivity as
well as special cases of the model.
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