Volume 1, Issue 2, April 2000
Research Agenda: Search Theory beyond the Matching Function,
by Shouyong Shi
predominant theory for analyzing a frictional market
is the search theory developed by Diamond (1982), Mortensen
(1982) and Pissarides (1990). This theory has two distinctive
elements. One is an exogenous matching function that
captures a time-consuming matching process and generates
unemployment in equilibrium. The other is an ex post
(after-match) wage determination scheme, often the Nash
bargaining formula, which splits the match surplus between
the two sides of the match. This theory has been used
to organize a wide range of facts related to unemployment,
both over the business cycles and along the growth trend,
and to make policy recommendations. In contrast to other
unemployment models (e.g., efficiency-wage models),
the search theory can be easily integrated into an intertemporal
Shi is Associate Professor at the Department of Economics
at Queen's University (Kingston, Canada). He has published
extensively on search models, especially applied to
monetary economics. His interests also include capital
accumulation, specialization, and financial intermediation.
the exogenous matching function and the exogenous surplus-sharing
rule remain unsatisfactory. First, these exogenous features
critically affect the model's predictions on efficiency
(see Hosios (1990)) and on the effects of labor market
policies (Shi and Wen (1999)). Second, and more fundamentally,
they eliminate any role for wages to direct matches
ex ante (before matches occur) and deprive agents of
the ability to actively influence their matches. In
my current research I develop search models that do
not rely on these exogenous elements and apply them
to analyze wage inequality.
simple way to allow agents to actively organize their
matches is to replace the matching function by a two-stage,
wage-posting game, where firms simultaneously post wages
first and then workers apply to jobs after observing
the wages. Such a price/wage-posting model, developed
by Peters (1991) and Montgomery (1991), preserves the
time-consuming feature of the search theory by assuming
that a worker can only apply to a small fraction of
the job openings in each period. In contrast to the
standard search model, wages are determined before,
not after, matches occur and so wages "direct" workers'
search. The matching process and the surplus division
are both endogenous outcomes of agents' actions. Each
firm can deliberately change the posted wage to affect
the number of applicants it receives. Firms and workers
maximize the expected gains from a match, making a trade-off
between the matching probability and the ex post gains
from a match.
further develop this model and use it to examine the
"Pricing with Frictions". In this paper with Kenneth
Burdett and Randall Wright, we first show that the price-posting
equilibrium in a market with finite numbers of sellers
and buyers converges to the equilibrium with infinitely
many buyers and sellers. Since the latter is considerably
easier to characterize, this result greatly simplifies
the price/wage-posting game in large markets.
we allow firms to differ in capacity. The main finding
is that the equilibrium price and the endogenous matching
function both depend on not only the number of buyers
and the number of goods for sale in the market, but
also on how those goods are distributed across sellers.
This result suggests that the standard matching function
adopted in the literature is mis-specified. That is,
the number of new matches should depend on whether there
are many firms, each with a few vacancies, or a few
firms, each with many vacancies.
"Product Market and the Size-Wage Differential". In
this paper I examine whether the wage-posting model
can be useful for explaining the size-wage differential,
i.e., the fact that employers with more workers pay
higher wages than smaller employers do to workers with
the same observable skills. This size-wage differential
is a significant fraction of the overall wage inequality
but has not been well explained by traditional theories.
this task, I integrate the product market and the labor
market into a price/wage-posting framework. In the product
market the price-posting game generates the outcome
that buyers pay a higher price to a larger seller than
to a smaller seller for the higher service probability
the larger seller provides. Thus, a large firm obtains
a higher expected revenue per worker than a small firm.
To capture this revenue differential, a large firm posts
a higher wage to fill the vacancy than a small firm
does. High and low wages generate the same expected
wage to a searching worker because a high wage attracts
more applicants and hence is more difficult to obtain.
Thus, large firms not only pay a higher wage than small
firms but also have higher expected profit, although
the workers are identical and the firms are identical
(except for size).
increase in the product demand changes the distribution
of employment across firms with different sizes and
has ambiguous effects on the size-wage differential.
In particular, trade liberalization increases wage inequality
when the product demand is initially low but decreases
wage inequality when the product demand is already high.
"Unskilled Workers in an Economy with Skill-Biased Technology".
In this paper I extend the wage-posting model to incorporate
skill differences and skill-biased technology. The purpose
is to check whether search frictions are important for
explaining the following facts in the US data: In the
1970s, the skill premium fell but the within-group wage
differential rose; in 1980s, the skill premium and the
within-group wage differential both rose.
this model workers are either skilled or unskilled,
while firms use either a high technology or a low technology.
The high technology is biased toward skilled workers.
High-tech firms prefer skilled workers to unskilled
workers and pay a skill premium, but they also post
wages for unskilled workers in case they do not receive
any skilled applicants. There is a wage differential
among unskilled workers, i.e., unskilled workers in
high-tech firms are paid more than those in low-tech
firms. This within-group wage differential arises not
from match-specific productivity or the complementarity
between skilled and unskilled workers, but rather from
the trade-off between a wage and the matching probability.
A high-tech firm's high wage comes with a low matching
probability for an unskilled worker while a low-tech
firm's low wage comes with a high matching probability.
this framework an increase in the skill-biased productivity
increases the skill premium and the wage differential
among unskilled workers simultaneously. In contrast,
an increase in the general productivity of all workers
increases the skill premium but reduces the wage differential
among unskilled workers. These results indicate that
search frictions can be important for accounting for
both the skill premium and the within-group wage differential.
"Frictional Assignment". In this paper I examine the
assignment problem in a frictional market, i.e., the
two-sided matching problem in a market where agents
on each side are heterogeneous. In a frictionless market,
Becker (1973) has shown that the market assignment is
efficient and positively assortative (i.e., it matches
high attributes on one side with high attributes on
the other side of the market). Neither feature holds
in a frictional matching market modeled in the standard
search theory. I re-examine these issues with a wage-posting
framework and focus on the assignment between skills
results emerge. First, the efficient assignment in this
frictional world may not be positively assortative even
when skills and machine qualities are complementary
with each other in production. This is because skills
and machines are not fully utilized and so, by matching
high skills with low-quality machines and high-quality
machines with low skills, efficiency may be improved
if such a matching scheme increases the utilization
of both high skills and high-quality machines. Second,
the efficient assignment can be decentralized as follows.
Each firm chooses three things before matches occur:
a machine quality, a desired skill to be matched with,
and a wage for the skill. After observing these choices,
workers apply to the firms. The ex ante competition
between firms and the endogenous division of the match
surplus encourage the right number of firms to enter
the market to target each skill and induce them to select
the efficient machine quality for each skill.
price/wage-posting framework is tractable and useful
for modeling large, frictional labor markets. It allows
search theory to go beyond exogenous matching functions
and exogenous surplus-splitting rules, to make predictions
and policy recommendations that are not vulnerable to
these exogenous elements, and to explain some well-known
facts about inequality. More fundamentally, the framework
reinstates prices the ex ante role of allocating resources.
Gary S., 1973, "A
theory of marriage: part I
of Political Economy
Kenneth, Shouyong Shi and Randall Wright, 1998, "Pricing
, Federal Reserve Bank of Philadelphia
Working Paper 98-9.
Peter, 1982, "Wage determination and efficiency in search
equilibrium," Review of Economic Studies
Arthur, 1990, "On the efficiency of matching and related
models of search unemployment," Review of Economic
James D., 1991, "Equilibrium
wage dispersion and interindustry
," Quarterly Journal of Economics
Dale T., 1982, "The matching process as a non-cooperative/bargaining
game," in J.J. McCall (ed.) The Economics of Information
, Chicago: University of Chicago
Michael, 1991, "Ex
ante price offers in matching games:
Christopher A., 1990, Equilibrium Unemployment Theory
Shouyong, 1997, "Product
Market and the Size-Wage Differential
Shouyong, 1998, "Unskilled Workers
in an Economy with Skill-Biased Technology"
working paper 73.
Shouyong, 1998 "Frictional
CREFE working paper 74.
Shouyong and Quan Wen, 1999, "Labor market search and
the dynamic effects of taxes and subsidies," Journal
of Monetary Economics
Interviews Lee Ohanian on the Great Depression
Ohanian is Associate Professor at the Department of
Economics, University of California, Los Angeles. He
specializes in macroeconomic theory, the study of business
cycles and growth. He has published in the best journals
on monetary policy, war finance, VARs, and other topics.
With Hal Cole, you show in your Minneapolis Fed
Quarterly Review article that the major peculiarity
of the Great Depression was not so much the sharp
decline in 1929-33 but rather the extremely slow
recovery until 1939. You argue that the key fact
to explain is stagnant hours. Why?
Ohanian: Productivity grew rapidly after 1933. Theory
predicts that the economy should have recovered
to trend by 1936, with above-trend labor input supporting
higher consumption and investment. But hours worked
remained 20-25 % below trend until World War II.
So why was labor input so low given rapid productivity
growth? It wasn't because other shocks were negative
- banking panics and deflation ended in 1933, and
real interest rates were low. Hours per adult should
have been a lot higher after 1933.
In current work with Hal Cole, you argue that New
Deal policies encouraging cartelization linked to
high wages are responsible for the slow recovery.
Why? How could the government be so wrong?
There must have been a major negative shock to offset
the recovery of economic fundamentals and keep the
economy depressed. The government adopted some extreme
labor and industrial policies (the National Industrial
Recovery Act) in 1933 that really distorted markets.
These policies suspended the antitrust laws and
permitted collusion, provided that the rents were
shared with labor. This was accomplished through
immediate wage increases and collective bargaining.
new paper, "New Deal Policies and the Persistence
of the Great Depression", quantitatively analyzes
these policies. We build a model of the policies,
and embed that model within a dynamic GE business
cycle model. In contrast to the fast recovery predicted
by standard theory, our model predicts economic
activity remains far below trend after 1933. We
concluded that these policies were a key factor
behind the persistence of the Depression - they
can account for about 60 % of the deviation between
the predicted trend levels and the actual data.
President Roosevelt thought that "excessive" competition
was responsible for the Depression, and that these
policies would bring recovery. He was wrong. My
colleague Armen Alchian was a student at Stanford
at the time, and told me that his professors thought
the policies were crazy - they couldn't understand
how promoting monopoly could raise employment. It
is unfortunate that Roosevelt didn't listen to these
mainstream economists - if he had, the recovery
would have been much stronger. These policies were
finally weakened during World War II - and employment
also seemed to be a sentiment to redistribute income
during the 1930s. But this policy was a really inefficient
method of redistribution. It created a lot of inequality
by shutting down employment.
Why do you think it is necessary to use a dynamic
general equilibrium model to study the Great Depression?
We have all been taught that the economy was not
in equilibrium during that period.
Theory has changed a lot since the Depression. I
believe that economists took the disequilibrium
route because the general equilibrium language of
Arrow, Debreu, and McKenzie wasn't well known at
the time. We now know that disequilibrium models
should be used very reluctantly, because there are
an infinite number of ways an economy can be out
of equilibrium. The model Hal and I developed for
1933-1939 is a dynamic general equilibrium model
- but with a cartel policy arrangement that generates
very low labor input, consumption, and investment.
theory is important for understanding the Depression.
There are a lot of stories about the Depression,
but without an explicit GE model you don't know
if the stories hold water. One of the benefits of
GE theory is that it forces you to look beyond the
direct effects of shocks, and assess the indirect
effects. Hal and I are writing a paper for the NBER
Macro Annual that uses GE models to study the two
most popular shocks for 1929-33: the money stock
decline and bank failures. Using GE models, we found
that many of the indirect effects of these shocks
offset the direct effects, or were at variance with
example, several economists think money shocks depressed
the economy through imperfectly flexible wages.
Nominal wages were high in manufacturing because
President Hoover told the Fortune 500 C.E.O.'s not
to cut wages. But wages did fall in other sectors,
so a multi-sector GE model is needed to evaluate
this story. We found that high manufacturing wages
reduced aggregate output only about 3 % between
1929-33. This is because the direct effect of the
wage shock is pretty small, and because the indirect,
general equilibrium effects offset some of the direct
paper also develops a GE model with a banking sector.
The model predicts that bank failures should lead
firms to substantially increase retained earnings
as a substitute for bank finance. However, firms
cut retained earnings like crazy during the Depression
- In 1930, dividend payments fell by 4% while profits
fell by 63%. The model also predicts that regions
with more bank failures should have had deeper depressions.
But we found little correlation between state-level
economic activity and state-level bank failures.
and I thought monetary shocks were the key factor
for 1929-33 when we wrote our Minneapolis Fed QR
paper. Our view has changed - either we need alternative
theories to revive the money and banking hypothesis,
or some other shock was responsible for 1929-33.
Were Keynes, and Friedman and Schwartz all wrong?
Keynes didn't have the benefit of modern theory
to help understand the Depression. He was wrong
about "animal spirits" driving down investment,
employment, and output. Ed Prescott argues in his
review of our Minneapolis Fed Quarterly Review paper
that the investment decline of the 1930s is not
a mystery - it is exactly what theory predicts,
given the policy shock that kept labor input so
and Schwartz suggest that government policies contributed
to the post-1933 depression, which is consistent
with our view. But we suspect their emphasis on
monetary shocks as a cause for 1929-33 may be misplaced.
Believe it or not, productivity (TFP) fell about
15 % relative to trend between 1929-33. This drop
isn't technological regress, and it doesn't seem
to be input measurement error. Hoover intervened
in the private economy significantly during this
period. Perhaps his interference went beyond wage
policies, and affected work practices and expectations
about future returns to investment. We don't know
the source of this TFP drop, or all the consequences
of Hoover's actions, but these factors might be
important for 1929-33.
Would you make a parallel between the slow recovery
of the Great Depression and the "jobless recovery"
in the early 1990s?
There are some key differences between these two
recoveries. Employment growth was stagnant in the
1930s because of government policies that raised
wages and reduced competition. These types of policies
weren't in place during the 1990s. My guess is that
a mismatch between new technologies and the existing
stock of labor may have contributed to the more
recent "jobless recovery". It is interesting that
employment growth has been rapid the last few years
as the pool of workers able to use these technologies
Would you say, like Ed Prescott, that the conclusions
of your work with Hal Cole could be applied to contemporaneous
France, Spain, and Japan?
Economies normally recover rapidly from downturns.
It is pathological for a country to enjoy normal
productivity growth but remain depressed for many
years. Japan is one of these pathologies. Many economists
think that Japan's problems could be solved if their
banks could make more loans and if fiscal and monetary
policies stimulated aggregate demand. Some economists
even argue that higher inflation expectations would
believe that Japan has more fundamental problems
than finding the right mix of fiscal and monetary
policy. Japan has tried all sorts of Keynesian stimuli,
and it hasn't worked. When an economy stagnates
year after year, you have to ask: "What is preventing
people from working and producing more?" Banking
problems affected their economy, but we don't think
it is the whole story. 15 years ago, 80 % of Ireland's
banks shut down for six months because of a strike.
Their economy did not falter - people found substitutes
for closed banks.
banking is the key to Japan's Depression, why haven't
the Japanese found substitutes after all these years?
The persistence of their depression and the failure
of Keynesian policies suggest some other shock is
responsible for Japan's stagnation. My work with
Hal suggests we should look for policies that keep
employment low. Ed, Hal, and I are planning to start
research along these lines soon.
Harold L., and Lee E. Ohanian, 1999, "The
Great Depression in the United States from a neoclassical
", Federal Reserve Bank of Minneapolis
Quarterly Review v. 23, p. 2-24 (Winter).
Harold L., and Lee E. Ohanian, 2000, "New Deal Policies
and the Persistence of the Great Depression", mimeo.
Harold L., and Lee E. Ohanian, 2000, "How Much did
and Banking Shocks Contribute to the
Harold L., Lee E. Ohanian and Edward C. Prescott, 2000,
"Cartelization, Policy and the Great Depression", in
Milton, and Anna Schwartz, 1963, Monetary History
of the United States, 1867-1960
, Princeton University
Edward C., 1999, "Some
observations on the Great Depression
", Federal Reserve
Bank of Minneapolis Quarterly Review v. 23, p. 25-29
Review of Economic Dynamics: A Progress Report
As the coordinating editor of
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Review of Economic Dynamics
for Economic Dynamics: 2000 Meetings in Costa Rica
The 2000 Meetings of the Society
for Economic Dynamics will be held June 29-July
2 (Thursday-Sunday), 2000 in San José, Costa Rica. The
conference is hosted by INCAE with the co-sponsorship of the Central Bank of Costa Rica. Registration and
welcome reception will be held on Wednesday, June 28,
2000. The conference director is Alberto Trejos and
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editions, the program will consist of several rounds
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NEOS: Network-Enabled Optimization System
is mostly about constrained optimization. With the increasing
complexity or size of models, computers have been gradually
taking over the task of finding optima. For such numerical
analyses, techniques developed in operations research
have helped a lot to solve problems that grew faster
in complexity than the power of the computers. But one
has to be aware that not all models can be solved efficiently
with the same algorithm. Many solution methods have
been developed, each geared to a particular set of problems.
In fact, there are now so many methods that it becomes
a complex task in itself to select the appropriate algorithm.
richness in algorithms has also the drawback that one
has to learn new tools for each model. To help reduce
this type of cost to the researcher, the Optimization
Technology Center of the Argonne National Laboratory
has put together a web site introducing the many techniques,
the Network-Enabled Optimization System (NEOS) at http://www-fp.mcs.anl.gov/otc/. This
very complete site guides the reader through the various
types of problems, showing for each several solution
algorithms that are explained and that can even be tried
online. In fact, it is possible to have very large and
complex problems solved on the NEOS server, a great
opportunity for those who do not have the necessary
resources available to them directly.
of the algorithms on NEOS deal with rather simple objective
functions with numerous but simple constraints. In economic
dynamics, problems have usually more complex functions
and fewer constraints. Yet, the latter can be converted
to the former, as shown for example by Trick and Zin
(1997) who demonstrate that a standard dynamic problem
is equivalent to a linear programming problem with one
constraint for each state. Such problems can be solved
easily now, even if they have millions of constraints.
Michael, and Stanley Zin, 1997, "Spline approximations
to value functions: A linear programming approach",
Macroeconomic Dynamics, v.1, p. 255-277.
Links: QM&RBC: Quantitative Macroeconomics and Real
Dynamics covers many fields, but Real Business Cycle
theory is certainly one of the more prominent ones.
Yet, his theory has difficulties getting mainstream
economics because of its technical difficulty. For example,
very few undergraduates study it, and for a long time
only PhDs coming from some schools could master its
techniques. This is changing now, and this is partly
due to the Quantitative Macroeconomics & Real
Cycle home page. The web has democratized the access
to information, and this includes getting access to
latest research, data and solution techniques.
since early 1995, QM&RBC has provided sample codes
for solving some of the standard problems in the field.
Also, it features links to selected home pages of researchers
who provide their latest results online. QM&RBC
has provided complementary reading material for many
classes, in fact it has even lead many to discover the
RBC models they would not have covered in the regular
is still being maintained to continue to serve the research
community and the aspiring researchers. But the field
has evolved and RBC is now synonymous with much more
that "real" shocks or "business cycles". This is why
is currently being conducted to choose for a new acronym
for RBC that would more appropriately describe it. We
encourage you to provide your input.
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