Jan Eeckhout is a Professor of Economics at University College London and at
Barcelona GSE/UPF. Eeckhout's research has been concerned with labor
markets, matching and sorting. Eeckhout's RePEC/IDEAS profile.
Philipp Kircher is a Reader of Economics at the London School of Economics.
Kircher's research has been concerned with labor markets, matching and
sorting. Kircher's RePEC/IDEAS profile.
1. Introduction
We address the notion of skill allocation across firms and across jobs, and
how we can introduce the allocation of skills in otherwise standard macro
models. Heterogeneity in skills and jobs is without doubt an important
component of the labor market. Individuals are born with different innate
ability and non-cognitive skills, they are brought up in diverse households,
they have varying educational backgrounds, and their work experience and
learning tends to further exacerbate differences between workers. In
addition there are also differences on the demand side as jobs differ in
their productivity, the span of control of managers over their workers
varies, and firms employ different technologies.
In the presence of two-sided heterogeneity, the key determinant of the
observed allocation and wages is whether there are complementarities between
worker skills and job characteristics. Without complementarities (for
example when individuals only differ in efficiency units of labor) it does
not matter for efficiency where each individual is working. Putting it
stark: A CEO would add no more to the value of the economy cleaning offices
than orchestrating mergers and acquisitions. In a competitive market she
would earn no more in one activity than the other.
Her productivity could be decomposed in an additive effect for the worker
and the firm: output might be higher in some occupations such orchestrating
mergers and acquisitions, but it is the same for high-trained professionals
as for untrained high-school dropouts.
Instead, symptomatic of complementarities in value creation is that
equilibrium wages depend on both the worker characteristics and the firm
types in ways that are not easily decomposable. Sorting, i.e., the matching
pattern between jobs and workers, is crucial for the efficiency of the
market. Efficiency is no longer simply about whether workers are employed,
but the central question is whether they are employed at the right jobs. And
whether the right number of people are employed in the right kind of job. A
central theme in our research is the question how such complementarities
shape employment patterns and wages, how this changes our modeling and
thinking about the labor market, and how one might conceptually measure the
importance of complementarities in existing datasets.
The aim of this research is investigate how the issue of complementarity can
be embedded into standard macro environments. The models should be
sufficiently tractable to gain understanding by deriving analytical
results, and sufficiently rich so they answer interesting macroeconomic questions.
We illustrate this approach by considering three recent strands of research
on two-sided matching environments: (1) the interplay firm size and workforce quality, (2) the implications of search frictions
on the sorting between firms of different productivity and workers of
different qualities, and (3) the quest for evidence of sorting in existing
datasets. We will discuss applications to labor economics, trade, and
management as we proceed.
2. Sorting, Span of Control, and Factor Intensity
First, we consider the role of span of control and the size of firms in
labor markets with heterogeneously skilled workers. Can we explain for
example why the high skilled upper management in firms like Walmart have an
enormous span of control over relatively low skilled workers, while in
mom-and-pop retail stores the span of control is small and skills of both
managers and workers are average? Or what are the consequences of
information technology that improves the ability to manage many workers,
such as monitoring and GPS tracking devices?
Most theories of sorting follow the tradition on Becker's (1973) canonical
model of the labor market where each firm consists of exactly one job. There
the firm's choice is about the extensive margin, i.e., which worker
to hire. For a given job type, the firm chooses the optimal worker type
taking wages as given. To get an intuition for the operation of this market,
one key insight is the following: if more productive firms have a higher
marginal product from better workers, then in equilibrium these will be the
firms that indeed hire the better workers. Such complementarity between firm
productivity and worker skill shapes the matching pattern. This simple
theory provides interesting links between firm heterogeneity and worker's
wages. For example, if the heterogeneity of firms increases, worker's wages
become more spread out and increase especially at the top, which has been
used for example to explain the changes of CEO compensation (e.g., Terviö,
2008, and Gabaix and Landier, 2007).
The main drawback of this theory is that it misses the intensive
margin that is at the heart of most macro-economic models: How many workers
does the firm employ? How much of the resources should be devoted to each
worker in the work force? Models in the tradition of Lucas (1978) that are
used to explain the size distribution of firms, address this issue of the
intensive margin. They consist of a firm with one scarce resource, the time
of its manager. Managers differ in productivity and they can leverage their
ability over more or less workers, which are assumed to be homogenous. The
key question is how many workers each manager hires. Here the
complementarity is between the productivity of the manager and the size of
her workforce, i.e. the intensive margin: if this is positive then more
productive managers will lead larger teams, explaining the firm-size
distribution in plausibly calibrated models. In recent applications
Restuccia-Rogerson (2008) and Hsieh-Klenow (2010), amongst others, argue
that such heterogeneity levied across different workforce size can help to
explain differences across countries in capital, TFP, and factor prices.
While both the extensive and intensive margin in isolation have attracted
interest, their combination raises interesting issues: Would more productive
firms hire more workers, better workers, or both? How are workers with
different skills affected? How does this affect managerial compensation?
What are the effects of improved information technology that allows the
supervision of a larger workforce? And does it depend on the particular
industry and country we are considering? The objective is to incorporate a
broad notion of heterogeneity on both sides of the market.
In Eeckhout and Kircher (2011b) we extend the idea of span-of-control to a
heterogeneous workforce. Managers simultaneously decides on both margins:
the extensive margin of worker skills and the intensive margin of workforce
size. The latter determines how much managerial time can be devoted to each
of the workers. The output of each worker depends on his own skill, on the
quality of the manager, and the amount of supervision time that he receives.
Our goal is to understand the equilibrium assignment, wages and managerial
profits, and firm size.
This general setup was also proposed in Rosen (1982), but solved only for a
functional form that is a special case of our model, that of efficiency
units of labor. Our setup also includes as special or limiting cases the
functional forms of several existing models in this line of research such as
Sattinger (1975), Garicano (2000), and Van Nieuwerburgh and Weill (2010). We can also adjust the setup to match the features of the Roy model (Heckman and Honore, 1990). Here we consider the
competitive equilibrium outcome of the general model.
The interpretation of our results obviously extends to other setting beyond
managers and workers: managerial time can as well be interpreted as the
firm's capital, time per worker represents the capital intensity, and
differences in managerial skills constitute the technological productivity
differences among firms. Our analysis reveals that the equilibrium sorting
patterns in these markets by and large be understood by looking at four key
margins. (1) Complementarities in types (extensive margins): Do better
managers have a higher marginal product from working with better workers?
This is the standard requirement in Becker (1973). (2) Complementarities in
quantities (intensive margins): the marginal product of having more workers
is increasing if more time is spent by the manager. This is standard for
example in CES technologies. (3) Complementarities between manager skill and
workforce size, or span-of-control: Do better managers have a higher
marginal product of supervising more workers of a given skill? This is the
span-of-control condition that features in Lucas (1978). (4)
Complementarities between worker skills and managerial time: Do better
workers have a higher marginal product of receiving more supervision time?
In general, these different margins are present, and the interesting
question is how these complementarities trade off against each other. We
find that better managers hire better workers if the product of the first
two complementarities outweighs the product of the latter two
complementarities, i.e., if (1) * (2)>(3) * (4). From standard
assumptions on quantities, (2) is always positive. So the left hand side
simply captures the standard "Becker" effect, and if we
shut down the intensive margin by means of a Leontieff structure we recover
exactly Becker's condition ((1)>0). Yet in the presence of the intensive
margin, better managers can be good in two dimensions: they can be good at
working with better workers ((1) large) or they can be good at managing many
worker ((3) large). And as a result, the span-of-control effect can override
the standard Beckerian complementarity. Good managers have so much span that
it is efficient to manage many low skilled workers rather than few high
skilled ones. This holds despite the Beckerian skill complementarity. This
then also gives a prediction for the firm size distribution: the better
managers supervise larger groups if (3)-(4)>0 under positive sorting (and
(3)+(4)>0 under negative sorting). Managers end up managing larger teams if
the span effect (3) outweighs the complementarity between time spent and
worker type (4). If the marginal benefit of spending time is larger than
the effect of span-of-control, efficient teams are smaller for better
managers.
How does this manifest itself in different industries? In the retail sector
for example, high profit companies such as Walmart invest in information
technology that reduces the need for high skills relative to smaller mom and
pop stores ((1) small or even negative) because the cash registers and
inventories are nearly trivial to operate. They also heavily invest in
management and control tools that allow the supervision of many workers ((3)
positive and large) because it allows them to get centralized information on
performance on all registers and inventories. If supervision and training
time generates more impact with better workers ((4) positive), then stores
like Walmart employ the unskilled workers relative to their mom and pop
counterparts. This implies negative sorting. Under negative sorting this (3)
and (4) work in the same direction to create very large firms at the top:
They do not need to spend much time with each employee because it is not
worthwhile, and have the tools to supervise many. In that light it might not
be surprising that Walmart is the largest employer worldwide. In industries
with positive sorting it is much more difficult to form large teams, since
it is worthwhile to spend time with each high-skilled employee. Consider
management consulting, with strong complementarities in manager and
subordinate skill ((1) large) but moderate span of control technologies (3
moderate). This implies positive sorting. Top firms are only larger than
bottom firms if their span of control (3) outweighs the benefits from
training and interacting with employees (4). Given that the two counteract,
top consulting firms tend to be only moderately larger than other firms in
the industry.
How can we view changes in technology? Skill-biased technological change is
usually viewed as a change that makes the complementarity between worker
skill and firm technology larger. But much of technological change is in
terms of information technology that changes the complementarity between
manager skill and the amount of workers he supervises. In this model,
increases in (3) change the sorting pattern, but in particular it spreads
out the firm size distribution. It makes the difference between the two
parts of the second condition even larger. Big firms become even bigger
relative to the small firms.
The exact levels of wages, managerial profits, and skill assignment are
characterized by a simple system of two differential equations. Changes in
skills or changes in technology can explicitly be analyzed by studying the
response to this system, which will give deeper insights into the
consequences of technological change. This is particularly relevant for
international trade, where trade changes the availability of factors of
production and sometimes introduces new technologies. So far, such changes
have been analyzed mainly for settings in which the size of each firm is
limited by the extent of the demand. Typically, firms operate in
Dixit-Stiglitz type markets where consumers have preference for variety
(e.g., Costinot (2010)). Our framework is different and adds to those models
of trade: output has decreasing returns because of scarce managerial
resources, which limits the size of the firms. The advantage is that it can
be studied without functional form assumptions. But it can also be
integrated into a Dixit-Stiglitz type framework. Finally, the framework is
easily extended to unemployment as well, which allows to study both the
compensation and unemployment for workers of different skills. Again, this
might be important in trade settings, where this has been studied recently
by Helpman, Itskohki and Redding (2011), yet in their setting workers are
ex-ante identical and earn identical expected-payoffs, while in many trade
settings we would like to start from a situation where workers of different
types exist in the population.
Returning to the discussion of cross-country TFP differences, it will be
interesting to see to which extent not only the heterogeneity in firm size
as in Restuccia-Rogerson (2008) and Hsieh-Klenow (2010) matters to explain
the differences. By introducing firm size into an otherwise standard model
of sorting, the debate can be illuminated taking into account differences in
skill distributions across countries, as well as the size distribution
across firms. We should mention, though, that the tractability of this line
of research relies on the assumption that workers and supervisors interact,
but the interaction among workers is limited. They interact only to the
extent that more resources devoted to one worker means that less resources
(supervision time) is available for another. While substantial work on
competitive markets and on combinatorial matching theory has been devoted to
capture complementarities among workers (e.g., Kelso and Crawford (1982),
Cole and Prescott (1997), Gul and Stacchetti (1999), Milgrom and Hatfield
(2010)) the results are usually confined to existence theorems. The line of
work that we follow is more restrictive, but allows clear characterizations
of the size and skill level of firms, and of wages and firm profits.
Conditions like the one characterizing the equilibrium allocation in our
model can help build intuition for the economic mechanisms in these markets.
3. Market Frictions and Sorting
The allocation of heterogeneously skilled workers across different jobs
plays a crucial role in markets with frictions. Frictions are non-negligible
in the allocation process of many environments. For example in the labor
market, unemployment is considered to be a natural feature that arises when
firms and workers need time to find a suitable match. Sorting models that go
beyond the competitive market conditions can describe unemployment patterns
across worker skills.
Recall that Becker (1973) showed that in a market without frictions,
complementarities -- or equivalently supermodularity of the match output --
between firm and worker types lead to positive sorting where more productive
firms hire better skilled workers. The match surplus is supermodular if the
marginal contribution of a better worker is higher in a better firm, i.e.,
if the cross-partial of match output with respect to worker and firm type is
positive. For the case of frictions, the most well-known analytic result by
Shimer and Smith (2000) is derived in a setting with random search frictions
and pairwise matching. Parties that are matched bargain whether to stay
together and produce, or to separate and wait for another meeting, where the
future is discounted. They prove that complementarities between worker and
firm types (supermodularity of the match surplus) are not sufficient to
ensure that more productive firms hire more productive workers.
That means that there are production technologies where the better firms
have a larger gain from hiring the better workers, but still they tend to
hire less able workers.
Intuitively the reason is the following. In competitive markets the firms
know they can trade, and their only consideration is which worker they would
rather hire. In the presence of frictions, they do not only care about whom
to hire, but also about whether they can hire at all. For a more productive
firm the opportunity cost of being without a worker is higher, and so they
are more eager to ensure a match now rather than waiting.
This logic extends to matching patterns in the marriage and housing markets,
which makes the model generally applicable. Unfortunately, because of the
mismatch inherent in random search, the mathematical conditions to ensure
positive sorting do not relate directly to the matching frictions, and it is
difficult to get an intuition about the forces that operate in this market.
Nor are the wages or employment patterns easily characterized because the
randomness of the process exposes firms and workers to many trading partners.
In Eeckhout and Kircher (2010) we build on this work and that by Shi (2001).
We point out that when there is heterogeneity, the absence of information
about prices in the random search model is a strong assumption. Agents are
assumed to meet many trading partners that they would have rather avoided,
and the transfer price has to be determined at the time of the meeting
through bargaining. In contrast, we analyze a world where buyers can observe
the type of their trading partner as well as the price the seller posts.
Because trade is decentralized, trading frictions still exist, for example
due to congestion. In this world, prices guide the trading decisions just
like in the Walrasian model of Becker (1973), only now delay remains an
equilibrium feature that is taken into account in the price setting.
We address the role of price competition in markets with matching
frictions and how it leads to sorting of heterogeneous agents. With
frictions there are two aspects of value creation: the match-value when two
agents actually trade, and the probability of trading governed by the search
technology. We find that positive assortative matching obtains if the
complementarities in output creation are larger than the complementarities
in finding a trading partner, as measured by the elasticity of substitution
in the output and the matching function. The condition has a simple economic
interpretation. Complementarities in matching mean that better firms would
like to employ better workers, capturing the forces in Becker (1973). But
in case a firm does not manage to find a worker is cannot produce, and the
productive firms have most to lose from inactivity. If they can increase
their matching prospects by attracting low-skilled workers, they would do
this, given a tendency against positive sorting captured through the
matching function.
For standard matching functions, our condition is fullfiled if and
only if the output function is root-supermodular, i.e., the (square-)root of
the output function is supermodular. This means that the extent of
complementarity needed is less than under random search, but still stronger
than in the frictionless environment. To see this, we show that in the
presence of random search frictions as in Shimer and Smith (2000),
log-supermodularity is neccessary for positive assortative matching, while
with no frictions at all (Becker 1973) there is positive assortative
matching under mere supermodularity. In the neoclassical world, there are no
frictions and all agents are assumed to have full information about the
prices and types when they decide which type to accept. At the other
extreme, Shimer and Smith (2000) assume that there are random search
frictions and agents cannot observe prices and types until after they meet.
When there is price competition, prices partly mitigate frictions by
directing the heterogeneous types to the most adequate market, thus avoiding
inefficient meetings with undesirable types.
The economic interpretation of this result is transparent in terms of the
fundamentals of the economy, and it prominently features the role of
heterogeneity together with matching frictions. In the absence of any
complementarities, sorting is not important for the creation of match-value.
The key aspect is to get matched at all. Due to congestion, high-type buyers
would like to trade where few other buyers attempt to trade. This allows
them to secure trade with high probability, and they are willing to pay for
this. While sellers know that they might be idle if they attract few buyers
on average, some are willing to do this at a high enough price. The low-type
sellers are those who find it optimal to provide this trading security, as
their opportunity cost of not trading is lowest. This results in negative
assortative matching: high-type buyers match with low-type sellers. It
follows that sufficient complementarity is needed in order to obtain
positive assortative matching.
We can also introduce frictions when firms differ in size, i.e. as above,
when there is both an intensive and an extensive margin to the firm
decision. Integrating labor market frictions into the model, we show how
unemployment varies across worker types. It naturally follows form the setup
that unemployment decreases in the skill type of the worker. Instead, the
frictions of the firms in vacancy creating are ambiguous. Larger firms can
in general face higher or lower frictions, depending on whether firm size is
increasing in type.
4. Using Mismatch to Identify Complementarities
Despite the casual observation that better firms hire better workers, there
is unfortunately little or no evidence to support this. Are more skilled
workers really more productive in better firms? The amount of effort and
resources organizations invest in hiring the ``right'' person for the job
indicates that they are. This then is indirect evidence of complementarities
in production and implies that the exact allocation is important for
efficiency. Yet, there is little direct evidence. The most widely cited work
concludes that there is no corroboration of complementarity between workers
and jobs. In a seminal paper, Abowd, Kramarz and Margolis (1999) analyze the
correlation between firm and worker fixed effects from wage regressions. The
obtained correlation aims to provide evidence whether or not there is
complementarity or substitutability, and if so how big the coefficient is.
The idea is that more productive firms pay higher wages than lower wage
firms irrespective of the exact worker they hire, and the firm fixed effect
therefore recovers the ranking of the firms.
While this appears plausible, it turns out that in a simple model this logic
is flawed.
The key ingredient to identify the presence of complementarities is
mismatch. Whether it be due to search frictions or information frictions,
the fact that we observe agents in less than the optimal job generates an
inefficient allocation relative to the frictionless outcome, and at the same
time it provides sufficient information on the extent of the
complementarity. Consider a worker-job pair with mismatch. In the presence
of a friction, there is a tradeoff between separation followed by a new
match and staying in the current match. For given frictions, the larger the
mismatch, the larger the incentive to face the cost of search and rematch.
This has implications for how the wages are determined. In Eeckhout and
Kircher (2011a) we show first that the wage for a given worker is
non-monotonic in the type of his employer. This is due to the fact that in a
sorting model, wages reflect the opportunity cost of mismatch. The key
observation here is that for a given worker there can be mismatch both with
too bad a firm and too good a firm. The surplus of a match is determined by
the value of the match after subtracting the outside option of rematching.
When matched with too low a firm type, the worker is better off with a
higher firm type, and when matched with too high a firm type, the worker is
better off matching with a worse firm type. Therefore match surplus for a
given worker is inverted U-shaped in firm type. With transferable utility,
this surplus is divided and therefore wages are also inverted U-shaped. In
particular, the marginal firm type that is too low and the marginal firm
type that is too high must generate a surplus that is zero in both cases:
continuing the match must generate the same value as separation. This then
implies that wages at the marginal firm type are the same.
The non-monotonicity of wages in firm type implies that the standard
procedure to use firm fixed effects and correlate it with worker type is
ill-suited. That procedure requires the identifying assumption that wages
are monotonic in firm type, which is not the case when there is mismatch.
Because of the non-monotonic effect of firm type on wages, the wage cannot
be decomposed in an additively separable firm and worker fixed effect. We
show analytically that the misspecification is not innocuous: for the most
common specifications in the literature the firm fixed effect misses any
direct connection to the true type of the firm.
Instead, a simple algorithm allows us to back out (the absolute value of)
the degree of complementarity. The main source of identification is the
search behavior by workers that differs when the degree of complementarity
is high, and when as a result, sorting is important. First, we extract from
the range of wages paid what the cost of search is. The highest observed
wage corresponds to the wage obtained in a frictionless market and we use
this to order the workers and obtain the type distribution. Likewise, we can
obtain an order of the firms by the level of wages that they pay. The
difference between the highest and the lowest wage corresponds to the cost
of search. Second, given the search cost, the fraction of the firm
population that an agent is willing to match with, i.e., the matching set,
identifies the strength of the complementarity as expressed by the (absolute
value of the) cross-partial of the production function. This is possible
because the strength of the cross-partial directly reflects the output loss
due to mismatch.
The shortcomings of the fixed effects regressions have also been pointed out
in other work (Lopes de Melo, 2008, Lise, Meghir and Robin, 2008, and Bagger
and Lentz, 2008). Their simulations and calibrations of search models with
strong complementarities and sorting nonetheless generate small or even
negative correlations of the simulated fixed effects of workers and firms.
We provide a theoretical foundation for this finding, and Gautier and
Teulings (2004, 2006) propose a second-order approximation method to get
around the shortcomings of the fixed effect regressions.
Looking forward, for applied work it is desirable to introduce heterogeneity
and allocative efficiency in otherwise standard macro models. Too often
models of heterogeneity are augmented representative agent models. For good
reasons of course, because modeling is complicated. That makes the quest to
find simple results and a tractable setup in the context of sufficiently
rich economic heterogeneity important, despite the obvious challenges.
5. References
Abowd, John M., Francis Kramarz and David N. Margolis, 1999.
"High Wage Workers and High Wage Firms,"
Econometrica,
Econometric Society, vol. 67(2), pages 251-334.
Bagger, Jesper and Rasmus Lentz, 2008. "An
Empirical Model of Wage Dispersion with Sorting,"
University of Wisconsin manuscript.
Becker, Gary S, 1973.
"A Theory of Marriage: Part I,"
Journal of Political Economy,
University of Chicago Press, vol. 81(4), pages 813-46.
Cole, Harold L. and Edward C. Prescott, 1997.
"Valuation Equilibrium with Clubs,"
Journal of Economic Theory,
Elsevier, vol. 74(1), pages 19-39.
Costinot, Arnaud,2009.
"An Elementary Theory of Comparative Advantage,"
Econometrica,
Econometric Society, vol. 77(4), pages 1165-1192.
Eeckhout, Jan and Philipp Kircher, 2010.
"Sorting and Decentralized Price Competition,"
Econometrica,
Econometric Society, vol. 78(2), pages 539-574.
Eeckhout, Jan and Philipp Kircher, 2011a.
"Identifying Sorting--In Theory,"
Review of Economic Studies,
Oxford University Press, vol. 78(3), pages 872-906.
Eeckhout, Jan and Philipp Kircher, 2011b. "Assortative
Matching and the Size of the Firm", manuscript.
Gabaix, Xavier and Augustin Landier, 2008.
"Why Has CEO Pay Increased So Much?,"
The Quarterly Journal of Economics,
MIT Press, vol. 123(1), pages 49-100.
Garicano, Luis, 2000.
"Hierarchies and the Organization of Knowledge in Production,"
Journal of Political Economy,
University of Chicago Press, vol. 108(5), pages 874-904.
Gautier, Pieter A. and Coen N. Teulings, 2004.
"The Right Man for the Job,"
Review of Economic Studies,
Wiley Blackwell, vol. 71(2), pages 553-580.
Gautier, Pieter A. and Coen N. Teulings, 2006.
"How Large are Search Frictions?,"
Journal of the European Economic Association,
MIT Press, vol. 4(6), pages 1193-1225.
Gul, Faruk and Ennio Stacchetti, 1999.
"Walrasian Equilibrium with Gross Substitutes,"
Journal of Economic Theory,
Elsevier, vol. 87(1), pages 95-124.
Hatfield, John William and Paul R. Milgrom, 2005.
"Matching with Contracts,"
American Economic Review,
American Economic Association, vol. 95(4), pages 913-935.
Heckman, James J. and Bo E. Honoré, 1990.
"The Empirical Content of the Roy Model,"
Econometrica,
Econometric Society, vol. 58(5), pages 1121-49.
Helpman, Elhanan, Oleg Itskhoki and Stephen Redding, 2010.
"Inequality and Unemployment in a Global Economy,"
Econometrica,
Econometric Society, vol. 78(4), pages 1239-1283.
Hsieh, Chang-Tai Peter J. Klenow, 2010.
"Development Accounting,"
American Economic Journal: Macroeconomics,
American Economic Association, vol. 2(1), pages 207-23.
Kelso, Alexander S. Jr and Vincent P. Crawford, 1982.
"Job Matching, Coalition Formation, and Gross Substitutes,"
Econometrica,
Econometric Society, vol. 50(6), pages 1483-1504.
Lise, Jeremy, Costas Meghir, and Jean-Marc Robin, 2008.
"Matching, Sorting and Wages", UCL manuscript.
Lopes de Melo, Rafael, 2008.
"Sorting in the
Labor Market: Theory and Measurement", Yale manuscript.
Robert E. Lucas Jr., 1978.
"On the Size Distribution of Business Firms,"
Bell Journal of Economics,
The RAND Corporation, vol. 9(2), pages 508-523.
Restuccia, Diego and Richard Rogerson, 2008.
"Policy Distortions and Aggregate Productivity with Heterogeneous Plants,"
Review of Economic Dynamics,
Elsevier, vol. 11(4), pages 707-720.
Sattinger, Michael, 1975.
"Comparative Advantage and the Distributions of Earnings and Abilities,"
Econometrica,
Econometric Society, vol. 43(3), pages 455-68.
Shi, Shouyong, 2001.
"Frictional Assignment. I. Efficiency,"
Journal of Economic Theory,
Elsevier, vol. 98(2), pages 232-260.
Shimer, Robert and Lones Smith, 2000.
"Assortative Matching and Search,"
Econometrica,
Econometric Society, vol. 68(2), pages 343-370.
Terviö, Marko, 2008.
"The Difference That CEOs Make: An Assignment Model Approach,"
American Economic Review,
American Economic Association, vol. 98(3), pages 642-68.
Van Nieuwerburgh, Stijn and Pierre-Olivier Weill, 2010.
"Why Has House Price Dispersion Gone Up?,"
Review of Economic Studies,
Wiley Blackwell, vol. 77(4), pages 1567-1606.
