Guido Menzio
University of Pennsylvania and NBER
Research
Publications
“Intra Firm Bargaining and Shapley
Values,” with Bjoern Brugemann
and Pieter Gautier,
Review of Economic Studies,
Forthcoming.
We study two wage
bargaining games between a firm and multiple workers. We revisit the bargaining
game proposed by Stole and Zwiebel (1996a). We show
that, in the unique Subgame Perfect Equilibrium, the gains from trade captured
by workers who bargain earlier with the firm are larger than those captured by
workers who bargain later, as well as larger than those captured by the firm.
The resulting equilibrium payoffs are different from those reported in Stole
and Zwiebel (1996a) as they are not the Shapley
values. We propose a novel bargaining game, the Rolodex game, which follows a
simple and realistic protocol. In the unique no-delay Subgame Perfect
Equilibrium of this game, the payoffs to the firm and to the workers are their
Shapley values.
“The (Q,S,s)
Pricing Rule,” with Kenneth Burdett,
Review of Economic Studies, 2018,
85 (2), 892-928.
We introduce menu costs in the
search-theoretic model of imperfect competition of Burdett and Judd (1983).
When menu costs are not too large, the equilibrium is such that sellers follow
a (Q,S,s) pricing rule. According to the rule, a
seller lets inflation erode the real value of its nominal price until it
reaches some point s. Then, the seller pays the menu cost and resets the real
value of its nominal price to a point randomly drawn from a distribution with
support [S,Q], where s<S<Q. A (Q,S,s)
equilibrium differs with respect to a standard (S,s) equilibrium: (i) In a (Q,S,s) equilibrium, sellers sometimes keep their
nominal price constant to avoid paying the menu cost, other times because they
are indifferent to changes in the real value of their price. An exploratory
calibration reveals that menu costs account less than half of the observed
duration of nominal prices. (ii) In a (Q,S,s) equilibrium, higher inflation
leads to higher real prices, as sellers pass onto buyers the cost of more
frequent price adjustments, and to lower welfare.
“Equilibrium Price Dispersion Across
and Within Stores,” with Nicholas Trachter, Review of Economic Dynamics, 2018, 28
(2), 205-220.
We develop a
search-theoretic model of the product market that generates price dispersion
across and within stores. Buyers differ with respect to their ability to shop
around, both at different stores and at different times. The fact that some
buyers can shop from only one seller while others can shop from multiple
sellers causes price dispersion across stores. The fact that the buyers who can
shop from multiple sellers are more likely to be able to shop at multiple times
causes price dispersion within stores. Specifically,
it causes sellers to post different prices for the same good at different times
in order to discriminate between different types of buyers.
“Evidence on the Relationship between
Recruiting and Starting Wage,” with Jason Faberman,
Labour Economics, 2018, 50 (1), 67-79.
Using data from the Employment Opportunity Pilot Project, we examine the relationship between the starting wage paid to the worker filling a vacancy, the number of applications attracted by the vacancy, the number of candidates interviewed for the vacancy, and the duration of the vacancy. We find that the wage is positively related to the duration of a vacancy and negatively related to the number of applications and interviews per week. We show that these surprising findings are consistent with a view of the labor market in which firms post wages and workers direct their search based on these wages if workers and jobs are heterogeneous and the interaction between worker’s type and job’s type in production satisfies some rather natural assumptions.
“The (Q,S,s)
Pricing Rule: A Quantitative Analysis,” with Kenneth Burdett,
Research in Economics, 2017,
71 (4), 784-797.
Are nominal prices sticky because menu
costs prevent sellers from continuously adjusting their prices to keep up with
inflation or because search frictions make sellers indifferent to any real
price over some non-degenerate interval? The paper answers the question by
developing and calibrating a model in which both search frictions and menu
costs may generate price stickiness and sellers are subject to idiosyncratic
shocks. The equilibrium of the calibrated model is such that sellers follow a
(Q,S,s) pricing rule: each seller lets inflation erode
the effective real value of the nominal prices until it reaches some point s
and then pays the menu cost and sets a new nominal price with an effective real
value drawn from a distribution with support [S,Q], with s<S<Q.
Idiosyncratic shocks short-circuit the repricing cycle and may lead to negative
price changes. The calibrated model reproduces closely the properties of the
empirical price and price-change distributions. The calibrated model implies
that search frictions are the main source of nominal price stickiness.
“Shopping Externalities and
Self-Fulfilling Unemployment Fluctuations,” with Greg Kaplan,
Journal of Political Economy,
2016, 124 (3), 771-825.
We propose a novel theory of
self-fulfilling unemployment fluctuations. When a firm increases its workforce,
it increases the demand facing other firms---as employed workers spend more
than unemployed workers---and decreases the extent of competition facing other
firms---as employed workers have less time to search for low prices than
unemployed workers. In turn, the increase in demand and the decline in
competition induces other firms to hire more labor in order to scale-up their
presence in the product market. The feedback between employment and product market
conditions generates multiple equilibria---and the possibility of
self-fulfilling fluctuations---if the differences in the shopping behavior of
employed and unemployed workers are large enough. Empirical evidence on
spending, shopping and prices paid suggests that this is the case.
“Directed Search over the Life Cycle,”
with Irina Telyukova
and Ludo Visschers,
Review of Economic Dynamics,
2016, 19 (1), 38-62.
We develop a life-cycle model of the labor
market in which different worker-firm matches have different quality and the
assignment of the right workers to the right firms is time consuming because of
search and learning frictions. The rate at which workers move between
unemployment, employment and across different firms is endogenous because
search is directed and, hence, workers can choose whether to seek low-wage jobs
that are easy to find or high-wage jobs that are hard to find. We calibrate our
theory using data on labor market transitions aggregated across workers of
different ages. We validate our theory by showing that it correctly predicts
the pattern of labor market transitions for workers of different ages. Finally,
we use our theory to decompose the age profiles of transition rates, wages and
productivity into the effect of age variation in work-life expectancy, human
capital and match quality.
“Equilibrium Price Dispersion with
Sequential Search,” with Nicholas Trachter, Journal of Economic Theory, 2015, 160
(6), 188-215.
The paper studies
equilibrium pricing in a product market for an indivisible good where buyers
search for sellers. Buyers search sequentially for sellers, but do not meet
every sellers with the same probability. Specifically, a fraction of the
buyers’ meetings lead to one particular large seller, while the remaining
meetings lead to one of a continuum of small sellers. In this environment, the
small sellers would like to set a price that makes the buyers indifferent
between purchasing the good and searching for another seller. The large seller
would like to price the small sellers out of the market by posting a price that
is low enough to induce buyers not to purchase from the small sellers. These
incentives give rise to a game of cat and mouse, whose only equilibrium
involves mixed strategies for both the large and the small sellers. The fact
that the small sellers play mixed strategies implies that there is price
dispersion. The fact that the large seller plays mixed strategies implies that
prices and allocations vary over time. We show that the fraction of the gains
from trade accruing to the buyers is positive and non-monotonic in the degree
of market power of the large seller. As long as the large seller has some
positive but incomplete market power, the fraction of the gains from trade
accruing to the buyers depends in a natural way on the extent of search
frictions.
“The Morphology of Price Dispersion,”
with Greg Kaplan,
International Economic Review, 2015,
56 (4), 1165-1206.
This paper is a study
of the shape and structure of the distribution of prices at which an identical
good is sold in a given market and time period. We find that the typical price
distribution is symmetric and leptokurtic, with a standard deviation between
19% and 36%. Only 10% of the variance of prices is due to variation in the
expensiveness of the stores at which a good is sold, while the remaining 90% is
due, in approximately equal parts, to differences in the average price of a
good across equally expensive stores and to differences in the price of a good
across transactions at the same store. We show that the distribution of prices
that households pay for the same bundle of goods is approximately Normal, with
a standard deviation between 9% and 14%. Half of this dispersion is due to
differences in the expensiveness of the stores where households shop, while the
other half is mostly due to differences in households’ choices of which goods
to purchase at which stores. We find that households with fewer employed
members pay lower prices, and do so by visiting a larger number of stores,
rather than by shopping more frequently.
“Taxation and Redistribution of
Residual Income Inequality,” with Mikhail Golosov and
Pricila Maziero, Journal of Political Economy, 2013, 121 (6), 1160-1204.
This paper studies the optimal
redistribution of income inequality caused by the presence of search and
matching frictions in the labor market. We study this problem in the context of
a directed search model of the labor market populated by homogenous workers and
heterogeneous firms. The optimal redistribution can be attained using a
positive unemployment benefit and an increasing and regressive labor income
tax. The positive unemployment benefit serves the purpose of lowering the
search risk faced by workers. The increasing and regressive labor tax serves the
purpose of aligning the cost to the firm of attracting an additional applicant
with the value of an application to society.
“Monetary Theory with Non-Degenerate
Distributions,” with Shouyong Shi and Hongfei Sun, Journal of Economic Theory, 2013, 148 (6), 2266-2312.
We construct and
analyze a tractable search model of money with a non-degenerate distribution of
money holdings. We assume search to be directed in the sense that buyers know
the terms of trade before visiting particular sellers. Directed search makes
the monetary steady state block recursive in the sense that individuals' policy
functions, value functions and the market tightness function are all
independent of the distribution of individuals over money balances, although
the distribution affects the aggregate activity by itself. Block recursivity
enables us to characterize the equilibrium analytically. By adapting lattice-theoretic
techniques, we characterize individuals' policy and value functions, and show
that these functions satisfy the standard conditions of optimization. We prove
that a unique monetary steady state exists. Moreover, we provide conditions under
which the steady-state distribution of buyers over money balances is
non-degenerate and analyze the properties of this distribution.
“Sticky Prices: A New Monetarist Approach,”
with Allen Head,
Lucy Qian Liu and Randall Wright,
Journal of the European Economic
Association, 2012, 10 (5), 939-973 (Lead
article).
Why do some sellers set prices in nominal
terms that do not respond to changes in the aggregate price level? In many
models, prices are sticky by assumption. Here it is a result. We use search
theory, with two consequences: prices are set in dollars since money is the
medium of exchange; and equilibrium implies a nondegenerate price distribution.
When money increases, some sellers keep prices constant, earning less per unit
but making it up on volume, so profit is unaffected. The model is consistent
with the micro data. But, in contrast with other sticky-price models, money is
neutral.
“Efficient Search on the Job and the
Business Cycle,” with Shouyong Shi, Journal of Political Economy, 2011, 119
(3), 468-510.
The paper develops a
model of directed search on the job where transitions of workers between
unemployment, employment and across employers are driven by heterogeneity in
the quality of firm-worker matches. The equilibrium is such that the agents'
value and policy functions are independent of the distribution of workers
across employment states. Hence, the model can be solved outside of
steady-state and used to measure the effect of cyclical productivity shocks on
the labor market. Productivity shocks are found to generate large fluctuations
in workers' transitions, unemployment and vacancies when matches are experience
good, but not when matches are inspection goods.
“Job Search with Bidder Memories,”
with Carlos Carrillo-Tudela and Eric Smith, International Economic Review, 2011, 52 (3), 639-655.
This paper
revisits the no-recall assumption in job search models with take-it-or-leave-it
offers. Workers who can recall previously encountered potential employers in
order to engage them in Bertrand bidding have a distinct advantage over workers
without such attachments. Firms account for this difference when hiring a
worker. When a worker first meets a firm, the firm offers the worker a
sufficient share of the match rents to avoid a bidding war in the future. The
pair share the gains to trade. In this case, the Diamond paradox no longer
holds.
“Inflation and Unemployment in the
Long Run,” with Aleksander
Berentsen and Randall Wright,
American Economic Review, 2011, 101
(1), 371-398.
We study the long-run
relation between money (inflation or interest rates) and unemployment. We
document positive relationships between these variables at low frequencies. We
develop a framework where money and unemployment are modeled using explicit
microfoundations, providing a unified theory to analyze labor and goods
markets. We calibrate the model and ask how monetary factors account for labor
market behavior. We can account for a sizable fraction of the increase in
unemployment rates during the 1970s. We show how it matters whether one uses
monetary theory based on the search-and-bargaining approach or on an ad hoc
cash-in-advance constraint.
“Worker Replacement,” with Espen Moen, Journal of Monetary Economics, 2010, 57
(6), 623-636 (Lead article).
Consider a labor
market in which firms want to insure existing employees against income fluctuations
and, simultaneously, want to recruit new employees to fill vacant jobs. Firms
can commit to a wage policy, i.e. a policy that specifies the wage paid to
their employees as a function of tenure, productivity and other observables.
However, firms cannot commit to employ workers. In this environment, the
optimal wage policy prescribes not only a rigid wage for senior workers, but
also a downward rigid wage for new hires. The downward rigidity in the hiring
wage magnifies the response of unemployment to negative shocks.
“Directed Search on the Job,
Heterogeneity and Aggregate Fluctuations,” with Shouyong Shi, American Economic Review, 2010, 100 (2),
327-332.
In this paper, we prove the existence of a Block Recursive
Equilibrium for a model of directed search on the job in which workers are
ex-ante heterogeneous with respect to some observable characteristic such as
education.
“Block Recursive Equilibria for
Stochastic Models of Search on the Job,” with Shouyong Shi, Journal of Economic Theory, 2010, 145
(4), 1453-1494.
We develop a general
stochastic model of directed search on the job. Directed search allows us to
focus on a Block Recursive Equilibrium (BRE) where agents’ value functions,
policy functions and market tightness do not depend on the distribution of
workers over wages and unemployment. We formally prove existence of a BRE under
various specifications of workers’ preferences and contractual environments,
including dynamic contracts and fixed-wage contracts. Solving a BRE is as easy
as solving a representative agent model, in contrast to the analytical and
computational difficulties in models of random search on the job.
“A Theory of Partially Directed Search,”
Journal of Political Economy, 2007,
115 (5), 748-769.
This paper studies a search model of the
labor market where firms have private information about the quality of their
vacancies, they can costlessly communicate with unemployed workers before the
beginning of the application process, but the content of the communication does
not constitute a contractual obligation. At the end of the application process,
wages are determined as the outcome of an alternating offer bargaining game.
The model is used to show that vague non-contractual announcements about
compensation---such as those one is likely to find in help-wanted ads---can be
correlated with actual wages and can partially direct the search strategy of
workers.
Working
Papers
“Agency Business Cycles,”
with Mikhail Golosov, NBER
Working Paper 21743, Reject and Revise at Econometrica (January
2018).
We develop a theory of endogenous and stochastic
fluctuations in aggregate economic activity. Individual firms choose to
randomize over firing or keeping workers who performed poorly in the past to
give them an ex-ante incentive to perform. Different firms choose to correlate
the outcome of their randomization to reduce the probability with which they
fire non-performing workers. Correlated randomization leads to aggregate
fluctuations. Aggregate fluctuations are endogenous---they emerge because firms
choose to randomize and they choose to randomize in a correlated fashion---and
they are stochastic---they are the manifestation of a randomization process.
The hallmark of a theory of endogenous and stochastic fluctuations is that the
stochastic process for aggregate "shocks" is an equilibrium object.
“Relative Price Dispersion: Evidence
and Theory,” with Greg Kaplan, Leena Rudanko and Nicholas Trachter, NBER
Working Paper, Revise and Resubmit at American
Economic Journal: Microeconomics (September 2017).
We use a large dataset on retail pricing to document that a sizeable portion of the cross-sectional variation in the price at which the same good trades in the same period and in the same market is due to the fact that stores that are, on average, equally expensive set persistently different prices for the same good. We refer to this phenomenon as relative price dispersion. We show that relative price dispersion might stem from sellers' attempts to discriminate between high-valuation buyers who need to make all of their purchases in the same store and low-valuation buyers who are willing to purchase different items from different stores. We calibrate our theory and show that it is not only consistent with the extent and sources of dispersion in the price that different sellers charge for the same good, but also with the extent and sources of dispersion in the prices that different households pay for the same basket of goods.
“Declining Search Frictions,
Unemployment and Growth,” with Paolo Martellini,
NBER Working Paper (April 2018).
Over the last century, unemployment, vacancy, job-finding and job-loss rates as well as the Beveridge curve have no trend. Yet, the last century has seen the development and diffusion of many information technologies—such as telephones, fax machines, computers, the Internet—which presumably have increased the efficiency of search in the labor market. We explain this phenomenon using a textbook search-theoretic model of the labor market. We show that there exists an equilibrium in which unemployment, vacancies, job-finding and job-loss rates are constant while the search technology improves over time if and only if firm-worker matches are heterogeneous in quality, the distribution of match qualities is Pareto, and the quality of a match is observed before the start of the employment relationship. Under these conditions, improvements in search lead to an increase in the rate at which workers meet firms and to a proportional decline in the probability that the quality of a firm-worker match is acceptable leading to a constant job-finding rate, unemployment, etc... Interestingly, under the same conditions, unemployment, vacancies, job-finding and job-loss rates are independent of the size of the labor market even in the presence of increasing returns to scale in search. While declining search frictions do not lower unemployment, they contribute to growth. The magnitude of the contribution depends on the thickness of the tail of the Pareto distribution. We present a simple strategy to measure the decline in search frictions and its contribution to growth. A rudimentary implementation of this strategy suggests that the decline in search frictions has been substantial, it has been caused by both improvements in the search technology and increasing returns to scale in the search process, and it has had a non-negligible impact on growth.
“Intermediation as Rent Extraction,”
with Maryam Farboodi and Gregor Jarosch, NBER
Working Paper 24171 (December 2017).
We propose a theory of intermediation as rent extraction, and explore its implications for the extent of intermediation, welfare and policy. A frictional asset market is populated by agents who are heterogeneous with respect to their bargaining skills, as some can commit to take-it-or-leave-it offers and others cannot. In equilibrium, agents with commitment power act as intermediaries and those without act as final users. Agents with commitment trade on behalf of agents without commitment to extract more rents from third parties. If agents can invest in a commitment technology, there are multiple equilibria differing in the fraction of intermediaries. Equilibria with more intermediaries have lower welfare and any equilibrium with intermediation is inefficient. Intermediation grows as trading frictions become small and during times when interest rates are low. A simple transaction tax can restore efficiency by eliminating any scope for bargaining.
“Rolodex Game in Networks,”
with Bjoern Brugemann
and Pieter Gautier,
Manuscript (August 2017).
The paper studies the
Rolodex bargaining game in networks. We first revisit the Rolodex game originally
proposed in the context of intra firm bargaining, in which a central player
bargains sequentially with multiple peripheral players. We show that the unique
no-delay SPE of this game yields the Myerson-Shapley value for the star graph
in which the central player is linked to all peripheral players. Second, we
propose a Rolodex game for a general graph. Links in the graph negotiate
sequentially, with one of the linked players making an offer to the other. If
the respondent rejects, the link moves to the end of the line and the direction
of the offer is reversed for the next negotiation of this link. As in the
original Rolodex game, all agreements are renegotiated in the event of a
breakdown. We show that the unique no-delay SPE of this game yields the
Myerson-Shapley value for the corresponding graph.
“A Search Theory of Rigid Prices,”
PIER Working Paper 07-031 (2007).
This paper studies price dynamics in a
product markets characterized by: (a) search
frictions—in the sense that it takes time for a buyer to find a seller that
produces a version of the good he likes; (b) anonymity—in the sense that sellers cannot price discriminate
between first-time buyers and returning costumers; (c) asymmetric information—in the sense that sellers are subject to
idiosyncratic shocks to their marginal cost of production and privately observe
the shocks’ realizations. I find that the joint dynamics of costs and prices
may be very different than in a standard Walrasian market. When shocks are
i.i.d., the price remains constant in the face of fluctuations in a seller’s
marginal cost. When shocks are moderately persistent, the price adjusts slowly
and imperfectly in response to changes in a seller’s cost. Finally, when shocks
are sufficiently persistent, the price adjusts instantaneously and efficiently
as soon as a seller’s production cost varies.
“A Cheap-Talk Theory of Random and Directed Search,”
Revised for the Journal of Political
Economy as “A Theory of Partially Directed Search”
(2006).
This paper studies a search model of the
labor market where firms have private information about the gains from trade
and post cheap-talk messages to advertise their vacancies before workers decide
which location to visit. The surplus of a match is divided ex-post according to
the outcome of an alternating-offer bargaining game of asymmetric information.
When this bargaining game is fast, I show that the maximum amount of
information that can be transmitted through the cheap-talk depends
non-monotonically on the tightness of the labor market. In particular, if the
ratio of unemployed workers to vacancies is either sufficiently high or
sufficiently low, the unique equilibrium has the firms babbling and search is
random. If the tightness of the labor market takes on intermediate values,
there is also an equilibrium where the cheap-talk is informative, high and low
productivity firms post different messages and the search process of the
workers is directed.
“High-Frequency Wage Rigidity,” Job Market Paper
(2005).
In the context of a frictional model of
the labor market with off and on the job search, I advance a novel model of
wage determination where contracts are non-binding and firms have private
information about the productivity of labor. The characterization of the
intra-firm bargaining game leads to a reduced-form model where the firm chooses
the wage subject to a non-discrimination and consistency constraints. The
fundamental property of the optimal firm-wage policy is high-frequency wage
rigidity. While the firm does not respond to productivity shocks whose
persistence falls below a critical threshold, the wage is a non-degenerate
function of the long-term component of labor productivity. A calibrated version
of the model shows that the cyclical behavior of the model is quantitatively
consistent with the empirical regularities of the labor market at the business
cycle frequency. Among other things, wages are nearly acyclical, the
semi-elasticity of the average labor productivity to unemployment is smaller
than one, and vacancies are almost perfectly correlated with unemployment.
Work in
Progress
“Workers Transitions and the Diffusion of Knowledge,” with Kyle Herkenhoff and Jeremy Lise.
“Exploitation of Labor,” with Claudio Michelacci.
“The Strategic Origin of Search Frictions,” with Pieter Gautier.