Volume 10, Issue 1, November 2008
The Research Agenda: Ricardo Lagos on Liquidity and the Search Theory of Money
Ricardo Lagos is Associate Professor of Economics at New York University. He is interested in monetary economics, especially the theory of search in money.
Lagos's RePEc/IDEAS entry
There is no ambiguity among economists regarding what it means for an asset
to be risky, or for markets to be complete. There seems to be, however, no
definition of "liquidity" that is
generally agreed upon. The notion of liquidity is sometimes used as an
attribute of an asset, e.g., U.S. Treasuries are considered to be more
liquid than equity shares. The notion of liquidity is often also used to
describe the state or nature of a market, e.g., the market for municipal
bonds is commonly regarded as illiquid. Sometimes researchers describe
economic agents as being "liquidity
constrained," to mean that the agents face binding
borrowing constraints. In what follows, I will focus on the first two
notions of liquidity.
In financial economics, the liquidity of assets and markets is associated
with the cost of trading. An asset is considered to be liquid if trading it
entails relatively low transaction costs, e.g., transaction taxes, brokerage
fees, or bid-ask spreads. A market is regarded as liquid if individual
traders can find a counterpart for trade relatively quickly, and if the
out-of-pocket costs involved in consummating trades are relatively small.
There is a vast literature in finance that uses liquidity differences
measured by differences in transaction costs to rationalize various
asset-pricing puzzles, i.e., asset-return differentials that seem too large
to be accounted for by the differences in the stochastic properties of the
flows of payments that the assets represent. (For an extensive list of
references, see Amihud et al., 2005.)
In monetary economics, "liquidity" refers
to the degree to which an asset is useful as a medium of exchange. An asset
is illiquid if it cannot be used as means of payment in quid pro quo
trades. In particular, the Search Theory of Money--by which I mean the
class of models that use search theory to provide micro foundations for
monetary exchange that was pioneered by Kiyotaki and Wright (1989)--is
built around the premise that assets can be valued not only for the
intrinsic value of the real payoffs they represent, but also for their
usefulness in the mechanism of exchange. This approach has deepened our
understanding of the nature of monetary exchange by making explicit the
frictions--e.g., specialization patterns, the configuration of the
decentralized exchange mechanism, information structure, and so on--that
make monetary exchange an equilibrium. In other words, this approach has
proven useful for explaining the grandfather of all asset pricing puzzles:
the existence of fiat money; an asset that is a formal claim to nothing yet
sells at a positive price. Despite the evident conceptual connection and the
potential for cross-fertilization, the Search Theory of Money and the
mainstream asset-pricing literature have managed to stay disconnected for
In the sections that follow, I will review some of my recent research and an
ongoing research agenda, parts of which I have pursued, or am currently
pursuing, with Guillaume Rocheteau, Pierre-Olivier Weill, and Randy Wright.
In Sections 2-5 I will survey several papers that represent an effort to
develop models in which, much as in the Search Theory of Money, financial
assets are valued not only as claims to streams of consumption goods but
also for their usefulness in the mechanism of exchange--i.e., for their
moneyness, or exchange liquidity. In Section 6 I focus on
the notion of transaction liquidity associated with transaction
costs that is used in the financial literature, and review two papers that
represent an effort to trace this notion of liquidity back to the
microstructure of the market in which the assets are traded.
2. From indivisibility and upper bounds to Euler equations
The approach to monetary economics that started with Kiyotaki and Wright
(1989) consists of using search theory to provide an explicit model of the
type of decentralized trading activity that can give rise to a meaningful
role for a medium of exchange. This literature made significant progress
along several dimensions, but for a number of years, the depth of the
analysis and the breadth of its fundamental insights were limited by stark
modeling restrictions on asset holdings. Specifically, in order to keep the
endogenous distribution of money holdings manageable, agents were typically
restricted to hold either 0 units or 1 unit of an indivisible asset. These
restrictions meant that agents never faced a standard portfolio problem
leading to standard Euler equations, namely, the basic building block of any
modern theory that--much like search-theoretic models--seeks to explain
asset prices and asset demand patterns.
In "A Unified Framework for Monetary Theory and Policy
Analysis" (hereafter LW), Randy Wright and I propose a
search-based framework that combines some features of search models, such as
an explicit mathematical formulation of the decentralized trading and the
price-setting mechanisms, with some features of competitive models.
Specifically, agents sometimes trade in a decentralized manner as in search
theory--bilaterally, at prices determined by bargaining--and sometimes as
in competitive theory--with the market, at market clearing prices. There
are at least two important benefits from taking this step from pure search
theory toward competitive theory. First, it becomes relatively easy to
integrate search-based micro foundations for money demand with the rest of
macroeconomic theory. For example, some real-world markets may be better
approximated by competitive markets, so it may be convenient in applications
to be able to incorporate a segment of competitive trades into our
search-based theories. Second, it turns out that under certain conditions on
preferences (quasi-linearity in one of the goods that is traded
competitively), allowing agents periodic access to competitive markets
implies that the model remains tractable--even if we work with divisible
money and allow agents to carry any nonnegative amount. (Quasi-linearity
eliminates wealth effects in the demand for money, which simplifies the
dynamics of the endogenous distribution of money holdings. In the simplest
version, all agents who trade in the competitive market choose to carry the
same money balances into the next round of decentralized trade, therefore
periodically, the endogenous distribution of money holdings becomes
degenerate. This allows for sharp analytic results, and makes the framework
easy to work with. An alternative approach was proposed by Shi, 1997, who
develops a tractable search model with divisible money that relies on a
large-household construct to avoid distributional issues.)
Just as incorporating a competitive segment brings the search theory of
money closer to mainstream macroeconomic theory, relaxing the stark
restrictions on money holdings implies that the search-theoretic models can
now deliver standard Euler equations. This brings the field within a step of
mainstream asset-pricing theory. The missing step is a meaningful portfolio
choice problem; something that requires introducing financial assets that
agents can hold alongside money balances.
3. A first look at competing assets: money and capital
Initially, the new search-theoretic literature with divisible money and
unrestricted holdings tended to shy away from formulations in which the role
of money as a medium of exchange could be challenged by other assets. This
issue was circumvented either by assuming that money is the only asset
(e.g., Lagos and Wright, 2003, Lagos and Rocheteau, 2005), or by assuming
that assets other than money simply cannot be used in exchange (e.g., Aruoba
and Wright, 2003). The implicit presumption being, perhaps, that in the face
of competition from other assets, money would be driven out of circulation,
or rendered "inessential" (a term used by
monetary theorists to mean that the set of Pareto optimal allocations
implementable by a monetary equilibrium is no larger than the set of Pareto
optimal allocations implementable by a nonmonetary equilibrium).
In "Money and Capital as Competing Media of
Exchange," Guillaume Rocheteau and I build on LW and
consider a model where real assets (reproducible capital goods) can compete
with fiat money as a medium of exchange. Our theory allows agents to choose
which assets to exchange in decentralized trades and imposes no restrictions
on their portfolios. We establish that a monetary equilibrium exists if and
only if money is essential, and offer a condition on fundamentals under
which this is the case. The condition states that money is essential when
the capital stock that a social planner would choose to accumulate is
smaller than the stock of assets that agents need to conduct transactions.
In the nonmonetary equilibrium, this liquidity shortage manifests itself as
a premium on the rate of return on the assets that can be used as a medium
of exchange, and this premium induces agents to over-accumulate capital.
Capital plays two roles in this economy: it has a productive role and it
serves as a medium of exchange in decentralized trades. The introduction of
fiat money helps to disentangle the productive use of capital from its
liquidity use, and induces agents to reduce the inefficiently high stock of
capital goods. In the monetary equilibrium, money has the same rate of
return as capital since both assets can be used in decentralized trade and
agents can exploit arbitrage opportunities in the centralized market. We
find that when a monetary equilibrium exists, the policy of contracting the
money supply at the rate of time preference is optimal.
4. Exchange liquidity and the asset-pricing puzzles
In "Asset Prices and Liquidity in an Exchange
Economy," I develop an asset-pricing model in which
financial assets are valued for their exchange liquidity--the extent to
which they are useful in facilitating exchange--as well as for being claims
to streams of consumption goods. I use the theory to study the implications
of this liquidity channel for average asset returns, the equity-premium
puzzle and the risk-free rate puzzle. I consider a real LW economy with two
assets: a one-period government-issued risk-free real bill (a
"bond"), and an equity share that
represents the bearer's ownership of a "Lucas
tree" and confers him the right to collect a stochastic
stream of real dividends. The model can be thought of as a version of Mehra
and Prescott (1985), but extended to incorporate some trades that take place
in a decentralized manner, away from competitive markets. As in the
prototypical search model of money, agents face quid pro quo
constraints in decentralized trades.
In the basic formulation, assets differ only in the stochastic properties of
their payoffs, and agents are free to choose which assets to use as means of
payment in decentralized trades. The theory unambiguously predicts that
someone testing an agent's Euler equation for the risk-free bill using its
measured rate of return would find that, at the margin, this agent can gain
from transferring consumption from the future to the present. That is, there
would appear to be a risk-free rate puzzle. I also find that, at
least qualitatively, the theory may also be consistent with an equity
premium in excess of the risk premium that compensates equity holders for
bearing undiversifiable aggregate risk. I calibrate the model economies and
study the extent to which they are able to generate average equity returns
and risk-free rates that are in line with U.S. data. Mehra and Prescott's
test of their theory essentially consisted of experimenting with different
values of the curvature of the agent's utility function (call it sigma)
to find the values for which the average risk-free rate and equity premium
in the model matched those in the U.S. economy. I carry out a similar
First, I consider a baseline economy in which agents are free to use bonds
and equity shares in all decentralized trades. I find that for relatively
low values of sigma, the liquidity mechanism is inactive and the
equilibrium is the one in Mehra-Prescott. For larger values of sigma
(equal to or greater than 8) equity shares and bills are valuable in
decentralized exchange. This additional motive for holding the assets lowers
the return on equity and the risk-free rate from what they would be in the
Mehra-Prescott economy, and brings them closer to the data. There is a
precise sense in which even if shares are just as useful as bonds for
exchange purposes, quantitatively, the model performs better than the
Mehra-Prescott frictionless benchmark. For example, with standard constant
relative risk aversion preferences, it takes a value of sigma of about
10 for the model to be consistent with asset return data in the
Hansen-Jagannathan sense (as opposed to a value of sigma above 20 in
Mehra-Prescott). Despite equity shares and bonds being equally acceptable in
decentralized exchange, the model is capable of increasing the size of the
equity premium somewhat relative to the Mehra-Prescott benchmark. The reason
is that equity is a worse hedge against the risk of facing binding trading
constraints in the decentralized market than bonds (trading constraints tend
to bind more in states where the equity return is low).
Equity and bonds are equally liquid (equally useful to finance decentralize
trades) in the baseline model. In order to assess the extent to which
liquidity differences (differences in acceptability) can magnify the return
differential between equity and bonds, I also analyze specifications in
which exogenous restrictions, which can be interpreted as arising from
institutional or legal arrangements, give bonds an advantage over equity as
a medium of exchange. Specifically, I consider the case in which equity
shares cannot be used in a fraction theta of decentralized exchanges (theta =0 is the case with no exogenous liquidity differences analyzed
previously). For a calibrated version of this model, I formulate the
following question: For a given value of sigma, how large does theta
(the relative illiquidity of equity) have to be for the model to generate an
average yearly risk-free rate of 1% and an equity premium that matches the
long-term average for the U.S. economy? The answer is, quite small: If one
allows for the fact that bonds may be slightly better suited than equity
shares to play the medium-of-exchange role, then the model is able to match
the historical average return to equity and the risk-free rate for the
United States with values of sigma between 3 and 5.
I take these results as an indication that prying deeper into the
microeconomics of the decentralized exchange process can add to our
understanding of how asset prices and returns are determined in actual
economies. The quantitative results also highlight the importance of a
fundamental question: why is asset X more generally accepted or better
suited to function as a medium of exchange than asset Y? The finding that
small differences in the acceptability of an asset can generate relatively
large return differentials underscores the importance of tackling this
question. Some research along these lines is already underway. For example,
Kim and Lee (2008), Lester et al. (2008), and Rocheteau (2008) are exploring
the possibility that differences in acceptability may arise due to a moral
hazard problem in an environment where some assets are more susceptible to
counterfeiting than others. Lagos and Rocheteau (2008) are focusing on the
differences in acceptability that arise from an adverse selection problem
due to the fact that some agents may be better informed about the return
characteristics of certain assets than other agents. Nosal and Rocheteau
(2008) are exploring trading mechanisms that may give some assets an
advantage in exchange as in Zhu and Wallace (2007).
5. Asset prices, exchange liquidity, and monetary policy
The work described in the previous section studies the implications of
exchange liquidity for real asset returns in economies with no money. Since
much of the existing work on asset pricing abstracts from monetary
considerations, this seemed like a natural starting point. However, given
the emphasis on exchange liquidity, it would be odd to neglect fiat
money--the quintessential medium of exchange--indefinitely. For one thing,
the primary role of fiat money is precisely to provide exchange liquidity,
so to the extent that the valuations of other financial assets have a
liquidity component, the interactions between these other assets and money
through the agents' portfolio choices should not be ignored. Also, by
setting monetary policy, governments can affect real money balances and in
this way supply the economy with the liquidity it needs to lubricate the
mechanism of decentralized exchange. So again, to the extent that the
valuations of financial assets have a liquidity component, monetary policy
will be a key determinant of their (real) measured returns.
In "Some Results on the Optimality and Implementation of
the Friedman Rule in the Search Theory of Money," I
consider a physical environment similar to the one described in the previous
section, but replace the one-period government-issued risk-free real bill
with government-issued fiat money. In this context, I show that the
quantities in a monetary equilibrium are Pareto optimal if and only if the
nominal interest rate, i.e., the marginal (indirect) utility of holding an
additional dollar, is constant and equal to zero. Thus, a monetary authority
that wishes to maximize welfare ought to follow Milton Friedman's
prescription that monetary policy should be conducted with the objective of
inducing a zero nominal interest rate. I characterize a large family of
deterministic monetary policies that implement Milton Friedman's
prescription, in the sense that these policies are consistent with the
existence of a monetary equilibrium with zero nominal interest rates. This
family of optimal policies is defined by two properties: (i) the money
supply must be arbitrarily close to zero for an infinite number of dates,
and (ii) asymptotically, on average, the growth rate of the money supply
must be at least as large as the rate of time preference. Interestingly,
even though the agents' liquidity needs are stochastic in this environment
(because equity, whose price is stochastic, can be used alongside money in
decentralized trades) this is the same class of monetary policies that
implements the Friedman rule in the context of deterministic cash-in-advance
economies, as shown by Cole and Kocherlakota (1998) and Wilson (1979).
Under an optimal policy, the quantity of real money balances is large enough
so that agents' liquidity needs are satiated, so the real equity price and
return are independent of monetary and liquidity considerations. The
monetary equilibrium under an optimal monetary policy also exhibits some
peculiarities: the price level is indeterminate, and the inflation rate can
be independent of the path of the money supply, as was emphasized by Cole
and Kocherlakota (1998) in the context of their deterministic
cash-in-advance economy. Some may find the failure of the quantity theory
and the ensuing price-level indeterminacy unappealing if the model is to be
used for applied research. One way to eschew these issues, is to consider a
perturbation of a certain class of optimal policies that implements a
constant but positive nominal interest rate. A policy that targets a
constant nonzero nominal rate in this stochastic environment, however, will
typically involve a stochastic monetary policy rule. This is the direction I
pursue in "Asset Prices, Liquidity, and Monetary Policy in
an Exchange Economy" to study the positive implications of
monetary policy for asset prices and returns. The analysis provides insights
on how monetary policy must be conducted in order to support a recursive
monetary equilibrium with a constant nominal interest rate (with the Pareto
optimal equilibrium in which the nominal rate is zero as a limiting case):
The growth rate of the money supply must be relatively low in states in
which the real value of the equilibrium equity holdings is below average.
Something similar happens with the implied inflation rate: it is relatively
low between state x and a next-period state x', if the realized real value
of the equilibrium equity holdings in state x' is below its state-x
I also find that on average, liquidity considerations can introduce a
negative relationship between the nominal interest rate (and the inflation
rate) and real equity returns. Intuitively, since agents are free to use any
combination of assets for exchange purposes, even if the equity yields a
real and exogenous dividend stream, part of the equity return will be linked
to its liquidity return, and this liquidity return in turn depends on the
quantity of real money balances--which is a function of the inflation rate.
On average, if the rate of inflation is higher, real money balances are
lower, and the liquidity return on equity rises, which causes its price to
rise and its real measured rate of return (dividend yield plus capital
gains) to fall. This type of logic could perhaps help to rationalize the
fact that historically, real stock returns and inflation have been
negatively correlated--an observation long considered anomalous in the
finance literature (e.g., Fama and Schwert, 1977).
The model has a number of implications for the time-paths of output,
inflation, interest rates, equity prices, and equity returns, and it would
be interesting to explore these implications further. For example, even
though variations in aggregate output are effectively exogenous under the
types of monetary policies considered, for some parametrizations the theory
produces a negative correlation between the inflation rate and the growth
rate of output--a short-run "Phillips
curve" --but one that is entirely generated by a monetary
policy designed to provide liquidity in an economy with stochastic liquidity
6. Transaction liquidity and the structure of financial markets
In the introductory section I mentioned that in finance, the liquidity of
assets and markets is associated to the cost of trading: this
transaction liquidity is, loosely speaking, the ability to trade cheaply.
Central to this literature is the notion that actual financial trade is not
costless and seamless as in competitive theory. To capture the idea that
trade is not costless, much of the work in this area maintains the
competitive market structure, but incorporates transaction costs of various
forms (e.g., fixed costs of trading, or costs that are proportional to the
size of the trade). In many of these models, transaction costs affect asset
prices because in equilibrium, investors must be compensated for bearing
these costs. Hence for any given dividend flow that the asset generates,
transaction costs lower the asset price and increase the asset return, i.e.,
higher transaction costs reduce the transaction liquidity of the asset.
A recent related strand of work in theoretical finance started by Duffie et
al. (2005) subscribes to the notion of market liquidity as trading costs,
but goes deeper into the nature of these trading costs by building explicit
models of the mechanism of exchange in financial markets. The starting point
is the observation that many financial securities (e.g., unlisted stocks,
currencies, derivatives, corporate bonds, municipal bonds, federal funds)
are traded in over-the-counter (OTC) markets. The defining feature of OTC
markets is that they have no formal organization: unlike organized
securities exchanges, OTC markets are completely decentralized and do not
operate in a particular location at set times. An agent wishing to trade a
security in an OTC market is confronted with two fundamental trading
frictions: he must first search for a counterpart, and once a potential
counterpart has been found, the two parties will typically negotiate the
terms of the trade to share the gains.
Duffie et al. (2005) show that a search-based model of an OTC market can
parsimoniously rationalize standard measures of transaction liquidity
discussed in the finance literature, such as trade volume, bid-ask spreads,
and trading delays. A virtue of their formulation is that it is analytically
tractable, so all these mechanisms can be well understood. The literature
spurred by Duffie et al. (2005), however, keeps the framework tractable by
imposing a stark restriction on asset holdings: agents can only hold either
0 units or 1 unit of the asset.
In "Liquidity in Asset Markets with Search
Frictions," Guillaume Rocheteau and I develop a
search-based model of trade in an OTC market with no restrictions on
investors' asset holdings. The model is close in structure and spirit to
Duffie et al. (2005): there are two types of agents, investors and dealers.
The asset is only held by investors (they can hold any nonnegative
position), and their idiosyncratic willingness to hold the asset changes
over time, which creates a motive for trade among investors. Trades are
intermediated by dealers, and investors contact dealers at random times,
with the period of time preceding a trade interpreted as an execution delay.
We find that as a result of the restrictions they impose on asset holdings,
existing search-based theories of trade in OTC markets neglect a critical
feature of illiquid markets, namely, that market participants can mitigate
trading frictions by adjusting their asset positions to reduce their trading
The key theoretical observation is that an investor's asset demand in an OTC
market depends not only on his valuation for the asset at the time of the
trade, but also on his expected valuation over the holding period until his
next opportunity to trade. A reduction in trading frictions (e.g., a
reduction in the average time it takes for an investor to contact a dealer)
makes investors less likely to remain locked into an undesirable asset
position and therefore induces them to put more weight on their current
valuation. As a result, a reduction in trading frictions induces an investor
to demand a larger asset position if his current valuation is relatively
high, and a smaller position if it is relatively low, which tends to
increase the spread of the distribution of asset holdings. We find that this
effect is a key channel through which trading frictions determine trade
volume, bid-ask spreads, and trading delays--the dimensions of transaction
liquidity that search-based theories of financial intermediation are
designed to explain.
In "Search in Asset Markets: Market Structure, Liquidity,
and Welfare," Guillaume Rocheteau and I consider a version
of this model with free entry of dealers as a way to endogenize trading
delays. We show that when interacted with investors' unrestricted asset
holding decisions, the dealers' incentives to make markets generate a
liquidity externality that can give rise to multiple steady states. This
finding suggests that all the symptoms of an illiquid market--large
spreads, small trade volume, and long trading delays--can simultaneously
arise as a self-fulfilling phenomenon in asset markets with an OTC structure.
In many financial markets, the search-for-a-counterpart problem is
alleviated by dealers who trade assets from their own inventories. During
market crashes, for instance, it can take a long time for an investor to
find a counterpart for trade, either because of the technological
limitations of order-handling systems or, as in OTC markets, due to the
decentralized nature of the trading process. In these circumstances,
liquidity provision by dealers (in the sense of their alleviating the
investors' search problem by becoming themselves a counterpart for trade)
can become critical, as shown by Weill (2007). In "Crashes
and Recoveries in Illiquid Markets," Guillaume Rocheteau,
Pierre-Olivier Weill and I extend the model in "Liquidity
in Asset Markets with Search Frictions" to allow dealers
to accumulate asset inventories. We use the theory to study the equilibrium
and the socially optimal inventory policies of dealers during a market
crash, which we model as a temporary negative shock to investors'
willingness to hold the asset, followed by a (possibly stochastic) recovery
Our model can rationalize why dealers intervene in some crises and withdraw
in others. We derive conditions under which dealers will find it in their
interest to provide liquidity in the aftermath of a crash, as well as
conditions under which their incentives to provide liquidity are consistent
with market efficiency. We relate the liquidity provision by dealers to the
details of the market structure, e.g., dealers' degree of market power or
the extent of the search frictions (the average length of time it takes for
an investor to contact a dealer), and the characteristics of the crash, such
as the severity and persistence of the shock to investors' demands.
We find that the amount of liquidity provided by dealers following a crash
varies nonmonotonically with the magnitude of search frictions. When search
frictions are small, investors with higher-than-average utility for assets
become more willing to hold larger-than-average positions and absorb more of
the selling pressure coming from investors whose demands for the asset are
lower than normal. In some cases, the former are so willing to buy large
quantities of the asset from the other investors, i.e., so willing to serve
as a counterpart for trade, that dealers don't find it profitable to step
in. If, on the contrary, search frictions are large enough, dealers do not
accumulate inventories either, but for a different reason: Trading frictions
reduce the investors' need for liquidity provision by dealers. Indeed, in
order to reduce their exposure to the search frictions, investors choose to
take less extreme asset positions, so the problem of finding a counterpart
for trade becomes less relevant. In fact, it is possible that the investors
reduce their trading needs so much that dealers don't find it profitable to
accumulate inventories following a crash. Thus, if one considers a spectrum
of asset markets ranging from those with very small search frictions, such
as the New York Stock Exchange (NYSE), to those with severe search
frictions, such as the corporate bond market, one would expect to see
dealers accumulate more asset inventories during a crash in markets which
are in the intermediate range of the spectrum.
7. Concluding remarks
A single underlying theme runs through the work I have reviewed in the
preceding sections: in many instances, the demand for an asset (and
consequently the asset price and return) depends not only on the demand for
the fundamentals that the asset represents, but also on the nature of the
mechanism of exchange through which the asset is traded. Financial
economists associate the "mechanism of
exchange" to the microstructure of the market where the
asset trades, and call the asset "liquid"
if it can be traded cheaply in terms of time, and out-of-pocket costs.
Monetary theorists associate the "mechanism of
exchange" to the explicit microeconomic process through
which goods and the assets used to pay for those goods flow between buyers
and sellers, and call an asset "liquid"
if it is generally accepted and used in this exchange process.
On the one hand, by conceptualizing financial assets in the way monetary
theorists think of fiat money, we can develop theories of liquidity that
afford new insights into the fundamental features of assets and markets that
can make some assets useful in the mechanism of exchange, and hence more
prone to exhibit returns that exceed their fundamental valuations. A better
understanding of the deeper determinants of the liquidity component of asset
valuations can shed new light on a number of asset-pricing anomalies, as
well as on the role that monetary policy plays, and the role it ought to
play, in the determination of asset prices. On the other hand, the finance
microstructure perspective reviewed in Section 6, formalizes some of the key
micro elements of the exchange process in actual financial markets, which
include trading delays, bilateral decentralized exchange, and other
distinctively non-Walrasian elements, much like those which characterize the
stylized "decentralized market" of the
macro models in Sections 2-5. It seems to me that incorporating these
microstructure considerations into those macro models would be a fertile
avenue for future research. The hope I hold for this research agenda, is
that by continuing to develop the association between the monetary and the
financial perspectives on liquidity, we may be able to make progress on some
deeper questions, such as which assets are better suited to satisfy the
quid pro quo constraints in the Search Theory of Money, and why
certain assets seem more prone to be traded in frictional market structures
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Lagos, Ricardo, and Guillaume Rocheteau, 2008b.
"The Informational Foundations of Asset Liquidity," Working
Lagos, Ricardo, and Guillaume Rocheteau, forthcoming.
"Liquidity in Asset Markets with Search Frictions
Lagos, Ricardo, Guillaume Rocheteau, and Pierre-Olivier Weill, 2007.
"Crashes and Recoveries in Illiquid
," Federal Reserve Bank of Cleveland Working paper 0708.
Lagos, Ricardo, and Randall Wright, 2003. "Dynamics,
Cycles and Sunspot Equilibria in `Genuinely Dynamic, Fundamentally
Disaggregative' Models of Money
," Journal of
, vol. 109(2), pages 156-171.
Lagos, Ricardo, and Randall Wright, 2005. "A Unified
Framework for Monetary Theory and Policy Analysis
Journal of Political Economy
, vol. 113(3), pages 463-484.
Lester, Benjamin, Andrew Postlewaite and Randall Wright, 2008.
"Information, Liquidity and Asset
," PIER Working paper, 08-039.
Lucas, Robert E., Jr., 1978. "Asset Prices in an
, vol. 46(6), pages 1426-1445.
Mehra, Rajnish, and Edward C. Prescott, 1985.
"The Equity Premium: A Puzzle
," Journal of Monetary
, vol. 15(2), pages 145-161.
Nosal, Ed, and Guillaume Rocheteau, 2008. "Pairwise
Trade, Asset Prices, and Monetary Policy," Working paper.
Rocheteau, Guillaume, 2008. "Information and
Liquidity: A Discussion," Working paper.
Shi, Shouyong, 1997. "A Divisible Search Model of Fiat
, vol. 64(1), pages 75-102.
Weill, Pierre-Olivier, 2007. "Leaning Against the
," Review of Economic Studies
, vol. 74(4), pages 1329-1354.
Wilson, Charles, 1979. "An Infinite Horizon Model with
Money," in: Jerry R. Green and José A. Scheinkman (eds.), In General Equilibrium, Growth, and Trade
, pages 79-104. New York: Academic
Zhu, Tao, and Neil Wallace, 2007. "Pairwise Trade and
Coexistence of Money and Higher-Return Assets
Journal of Economic Theory
, vol. 133(1), pages 524-35.
EconomicDynamics Interviews Christopher Pissarides on the Matching Function
Christopher Pissarides holds the Norman Sosnow Chair in Economics at the London School of Economics. He is interested in the macroeconomics of the labor market, structural change and economic growth.
Pissarides's RePEc/IDEAS entry
EconomicDynamics: The Mortensen-Pissarides matching function has been a standard feature of
the analysis of labor markets with unemployment, in particular over the
business cycle. With Shimer (2005), its business cycle features have come
under fire. Do you see the matching function survive the Shimer (2005)
Christopher Pissarides: The matching function has been influential in the modeling of labor markets
because it is a simple device for capturing the impact of frictions on
individuals and market equilibrium. It is the kind of function that
economists like to work with, a stable function of a small number of
variables, increasing and concave in its arguments and homogenous of degree
one. It gives the rate at which jobs form (or "created") over time as a
function of the search effort of workers and firms, which in the simplest
and most common form are represented by unemployment and job vacancies. In a
market without frictions this rate is infinite. So for any given search
effort from each side of the market, the speed at which jobs are created is
a measure of the frictions in the market. If two countries have identical
search inputs, the one with a lower speed of job creation - or
alternatively, with a matching function further away from the origin in
vacancy-unemployment space - has more frictions.
Once the matching function is introduced to capture frictions in an
otherwise conventional model of the labor market, the modeling needs to
change fundamentally. The frictions give monopoly power to both firms and
workers, and job creation becomes like an investment decision by the firm.
Models with a matching function have found many applications, such as the
study of unemployment durations, disincentives from social security,
employment protection legislation and many others. Empirically it has
performed well in its simplest forms for many countries.
The claim made in Pissarides (1985) was that the rents created by the
matching function imply that outside non-cyclical variables, such as the
imputed value of leisure, influence directly the wage rate. When there are
shocks to the productivity variables that also influence the wage rate, the
outside influences stop the wage rate short from fully reacting to the
shock. This "wage stickiness" implies more volatility in job creation and
employment than in a frictionless equilibrium model and less volatility in
Shimer's critique was about the quantitative implications of this model. He
argued that although in principle the claim was correct, at conventional
parameter values the volatility of employment increased by very little, far
less than in the data that it was supposed to match, and the volatility of
wages decreased by even less. However, as shown by Hagedorn and Manovskii
(2008) in particular, other parameter values that restrict the firm's profit
flow to a small fraction of the revenue from the job, deliver more
employment volatility. And as shown by Hall (2005) and Hall and Milgrom
(2008), other wage mechanisms from the conventional Nash wage equation, can
also deliver more employment volatility.
In these (and in many others) extensions the matching function has been
preserved intact. Frictions are still represented by the simple matching
functions with constant returns and a very small number of arguments. So one
cannot really argue that Shimer's critique has diminished the usefulness of
the matching function. His critique was about other aspects of the model and
was targeted at some popular versions of the model that have been used in
the recent literature. It also shifted the focus to wage behavior, which
intensified research in this area within the framework of the matching
ED: Search models have made considerable advances in recent years, in
particular by trying to make explicit relationships that were typically
represented in reduced form. Will the matching function survive this as
well as the production function?
CP: Search models are aggregative models with all matching frictions
represented by an aggregate matching function. I take it that this is
what you mean by "reduced form", that instead of representing frictions
more specifically according to their origin and their type, we lump them
all together into an aggregate function. My reaction to this is that our
understanding of labor markets would improve if we could represent
frictions in more specific forms, but I don't see it happening yet. We
can represent some very special types of frictions by more explicit
processes. For example, the most famous one, the urn-ball game, assumes
that the frictions are due to conflicts when two workers apply for the
same job and only one gets it. The transition of workers from
unemployment to employment derived from this friction is well behaved
and satisfies specific restrictions. Significantly, it can be
represented as a special case of the more general "black-box" matching
function used in the standard model. But unfortunately the special case
that the urn-ball game supports has found no support at all in the
Other types of frictions have also been explored in the recent
literature. For example, in stock-flow matching, originally due to
Melvyn Coles and Eric Smith (1998), the friction is that in the local
market there is no match that can be made, as opposed to the implicit
assumption of the aggregate function that there are matches that can be
made if only the partners knew where to find each other. In stock-flow
matching an unmatched agent has to wait for new entry to try and match.
The transitions derived from this specification are again well-behaved
and not different from the transitions that can be derived from special
forms of the aggregate matching function (as shown by Shimer, 2008).
This specification has found more support in the data than the urn-ball
one has, but again I wouldn't say that finding support for stock-flow
matching makes the reduced-form matching function obsolete.
My point more generally is that although some special cases can be
worked out from more primitive assumptions about frictions, none of them
has contradicted the aggregate matching function. Frictions in labor
markets are due to so many different reasons that I do not yet see
either a complete or near complete characterization of frictions in a
micro model. The convenience of the aggregate matching function, its
support in the data and our experience with more micro models so far are
such that they convince me that there is a bright future for the
aggregate matching function for a long time to come. We shouldn't miss
the fact that the success of the aggregate matching function stimulated
a lot more research in the role of frictions in labor markets and in its
foundations. If one were to succeed to come up with a good micro founded
alternative it would be real progress.
Coles, Melvyn G., and Smith, Eric, 1998. "Marketplaces and Matching
," International Economic Review
, vol. 39(1), pages 239-54.
Hagedorn, Marcus, and Iourii Manovskii, 2008. "The Cyclical Behavior of Equilibrium Unemployment and Vacancies Revisited
," American Economic Review
, vol. 98(4), pages 1692-1706.
Hall, Robert E., 2005. "Employment Fluctuations with Equilibrium Wage Stickiness
," American Economic Review
, vol. 95(1), pages 50-65.
Hall, Robert E., and Paul R. Milgrom, 2008. "The Limited Influence of Unemployment on the Wage Bargain
," American Economic Review
, vol. 98(4), pages 1653-74.
Pissarides, Christopher A, 1985. "Short-run Equilibrium Dynamics of Unemployment Vacancies, and Real Wages
," American Economic Review
, vol. 75(4), pages 676-90.
Shimer, Robert, 2005. "The Cyclical Behavior of Equilibrium Unemployment and Vacancies
," American Economic Review
, vol. 95(1), pages 25-49.
Shimer, Robert, 2008. "Stock-Flow Matching," working paper.
Society for Economic Dynamics: Letter from the President
Members and Friends:
We are now a formal organization, and thanks to our Treasurer Ellen
McGrattan's efforts, a non-profit corporation. You can see our Charter
here (pdf). The Society is governed as it
has always been by a committee consisting of the former Presidents of the
Society, now formally constituted as the Board of Directors, with terms
limits, rules for voting, and everything you would expect of a formal
Some important leadership changes take place this year. My own dictatorship
ends with the upcoming meetings in Istanbul. The Board of Directors
unanimously agreed that Richard Rogerson would be an outstanding successor,
and luckily he agreed to do it. I expect the Society to continue to flourish
under his leadership. I also have bad news and good news to report. After
his strong and devoted leadership Narayana Kocherlakota has asked to step
down as managing editor of RED. During his tenure as editor-in-chief RED has
continued its rise to become the premier specialty "macroeconomic" journal.
Fortunately for us Gianluca Violante has agreed to take over beginning in
January, and Narayana has agreed to stay on for a while longer as co-editor,
so the journal remains in the best of hands. We have further strengthened
the board by adding Matthias Doepke as a co-editor. Concerning RED, one
issue that remains important is the credentialing of the journal. If you
know about institutions that maintain lists or ranking of journals to whom
we might usefully provide information about why the Review is a first rate
journal, drop me an email. Narayana's report contains a lot more of the
detail about what is happening with RED.
Our summer meeting in Cambridge was terrific. The program chairs
George-Marios Angeletos, Ariel Burstein, Mikhail Golosov, and Christian
Hellwig put together an outstanding intellectual program, including great
plenary talks by James Poterba, José Scheinkman, and Per Krusell. They also
handled the local organization, creating a great environment for the
conference, and making sure that everything went smoothly.
Our upcoming meetings will take place in Istanbul, Turkey July 2-4, 2009,
hosted by Bahçeşhir University. Our co-chairs Jesus
Fernandez-Villaverde and Martin Schneider are hard at work putting things
together, and we already have lined up a great set of plenary speakers: Matt
Jackson, Tim Kehoe and Chris Sims. Our local organizers Nezih Guner, Refet
Gürkaynak, Selo Imrohoroglu, Gokce Kolasin and Kamil Yilmaz have lined up some great venues and activities. Details as they are available, including
the submission deadline, will be found at
http://www.economicdynamics.org/sed2009.htm. I look forward to seeing all of
you in Istanbul.
For 2010, we plan to hold the meetings in Montreal. Montreal is a great
city, and I expect we will put together our usual strong scientific program.
Tentatively for 2011 we plan to go to Gent Belgium, and we will probably
switch from alternating one year in North America, one year overseas to one
year in North America with two years overseas.
As always we are fortunate to have strong officers running things. Our
Treasurer Ellen McGrattan avoided investing in mortgage backed securities,
and as a result our endowment remains in fine shape. Our Secretary Christian
Zimmermann continues to run our website and edit this newsletter, and is
moving to write down some of our institutional knowledge about running the
Society and our conferences.
David Levine, President
Society for Economic Dynamics
Review of Economic Dynamics: Letter from the Co-ordinating Editor
In this letter, I'll describe some upcoming issues, the general state of
the journal, and an exciting change in journal leadership.
Let me first tell you about three upcoming issues of the journal. All of
the papers in the January 2009 issue of the journal will be dedicated to
labor economics. The lead article will be jointly authored by Michael
Keane and Kenneth Wolpin, and is based on Wolpin's plenary lecture at the
2006 Society for Economic Dynamics conference. The issue will also
Later in 2009, we plan to publish another special issue on the nexus of
macroeconomics and labor economics. The issue will contain papers that
document the behavior of household labor income, hours worked, and
consumption for a number of countries, including among others Italy, the
US, the UK, and Sweden. The co-editors of this issue are Dirk Krueger, Fabrizio Perri,
Luigi Pistaferri, and Gianluca Violante. Contributing authors include (among many others)
the co-editors of the issue, Richard Blundell and Orazio Attanasio. I
believe this issue will be a crucial reference in both labor and macro for
years to come. The papers are currently under review at the journal, but
initial drafts are available at http://www.econ.umn.edu/~fperri/Cross.html.
In July 2009, Stephanie Schmitt-Grohé and Martín Uribe of Columbia
University will organize a mini-conference that will take place within the
SED meetings. The mini-conference will focus on business cycle shocks.
The organizers are especially interested in the recent exciting work on
news shocks. The papers submitted to the 2009 mini-conference will all be
considered for a special issue of the RED, to be published in 2010. If you
want to submit a paper to the mini-conference, check out the conference website for details. Please
note that to submit a paper to the mini-conference, you must simultaneously
submit it to the Review of Economic Dynamics for consideration by the
I now turn to some journal news. In 2006-2008, we have averaged 210
submissions per year--about 50% more than our highest year before 2006. We are processing these submissions rapidly: in 2007, 75% of papers received
first decisions within 4 months, 93% within 6 months, and all but one
within eight months.
The quality of the published papers is also higher than ever before. I have
heard this subjective opinion from many readers. But there is also hard
objective evidence to back it up. Journals are typically ranked in terms
of impact factors: this is the per-article citation in a given year to
articles published in the preceding two years. In the year 2005, our
impact factor was 0.43. In the year 2007, our impact factor was close to
0.97. This doubling (really more) in such a short span is remarkable. We
now rank higher than prestigious journals like the International Economic
Review and the Journal of Money, Credit, and Banking.
I close by discussing the exciting change in journal leadership. Beginning
in January 2009, I will return to my old job as an editor of the journal.
Gianluca Violante of New York University will replace me as co-ordinating
editor. Gianluca has an impressive record of scholarly publications which
address fundamental issues in macroeconomics and labor economics. Beyond
this record, he has done a remarkable job as associate editor and editor.
He has a wealth of great ideas about how to make the journal even better.
I am looking forward to seeing these ideas implemented!
I have enjoyed my three and half years as co-ordinating editor. It has been
highly rewarding: we have ve made progress on a number of dimensions. And I have learned a tremendous amount by reading a lot of excellent economics.
In my last words to you as co-ordinating editor, I will echo my first
words. Macroeconomics is intrinsically dynamic, and so the Review of
Economic Dynamics publishes a lot of papers in macroeconomics. But we are
certainly not a macroeconomics journal. There is a natural link between
dynamic economics and the use of computational experiments, and so the RED
publishes many papers that use calibration methods. But we are certainly
not a calibration journal. We are willing and eager to publish excellent
research in any area of dynamic economics that uses any mode of analysis.
This is not empty rhetoric. In chronological order, the three most-cited
papers in journal history are:
These three great papers illustrate beautifully that our journal imposes no
area or methodological restrictions.
Narayana Kocherlakota, Co-ordinating Editor
Review of Economic Dynamics
Society for Economic Dynamics: 2009 Meetings Call for Papers
The 20th annual meetings of the Society for Economic Dynamics will be held
July 2-4, 2009 in Istanbul, Turkey. The plenary speakers are Matthew
Jackson (Stanford University), Timothy
Kehoe (University of Minnesota), and Christopher Sims (Princeton University). The program co-chairs
are Jesus Fernandez-Villaverde (University of Pennsylvania), and Martin Schneider (Stanford University), while local organization is in the hands of Nezih Guner
(Universidad Carlos III), Refet Gürkaynak (Bilkent Üniversitesi), Selahattin Imrohoroglu (University of Southern California), Gokce Kolasin (Bahçeşhir Üniversitesi), and Kamil Yilmaz (Koç Üniversitesi).
The program will be made up from a selection of invited and submitted
papers. The Society now welcomes submissions for the Instanbul program.
Submissions may be from any area in economics. A program committee will
select the papers for the conference. The deadline for submissions is
February 15, 2009. Further details and instructions on how to submit a
paper are available at
Review: The Economics of Inaction
The Economics of Inaction: Stochastic Control Models with Fixed Costs
by Nancy Stokey
A reality mostly ignored in economic modeling is that we do nothing most of the time: portfolios lay unadjusted, prices are unchanged, investment is
chunky, hiring and firing are lumpy. One way to explain this is that some
fix cost is involved, generating a region of inaction. This book lays the
foundations on how to think about fix costs in a dynamic setting. It turns
out that continuous-time models are very appealing in the context of such
costs and Nancy Stokey delivers a series of example models using this
The book is self-contained, thus it includes a substantial part with
mathematical preliminaries on stochastic processes, Brownian motions and
other diffusions. It covers the essential theorems for these concepts and
then applies them to various situations. There are essentially two types of
models. First, impulse control models, where a fix cost leads to a lumpy
decision. Examples are exercising an option, pricing with menu costs,
inventory management and portfolio adjustment. Second, instantaneous
control models, where the fix cost leads to a change in a rate of
adjustment. Examples are inventory management again and irreversible
investment. Finally, the book covers the issue of aggregating individually
This is a very technical book, but it tackles a hard and important
problem. As it covers the necessarily preliminaires, someone with only
passing familiarity with Brownian motions should be able to work through
it. This book will prove to be a timeless reference.
"The Economics of Inaction" is published by Princeton University Press.
The EconomicDynamics Newsletter is a free supplement
the Review of Economic
(RED). It is distributed through the
mailing list and archived at http://www.EconomicDynamics.org/newsletter/. The
editors are Christian
Zimmermann (RED associate editor)
and Narayana Kocherlakota (RED coordinating editor).
The EconomicDynamics Newsletter is published twice a
in April and November.
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