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Optimal Monetary Policy
In a Model with Agency Costs
Charles T. Carlstrom
a
, Timothy S. Fuerst
b
, Matthias Paustian
c
a
Senior Economic Advisor, Federal Reserve Bank of Cleveland, Cleveland, OH 44101, USA.
charles.t.carlstrom@clev.frb.org
.
b
Professor, Department of Economics, Bowling Green State University, Bowling Green, OH 43403, USA; and
Senior Economic Advisor, Federal Reserve Bank of Cleveland. tfuerst@bgsu.edu
.
c
Economist, Bank of England, Threadneedle Street, London EC2R 8AH, England.
matthias.paustian@bankofengland.co.uk
.
May 4, 2009
Abstract: This paper integrates a fully explicit model of agency costs into an otherwise standard
Dynamic New Keynesian (DNK) model in a particularly transparent way. A principle result is the
characterization of agency costs as endogenous mark-up shocks in an output-gap version of the Phillips
curve. The model’s utility-based welfare criterion is derived explicitly and includes a measure of credit
market tightness which we interpret as a risk premium. The paper also fully characterizes optimal
monetary policy and provides conditions under which zero inflation is the optimal policy. Finally,
optimal policy can be expressed as an inflation targeting criterion that (depending upon parameter values)
can be either forward or backward-looking.
We would like to thank Tony Yates and Jens Sondergaard for comments on an earlier draft of this paper.
The views expresses in this paper are those of the authors only and do not represent the US Federal
Reserve System or the Bank of England.
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1. Introduction
The macroeconomic events in the latter half of 2008 have sparked renewed interest in the
role of financial shocks in the business cycle and the appropriate response of monetary policy to
these shocks. This paper adds to this discussion by formally integrating a model of agency costs
into an otherwise standard Dynamic New Keynesian (DNK) model. We do so in such a way that
the agency-cost mechanism is quite transparent so that interactions between sticky prices and
agency cost distortions are clearly identified. In addition our framework enables us to derive
analytical expressions for the model-consistent welfare function.
We study the interaction of agency costs and sticky prices in a simple extension of the
standard DNK model. Agency costs are modeled as a constraint on the firm’s hiring of labor as
in the hold-up problem of Kiyotaki and Moore (1997). We assume that the entrepreneur’s hiring
of one productive factor (labor) is constrained by entrepreneurial net worth. More generally, the
constraint proxies for the effect that asset prices have on the ability of firms to finance
operations. Net worth is accumulated over time via purchases of shares that are claims on the
profit flow of sticky-price firms that produce the final good. This leads to a natural interplay
between price stickiness and collateral constraints. In our setup, monetary policy affects
dividends and thus share prices by altering the profit flow of these sticky price firms. Share
prices in turn affect the hiring of labor via the collateral constraint.
How should monetary policy be conducted in such an environment? From a public
finance perspective, prices stickiness implies that real marginal cost acts like a distortionary
subsidy on both factor inputs, while agency costs act like a distortionary tax on only one input
(the constrained input). This suggests that a tradeoff between stabilizing these two distortions
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may exist. We study this question formally by deriving the quadratic welfare function that is
consistent with the underlying model and analyze optimal monetary policy in a linear-quadratic
framework. Inflation and the output gap enter our loss function with the same coefficients as in
the standard sticky price model. In addition, agency costs give rise to a new term that captures
the variations in the tightness of the collateral constraint and that can be interpreted as a risk
premium more generally. Thus, the recent concerns by central banks about credit market
tightness and the volatility of risk premia have a counterpart in our welfare based loss function.
If credit constraints were absent from our model, we would obtain the standard result that
central banks should fully stabilize inflation at all times in response to technology shocks. With
agency costs and sticky prices, there is a special case where all distortions can again be closed in
response to technology shocks by fully stabilizing inflation. This special case requires
preferences that are logarithmic in consumption and an efficient initial value for the model’s
state variable. In this case net worth happens to move by exactly the amount required to hire the
first best quantity of labor when inflation is fully stabilized. Outside of this special case, it is not
optimal to fully stabilize inflation in response to technology shocks. However, the optimal
deviation from inflation stability is small, so inflation stabilization is nearly optimal in this
environment. Hence, the preferred interest rate rule should feature a strong anti-inflationary
response, i.e. an inflation coefficient that is well in excess of the value originally proposed by
Taylor.
We model financial shocks as shocks to the net worth of entrepreneurs and show that
they act like endogenous markup shocks. Net worth shocks imply that inflation stabilization
comes at the cost of increased fluctuations in the output gap and in the tightness of the collateral
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constraint that enter our loss function. Consequently, a temporary deviation from full price
stability is warranted under optimal policy when financial sector shocks hit the economy.
We conclude this introduction with a brief review of the literature. Bernanke and Gertler
(1989) provided the first attempt to build agency cost effects into an otherwise standard model of
the business cycle. Their analysis was entirely qualitative. In a series of papers, Carlstrom and
Fuerst (1997, 1998, 2001) built on this earlier work to make the analysis quantitative. These
papers were in the tradition of flexible prices. Bernanke, Gertler, and Gilchrist (1999) took the
next logical step to integrate these agency cost effects into a DNK model. These models helped
to quantity two distinct effects of agency costs: (1) a change in the economy’s response to
macroeconomic shocks because of the dynamics of borrower net worth, and (2) an additional
source of shocks to the economy such as shocks to borrowers’ balance sheets. But these
previous analyses did not consider the question of optimal monetary policy.
Several recent papers have analyzed the performance of simple interest rate rules in
agency cost models, e.g., Bernanke and Gertler (2001), Gilchrist and Leahy (2002), Faia and
Monacelli (2007). Faia and Monacelli (2007) consider a model with sticky prices and credit
frictions similar to Bernanke, Gertler and Gilchrist (1999). They employ numerical second-order
approximations to evaluate welfare of a parametric family of interest rate rules. Faia and
Monacelli (2007) find that strict inflation targeting is the welfare maximizing policy rule within
the restricted set of rules. They argue that the marginal benefit from of neutralizing the price
stickiness distortion largely outweighs the marginal benefit from neutralizing the credit friction
distortion. Our linear-quadratic confirms this basic finding in the sense that the welfare weight
on the risk premium is orders of magnitude smaller than the weight on inflation. In addition,
Faia and Monacelli (2007) focus mainly on technology shocks. Our analysis considers shocks to
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net worth for which the optimal departure from price stability is larger than for productivity
shocks.
Our work is most closely related to the papers by DeFiore and Tristani (2008) and Curdia
and Woodford (2008). These authors also provide small scale sticky price models with credit
frictions and characterize optimal policy within a linear-quadratic framework. Curdia and
Woodford (2008) focus on interest rate spreads between bank’s lending and deposit rates that
arise because loans are costly to produce. The analysis of these credit frictions is limited to a
reduced form relationship between credit spreads and macroeconomic conditions.
De Fiore and Tristani (2008) add a more complete underlying structure by including a
costly state verification framework within the standard DNK model. But De Fiore and Tristani
(2008) abstract from the endogenous evolution of net worth by assuming that entrepreneurs
receive a fixed endowment in every period. This assumption simplifies matters but eliminates the
endogenous state variable that is of fundamental importance to the agency cost mechanism.
Further, both of these previous papers do not feature any feedback between asset prices and net
worth of credit constrained agents. In contrast, the interplay between the share price, net worth
and the agency cost distortion is central to the dynamics of our model.
The present paper proceeds as follows. In the next section we outline the model,
culminating in an expression for the welfare criterion. Section three analyzes the model
quantitatively. Section four concludes.
