Michael Woodford

An Optimization-Based Econometric Framework for the Evaluation of Monetary Policy

This paper considers a simple quantitative model of output, interest rate and inflation determination in the United States, and uses it to evaluate alternative rules by which the Fed may set interest rates. The model is derived from optimizing behavior under rational expectations, both on the part of the purchasers of goods (who choose quantities to purchase given the expected path of real interest rates), and upon that of the sellers of goods (who set prices on the basis of the expected evolution of demand). Numerical parameter values are obtained in part by seeking to match the actual responses of the economy to a monetary shock to the responses predicted by the model. The resulting model matches the empirical responses quite well and, once due account is taken of its structural disturbances, can account for our data nearly as well as an unrestricted VAR. The monetary policy rule that most reduces inflation variability (and is best on this account) requires very variable interest rates, which in turn is possible only in the case of a high average inflation rate. But even in the case of a constrained-optimal policy, that takes into account some of the costs of average inflation and constrains the variability of interest rates so as to keep average inflation low, inflation would be stabilized considerably more and output stabilized considerably less than under our estimates of current policy. Moreover, this constrained-optimal policy also allows average inflation to be much smaller.

Interest-Rate Rules in an Estimated Sticky Price Model

This paper evaluates alternative rules by which the Fed may set interest rates using the small model of the U.S. economy estimated in Rotemberg and Woodford (1997). Our main substantive finding is that low and stable inflation together with stable interest rates can be achieved by letting the funds rate respond positively to inflation while also responding, with a coefficient bigger than one, to the lagged funds rate itself. A rule in which the interest rate is set in this extremely simple way does almost as well as a more complicated rule which is optimal in our setting, in the sense of maximizing expected utility to the representative household. Furthermore, when the funds rate responds to inflation only with a delay, due to delay in the availability of inflation data, performance under the rule is only slightly reduced.

Monetary Policy and Price Level Determinacy in a Cash-in-Advance Economy

SummaryThe paper considers the determinacy of the equilibrium price level in the cash-in-advance monetary economy of Lucas and Stokey (1983, 1987), in the case of deterministic “fundamentals”. The possibilities both of a multiplicity of perfect foresight equilibria and of “sunspot equilibria” are considered. Two types of monetary policy regimes are considered and compared, one in which the money supply grows at a given exogenous rate (that may be positive or negative), and one in which the nominal interest rate on one-period government debt is pegged at a given non-negative level. In the case of constant money growth rate regimes, it is shown that one can easily have both indeterminacy of perfect foresight equilibrium and existence of sunspot equilibria; indeed, in the case of negative rates of money growth (as called for by Friedman (1969)), both types of indeterminacy necessarily occur. On the other hand, sufficient conditions for uniqueness of equilibrium (and non-existence of equilibria other than a deterministic steady state) are also given, and a class of cases is identified in which a sufficiently high rate of money growth guarantees this. Thus there may be a conflict between the aims of choosing a rate of money growth that results in a high level of welfare in the steady state equilibrium and choosing a rate that makes this steady state the unique equilibrium.) In the case of the interest rate pegging regimes, sufficient conditions are given for uniqueness of equilibrium (and impossibility of sunspot equilibria), and it is shown that these necessarily hold in the case of any low enough nominal interest rate. Thus the nominal interest rate peg allows simultaneous achievement of price level determinacy and a high level of welfare in the unique (steady state) equilibrium.In this paper I consider the consequences of alternative choices of the monetary policy regime for the determinacy of the rational expectations equilibrium value of money, and in particular for the existence or not of “sunspot” equilibria, i.e., rational expectations equilibria in which fluctuations in the price level occur in response to random events that represent no change in economic “fundamentals”, simply due to self-fulfilling revisions of peoples expectations. I am interested in particular in making the point that a consideration of the complete set of possible equilibria associated with a given policy regime may alter ones evaluation of the relative desirability of alternative policies, relative to the conclusion that one might reach if one considered only a single possible equilibrium associated with each policy regime (perhaps a unique equilibrium involving a “minimum set of state variables”). In view of this I give particular attention to policy regimes of types that have sometimes been advocated as ways of reducing the inefficiency associated with a rate of return differential between money and other financial assets, and show that policies that might otherwise be desirable (policies that make possible a more desirable equilibrium than would otherwise be possible) can have the unfortunate consequence of rendering equilibrium indeterminate and making possible equilibrium fluctuations in response to “sunspot” events.Two classes of policy regimes are considered in particular: on the one hand, alternative constant rates of growth or contraction of the money supply, financed through lump sum taxes or transfers, with zero net government assets at all times; and on the other, alternative constant nominal interest rate pegs, to be maintained through open market operations between money and interest-bearing debt, with an exogenously fixed level of net transfer payments. The first class of policies is considered because of Friedmans (1969) well-known proposal that a constant contraction of the money supply of this sort would be welfare improving. I find that while thestationary equilibrium associated with the Friedman regime achieves the maximum possible level of utility for the representative consumer, and while the level of utility associated with stationary equilibrium may be monotonically decreasing in the rate of money growth, lower rates of money growth (in particular, rates near that called for by Friedman) are associated with indeterminacy of equilibrium and the existence of sunspot equilibria, while these problems need not arise in the case of higher rates of money growth.The second class of policies is considered because they represent an obvious alternative approach to the elimination of the same rate of return differential with which Friedman is concerned. Achievement of permanently low nominal interest rates through a simple interest rate peg is not often advocated; one reason is that it is often asserted that such a policy must result in price level indeterminacy. In fact, I find that if the interest rate pegging regime is properly specified, it results in aunique rational expectations equilibrium, regardless of the level at which interest rates are to be pegged. Thus not only does the interest rate peg not result in price level indeterminacy but it allows nominal interest rates to be maintained permanently at a level lower than that which can be obtained through a policy regime of the first sort without creating price level indeterminacy. It would hence appear, at least in the case of the kind of economy modeled here, that interest rate pegging is a more reliable way of trying to reduce the inefficiency associated with consumers being forced to “economize on liquidity”.

Control of the Public Debt: A Requirement for Price Stability?

The paper considers the role of limits upon the permissible growth of public debt, like those stipulated in the Maastricht treaty, in making price stability possible. It is shown that a certain type of fiscal instability, namely variations in the present value of current and future primary government budgets, necessarily results in price level instability, in the sense that there exists no possible monetary policy that results in an equilibrium with stable prices. In the presence of sluggish price adjustment, the fiscal shocks disturb real output and real interest rates as well. On the other hand, shocks of this kind can be eliminated by a Maastricht-type limit on the value of the public debt. In the presence of the debt limit (and under assumptions of frictionless financial markets, etc.), Ricardian equivalence holds, and fiscal shocks have no effects upon real or nominal variables. Furthermore, an appropriate monetary policy rule can ensure price stability even in the face of other kinds of real shocks. Thus the debt limit serves as a precondition for the common central bank in a monetary union to be charged with responsibility for maintaining a stable value for the common currency.

Credit Spreads and Monetary Policy

We consider the desirability of modifying a standard Taylor rule for a central banks interest rate policy to incorporate either an adjustment for changes in interest rate spreads (as proposed by Taylor [2008] and McCulley and Toloui [2008]) or a response to variations in the aggregate volume of credit (as proposed by Christiano et al. [2007]). We then examine how, under those adjustments, policy would respond to various types of economic disturbances, including those originating in the financial sector that increase equilibrium spreads and contract the supply of credit. We conduct our analysis using a simple DSGE model with credit frictions (Curdia and Woodford 2009), comparing the equilibrium responses to various disturbances under the modified Taylor rules with those under a policy that would maximize average expected utility. According to our model, a spread adjustment can improve on the standard Taylor rule, but the optimal size of the adjustment is unlikely to be as large as the one proposed, and the same type of adjustment is not desirable regardless of the source of variation in credit spreads. A response to credit is less likely to be helpful, and its desirable size (and even sign) is less robust to alternative assumptions about the nature and persistence of economic disturbances.

Rational Asset Pricing Bubbles

This paper provides a fairly systematic study of general economic conditions under which rational asset pricing bubbles may arise in an intertemporal competitive equilibrium framework. Our main results are concerned with nonexistence of asset pricing bubbles in those economies. These results imply that the conditions under which bubbles are possible --including some well-known examples of monetary equilibria-- are relatively fragile.

An Optimization-Based Econometric Framework for the Evaluation of Monetary Policy: Expanded Version

This paper considers a simple quantitative model of output, interest rate and inflation determination in the United States, and uses it to evaluate alternative rules by which the Fed may set interest rates. The model is derived from optimizing behavior under rational expectations, both on the part of the purchasers of goods and upon that of the sellers. The model matches the estimates responses to a monetary policy shock quite well and, once due account is taken of other disturbances, can account for our data nearly as well as an unrestricted VAR. The monetary policy rule that most reduces inflation variability (and is best on this account) requires very variable interest rates, which in turn is possible only in the case of a high average inflation rate. But even in the case of a constrained-optimal policy, that takes into account some of the costs of average inflation and constrains the variability of interest rates so as to keep average inflation low, inflation would be stabilized considerably more and output stabilized considerably less than under our estimates of current policy. Moreover, this constrained-optimal policy also allows average inflation to be much smaller. This version contains additional details of our derivations and calculations, including three technical appendices, not included in the version published in NBER Macroeconomics Annual 1997.

Optimal Monetary and Fiscal Policy: A Linear Quadratic Approach

We propose an integrated treatment of the problems of optimal monetary and fiscal policy, for an economy in which prices are sticky and the only available sources of government revenue are distorting taxes. Our linear-quadratic approach allows us to nest both conventional analyses of optimal monetary stabilization policy and analyses of optimal tax-smoothing as special cases of our more general framework. We show how a linear-quadratic policy problem can be derived which yields a correct linear approximation to the optimal policy rules from the point of view of the maximization of expected discounted utility in a dynamic stochastic general-equilibrium model. Finally, we derive targeting rules through which the monetary and fiscal authorities may implement the optimal equilibrium.

Stationary sunspot equilibria in a finance constrained economy

Abstract Stationary sunspot equilibria are shown to exist in a production economy with infinite lived agents, when it is not possible to borrow against future wage income. Equilibrium fluctuations exhibit persistence over time scales of the same order of magnitude as observed “business cycles.” An active fiscal policy that stabilizes aggregate money expenditures can prevent such fluctuations.

Real-Business-Cycle Models and the Forecastable Movements in Output, Hours, and Consumption

The authors study the movements in output, consumption, and hours that are forecastable from a vector autoregression and analyze how they differ from those predicted by standard real-business-cycle models. They show that actual forecastable movements in output have a variance about one hundred times larger than those predicted by the model. The authors also find that forecastable changes in the three series are strongly positively correlated with each other. On the other hand, for parameters whose implications are plausible in other respects, the model implies that output, consumption, and hours should not all be expected to move in the same direction. Copyright 1996 by American Economic Association.