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helpful conversation and Philip Jefferson for providing data on currency holdings. In addition, we would like to thank participants in the Banco de Portugal Conference on Monetary Economics, the June 2000 meetings of the Society for Economic Dynamics, and seminar participants at Rutgers. Errors are our own. The views expressed here are the authors ’ and not necessarily those of the Federal Reserve Banks of Philadelphia or Richmond or the Federal Reserve System. 1

We consider a general class of nonlinear optimal policy problems involving forward-looking constraints (such as the Euler equations that are typically present as structural equations in DSGE models), and show that it is possible, under regularity conditions that are straightforward to check, to derive a problem with linear constraints and a quadratic objective that approximates the exact problem. The LQ approximate problem is computationally simple to solve, even in the case of moderately large state spaces and flexibly parameterized disturbance processes, and its solution represents a local linear approximation to the optimal policy for the exact model in the case that stochastic disturbances are small enough. We derive the second-order conditions that must be satisfied in order for the LQ problem to have a solution, and show that these are stronger, in general, than those required for LQ problems without forwardlooking constraints. We also show how the same linear approximations to the model structural equations and quadratic approximation to the exact welfare measure can be used to correctly rank alternative simple policy rules, again in the case of small enough shocks.

Two Arrow–Debreu market games are formulated whose straightforward Nash equilibria are Walrasian. Both have an auctioneer setting prices to maximize net sales value. In the second an additional redistributive agency maximizes welfare through optimal lump-sum transfers. In intertemporal economies, however, subgame imperfections can arise because agents understand how current decisions such as those determining investment influence either future prices (with finitely many agents), or future redistribution (even in continuum economies). The latter observation undermines the second efficiency theorem of welfare economics. Indeed, when the state of the economy affects future policy, it functions like a “widespread externality.” 1.

This paper studies optimal taxation in the stochastic growh model when the goverment cannot commit. We use recursive game theory to characterize the set of Sustainable Equilibria and to build strategies that support equilibrium payoffs. We calibrate our model to match U.S. data and compute both the set of sustainable equilibria payoffs, strategies that implement them and triggers. We also look at the Best Equilibrium under no commitment and compare it with the Markov Perfect Equilibrium and with the Ramsey Equilibrium.

Bank of Canada working papers are theoretical or empirical works-in-progress on subjects in economics and finance. The views expressed in this paper are those of the authors. No responsibility for them should be attributed to the Bank of Canada. ISSN 1701-9397 © 2007 Bank of CanadaAcknowledgements

Policy Regimes, Identification. This paper takes the parameters in central bank loss functions as fundamental preferences to be estimated from the data. It is these preferences (along with target values) that define the policy regime in operation and that potentially change with senior central bank appointments. Optimizing central banks apply policy rules whose feedback coefficients are functions of its preferences. Consequently, under some conditions, it is possible to back out estimates of the preference parameters from estimated policy reaction functions. This paper establishes conditions under which a policy regime can be identified and illustrates these conditions using a number of popular models.

University, and the University of Western Ontario. The views expressed here are the authors’ and not necessarily those of the Federal Reserve Banks of Philadelphia or Richmond Optimal monetary policy maximizes the welfare of a representative agent, given frictions in the economic environment. Constructing a model with two sets of frictions — costly price adjustment by imperfectly competitive firms and costly exchange of wealth for goods — we find optimal monetary policy is governed by two familiar principles. First, the average level of the nominal interest rate should be sufficiently low, as suggested by Milton Friedman, that there should be deflation on average. Yet, the Keynesian frictions imply that the optimal nominal interest rate is positive. Second, as various shocks occur to the real and monetary sectors, the price level should be largely stabilized, as suggested by Irving Fisher, albeit around a deflationary trend path. (In modern language, there is only small “base drift ” for the price level path in response to shocks). Since expected inflation is roughly constant through