We study a structural dynamic monetary economy submitted to technological, monetary, and real demand shocks, and investigate the nature of optimal monetary and fiscal policies under Walrasian or preset wages and prices. If prices and wages are Walrasian, then the optimal policies are both nonactivist and derive directly from Milton Friedman's prescriptions. If prices or wages are preset, however, optimal policies, and, notably, the fiscal part, become activist and countercyclical.

This paper attempts to derive several economic conservation laws and to test the validity of the optimal growth models using the income/wealth ratios for the United States, Japan, and other OECD countries. Conservation laws vary with the type of the objective function depicted, such as the maximization of the aggregate consumption or the maximization of per-capita consumption. The operational concept of “wealth-like quantity” is identified, although the Goldsmith-Kendrick standard definition of “net national wealth” should not always be used. The last section of the paper takes up an empirical analysis to determine how different economies have achieved long-term (optimal) growth. The U.S. economy has been operating rather efficiently, whereas the Japanese economy, after the oil shocks of the 1970's, has behaved differently, leading into the bubble period of the early 1990's.

This paper examines monetary policy in a two-equation macroeconomic model when the policymaker recognizes that the model is an approximation and is uncertain about the quality of that approximation. It is argued that the minimax approach of robust control provides a general and tractable alternative to the conventional Bayesian decision theoretic approach. Robust control techniques are used to construct robust monetary policies. In most (but not all) cases, these robust policies are more aggressive than the optimal policies absent model uncertainty. The specific robust policies depend strongly on the formulation of model uncertainty used, and we make some suggestions about which formulation is most relevant for monetary policy applications.

The paper studies multivariate non linear economic dynamical systems with an expectations feedback subjected to exogenous perturbations. In these systems, agents form expectations on future variables based on subjective transition probabilities given by a Markov kernel. The notion of a perfect Markov kernel that generates rational expectations along all orbits of the system is proposed. Conditions are provided under which perfect Markov kernels exist. Applications are given to models of the Cobweb type, to multivariate affine-linear systems, and to the stochastic OLG model of economic growth. For the latter two models, it is shown when a globally attracting random fixed point with rational expectations exists.

We examine minimal sufficient state spaces for equilibria in a Lucas asset pricing model with heterogeneous agents and incomplete markets. It is clear that even if all fundamentals of the economy follow a first-order Markov process, equilibrium prices and allocations generally will depend not only on the current exogenous shock but also on the distribution of wealth among the heterogeneous agents. The main contribution of this paper is to give an example of an infinite-horizon economy with Markovian fundamentals, where the joint process of equilibrium asset holdings and exogenous shocks does not constitute a sufficient state space either.

This paper proposes a general method based on a property of zero-sum two-player games to derive robust optimal monetary policy rules—the best rules among those that yield an acceptable performance in a specified range of models—when the true model is unknown and model uncertainty is viewed as uncertainty about parameters of the structural model. The method is applied to characterize robust optimal Taylor rules in a simple forward-looking macroeconomic model that can be derived from first principles. Although it is commonly believed that monetary policy should be less responsive when there is parameter uncertainty, we show that robust optimal Taylor rules prescribe in general a stronger response of the interest rate to fluctuations in inflation and the output gap than is the case in the absence of uncertainty. Thus model uncertainty does not necessarily justify a relatively small response of actual monetary policy.

We obtain the transitional dynamics of the decentralized economy described by P.M. Romer and characterize the dynamic behavior of the most relevant variables. We determine the existence of a stable one-dimensional manifold containing a steady state with innovation, unique in ratios, and also find a threshold in the accumulation of physical capital below which the economy is not innovating. Finally, using simulations, we assess the significance of this threshold and analyze the influence that technological and utility parameters have on it.

Macrodynamic models of small open economies are inevitably characterized by “knife-edge conditions,” meaning that certain parameters are constrained for a viable equilibrium to exist. This paper examines the macrodynamic structure of such an economy and considers the role played by various standard knife-edge conditions. The dynamic model presented is sufficiently general so as to provide a unifying framework within which alternative models can be embedded. We identify three important models as special cases of this generic structure: (i) The traditional stationary Ramsey model, (ii) the endogenous growth model, and (iii) the nonscale growth model. We consider three margins along which knife-edge conditions are imposed. These include (i) preference parameters, (ii) production and employment characteristics, and (iii) openness of international financial markets. These restrictions are shown to play key roles in determining the equilibrium dynamics, and how the economy responds to various shocks. The existence of trade-offs between these knife-edge conditions is discussed.

Taken literally, the concept of “stabilization policy” implicitly assumes that the macroeconomy is unstable without imposition of a policy. Hence, selection of a “stabilization policy” can be viewed as selection of a policy to bifurcate the system from an unstable to a stable operating regime. The literature on dynamics of high-dimensional systems suggests that successful bifurcation selection is challenging. As an experiment to investigate this point of view, we use the continuous-time UK dynamic macroeconometric model. Under assumptions designed to be most favorable to stabilization policy, we find that policies that would produce successful bifurcation are very complicated. We also find that less complicated policies based upon reasonable economic intuition can be counterproductive, since such policies can contract the size of the stable subset of the parameter space. In fact, an economy that is dynamically stable without policy, but subject to stochastic shocks, could be bifurcated to instability with imposition of a poorly designed “stabilization” policy.

Building on a nonlinear additively separable representation for the generator of preferences, this article provides an extensive characterization of intertemporal consumption—leisure arbitrages with an endogenous measure of impatience. A joint characterization of the comparative dynamics of consumption and leisure is undertaken. An analytical approach first puts in evidence a classical Slutsky decomposition between revenue and substitution effects after various perturbations. Those conclusions are at a second stage illustrated by a three-dimensional geometric argument.

It has been argued that a clear understanding of the stochastic growth model can best be achieved by working out an approximate analytical solution. This paper follows that idea but streamlines the presentation of the loglinear approximate solution for the neoclassical model of capital accumulation. By focusing on the partial elasticity of capital stock with respect to its lag term, this paper is able to confirm analytically some conclusions based on numerical calculations in previous papers, and to clarify why a simpler solution arises in several special cases.

Using results from the literature on H∞ control, this paper incorporates model uncertainty into a frequency-domain approach to stabilization policy. The derived policies guarantee a minimum performance level even in the worst of (a bounded set of) circumstances. Robust H∞ policies are shown to be more “activist” than H2 policies in the sense that their impulse responses are larger. Robust policies also tend to be more autocorrelated. Consequently, the premium associated with being able to commit is greater under model uncertainty. Without commitment, the policymaker is not able to (credibly) smooth his response to the degree that he would like. A contribution of this paper is its analysis of robust control in a model featuring a forward-looking state transition equation, which arises from the fact that the private sector bases its decisions on expectations of future government policy. Existing applications of H∞ control in economics follow the engineering literature, and only consider backward-looking state transition equations.

In this paper, we reconsider the theoretical basis for the Lucas critique from the point of view of robust decision theory. We first emphasize that the Lucas critique rests on a weak theoretical paradigm in that it fails to consider the motivation for the policy change by the government and hence inconsistently assumes limited rationality by the government. When placed in a proper dynamic general equilibrium framework of a dynamic game between the government and the private sector, much of the force of the critique simply vanishes. We also reconsider the critique by adopting an alternative theoretical paradigm and notion of rationality based on robust decision theory. This view of rationality might be regarded as more relevant than the nonrobust rationality employed by Lucas and, critically, it is one in which the Lucas critique can be shown simply not to apply, provided the private sector has adopted suitably robust decision rules.