Existence of solutions in continuous-time optimal growth models

This paper studies the existence of solutions in continuous time optimization problems. It provides a theorem whose conditions can be easily checked in most models of the optimal growth theory, including those with increasing returns and multi-sector economies.      

On Lipschitz continuity of policy functions in continuous-time optimal growth models

Summary. This paper proves the C ^1,1 differentiability of the value function for continuous time concave dynamic optimization problems, under the assumption that the instantaneous utility is C ^1,1 and the initial segment of optimal solutions is interior. From this result, the Lipschitz dependence of optimal solutions on initial data and the Lipschitz continuity of the policy function are derived, by adding an assumption of strong concavity of the integrand. Received: July 29, 1996; revised version: November 25, 1997     

A general method for comparative dynamics in continuous-time models

This paper develops a general and applicable method for the computation of comparative dynamics in continuous-time perfect foresight models. The key technique in our method is the Jordan decomposition of the Jacobian matrix. This enables us to derive analytical solutions when dealing with high-dimensional systems with repeated eigenvalues. In an application, we compute comparative dynamics of an unanticipated expansionary monetary policy in scenarios with and without repeated eigenvalues. We find that the short-run effects on the social welfare are opposite in the two scenarios, while the long-run effects are similar.     

Almost sure convergence to zero in stochastic growth models

This paper considers the resource constraint commonly used in stochastic one-sector growth models. Shocks are not required to be i.i.d. It is shown that any feasible path converges to zero exponentially fast almost surely under a certain condition. In the case of multiplicative shocks, the condition means that the shocks are sufficiently volatile. Convergence is faster the larger their volatility, and the smaller the maximum average product of capital.I would like to thank Santanu Roy, John Stachurski, Lars J. Olson, and an anonymous referee for helpful comments and suggestions. The general result in section 2 owes much to the referee’s comments on an earlier version of this paper. Financial support from the 21 Century COE Program at GSE and RIEB, Kobe University is gratefully acknowledged.     

Stability of stochastic optimal growth models: a new approach

The paper proposes an Euler equation technique for analyzing the stability of differentiable stochastic programs. The main innovation is to use marginal reward directly as a Foster-Lyapunov function. This allows us to extend known stability results for stochastic optimal growth models, both weakening hypotheses and strengthening conclusions.     

On the controllability of continuous-time macroeconomic models

Summary (Abstract) It is argued in this paper that an independent control of target variables over time in continuous dynamic macroeconomic systems may not be achievable even though Aoki's well-known rank test for target path controllability is satisfied. It is shown that in many dynamical systems impulse controls are needed to steer the targets along arbitrarily given time paths. Such controls are not admissible from the macroeconomic point of view. By means of the structure algorithm by Silverman and Payne (1971) conditions for target path controllability that depend on the choice of the admissible spaces for the target and the instrument variables, are derived.The author is grateful to Professor Dr. Helmut Kuhn, Göttingen, and two anonymous referees for valuable comments on an earlier draft of this paper.     

On perfect equilibria in stochastic models of growth with intergenerational altruism

Summary. The well-known model of altruistic growth/strategic bequest is studied. A stochastic transition function is considered and fairly general sufficient conditions for the existence of Markov-stationary subgame-perfect equilibrium are given. Also some special cases in which the equilibrium policy is continuous and nondecreasing are discussed.Received: 20 September 2003, Revised: 11 December 2004, JEL Classification Numbers: C73, D91, O40.Research was partially supported by KBN grant 5 PO3A 01420.     

Markovian equilibrium in a class of stochastic games: existence theorems for discounted and undiscounted models

Summary We study a strategic version of the neoclassical growth model under possible production uncertainty. For a general specification of the problem, we establish (i) the existence of stationary Markov equilibria in pure strategies for the discounted game, and (ii) the convergence, under a boundedness condition, of discounted equilibrium strategies to a pure strategy stationary Markovian equilibrium of the undiscounted game as the discount factor tends to unity. The same techniques can be used to prove that such convergence also obtains in all finitestate, finite-action stochastic games satisfying a certain full communicability condition. These results are of special interest since there are well known examples in the literature in which the limit of discounted equilibria fails to be an equilibrium of the undiscounted game.We are grateful to Marcus Berliant, M. Ali Khan, Mukul Majumdar, and an anonymous referee for helpful suggestions, and to Bonnie Huck for technical assistance. The first author acknowledges research support from the Columbia University Council for the Social Sciences.     

Nonparametric estimation of stochastic volatility models

This letter introduces nonparametric estimators of the drift and diffusion coefficient of stochastic volatility models which exploit techniques for estimating integrated volatility with high-frequency data. The performance of the proposed estimators is assessed on simulations of two popular stochastic volatility models.     

Testing separate models with stochastic regressors

In this paper we generalize the R procedure to test a null linear regression model against a separate alternative in the context of generalized instrumental variable estimation, and thereby motivate the use of the standard F test. The relations between the F test and several one-degree-of-freedom separate tests are examined under the null, and the asymptotic distributions of the statistics are evaluated under local alternatives. It is shown that the one-degree-of-freedom tests can be more powerful than the F test under a Pesaran-type local alternative, and that the F test is more widely consistent than the one-degree-of-freedom tests.     

A note on the underestimation and overestimation in stochastic input-output models

Here we show that (i) the Leontief inverse (I – A)^-1 is underestimated when the elements of A, the fixed coefficient input–output matrix, are biproportionally stochastic, and (ii) the output vector in a non-linear input–output system is overestimated when the final demand vector is stochastic.     

Indeterminacy of equilibrium in stochastic OLG models

Summary. This paper studies the equilibria of a stochastic OLG exchange economies consisting of identical agents living for two periods, and having the opportunity to trade a single infinitely-lived asset in constant supply. The agents have uncertain endowments and the stochastic process determining the endowments is Markovian. For such economies, the literature has focused on studying strongly stationary equilibria in which quantities and prices are functions of the exogenous states of nature which describe the uncertainty: such equilibria are generalizations of deterministic steady states, and this paper investigates if they have the same special status as asymptotic limits of other equilibrium paths. The difficulty in extending the analysis of equilibria beyond the class of strongly stationary equilibria comes from the presence of indeterminacy: we propose a procedure for overcoming this difficulty which can be decomposed into two steps. First backward induction arguments are used to restrict the domain of possible prices; then if some indeterminacy is left, expectation functions are introduced to make the forward equilibrium equations determinate. The properties of the resulting trajectories, in particular their asymptotic properties, can then be studied. For the class of models that we study this procedure provides a justification for focusing on strongly stationary equilibria. For the model with positive dividends (equity or land) the justification is complete, since we show that the strongly stationary equilibrium is the unique equilibrium. For the model with zero dividends (money) there is a continuum of self-fulfilling expectation functions resulting in a continuum of equilibrium paths starting from any admissible initial condition: under conditions given in the paper, these equilibrium paths converge almost surely to one of the strongly stationary equilibria-either autarchy or the stochastic analogue of the Golden Rule. Received: November 19, 2001; revised version: March 22, 2002 RID="*" ID="*" We are grateful for the stimulating environment and research support provided by the Cowles Foundation at Yale University during the Fall 2000 when this paper was first conceived. We are also grateful to the participants of the SITE Workshop at Stanford University and the Incomplete Markets Workshop at SUNY Stony Brook during the summer 2001 for helpful discussions. Correspondence to: M. Magill     

Bayesian inference in threshold stochastic frontier models

In this paper, we generalize the stochastic frontier model to allow for heterogeneous technologies and inefficiencies in a structured way that allows for l     

Deterministic versus stochastic mechanisms in principal-agent models

This paper shows that, contrary to what is generally believed, decreasing concavity of the agent's utility function with respect to the screening variable is not sufficient to ensure that stochastic mechanisms are suboptimal. The paper demonstrates, however, that they are suboptimal whenever the optimal deterministic mechanism exhibits no bunching. This is the case for most applications of the theory and therefore validates the literature's usual focus on deterministic mechanisms.     

Technological growth curves : A competition of forecasting models

In order to determine procedures for appropriate model selection of technological growth curves, numerous time series that were representative of growth behavior were collected and categorized according to data characteristics. Nine different growth curve models were each fitted onto the various data sets in an attempt to determine which growth curve models achieved the best forecasts for differing types of growth data. The analysis of the results gives rise to a new approach for selecting appropriate growth curve models for a given set of data, prior to fitting the models, based on the characteristics of the data sets.     

A general equilibrium framework for the affine class of term structure models

The Duffie and Kan (1966) model, which can be considered as the most general affine term structure formulation, was originally specified in terms of risk-adjusted stochastic processes for its state variables. The goal of the present paper is to derive a Duffie and Kan (1966) model specification under the physical probability measure that is compatible with the formulation given by the authors under the equivalent martingale (money market account) measure. For that purpose, the Duffie and Kan (1966) model will be fitted into a general equilibrium monetary framework. The resulting analytical solution for the vector of factor risk premiums enables the econometric estimation of the model parameters using a time-series or a panel-data approach, and nests, as special cases, several other specifications already proposed in the literature.Received: November 2002, Accepted: February 2004, JEL Classification: E43, G11, G12Financial support by FCTs research grant PRAXISXXI/BD/5712/95 is gratefully acknowledged.