Research Database

This paper describes an algorithm that takes advantage of parallel computing to solve discrete-time recursive systems that have an endogenous state variable.

During the 1882–1914 period, U.S. national banks could issue circulating notes backed by specified government securities. Earlier attempts to explain yields on those securities by costs of note issue discovered a paradox: yields were too high. We point out two previously ignored sources of costs: idle notes and note redemptions that were highly variable, thereby exacerbating the problem of managing reserves. We present data on idle notes and estimate, from partial data on redemptions, the uncertainty due to redemptions. We also present a semiannual time series of an upper bound on the average additional return on equity a national bank would earn by fully using its note issue privilege. Since the median of this series is 0.5 percent and since this upper bound does not include the average costs stemming from the exacerbated reserve management problem, we conclude that the specified government securities did not have paradoxically high yields.

This paper presents new empirical evidence to support the hypothesis that positive money supply shocks drive short-term interest rates down. We then present a quantitative, general equilibrium model which is consistent with this hypothesis. The two key features of our model are that (i) money shocks have a heterogeneous impact on agents and (ii) ex post inflexibilities in production give rise to a very low short-run interest elasticity of money demand. Together, these imply that, in our model, a positive money supply shock generates a large drop in the interest rate comparable in magnitude to what we find in the data. In sharp contrast to sticky nominal wage models, our model implies that positive money supply shocks lead to increases in the real wage. We report evidence that this is consistent with the U.S. data. Finally, we show that our model can rationalize a version of the Real Bills Doctrine in which the monetary authority accommodates technology shocks, thereby smoothing interest rates.

We examine nominal and real exchange rates, interest rates, prices, and evolutions of real variables in a two-country, monetary general-equilibrium model that includes a financial sector and shocks to technologies and money growth rates. Qualitative properties of the model are provided and moment predictions from a calibrated version of the model are compared to moments of time series drawn from actual economies. We focus on international monetary shock transmissions, and effects of monetary innovations on nominal and real exchange rates and nominal interest rates.

We study the effect on the growth of an economy of alternative financing opportunities in a stochastic growth model with incentive constraints. Efficient accumulation mechanisms are designed and computed for economies that differ in their incentive structure. We show that when borrowing is subject to information constraints, there is a computable efficient transfer mechanism that does not affect capital accumulation and investment patterns, even though consumption patterns and the distribution of wealth are affected. In contrast, enforcement constraints can severely reduce the outside financing opportunities and affect investment patterns and economic growth. We adapt numerical algorithms for obtaining numerical solutions of these models.

A real business cycle model with heterogeneous agents is parameterized, calibrated, and simulated to see if it can account for some stylized facts characterizing postwar U.S. business cycle fluctuations, such as the countercyclical movement of labor’s share of income, and the acyclical behavior of real wages. There are two types of agents in the model, workers and entrepreneurs, who participate on an economy-wide market for contingent claims. On this market workers purchase insurance from entrepreneurs, through optimal labor contracts, against losses in income due to business cycle fluctuations. The model is used to study the allocation of risk and the distribution of income over the business cycle.

This paper provides an algorithm for computing Markov Perfect Nash Equilibria (Maskin and Tirole, 1988a and b) for dynamic models that allow for heterogeneity among firms and idiosyncratic (or firm specific) sources of uncertainty. It has two purposes. To illustrate the ability of such models to reproduce important aspects of reality, and to provide a tool which, given appropriate parameter estimates, can be used for both descriptive and policy analysis in a setting which allows firms to differ from one another in ways that are consistent with the information in firm level data sets.

We illustrate by computing the policy functions, and simulating the industry structures, generated by a class of dynamic differentiated product models in which the idiosyncratic uncertainty is due to both the random outcomes of each firm's research process, and to an autonomous aggregate demand process. The illustration focuses on comparing the effect of different regulatory and behavioral assumptions on market structure and on welfare for one particular set of parameter values. The results here are of some independent interest and can be read without delving into the technical detail of the computational algorithm.

The last part of the paper begins with an explicit consideration of the computational burden of the algorithm, and then introduces approximation techniques designed to make computation easier. The purpose of this section is to enable us to compute equilibria for industries in which a large number of firms are typically active. Its major result is analytic. We show that if the value function of a given firm is exchangeable in the state vectors of its competitors, then the number of polynomial coefficients one needs for a given order of a polynomial approximation to that function is both independent of the number of firms active in the market, and a relatively small number. This enables us to use the approximation technique to reduce the computational burden of the algorithm dramatically.