Recursive Competitive Equilibrium Research Articles

On the existence and uniqueness of stationary equilibrium in Bewley economies with production

I prove existence of stationary recursive competitive equilibrium in Bewley economies with production under specifications in which (i) the utility function is allowed to be unbounded, and (ii) the underlying discrete idiosyncratic productivity process can take any form, aside from mild restrictions. Some of the intermediate results provide theoretical basis for assumptions often made in the quantitative macroeconomics literature. By providing an example, I illustrate that the equilibrium is not necessarily unique, even under typical specifications of the model, and discuss the underlying reasons for multiplicity.

RECURSIVE EQUILIBRIA IN AN AIYAGARI‐STYLE ECONOMY WITH PERMANENT INCOME SHOCKS

We prove existence of a recursive competitive equilibrium (RCE) for an Aiyagari‐style economy with permanent income shocks and derive important economic implications. We show that there exist equilibria where borrowing constraints are never binding and establish a nontrivial lower bound on the equilibrium interest rate. These results imply distinct consumption dynamics compared to existing studies. We present a new approach to solve the agent's problem that uses lattices of consumption functions to deal with permanent income shocks and an unbounded utility function. The approach provides a theoretical foundation for convergence of the time iteration algorithm widely used in applied work.

Endogenous market incompleteness without market frictions: Dynamic suboptimality of competitive equilibrium in multiperiod overlapping generations economies

Abstract In this paper, we show that within the set of stochastic three-period-lived OLG economies with productive assets (such as land), markets are necessarily sequentially incomplete, and agents in the model do not share risk optimally. We start by characterizing perfect risk-sharing and find that it requires state-dependent consumption claims which depend only on the exogenous shock realizations. We show then that the recursive competitive equilibrium of any overlapping generations economy with weakly more than three generations is not strongly stationary. This then allows us to show directly that there are short-run Pareto improvements possible in terms of risk-sharing and hence, that the recursive competitive equilibrium is not Pareto optimal. We then show that a financial reform which eliminates the equity asset and replaces it with zero net supply insurance contracts (Arrow securities) will implement to Pareto optimal stochastic steady-state known to exist in the model. Finally, we also show via numerical simulations that a system of government taxes and transfers can lead to a Pareto improvement over the competitive equilibrium in the model.

Investment options and the business cycle

This paper extends [R. Mehra, E.C. Prescott, Recursive competitive equilibrium: The case of homogeneous households, Econometrica 48 (1980) 1365–1380] to a production economy with two capital goods. It is an RBC model in which each unit of investment requires a new idea, an ‘option.’ When options are scarce, new capital is harder to put in place and the value of old capital rises. Thus the stock market and Tobin's Q are negative indexes of intangibles. During a boom, Q rises gradually, as options are used up. Because investment represents an exercise of options, it has an intertemporal substitution tradeoff that is absent from the adjustment-cost model. Equilibrium may be efficient even without markets for knowledge; the stock market may suffice.

Capital Accumulation in Private Information Economies

Abstract This paper provides a general methodology for introducing capital accumulation into economies with private information and heterogeneous agents. The agents operate a stochastic neoclassical production technology with capital and labor input. I study a moral hazard economy with unobservable input (hidden action). I characterize the efficient allocation of capital, labor, and consumption in a stationary recursive competitive equilibrium. The economy is decentralized by the component planner approach developed by Atkeson and Lucas (1995). Accumulation of capital is facilitated by a "capital planner" who serves as a financial intermediary for the component planners. In the unique, feasible and non-degenerate stationary equilibrium, private information lowers the market-clearing interest rate below agents' discount rate.

Existence and Uniqueness of Equilibrium in Distorted Dynamic Economies with Capital and Labor

In this paper, we provide a set of sufficient conditions under which recursive competitive equilibrium exists and is unique for a large class of distorted dynamic equilibrium models with capital and elastic labor supply. We develop a lattice based approach to the problem. The class of economies for which we are able to obtain our existence and uniqueness result is considerably larger than those considered in previous work. We conclude by applying the new results to some important examples of monetary economies often used in applied work. Journal of Economic Literature Classification Numbers: C62, D51, D90, E10.

Existence and Uniqueness of Equilibrium in Distorted Dynamic Economies with Capital and Labor

In this paper, we provide a set of sufficient conditions under which recursive competitive equilibrium exist and are unique for a large class of distorted dynamic equilibrium models with capital and elastic labor supply. We develop a monotone map approach to the problem. The class of economies for which we are able to obtain our existence result is apparently considerably larger than those considered in previous work. Additionally unlike previous work, we are able to also prove that this equilibrium is unique. We conclude by applying the new results to some important examples of monetary economies often used in applied work.

The business cycle with nominal contracts

In this paper we study the quantitative implications of nominal wage contracts for business cycle fluctuations. We address this issue using a model economy based on the neoclassical growth model supplemented by the assumption that cash is needed to purchase goods. We consider a variation of the standard recursive competitive equilibrium concept that is intended to capture the important features of wage contracting. We use this equilibrium construct to address three issues. First, we consider whether monetary shocks, propagated by nominal contracts, constitute a viable alternative to technology shocks as a source of aggregate fluctuations. Our results suggest that, while monetary shocks and nominal rigidities succeed in causing output volatility of the required magnitude, the resulting data have properties that are inconsistent with several key features of U.S. data. Second, we consider how the behavior of the economy varies with contract length. We find that the volatility induced by both monetary and technology shocks increases sharply with contract length. Finally we consider how much rigidity would be necessary to match the volatility of U.S. output. We find that only a very small amount of rigidity would be necessary to cause output volatility of the magnitude observed.

A State Space Model of the Economic Fundamentals

This paper presents a state space model of the economic fundamentals. In theory the economic fundamentals -- tastes, technology, stochastic shocks, and initial wealth -- determine the allocation of real resources and the values of financial assets. We show that in a recursive competitive equilibrium the minimal dimensional dynamic programming state vector is a sufficient statistic for the economic fundamentals. The dynamic programming state vector drives the allocation of real resources and the values of financial assets. We test this representation using the state space time series techniques recently introduced by Aoki. Financial and real capital do not have the same state space representation.

A state space model of the economic fundamentals

This paper presents a state space model of the economic fundamentals. In theory the economic fundamentals—tastes, technology, stochastic shocks, and initial wealth—determine the allocation of real resources and the values of financial assets. We show that in a recursive competitive equilibrium the minimal dimensional dynamic programming state vector is a sufficient statistic for the economic fundamentals. The dynamic programming state vector drives the allocation of real resources and the values of financial assets. We test this representation using the state space time series techniques recently introduced by Aoki. Financial and real capital do not have the same state space representation.

Recursive Competitive Equilibrium in Multi-Sector Economies

This paper extends the theory of recursive competitive equilibrium developed by Mehra and Prescott (1980) to a class of multisector economies in which mobility is costly. By introducing l otteries into the consumption sets of individuals, it is shown that e quilibrium allocations can be obtained as the solution to a recursive programming problem. The Lucas and Prescott (1974) search environmen t is a special case of the environment studied here. Copyright 1988 by Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.

Recursive Competitive Equilibrium: The Case of Homogeneous Households

AbstractRecursive equilibrium theory is extended and generalized. Optimality of equilibria and supportability of optima are established in a direct way. Four economic applications are reformulated as recursive competitive equilibria and analyzed.