Recursive Equilibrium Research Articles

Recursive equilibrium in endogenous growth models with incomplete markets

This paper analyzes the existence of recursive equilibria in a class of convex growth models with incomplete markets. Households have identical CRRA-preferences, production displays constant returns to scale with respect to physical and human capital, and all markets are competitive. There are aggregate productivity shocks that affect aggregate returns to physical and human capital investment (stock returns and wages), and there are idiosyncratic shocks to human capital (idiosyncratic depreciation shocks) that only affect individual human capital returns. Aggregate and idiosyncratic shocks follow a joint Markov process. Conditional on the aggregate state, idiosyncratic shocks are independently distributed over time and identically distributed across households. Finally, households have the opportunity to trade assets in zero net supply with payoffs that depend on the aggregate shock, but markets are incomplete in the sense that there are no assets with payoffs depending on idiosyncratic shocks. It is shown that there exists a recursive equilibrium for which equilibrium prices (returns) only depend on the exogenous aggregate shock variable (the wealth distribution is not a relevant state variable). Moreover, the allocation associated with this recursive equilibrium is identical to the equilibrium allocation of an economy in which households live in autarky and face both aggregate and idiosyncratic risk.

Long-run Implications of the Brazilian Capital Stock and Income Estimates

The present study aims to analyze the empirical as well as theoretical implications related to the possible inconsistencies between the Brazilian capital stock estimate and its associated investment decision. The common practice of using the country’s accumulated (depreciated) fixed capital formation data as a proxy for the capital stock series generates a set of incompatible facts with dynamic models built on balanced growth and on aggregate production functions. Moreover, a related issue on the Brazilian capital income is considered in our analysis. According to the country’s National Accounts, the participation of capital income reaches about half of the aggregate income which is an unusual high share compared to international standards. It is shown that this problem can also be solved using alternative methods that lead to a more suitable capital stock series to be used in recursive equilibrium models. Finally, the long-run impacts of using the proposed capital stock series is studied using a modified basic growth model calibrated to reproduce some Brazilian empirical facts

Competitive equilibria of economies with a continuum of consumers and aggregate shocks

This paper studies competitive equilibria of a production economy with aggregate productivity shocks. There is a continuum of consumers who face borrowing constraints and individual labor endowment shocks. The dynamic economy is described in terms of sequences of aggregate distributions. The existence of competitive equilibrium is proven and a recursive characterization is established. In particular, it is shown that for any competitive equilibrium, there is a payoff equivalent competitive equilibrium that is generated by a suitably defined recursive equilibrium.

Non-existence of recursive equilibria on compact state spaces when markets are incomplete

This paper analyzes one-good exchange economies with two infinitely lived agents and incomplete markets. It is shown that there are no recursive (Markov) equilibria for which borrowing (debt) constraints never bind if the state space of exogenous and endogenous variables is a compact subset of R n . Moreover, for large enough (but finite) borrowing limits, no recursive equilibrium with compact state space exists. These non-existence results hold for any economy satisfying the following standard assumptions: preferences are additively separable across time and states; the one-period utility function is time- and state-independent and unbounded from below; endowments are bounded and follow a Markov chain with stationary transition matrix; there is some idiosyncratic risk and no aggregate risk.

Competitive Equilibria of Economies with a Continuum of Consumers and Aggregate Shocks

This paper studies competitive equilibria of a production economy with aggregate productivity shocks. There is a continuum of consumers who face borrowing constraints and individual labor endowment shocks. The dynamic economy is described in terms of sequences of aggregate distributions. The existence of sequential competitive equilibria is proven and a recursive characterization is established. In particular, it is shown that for any sequential competitive equilibrium, there exists a payoff equivalent sequential competitive equilibrium that is generated by a suitably defined recursive equilibrium with state variables including continuation value.

The Efficiency-Equality Tradeoff in Welfare State Economies

This paper studies the effects of different levels of social insurance on efficiency and distribution of resources in a general equilibrium model of a closed economy with heterogeneous agents and moral hazard. I compare optimal allocations of capital, labor supply, and consumption in stationary recursive equilibria for economies with different guaranteed minimum consumption levels (social insurance). I show that the efficiency-equality tradeoff associated with welfare state economies does not hold. Efficiency decreases and equality rises as the minimal guaranteed consumption increases from zero to around one third of the average consumption. However, if social insurance expands even further, the efficiency loss becomes very high and equality worsens. Average welfare is greater in economies with high social insurance while the median agent is better off in economies with low social insurance. Finally, I study the transitions between welfare regimes' steady states to evaluate the effects of social insurance reforms.

The Efficiency-Equality Tradeoff in Welfare State Economies

This paper studies the effects of different levels of social insurance on efficiency and distribution of resources in a general equilibrium model of a closed economy with heterogeneous agents and moral hazard. I compare optimal allocations of capital, labor supply, and consumption in stationary recursive equilibria for economies with different guaranteed minimum consumption levels (social insurance). I show that the efficiency-equality tradeoff associated with welfare state economies does not hold. Efficiency decreases and equality rises as the minimal guaranteed consumption increases from zero to around one third of the average consumption. However, if social insurance expands even further, the efficiency loss becomes very high and equality worsens. Average welfare is greater in economies with high social insurance while the median agent is better off in economies with low social insurance. Finally, I study the transitions between welfare regimes' steady states to evaluate the effects of social insurance reforms.

Capital Accumulation in an Economy with Heterogeneous Agents and Moral Hazard

This paper studies a closed economy with a continuum of agents and moral hazard. Economic agents in the economy operate a stochastic production technology with capital and labor inputs in which the latter is private information. I characterize efficient allocations of capital, labor, and consumption in a stationary recursive equilibrium for a decentralized economy with component planners. Allocation and accumulation of capital are facilitated by a `capital planner' who serves as a financial intermediary for the component planners. In equilibrium, private information lowers the equilibrium interest rate below agents' discount rate and I show that contrary to the private-information endowment economies, a moral-hazard productive economy can exhibit both endogenous lower and upper bounds on the stationary distribution of utility entitlements.

Risk aversion and stock price volatility when dividends are difference stationary

The relationship between stock price volatility and agents' risk aversion is studied within a recursive equilibrium asset pricing model in which the endowment growth rate is assumed to follow a two-state stationary process. In contrast to a model that is stationary in the level of the endowment, the volatility of stock prices is not generally an increasing function of agents' risk aversion. The specific relationship between risk aversion and stock price volatility is shown to depend on the autorcorrelation properties of the growth rate.