Jaroslav Borovička

Survival and long-run dynamics with heterogeneous beliefs under recursive preferences

I study the long-run behavior of an economy with two types of agents who differ in their beliefs and are endowed with homothetic recursive preferences of the Duffie-Epstein-Zin type. Contrary to models with separable preferences in which the wealth of agents with incorrect beliefs vanishes in the long run, recursive preference specifications lead to long-run outcomes where both agents survive, or more incorrect agents dominate. I derive analytical conditions for the existence of nondegenerate long-run equilibria in which agents with differently accurate beliefs coexist in the long run, and show that these equilibria exist for broad ranges of plausible parameterizations when risk aversion is larger than the inverse of the intertemporal elasticity of substitution. The results highlight a crucial interaction between risk sharing, speculative behavior and consumption-saving choice of agents with heterogeneous beliefs, and the role of equilibrium prices in shaping long-run outcomes.

Shock Elasticities and Impulse Responses

We construct shock elasticities that are pricing counterparts to impulse response functions. Recall that impulse response functions measure the importance of next-period shocks for future values of a time series. Shock elasticities measure the contributions to the price and to the expected future cash flow from changes in the exposure to a shock in the next period. They are elasticities because their measurements compute proportionate changes. We show a particularly close link between these objects in environments with Brownian information structures.

Term Structure of Uncertainty in the Macroeconomy

Dynamic economic models make predictions about impulse responses that characterize how macroeconomic processes respond to alternative shocks over different horizons. From the perspective of asset pricing, impulse responses quantify the exposure of macroeconomic processes and other cash flows to macroeconomic shocks. Financial markets provide compensations to investors who are exposed to these shocks. Adopting an asset pricing vantage point, we describe and apply methods for computing exposures to macroeconomic shocks and the implied compensations represented as elasticities over alternative payoff horizons. The outcome is a term structure of macroeconomic uncertainty.

Identifying Ambiguity Shocks in Business Cycle Models Using Survey Data

This paper develops a theory of subjective beliefs that departs from rational expectations, and shows that biases in household beliefs have quantitatively large effects on macroeconomic aggregates. The departures are formalized using model-consistent notions of pessimism and optimism and are disciplined by data on household forecasts. The role of subjective beliefs is quantified in a business cycle model with goods and labor market frictions. Consistent with the survey evidence, an increase in pessimism generates upward biases in unemployment and inflation forecasts and lowers economic activity. The underlying belief distortions reduce aggregate demand and propagate through frictional goods and labor markets. As a by-product of the analysis, solution techniques that preserve the effects of time-varying belief distortions in the class of linear solutions are developed.

Necessary and Sufficient Conditions for Existence and Uniqueness of Recursive Utilities

We study existence, uniqueness and computability of solutions for a class of discrete time recursive utilities models. By combining two streams of the recent literature on recursive preferences---one that analyzes principal eigenvalues of valuation operators and another that exploits the theory of monotone concave operators---we obtain conditions that are both necessary and sufficient for existence and uniqueness of solutions. We also show that the natural iterative algorithm is convergent if and only if a solution exists. Consumption processes are allowed to be nonstationary.