Asset pricing in a production economy with Chew–Dekel preferences

In this paper we provide a thorough characterization of the asset returns implied by a simple general equilibrium production economy with Chew–Dekel risk preferences and convex capital adjustment costs. When households display levels of disappointment aversion consistent with the experimental evidence, a version of the model parameterized to match the volatility of output and consumption growth generates unconditional expected asset returns and price of risk in line with the historical data. For the model with Epstein–Zin preferences to generate similar statistics, the relative risk aversion coefficient needs to be about 55, two orders of magnitude higher than the available estimates. We argue that this is not surprising, given the limited risk imposed on agents by a reasonably calibrated stochastic growth model.     

Epstein–Zin Utility,Asset Prices,and the Business Cycle Revisited

This paper discusses the advantages of Epstein and Zin (1989) (EZ) preferences when building dynamic stochastic general equilibrium (DSGE) models that are consistent with well‐known stylized facts of both the business cycle and asset markets. To this end, we combine EZ preferences with several building blocks from the DSGE literature that has tried to solve the equity premium puzzle and to replicate characteristic statistics of the labor market. Our goal is to guide researchers in this area to useful modeling devices and to discuss EZ preferences vis‐a‐vis the standard time‐additive expected utility function. EZ preferences separate the attitude toward risk from the attitude toward intertemporal substitution. We demonstrate that this additional degree of freedom allows us to closely match the empirical facts already in a frictionless production economy with endogenous labor supply. Our study follows Heer and Maußner (2013). We examine models that consider adjustment costs of capital accumulation, consumption habits, and frictions in the allocation of labor. Our empirical targets are estimated from German data.     

Risk and intertemporal substitution: Livestock portfolios and off-take among Kenyan pastoralists

Most decisions involve variability in two dimensions: uncertainty across states of nature and fluctuations over time. The stakes involved in tradeoffs between these variability dimensions are especially high for the poor who have difficulty managing and recovering from shocks. We assume Epstein and Zin recursive preferences and estimate risk aversion and intertemporal substitution as distinct preferences using data from Kenyan herders. Results suggest that the assumption implicit in additive expected utility models that relative risk aversion (RRA) is the inverse of the elasticity of intertemporal substitution (EIS) is flawed. Specifically, our RRA and EIS estimates are consistent with a preference for the early resolution of uncertainty, which we believe is driven importantly by the instrumental value of early uncertainty resolution. This same preference pattern is consistent with asset smoothing in response to a dynamic asset threshold.     

Market equilibrium with heterogeneous recursive-utility-maximizing agents

Summary This paper considers a heterogeneous agent Lucas style exchange economy. For a class of recursive utility functions containing the standard additive expected utility functions, I demonstrate that there exist market equilibria characterized by stationary (ergodic) Markov processes for consumption, portfolio holdings, asset prices and the unobserved utilities. No assumptions about market completeness are made, and there are no restrictions on the underlying information filtration.Other contributions of this paper include: (i) an existence and uniqueness theorem of intertemporal utility for the general class of recursive generators; (ii) the optimum principle as well as its corresponding Euler equation derived for the agent's consumption and portfolio choice problem under recursive utility, and (iii) a single-agent equilibrium asset pricing formula which generalizes that of Epstein and Zin (1989).This paper is a part of my PhD dissertation at the University of Toronto. I would like to thank Larry Epstein for his enthusiastic supervision, helpful discussion and valuable comments. Thanks also to Tan Wang and especially Darrell Duffie for valuable comments.     

Epstein–Zin Utility in DICE: Is Risk Aversion Irrelevant to Climate Policy?

Climate change involves uncertain probabilities of catastrophic risks, and very longterm consequences of current actions. Climate economics, therefore, is centrally concerned with the treatment of risk and time. Yet conventional assumptions about utility and optimal economic growth create a perverse connection between risk aversion and time preference, such that more aversion to current risks implies less concern for future outcomes, and vice versa. The same conflation of risk aversion and time preference leads to the equity premium puzzle in finance. A promising response to the equity premium puzzle, the recursive utility of Epstein and Zin, allows separation of risk aversion and time preference—at the cost of considerable analytic complexity. We introduce an accessible implementation of Epstein–Zin utility into the DICE model of climate economics, creating a hybrid “EZ-DICE” model. Using Epstein–Zin parameters from the finance literature and climate uncertainty parameters from the science literature, we find that the optimal climate policy in EZ-DICE calls for rapid abatement of carbon emissions; it is similar to standard DICE results with the discount rate set to equal the risk-free rate of return. EZ-DICE solutions are sensitive to the intertemporal elasticity of substitution, but remarkably insensitive to risk aversion. Insensitivity to risk aversion may reflect the difficulty of modeling catastrophic risks within DICE. Implicit in DICE are strong assumptions about the cost of climate stabilization and the certainty and speed of success; under these assumptions, risk aversion would in fact be unimportant. A more realistic analysis will require a subtler treatment of catastrophic climate risk.     

Optimal climate change mitigation under long-term growth uncertainty: Stochastic integrated assessment and analytic findings

Economic growth over the coming centuries is one of the major determinants of today׳s optimal greenhouse gas mitigation policy. At the same time, long-run economic growth is highly uncertain. This paper is the first to evaluate optimal mitigation policy under long-term growth uncertainty in a stochastic integrated assessment model of climate change. The sign and magnitude of the impact depend on preference characteristics and on how damages scale with production. We explain the different mechanisms driving optimal mitigation under certain growth, under uncertain technological progress in the discounted expected utility model, and under uncertain technological progress in a more comprehensive asset pricing model based on Epstein–Zin–Weil preferences. In the latter framework, the dominating uncertainty impact has the opposite sign of a deterministic growth impact; the sign switch results from an endogenous pessimism weighting. All of our numeric scenarios use a DICE based assessment model and find a higher optimal carbon tax than the deterministic DICE base case calibration.     

Dynamic asset allocation with ambiguous return predictability

We study an investor's optimal consumption and portfolio choice problem when he is confronted with two possibly misspecified submodels of stock returns: one with IID returns and the other with predictability. We adopt a generalized recursive ambiguity model to accommodate the investor's aversion to model uncertainty. The investor deals with specification doubts by slanting his beliefs about submodels of returns pessimistically, causing his investment strategy to be more conservative than the Bayesian strategy. Unlike in the Bayesian framework, the hedging demand against model uncertainty may cause the investor's stock allocation to decrease sharply given a small doubt of return predictability, even though the expected return according to the VAR model is large. Over much of the parameter space, the robust strategy is very close to the Bayesian strategy with Epstein–Zin preferences and risk aversion chosen to match the same average portfolio holdings. This is true in particular when the IID model is unlikely and the dividend yield is low, as in recent years. However, differences in strategies can be substantial if the IID model is unlikely and the dividend yield is high.     

The fundamentals of Intertemporal Optimization in the Continuous Time Modelling of Consumer Behaviour

This note explains the fundamentals of intertemporal optimization for consumer behaviour modelled in continuous time when preferences are recursive as in Uzawa and Epstein. After the differential in utility and the differential in the value of assets have been defined and computed, the optimization principle is summarized and fully set out in one equation equating the former with the utility value of the latter. This equation is then shown to be equivalent to Pontryagin's maximum principle, and a close analogy is drawn between static and dynamic consumer theory.     

Recursive methods for incentive problems

Many dynamic incentive problems have a primal recursive formulation in which utility promises serve as state variables. We associate dual recursive formulations with these problems. We make transparent the connections between recursive primal and dual approaches, relate value iteration under each and give conditions for such value iteration to be convergent to the true value function.     

Welfare cost of inflation in a stochastic balanced growth model

There is a large and growing literature on the welfare cost of inflation. However, work in this area tend to find moderate estimates of welfare gains. In this paper we reexamine welfare costs of inflation within a stochastic general equilibrium balanced growth model paying a particular attention to recursive utility, portfolio balance effects, and monetary volatility and monetary policy uncertainty. Our numerical analysis shows that a monetary policy that brings down inflation to the optimum level can have substantial welfare effects. Portfolio adjustment effects seem to be the dominant factor behind the welfare gains.     

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

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.     

On the sources of macroeconomic stability in the euro area

In the mid-1990s the euro area experienced a change in macroeconomic volatility. Around the same time, at business cycle frequencies the correlation between inflation and money growth changed markedly, turning from positive to negative. Distinguishing the periods pre- and post-1994, we estimate a dynamic stochastic general equilibrium model with money for the euro area. The model accounts for the salient facts. We then perform several counterfactual exercises to assess the drivers of these phenomena. The moderation of real variables was essentially due to relatively smaller shocks to investment, wage markups and preferences. The apparent lack of evidence for the quantity theory of money in the short run and the changes in the volatility of nominal variables resulted primarily from a more anti-inflationary and gradual monetary policy.     

Comparative risk aversion: A formal approach with applications to saving behavior

We consider a formal approach to comparative risk aversion and apply it to intertemporal choice models. This allows us to ask whether standard classes of utility functions, such as those inspired by Kihlstrom and Mirman (1974) [16], Selden (1978) [27], Epstein and Zin (1989) [10] and Quiggin (1982) [25] are well ordered in terms of risk aversion. Moreover, opting for this model-free approach allows us to establish new general results on the impact of risk aversion on savings behaviors. In particular, we show that risk aversion enhances precautionary savings, clarifying the link that exists between the notions of prudence and risk aversion.     

Capital Income Taxes and Growth in a Stochastic Economy: A Numerical Analysis of the Role of Risk Aversion and Intertemporal Substitution

This paper undertakes a numerical analysis of the effects of changes in the tax rates on domestic and foreign capital income in a stochastically growing open economy under recursive preferences, in which the rate of time preference, ?, and the coefficient of risk aversion, R, can be set independently. The responses of the equilibrium growth rate, its volatility, and welfare to changes in the tax changes considered are highly sensitive to the independent variations in both ? and R. Consequently, the errors committed by using the conventional constant elasticity utility function, even for small violations of the compatibility condition (R= 1/?) can be significant, suggesting that this functional form should be employed with caution.     

Dynamic mechanism design with hidden income and hidden actions

We develop general recursive methods to solve for optimal contracts in dynamic principal-agent environments with hidden states and hidden actions. Starting from a general mechanism with arbitrary communication, randomization, full history dependence, and without restrictions on preferences or technology, we show that the optimal contract can be implemented as a recursive direct mechanism. A curse of dimensionality which arises from the interaction of hidden income and hidden actions can be overcome by introducing utility bounds for behavior off the equilibrium path. Environments with multiple actions are implemented using multiple layers of such off-path utility bounds.     

Terms‐of‐Trade Shocks and Exchange Rate Regimes in a Small Open Economy*

We examine the impact of terms‐of‐trade shocks on key macroeconomic variables by numerically solving a dynamic stochastic general equilibrium model of a small open economy. The model considers nominal price rigidity under different exchange rate regimes. The numerical solutions obtained are consistent with the empirical regularities documented by Broda (2004), in which output responses to shocks are smoother in floats than in pegs; in moving from pegs to floats, the rise in nominal exchange rate volatility is coupled by the rise in real exchange rate volatility; and in both exchange rate regimes, net foreign assets is the most volatile variable.     

The recursive approach to time inconsistency

We introduce a new class of finite horizon stochastic decision problems in which preferences change over time, and provide a proof of the existence of a recursively optimal strategy. Recursive optimization techniques dominate many areas of economic dynamics. However, in decision problems in which tastes change over time, the solution technique most commonly applied is not recursive, but rather strategic (subgame perfection). In this paper we argue in favor of the recursive approach, and we take the necessary theoretical steps to make the recursive methodology applicable.     

The FMLS-based CUSUM statistic for testing the null of smooth time-varying cointegration in the presence of a structural break

In this paper we extend the FMLS-based CUSUM cointegration test (Xiao and Phillips, 2002) for testing the smooth time-varying cointegration null hypothesis. For this purpose we use Chebyshev time polynomials to specify time-varying coefficients under the null. We derive the limiting distribution of the statistic, which is pivotal with the order of the Chebyshev time polynomials, and we provide the critical values to conduct the proposed test.     

FORECASTING GLOBAL EQUITY INDICES USING LARGE BAYESIAN VARS

This paper proposes a large Bayesian Vector Autoregressive (BVAR) model with common stochastic volatility to forecast global equity indices. Using a monthly dataset on global stock indices, the BVAR model controls for co‐movement commonly observed in global stock markets. Moreover, the time‐varying specification of the covariance structure accounts for sudden shifts in the level of volatility. In an out‐of‐sample forecasting application we show that the BVAR model with stochastic volatility significantly outperforms the random walk both in terms of point as well as density predictions. The BVAR model without stochastic volatility, on the other hand, shows some merits relative to the random walk for forecast horizons greater than six months ahead. In a portfolio allocation exercise we moreover provide evidence that it is possible to use the forecasts obtained from our model with common stochastic volatility to set up simple investment strategies. Our results indicate that these simple investment schemes outperform a naive buy‐and‐hold strategy.     

Computing minimal state space recursive equilibrium in OLG models with stochastic production

Using order-theoretic methods, we derive sufficient conditions for the existence, characterization, and computation of minimal state space recursive equilibrium (RE), as well as Stationary Markov equilibrium (SME) for various classes of stochastic overlapping generations models. In contrast to previous work, our methods focus on constructive methods. Our existence results are obtained for models that include public policy (e.g., social security policies, transfers, taxes, etc), production nonconvexities, elastic labor supply, non-monotone income processes, and long-lived agents. We distinguish conditions under which there exist various subclasses of minimal state space RE, including bounded, monotone, non-monotone, semicontinuous, Lipschitz continuous RE. Finally, we provide monotone equilibrium comparative statics results on the space of economies for some RE.