Larry G. Epstein

Substitution, Risk Aversion, and the Temporal Behavior of Consumption and Asset Returns: An Empirical Analysis

This paper investigates the testable restrictions on the time-series behavior of consumption and asset returns implied by a representative agent model in which intertemporal preferences are represented by utility functions that generalize conventional, time-additive, expected utility. The model based on these preferences allows a clearer separation of observable behavior attributable to risk aversion and to intertemporal substitution. Further, it nests the predictions of both the consumption CAPM and the static CAPM, and it allows direct tests of the expected utility hypothesis. We find that the performance of the non-expected utility model and tests of the expected utility hypothesis are sensitive to the choice of both consumption measure and instrumental variables.

Ambiguity, Risk, and Asset Returns in Continuous Time

Models of utility in stochastic continuous-time settings typically assume that beliefs are represented by a probability measure, hence ruling out a priori any concern with ambiguity. This paper formulates a continuous-time intertemporal version of multiple-priors utility, where aversion to ambiguity is admissible. In a representative agent asset market setting, the model delivers restrictions on excess returns that admit interpretations reflecting a premium for risk and a separate premium for ambiguity.

A DEFINITION OF UNCERTAINTY AVERSION

A definition of uncertainty or ambiguity aversion is proposed. It is argued that the definition is well-suited to modelling within the Savage (as opposed to Anscombe and Aumann) domain of acts. The defined property of uncertainty aversion has intuitive empirical content, behaves well in specific models of preference (multiple-priors and Choquet expected utility) and is tractable. Tractability is established through use of a novel notion of differentiability for utility functions, called eventwise differentiability.

'First-order' risk aversion and the equity premium puzzle

Abstract This paper integrates Yaaris dual theory of choice under uncertainty into a multiperiod context and examines its implications for the equity premium puzzle. An important property of these preferences is that of ‘first-order risk aversion’ which implies, in our model, that the risk premium for a small gamble is proportional to the standard deviation rather than the variance. Since the standard deviation of the growth rate in aggregate consumption is considerably larger than its variance, the model can generate both a small risk-free rate and a moderate equity premium.

The Rate of Time Preference and Dynamic Economic Analysis

Strong restrictions on the structure of preferences are a central feature in the received theory of intertemporal allocation. In fact, most of the modern literature concerned with capital-theoretic problems represents preferences by a functional in which an additive utility function is discounted by a constant rate of time preference. This specification is attractive because it is analytically tractable in dynamic models, and it clearly delineates how tastes and opportunities interact to determine an economys (households) paths of consumption and capital formation. However, its rigid structure (constancy of time preference) severely limits the conclusions and explanatory power of the corresponding models. This paper considers a class of utility functionals (in continuous time) which have the appealing feature that the rate of time preference depends systematically on an index of aggregate future consumption. The more flexible structure embodied in these functionals leads to important generalizations and modifications of standard conclusions. We highlight this added richness by examining five basic problems in dynamic economic analysis.

A simple dynamic general equilibrium model

Abstract We analyse a single sector economy with H > 1 infinitely-lived agents that operate in a continuous-time framework. Utility functions are recursive but not additive. Both efficient and perfect foresight competitive equilibrium allocations are considered. The existence and stability of such allocations are investigated locally, i.e., in a neighbourhood of steady-state allocations. The model is shown to be useful for explaining the distribution of wealth and consumption across agents, and for analysing the way in which wealth redistribution can affect the dynamics of aggregate economic variables.

Duality Theory and Functional Forms for Dynamic Factor Demands

A large body of empirical studies of factor demand systems (Christensen, Jorgenson and Lau (1973), Berndt and Christensen (1973), Fuss and McFadden (1978)) is based on the assumption of instantaneous adjustment by firms to prevailing prices. An exhaustive set of integrability conditions derived from the theory of static profit maximization is applied to guide the specification of functional forms and to motivate meaningful hypotheses to be tested or maintained. In contrast, such a sound theoretical basis is lacking for most of the empirical literature on dynamic factor demand (investment and employment) models. For example, Jorgenson (1965) appends an ad hoc lag structure to a theory of static profit maximization to generate an investment demand function. The recent developments in the adjustmentcost model of the firm (Lucas (1967), Treadway (1969), (1971), Mortensen (1973)) have provided a consistent dynamic theoretical framework for the determination of all inputs and outputs. Yet there still remains a gap between the theoretical model and most econometric factor demand models (Schramm (1970), Nadiri and Rosen (1969), Brechling (1975)); the latter maintain a flexible accelerator adjustment with constant adjustment coefficients while the theory implies that the flexible accelerator is generally optimal only locally in a neighbourhood of the steady state and that the adjustment coefficients generally depend on exogenous variables. (See Treadway (1974).) The studies cited also fail to relate satisfactorily the hypothesized adjustment matrices to the specified technologies. They thereby overlook some of the testable properties of the theory. Only Berndt, Fuss and Waverman (1977) have estimated a model that is fully consistent with the adjustment-cost theory. The objective of this paper is to describe a practical procedure for generating a large class of functional forms for dynamic factor demand functions that can be used to test and apply the adjustment-cost theory of the firm. Three limitations of the approach adopted by Berndt, Fuss and Waverman may be noted. First, their approach is practical only when there is a single quasi-fixed stock (or (footnote 6) perhaps at most when there are two quasi-fixed stocks). Second, the flexible accelerator is the only adjustment mechanism that can follow from their approach. Finally, they assume that firms expect current prices to persist indefinitely. In contrast the procedure developed below is applicable to any number of quasi-fixed stocks and is capable of generating a richer class of dynamic adjustment mechanisms, e.g. the hump-shaped lag distributions that have been estimated in the empirical literature on investment (Evans (1969; pp. 95-105)) and which have been modelled by various ad hoc lag structures such as the Almon, Pascal and rational distributed lags. However, the assumption of static expectations, common in the adjustment-cost literature, is maintained.

Decision Making and the Temporal Resolution of Uncertainty

There exist in the literature many two-period analyses of behavior under uncertainty. (See, for example, Sandmo [1970] and [1971], Rothschild and Stiglitz [1971], Turnovsky [1973] and Epstein [1975, 1978].) These works typically assume that a decision must be made in period 1 subject to uncertainty about the environment that will prevail in period 2. At the start of period 2 the true state of the environment becomes known and perhaps some further decisions are made. The effects on the period 1 decision of the prior uncertainty in expectations are closely examined. Clearly the above framework is inadequate for modelling the more general situation where n >1 decisions are made sequentially and subject to improving information about the eventual state of the world. In this general framework the influence on decisions of the way in which uncertainty is resolved through time represents an interesting area of investigation. This paper undertakes such an investigation in the context of several specific decision problems. For simplicity (see footnote 4), we adopt a minimal extension of the two-period model that makes possible the analysis of the temporal resolution of uncertainty, namely, a three-period model. Thus the decision-making framework considered in this paper may be described as follows: an expected utility maximizing agent faces a three-period planning horizon. He makes decisions in each period. Period 3 decisions are made after all uncertainty has been resolved. In period 1 the decision is made subject to prior expectations about the state of the world that will prevail in period 3. The uncertain future environment is represented by a random variable Z. Before the start of period 2 new information about the ultimate value of Z becomes available. The information is forthcoming through the observation of another random variable Y which in general is correlated with Z. The agent is a Bayesian decision maker and revises his prior probability distribution about Z after observing Y. The amount of additional information about Z provided by Y is a parameter in the model. The objective of the paper is to compare the decisions in period I in two choice problems that differ only with respect to the amount of information provided by Y about Z. Note that in both problems the agent faces the identical prior uncertainty about Z. The difference in the two problems is only in the amount of

A Two-Person Dynamic Equilibrium under Ambiguity

This paper describes a pure-exchange, continuous-time economy with two heterogeneous agents and complete markets. A novel feature of the economy is that agents perceive some security returns as ambiguous in the sense often attributed to frank Knight. The equilibrium is described completely in closed-form. In particular, closed-form solutions are obtained for the equilibrium processes describing individual consumption, the interest rate, the market price of uncertainty, security prices and trading strategies. After identifying agents as countries, the model is applied to address the consumption home-bias puzzles.

SUBJECTIVE PROBABILITIES ON SUBJECTIVELY UNAMBIGUOUS EVENTS

This paper suggests a behavioral definition of (subjective) ambiguity in an abstract setting where objects of choice are Savage-style acts. Then axioms are described that deliver probabilistic sophistication of preference on the set of unambiguous acts. In particular, both the domain and the values of the decision-makers probability measure are derived from preference. It is argued that the noted result also provides a decision-theoretic foundation for the Knightian distinction between risk and ambiguity.