Lars Peter Hansen

Forward Exchange Rates as Optimal Predictors of Future Spot Rates: An Econometric Analysis

This paper examines the hypothesis that the expected rate of return to speculation in the forward foreign exchange market is zero; that is, the logarithm of the forward exchange rate is the markets conditional expectation of the logarithm of the future spot rate. A new computationally tractable econometric methodology for examining restrictions on a k-step-ahead forecasting equation is employed. Using data sampled more finely than the forecast interval, we are able to reject the simple market efficiency hypothesis for exchange rates from the 1970s and the 1920s. For the modern experience, the tests are also inconsistent with several alternative hypotheses which typically characterize the relationship between spot and forward exchange rates.

Stochastic Consumption, Risk Aversion, and the Temporal Behavior of Asset Returns

This paper studies the time-series behavior of asset returns and aggregate consumption. Using a representative consumer model and imposing restrictions on preferences and the joint distribution of consumption and returns, we deduce a restricted log-linear time-series representation. Preference parameters for the representative agent are estimated and the implied restrictions are tested using postwar data.

Implications of Security Market Data for Models of Dynamic Economies

We show how to use security market data to restrict the admissible region for means and standard deviations of intertemporal marginal rates of substitution (IMRSs) of consumers. Our approach (i) is nonparametric and applies to a rich class of models of dynamic economies, (ii) characterizes the duality between the mean--standard deviation frontier for IMRSs and the familiear mean- standard deviation frontier for asset returns, and (iii) exploits the restriction that IMRSs are positive random variables. The region provides a convenient summary of the sense in which asset market data are anaomalous from the vantage point of intertemporal asset pricing theory.

Finite-Sample Properties of Some Alternative GMM Estimators

We investigate the small-sample properties of three alternative generalized method of moments (GMM) estimators of asset-pricing models. The estimators that we consider include ones in which the weighting matrix is iterated to convergence and ones in which the weighting matrix is changed with each choice of the parameters. Particular attention is devoted to assessing the performance of the asymptotic theory for making inferences based directly on the deterioration of GMM criterion functions.

Formulating and estimating dynamic linear rational expectations models

This paper describes methods for conveniently formulating and estimating dynamic linear econometric models under the hypothesis of rational expectations. An econometrically convenient formula for the cross-equation rational expectations restrictions is derived. Models of error terms and the role of the concept of Granger causality in formulating rational expectations models are both discussed. Tests of hypothesis of strict econometric exogeneity along the lines of Sim’s are compared with a test that is related to Wu’s.

THE ROLE OF CONDITIONING INFORMATION IN DEDUCING TESTABLE RESTRICTIONS IMPLIED BY DYNAMIC ASSET PRICING MODELS1

The purpose of this paper is to investigate testable implications of equilibrium asset pricing models. The authors derive a general representation for asset prices that displays the role of conditioning information. This representation is then used to examine restrictions implied by asset pricing models on the unconditional moments of asset payoffs and prices. In particular, they analyze the effect of information omission on the mean-variance frontier of one- period returns on portfolios of securities. Also, the authors deduce an information extension of equilibrium pricing functions that is useful in deriving restrictions on the unconditional moments of payoffs and prices. Copyright 1987 by The Econometric Society.

A Time Series Analysis of Representative Agent Models of Consumption and Leisure Choice Under Uncertainty

This paper investigates empirically a model of aggregate consumption and leisure decisions in which utility from goods and leisure is nontime-separable. The nonseparability of preferences accommodates intertemporal substitution or complementarity of leisure and thereby affects the comovements in aggregate compensation and hours worked. These cross-relations are examined empirically using postwar monthly U. S. data on quantities, real wages, and the real return on the one-month Treasury bill. The estimated values of the parameters governing preferences differ significantly from the values assumed in several studies of real business models. Several possible explanations of these discrepancies are discussed.

Consumption Strikes Back? Measuring Long‐Run Risk

We characterize and measure a long‐term risk‐return trade‐off for the valuation of cash flows exposed to fluctuations in macroeconomic growth. This trade‐off features risk prices of cash flows that are realized far into the future but continue to be reflected in asset values. We apply this analysis to claims on aggregate cash flows and to cash flows from value and growth portfolios by imputing values to the long‐run dynamic responses of cash flows to macroeconomic shocks. We explore the sensitivity of our results to features of the economic valuation model and of the model cash flow dynamics.

Back to the Future: Generating Moment Implications for Continuous-Time Markov Processes

Continuous-time Markov processes can be characterized conveniently by their infinitesimal generators. For such processes there exist forward and reverse-time generators. We show how to use these generators to construct moment conditions implied by stationary Markov processes. Generalized method of moments estimators and tests can be constructed using these moment conditions. The resulting econometric methods are designed to be applied to discrete-time data obtained by sampling continuous-time Markov processes.

Asset Pricing Explorations for Macroeconomics

In this paper we argue that financial data are a useful proving ground for macroeconomic models, and we explore the channels that link asset market data to such models. We use Hansen and Jagannathans bounds on the mean and standard deviation of discount factors to survey several asset pricing puzzles. We then extend the bounds to reflect the correlation of discount factors with asset returns and to characterize conditional moments of discount factors. These characterizations help us to understand the behavior of a variety of models studied in the literature. We also incorporate borrowing constraints into the calculations. The borrowing constraints loosen the required properties of aggregate measurements of intertemporal marginal rates of substitution, but also sharpen the implications of asset market data for the marginal rates of substitution of unconstrained individuals.