Computing Semiparametric Efficiency Bounds for Linear Time Series Models

Asset Pricing Explorations for Macroeconomics

Asset market data are often ignored in evaluating macroeconomic models, and aggregate quantity data are often avoided in empirical investigations of asset market returns. While there may be short-term benefits to proceeding along separate lines, we argue that security market data are among the most sensitive and, hence, attractive proving grounds for models of the aggregate economy.

Seasonality and Approximation Errors in Rational-Expectations Models

A frequency domain representation of the approximation criterion that is implicit in Gaussian maximum likelihood estimation is applied to study the effects of using seasonally adjusted versus seasonally unadjusted data to estimate rational expectations models. Three classes of economic mechanisms for generating seasonality are described. Approximating parameter estimates are computed numerically for several examples.

Discounted Linear Exponential Quadratic Gaussian Control

In this note, we describe a recursive formulation of discounted costs for a linear quadratic exponential Gaussian linear regulator problem which implies time-invariant linear decision rules in the infinite horizon case. Time invariance in the discounted case is attained by surrendering state-separability of the risk-adjusted costs.

Econometric Evaluation of Asset Pricing Models

In this article we provide econometric tools for the evaluation of intertemporal asset pricing models using specification-error and volatility bounds. We formulate analog estimators of these bounds, give conditions for consistency, and derive the limiting distribution of these estimators. The analysis incorporates market frictions such as short-sale constraints and proportional transactions costs. Among several applications we show how to use the methods to assess specific asset pricing models and to provide non-parametric characterizations of asset pricing anomalies.

Efficient Estimation of Linear Asset-Pricing Models with Moving Average Errors

This article studies alternative methods for estimating parameters from multiperiod conditional moment restrictions. Our discussion is couched in the context of a multivariate linear time series model, and we use the log-linear intertemporal asset-pricing model as a prototype when comparing alternative econometric methods. We propose a generalized method of moments estimator that is scale invariant and is asymptotically equivalent to one used previously in empirical work on asset pricing. We then show how to improve the efficiency of this estimator. Finally, we apply these methods in an empirical investigation of the log-linear intertemporal asset-pricing model.

The Empirical Foundations of Calibration

Interest in simulating recently developed dynamic stochastic general equilibrium models of the economy stimulated a demand for parameters. This has given rise to calibration as advocated by Finn E. Kydland and Edward C. Prescott (1982). This paper explores the implicit assumptions underlying their calibration method. The authors question that there is a ready supply of micro estimates available to calibrate macroeconomic models. Measures of parameter uncertainty and specification sensitivity should be routinely reported. They propose a more symbiotic role for calibration as providing signals to microeconomists about important gaps in knowledge, which when filled will solidify the empirical underpinning, improving the credibility of the quantitative output.

Mechanics of Forming and Estimating Dynamic Linear Economies

This paper catalogues formulas that are useful for estimating dynamic linear economic models. We describe algorithms for computing equilibria of an economic model and for recursively computing a Gaussian likelihood function and its gradient with respect to parameters. We display an application to Rosen, Murphy, and Scheinkman’s (1994) model of cattle cycles.

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.

Assessing Specification Errors in Stochastic Discount Factor Models

In this article we develop alternative ways to compare asset pricing models when it is understood that their implied stochastic discount factors do not price all portfolios correctly. Unlike comparisons based on χ 2 statistics associated with null hypotheses that models are correct, our measures of model performance do not reward variability of discount factor proxies. One of our measures is designed to exploit fully the implications of arbitrage-free pricing of derivative claims. We demonstrate empirically the usefulness of our methods in assessing some alternative stochastic factor models that have been proposed in asset pricing literature.