George Tauchen

Finite state markov-chain approximations to univariate and vector autoregressions

The paper develops a procedure for finding a discrete-valued Markov chain whose sample paths approximate well those of a vector autoregression. The procedure has applications in those areas of economics, finance, and econometrics where approximate solutions to integral equations are required.

Quadrature-Based Methods for Obtaining Approximate Solutions to Nonlinear Asset Pricing Models

This paper develops a discrete state space solution method for a class of nonlinear rational expectations models. The method works by using numerical quadrature rules to approximate the integral operators that arise in stochastic intertemporal models. It is particularly useful for approximating asset pricing models and has potential applications in other problems as well. An empirical application uses the method to study the relationship between the risk premium and the conditional variability of the equity returns under ARCH endowment processes. Copyright 1991 by The Econometric Society.

The Relative Contribution of Jumps to Total Price Variance

We examine tests for jumps based on recent asymptotic results; we interpret the tests as Hausman-type tests. Monte Carlo evidence suggests that the daily ratio z-statistic has appropriate size, good power, and good jump detection capabilities revealed by the confusion matrix comprised of jump classification probabilities. We identify a pitfall in applying the asymptotic approximation over an entire sample. Theoretical and Monte Carlo analysis indicates that microstructure noise biases the tests against detecting jumps, and that a simple lagging strategy corrects the bias. Empirical work documents evidence for jumps that account for 7% of stock market price variance. Copyright 2005, Oxford University Press.

Seminonparametric Estimation of Conditionally Constrained Heterogeneous Processes: Asset Pricing Applications

The extent to which specification error can explain rejection of the intertemporal capital asset pricing model is investigated using seminonparametric representations of the law of motion and utility. The authors find (1) consumption growth and asset returns display conditional heterogeneity, but this does not account for rejection of models assuming additively separable, constant relative risk aversion utility; (2) the model is accepted upon relaxation of the utility function in the direction of nonseparable utility; and (3) relaxation reduces overprediction of the conditional variance of consumption growth, overprediction of the conditional covariance of asset returns with consumption growth, and the equity premium. Copyright 1989 by The Econometric Society.

Diagnostic testing and evaluation of maximum likelihood models

Abstract The paper develops a unified theory of likelihood specification testing based on M-estimators of auxiliary parameters. The theory is sufficiently general to encompass a wide class of specification tests including moment-based tests, Pearson-type goodness of fit tests, the information matrix test, and the Cox test. The paper also presents a framework based on Frechet differentiation for determining the effects of misspecification on the almost sure limits of parameter estimates and specification test statistics.

Statistical Properties of Generalized Method-of-Moments Estimators of Structural Parameters Obtained From Financial Market Data

The article examines the properties of generalized method of moments GMM estimators of utility function parameters. The research strategy is to apply the GMM procedure to generated data on asset returns from stochastic exchange economies; discrete methods and Markov chain models are used to approximate the solutions to the integral equations for the asset prices. The findings are as follows: (a) There is variance/bias trade-off regarding the number of lags used to form instruments; with short lags, the estimates of utility function parameters are nearly asymptotically optimal, but with longer lags the estimates concentrate around biased values and confidence intervals become misleading, (b) The test of the overidentifying restrictions performs well in small samples; if anything, the test is biased toward acceptance of the null hypothesis.

Nonparametric and Semiparametric Methods in Econometrics and Statistics

This collection of papers delivered at the Fifth International Symposium in Economic Theory and Econometrics in 1988 is devoted to the estimation and testing of models that impose relatively weak restrictions on the stochastic behaviour of data. Particularly in highly non-linear models, empirical results are very sensitive to the choice of the parametric form of the distribution of the observable variables, and often nonparametric and semiparametric models are a preferable alternative. Methods and applications that do not require string parametric assumptions for their validity, that are based on kernels and on series expansions, and methods for independent and dependent observations are investigated and developed in these essays by renowned econometricians.

Reprojecting Partially Observed Systems with Application to Interest Rate Diffusions

Abstract We introduce reprojection as a general purpose technique for characterizing the dynamic response of a partially observed nonlinear system to its observable history. Reprojection is the third step of a procedure wherein first data are summarized by projection onto a Hermite series representation of the unconstrained transition density for observables; second, system parameters are estimated by minimum chi-squared, where the chi-squared criterion is a quadratic form in the expected score of the projection; and third, the constraints on dynamics implied by the nonlinear system are imposed by projecting a long simulation of the estimated system onto a Hermite series representation of the constrained transition density for observables. The constrained transition density can be used to study the response of the system to its observable history. We utilize the technique to assess the dynamics of several diffusion models for the short-term interest rate that have been proposed and to compare them to a ne...

The Effect of Minimum Drinking Age Legislation on Youthful Auto Fatalities, 1970-1977

Composition particularly adapted to stabilize polymeric organic materials such as alpha -olefin polymers and copolymers against the deleterious effects of oxygen, heat and light comprising a mixture of 2,6-ditertiarybutyl-4-nonylphenol and hydrazine and the resultant stabilized materials.

Using conditional moments of asset payoffs to infer the volatility of intertemporal marginal rates of substitution

Previously Hansen and Jagannathan (1990a) derived and computed mean-standard deviation frontiers for intertemporal marginal rates of substitution (IMRS) implied by asset market data. These frontiers give the lower bounds on the standard deviations as a function of the mean. In this paper we develop a strategy for utilizing conditioning information efficiently, and hence improve on the standard deviation bounds computed by Hansen and Jagannathan. We implement this strategy empirically by using the seminonparametric (SNP) methodology suggested by Gallant and Tauchen (1989) to estimate the conditional distribution of a vector of monthly asset payoffs. We use the fitted conditional distributions to calculate both conditional and unconditional standard deviation bounds for the IMRS. The unconditional bounds are as sharp as possible subject to robustness considerations. We also use the fitted distributions to compute the moments of various candidate marginal rates of substitution suggested by economic theory, and in particular the time-nonseparable preferences of Dunn and Singleton (1986) and Eichenbaum and Hansen (1990). For these preferences, our findings suggest that habit persistence will put the moments of the IMRS inside the frontier at reasonable values of the curvature parameter. At the same time we uncover evidence that the implied IMRS fails to satisfy all of the restrictions inherent in the Euler equation. The findings help explain why Euler equation estimation methods typically find evidence in favor of local durability instead of habit persistence for monthly data.