Nicholas M. Kiefer

The information content of the trading process

Abstract The trade process is a stochastic process of transactions interspersed with periods of inactivity. The realizations of this process are a source of information to market participants. They cause prices to move as they affect the market makers beliefs about the value of the stock. We fit a model of the trade process that allows us to ask whether trade size is important, in that large and small trades may have different information content (they do, but this varies across stocks); whether uninformed trade is i.i.d. (it is not); and, whether large buys and large sells are equally informative (they differ only marginally). The model is fitted by maximum likelihood using transactions data on six stocks over 60 days.

A NEW ASYMPTOTIC THEORY FOR HETEROSKEDASTICITY-AUTOCORRELATION ROBUST TESTS

A new first order asymptotic theory for heteroskedasticity-autocorrelation (HAC) robust tests based on nonparametric covariance matrix estimators is developed. The bandwidth of the covariance matrix estimator is modeled as a fixed proportion of the sample size. This leads to a distribution theory for HAC robust tests that explicitly captures the choice of bandwidth and kernel. This contrasts with the traditional asymptotics (where the bandwidth increases slower than the sample size) where the asymptotic distributions of HAC robust tests do not depend on the bandwidth or kernel. Finite sample simulations show that the new approach is more accurate than the traditional asymptotics. The impact of bandwidth and kernel choice on size and power of t-tests is analyzed. Smaller bandwidths lead to tests with higher power but greater size distortions and large bandwidths lead to tests with lower power but less size distortions. Size distortions across bandwidths increase as the serial correlation in the data becomes stronger. A new data dependent bandwidth is proposed in light of these results. Within a group of popular kernels, it shown that the Bartlett kernel has approximately the highest power and the quadratic spectral (QS) kernel has the lowest power regardless of the bandwidth. However, the Bartlett kernel gives the most size distorted tests whereas the QS kernels give the least size distorted tests. Overall, the results clearly indicate that for bandwidth and kernel choice there is a trade-off between size distortions and power.

Controlling a Stochastic Process with Unknown Parameters

The problem of controlling a stochastic process, with unknown parameters over an infinite horizon, with discounting is considered. Agents express beliefs about unknown parameters in terms of distributions. Under general conditions, the sequence of beliefs converges to a limit distribution. The limit distribution may or may not be concentrated at the true parameter value. In some cases, complete learning is optimal; in others, the optimal strategy does not imply complete learning. The paper concludes with examination of some special cases and a discussion of a procedure for generating examples in which incomplete learning is optimal. Copyright 1988 by The Econometric Society.

Heteroskedasticity-Autocorrelation Robust Standard Errors Using The Bartlett Kernel Without Truncation

In this paper we analyze heteroskedasticity-autocorrelation (HAC) robust tests constructed using the Bartlett kernel without truncation. We show that while such an HAC estimator is not consistent, asymptotically valid testing is still possible. We show that tests using the Bartlett kernel without truncation are exactly equivalent to recent HAC robust tests proposed by Kiefer, Vogelsang and Bunzel (2000, Econometrica, 68, pp 695-714).

Heteroskedasticity-Autocorrelation Robust Testing Using Bandwidth Equal To Sample Size

Asymptotic theory for heteroskedasticity autocorrelation consistent (HAC) covariance matrix estimators requires the truncation lag, or bandwidth, to increase more slowly than the sample size. This paper considers an alternative approach covering the case with the asymptotic covariance matrix estimated by kernel methods with truncation lag equal to sample size. Although such estimators are inconsistent, valid tests (asymptotically pivotal) for regression parameters can be constructed. The limiting distributions explicitly capture the truncation lag and choice of kernel. A local asymptotic power analysis shows that the Bartlett kernel delivers the highest power within a group of popular kernels. Finite sample simulations suggest that, regardless of the kernel chosen, the null asymptotic approximation of the new tests is often more accurate than that for conventional HAC estimators and asymptotics. Finite sample results on power show that the new approach is competitive.

Earnings, Unemployment, and the Allocation of Time Over Time

A stochastic dynamic model of labour supply is specified and analysed empirically. The theoretical model provides a sound structural economic basis for a class of empirical models which have been shown useful. The implications of the estimated model are explored and diagnostic checks are suggested and implemented.

Testing normality in econometric models

A specification test based on an Edgeworth expansion is proposed and some of its useful properties are noted. In particular the test has an important additivity property, in that a test for higher-order alternatives simply adds additional, asymptotically independent variates to tests lower order alternatives.

OPTIMAL CONTROL OF AN UNKNOWN LINEAR PROCESS WITH LEARNING

Optimal control of a linear process with unknown parameters is considered when the horizon is infinite and rewards are discounted. Active learning strategies are considered, i.e., agents consider the information value of possible actions, as well as current reward. Distributional assumptions are minimal in that no restriction to conjugate families is made. Convergence of beliefs and actions is established. Copyright 1989 by Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.

Estimation of fixed effect models for time series of cross-sections with arbitrary intertemporal covariance

Abstract Models for time series of cross-sections with fixed effects and with intertemporal correlation are considered. The regression coefficients, and their standard errors, can be estimated by generalized least squares applied to a transformed model. The procedure is given a conditional likelihood interpretation.

Equilibrium Search Models and the Transition from School to Work

This paper applies an equilibrium search to study the transition from schooling to work of U.S. high school graduates. We consider the case where there is heterogeneity in firm productivity and the number of firm types is discrete. For this case the estimation problem is non-standard and the likelihood function is non-differentiable. This paper provides a computational method to obtain the MLE and, through several Monte Carlo studies, characterizes the behavior of the estimator. Applying these methods to the transition from school to work, our results show that nonemployed blacks receive fewer offers than whites and employed blacks are more likely to lose their jobs. Importantly, employed blacks and whites receive job offers at the same rate. However, the difference in job destruction rates is so great that it accounts for three-quarters of the black-white wage differential.