Mark Coppejans

Cross Validated SNP Density Estimates

We consider cross-validation strategies for the SNP nonparametric density estimator, which is a truncation (or sieve) estimator based upon a Hermite series expansion. Our main focus is on the use of SNP density estimators as an adjunct to EMM structural estimation. It is known that for this purpose a desirable truncation point occurs at the last point at which the MSE curve of the SNP density estimate declines abruptly. We study the determination of the MSE curve on a per sample basis for iid data by means of leave-one-out cross-validation and hold-out-sample cross-validation through an examination of their performance over the Marron-Wand test suite and models related to asset pricing and auction applications. We find that both methods are informative as to the location of abrupt drops. The hold-out-sample method is cheaper to compute because it requires fewer nonlinear optimizations. The minimum of the hold-out-sample cross-validation curve also seems to be a better indicator of the minimum of the true MSE curve. We consider the asymptotic justification of hold-out-sample cross-validation. For this purpose, we establish rates of convergence of the SNP estimator under the Hellinger norm that are of interest in their own right.

Pricing behavior in an off-hours computerized market

Abstract Automated markets are becoming increasingly widespread, and their efficiency properties are of corresponding concern to regulators and exchange policy makers. Many systems are implemented in settings characterized by a distinct lack of liquidity, however, often by design. We evaluate the performance of such a market, the GLOBEX overnight trading system, in absolute terms and relative to a liquid benchmark, the floor market of the Chicago Mercantile Exchange (CME). Our results with respect to bid–ask spreads and adverse selection suggest that the nature of the environment is an important determinant of market performance, but that an automated market can operate well in a relatively illiquid setting. Price clustering, indicative of a lack of pricing efficiency, is prevalent on the automated system, but price resolution improves as trading frequency increases.

Estimation of the binary response model using a mixture of distributions estimator (MOD)

Abstract In this paper, we develop a semiparametric sieve estimator, which is termed a mixture of distributions estimator (MOD), to estimate a binary response model when the distribution of the errors is unknown. The estimator of the distribution function is composed of a mixture of smooth distributions, where the number of mixtures increases with the sample size. The model is semiparametric because it is assumed that a parametric index type restriction holds. Optimal rates of convergence are established for the distribution function under the L 2 norm, and conditions are derived under which estimates of the parametric component are asymptotically normal. An appealing feature about MOD is that it is possible to restrict the estimator of the distribution function, a priori, to be smooth, nonnegative, nondecreasing, and to integrate to one. This has important practical and theoretical implications.

The Impact of Foreign Equity Ownership on Emerging Market Share Price Volatility

We ask whether foreign equity ownership affects the stability of share prices in an emerging economy. We address the effect of ownership restrictions exogenously imposed on stock ownership and the impact of introducing or widening foreign ownership through cross-listing. A methodology for variance ratio analysis is introduced that corrects for liquidity and volume differences across stock series experiencing different degrees of foreign ownership. We find that foreign ownership does not affect volatility in the absence of cross-listing. Foreign ownership introduced or accompanied by cross-listing of a stock series raises the variance of returns. This effect is found to operate in part through increases in volume traded on the domestic market following the listing, and through an identifiable increase in the volatility of information net of volume effects. Copyright 2000 by Blackwell Publishers Ltd.

Effective nonparametric estimation in the case of severely discretized data

Almost all economic data sets are discretized or rounded to some extent. This paper proposes a regression and a density estimator that work especially well when the data is very discrete. The estimators are a weighted average of the data, and the weights are composed of cubic B-splines. Unlike most nonparametric settings, where it is assumed that the observed data comes from a continuum of possibilities, we base our work on the assumption that the discreteness becomes finer as the sample size increases. Rates of convergence and asymptotic distributional results are derived under this condition.

Noise In the Price Discovery Process: A Comparison of Periodicand Continuous Auctions

We examine market volatility across an automated periodic auction mechanism and a continuous automated auction, using data on five futures contracts traded on the GLOBEX trading system. The analysis is supplemented by a comparison of the periodic market with floor trading. Our data permit virtually no lag between the close of continuous trading and the periodic auction just preceding further continuous trading, avoiding ambiguities in results due to periods of non-trading. Theoretical results are summarized, which suggest greater volatility in the continuous market, but which also imply equality of price volatility across periodic and continuous mechanisms for some market conditions. The empirical analysis consists both of direct comparisons via variance ratios and variance ratio tests conditional on a model of price and value adjustment previously suggested by Amihud and Mendelson (1987). We show how to directly estimate the structural parameters of the model, and derive a test of market efficiency conditional on the models structure. Our results indicate that the periodic auction yields the same volatility as the automated continuous market for a stock index contract, but that the periodic market is associated with relatively lower volatility for currency futures. Tests fail to reject market efficiency for the index contract and three out of four currency futures.