Douglas J. Hodgson

Testing the capital asset pricing model efficiently under elliptical symmetry: a semiparametric approach

We develop new tests of the capital asset pricing model that take account of and are valid under the assumption that the distribution generating returns is elliptically symmetric; this assumption is necessary and sufficient for the validity of the CAPM. Our test is based on semiparametric efficient estimation procedures for a seemingly unrelated regression model where the multivariate error density is elliptically symmetric, but otherwise unrestricted. The elliptical symmetry assumption allows us to avoid the curse of dimensionality problem that typically arises in multivariate semiparametric estimation procedures, because the multivariate elliptically symmetric density function can be written as a function of a scalar transformation of the observed multivariate data. The elliptically symmetric family includes a number of thick-tailed distributions and so is potentially relevant in financial applications. Our estimated betas are lower than the OLS estimates, and our parameter estimates are much less consistent with the CAPM restrictions than the corresponding OLS estimates. Copyright

Adaptive Estimation of Cointegrating Regressions with ARMA Errors

Adaptive maximum likelihood estimators are derived for the parameters of a cointegrating regression whose errors follow a stationary and invertible ARMA process with innovations of unknown distribution. It is shown how to use preliminary estimates of these innovations to nonparametrically estimate their density, which can in turn be used to construct an asymptotically efficient iterative estimator of the cointegrating vector. The asymptotic distribution of this estimator is derived, as are its efficiency gains relative to the Gaussian pseudo-MLE. We evaluate the finite sample behaviour of the estimator through a small Monte Carlo experiment, and report the results of an empirical application to the foreign exchange market.

ADAPTIVE ESTIMATION OF ERROR CORRECTION MODELS

This paper considers adaptive maximum likelihood estimation of reduced rank vector error correction models. It is shown that such models can be asymptotically efficiently estimated even in the absence of knowledge of the shape of the density function of the innovation sequence, provided that this density is symmetric. The construction of the estimator, involving the nonparametric kernel estimation of the unknown density using the residuals of a consistent preliminary estimator, is described, and its asymptotic distribution is derived. Asymptotic efficiency gains over the Gaussian pseudo–maximum likelihood estimator are evaluated for elliptically symmetric innovations.

Efficient Estimation of Conditional Asset-Pricing Models

A semiparametric efficient estimation procedure is developed for the parameters of multivariate generalized autoregressive conditional heteroscedasticity-in-mean models when the disturbances have a conditional distribution assumed to be elliptically symmetric but otherwise unrestricted. Under high-level assumptions, the resulting estimator achieves the asymptotic semiparametric efficiency bound. The elliptical symmetry assumption allows us to avert the curse of dimensionality problem that would otherwise arise in estimating the unknown error distribution. This framework is suitable for the estimation and testing of conditional asset-pricing models, such as the conditional capital asset-pricing model. We apply our procedure in an empirical study of stock prices, with Monte Carlo simulation results also reported.

Age-Price Profiles for Canadian Painters at Auction

We conduct an empirical analysis of the effect on the auction price of a Canadian painting of the age of the painter at the time of creation of the painting. We consider over two hundred artists, active over the entire history of Canadian art, who are pooled in the estimation of a hedonic regression in which a polynomial function in age enters as a regressor along with several other control variables. We consider the possibility that the age–price relationship has changed over time by: (a) estimating separate age–price functions for three generational groups of artists—those born before 1880, between 1880 and 1920, and after 1920 and thus coming of age in the world of post-war ‘contemporary art’ and (b) estimating a parameterization where the shape of the age–price profile is permitted to change continuously depending on the year of birth of the artist. Our principal result is that artists born more recently tend to ‘peak’ earlier in their careers than those of previous generations.

Adaptive estimation of cointegrated models: simulation evidence and an application to the forward exchange market

The paper reports simulation and empirical evidence on the finite-sample performance of adaptive estimators in cointegrated systems. Adaptive estimators are asymptotically efficient, even when the shape of the likelihood function is unknown. We consider two representations of cointegrated systems--triangular cointegrating regressions and error correction models. The motivation for and advantages of adaptive estimators in such systems are discussed and their construction is described. We report results from the estimation of a forward exchange market unbiasedness regression using the adaptive and competing estimators, and provide related Monte Carlo simulation evidence on the performance of the estimators.

Dynamic Price Dependence of Canadian and International Art Markets: An Empirical Analysis

Although the market for Canadian paintings is now of substantial magnitude, with several works having recently been sold for well over a million dollars, it remains true that with very few exceptions, the works of Canadian painters are bought and sold only in Canada and seem to be held only by Canadian collectors. This market can thus be viewed as largely local, and it is therefore not clear whether there should be any linkage between price movements for Canadian art and those for the mainstream international market in old master, impressionist, and modern art. This article investigates the presence and nature of such time series dependence econometrically, both in terms of long-term trends as reflected in the co-integrating relationship between Canadian and the international market, and in terms of short-run co-movements as represented in correlations. The possibility that the local market “follows” the international one is also considered through an analysis of Granger causality. For Canadian art prices, we use a new hedonic index that has been computed using an updated version of the dataset of Hodgson and Vorkink (Can J Econ 37:629–655, 2004 ), while for the international prices, we use an index provided by Mei and Moses (Am Econ Rev 92:1656–1668, 2002 ). Copyright Springer-Verlag 2012

An analysis of pricing and returns in the market for French Canadian paintings

The valuation of French Canadian paintings is analysed empirically. Using a sample of auction prices for major French Canadian painters for the period 1968 to 2005, we run hedonic regressions to determine the influence of various factors, including painter identity, on auction prices, as well as to construct a market price index. This is then used in a second stage analysis of the properties of these art works viewed as investment assets. We consider the extent to which standard asset pricing theory, as represented by the capital asset pricing model, can account for price movements in the market for French Canadian paintings.

Semiparametric Efficiency Bounds in Dynamic Non-Linear Systems under Elliptical Symmetry

We analyze semiparametric efficient estimation of non-linear simultaneous equation models in a time series context and derive a semiparametric efficiency bound for estimation of the parameters when the errors are i.i.d. from an unknown elliptically symmetric density. We derive the bound in the case of errors that are elliptically symmetric conditional on predetermined variables. Copyright Royal Economic Society 2007

Testing the Capital Asset Pricing Model Efficiently Under Elliptical Symmetry: A Semiparametric Approach

We develop new tests of the capital asset pricing model that take account of and are valid under the assumption that the distribution generating returns is elliptically symmetric; this assumption is neccessary and sufficient for the validity of the CAPM. Our test is based on semi-parametric efficient estimation procedures for a seemingly unrelated regression model where the multvariate error density is elliptically symmetric, but otherwise unrestricted. The elliptical symmetry assumption allows us to avoid the curse of dimensionality problem that typically arises in multivariate semiparametric estimation procedures, because the multivariate elliptically symmetric density function can be written as a function of a scalar transformation of the observed multivariate data. The elliptically symmetric family includes a number of thick-tailed distributions and so is potentially relevant in financial applications. Our estimated betas are lower than the OLS estimates, and our parametric estimates are much less consistent with the CAPM restrictions than the corresponding OLS estimates.