The Seemingly Unrelated Dynamic Cointegration Regression Model and Testing for Purching Power Parity.

This paper studies seemingly unrelated linear models with integrated regressors and stationary errors. By adding leads and lags of the first differences of the regressors and estimating this augmented dynamic regression model by feasible generalized least squares using the long-run covariance matrix, we obtain an efficient estimator of the cointegrating vector that has a limiting mixed normal distribution. Simulation results suggest that this new estimator compares favorably with others already proposed in the literature. We apply these new estimators to the testing of purchasing power parity (PPP) among the G-7 countries. The test based on the efficient estimates rejects the PPP hypothesis for most countries.

Simulation-Based Finite-Sample Tests for Heteroskedasticity and ARCH Effects.

A wide range of tests for heteroskedasticity have been proposed in the econometric and statistics literature. Although a few exact homoskedasticity tests are available, the commonly employed procedures are quite generally based on asymptotic approximations which may not provide good size control in finite samples. There has been a number of recent studies that seek to improve the reliability of common heteroskedasticity tests using Edgeworth, Bartlett, jackknife and bootstrap methods. Yet the latter remain approximate. In this paper, we describe a solution to the problem of controlling the size of homoskedasticity tests in linear regression contexts. We study procedures based on the standard test statistics [e.g., the Goldfeld-Quandt, Glejser, Bartlett, Cochran, Hartley, Breusch-Pagan-Godfrey, White and Szroeter criteria] as well as tests for autoregressive conditional heteroskedasticity (ARCH-type models). We also suggest several extensions of the existing procedures (sup-type of combined test statistics) to allow for unknown breakpoints in the error variance. We exploit the technique of Monte Carlo tests to obtain provably exact p-values, for both the standard and the new tests suggested. We show that the MC test procedure conveniently solves the intractable null distribution problem, in particular those raised by the sup-type and combined test statistics as well as (when relevant) unidentified nuisance parameter problems under the null hypothesis. The method proposed works in exactly the same way with both Gaussian and non-Gaussian disturbance distributions [such as heavy-tailed or stable distributions]. The performance of the procedures is examined by simulation. The Monte Carlo experiments conducted focus on : (1) ARCH, GARCH, and ARCH-in-mean alternatives; (2) the case where the variance increases monotonically with : (i) one exogenous variable, and (ii) the mean of the dependent variable; (3) grouped heteroskedasticity; (4) breaks in variance at unknown points. We find that the proposed tests achieve perfect size control and have good power.

Aggregations and Marginalization of GARCH and Stochastic Volatility Models

The GARCH and Stochastic Volatility paradigms are often brought into conflict as two competitive views of the appropriate conditional variance concept : conditional variance given past values of the same series or conditional variance given a larger past information (including possibly unobservable state variables). The main thesis of this paper is that, since in general the econometrician has no idea about something like a structural level of disaggregation, a well-written volatility model should be specified in such a way that one is always allowed to reduce the information set without invalidating the model. To this respect, the debate between observable past information (in the GARCH spirit) versus unobservable conditioning information (in the state-space spirit) is irrelevant. In this paper, we stress a square-root autoregressive stochastic volatility (SR-SARV) model which remains true to the GARCH paradigm of ARMA dynamics for squared innovations but weakens the GARCH structure in order to obtain required robustness properties with respect to various kinds of aggregation. It is shown that the lack of robustness of the usual GARCH setting is due to two very restrictive assumptions : perfect linear correlation between squared innovations and conditional variance on the one hand and linear relationship between the conditional variance of the future conditional variance and the squared conditional variance on the other hand. By relaxing these assumptions, thanks to a state-space setting, we obtain aggregation results without renouncing to the conditional variance concept (and related leverage effects), as it is the case for the recently suggested weak GARCH model which gets aggregation results by replacing conditional expectations by linear projections on symmetric past innovations. Moreover, unlike the weak GARCH literature, we are able to define multivariate models, including higher order dynamics and risk premiums (in the spirit of GARCH (p,p) and GARCH in mean) and to derive conditional moment restrictions well suited for statistical inference. Finally, we are able to characterize the exact relationships between our SR-SARV models (including higher order dynamics, leverage effect and in-mean effect), usual GARCH models and continuous time stochastic volatility models, so that previous results about aggregation of weak GARCH and continuous time GARCH modeling can be recovered in our framework.

Identification, Weak Instruments and Statistical Inference in Econometrics

We discuss statistical inference problems associated with identification and testability in econometrics, and we emphasize the common nature of the two issues. After reviewing the relevant statistical notions, we consider in turn inference in nonparametric models and recent developments on weakly identified models (or weak instruments). We point out that many hypotheses, for which test procedures are commonly proposed, are not testable at all, while some frequently used econometric methods are fundamentally inappropriate for the models considered. Such situations lead to ill-defined statistical problems and are often associated with a misguided use of asymptotic distributional results. Concerning nonparametric hypotheses, we discuss three basic problems for which such difficulties occur: (1) testing a mean (or a moment) under (too) weak distributional assumptions; (2) inference under heteroskedasticity of unknown form; (3) inference in dynamic models with an unlimited number of parameters. Concerning weakly identified models, we stress that valid inference should be based on proper pivotal functions —a condition not satisfied by standard Wald-type methods based on standard errors — and we discuss recent developments in this field, mainly from the viewpoint of building valid tests and confidence sets. The techniques discussed include alternative proposed statistics, bounds, projection, split-sampling, conditioning, Monte Carlo tests. The possibility of deriving a finite-sample distributional theory, robustness to the presence of weak instruments, and robustness to the specification of a model for endogenous explanatory variables are stressed as important criteria assessing alternative procedures.

Bayesian Analysis for a Theory of Random Consumer Demand: The Case of Indivisible Goods

McCausland (2004a) describes a new theory of random consumer demand. Theoretically consistent random demand can be represented by a \"regular\" \"L-utility\" function on the consumption set X. The present paper is about Bayesian inference for regular L-utility functions. We express prior and posterior uncertainty in terms of distributions over the indefinite-dimensional parameter set of a flexible functional form. We propose a class of proper priors on the parameter set. The priors are flexible, in the sense that they put positive probability in the neighborhood of any L-utility function that is regular on a large subset bar(X) of X; and regular, in the sense that they assign zero probability to the set of L-utility functions that are irregular on bar(X). We propose methods of Bayesian inference for an environment with indivisible goods, leaving the more difficult case of indefinitely divisible goods for another paper. We analyse individual choice data from a consumer experiment described in Harbaugh et al. (2001).

Distribution-Free Bounds for Serial Correlation Coefficients in Heteroskedastic Symmetric Time Series

We consider the problem of testing whether the observations X1, ..., Xn of a time series are independent with unspecified (possibly nonidentical) distributions symmetric about a common known median. Various bounds on the distributions of serial correlation coefficients are proposed: exponential bounds, Eaton-type bounds, Chebyshev bounds and Berry-Esséen-Zolotarev bounds. The bounds are exact in finite samples, distribution-free and easy to compute. The performance of the bounds is evaluated and compared with traditional serial dependence tests in a simulation experiment. The procedures proposed are applied to U.S. data on interest rates (commercial paper rate).

Parametric and Nonparametric Approaches to Price and Tax Reform.

In the analysis of tax reform, when equity is traded off against efficiency, the measurement of the latter requires us to know how tax-induced price changes affect quantities supplied and demanded. in this paper, we present various econometric procedures for estimating how taxes affect demand.

El Tropel, un sitio arqueológico del Clásico en el Occidente Mesoamericano.

Cette recherche doctorale a été réalisée dans le cadre d’un projet de sauvetage archéologique à Villa de Álvarez, dans l’état de Colima (Mexique). Dans la zone géographique à l’étude, plusieurs traces indiquant la présence de contextes funéraires ont été relevées par le passé, mais aucun de ces sites n’a fait l’objet d’un rapport archéologique. L’état de Colima est connu pour ses tombes à puits (tumbas de tiro), ses céramiques de manufacture typique, ainsi que pour les fameux « chiens de Colima ». Malgré la relation entre ces objets et les contextes funéraires, peu d’études se sont attardées à comprendre la composante biologique de ces contextes, c’est-à-dire les êtres humains. Ainsi, la richesse du projet de sauvetage archéologique nous a donné l’opportunité de structurer un projet de recherche de thèse doctorale beaucoup plus profond en ce qui concerne un des sujets les plus importants de cette région mésoaméricaine : les traditions funéraires. C’est de cette façon, à la lumière des résultats particuliers obtenus sur le site du Tropel, que nous avons décidé de travailler les liens culturels existants entre ce dernier, la région de Colima, l’Ouest mésoaméricain et l’aire culturelle dans son ensemble. La campagne de fouille ainsi menée a permis la récupération de vingt-six individus de différents sexes et âges. Au moins quatre périodes d’occupation ont été enregistrées sur le site. La présence humaine sur le site s’étend donc de 339AD à 682 AD (datations au radiocarbone sur trois individus du site El Tropel), ce qui correspond à la phase archéologique Comala à Colima. L’abondance d’artefacts de cette phase dans les quatre strates culturelles du site a permis de réaliser une datation relative en relation avec l’apparition et la fréquence de céramiques d’autres phases culturelles connues : Ortices, Colima, Armería y Chanal. Concernant les pratiques funéraires, la fouille a permis de constater le traitement des cadavres avant, pendant et après l’enterrement des défunts. Bien que des contextes funéraires similaires aient déjà été mentionnés dans la région, aucun d’entre eux n’a pu être identifié clairement. Ces traitements funéraires démontrent l’existence chez les anciens habitants de Colima d’une transmission des connaissances concernant l’anatomie, les processus de décomposition des cadavres, et même possiblement d’un culte des os humains. Une étude ostéologique a été menée sur les squelettes afin de documenter les aspects démographiques, pathologiques, sociaux et économiques de la population du site. Parmi les éléments les plus significatifs de l’étude, il est possible de mentionner la présence de certaines pathologies peu connues dans cette région de la Mésoamérique telles que la syphilis et la tuberculose. Des déformations crâniennes ont aussi été observées, ainsi que la présence d’un déformateur crânien en céramique. De plus, de nombreuses données ont été relevées concernant la présence d’os wormiens sur les crânes déformés artificiellement. Finalement, des analyses d’isotopes stables ont été pratiquées sur des os des individus, ainsi que sur des os de chiens et de cerfs retrouvés sur le site, afin de mieux connaître l’alimentation et la vie des communautés anciennes de la région.