
Recent papers
Professor Richard's talk, "An Integrated Treatment
of Monte Carlo Numerical Integration Techniques," presented at the
SCE
11th International Conference, June 2005, is now available.
The GDP
Forecast Model at the University of Pittsburgh is devoted to reporting
forecasts of GDP growth, and characterizations of the current state of
the macroeconomy.



Use of Prior Information
in the Analysis and Estimation of CobbDouglas Production Function Models,
(with A. Zellner), International Economic Review, 14(1),
1973, 107119.
Abstract: In the present paper, we review a samplingtheory analysis
of the CobbDouglas production function put forward by Morishima and Saito,
in which nondatabased prior information was added to aggregate timeseries
information in order to deal with what appeals to be a muticollinearity
problem. Then we turn to an analysis of the MorishimaSaito (MS) production
function problem, using the Bayesian approach in which nondatabased prior
information is introduced by use of prior probability density functions
(PDFs) for the parameters. By the use of prior PDFs in the Bayesian approach,
it will be seen that prior information can be introduced in a rather flexible
manner, and posterior PDFs for parameters of interest, which reflect both
sample and prior information, can be readily computed.
Bayesian Inference in ErrorinVariables
Models, (with J.P. Florens and M. Mouchart), Journal of Multivariate
Analysis, 1974, 419452.
A Note on the Information
Matrix of the Multivariate Normal Distribution, Journal of Econometrics,
3, 1975, 5760
Bayesian Analysis of the
Regression Model when the Disturbances are Generated by an Autoregressive
Process, in New Developments in the Applications of Bayesian
Methods, (Chapter 11), edited by Aykac, A. and C. Brumat, North Holland,
1977, 185210.
Models with Several Regimes
and Changes in Exogeneity, Review of Economic Studies,
XLVII, 1980, 120.
Abstract: In recent years, increasing attention has been devoted
to models with a finite (usually small) number of regimes. Various strategies
have been discussed in the literature to handle situations where each
regime is characterized by a different value of a common parameter vector.
It appears however that no satisfactory treatment has yet been given to
cases where the partitioning between "endogenous" and "exogenous" variables
changes over time. Our objective is therefore to define a class of models
with several regimes which is flexible enough to cover such situations.
On the Evaluation of Polyt
Density Functions, (with H. Tompa), Journal of Econometrics,
12, 1980, 335351.
Abstract: Polyt densities are defined by the property that
their kernel is a product, or a ratio of products, of multivariate tdensity
kernels. As discussed in Drèze (1977), these densities arise as
Bayesian posterior densities for regression coefficients under a variety
of specifications for the prior density and the data generating process.
We have therefore developed methods and computer algorithms. To evaluate
integrating constants and other characteristics of polyt densities
with no more than a single quadratic form in the numerator (section 2).
As a byproduct of our analysis we have also derived an algorithm for
the computation of moments of positive definite quadratic forms in Normal
variables (section 3). In section 4 we discuss inference on the sampling
variances associated with the models discussed in Drèze (1977).
Bayesian Analysis of Simultaneous
Equation Systems, (with J. Drèze), The Handbook of Econometrics,
Volume 1, (Chapter 9), edited by Z. Griliches and M.D. Intriligator, North
Holland, 1983, 519598.
The Econometric Analysis
of Economic Time Series, (with D.F. Hendry), The International
Statistical Review, 51, 1983, 111163. Reprinted in Econometrics
Alchemy or Science?, (Chapter 17), edited by D. F. Hendry , 1993,
Blackwell, Oxford. Reprinted in Foundations of Probability, Econometrics
and Economic Games, edited by O.F. Hamouda and J.C.R. Rowley, Edward
Elgar, 1996. (~21 Mb)
Abstract: A framework is proposed for interpreting recent developments
in time series econometrics, emphasizing the problems of linking economics
and statistics. There are six main expository themes: models are viewed
as (reduced) reparameterizations of data processes through marginalizing
and conditioning; the latter operation is related to the economic notion
of contingent plans based on weakly exogenous variables; a typology of
dynamic equations clarifies the properties of conditional models; estimation
of unknown parameters is treated using estimator generating equations;
and tests are interrelated in terms of the efficient score statistic;
finally, the concept of encompassing rival hypotheses (separate or nested)
provides an 'overview' criterion for evaluating empirical estimates which
have been selected to satisfy conventional criteria. The discussion is
illustrated by an estimated model of the demand for money.
Exogeneity, (with
R.F. Engle and D.F. Hendry), Econometrica, 51, 1983, 277304.
Reprinted in Testing Exogeneity, (Chapter 2), edited by N. R. Ericsson
and J. S. Irons, 1994, Oxford University Press, Oxford. Reprinted in Econometrics
Alchemy or Science? (Chapter 15), edited by D. F. Hendry, Blackwell,
1993. Reprinted in The Methodology of Econometrics, edited by D.J.
Poirer, Edward Elgar, 1994. Reprinted in Time Series, edited by
A. Harvey, Edward Elgar, 1994. Reprinted in Foundations of Probability,
Econometrics and Economic Games, edited by O.F. Hamouda and J.C.R.
Rowley, Edward Elgar, 1996. Reprinted in General to Specific Modelling,
edited by J. Campos, N. Ericsson and D. F. Hendry, Edward Elgar, 2005.
Abstract: Definitions are proposed for weak and strong
exogeneity in terms of the distribution of observable variables.
The objectives of the paper are to clarify the concepts involved, isolate
the essential requirements for a variable to be exogenous, and relate
them to notions of predeterminedness, strict exogeneity and causality
in order to facilitate econometric modelling. Worlds of parameter change
are considered and exogeneity is related to structural invariance leading
to a definition of super exogeneity. Throughout the paper, illustrative
models are used to exposit the analysis.
Classical
and Bayesian Analysis of Univariate and Multivariate Stochastic Volatility
Models, (with Roman Liesenfeld), Economics working paper, ChristianAlbrechtsUniversität
Kiel, Department of Economics; 2004,12.
Abstract: In this paper, Efficient Importance Sampling (EIS) is
used to perform a classical and Bayesian analysis of univariate and multivariate
Stochastic Volatility (SV) models for financial return series. EIS provides
a highly generic and very accurate procedure for the Monte Carlo (MC)
evaluation of highdimensional interdependent integrals. It can be used
to carry out MLestimation of SV models as well as simulation smoothing
where the latent volatilities are sampled at once. Based on this EIS simulation
smoother a Bayesian Markov Chain Monte Carlo (MCDC) posterior analysis
of the parameters of SV models can be performed.
Efficient
HighDimensional Importance Sampling (with Wei Zhang), Unpublished
manuscript, University of Pittsburgh, Department of Economics, 2005.
Abstract: The paper describes a simple, generic, and yet highly
accurate Efficient Importance Sampling (EIS) Monte Carlo (MC) procedure
for the evaluation of highdimensional numerical integrals. EIS is based
upon a sequence of auxiliary weighted regressions which actually are linear
under appropriate conditions. It can be used to evaluate likelihood functions
and byproducts thereof, such as ML estimators, for models which depend
upon unobservable variances. A dynamic stochastic volatility model and
a logit panel data model with unobserved heterogeneity (random effects)
in both dimensions are used to provide illustrations of EIS high numerical
accuracy, even under a small number of MC draws. MC simulations are used
to characterize the finite sample numerical and statistical properties
of EISbased ML estimators.


