
on Econometrics 
By:  Roger Hammersland (Norges Bank) 
Abstract:  This paper addresses cointegration in small crosssectional panel data models. In addition to dealing with cointegrating relationships within the crosssectional dimension, the paper explicitly addresses the issue of cointegration between crosssections. The approach is based upon a wellknown distributional result for the trace test when some of the cointegrating vectors are a priori known, and advocates a threestep procedure for the identification of the cointegrating space when dealing with twodimensional data. The first step of this procedure utilizes traditional techniques to identify the longrun relationships within each crosssectional unit separately. In the second step these first step relationships are then treated as known when searching for potential long run relationships between units in a joint analysis comprising the whole crosssectional dimension. The third step of the procedure then finally reestimate all free parameters of the identified longrun structure to get rid of a potential simultaneity bias as a result of a nondiagonal covariance matrix. Identification of the longrun structures of Norwegian exports and international interest rate relationships are used as examples. Norwegian mainland exports have here been divided into two crosssectional units; the traditional goods sector and the service sector. While in the study of international interest rate relationships the two sectors investigated are Germany and the US. The examples are used to address the more general issues of the degree of independence in capital markets and in goods markets of small open economies. 
Keywords:  Cointegration, Panel data, transmission mechanism, monopolistic competition, exports 
JEL:  C32 C33 E43 F12 F41 
Date:  2004–11–12 
URL:  http://d.repec.org/n?u=RePEc:bno:worpap:2004_15&r=ecm 
By:  M. Hashem Pesaran; Takashi Yamagata 
Abstract:  This paper proposes a modified version of Swamy’s test of slope homogeneity for panel data models where the cross section dimension (N) could be large relative to the time series dimension (T). We exploit the cross section dispersion of individual slopes weighted by their relative precision. Using Monte Carlo experiments, we show that the test has the correct size and satisfactory power in panels with strictly exogenous regressors for various combinations of N and T. For autoregressive (AR) models the test performs well for moderate values of the root of the autoregressive process, but with roots near unity a biascorrected bootstrapped version performs well even if N is large relative to T. The cross section dispersion tests are used to test the homogeneity of slopes in autoregressive models of individual earnings using the PSID data and show statistically significant evidence of slope heterogeneity in the earnings dynamics. 
Keywords:  Testing Slope Homogeneity, Hausman Type Tests, Cross Section Dispersion Tests, Monte Carlo Results, PSID Earnings Dynamics 
JEL:  C12 C33 
Date:  2005–03 
URL:  http://d.repec.org/n?u=RePEc:cam:camdae:0513&r=ecm 
By:  JeanMarie Dufour; Tarek Jouini 
Abstract:  In this paper, we study the asymptotic distribution of a simple twostage (HannanRissanentype) linear estimator for stationary invertible vector autoregressive moving average (VARMA) models in the echelon form representation. General conditions for consistency and asymptotic normality are given. A consistent estimator of the asymptotic covariance matrix of the estimator is also provided, so that tests and confidence intervals can easily be constructed. <P>Dans cet article, nous étudions la distribution asymptotique d’un estimateur linéaire simple en deux étapes (de type HannanRissanen) pour un processus vectoriel autorégressifmoyennemobile (VARMA) stationnaire et inversible, formulé sous la forme échelon. Nous donnons des conditions générales qui assurent la convergence et la normalité asymptotique de l’estimateur. Nous fournissons aussi un estimateur convergent de la matrice de covariance asymptotique de l’estimateur, ce qui permet de construire facilement des tests et des intervalles de confiance. 
Keywords:  time series, VARMA, stationary; invertible; echelon form, estimation, asymptotic normality, bootstrap, HannanRissanen, séries chronologiques; VARMA, stationnaire, inversible, forme échelon, estimation, normalité asymptotique, bootstrap, HannanRissanen 
JEL:  C3 C32 C53 
Date:  2005–02–01 
URL:  http://d.repec.org/n?u=RePEc:cir:cirwor:2005s06&r=ecm 
By:  A Garratt; K Lee; M H Pesaran; Yongcheol Shin 
Abstract:  In this paper we discuss the 'structural cointegrating VAR' approach to macroeconometric modelling and compare it to other approaches currently followed in the literature, namely the largescale simultaneous equation macroeconometric models, the structural VARs, and the dynamic stochastic general equilibrium models. The structural cointegrating VAR approach has the attractive features that the estimated longrun relationships embedded in the model are theory consistent, and have a clear economic interpretation, and yet the shortrun dynamics are flexibly estimated within a VAR framework. The approach is illustrated using a small quarterly macroeconometric model of the UK. The uses of the model in impulse response analysis and probability forecasting is also discussed. 
Keywords:  Structural Cointegrating VAR, Macroeconomic Modelling, Generalised Impulse Responses, Persistence Profiles, Probability Forecasts. 
JEL:  C32 C5 E17 
URL:  http://d.repec.org/n?u=RePEc:edn:esedps:8&r=ecm 
By:  Michel Normandin (IEA, HEC Montréal) 
Abstract:  This paper presents and assesses a procedure to estimate conventional parameters characterizing fluctuations at the business cycle frequency, when the economic agents’ information set is superior to the econometrician’s one. Specifically, we first generalize the conditions under which the econometrician can estimate these ‘cyclical fluctuation’ parameters from augmented laws of motion for forcing variables that fully recover the agents’ superior information. Second, we document the econometric properties of the estimates when the augmented laws of motion are possibly misspecified. Third, we assess the ability of certain information criteria to detect the presence of superior information. 
Keywords:  Block bootstrap; Hidden variables; Laws of motion for forcing variables; Monte Carlo simulations. 
JEL:  C14 C15 C32 E32 
Date:  2004–12 
URL:  http://d.repec.org/n?u=RePEc:iea:carech:0413&r=ecm 
By:  Rodney W. Strachan; Herman K. van Dijk 
Abstract:  While some improper priors have attractive properties, it is generally claimed that Bartlett's paradox implies that using improper priors for the parameters in alternative models results in Bayes factors that are not well defined, thus preventing model comparison in this case. In this paper we demonstrate, using well understood principles underlying what is already common practice, that this latter result is not generally true and so expand the class of priors that may be used for computing posterior odds to two classes of improper priors: the shrink age prior; and a prior based upon a nesting argument. Using a new representation of the issue of undefined Bayes factors, we develop classes of improper priors from which well defined Bayes factors result. However, as the use of such priors is not free of problems, we include discussion on the issues with using such priors for model comparison. 
Keywords:  Improper prior; Bayes factor; marginal likelihood; shrinkage prior; measure 
Date:  2005–03 
URL:  http://d.repec.org/n?u=RePEc:lec:leecon:05/4&r=ecm 
By:  Angela Huang (Reserve Bank of New Zealand) 
Abstract:  Numerous empirical studies investigate whether exchange rates are related to `economic fundamentals' in the longrun and find a range of relationships through cointegration analysis. We report similar cointegrating relationships for the value of the New Zealand dollar relative to the US dollar (NZD/USD) and for the value of the New Zealand dollar relative to the Australian dollar (NZD/AUD). These include determinants such as commodity prices, 90day interest rate differentials, and inflation and growth differentials. However, Godbout and van Norden (1997) demonstrate that finitesample problems may have affected the conclusions of such cointegration studies. Through a simple Monte Carlo study, we consider whether the cointegration coefficients can reasonably be interpreted as `longrun' elasticities of the exchange rate to changes in fundamental variables. The simulation results suggest that given a relatively short span of data it is possible for cointegration analysis to indicate that a longrun relationship has been found when in fact there is only a cyclical relationship. Therefore caution is advised when interpreting the empirical results and making policy assessments about the nature of exchange movements relative to its broad trend. 
JEL:  F31 C15 C22 
Date:  2004–10 
URL:  http://d.repec.org/n?u=RePEc:nzb:nzbdps:2004/08&r=ecm 
By:  John Stachurski (CORE); Cuong Le Van (CERMSEM) 
Abstract:  The paper gives conditions under which stationary distributions of Markov models depend continuously on the parameters. It extends a wellknown parametric continuity theorem for compact state space to the unbounded setting of standard econometrics and time series analysis. Applications to several theoretical and estimation problems are outlined. 
Keywords:  Stationary distribution; parametric continuity; Markov process; SolowPhelps golden rule; Foias operator; V normlike function; Feller property 
JEL:  O41 
Date:  2004–06 
URL:  http://d.repec.org/n?u=RePEc:mse:wpsorb:b04059&r=ecm 
By:  Cuong Le Van (CERMSEM); John Stachurski (CORE) 
Abstract:  We consider discrete time Markov chains on general state space. It is shown that a certain property referred to here as nondecomposability is equivalent to irreducibility and that a Markov chain with invariant distribution is irreducible if and only if the invariant distribution is unique and assigns positive probability to all absorbing sets. 
Keywords:  Discrete time Markov chains; invariant distribution; nondecomposability; irreducibility; absorbing set 
JEL:  O41 
Date:  2004–06 
URL:  http://d.repec.org/n?u=RePEc:mse:wpsorb:b04061&r=ecm 
By:  Nicolas Bouleau (CERMICS  Ecole Nationale des Ponts & Chaussées); Christophe Chorro (CERMSEM et CERMICS) 
Abstract:  This article proposes and studies a link between statistics and the theory of Dirichlet forms used to compute errors. The error calculus based on Dirichlet forms is an extension of classical Gauss' approach to error propagation. The aim of this paper is to derive error structures from measurements. The links with Fisher's information lay the foundations of a strong connection with experiment. Here we show that this connection behaves well towards changes of variables and is related to the theory of asymptotic statistics. Finally the study of products permits to lay the premise of an infinite dimensional empirical error calculus 
Keywords:  Error; sensitivity; Dirichlet forms; squared field operator; CramerRao inequality; Fischer information 
Date:  2004–07 
URL:  http://d.repec.org/n?u=RePEc:mse:wpsorb:b04079&r=ecm 
By:  Christophe Chorro (CERMSEM et CERMICS) 
Abstract:  In a recent paper, Bouleau provides a new tool, based on the language of Dirichlet forms, to study the errors propagation and reinforce the historical approach of Gauss. As the classical central limit theorem is a theoric justification of the employment of normal laws in statistics, the aim of this article is to underline the importance of certain classes of error structures by asymptotic arguments. Thus, we extend the notions of independence and convergence in distribution for random variables in order to prove a refinement of the hilbertian central limit theorem that highlights the fundamental role of the error structures of the OrnsteinUlhenbeck type 
Keywords:  Error; sensitivity; Dirichlet forms; squared field operator; vectorial domain; central limit theorem 
Date:  2004–07 
URL:  http://d.repec.org/n?u=RePEc:mse:wpsorb:b04080&r=ecm 
By:  Torben G. Andersen (Kellogg School of Management, Northwestern University); Tim Bollerslev (Department of Economics, Duke University); Peter F. Christoffersen (Faculty of Management, McGill University); Francis X. Diebold (Department of Economics, University of Pennsylvania) 
Abstract:  Volatility has been one of the most active and successful areas of research in time series econometrics and economic forecasting in recent decades. This chapter provides a selective survey of the most important theoretical developments and empirical insights to emerge from this burgeoning literature, with a distinct focus on forecasting applications. Volatility is inherently latent, and Section 1 begins with a brief intuitive account of various key volatility concepts. Section 2 then discusses a series of different economic situations in which volatility plays a crucial role, ranging from the use of volatility forecasts in portfolio allocation to density forecasting in risk management. Sections 3, 4 and 5 present a variety of alternative procedures for univariate volatility modeling and forecasting based on the GARCH, stochastic volatility and realized volatility paradigms, respectively. Section 6 extends the discussion to the multivariate problem of forecasting conditional covariances and correlations, and Section 7 discusses volatility forecast evaluation methods in both univariate and multivariate cases. Section 8 concludes briefly. 
JEL:  C10 C53 G1 
Date:  2005–02–22 
URL:  http://d.repec.org/n?u=RePEc:pen:papers:05011&r=ecm 