A Bayesian analysis of simultaneous equation models by combining recursive analytical and numerical approaches

Abstract Inference on simultaneous equation models using a Bayesian approach is still far from a routine procedure: serious numerical problems may occur in most practical situations. In this paper a unifying framework is proposed using recent analytical [see Steel (1988)] and well-documented poly-t based methods in order to reduce the dimension of the final Monte Carlo integration. Different integration sequences are examined and the implications for various model and prior assumptions are tabulated. An application to Klein's model I clearly illustrates the computational feasibility and numerical stability of the hybrid method proposed.

[1]  Jan R. Magnus,et al.  The exact multi-period mean-square forecast error for the first-order autoregressive model , 1988 .

[2]  T. Klundert,et al.  Unemployment persistence and loss of productive capacity: A Keynesian approach , 1990 .

[3]  J. Richard.  Posterior and Predictive Densities for Simultaneous Equation Models , 1973 .

[4]  J. C. Naylor,et al.  Econometric illustrations of novel numerical integration strategies for Bayesian inference , 1988 .

[5]  Mark F. J. Steel,et al.  Bayesian-analysis of Systems of Seemingly Unrelated Regression Equations Under a Recursive Extended Natural Conjugate Prior Density , 1988 .

[6]  Jan R. Magnus,et al.  A note on instrumental variables and maximum likelihood estimation procedures , 1986 .

[7]  Jean-François Richard,et al.  On the evaluation of poly-t density functions , 1980 .

[8]  Tom Wansbeek,et al.  Estimation of the error-components model with incomplete panels , 1989 .

[9]  Jacques H. Dreze,et al.  BAYESIAN ANALYSIS OF SIMULTANEOUS EQUATION SYSTEMS , 1983 .

[10]  Jacques H. Dreze,et al.  Bayesian Limited Information Analysis of the Simultaneous Equations Model , 1976 .

[11]  J. Geweke,et al.  Bayesian Inference in Econometric Models Using Monte Carlo Integration , 1989 .

[12]  Jan R. Magnus,et al.  On the maximum likelihood estimation of multivariate regression models containing serially correlated error components , 1988 .

[13]  Audra E. Kosh,et al.  Linear Algebra and its Applications , 1992 .

[14]  A. Kapteyn,et al.  Unemployment Benefits and the Labor Market, A Micro / Macro Approach , 1989 .

[15]  F. van der Ploeg,et al.  Perfect equilibrium in a model of competitive arms accumulation , 2010 .

[16]  J.-A. Morales.  Bayesian full information structural analysis , 1971 .

[17]  F. van der Ploeg,et al.  Two essays on political economy : (I) The political economy of overvaluation (II) Election outcomes and the stockmarket , 1990 .

[18]  Bertrand Melenberg,et al.  The effects of liquidity constraints on consumption: Estimation from household panel data , 1989 .

[19]  E. Damme.  Stable equilibria and forward induction , 1989 .

[20]  F. van der Ploeg,et al.  Conflict over arms accumulation in market and command economies , 1987 .

[21]  E. Driffill,et al.  Macroeconomic policy games with incomplete information : Some extensions , 1987 .

[22]  E. Malinvaud.  Méthodes Statistiques de L'Économétrie , 1964 .

[23]  F. van der Ploeg,et al.  International interdependence and policy coordination in economies with real and nominal wage rigidity , 1987 .

[24]  J. Geweke,et al.  Antithetic acceleration of Monte Carlo integration in Bayesian inference , 1988 .

[25]  Mark F. J. Steel.  A Bayesian analysis of multivariate exogeneity : a Monte Carlo approach , 1987 .

[26]  Jan R. Magnus,et al.  The exact multi-period mean-square forecast error for the first-order autoregressive model , 1988 .

[27]  A. Zellner.  An Introduction to Bayesian Inference in Econometrics , 1971 .

[28]  T. Haavelmo.  The Statistical Implications of a System of Simultaneous Equations , 1943 .

[29]  D. Poirier.  Frequentist and Subjectivist Perspectives on the Problems of Model Building in Economics , 1988 .

[30]  Classical and Bayesian inference in incomplete simultaneous equation models , 1984 .

[31]  Warren E. Stewart.  Multiresponse parameter estimation with a new and noninformative prior , 1987 .

[32]  L. Bauwens,et al.  A 1-1 poly-t Random variable generator with application to Monte Carlo integration , 1985 .

[33]  Dolf Talman,et al.  A Simplicial Algorithm for Stationary Point Problems on Polytopes , 1989, Math. Oper. Res..

[34]  Jan R. Magnus,et al.  On certain moments relating to ratios of quadratic forms in normal variables : Further results , 1990 .

[35]  T. Kloek,et al.  Bayesian estimates of equation system parameters, An application of integration by Monte Carlo , 1976 .

[36]  T. Klundert,et al.  On socioeconomic causes of ‘wait unemployment’ , 1990 .

[37]  Lawrence R. Klein,et al.  Economic Fluctuations in the United States , 1951 .

[38]  J. Hammersley,et al.  Monte Carlo Methods , 1965 .

[39]  M. Steel.  Seemingly unrelated regression equation systems under diffuse stochastic prior information: A recursive analytical approach , 1988 .

[40]  A. Barten,et al.  Price formation of fish: An application of an inverse demand system , 1989 .

[41]  Jacques H. Dreze,et al.  Bayesian regression analysis using poly-t densities , 1977 .

[42]  R. Harkema,et al.  Simultaneous Equations: A Bayesian Approach , 1971 .

[43]  Thijs ten Raa,et al.  The Choice Of Model In The Construction Of Input-Output Coefficients Matrices , 1990 .

[44]  E. Frickey,et al.  Economic Fluctuations in the United States. , 1943 .

[45]  F. van der Ploeg,et al.  International coordination of monetary policies under alternative exchange-rate regimes , 1990 .

[46]  Eric van Damme,et al.  Signaling and forward induction in a market entry context , 1990 .

[47]  Geert Dhaene,et al.  When it all began: The 1936 Tinbergen model revisited , 1989 .

[48]  Jan R. Magnus,et al.  Fiscal policy and finite lives in interdependent economies with real and nominal wage rigidity , 1988 .

[49]  Luc Bauwens,et al.  Bayesian Full Information Analysis of Simultaneous Equation Models Using Integration by Monte Carlo , 1984 .

[50]  Herman Koene van Dijk.  Posterior analysis of econometric models using Monte Carlo integration = Analyse a posteriori van econometrische modellen met behulp van monte Carlo integratie : proefschrift ter verkrijging van de ... , 1984 .

[51]  R. Alessie,et al.  Individual effects in utility consistent models of demand , 1990 .

[52]  Arnold Zellner,et al.  Bayesian specification analysis and estimation of simultaneous equation models using Monte Carlo methods , 1988 .

[53]  H. K. Van Dijk,et al.  Further experience in Bayesian analysis using Monte Carlo integration , 1980 .