BAYESIAN ANALYSIS OF CARTEL STABILITY AND REGIME SWITCHING

Empirical analysis of collusive regimes typically requires the construction of structural econometric models, with explicit ties to theoretical models of firm behavior in equilibrium. To that end, theory often elicits a wealth of important information regarding the structural parameters, information that is indispensable in accurately identifying desired phenomena, but nevertheless, is inevitably disregarded by classical techniques. Motivated by these considerations, the paper demonstrates how Bayesian methods may be used to better incorporate such structural knowledge through prior probabilistic beliefs. As a result, Bayesian posterior inference provides a clear and precise empirical interpretation of collusive behavior and cartel stability.Cartel; dynamic oligopoly; collusion detection; regime switching; structural modeling; Bayesian methods

A Comment on “A Review of Student Test Properties in Condition of Multifactorial Linear Regression”

A recent article (Pavelescu, 2009) proposes a correction to the conventional student-t test of significance in linear regression models, but offers no formal description of its properties. This comment formally characterizes the sampling properties of the corrected student-t statistic. In application to multifactorial regressions, it turns out that the corrected student-t statistic is not ancillary – its sampling distribution depends on unknown nuisance parameters.Therefore, it is impossible to reasonably compute critical values and operatively designate a rejection criterion using such a test statistic, which makes the proposed testing procedure impractical. Some suggestions regarding the search for similar testing procedures are proposed and a Bayesian alternative is further discussed.multifactorial classical normal regression, collinearity, multicollinearity, significance test, sampling distributions, power functions, Bayesian linear regression, prior information, posterior distributions

Marginal Likelihood Estimation with the Cross-Entropy Method

We consider an adaptive importance sampling approach to estimating the marginal likelihood, a quantity that is fundamental in Bayesian model comparison and Bayesian model averaging. This approach is motivated by the difficulty of obtaining an accurate estimate through existing algorithms that use Markov chain Monte Carlo (MCMC) draws, where the draws are typically costly to obtain and highly correlated in high-dimensional settings. In contrast, we use the cross-entropy (CE) method, a versatile adaptive Monte Carlo algorithm originally developed for rare-event simulation. The main advantage of the importance sampling approach is that random samples can be obtained from some convenient density with little additional costs. As we are generating independent draws instead of correlated MCMC draws, the increase in simulation effort is much smaller should one wish to reduce the numerical standard error of the estimator. Moreover, the importance density derived via the CE method is in a well-defined sense optimal. We demonstrate the utility of the proposed approach by two empirical applications involving women's labor market participation and U.S. macroeconomic time series. In both applications the proposed CE method compares favorably to existing estimators

Linear systems solvers - recent developments and implications for lattice computations

We review the numerical analysis' understanding of Krylov subspace methods for solving (non-hermitian) systems of equations and discuss its implications for lattice gauge theory computations using the example of the Wilson fermion matrix. Our thesis is that mature methods like QMR, BiCGStab or restarted GMRES are close to optimal for the Wilson fermion matrix. Consequently, preconditioning appears to be the crucial issue for further improvements.Comment: 7 pages, LaTeX using espcrc2.sty, 2 figures, 9 eps-files, Talk presented at LATTICE96(algorithms), submitted to Nucl. Phys. B, Proc. Supp

Multicollinearity in applied economics research and the Bayesian linear regression

This article revises the popular issue of collinearity amongst explanatory variables in the context of a multiple linear regression analysis, particularly in empirical studies within social science related fields. Some important interpretations and explanations are highlighted from the econometrics literature with respect to the effects of multicollinearity on statistical inference, as well as the general shortcomings of the once fervent search for methods intended to detect and mitigate these effects. Consequently, it is argued and demonstrated through simulation how these views may be resolved against an alternative methodology by integrating a researcher’s subjective information in a formal and systematic way through a Bayesian approach