Non-Markovian Regime Switching with Endogenous States and Time-Varying State Strengths

This article presents a non-Markovian regime switching model in which the regime states depend on the sign of an autoregressive latent variable. The magnitude of the latent variable indexes the `strength' of the state or how deeply the system is embedded in the current regime. The autoregressive nature of this non-Markovian regime switching implies time-varying state transition probabilities, even in the absence of an exogenous covariate. Furthermore, with time-varying regime strengths, the expected duration of a regime is time-varying. In this framework, it is natural to allow the autoregressive latent variable to be endogenous so that regimes are determined jointly with the observed data. We apply the model to GDP growth, as in Hamilton (1989), Albert and Chib (1993) and Filardo and Gordon (1998) to illustrate the relation of the regimes to NBER-dated recessions and the time-varying expected durations of regimesRegime switching; Markov Chain Monte Carlo

Markov Chain Monte Carlo Technology

In the past fifteen years computational statistics has been enriched by a powerful, somewhat abstract method of generating variates from a target probability distribution that is based on Markov chains whose stationary distribution is the probability distribution of interest. This class of methods, popularly referred to as Markov chain Monte Carlo methods, or simply MCMC methods, have been influential in the modern practice of Bayesian statistics where these methods are used to summarize the posterior distributions that arise in the context of the Bayesian prior-posterior analysis (Tanner and Wong, 1987; Gelfand and Smith, 1990; Smith and Roberts, 1993; Tierney, 1994; Besaget al., 1995; Chib and Greenberg, 1995, 1996; Gilks et al., 1996; Tanner, 1996; Gammerman, 1997; Robert and Casella, 1999; Carlin and Louis, 2000; Chen et al., 2000; Chib, 2001; Congdon, 2001; Liu, 2001; Robert, 2001; Gelman at al, 2003). MCMC methods have proved useful in practically all aspects of Bayesian inference, for example, in the context of prediction problems and in the computation of quantities, such as the marginal likelihood, that are used for comparing competing Bayesian models. --

Estimation of heterogeneous preferences, with an application to demand for internet services

This paper presents a structural econometric framework for discrete and continuous consumer choices in which unobserved intrapersonal and interpersonal preference heterogeneity is modeled explicitly. It outlines a simulation-assisted estimation methodology applicable in this framework. This methodology is illustrated in an application to analyze data from the U.C. Berkeley Internet Demand Experiment

Returns to Compulsory Schooling in Britain: Evidence from a Bayesian Fuzzy Regression Discontinuity Analysis

In this paper we reevaluate the returns to education based on the increase in the compulsory schooling age from 14 to 15 in the UK in 1947. We provide a Bayesian fuzzy regression discontinuity approach to infer the effect on earnings for a subset of subjects who turned 14 in a narrow window around the policy change and whose schooling was affected by the policy change. Our approach and our results are quite different from previous work that has focused on large sets of cohorts and 2SLS based approaches and has reported positive earnings and wage effects of 5% and above. Our empirical analysis, using data from the UK General Household Surveys, yields considerably lower earnings and wage effects for the additional year of compulsory schooling than previous work. These findings are consistent with the implementation of the policy change that affected students at the lower end of the schooling distribution and did not lead students to acquire additional qualifications. The results add further evidence to a number of recent studies that have found no effect from this policy change on socio-economic outcomes correlated with earnings.Bayesian inference, causal effects, imperfect compliance, natural experiment, principal stratification, regression discontinuity, returns to schooling

Non-Markovian regime switching with endogenous states and time-varying state strengths

This article presents a non-Markovian regime switching model in which the regime states depend on the sign of an autoregressive latent variable. The magnitude of the latent variable indexes the 'strength' of the state or how deeply the system is embedded in the current regime. In this model, regimes have dynamics, not only persistence, so that one regime can gradually give way to another. In this framework, it is natural to allow the autoregressive latent variable to be endogenous so that regimes are determined jointly with the observed data. We apply the model to GDP growth, as in Hamilton (1989), Albert and Chib (1993) and Filardo and Gordon (1998) to illustrate the relation of the regimes to NBER-dated recessions and the time-varying expected durations of regimes. The article makes use of the Metropolis-Hastings algorithm to make multi-move draws of the latent regime strength variable, where the extended Kalman filter provides a valid proposal density for the latent variable.Time-series analysis ; Business cycles

Posterior inference on the degrees of freedom parameter in multivariate-t regression models

Economics

Regression models under competing covariance matrices: A Bayesian perspective

Economics

A Bayesian note on competing correlation structures in the dynamic linear regression model

Economics