Creator: Geweke, John and Keane, Michael P. Series: Staff report (Federal Reserve Bank of Minneapolis. Research Department) Number: 233 Abstract:
This study uses data from the Panel Survey of Income Dynamics (PSID) to address a number of questions about life cycle earnings mobility. It develops a dynamic reduced form model of earnings and marital status that is nonstationary over the life cycle. The study reaches several firm conclusions about life cycle earnings mobility. Incorporating non-Gaussian shocks makes it possible to account for transitions between low and higher earnings states, a heretofore unresolved problem. The non-Gaussian distribution substantially increases the lifetime return to post-secondary education, and substantially reduces differences in lifetime wages attributable to race. In a given year, the majority of variance in earnings not accounted for by race, education and age is due to transitory shocks, but over a lifetime the majority is due to unobserved individual heterogeneity. Consequently, low earnings at early ages are strong predictors of low earnings later in life, even conditioning on observed individual characteristics.
Creator: Geweke, John and Keane, Michael P. Series: Staff report (Federal Reserve Bank of Minneapolis. Research Department) Number: 237 Abstract:
This paper generalizes the normal probit model of dichotomous choice by introducing mixtures of normals distributions for the disturbance term. By mixing on both the mean and variance parameters and by increasing the number of distributions in the mixture these models effectively remove the normality assumption and are much closer to semiparametric models. When a Bayesian approach is taken, there is an exact finite-sample distribution theory for the choice probability conditional on the covariates. The paper uses artificial data to show how posterior odds ratios can discriminate between normal and nonnormal distributions in probit models. The method is also applied to female labor force participation decisions in a sample with 1,555 observations from the PSID. In this application, Bayes factors strongly favor mixture of normals probit models over the conventional probit model, and the most favored models have mixtures of four normal distributions for the disturbance term.
Keyword: Normal mixture, Discrete choice, and Markov chain Monte Carlo Subject (JEL): C25 - Single Equation Models; Single Variables: Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities and C11 - Bayesian Analysis: General
Creator: Geweke, John Series: Staff report (Federal Reserve Bank of Minneapolis. Research Department) Number: 148 Abstract:
Data augmentation and Gibbs sampling are two closely related, sampling-based approaches to the calculation of posterior moments. The fact that each produces a sample whose constituents are neither independent nor identically distributed complicates the assessment of convergence and numerical accuracy of the approximations to the expected value of functions of interest under the posterior. In this paper methods for spectral analysis are used to evaluate numerical accuracy formally and construct diagnostics for convergence. These methods are illustrated in the normal linear model with informative priors, and in the Tobit-censored regression model.
Creator: Geweke, John, Keane, Michael P., and Runkle, David Edward Series: Staff report (Federal Reserve Bank of Minneapolis. Research Department) Number: 170 Abstract:
This research compares several approaches to inference in the multinomial probit model, based on Monte-Carlo results for a seven choice model. The experiment compares the simulated maximum likelihood estimator using the GHK recursive probability simulator, the method of simulated moments estimator using the GHK recursive simulator and kernel-smoothed frequency simulators, and posterior means using a Gibbs sampling-data augmentation algorithm. Each estimator is applied in nine different models, which have from 1 to 40 free parameters. The performance of all estimators is found to be satisfactory. However, the results indicate that the method of simulated moments estimator with the kernel-smoothed frequency simulator does not perform quite as well as the other three methods. Among those three, the Gibbs sampling-data augmentation algorithm appears to have a slight overall edge, with the relative performance of MSM and SML based on the GHK simulator difficult to determine.
Creator: Geweke, John, Keane, Michael P., and Runkle, David Edward Series: Staff report (Federal Reserve Bank of Minneapolis. Research Department) Number: 177 Abstract:
Statistical inference in multinomial multiperiod probit models has been hindered in the past by the high dimensional numerical integrations necessary to form the likelihood functions, posterior distributions, or moment conditions in these models. We describe three alternative approaches to inference that circumvent the integration problem: Bayesian inference using Gibbs sampling and data augmentation to compute posterior moments, simulated maximum likelihood (SML) estimation using the GHK recursive probability simulator, and method of simulated moment (MSM) estimation using the GHK simulator. We perform a set of Monte-Carlo experiments to compare the performance of these approaches. Although all the methods perform reasonably well, some important differences emerge. The root mean square errors (RMSEs) of the SML parameter estimates around the data generating values exceed those of the MSM estimates by 21 percent on average, while the RMSEs of the MSM estimates exceed those of the posterior parameter means obtained via agreement via Gibbs sampling by 18 percent on average. While MSM produces a good agreement between empirical RMSEs and asymptotic standard errors, the RMSEs of the SML estimates exceed the asymptotic standard errors by 28 percent on average. Also, the SML estimates of serial correlation parameters exhibit significant downward bias.
Keyword: Panel data, Discrete choice, Bayesian inference, Method of simulated moments, Simulated maximum likelihood, and Gibbs sampling Subject (JEL): C35 - Multiple or Simultaneous Equation Models: Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions and C15 - Statistical Simulation Methods: General
Creator: Geweke, John and Zhou, Guofo Series: Staff report (Federal Reserve Bank of Minneapolis. Research Department) Number: 189 Abstract:
This paper provides an exact Bayesian framework for analyzing the arbitrage pricing theory (APT). Based on the Gibbs sampler, we show how to obtain the exact posterior distributions for functions of interest in the factor model. In particular, we propose a measure of the APT pricing deviations and obtain its exact posterior distribution. Using monthly portfolio returns grouped by industry and market capitalization, we find that there is little improvement in reducing the pricing errors by including more factors beyond the first one.
Subject (JEL): G10 - General Financial Markets: General (includes Measurement and Data)
Creator: Geweke, John Series: Staff report (Federal Reserve Bank of Minneapolis. Research Department) Number: 192 Abstract:
This is a survey of simulation methods in economics, with a specific focus on integration problems. It describes acceptance methods, importance sampling procedures, and Markov chain Monte Carlo methods for simulation from univariate and multivariate distributions and their application to the approximation of integrals. The exposition gives emphasis to combinations of different approaches and assessment of the accuracy of numerical approximations to integrals and expectations. The survey illustrates these procedures with applications to simulation and integration problems in economics.
Creator: Geweke, John Series: Staff report (Federal Reserve Bank of Minneapolis. Research Department) Number: 249 Abstract:
This paper surveys the fundamental principles of subjective Bayesian inference in econometrics and the implementation of those principles using posterior simulation methods. The emphasis is on the combination of models and the development of predictive distributions. Moving beyond conditioning on a fixed number of completely specified models, the paper introduces subjective Bayesian tools for formal comparison of these models with as yet incompletely specified models. The paper then shows how posterior simulators can facilitate communication between investigators (for example, econometricians) on the one hand and remote clients (for example, decision makers) on the other, enabling clients to vary the prior distributions and functions of interest employed by investigators. A theme of the paper is the practicality of subjective Bayesian methods. To this end, the paper describes publicly available software for Bayesian inference, model development, and communication and provides illustrations using two simple econometric models.
Creator: Chin, Daniel M., Geweke, John, and Miller, Preston J. Series: Staff report (Federal Reserve Bank of Minneapolis. Research Department) Number: 267 Abstract:
This paper presents a new method for predicting turning points. The paper formally defines a turning point; develops a probit model for estimating the probability of a turning point; and then examines both the in-sample and out-of-sample forecasting performance of the model. The model performs better than some other methods for predicting turning points.
Creator: Geweke, John Series: Working paper (Federal Reserve Bank of Minneapolis. Research Department) Number: 539 Abstract:
In the specification of linear regression models it is common to indicate a list of candidate variables from which a subset enters the model with nonzero coefficients. This paper interprets this specification as a mixed continuous-discrete prior distribution for coefficient values. It then utilizes a Gibbs sampler to construct posterior moments. It is shown how this method can incorporate sign constraints and provide posterior probabilities for all possible subsets of regressors. The methods are illustrated using some standard data sets.