Simulating Correlated Multivariate Pseudorandom Numbers

A modification of the Kaiser and Dichman (1962) procedure of generating multivariate random numbers with specified intercorrelation is proposed. The procedure works with positive and non-positive definite population correlation matrix. A SAS module is also provided to run the procedure.

Another Look at what to do with Time-series Cross-section Data

Our study revisits Beck and Katz' (1995) comparison of the Parks and PCSE estimators using time-series, cross-sectional data (TSCS). Our innovation is that we construct simulated statistical environments that are designed to approximate actual TSCS data. We pattern our statistical environments after income and tax data on U.S. states from 1960-1999. While PCSE generally does a better job than Parks in estimating standard errors/confidence intervals, it too can be unreliable, sometimes producing standard errors/confidence intervals that are substantially off the mark. Further, we find that the benefits of PCSE can come at a large cost in estimator efficiency.Panel data, Parks model; PCSE estimator; Monte Carlo methods

Bayesian Estimation Under Informative Sampling

Bayesian analysis is increasingly popular for use in social science and other application areas where the data are observations from an informative sample. An informative sampling design leads to inclusion probabilities that are correlated with the response variable of interest. Model inference performed on the observed sample taken from the population will be biased for the population generative model under informative sampling since the balance of information in the sample data is different from that for the population. Typical approaches to account for an informative sampling design under Bayesian estimation are often difficult to implement because they require re-parameterization of the hypothesized generating model, or focus on design, rather than model-based, inference. We propose to construct a pseudo-posterior distribution that utilizes sampling weights based on the marginal inclusion probabilities to exponentiate the likelihood contribution of each sampled unit, which weights the information in the sample back to the population. Our approach provides a nearly automated estimation procedure applicable to any model specified by the data analyst for the population and retains the population model parameterization and posterior sampling geometry. We construct conditions on known marginal and pairwise inclusion probabilities that define a class of sampling designs where $L_{1}$ consistency of the pseudo posterior is guaranteed. We demonstrate our method on an application concerning the Bureau of Labor Statistics Job Openings and Labor Turnover Survey.Comment: 24 pages, 3 figure

Another Look At What To Do With Time-Series Cross-Section Data

Our study revisits Beck and Katz’ (1995) comparison of the Parks and PCSE estimators using time-series, cross-sectional data (TSCS). Our innovation is that we construct simulated statistical environments that are designed to closely match “real-world,” TSCS data. We pattern our statistical environments after income and tax data on U.S. states from 1960-1999. While PCSE generally does a better job than Parks in estimating standard errors, it too can be unreliable, sometimes producing standard errors that are substantially off the mark. Further, we find that the benefits of PCSE can come at a substantial cost in estimator efficiency. Based on our study, we would give the following advice to researchers using TSCS data: Given a choice between Parks and PCSE, we recommend that researchers use PCSE for hypothesis testing, and Parks if their primary interest is accurate coefficient estimates.Panel Data, Panel Corrected Standard Errors, Monte Carlo analysis

Issues and Observations on Applications of the Constrained-Path Monte Carlo Method to Many-Fermion Systems

We report several important observations that underscore the distinctions between the constrained-path Monte Carlo method and the continuum and lattice versions of the fixed-node method. The main distinctions stem from the differences in the state space in which the random walk occurs and in the manner in which the random walkers are constrained. One consequence is that in the constrained-path method the so-called mixed estimator for the energy is not an upper bound to the exact energy, as previously claimed. Several ways of producing an energy upper bound are given, and relevant methodological aspects are illustrated with simple examples.Comment: 28 pages, REVTEX, 5 ps figure

Scalable Rejection Sampling for Bayesian Hierarchical Models

Bayesian hierarchical modeling is a popular approach to capturing unobserved heterogeneity across individual units. However, standard estimation methods such as Markov chain Monte Carlo (MCMC) can be impracticable for modeling outcomes from a large number of units. We develop a new method to sample from posterior distributions of Bayesian models, without using MCMC. Samples are independent, so they can be collected in parallel, and we do not need to be concerned with issues like chain convergence and autocorrelation. The algorithm is scalable under the weak assumption that individual units are conditionally independent, making it applicable for large datasets. It can also be used to compute marginal likelihoods

A Monte Carlo Evaluation of Some Common Panel Data Estimators when Serial Correlation and Cross-sectional Dependence are Both Present

This study employs Monte Carlo experiments to evaluate the performances of a number of common panel data estimators when serial correlation and cross-sectional dependence are both present. It focuses on fixed effects models with less than 100 cross-sectional units and between 10 and 25 time periods (such as are commonly employed in empirical growth studies). Estimator performance is compared on two dimensions: (i) root mean square error and (ii) accuracy of estimated confidence intervals. An innovation of our study is that our simulated panel data sets are designed to look like “real-world” panel data. We find large differences in the performances of the respective estimators. Further, estimators that perform well on efficiency grounds may perform poorly when estimating confidence intervals, and vice versa. Our experimental results form the basis for a set of estimator recommendations. These are applied to “out of sample” simulated panel data sets and found to perform well.Panel Data estimation; Monte Carlo analysis; FGLS; PCSE; Groupwise Heteroscedasticity; Serial Correlation; Cross-sectional Dependence; Stata; EViews