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This paper is about estimating the parameters of the exponential random graph model, also known as the p # model, using frequentist Markov chain Monte Carlo (MCMC) methods. The exponential random graph model is simulated using Gibbs or Metropolis-Hastings sampling. The estimation procedures considered are based on the Robbins-Monro algorithm for approximating a solution to the likelihood equation.

The construction and implementation of a Gibbs sampler for efficient simulation from the truncated multivariate normal and Student-t distributions is described. It is shown how the accuracy and convergence of integrals based on the Gibbs sample may be constructed, and how an estimate of the probability of the constraint set under the unrestricted distribution may be produced. Keywords: Bayesian inference; Gibbs sampler; Monte Carlo; multiple integration; truncated normal This paper was prepared for a presentation at the meeting Computing Science and Statistics: the Twenty-Third Symposium on the Interface, Seattle, April 22-24, 1991. Research assistance from Zhenyu Wang and financial support from National Science Foundation Grant SES-8908365 are gratefully acknowledged. The software for the examples may be requested by electronic mail, and will be returned by that medium. 2 1. Introduction The generation of random samples from a truncated multivariate normal distribution, that is, a ...

ABSTRACT: This paper studies alternative empirical strategies for estimating the effects of organizational design practices on performance, as well as the factors which determine organizational design, in a cross-section of firms. In particular, we propose an approach for estimating the parameters of an “organizational design production function. ” Further, we identify consistent tests for two classes of hypotheses: first, that some sets of organizational design practices are mutually complementary; and second, that adoption patterns are consistent with static optimization of the organization’s profit. We develop an economic model where multiple organizational design practices are endogenously determined. The model includes exogenous variation in the costs and returns to each of the individual practices, which is the source of the heterogeneity among organizations. In many empirical applications, some of these variables will be unobserved to the econometrician. The model is used to evaluate how different econometric strategies can be interpreted under alternative assumptions about the economic and statistical environment. Of particular interest are a set of results which demonstrate that, under plausible hypotheses about the joint distribution of the unobservables, different reduced-form approaches used in the existing literature to test

We develop new methods for conducting a finite sample, likelihood-based analysis of the multinomial probit model. Using a variant of the Gibbs sampler, an algorithm is developed to draw from the exact posterior of the multinomial probit model with correlated errors. This approach avoids direct evaluation of the likelihood and, thus, avoids the problems associated with calculating choice probabilities which affect both the standard likelihood and method of simulated moments approaches. Both simulated and actual consumer panel data are used to fit six-dimensional choice models. We also develop methods for analyzing random coefficient and multiperiod probit models.

This paper shows how particle filtering facilitates likelihood-based inference in dynamic macroeconomic models. The economies can be nonlinear and/or nonnormal. We describe how to use the output from the particle filter to estimate the structural parameters of the model, those characterizing preferences and technology, and to compare different economies. Both tasks can be implemented from either a classical or a Bayesian perspective. We illustrate the technique by estimating a business cycle model with investment-specific technological change, preference shocks, and stochastic volatility.

Self-selected migration presents one potential explanation for why observed returns to a college education in local labor markets vary widely even though U.S. workers are highly mobile. To assess the impact of self-selection on estimated returns, this paper first develops a Roy model of mobility and earnings where workers choose in which of the 50 states (plus the District of Columbia) to live and work. Available estimation methods are either infeasible for a selection model with so many alternatives or place potentially severe restrictions on earnings and the selection process. This paper develops an alternative econometric methodology which combines Lee's (1983) parametric maximum order statistic approach to reduce the dimensionality of the error terms with more recent work on semiparametric estimation of selection models (e.g., Ahn and Powell, 1993). The resulting semiparametric correction is easy to implement and can be adapted to a variety of other polychotomous choice problems. The empirical work, which uses 1990 U.S. Census data, confirms the role of comparative advantage in mobility decisions. The results suggest that self-selection of higher educated individuals to states with higher returns to education generally leads to upward biases in OLS estimates of the returns to education in state-specific labor markets. While the estimated returns to a college education are significantly biased, correcting for the bias does not narrow the range of returns across states. Consistent with the finding that the corrected return to a college education differs across the U.S., the relative state-to-state migration flows of college- versus high school-educated individuals respond strongly to differences in the return to education and amenities across states.

ome detail more recent developments in the economic theory of choice, and modifications to this theory that are being forced by experimental evidence from cognitive psychology. I will close with a survey of statistical methods that have developed as part of the research program on economic choice behavior. Science is a cooperative enterprise, and my work on choice behavior reflects not only my own ideas, but the results of exchange and collaboration with many other scholars. 1 First, of course, is my co-laureate James Heckman, who among his many contributions pioneered the important area of dynamic discrete choice analysis. Nine other individuals who played a major role in channeling microeconometrics and choice theory toward their modern forms, and had a particularly important influence on my own work, are Zvi Griliches, L.L. Thurstone, Jacob Marschak, Duncan Luce, Danny Kahneman, Amos Tversky, Moshe Ben-Akiva, Charles Manski, and Kenneth Train. A gallery of their p

Retail markets constitute a large fraction of the economy in all industrialized countries. Yet economists know little about the way dispersed buyers and sellers aect the properties of markets. I attempt to answer several questions here. First, to what degree does geographic dierentiation provide retail stores with market power? Second, what are the implications of consumer borne travel costs and business stealing, which each result in dierences between private and social objectives, on store location and scale decisions. Using new data from movie theaters I estimate a random utility discrete choice model of retail demand in which products are location specic and consumers have preferences over product characteristics. Using simulation methods I show how to incorporate data from the decennial census into an econometric model of retail demand. Census data provide a detailed description of the geographic distribution of consumers, of their demographic characteristics and, implicitly,...

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