George G. Judge

Empirical evidence concerning the finite sample performance of El-type structural equation estimation and inference methods

This paper presents empirical evidence concerning the finite sample performance of conventional and generalized empirical likelihood-type estimators that utilize instruments in the context of linear structural models characterized by endogenous explanatory variables. There are suggestions in the literature that traditional and non-traditional asymptotically efficient estimators based on moment equations may, for the relatively small sample sizes usually encountered in econometric practice, have relatively large biases and/or variances and provide an inadequate basis for estimation and inference. Given this uncertainty we use a range of data sampling processes and Monte Carlo sampling procedures to accumulate finite sample empirical evidence concerning these questions for a family of generalized empirical likelihood-type estimators in comparison to conventional 2SLS and GMM estimators. Solutions to EL-type empirical momentconstrained optimization problems present formidable numerical challenges. We identify effective optimization algorithms for meeting these challenges.

An Information Theoretic Approach to Ecological Estimation and Inference

An Information Theoretic Approach to Ecological Estimation and Inference £ George G. Judge Ý University of California, Berkeley Douglas J. Miller Purdue University Wendy K. Tam Cho University of Illinois £ The authors gratefully acknowledge the many generous comments and suggestions pro- vided by Bruce Cain, David Freedman, Marian Grendar, Gary King, T. C. Lee, Jeffrey Lewis, Ken McCue, Art Owen, and Rogerio Silva de Mattos without implying their agreement with the full content of the paper. Ý Corresponding author: 207 Giannini Hall, University of California, Berkeley, CA

Generalized moment based estimation and inference

In this paper we consider the case of the general linear statistical model, where the stochastic design matrix has the property that its expectation and probability limits with the vector of unobserved disturbances does not equal to a zero vector and moreover, the explanatory and/or instrumental variables are ill-conditioned. In this context, we contemplate generalized moment based estimating functions that may be biased, and for which the corresponding system of moment conditions are overdetermined. To cope with this situation, we propose a new estimator with attractive finite and asymptotic sampling properties and that result in entropic densities on model parameters.

Estimating the Link Function in Multinomial Response Models under Endogeneity

This paper considers estimation and inference for the multinomial response model in the case where endogenous variables are included as arguments of the unknown link function. Semiparametric estimators are proposed that avoid the parametric assumptions underlying the likelihood approach as well as the loss of precision when using nonparametric estimation. The large sample properties of the estimators are also developed in the context of a quasi-likelihood modeling framework.

Combining Estimators to Improve Structural Model Estimation Under Quadratic Loss

Asymptotically, semi parametric estimators of the parameters in linear structural models have the same sampling properties. In finite samples the sampling properties of these estimators vary and large biases may result for sample sizes often found in practice. With a goal of improving asymptotic risk performance and finite sample efficiency properties, we investigate the idea of combining correlated structural equation estimators with different finite and asymptotic sampling characteristics. Based on a quadratic loss measure, we provide a risk domination result and present evidence that the finite sample performance of the resulting combination estimator is superior to that of a leading traditional moment based estimator. A basis for interval estimation and inference for the combination estimator is demonstrated.

Coordinate Based Empirical Likelihood-Like Estimation in Ill-Conditioned Inverse Problems

In the context of a semiparametric regression model with underlying probability distribution unspecified, an extremum estimator formulation is proposed that makes use of empirical likelihood and information theoretic estimation and inference concepts to mitigate the problem of an ill-conditioned design matrix. A squared error loss measure is used to assess estimator performance in finite samples. In large samples, the estimator can be designed to be consistent and asymptotically normal, so that limiting chi-squared distributions provide a basis for hypothesis tests and confidence intervals. Empirical risk results based on a large-scale Monte Carlo sampling experiment suggest that the estimator has, relative to traditional competitors, superior finite-sample properties under a squared error loss measure when the design matrix is ill-conditioned.

Econometric Information Recovery in Behavioral Networks

In this paper we suggest an approach to recovering behavior related, preference-choice network information from observational data. We model the process as a self-organized behavior based random exponential network-graph system. To address the unknown nature of the sampling model in recovering behavior related network information, we use the Cressie-Read (CR) family of divergence measures and the corresponding information theoretic entropy basis, for estimation, inference, model evaluation, and prediction. Examples are included to clarify how entropy based information theoretic methods are directly applicable to recovering the behavioral network probabilities in this fundamentally underdetermined ill posed recovery problem.