Stein-like 2SLS estimator

ABSTRACT

Maasoumi (1978 Maasoumi, E. (1978). A modified Stein-like estimator for the reduced form coefficients of simultaneous equations. Econometrica 46:695–703.[Crossref], [Web of Science ®] , [Google Scholar]) proposed a Stein-like estimator for simultaneous equations and showed that his Stein shrinkage estimator has bounded finite sample risk, unlike the three-stage least square estimator. We revisit his proposal by investigating Stein-like shrinkage in the context of two-stage least square (2SLS) estimation of a structural parameter. Our estimator follows Maasoumi (1978 Maasoumi, E. (1978). A modified Stein-like estimator for the reduced form coefficients of simultaneous equations. Econometrica 46:695–703.[Crossref], [Web of Science ®] , [Google Scholar]) in taking a weighted average of the 2SLS and ordinary least square estimators, with the weight depending inversely on the Hausman (1978 Hausman, J. A. (1978). Specification tests in econometrics. Econometrica 46:1251–1271.[Crossref], [Web of Science ®] , [Google Scholar]) statistic for exogeneity. Using a local-to-exogenous asymptotic theory, we derive the asymptotic distribution of the Stein estimator and calculate its asymptotic risk. We find that if the number of endogenous variables exceeds 2, then the shrinkage estimator has strictly smaller risk than the 2SLS estimator, extending the classic result of James and Stein (1961 James W, ., Stein, C. M. (1961). Estimation with quadratic loss. Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability 1:361–380. [Google Scholar]). In a simple simulation experiment, we show that the shrinkage estimator has substantially reduced finite sample median squared error relative to the standard 2SLS estimator.     

The Importance of Status Legitimacy for Intergroup Attitudes Among Numerical Minorities

This study investigated whether the legitimacy of the status structure influences the interactive effects of group status and numerical representation on intergroup attitudes. Participants were randomly assigned to conditions in a 2 (level of status; high, low) by 2 (legitimacy of status; legitimate, illegitimate) by 2 (numerical representation; majority, minority) between-subjects design. The predicted three-way interaction indicated that, when status was illegitimate, majority groups with high status showed more ingroup bias than majority groups with low status, but minority groups with high status did not show more ingroup bias than their counterparts with low status. By comparison, when status was legitimate, high-status groups were more biased than low-status groups, regardless of numerical representation.     

On Extending Russell and Krajewski's Algorithm for Economic Purchase Order Quantities*

Russell and Krajewski presented an optimal purchase order quantity algorithm that considered the effect of the transportation rate structure for less-than-truckload (LTL) shipments. The authors applied the Russell and Krajewski algorithm to a variety of freight classes and lengths-of-haul. Anomalous cases were found in which the freight rate schedule, when used with the suggested algorithm, resulted in incorrect order size decisions. In this comment, the authors consider the impact of these anomalies on the optimal order quantity and associated total costs. A procedure is presented to adjust the Russell and Krajewski algorithm to arrive at the optimal purchase order quantity and the lowest total annual cost.     

Likelihood inference for exchangeable continuous data with covariates and varying cluster sizes; use of the Farlie–Gumbel–Morgenstern model

This article investigates the Farlie–Gumbel–Morgenstern class of models for exchangeable continuous data. We show how the model specification can account for both individual and cluster level covariates, we derive insights from comparisons with the multivariate normal distribution, and we discuss maximum likelihood inference when a sample of independent clusters of varying sizes is available. We propose a method for maximum likelihood estimation which is an alternative to direct numerical maximization of the likelihood that sometimes exhibits non-convergence problems. We describe an algorithm for generating samples from the exchangeable multivariate Farlie–Gumbel–Morgenstern distribution with any marginals, using the structural properties of the distribution. Finally, we present the results of a simulation study designed to assess the properties of the maximum likelihood estimators, and we illustrate the use of the FGM distributions with the analysis of a small data set from a developmental toxicity study.     

Do Generous Welfare States Generate Efficiency Gains which Counterbalance Short Run Losses? Testing Downside Risk Theory with Economic Panel Data for the U.S., Germany and The Netherlands

The purpose of the paper is to assess the theory that the downside risk insurance provided by more generous welfare states generates long run efficiency gains, which counterbalance the short run efficiency losses caused by work disincentives in these states (Feldstein 1974, 1976; Sinn 1995, 1996). Testing downside risk theory requires long term data, so the paper makes use of the three longest running national socio-economic panel surveys. These are the American Panel Study of Income Dynamics (PSID, 1968-), the German Socio-Economic Panel (1984-) and the Dutch Socio-Economic Panel (SEP, 1984-). The paper focusses on prime age households (heads 25–59) and assesses their participation in and returns to adult education and job training. Our results indicate some support for the theory in so far as Dutch and German prime age adults, living in more generous welfare states, were much more likely than Americans to take the risk of foregoing current earnings and investing in additional education. In all three countries returns on investment were substantial.

Pet Dogs Benefit Owners’ Health: A ‘Natural Experiment’ in China

This paper reports results from a ‘natural experiment’ taking place in China on the impact of dogs on owners’ health. Previous Western research has reported modest health benefits, but results have remained controversial. In China pets were banned in urban areas until 1992. Since then dog ownership has grown quite rapidly in the major cities, especially among younger women. In these quasi-experimental conditions, we hypothesise that dog ownership will show greater health benefits than in the West. Results are given from a survey of women aged 25–40 in Beijing, Shanghai and Guangzhou (N = 3031). Half the respondents owned dogs and half did not. Owners reported better health-related outcomes. They exercised more frequently, slept better, had higher self-reported fitness and health, took fewer days off sick from work and were seen less by doctors. The concluding section indicates how these results may be integrated and suggests further research on the potential economic benefits of pets.