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Two-Stage Estimation of Non-Recursive Choice Models Alvarez, R. Michael Glasgow, Garrett Uploaded 03-02-1999 Keywords two-stage estimation probit endogeneity two-stage probit least squares two-stage conditional maximum likelihood Abstract Questions of causation are important issues in empirical research on political behavior. Most of the discussion of the econometric problems associated with multi-equation models with reciprocal causation has focused on models with continuous dependent variables (e.g. Markus and Converse 1979; Page and Jones 1979). Yet many models of political behavior involve discrete or dichotomous dependent variables; this paper describes two techniques which can consistently estimate reciprocal relationships between dichotomous and continuous dependent variables. The first, two-stage probit least squares (2SPLS), is very similar to two-stage instrumental variable techniques. The second, two-stage conditional maximum likelihood (2SCML), may overcome problems associated with 2SPLS, but has not been used in the political science literature. First, we demonstrate the potential pitfalls of ignoring the problems of reciprocal causation in non-recursive choice models. Then, we show the properties of both techniques using Monte Carlo simulations: both the two-stage models perform well in large samples, but in small samples the 2SPLS model has superior statistical properties. However, the 2SCML model offers an explicit statistical test for endogeneity. Last, we apply these techniques to an empirical example which focuses on the relationship between voter preferences in a presidential election and the voter's uncertainty about the policy positions taken by the candidates. This example demonstrates the importance of these techniques for political science research.

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The Revolution Against Affirmative Action in California: Politics, Economics, and Proposition 209 Alvarez, R. Michael Butterfield, Tara L. Uploaded 04-14-1998 Keywords discrete choice endogeneity generalized extreme value affirmative action race and politics California politics Abstract We consider two possible explanations --- economic anxiety and racial division --- for the appeal of Proposition 209 to California voters during the 1996 election. To test these hypotheses, we analyze voter exit poll data from teh 1996 California election. We utiliize a two--stage logit model to allow for the endogeneity of candidate endorsements. We find support for the second of our two hypotheses, which leads us to conclude that racial division fueled by a fear of arbitrary exclusion prompted voter support for Proposition 209.

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Advancement in the House of Representatives Wawro, Gregory Uploaded 00-00-0000 Keywords legislative entrepreneurship career concerns legislative institutions mobility Markov models endogeneity maximumlikelihood Abstract (None submitted)

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Explaining Fixed Effects: Random Effects modelling of Time-Series Cross-Sectional and Panel Data Bell, Andrew Jones, Kelvyn Uploaded 07-13-2012 Keywords Random Effects models Fixed Effects models Random coefficient models Mundlak formulation Fixed effects vector decomposition Hausman test Endogeneity Panel Data Time-Series Cross-Sectional Data Abstract This article challenges Fixed Effects (FE) modelling’s status as the ‘default option’ when using time-series-cross-sectional and panel data. We argue that understanding the difference between within- and between-effects of predictor variables is important when considering what modelling strategy to use. The downside of Random Effects (RE) compared to FE modelling – correlation between lower-level covariates and higher-level residuals - is a case of omitted variable bias, readily solvable using a variant of Mundlak’s (1978a) formulation. Consequently, RE modelling provides everything that FE modelling promises, and more. It allows time-invariant variables to be modelled, more parsimoniously than Plümper and Troeger’s (2007) suggested method. It is also readily extendable to Random Coefficients Models, allowing reliable, differential effects of variables without heavy parameterisation, the use of cross-level interactions between time-variant and invariant variables, and the modelling of complex variance functions. We are arguing not simply for technical solutions to endogeneity, but for the substantive importance of modelling context, and RE models’ ability to do so. Two empirical examples show that failing to do this can lead to misleading results. This paper is distinctive in stressing the substantive interpretations of within- and between-effects. This has implications beyond political science, to all datasets with multilevel structures.