Application of Theil group logit methods to district-level vote shares: tests of prospective and retrospective voting in the 1991, 1993, and 1997 Polish elections

Political scientists often wish to test hypotheses in the context of district-level vote-share models of elections involving more than two parties. Although a group logit framework for estimating such models was developed many years ago by Henri Theil, the complexity of its variance–covariance structure has prevented it from being widely applied. The authors demonstrate how data can be transformed to take account of the Theil variance–covariance structure so that seemingly unrelated regression can be used to estimate vote-share equations on either an intra- or inter-election basis. This method offers a simpler and more accessible way to analyze multiparty elections than the method proposed recently by Katz and King [Am. Polit. Sci. Rev. 97 (1999) 15]. The demonstration involves testing hypotheses about incumbency (retrospective) and policy (prospective) voting in the 1991, 1993, and 1997 Polish elections. The authors find that the estimations favor the policy voting hypothesis.