Switching Regressions with Imperfect Regime Classification Information: Theory and Applications
by
Vassilis Hajivassiliou
November 2019
Abstract
This paper discusses switching regressions econometric modelling with imperfect regime classification information. The econometric novelty is that misclassification probabilities are allowed to vary endogenously over time. Standard maximum likelihood estimation is infeasible in this case because each likelihood contribution requires the evaluation of 2 T terms (where T is the number of observations available). We develop an algorithm that allows efficient estimation when such imperfect information is available, by evaluating the exact likelihood through simply T matrix multiplications (each of a 2 2 matrix times a 2 1 vector.) Our methods are shown to be widely applicable to various areas of economic analysis such as to Hamilton's work on Markov-Switching models in Macroeconomics; to external financing problems faced by firms in Corporate Finance; and to game-theoretic models of price collusion in Industrial Organization. We proceed to apply our methods to analyze price fixing by the Joint Executive Committee railroad cartel from 1880 to 1886 and develop tests of two prototypical game-theoretic models of tacit collusion. The first model, due to Abreu, Pearce and Stacchetti (1986), predicts that price will switch across regimes according to a Markov process. The second model, by Rotemberg and Saloner (1986), concludes that price wars are more likely in periods of high industry demand. Switching regressions are used to model the firms shifting between collusive and punishment behaviour. The JEC data set is expanded to include measures of grain production to be shipped and availability of substitute transportation services. Our findings cast doubt on the applicability of the Rotemberg and Saloner model to the JEC railroad cartel, while they confirm the Markovian prediction of the Abreu et al. model.
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