Error Correction, Attractors, and Cointegration: Substantive and Methodological Issues

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Abstract
I am pleased to participate in this symposium because I agree that mutual criticism of our theories and of the methods used to test them helps to make social science objective and rational (Popper 1976). Space limitations preclude me from responding to all of the comments and suggestions of Beck and Williams (in this volume), but my interpretation of their key points is as follows: (1) estimating multiequation error correction models (ECMs) is unnecessary either because many theories provide us with exogeneity restrictions that imply single equation ECMs (Beck) or because statistical inference is unaffected by integration and cointegration in vector autoregressive systems (Williams); (2) using OLS in one step to estimate a single equation ECM is statistically superior to using the Engle-Granger two-step estimator (Beck); (3) commonly used classical hypothesis tests for nonstationarity favor the null hypothesis of a unit root, and therefore cannot be believed, but Bayesian inference with a flat prior solves this and other problems of inference (Williams); and (4) presidential approval is neither statistically nor conceptually an integrated random walk, but is either long memoried (Beck) or stationary (Williams). These are thought-provoking comments, and to one of them I will reply mea culpa. However, some of them need to be qualified, and others are incorrect. I begin by responding to comments (1) and (2) assuming that two or more time-series are integrated and cointegrated and then address comments (3) and (4), which question assumptions of and tests for integration and cointegration.