Understanding Equation Balance in Time Series Regression: An Extension

Most contributors to a recent Political Analysis symposium on time series analysis suggest that in order to maintain equation balance, one cannot combine stationary, integrated and/or fractionally integrated variables with general error correction models (GECMs) and the equivalent autoregressive distributed lag (ADL) models. This definition of equation balance implicates most previous uses of these models in political science and circumscribes their use moving forward. The claim thus is of real consequence and worthy of empirical substantiation, which the contributors did not provide. Here we address the issue. First, we highlight the difference between estimating unbalanced equations and mixing orders of integration, the former of which clearly is a problem and the latter of which is not, at least not necessarily. Second, we assess some of the consequences of mixing orders of integration by conducting simulations using stationary, integrated, and combined (stationary plus integrated) time series. Our simulations show that with an appropriately specified model, regressing a stationary variable on an integrated one or the reverse does not increase the risk of spurious results and that such regressions can detect true relationships when they exist. We then illustrate the potential importance of these conclusions with an applied example|income inequality in the United States.