Not Just for Cointegration: Error Correction Models with Stationary Data

The error correction model is generally thought to be isomorphic to integrated data and the modeling of cointegrated processes, and as such, is considered inappropriate for stationary data. Given that many political time series are not integrated, analysts are unable to take advantages of the error correction model’s ability to capture both long and short-term dynamics in a single statistical model. We use analytical results to demonstrate that error correction models are appropriate for stationary data. We use simulated data to then demonstrate the equivalency between auto-distributed lag models and error correction models. Finally, we reestimate a model of Supreme Court approval from the literature to demonstrate how the use of an error correction model enhances our understanding of political dynamics. In 1993, Political Analysis published a series of articles designed to introduce cointegration and error correction models to the political science literature. This set of six articles is perhaps one of the best introductions to cointegration and error correction methods in print. But what is particularly interesting in this set of articles, besides the lucid introduction to cointegration, is the debate that develops among the authors on what is by-and-large considered to be a non-controversial statistical technique in disciplines outside political science whether error correction models are suitable for stationary data. Two of the authors maintain that error correction models were developed prior to the theory of cointegration and are flexible enough to model stationary data that are long-memoried (Beck 1993; Williams 1993). Other authors argue that cointegration implies error correction and that error correction models in turn imply cointegration. As such, they see error correction models as unsuitable for stationary data (Durr 1993a,b; Smith 1993). As Smith (1993) argues, while error correction models predate the theory of cointegration, the data modeled with early error correction mechanisms were almost certainty cointegrated. This debate over error correction and stationary data is peripheral to the central points in these articles, and the debate remains unresolved. But this controversy has substantive implications for not just how time series data are modeled, but also for how theories of political dynamics are developed. Apart from the desire to apply the most suitable modeling strategy, error correction models also offer the important benefit of allowing estimation of both short and long-term effects. For analysts, this allows consideration of theories where the dynamic effects include both short-term shocks and longer equilibrium forces. But given the paucity of true cointegrating relationships in political data, the power of error correction models is either lost to most applied analysts in political science or requires tortured arguments for cointegration. In this paper, we take up the debate raised in that issue of Political Analysis, in order to investigate the properties of error correction models when used with stationary data. In doing so, we offer applied analysts a new tool that can change the way we think about political dynamics. 1 Error Correction and Cointegration The tight linkage between cointegration and error correction models stems from the Granger representation theorem. According to this theorem, two or more integrated time series that are cointegrated have an error correction representation, and two or more time