Time Series Analysis and Spurious Regression : An Error Correction ∗

For scholars interested in longitudinal analysis, the single-equation (i.e., one way) error correction model (ECM) has become an important analytic tool. The popularity of this method has stemmed, in part, from evidence that the ECM can be applied to both stationary and nonstationary data (e.g., De Boef and Keele, 2008). We highlight an underappreciated aspect of the ECM—when data are integrated or near-integrated, the ECM only avoids the spurious regression problem when (near-)cointegration is present. In fact, spurious regression results emerge close to 20 percent of the time when integrated or near integrated data that are not cointegrated are analyzed with an ECM. Given the near absence of cointegration tests in recent political science publications, we believe this is a fundamental point to emphasize. We also show, however, that when evidence of cointegration is present, the ECM performs well across a variety of data scenarios that political scientists are likely to encounter. ∗All files necessary to replicate our simulations and produce the figures and tables in this manuscript are available at: http://thedata.harvard. edu/dvn/dv/ECM. As political scientists, we are often interested in change. Why has inequality increased? Why do some authoritarian regimes persist and others transition to democracy? Why do attitudes toward the death penalty, immigration, or welfare vary over time? For researchers with an empirical approach to these types of political dynamics, the single equation (i.e., one way) error correction model (ECM) has become a popular analytic tool. The popularity of the ECM stems, in large part, from the long standing concern of observing “nonsensecorrelations” (Yule, 1926) or “spurious regression” (Granger and Newbold, 1974) in nonstationary time series. In fact, one of the most common reasons scholars cite for selecting the ECM is its applicability to nonstationary data (See, for example, Enns and McAvoy (2012, 634), Hellwig (2007, 150), Kayser (2009, 957), Kelly (2005, 873), Kono (2007, 751), McGuire (2004, 133), Ramirez (2009, 686), Voeten and Brewer (2006, 820)). In this article we demonstrate that despite attempts to avoid spurious findings, many prominent applications do not correctly apply the single equation ECM and thus the analyses do not fully address the spurious regression problem. Nathaniel Beck’s (1991) “Comparing Dynamic Specifications” and a subsequent Political Analysis symposium on error correction models (Beck, 1992; Durr, 1992a; Durr, 1992b; Ostrom and Smith, 1992; Smith, 1992; Williams, 1992) helped introduce ECMs to the political science community. Following the work of Clive Granger and Robert Engle (e.g., Granger, 1986; Engle and Granger, 1987), these articles emphasized the connection between integration, cointegration, and error correction. That is, if two (or more) series are integrated and they maintain a long run equilibrium relationship (i.e., they are cointegrated), this process can be specified with an error correction model. Smith (1992, 253-254), for example, explained, “Although Davidson et al. (1978) popularized the ECM before the concept of All of our analyses focus on standard time series models, but the arguments are also relevant to time series cross sectional analysis. A classic example of two integrated series that are also cointegrated is a drunk walking a dog (Murray, 1994). The path of the drunk and the dog each reflect an integrated time series, where the position at each time point is a function of the position at the previous time point plus the current stochastic step (integrated time series are often referred to as “random walks” or as having a “unit root”). Now, suppose every time the drunk calls for the dog, the dog moves a little closer to the drunk and every time the dog barks, the drunk aims in the direction of the dog. These movements represent the “error correction” and keep the two