Testing for Cointegrating Relationships with Near-Integrated Data

Abstract

Testing theories about political change requires analysts to make assumptions about the memory of their time series. Applied analyses are often based on inferences that time series are integrated and cointegrated. Typically analyses rest on Dickey—Fuller pretests for unit roots and a test for cointegration based on the Engle—Granger two-step method. We argue that this approach is not a good one and use Monte Carlo analysis to show that these tests can lead analysts to conclude falsely that the data are cointegrated (or nearly cointegrated) when the data are near-integrated and not cointegrating. Further, analysts are likely to conclude falsely that the relationship is not cointegrated when it is. We show how inferences are highly sensitive to sample size and the signal-to-noise ratio in the data. We suggest three things. First, analysts should use the single equation error correction test for cointegrating relationships; second, caution is in order in all cases where near-integration is a reasonable alternative to unit roots; and third, analysts should drop the language of cointegration in many cases and adopt single-equation error correction models when the theory of error correction is relevant.

The Rise of the Super-Rich

“…Third, ECMs accommodate stationary and integrated variables, which is useful because our analysis has a mix of both data types. In summary, the ECM is a very general model that is easy to implement and estimate, does not impose assumptions about cointegration, and can be applied to both stationary and nonstationary data (Banerjee et al 1993;De Boef and Granato 1999;De Boef and Keele 2008). 16 In this study we estimate single-equation ECMs, which are among the most flexible models of the error correction process.…”

The Dynamics of Political Attention: Public Opinion and the Queen's Speech in the United Kingdom

“…The presence of cointegration in political relationships remains contentious, while reliance upon the Engle-Granger two-step procedure has been shown to be problematic (De Boef and Granato 1999). Furthermore, most diagnostic tests for unit root possess low power against local alternatives Granato 1997, 1999), meaning it tends to be difficult to ascertain whether series are (co)integrated with confidence.…”

Access to Protection: Domestic Institutions and Trade Policy in Democracies

“…while permanent changes in the independent variables will change the equilibrium level of the dependent variable~as measured by the level variables!+ 52+ ECMs have traditionally been used when cointegration is present, which exists when two or more variables have unit roots that determine each other+ The search for unit roots in tariff data has often preoccupied previous researchers, such as Lohmann and O'Halloran 1994+ However, given that tariffs are bounded, unit roots are not technically possible+ Instead, tariffs are probably near-integrated+ See De Boef and Granato 1999;and De Boef 2000+ However, as Beck 1991argues, and De Boef and Keele 2004 proves, ECMs can be used even when unit roots or cointegration are not present+ 53+ The larger institutional changes, such as presidentialism, the number of electoral districts, pooling, and bicameralism, are only entered in levels, which means I can only examine long-term dynamics for these variables+ This is because these institutions rarely change within countries and, when they do, the political landscape is likely to be undergoing such radical change that policymakers are not focusing on changing trade policy in the immediate aftermath+ Inclusion of differenced variables, though, do not change the results presented below+ the miscoded tariff rates in the United Kingdom+ 54 The coefficients on the differenced, that is, change, variables are the short-term effects of these variables+ The coefficients on the lagged levels are used to determine the long-term effects by dividing this coefficient by~Ϫb 1 !+ 55 are economic control variables, which are followed by the political variables of interest~b 15 through b 23 !+ The last three variables are controls for the international environment, discussed below, and the control for 51+ See Beck 1991, for an introduction to ECMs and Franzese 2002 for an application of pooled ECMs to political economy issues+ An ECM models the equilibrium relationship between the variables by assuming that short-term changes in the independent variables will lead to corresponding shortterm changes in the dependent variable~the error correction as measured by the differenced variables!…”