Applied Time Series Analysis for the Social Sciences

10Regression with Non‐stationary Series: Cointegration and Error Correction Models

The coverage of ADL models in Chapter 9 emphasized three features common in more recent time series approaches. First, general‐to‐specific modeling provides a means of testing restrictions implied by theory, instead of merely assuming they are correct, and will therefore lead to better model specification. Second, modeling autocorrelation by adding lags of the dependent and/or independent variables mitigates the omitted variables bias that is introduced when autocorrelation driven by omitted variables is instead modeled in the error component of the equation. As a consequence, though, estimated coefficients do not typically represent marginal effects, so third, the catalogue of ADL(1,1) variations facilitates recognition of the dynamic relationship between the two variables – e.g., how the dependent variable changes over time in response to changes in the independent variable.

This chapter addresses the problem of spurious regressions that plagues associations involving non‐stationary series. In the case of ARIMA models, differencing non‐stationary series was a necessary first step, and working with differenced series is also an option in the ordinary regression context. Doing so, however, narrows the focus to short‐term relationships between variables and eliminates the possibility of examining their long‐term relationship. This problem provided the motivation for the work on cointegration that ...