Applied Time Series Analysis for the Social Sciences

9Dynamic Specification: Distributed Lag Models

Chapter 8 introduced the COMFAC critique of the reflexive use of GLS to “correct” autocorrelation in a static regression model. We learned that the simple generalized least squares (GLS) model

(9.1)

is mathematically equivalent to this model

(9.2)

with the constraint that and we are advised to test the constraint. If we reject the null hypothesis, we infer that the (GLS) model is misspecified and we are advised to include lags of the dependent and independent variable in the model and permit free estimation of the associated coefficients.

This often raises red flags for well‐trained analysts accustomed to working with cross‐sectional data. Presumably, we would have included the lagged terms in our initial specification if there were any theoretical motivation. Moreover, adding them ex post typically results in a smaller estimate for the coefficient on our variable of interest.

Doing so, however, addresses a second, and equally important weakness of the GLS fix. Equation (9.1) seems to indicate that any change in the independent variable X _t is associated with only a contemporaneous change in the dependent variable Y _t – for ...