Signs of impact effects in time series regression models

- The impact effect of a regressor is usually interpreted as the ceteris paribus effect.
- This can be misleading since it does not allow for indirect effects.
- We use continuous time models to show the importance of indirect effects through correlations.
- We show that the estimation of the total impact effect can be obtained using only the focus regressor.

In this paper we consider the problem of interpreting the signs of the estimated coefficients in multivariate time series regressions where the regressors are correlated. Using a continuous time model, we argue that focusing on the signs of individual coefficients in such regressions could be misleading and argue in favour of allowing for the indirect effects that arise due to the historical correlations amongst the regressors. For estimation from discrete time data we show that the sign of the total impact, including the direct and indirect effects, of a regressor can be obtained using a simple regression that only includes the regressor of interest.