How to study Granger Causality With Seasonality In Data?

Question:

I would like to ask something about Granger causality using seasonally unadjusted data. As far as my model is concerned, quarterly log-data is being observed with two endogenous variables specified: GDP and Z (autonomous demand), all in real terms. My question is, is it obligatory to include exogenous variables (dummies for seasonality) whilst determining the VAR model? Doing so, my result changes drastically comparing to one with excluded dummies. In first case (model without dummies) with all necessary condition satisfied, GDP Granger causes Z , but not vice versa, whereas the second model (included dummies) provides both directions but condition of normality of residuals is not satisfied.

Answer:

It is not a necessity to use a seasonally adjusted data for VAR and Granger Causality. If one, however, uses a data with seasonality for estimating VAR / Granger causality and does not do anything to deal with it, the results would capture both effects – one coming from the common seasonality and the other, which is not seasonal. Un-modeled seasonality tends to violate the constant parameter assumption of standard linear VAR models. Furthermore, it is important to determine the nature of seasonality – deterministic or stochastic. The most common form of deterministic seasonality involves adding seasonal dummies to the VAR model. In the model under consideration, if the researcher is using seasonal quarterly data, he/she should consider two options:

1. Removing the seasonal component from the data by applying some seasonal-adjustment procedure. One drawback, however, is that it may lead to distortion in the non-seasonal component. In addition, the procedure is applied to individual series and this would not take into account the possible interaction between the seasonal components of different series.
2. The other option is allow for seasonality within the model – one way is adding seasonal dummies given that the series has deterministic seasonality. As long as the modelled seasonality leaves the additive reduced-form error term unaffected, identification of structural shocks or granger causality method would work fine with this method.

The best would be to report and compare results with both – not seasonally adjusted and seasonally adjusted data (through adding dummies in case of deterministic seasonality).

Reference – Kilian, Lutz and Helmut Lütkepohl (2017). Structural Vector Autoregressive Analysis, Cambridge University Press.