I have two time series and I want to check the relationship between them. I would like to use vector autoregression (VAR) model to do this.
I'd like to specify the model so that both variables will be explained by the lagged values of both itself and the other variable.
Moreover, (and here I encountered the actual trouble,) one of the time series variables, x, will need to depend on the same period value of the other variable y.
In R, can I somehow use the package "vars" to do this?
I tried to look at the documentation but I could only figure out how to include lagged variables in the model.
Or is there some other (easy) way to do this? Preferably in R.
Best Answer
A multiple-equation VAR model where contemporaneous dependent variables enter as regressors in other equations is a structural VAR (SVAR) model. When it comes to estimation of such models, there is a problem of simultaneity bias; a SVAR model cannot be estimated as it is using standard techniques. What is normally done is obtaining a reduced-form counterpart VAR model of the original SVAR model, estimating the former, and backing the original SVAR model up from the reduced-form estimates. This is pretty standard and there is quite some literature that should be available online. Perhaps Pfaff "Analysis of Integrated and Cointegrated Time Series with R" (starting at p. 43) could be useful.