For my research I am interested in performing inferential and predictive analysis on a single response variable. I have already made one univariate and one multivariate regression model. In the multivariate model, the response variable which I am particularly interested in is modeled together with another response variable. The multivariate model that I use can be described as a vector autoregressive model with random effects.
For the inferential part of my research, I am already aware that my multivariate model has some advantages over the univariate model. However, I would like to ask the following:
'Does it make any sense to predict the single response variable I am interested in with my multivariate regression model rather than with my univariate regression model?'
I have some read some research where authors show that the prediction of for example multiple macroeconomic series can benefit from predicting them with a multivariate model rather than multiple univariate models. In my case I have a multivariate regression model in which I am actually only interested in one of the two response variables. The only reason why I made a multivariate model in the first case was because of the inferential part of my research.