Comparing models, one with more data than the other


I have developped two very similar DSGE model in which one has four observable variables and the other one has the same four observable variables with an additional fifth observable variable. I would like to compare both models to see which one is the better model. Clearly, the model that has five observed variables has a much higher log data density (1819.1) than the one that has only four observable variables (1477.2). Since technically the models do not have the same data, the posterior odds ratio doesn’t seem to be the way to go. I would still like to know if adding an additional observable variable improves the model or not. Is there a way to do this with the Dynare output? Thank you very much!