Hi Johannes,
Mathematically this makes sense indeed. But what doesn’t make sense to me is the story behind it, from an economic perspective. Here’s a picture of my IRFs.
So the story is that just because the value of the housing weighting factor goes up, when both C and H go down in deviation from the steady state, X goes up. So if X is the consumption basket, just increasing preferences for one of the goods in the basket increases the value of the basket, despite the fact that both of its components go down? For me this wouldn’t make sense.