Dear Professor Pfeifer,

When I was learning DSGE model with housing sector , I feel a bit confused about the two problems as bellow. Would you please give any advice ?

- Like the model in Iacoviello(2010), they generally use the data of residental investment to match new housing {{IH}_{t}} when running the bayesian estimation. While I thought the residental investment should be {{q}_{t}}{{IH}_{t}} , why don’t they use the data of residental investment to match {{q}_{t}}I{{H}_{t}} ?
- In a DSGE model, we often use output {{Y}_{t}} to define GDP. After adding housing sector, the definition of GDP becomes {{Y}_{t}}+\bar{q}I{{H}_{t}} . Is there any tips on how to define GDP in the model ? What kind of variables should be included in GDP ?

Thank you for your time.