**No. 4/2012: A DSGE Model with Housing in the Cointegrated VAR Framework**

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*Abstract
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In order to empirically investigate the assumptions underlying a theoretical dynamic stochastic general equilibrium (DSGE) model, the long-run and the short-run structure of the model may be imposed in the framework given by a cointegrated vector autoregression (CVAR) model. By following the method outlined in Juselius and Franchi (2007), I use the CVAR model to investigate the restrictions underlying the DSGE model in Iacoviello (2005), which is a monetary business cycle model that includes housing in order to include eects from the nancial accelerator. This yields a common trends representation of the data subject to the theoretical constraints of the DSGE model which can be used to calculate the impulse responses for dierent shocks. These impulse responses are then compared to the impulse responses presented in Iacoviello (2005). The main nding is that the results given by the estimated CVAR model do not correspond well to the restrictions of the DSGE model. This is shown both by testing the cointegrating relationships implied by the long-run relations, and the response to shocks in the period for which the model is estimated. Imposing theoretical restrictions pertaining to the DSGE model in Iacoviello (2005) on his estimated VAR model yields dierent impulse responses from various shocks which change some of the main ndings of the model. Particularly, imposing long-run homogeneity between housing prices and output and imposing the Fisher relationship which is assumed in the theoretical model seems to yield results which is opposite of what the nancial accelerator, which is one of the key motivations behind the model in Iacoviello (2005), suggests. The non-stationarity of in ation and the nominal interest rate may be important reasons for this, together with the non-acceptance of the imposed long-run hypotheses.