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Paper prepared for the Banco de España Conference on “Estimation and Empirical Validation of Structural Dynamic Stochastic Models for the spanish Economy,” Madrid, March 13, 2009. We are thankful to Michel Juillard for help with DYNARE programming. Oriol Aspachs-Bracons is an economist in the Research Department at Caixa d’Estalvis i Pensions de Barcelona, Avinguda Diagonal 621-629, 08028 Barcelona. Pau Rabanal is an economist in the IMF Research Department. This paper should not be reported as reflecting the views of Caixa d’Estalvis i Pensions de Barcelona (“la Caixa”) or the International Monetary Fund or its Executive Board. Any errors and omissions are our own.
Kiyotaki and Moore (1997) and Bernanke, Gertler and Gilchrist (1999) initiated the large literature emphasizing the role credit constraints play in the transmission mechanism of shocks. Aoki et al. (2004) formalize these ideas by building a model where housing plays a critical financial accelerator role for consumers in the UK.
Using other rates, such as 2 year government bonds, or interbank rates, delivers a very similar picture. We present the 3-month T-bill rate because we will be using this series when we estimate the model.
Darracq-Paries and Notarpietro (2008) have estimated a two-country model using US and EMU data. Rubio (2008) has also built a two-country model with housing in a currency union.
Since all households behave the same way, we drop the j subscripts in what follows.
Basically, we use standard methods to obtain a linear approximation and solve for the law of motion of the model, evaluate the likelihood function, and draw from the posterior distribution. The results we present in this section are based on 200,000 draws of the Metropolis-Hastings algorithm.
We have also estimated the same model by detrending the quantity series with a linear trend. The results that we obtained are very similar to the ones that we present by first-differencing the (log) of the real variables, and they are available upon request.
These results are available upon request. As explained by Fernández-Villaverde and Rubio-Ramírez (2004), the marginal likelihood tells the researcher how she would update her priors on which model is closer to the true one after observing the data. Hence, the marginal likelihood is key for model comparison exercises. We should remind the reader that the marginal likelihood averages all possible values of the likelihood of the model across the parameter space using the priors as weights. Hence, it tends to penalize overparametrization of a model if the extra parameter does not help in model fit.
We only present this figure to focus the discussion on the housing sector in Spain. All the other decompositions are available upon request.
In order to save space we omit the response of a risk premium shock in Spain because the results are the same than with a monetary policy shock. The main difference between the two shocks is the way that they affect the rest of the euro area, but they have a very similar effect on the spanish variables. That is, the risk premium shock does not affect the rest of the euro area variables, while the monetary policy shock does.
An Appendix available upon request details the full equilibrium conditions of the model.
The loan to value ratio is set at 0.8.