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Empirical Economics

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01-11-2014

A DSGE model with housing in the cointegrated VAR framework

Author: Bjørnar Karlsen Kivedal

Published in: Empirical Economics | Issue 3/2014

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Abstract

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. This allows testing restrictions pertaining to the model without filtering the data before estimating the model. A DSGE model which includes financial markets is tested in the CVAR framework, and restrictions from the theoretical model are mainly rejected. Comparing impulse response functions from the theoretical model and the restricted empirical model also show that the results from the theoretical model are not found in the data. This suggests that the theoretical model needs to be extended or modified before it can match the empirical observations.

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The log of a ratio is the same as the differences between the log of the variables in the ratio, e.g., \(\ln (y/x)=\ln \, y-\ln \, x\).

Iacoviello (2005) introduces both a “basic” and a “full” model, where the latter contains an impatient household sector in addition to the patient households as well as allowing for variable capital investment for the entrepreneurs. The full model is considered here.

\(\ln (\frac{1+\pi ^\mathrm{net}}{1+R^\mathrm{net}})\approx \pi ^\mathrm{net}-R^\mathrm{net}\Rightarrow \frac{1+\pi ^\mathrm{net}}{1+R^\mathrm{net}} = \exp \{\pi ^\mathrm{net}-R^\mathrm{net}\} \approx 1+\pi ^\mathrm{net}-R^\mathrm{net}+\frac{(\pi ^\mathrm{net}-R^\mathrm{net})^2}{2!}\approx 1+\pi ^\mathrm{net}-R^\mathrm{net}\)

Note the change of ordering of the variables in \(x_t\) in the estimated model compared to the ordering in the MA representation of the theoretical model. This is done to use similar ordering as in the estimated VAR model in Iacoviello (2005).

Although the model contains autoregressional conditional heteroskedasticity (ARCH), the VAR results should be robust to moderate ARCH effects (Rahbek et al. 2002).

The weakly exogenous variable \(\ln CRB_{t-1}\) is excluded here to ease notation.

Note that the impulse responses in Fig. 3 are shown from one period after the impact in order to match the IRFs shown in Iacoviello (2005)

permanent in the structural MA model and transitory in the VAR in Iacoviello (2005)

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Title: A DSGE model with housing in the cointegrated VAR framework
Author: Bjørnar Karlsen Kivedal
Publication date: 01-11-2014
Publisher: Springer Berlin Heidelberg
Published in: Empirical Economics / Issue 3/2014
Print ISSN: 0377-7332
Electronic ISSN: 1435-8921
DOI: https://doi.org/10.1007/s00181-013-0765-7

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