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Credit cycles and real activity: the Swiss case

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Abstract

The global Great Recession has sparked renewed interest in the relationships between financial conditions and real activity. This paper considers the Swiss experience, studying the impact of credit market conditions and housing prices on real activity over the last three decades through the lens of a medium-scale structural Bayesian vector autoregressive model. From a methodological point of view, the analysis is challenging for two reasons. First, we must cope with a large number of variables which leads to a high-dimensional parameter space in our model. Second, the identification of economically interpretable shocks is complicated by the interaction among many different relevant factors. As to the first challenge, we use Bayesian shrinkage techniques to make the estimation of a large number of parameters tractable. Specifically, we combine a Minnesota prior with information from training observations to form an informative prior for our parameter space. The second challenge, the identification of shocks, is overcome by combining zero and sign restrictions to narrow the plausible range of responses of observed variables to the shocks. Our empirical analysis indicates that while credit demand and, in particular, credit supply shocks explain a large fraction of housing price and credit fluctuation, they have a limited impact on real activity.

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Notes

  1. In this regard, we also abstract from the international transmission of credit market shocks and concentrate on domestic shocks.

  2. Beck et al. (2014) provide an excellent overview of recent advances in the incorporation of financial frictions into DSGE models.

  3. The marginal likelihood \(p(y | \lambda )\) can be derived analytically, see, e.g., Giannone et al. (2015). The parameters of gamma distribution are chosen such that the mean is 0.5 and the standard deviation is 1. Additionally, we normalize \(\gamma \) with the sample size of the training sample relative to the actual sample.

  4. More precisely, we randomly rotate an arbitrary initial \(Q_{0}\) by multiplying an orthonormal rotation matrix \(\varOmega \) drawn from the uniform distribution with respect to the (normalized) Haar measure on O(n) conditional on the zero restrictions, see Arias et al. (2014). Restrictions on combinations of variables can be implemented by calculating the responses of these combinations and checking whether they satisfy the restrictions.

  5. In principle, as shown by Baumeister and Hamilton (2015), the mere application of the uniform prior on the rotation matrix implemented in the procedure by Arias et al. (2014) leads to an informative prior on the responses, even if no actual sign restriction is imposed. However, for many responses, the posterior distributions are quite wide (or distinctly positive, as with the response of GDP to foreign demand shocks), which gives us some confidence that our results are not spurious due to unintended consequences of the uniform prior on the rotation matrix.

  6. Note that Giannone et al. (2015) define the Minnesota prior in a slightly different way: \(\mu =1/\sqrt{\lambda }\). This approach implies that our posterior mean of approximately 46 corresponds to a value of 0.15, which is between the modes of their large- and medium-scale BVAR model estimates. Our estimates for the Minnesota weight are quite large compared to our prior assumptions. However, reparameterizing the weight such that the prior refers to the square root of \(\lambda \) does not shift the posterior distribution to a relevant extent, suggesting that the prior is sufficiently loose.

  7. The shares in Table 3 are calculated based on the median contributions for each shock relative to the median contributions of all shocks evaluated for each draw. This approach guarantees that the contributions sum up to one.

  8. The historical contributions are calculated as the median historical contributions evaluated for each draw. Note that the calculated contributions do not necessarily exactly sum up to the actual data. Below we show the shock contributions for the four quarter moving-average growth rates.

  9. For instance, we replace some sign restrictions by means of zero restrictions (e.g., for identifying the monetary policy shock) without substantial impact on the results. Additionally, we estimate a model with a reduced variable set and with a flat prior (which is basically a standard VAR estimated with OLS). With this specification, many of the model features of our baseline specification can be recovered (for instance the responses to the foreign shock). Finally, we estimated a VAR in annual frequency and the same identification assumptions and found no large or significant deviations from the baseline model.

  10. The weight of the prior is set to the posterior mean.

  11. The draws for sign restriction combined with the Minnesota prior only diverge very quickly. Therefore, together with the fact that it takes very long to find draws satisfying all the sign restrictions, it turns out that the computation time to draw reliable HPD intervals is excessive. For this reason, we refrain from showing the results here.

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Authors and Affiliations

  1. Swiss National Bank, Economic Analysis, 8022, Zurich, Switzerland

    Gregor Bäurle & Rolf Scheufele

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  1. Gregor Bäurle
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  2. Rolf Scheufele
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Correspondence to Gregor Bäurle.

Additional information

We thank the participants at the Swiss National Bank Brown Bag Seminar, the 30th Annual Congress of the EEA Conference in Mannheim, the Congress of the SSES in Basel and the VfS Annual Conference in Muenster for helpful comments. The views expressed here are those of the authors and do not necessarily reflect the views of the Swiss National Bank. In particular, the model described in the paper is not part of the suite of models used for Swiss National Bank’s inflation forecast, published on a quarterly basis in its Quarterly Bulletin.

Appendix

Appendix

1.1 A.1 Additional figures and tables

Figure 12 displays the structural shocks.

Fig. 12
figure 12

Historical shocks

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1.2 A.2 Analyzing the a priori impact of identifying restrictions

In any Bayesian analysis, it is important to thoroughly discuss the properties of the prior distribution. In our case, the formal presentation of the prior is complicated for several reasons. First, the weights of the different elements in the prior are unknown, which makes the marginal density of the parameters non-standard even though the conditional distribution of the parameters is available in closed form. Second, the sign restrictions must be interpreted as part of the prior distribution (see, e.g., Baumeister and Hamilton 2015). Third, the statistics of interest, i.e., variance decompositions and impulse response functions, are a nonlinear transformation of the parameters. We mitigate this complication by numerically drawing from the prior distribution, including the sign restrictions, and graphically analyze its properties. Figure 13 shows the 50 and 80% highest posterior density (HPD) intervals of the impulse response function implied by the full set of prior information.Footnote 10 The response of the policy interest rate is normalized to a one-percentage-point decrease. We see that the prior is informative with respect to the short-term reaction of credit to monetary policy shocks but relatively uninformative with respect to the reaction of housing prices: A monetary policy shock leading to a one-percentage-point decrease in the interest rate leads to increases in credit volumes that are mostly below 1%, whereas the interval for housing prices goes up to 5%. In the case of GDP, the 80% interval easily covers the range of GDP responses found in previous studies of Switzerland, most of which find that a 1-percentage-point reduction in the policy interest rate leads to an increase in GDP of between 0 and approximately 2% after 2 years, see the overview in Bäurle and Steiner (2015). Overall, it is apparent that the prior is sufficiently loose, in the sense that the prior intervals are quite wide at least for GDP and housing prices. The fact that the prior is somewhat more informative with respect to the credit reaction may be the result of two channels. First, it is possible that the training observations are informative, which may be considered to be less problematic. A second reason may be that the sign restrictions have unintended ‘side-effects’ in the following sense. Baumeister and Hamilton (2015) show that for a given covariance matrix \(\varSigma \), the uniform prior on the rotation matrix implemented in the procedure proposed by Arias et al. (2014) is already informative regarding the impulse responses. However, in our case, further investigating the prior distribution by excluding the training sample information suggest that the somewhat tighter prior of the credit response is mainly a result of the training observation.Footnote 11 Thus, the result is not driven exclusively by the Minnesota prior combined with the sign restrictions.

Fig. 13
figure 13

Response to monetary policy shock according to training sample and Minnesota prior. Note Figures show the median and the 50 and 80% highest prior density (HPD) intervals

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Bäurle, G., Scheufele, R. Credit cycles and real activity: the Swiss case. Empir Econ 56, 1939–1966 (2019). https://doi.org/10.1007/s00181-018-1449-0

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