The perils of debt deflation in the Euro area: a multi regime model

Abstract

Academic research and policy makers in the Euro area are currently concerned with the threat of debt deflation and secular stagnation in Europe. Empirical evidence seems to suggest that secular stagnation and debt deflation in the Euro area may be rather slowly developing. Yet what appears as major peril is that debt deflation with a lack of economic growth, rising real interest rates and further rising debt may trigger household defaults, defaults of firms and banks, rise of risk premia, and default risk of certain sectors of the economy or sovereign defaults. It is this rising default and financial risk that may lead to a regime change to a slowly moving debt crisis with high financial risk and high financial stress. In order to explore those issues, a macro policy model of Svensson type is introduced, exhibiting a regime of low and high financial stress. Then, a four dimensional multi-regime VAR is employed to an Euro area data set to support the theoretical model and the claim that in particular Southern Euro area countries are affected by debt deflation and financial market stress.

Appendices

Appendix A: GIRF algorithm

We follow the approach of Caggiano et al. (2015) in computing the GRIF. The algorithm works the following way:

• 1. Consider the set of all observations which contains $T=129$ observations and runs from 1980Q4 until 2013Q1. This allows us to build $T-p+1$ histories. With a lag length of $p=1$ this implies that we have 129 histories to draw from (with replacement). The histories are split into M regime-subsets $({\varOmega }_{1},\ldots ,{\varOmega }_{M})$ according to the regime they belong to.

• 2. Take a set of histories $({\varOmega }_{i})$ out of one of the M subsets from step (1) and compute the regime-dependent Variance-Covariance Matrix ${\varSigma }_{i}$.

• 3. Cholesky decompose ${\varSigma }_{i}$ which gives ${\varSigma }_{i}=C_{i}C_{i}'$ and orthogonalize the regime-dependent residuals to get the structural shocks: $e_{i}=C_{i}^{-1}\epsilon _{i}$

• 4. Draw a history $\omega _{j}\in {\varOmega }_{i}$.

• 5. From $e_{i}$ draw a set of n four-dimensional structural errors $e_{i}^{*}=(e_{it},\ldots ,e_{it+n})$ with replacement, where the contemporaneous correlation of the structural errors is taken into account. Afterwards transform the residuals back into their reduced form representation: $\varepsilon _{i}^{*}=C_{i}e_{i}^{*}$.

• 6. Use the history from step (4) and the structural errors from step (5) to simulate the model with the parameters from the MRVAR model.

• 7. Take the structural errors from step (5) and add an additional shock in period $t:e_{i}^{v}=(e_{it}+v_{t},\ldots ,e_{it+n})$. Then compute the reduced form errors as in (5).

• 8. Use the history from step (4) and the structural errors from step (7) to simulate the model.

• 9. Repeat steps (5) through $(8)\,R=100$ times and take the average of the simulations from step (6) and from step (8). The difference of the averages represents the GIRF for history j.

• 10. Repeat steps (2) through $(9)\,l=500$ times for regime i where the histories are drawn from ${\varOmega }_{i}$ with replacement. Take the average over all estimated $GIRF^{i}(GIRF^{i,1},\ldots ,GIRF^{i,l})$ which represents the GIRF for regime i.

• 11. Repeat steps (2) through (10) for all regimes to get the GIRF for all M regimes.

• 12. The confidence intervals are computed by taking the $5\,\%$ and $95\,\%$ percentile of the densities of the simulated GIRF $(GIRF^{1},\ldots ,GIRF^{l})$ for each regime.

Appendix B: Data

Our dataset was constructed from two data sources. The first three variables (change in GDP, inflation rate and the interest rate spread) were taken from the GVAR project (Smith and Galesi 2014). Therefore our data is based on the International Financial Statistics (IFS) database where change in GDP is the first difference of real GDP (Concept: Gross Domestic Product, Real Index, Quarterly, 2005 = 100) and the inflation rate corresponds to Consumer Prices, All items, Quarterly, 2005 = 100. The interest rate spread is calculated as the difference between long-term and short-term interest rate, where the long-term interest rate corresponds to Interest Rates, Government Securities, Government Bonds concept, while the short term interest rate is taken from Interest Rates, Treasury Bill Rate.

Our fourth variable, the ZEW Financial Condition Indices (FCI), which acts as the endogenous threshold variable in our MRVAR model, is taken from Schleer and Semmler (2015). The index represents financial sector conditions and stress with a focus on the banking sector. The index covers the banking sector, securities markets and foreign exchange markets.

A more detailed description of the data can be found in Smith and Galesi (2014) and in Schleer and Semmler (2015).