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Published in:

09-04-2017

# Financial crises and time-varying risk premia in a small open economy: a Markov-switching DSGE model for Estonia

Author: Boris Blagov

Published in: Empirical Economics | Issue 3/2018

## Abstract

Under a currency board, the central bank relinquishes control over its monetary policy and domestic interest rates converge towards the foreign rates. Nevertheless, a spread between both usually remains. This spread can be persistently positive due to elevated risk in the economy. This paper models that feature by building a DSGE model with a currency board, where the domestic interest rate is endogenously derived as a function of the foreign rate, the external debt position and an exogenous risk premium component. Time variation in the volatility of the risk premium component is then modelled via a Markov-switching component. Estimating the model with Bayesian methods and Estonian data shows that the economy does not react much to shocks to domestic interest rates in quiet times but is much more sensitive during crises, and matches the financial and banking crises, which cannot be captured by the standard DSGE model.

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Appendix
Available only for authorised users
Footnotes
1
The idea is based on Benigno (2001) and Schmitt-Grohé and Uribe (2003), who introduce it in a floating exchange rate framework, and on Gelain and Kulikov (2009), who estimate a standard DSGE model for Estonia.

2
The model presents an alternative method to Justiniano and Primiceri (2008) in dealing with time variation in the volatility of macroeconomic shocks.

3
Following the convention of the open-economy literature, the foreign variables are denoted by an asterisk (*) and logs of the variables—with lower-case letters.

4
A detailed list of the equations is found in “Log-linearized system of equations” of Appendix.

5
The literature does not follow a single convention. Hamilton (1989) and Kim and Nelson (1999), for example, use $$p_{ij}=\hbox {Prob}(s_{t+1} = i \vert s_t = j)$$, so that $$p_{21}$$ is the transition probability from state 1 to state 2.

6
For example, Cho and White (2007) demonstrate that because of the unusually complicated nature of the null space, the appropriate measure for test of multiple regimes is a quasi-likelihood-ratio (QLR) statistic, for which an asymptotic null distribution and critical values for a small class of models may be computed. Unfortunately, Carter and Steigerwald (2012) show that the QLR-likelihood statistic is inconsistent if the covariates include lagged dependent variables.

7
The estimation of the posterior for a three-state MS-DSGE model is highly computationally intensive and, even more so, the computation of the predictive likelihood. Therefore, the calculation of p(Y|k) is based on the Laplace approximation of the predictive marginal likelihood around the posterior mode. The technical details are documented in Warne (2012, pp. 188–196).

8
A technical discussion of the solution method is found in “Solving a MS-DSGE model” of Appendix.

9
Due to having the switching component in the volatility, the steady state is the same for each regime. This avoids issues that are yet to be resolved in the literature, such as transitions between different steady states.

10
Both TALIBOR and EURIBOR exhibit non-stationary behaviour. Nevertheless, detrending of the interest rate is not a standard practice in the literature. Therefore, several models are estimated, with and without detrending, and the results remain qualitatively the same. In the main section, the model is estimated with an HP-filtered series. The robustness Sect. 5 discusses a model without detrending of the interest rate. The data span from the first quarter of 1996 to the last quarter of 2012.

11
Even though the use of Kim’s filter avoids a sample split, the overall sample size is relatively short. The model is constrained by the length of the interest rate series to 64 observations, and therefore, the estimates should be taken with a grain of salt.

12
The prior and posterior distributions for the parameters of $$\mathcal {M}_1$$ are plotted in the “$$\mathcal {M}_1$$: Convergence diagnostics—figures and tables” of Appendix.

13
Distribution plots and convergence diagnostics for this specification may be found in “$$\mathcal {M}_2$$: Convergence diagnostics—figures and tables” section of Appendix.

14
For a detailed timeline of the events, see Adahl (2002).

15
The variance decomposition of output, consumption, inflation, and interest rate can be found in “$$\mathcal {M}_2$$: Variance decomposition tables” of Appendix.

16
Two further robustness checks have been carried out—a linear detrending and a model with a VAR representation. The results are similar across all specifications.

17
To illustrate this point, assume a two-state model. Drawing $$p_{11} \in [0, 1]$$ ensures $$(1-p_{11})\in [0, 1]$$, hence allowing for an unconstrained maximization procedure given a suitable transformation $$g(p)\in (-\infty , \infty )$$. However, adding an additional regime with $$p_{11} \in [0, 1]$$ and $$p_{12} \in [0, 1]$$ does not ensure $$(1-p_{11}-p_{12}) \in [0, 1]$$ even under fairly tight priors.

18
The only notable difference between Figs. 3 and 6 regarding the second state is the period following the global financial crisis including 2011, when Estonia had already adopted the Euro and TALIBOR was equivalent to EURIBOR. This result might be an artefact of the smoothing of the regime probabilities.

19
Note that $$A(s_t,s_{t+1}) = B_1(s_t)^{-1} A_1(s_t,s_{t+1})$$ in (53). $$B(s_t)$$ and $$C(s_t)$$ are similarly defined.

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Title
Financial crises and time-varying risk premia in a small open economy: a Markov-switching DSGE model for Estonia
Author
Boris Blagov
Publication date
09-04-2017
Publisher
Springer Berlin Heidelberg
Published in
Empirical Economics / Issue 3/2018
Print ISSN: 0377-7332
Electronic ISSN: 1435-8921
DOI
https://doi.org/10.1007/s00181-017-1256-z

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