Given the above, the question arises as to what has triggered the occasional scepticism over the suitability and/or sustainability of Hong Kong’s currency board system? Since the inception of the global financial crisis of 2008 – 2009, which brought financial markets into turmoil, we now have extensive theoretical research suggesting that the pricing of assets, including exchange rates, may be non-linear. Recent papers have stressed the importance of non-linear effects and amplification dynamics during financial crises. The theory suggests that relatively small shocks can have large spillover effects [Brunnermeier and Pedersen (2008)]. Moreover, Brock et al. (2009) have shown that hedging instruments may produce non-linear dynamics and destabilize markets. Bianchi (2011) and Jermann and Quadrini (2012) have formalised the idea of a regime-dependent role of financial markets. Looking at exchange rates, Jeanne and Masson (2000) have addressed sunspot-driven multiple equilibria in the exchange rate context. They prove that the effects of sunspot shocks are absorbed by discrete jumps in the intercept of a regression of the currency devaluation probability on fundamental variables. Therefore, a Markov regime-switching test can be used to identify sunspot equilibria. An alternative theory for regime-switching uses the “animal spirits” concept of De Grauwe (2010) and De Grauwe and Kaltwasser (2012). Here, boundedly rational and imperfectly informed agents use heuristics to make decisions in the foreign exchange market. Again, agents’ psychological movements are self-fulfilling, as waves of optimism and pessimism lead to fluctuations of the exchange rate even when the underlying fundamentals are unaltered by an exogenous shock. However, it should be noted that different authors point to a variety of causal mechanisms. A number of studies have examined the idea of regime-switching credibility in exchange rate dynamics. See, for example, Sarantis and Piard (2004), Arestis and Mouratidis (2005), Chen (2006) and Altavilla and De Grauwe (2010). One way to capture (albeit in a reduced-form way) the impact of financial factors shaping credibility is to employ Markov-switching VAR (MS-VAR) models with time-varying transition probabilities. In our view, such models have much to contribute and offer us a promising avenue of empirical research. 5
The state space model with Markovswitching contains unobserved states X t and also unobserved Markov states. The presence of these two sets of unobservable variables implies that the standard Kalman filter cannot be applied, as it will not be possible to make inference X t and to calculate transition probabilities at the same time. However, with unobserved Markov states, the inference can be conditioned on the current and past values of S and s . As pointed out by Kim and Nelson (1999) , each iteration of the filter implies that the number of cases increases in M, where M stands for the number of regimes. This makes the problem with finding the solution to the model computationally intensive. That being said, Kim and Nelson (1999) proposed an approximation to make the filter more operational. This approximation causes a limited number of states to be taken along iterations in each period and to be “collapsed” at the end of each iteration. To apply the approximation, a new state variable is defined, S t ∗ , which indexes both S t and s t and whose transition matrix is given by P ∗ = P ⊗ Q , where ⊗ represents the Kronecker product. According to Kim and Nelson (1999) , S t ∗ , S t ∗ −1 and S t ∗ −2 can be traced out, which implies the existence of 4 3 = 64 possible paths for the state variables in each time period. Intuitively, Kim and Nelson’s (1999) algorithm runs the Kalman filter for each one of the paths and, thereafter, a weighted average is obtained using the weights given by the probabilities of each path.
Note: This figure shows the distribution of the difference between the non-parametric area under the receiver operating curve (AUROC) computed for the Markovswitching (MS) model and for the logit model (∆AU ROC h,s = AU ROC M S,h,s − AU ROC logit,h,s ) computed for many specifications s over dif-
ferent predictive horizons h. A positive value shown on the y-axis implies that the AUROC is higher for the MS model than for the logit model for the given forecast horizon, i.e. the forecasting power of the MS model for the respective forecast horizon is higher. The x-axis refers to the share of models, out of the total number of estimated models. The solid blue line corresponds to the one-quarter-ahead forecast of the high-financial-stress episode, the dashed red line corresponds to the three-quarter-ahead forecast and the dotted green line to the six-quarter-ahead forecast. Each point corresponds to a different estimation, with either a different structure of the MS model or a different definition of high financial stress. The grey area represents the average 95% confidence interval.
inflationary behavior, each period characterized by its own time-series properties depending on a probabilistic process.
This paper builds on an approach introduced by Hamilton (1989) for analyzing such discrete qualities of inflation. This approach is appealing for three reasons. First, it fits with the fact that inflation can perform differently in different sub- periods as it is a switching process where sudden changes can occur. Second, the Markov-switching modelling approach we apply in this study imposes a simpler- than-conventional structure on the inflation process within any given regime, but it gains power to fit the historical data by allowing regimes to change. The distinctive feature of this approach is the use of simple equations for inflation within a framework that allows for discrete regime shifts. Specifically, Markov- switching models allow for two or more processes to exist with a series of shifts between the states occurring in a probabilistic manner such that shifts occur endogenously rather than being imposed. Third, this Markov-switching methodology has been modified by the patterns of inflation for Tunisia that have historically switched in response to the many oil shocks.
This paper develops a general perturbation methodology for constructing first-order and second-order approximations to the solutions of MSDSGE models in which certain parameters vary over time according to discrete Markov processes. 1 The key is to derive high-order approximations to the equilibrium conditions implied by the original non- linear economic model when Markov-switching parameters are present. Our method- ology, therefore, overcomes the serious shortcomings associated with the MSLRE short- cut. By working with the original MSDSGE model directly rather than taking a system of linear rational expectations equations with fixed parameters as a shortcut, we maintain the congruity between the original economic model with Markov-switching parameters and the resultant approximations to the model solution. Such congruity is necessary for researchers to derive both first-order and higher-order approximations consistent with
Abstract This paper estimates Markovswitching models with daily happiness (GNH) data from New
Zealand for a period inclusive of the Covid-19 global health pandemic. This helps us understand the dynamics of happiness due to an external shock and provides valuable information about its future evolution. Furthermore, we determine the probabilities to transition between states of happiness and estimate the duration in these states. In addition, as maximising happiness is a policy priority, we determine the factors that increase happiness, especially during the pandemic to ensure rapid restoration of happiness levels post the Covid-19 shock. The results show New Zealand is currently in an unhappy state which is lasting longer than predicted. To increase the happiness levels to pre-pandemic levels, policymakers could allow free mobility, create economic stimuli, and allow international travel between New Zealand and low- risk Covid-19 countries.
The pronounced regime specific behavior displayed by CDS spreads has been previously documented by Alexander and Kaeck (2008) and Leppin and Reitz (2014) among others. Both studies report changes in the dynamics of CDS prices depending on high and low volatility regimes.However, previ- ous price discovery studies have neglected this characteristic. Blanco et al. (2005), Dimpfl and Peter (2013) and Grammig and Peter (2013) examine the contribution of the CDS and corporate bond market to the price discovery process. All of them determine the CDS market as the leading one. Blanco et al. (2005) apply the common measure of Hasbrouck (1995) information shares to quantify a market’s contribution. The Hasbrouck information share measure was modified by Grammig and Peter (2013), in order to resolve the problem of underterminancy inherent in the Hasbrouck approach and deliver a unique information share. Our approach extends their methodology by us- ing a Markovswitching framework that models CDS prices and bond spreads dependent on two different variance regimes. This approach renders a unique information share measure along the lines of Hasbrouck (1995) and at the same time accounts for regime dependent behaviour. We thereby rely on a model recently proposed by Herwartz and Luetkepohl (2014), which identi- fies shocks in a autoregressive system with Markovswitching by combining conventional with statistical identification methods. Applying their model to the context of price discovery allows a much more accurate assessment concerning the informationally leading market.
First, one can resort to the usual asymptotic critical values for residual-based tests, as the finite-sample distributions of the standardized residuals appear to be well approximated by the usual asymptotic distributions. Secondly, […] a Markovswitching approach is […] more flexible, as it allows for an unspecified number of breaks, of unknown location. Moreover, information on the timing of the breaks is a natural by-product of estimation. Thirdly, one can also assume changes in the variance of the long-run relationship. Furthermore, testing for cointegration arises naturally from the estimation step, since only standard cointegration testing procedures are used. Specifying long-run relationships in this way encompasses a number of empirically plausible and economically relevant models, including the case of a single permanent regime change. […] [Fourth,] one can interpret changes in the cointegration vector as shifts in fiscal regimes. (Gabriel and Sangduan 2011: 2–3)
Note: This figure shows the distribution of the difference between the non-parametric AUROC com-
puted for the Markovswitching (MS) model and for the logit model (∆AU ROC h,s = AU ROC M S,h,s −
AU ROC logit,h,s ) computed for many specifications s over different predictive horizons h. A positive value shown on the y-axis implies that the AUROC is higher for the MS model than for the logit model for the given forecast horizon, i.e. the forecasting power of the MS model for the respective forecast horizon is higher. The x-axis refers to the share of models, out of the total number of estimated models. The solid blue line corresponds to the one-quarter ahead forecast of the high financial stress episode, the dashed red line corresponds to the three-quarter ahead forecast and the dotted green line to the six-quarter ahead forecast. Each point corresponds to a different estimation, with either a different structure of the MS model or a different definition of high financial stress. The grey area represents the average 95% confidence interval.
November 29, 2017
In order to identify structural shocks that affect economic variables, restrictions need to be imposed on the parameters of structural vector autoregressive (SVAR) models. Economic theory is the primary source of such restrictions. However, only over-identifying restrictions can be tested with statistical methods which limits the statistical validation of many just-identified SVAR models. In this study, Bayesian inference is developed for SVAR models in which the structural parameters are identified via Markov-switching heteroskedasticity. In such a model, restrictions that are just-identifying in the homoskedastic case, become over-identifying and can be tested. A set of parametric restrictions is derived under which the structural matrix is globally identified and a Savage-Dickey density ratio is used to assess the validity of the identification conditions. For that purpose, a new probability distribution is defined that generalizes the beta, F, and compound gamma distributions. As an empirical example, monetary models are compared using heteroskedasticity as an additional device for identification. The empirical results support models with money in the interest rate reaction function.
5.3.2 A closer look at the Great Recession
Revisions to macroeconomic data are substantial (see e.g. Croushore and Stark (2001)). Using data available at the time the forecasts were made is therefore critical to evaluate realistically the models’ forecasting ability. Real-time employment data are available for all 50 states starting from the June 2007 vintage with last observation for May 2007. Hence, our first estimation sample extends from February 1960 to May 2007, and it is recursively expanded until August 2013. As a result, the evaluation sample extends from May 2007 to August 2013, that is 76 months. Note also that we use a real-time data series for the NBER recession dummy variable when calculating models’ weights so as to carefully reflect the information available at the time the forecasts were calculated. In this purely real-time experiment, since our evaluation sample covers only a limited period of time and only one recession, we do not calculate QPS statistics, but instead report the probability of being in a recession - defined as the last estimate available for the probability of being in a recession averaged across the different Markov-switching models (i.e., P (S t = 0|ψ t ) where t is the
We construct a new Markov-switching unobserved components framework for the analysis of hysteresis effects. Our model unifies the ingredients of trend-cycle de- composition, identification of spillovers between the components and asymmetry over the business cycle. Employing the model for Germany and the U.S. over 55 years, we find that the decades-long upward trend in German unemployment is fully explained by hysteresis. The Great Recession was well absorbed because both hysteresis effects and structural unemployment were substantially reduced after institutional reforms. In contrast, U.S. unemployment did not evolve according to hysteresis, not even during the Great Recession.
Other authors argue that the economy is subject to changes that give rise to important nonlinearities in the dynamic relationships among economic variables and that this calls for a model able to represent these changing states of the economy. As argued by Ang and Beekaert (2002), changes in business cycle conditions and monetary policy may cause interest rates to behave differently in different time periods. The Markov-Switching (MS) models, first introduced in economics by Hamilton (1988, 1989, 1990) and further developed in the subsequent literature, have proved to be adequate for the type of changing dynamics of the interest rates (Hamilton, 1988, Gray, 1996, Sola and Drifill, 1994, Blix, 1997, Beyaert and Perez-Castejon, 2000, Bekaert et al., 2001, Ang and Bekaert, 2002, Humala, 2005, etc.). Our paper belongs to this line of research. Our main objective is to develop a method of testing the Rational Expectations Hypothesis (REH) for the term structure of interest rates in VAR models that allow for unobservable Markovswitching regimes.
A final remark is necessary with regard to the type of clustering chosen. In this paper a hard clustering approach is used, i. e. each time-series belongs to one and only one cluster at a given time. An alternative would be soft clustering, where cluster membership is represented proba- bilistically. An example of the latter approach are finite mixture models. In the absence of panel data it is well established that soft clustering is preferable to hard clustering. By construction, the probabilistic assignment to clusters allows an assessment of the confidence of the cluster assign- ments. More importantly, in the absence of panel data hard clustering has been shown to lead to reasonable clusters, but inconsistent parameter estimates (Celeux and Govaert, 1993; Bryant, 1991; McLachlan, 1982). Soft clustering in the context of Markovswitching models is possible (Butler, 2003; Alon et al., 2003; Wichern, 2001; Cadez and Heckermann, 2003), but computationally very demanding and rarely used. In the context of the proposed model a further difficulty would arise: The Markovswitching clusters in this paper differ only with respect to the transition probabilities, but not with respect to the state coefficients. This implies that by construction the differences in the incomplete/complete-data log-likelihood functions tend to be small so that the traditional smoothed model probabilities, i. e. the probability that given the parameters the data has been generated by cluster m, are too close to each other to allow for a soft clustering mechanism to be well defined. Despite opting for the hard clustering approach, our model does not suffer from the inconsistency problem pointed out in the hard clustering of mixture models. Since panel data is available the cluster assignment is consistent for large enough time-series. If the cluster assignment is consistent, so are the parameter estimates. 24 However, since each time-series is deterministically
VAR model finds an aggressive and a less aggressive regime. The former is char- acterized by an aggressive reaction to the state of the economy and is related to periods of low output growth. Kuzin (2006) applies a backward-looking Taylor rule with a Markovswitching parameter on inflation to German data. He finds periods of high and low inflation aversion in the Bundesbank’s monetary policy. An interesting approach is put forward by Sims and Zha (2006) who check for regime switches in U.S. monetary policy with help of a multivariate model that allows for Markovswitching in coefficients and variances. However, they con- clude that the model with state-dependent variances and constant coefficients performs best in terms of model fit.
3 The Markovswitching SVAR model
The identification through heteroscedasticity is a powerful option to support iden- tification of shocks in SVAR models, see Rigobon (2003) or Lanne and Lütkepohl (2008), among others. In comparison to classical identifying techniques like short run, long run or sign restrictions, the identification through heteroscedasticity is a more data oriented approach. This is also in sharp contrast to the identification strategies for latent dynamic factor models, previously applied to inflation series in e.g. Mumtaz and Surico (2012), where factor loadings are restricted to zero such that country specific factors are easily characterized by having no impact on foreign in- flation. With the SVAR model and the identification through heteroscedasticity, we attempt to explore transmission channels and the economic nature of driving forces more deeply. We let the data speak about the statistical identification and check in a second step whether some economic meaning can be attached to the individual structural shocks. In general, our statistical procedure allows some country specific shock to transmit to foreign inflation expectations.
would provide a strong indication for the existence of a common Euro-zone cycle.
This paper deals with the existence, identification and dating of the Euro-zone business cycle. We use the ap- proach innovated by Hamilton in his analysis of the U.S. business cycle to identify regime shifts in the stochastic process of economic growth in the Euro-zone over the last two decades. The first aim of the paper is to formulate eco- nometric models of aggregated Euro-zone real GDP growth data, which allow the dating of the Euro-zone busi- ness cycle based of the smoothed regime probabilities implied by the model. The second aim is to investigate the degree of business cycle synchronization in the Euro zone by modelling a Markov-switching vector autoregres- sion of real GDP growth rates in eight EMU member states.
Given the above, the current study makes the following contributions, i) it is the first study to use a MarkovSwitching Dynamic Regression Model (MSDR) to investigate the dynamics of happiness, ii) the MSDR provides us with new insights into the probabilities of transitioning from one state to another, the duration of these happiness states and the volatility of the happiness states, iii) no other study, to the knowledge of the authors, has predicted the evolution of the unobserved switches in happiness including a time period with a pandemic as an exogenous shock, and iv) it determines those factors which might increase the probability to be happy during a pandemic. In addition, it is one of a handful of studies to use Big Data methods combined with other data collection methods in the analysis (for comparative studies, see Brodeur et al. 2020; Greyling et al. 2021a, b; Hamermesh 2020; Li et al. 2020; Rossouw et al. 2021).
4.2 Testing for within–regime correlation dynamics and comparison with other models
One of the most popular approaches to time–varying conditional correlations is the dynamic conditional correlation (DCC) model of Engle (2002). In the DCC, conditional correlations are driven by standardized shocks rather than by discrete regime shifts as in the Markov– switching processes studied herein. Both models can be combined to produce an even more flexible structure which allows the conditional correlations in each regime to be driven by DCC–type dynamics (e.g., Billio and Caporin, 2005; Otranto, 2010). However, the MS CCC– GARCH model has several advantages over its DCC–type generalization, since it is easier to estimate and admits the computation of multi–step–ahead conditional covariance matrices. In view of these advantages, it is desirable to have at one’s disposal a simple test of the regime– switching CCC against the alternative of within–regime correlation dynamics. To this end, we extend Tse’s (2000) Lagrange Multiplier (LM) test for constant conditional correlations to the multi–regime framework and allowing for fat–tailed (Student’s t) innovations. 10 The details of this test, which fits into the general framework described by Hamilton (1996), are developed in
In this paper, the ADF and PP testing results show that PHO, FIW, and GGW at 1%; and PIO at 5% level of significance. Both unit root tests confirm that the ADF and PP tests consistently reject the null hypothesis and the funds’ returns those of stocks are stationary.
The transition probabilities show that there is a high and low probability of switching between Regimes 1 and 3, respectively. The transition probabilities show that three regimes are both highly and lowly volatile. The Markovswitching model results show that the idiosyncratic risk of the ex- change traded funds (ETFs) are not constant across the three regimes and that the water ETFs ap- pear to have little influence on the idiosyncratic risk. Moreover, the “standard error” terms for regressions across regimes outputs are rather low. In a similar manner, water ETFs affect the total risk. We also identify that the beta coefficients are positive and entire values are less than 1 at Regime 1, Regime 2, and Regime 3, respectively. It seems that water investment has a lower system- atic risk and a positive effect on the water ETFs returns during different regimes. Thus, as the Markovswitching model is changing when the regime either falls or rises, higher idiosyncratic risk of differ- ent regimes illuminating greater returns of water ETFs accordingly.