The aim of this paper is to investigate, and possibly to explain, how the financial crises observed during the last decade spillover across countries. Of particular interest is why some of the crises, which begin as country specific events, quickly spread over countries and regions like Latin America. This type of codependence has been named, at least within the financial econometrics community, contagion.
The empirical literature for testing whether contagion exists is extensive, as it is the various ways it has been defined. Among the available strategies to evaluate contagion only two will mentioned in this paper. The most common strategy contrasts the correlation in returns between two markets during a stable period with the same correlation after the occurrence of some shock. The other approach is due to using GARCH models to make inference about the variance-covariance transmission mechanism across countries. Forbes and Rigobon (2000) and Edward and Susmel (2000) are central to understand those alternatives classes of models. Particularly in the latter, interest rate volatility for a group of Latin American countries were examined based on weekly data from 1994 up to 1999. Both conclude that the results are not overly supportive of contagion stories. An alternative approach was proposed by Agénon, Aizenman and Hoffmaister (1998) in studying the effects of contagion on bank lending spreads and output fluctuations in Argentina. The effects of a positive historical shock in the external interest rate spread were analyzed using generalized impulse response functions in the context of a VAR model relating the ex ante bank lending spread, the cyclical component of output , real bank lending rate and external interest rate spread.
In this article we apply factor models (Bartholomew, 1995), to characterize covariance structures in certain classes of multivariate stochastic volatility models, or more specifically, factor stochastic volatility models (FSV), with a particular view to applications in economics and finance. Stochastic volatility models are basically a class of time-series models that allow the time-series variances and covariances to evolve with time as stochastic functionals of past variances, covariances and possibly other information available. Further details about univariate stochastic volatility models, as well as comparisons with the well-known class of autoregressive conditionally heterokedastic (ARCH) models, can be found in Shephard (1996) and Kim, Shephard and Chib (1998). Although generalizations to multivariate situations are theoretically and conceptually simple, academics and practitioners experienced computational problems with the statistical inference. Many attempts have been made to overcome dimensionality problems and factor models opened the possibility to solve the problems for the same reasons stressed above. Diebold and Nerlove (1989) introduce the latent factor ARCH models, which is further explored and compared with other variance models in Sentana (1998) and Giakoumatos, Dellaportas and Politis (1999). The former studied the differences between Diebold and Nerlove’s latent factor ARCH models and Engle’s (1987) factor ARCH models, while the latter compared a latent one-factor ARCH model with Shephard’s unobserved ARCH model.
The works of Harvey, Ruiz and Shephard (1994) followed by Jacquier, Polson and Rossi (1995) and Kim et al (1998), and more recently by Lopes, Aguilar and West (2000), Aguilar and West (2000) and Pitt and Shephard (1999) , form the basis for the model developments we consider here. They basically model the levels of a set of time-series by a factor model where both the common factor variances and the specific (or idiosyncratic) variances follow multivariate and univariate first order stochastic volatility structures respectively.
From a more methodological viewpoint, we build on these works in some theoretical and practical directions by allowing the factor loadings to evolve in time. The rationale behind these extensions is that by allowing the factor loadings to change over time we maintain the factor scores interpretability virtually the same across time and give more flexibility to the model. In other words, our model incorporates the idea that the weight that some factors have on a particular time series might change with time, mimicking real financial/economic scenarios. A simple example is when a country (or countries) enter/leave a particular market, and when such a market is been represented by a group of stable latent factors. Moreover, in a more general framework and with the current global market integration, financial and economic indicators tend to be driven by latent factors which importance is constantly changing. This is clearly the case in most Latin American stock markets.
The rest of the article is organized as follows. Section 2 sets up the model which has two major components. In the first component, a factor model is used to represent the level of time series dependence structure where we allow the loadings matrix to change overtime by specifying a stochastic evolution process. In the second component, we follow previous work on multivariate stochastic volatility models by specifying multiple time series models for the log volatilities of the common factors. In this section, we also setup the environment for Bayesian inference and we lay down the prior distributions for the model’s parameters.
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