Flexible markov-switching models with evolving regime-specific parameters: an application to Brazilian business cycles

ABSTRACT

This article develops a flexible class of Markov-switching models in which the GDP growth rate is decomposed into a long-run growth trend and evolving regime-dependent means. The models can account for multiple regimes, breaks in the long-run trend, stochastic volatility, and time-varying transition probabilities. They can also handle data outliers that may arise from rare events, such as the COVID-19 crisis. We illustrate our methodology by modelling Brazilian GDP growth, which has exhibited complicated dynamics over the past four decades. Our results suggest two regimes, one long-run trend break, significant time variation in volatility, and the presence of outliers. Moreover, the selected model features time-varying transition probabilities driven by domestic variables (fiscal stance, reserves, and the real interest rate). Significantly, our findings indicate a marked decline in Brazil’s long-run growth in recent years.

KEYWORDS:

• Markov switching
• business cycles
• stochastic volatility
• structural breaks
• outliers

JEL CLASSIFICATION:

• C11
• C32
• E44
• E32

Disclosure statement

No potential conflict of interest was reported by the author(s).

Supplementary material

Supplemental data for this article can be accessed online at https://doi.org/10.1080/00036846.2024.2305621

Notes

¹ Indeed, concerns about the presence of outliers in the context of nonlinear business cycle models are justified. Perron and Wada (2016) shows that outliers might cause severe problems in trend-cycle decomposition for the G7 countries. Naturally, this issue is not confined to developed countries and can affect emerging and developing nations.

² Matlab codes associated with the article are available from the corresponding author.

³ Details are presented in Online Appendix A.:

⁴ In fact, models could be directly compared through the marginal likelihood.

⁵ Typical methods such as that in Chib (1995) can be biased in the context of Markov-switching models, requiring alternative approaches such as the bridge-sampling scheme in Frühwirth-Schnatter (2004), which is not straightforwardly extended to incorporate additional latent variables.

⁶ See Table 1 in Online Appendix C for data sources.

⁷ The same restriction is applied in the TVTP model with two regimes.

⁸ Domestic variables are selected given data availability for the sample period. Data are drawn from multiple sources and presented in Online Appendix C.:

⁹ Naturally, there may be scepticism around our criteria for variable selection. However, we emphasize that the selection process is user-determined, and our model is intended to be illustrative.

¹⁰ In Online Appendix E, we offer, for illustration, more specific details on the model with $\mathit{R}=3$ and TVTP.

¹¹ In models with constant regime-dependent means, large outliers could impact the estimation of all parameters across all regimes.

Additional information

Funding

The author acknowledges the partial financial support from the CNPq– Brazil.