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Time-Varying Effects of External Shocks on Macroeconomic Fluctuations in Peru: An Empirical Application using TVP-VAR-SV Models

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Abstract

This study uses a family of VAR models with time-varying parameters and stochastic volatility (TVP-VAR-SV) to analyze the impact of external shocks on output growth and inflation in Peru in 1992Q1-2017Q1. The statistical relevance of the models is assessed using the deviance information criterion (DIC) and the marginal log-likelihood calculated using the cross-entropy method. The results show that: (i) it is more relevant to introduce SV than TVP; i.e., the best fitting model admits only varying intercepts and SV; and TVP-VAR and CVAR are the least performing models; (ii) the models’ impulse response functions indicate that the impacts from external shocks are different under high inflation, economic crisis, and monetary policy change, with a greater impact in episodes of high uncertainty; (iii) the impact and importance of external shocks have increased over time; and (iv) the results are robust to changes in the priors, the lag structure, order of the variables, the choice of the external variable, and the selection of the variable for domestic economic activity.

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Notes

  1. Studies done before this period, such as the works by Obstfeld (1982) and Svensson and Razin (1983), assess the possible impact of the terms of trade (as part of an external shock) on the current account and domestic output (known as the HLM effect), as suggested by Harberger (1950) and Laursen and Metzler (1950). The authors conclude that the effects estimated depend on the duration of shocks: while a negative and transitory shock deteriorates the current account, a permanent external shock does not have a relevant impact on the current account.

  2. Estimation by traditional or frequentist methods is clearly impossible given that our model has 40 parameters if we want to allow each of them to vary over time (32 associated with lags, 4 intercepts and 4 variances). This is why we use Bayesian methods, specifically MCMCS methods through which we approximate the posterior densities through the likelihood together with the prior densities. Although we cannot apply asymptotic frequentist theory (\(T\Rightarrow \infty\)) since we have around 100 observations, the number of draws (after burning, thinning and the number of chains used) allow us to invoke asymptotic properties for the posterior densities as the number of draws (\(N\Rightarrow \infty\)).

  3. For example, when \(n=3\), \(\textbf{W}_{t}\) has the form:

    $$\begin{aligned} \textbf{W}_{t}=\begin{bmatrix}0 &{} 0 &{} 0\\ -y_{1,t} &{} 0 &{} 0\\ 0 &{} -y_{1,t} &{} -y_{2,t} \end{bmatrix} \end{aligned}$$

    where \(y_{it}\) is the ith element of \(\textbf{y}_{t}\) for \(i=1,2\).

  4. Complete details about the algorithm for estimating the TVP-VAR-SV model and other restricted models can be found in Section 4 and Appendix A of Chan and Eisenstat (2018).

  5. Complete details may be found in Section 4 and Appendix B of Chan and Eisenstat (2018).

  6. Gelfand and Dey (1994), Chib (1995) and Chib and Jeliazkov (2001), among others, propose alternative methods for calculating the marginal likelihood. However, Frühwirth-Schnatter and Wagner (2008) show that using the conditional likelihood or the complete data likelihood obtained through the method suggested by Chib (1995) results in an incorrect choice of models. Moreover, Chan and Eisenstat (2015) use empirical results to show that the CE method is faster and more accurate that the three mentioned before.

  7. Spiegelhalter et al. (2002) provide the DIC expressions presented here; and Celeux et al. (2006) propose up to eight DIC versions, each with a different calculation method for likelhood according to the treatment of latent variables.

  8. Akaike’s information criterion (AIC) selects 4 lags. However, this may imply an over parameterization and loss of efficiency in the estimates. Therefore, in terms of parsimony, we choose 2 lags. Furthermore, we follow Ivanov and Kilian (2005) who recommend using SIC and HQIC for quarterly series.

  9. The Log ML criterion does not offer a trade-off criterion between model complexity and model flexibility; rather, it assesses how likely it is that the observed data is generated by a particular model. Instead, the DIC makes a balance (or trade-off) between the complexity and flexibility of the different models and chooses the model with its lowest value.

  10. We also estimated regime-switching (RS) VAR models with SV, three with 2 regimes (\(r=2\)) and three with 3 regimes (\(r=3\)). The only RS models that are better than the main ones (TVP-VAR and CVAR) are those that allow a change in volatility between regimes, with a log-ML\(_{CE}\) of \(-1059.717\) and \(-1067.507\) for \(r=2\) and \(r=3\text {,}\) respectively. However, both TVP-VAR-SV and CVAR-SV are preferred over the best RS model (RS-VAR-R1-SV, \(r=2\)), as they show a BF of \(1.7\times 10^{21}\) and \(2.8\times 10^{28}\), respectively. This indicates that a smooth and continuous change in the variance, the VAR coefficients, and the intercepts are preferable to an abrupt and discrete change, as in the RS models, and therefore we discard them in this study. Chávez and Rodríguez (2023) estimate an extension of the RS-VAR-SV models, with similar results as ours.

  11. In some cases the share is close to 100% (TVP-VAR-SV, TVP-VAR-R1-SV, and TVP-VAR-R2-SV models).

  12. The share of AD shocks is more important in explaining output fluctuations before IT adoption; and drops to around 20% more recently. In contrast, the share of AS shocks is not important (always below 5%). Additionally, the share of MP shocks is high in the first years of the sample, especially since 1997 due to the interest rate increase caused by the Asian crisis, as suggested by Velarde and Rodríguez (2001), until 2002. This result is in line with Castillo et al. (2009) regarding the high interest rate variability in 1994-2001 and stabilization since 2002.

  13. HD calculation is based on the method suggested by Wong (2017) for non-linear models.

  14. We calculate the IRFs, FEVD, and HD for each robustness exercise. The Figures are in an Appendix available upon request.

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Authors and Affiliations

  1. Department of Economics, Pontificia Universidad Católica del Perú, 1801 Universitaria Avenue, Lima 32, Perú

    Gabriel Rodriguez, Paul Castillo B. & Junior A. Ojeda Cunya

  2. Central Reserve Bank of Peru, 441-445 Santa Rosa Street, Lima 1, Lima, Peru

    Paul Castillo B.

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  1. Gabriel Rodriguez
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  3. Junior A. Ojeda Cunya
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Correspondence to Gabriel Rodriguez.

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This paper is drawn from the Master’s Thesis of Junior A. Ojeda Cunya at the Graduate School of the Pontificia Universidad Católica del Perú (PUCP). It is a substantially revised version of Ojeda Cunya and Rodríguez (2022). We thank the useful comments of David Florián (Central Reserve Bank of Peru), the Editor-in-Chief of the Journal, Professor George S. Tavlas and two anonymous Referees, all of whom have contributed to improving the document. Any remaining errors are our responsibility.

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Rodriguez, G., Castillo B., P. & Ojeda Cunya, J.A. Time-Varying Effects of External Shocks on Macroeconomic Fluctuations in Peru: An Empirical Application using TVP-VAR-SV Models. Open Econ Rev (2023). https://doi.org/10.1007/s11079-023-09742-5

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