DEPARTAMENTO DE ECONOMÍA Pontificia Universidad Católica del Perú DEPARTAMENTO DE ECONOMÍA Pontificia Universidad Católica del Perú DEPARTAMENTO DE ECONOMÍA Pontificia Universidad Católica del Perú DEPARTAMENTO DE ECONOMÍA Pontificia Universidad Católica del Perú DEPARTAMENTO DE ECONOMÍA Pontificia Universidad Católica del Perú DEPARTAMENTO DE ECONOMÍA Pontificia Universidad Católica del Perú DEPARTAMENTO DE ECONOMÍA Pontificia Universidad Católica del Perú DEPARTAMENTO DE ECONOMÍA Pontificia Universidad Católica del Perú DT DECON DOCUMENTO DE TRABAJO TIME EVOLUTION OF EXTERNAL SHOCKS ON MACROECONOMIC FLUCTUATIONS IN PACIFIC ALLIANCE COUNTRIES: EMPIRICAL APPLICATION USING TVP-VAR-SV MODELS Nº 508 Gabriel Rodríguez y Renato Vassallo DOCUMENTO DE TRABAJO N° 508 Time Evolution of External Shocks on Macroeconomic Fluctuations in Pacific Alliance Countries: Empirical Application using TVP-VAR-SV Models Gabriel Rodríguez y Renato Vassallo Marzo, 2022 DOCUMENTO DE TRABAJO 508 http://doi.org/10.18800/2079-8474.0508 http://doi.org/10.18800/2079-8474.0508 Time Evolution of External Shocks on Macroeconomic Fluctuations in Pacific Alliance Countries: Empirical Application using TVP-VAR-SV Models Documento de Trabajo 508 © Gabriel Rodríguez y Renato Vassallo Editado e Impreso: © Departamento de Economía – Pontificia Universidad Católica del Perú Av. Universitaria 1801, Lima 32 – Perú. Teléfono: (51-1) 626-2000 anexos 4950 - 4951 econo@pucp.edu.pe http://departamento.pucp.edu.pe/economia/publicaciones/documentos-de-trabajo/ Encargada de la Serie: Roxana Barrantes Cáceres Departamento de Economía – Pontificia Universidad Católica del Perú Barrantes.r@pucp.edu.pe Primera edición – Marzo, 2022 ISSN 2079-8474 (En línea) mailto:econo@pucp.edu.pe mailto:Barrantes.r@pucp.edu.pe Time Evolution of External Shocks on Macroeconomic Fluctuations in Pacific Alliance Countries: Empirical Application using TVP-VAR-SV Models∗ Gabriel Rodríguez† Pontificia Universidad Católica del Perú Renato Vassallo‡ Consejo Fiscal del Perú March 15, 2022 Abstract This article provides empirical evidence on the evolution of the impact of external shocks on the macroeconomic dynamics of the Pacific Alliance (PA) countries. For this purpose, we estimate a family of VAR models that allows time variation (or constancy) of parameters, including the variance matrix (TVP-VAR-SV). The results suggest that: (i) fluctuations from China create the most significant and persistent responses: a 1% increase in China’s growth raises growth by 0.3%-0.4% during the first year in Chile, Colombia, and Mexico; and by 0.8% in Peru; (ii) responses to export price shocks evolve considerably over time; e.g., the impact on growth in Chile and Peru tripled in 1994-2009 and then moderated until 2019; and (iii) unexpected Fed rate increases result in significant increases in AP countries’ monetary policy rates, an effect that escalates during crisis periods and further deepens the negative impact on domestic output growth. Additionally, variance decomposition shows that external factors explained over 50% of deviations in the domestic variables considered in this work. In particular, the results show that external shock absorption over the sample is higher in Mexico and Peru. In contrast, the change in domestic dynamics in absence of external disturbances would have been milder in Chile and Colombia. Finally, we perform four robustness exercises, which imply the following modifications to the baseline model: (i) changing priors; (ii) modifying two external variables; (iii) using low- dimensional models (4, 5, and 6 variables); and (iv) expanding the model by adding a fiscal policy variable. The results do not change significantly relative to those found using the baseline model. JEL Classification: C11, C32, F41, F44, F62. Keywords: Macroeconomic Fluctuations, External Shocks, Autoregressive Vectors with Time- Varying Parameters, Stochastic Volatility, Bayesian Estimation and Comparison, Pacific Alliance Countries. ∗This document is drawn from the Master’s Thesis in Economics of Renato Vassallo at the Graduate School of the Ponticia Universidad Católica del Perú (PUCP). The authors are grateful for the comments by Paul Castillo (Central Reserve Bank of Peru and PUCP), Waldo Mendoza (PUCP), and the members of Peru’s Fiscal Council. The points of view expressed in this document are those of the authors and do not necessarily represent the official position of the Fiscal Council. Any remaining errors are our responsibility. †Address for Correspondence: Gabriel Rodríguez, Department of Economics, Ponticia Universidad Católica del Perú, 1801 Universitaria Avenue, Lima 32, Lima, Perú, Telephone: +511-626-2000 (4998). E-Mail Address: gabriel.rodriguez@pucp.edu.pe, ORCID ID: https://orcid.org/0000-0003-1174-9642. ‡E-Mail Addresses: renato.vassallo@cf.gob.pe and renato.vassallo@pucp.edu.pe. Evolución Temporal de Choques Externos sobre Fluctuaciones Macroeconómicas en Países de la Alianza del Pacífico: Aplicación Empírica usando Modelos TVP-VAR-SV∗ Gabriel Rodríguez† Pontificia Universidad Católica del Perú Renato Vassallo‡ Consejo Fiscal del Perú 15 de Marzo 2022 Resumen Este artículo proporciona evidencia empírica sobre la evolución del impacto de los choques externos en la dinámica macroeconómica de los países de la Alianza del Pacífico (AP). Para ello estimamos una familia de modelos VAR que permite la variación (o constancia) temporal de los parámetros, incluyendo la matriz de varianzas (TVP-VAR-SV). Los resultados sugieren que: (i) las fluctuaciones de China crean las respuestas más significativas y persistentes: un aumento del 1% en el crecimiento de China aumenta el crecimiento en un 0.3%-0.4% durante el primer año en Chile, Colombia y México; y un 0.8% en Perú; (ii) las respuestas a los choques de precios de exportación evolucionan considerablemente con el tiempo; por ejemplo, el impacto sobre el crecimiento en Chile y Perú se triplicó en 1994-2009 y luego se moderó hasta 2019; y (iii) los aumentos inesperados de la tasa de la Fed dan como resultado aumentos significativos en las tasas de política monetaria de los países AP, un efecto que aumenta durante los períodos de crisis y profundiza aún más el impacto negativo en el crecimiento de la producción interna. Adicionalmente, la descomposición de la varianza muestra que los factores externos explican más del 50% de las desviaciones en las variables domésticas consideradas en este trabajo. En particular, los resultados muestran que la absorción de choques externos sobre la muestra es mayor en México y Perú. En contraste, el cambio en la dinámica interna en ausencia de perturbaciones externas hubiera sido más leve en Chile y Colombia. Finalmente, realizamos cuatro ejercicios de robustez, que implican las siguientes modificaciones al modelo de base: (i) cambio de priors; (ii) modificación de dos variables externas; (iii) uso de modelos de menor dimensión (4, 5 y 6 variables); y (iv) ampliar el modelo agregando una variable de política fiscal. Los resultados no cambian significativamente en relación con los encontrados utilizando el modelo de referencia. Clasificación JEL: C11, C32, F41, F44, F62. Palabras Claves: Fluctuaciones macroeconómicas, Choques Externos, Vectores Autorregresivos con parámet- ros Cambiantes en el tiempo, Volatilidad Estocástica, Estimación y Comparación Bayesiana, Países de la Alianza del Pacífico. ∗Este documento está basado en la Tesis de Maestría en Economía de Renato Vassallo de la Escuela de PosGrado de la Pontificia Universidad Católica del Perú (PUCP). Los autores agradecen los comentarios de Paul Castillo (Banco Central de Reserva del Perú y PUCP), Waldo Mendoza (PUCP) y los miembros del Consejo Fiscal del Perú. Los puntos de vista expresados en este documento son los de los autores y no representan necesariamente la posición oficial del Consejo Fiscal. Cualquier error remanente es nuestra responsabilidad. †Dirección de Correspondencia: Gabriel Rodríguez, Departamento de Economía, Pontificia Universidad Católica del Perú, Av. Universitaria 1801, Lima 32, Lima, Perú, Teléfono: +511-626-2000 (4998). Correo Electrónico: gabriel.rodriguez@pucp.edu.pe, ORCID ID: https://orcid.org/0000-0003-1174-9642. ‡Correo Electrónico: renato.vassallo@cf.gob.pe y renato.vassallo@pucp.edu.pe. 1 Introduction Historically, emerging market economies (EMEs) have been considerably a¤ected by evolving inter- national conditions. On the one hand, their good economic performance in 2002-2011 was driven to a considerable extent by a commodity price boom (in turn spurred by a surge in global activity) and a weakened U.S. dollar. On the other hand, economic deceleration caused by the structural implications of the Global Financial Crisis (GFC), and the subsequent withdrawal of monetary stimulus from advanced economies, created lingering policy challenges in EMEs. This article seeks to explain the external environment�s impact on macroeconomic �uctuations in EMEs as a basis for exploring potential responses to future changes in international conditions. Towards this end, we assess and quantify the impact of external shocks on output growth, in�ation, and the interest rate in four important Latin American economies: Chile, Colombia, Mexico, and Peru, the members of the Paci�c Alliance (PA) founded in 2012. The PA bloc is intended as a mechanism for economic and trade integration aimed to promote macroeconomic policy coordination among member countries. This is aided by several common historic and economic features: all PA countries are commodity exporters; and have similar mon- etary frameworks (they adopted in�ation targeting (IT) at the turn of the century) and �scal rules (except Peru). Notably, they show high trade openness indices (55% on average, compared with 42% for the rest of Latin America). This article seeks to contribute to the literature regarding three issues. First, we �nd evid- ence supporting the traditional view that external factors are the main source of macroeconomic �uctuations in EMEs (Calvo et al. (1993), Mendoza (1995), Kose (2002), Izquierdo et al. (2007), Rodríguez et al. (2018), Ojeda Cunya and Rodríguez (2022), Chávez and Rodríguez (2022), and Guevara et al. (2022), among others), in contrast with a body of research that maintains that the impact of external factors is overestimated (Lubik and Teo (2005), Aguirre (2011), and Schmitt- Grohé and Uribe (2018)). Along these lines, we estimate a family of VAR models that allow time variation (or constancy) of parameters, including the variance matrix (TVP-VAR-SV). Time vari- ation is needed to control for eventual non-linearities associated with structural economic changes and heteroscedastic shocks. Additionally, we carry out the estimations using Bayesian methods to address the high dimensionality of the parameter space and non-linearities in the model. Second, we jointly analyze the three transmission channels whereby shocks propagate into small open econom- ies: (i) the trade channel, via trading partners�demand; (ii) the �nancial channel, via international interest rate movements; and (iii) the price channel, via export price �uctuations. Finally, in view of the scarce evidence on PA countries�behavior during external shocks, we seek to understand the impact of evolving external conditions on the PA bloc�s main macroeconomic variables, with an aim to identify macroeconomic reactions and policy implications for each member country. Using quarterly data for 1994Q1-2019Q4, the results for the four economies suggest that models that allow time variation for certain (not all) groups of parameters and include stochastic volatility (SV) perform better than traditional VAR models and models where all parameters are time- varying, as in Primiceri (2005) and Cogley and Sargent (2005). The results show that shocks originated by external demand, international prices, and �nancing conditions have signi�cant and evolving repercussions on macroeconomic performance in PA coun- tries. Real shocks originated in China stand out in impulse-response functions (IRFs): the two-year cumulative impact of a 1% increase in China�s growth results in growth increases of 0.6% in Chile and Colombia, 0.8% in Mexico, and 1.2% in Peru. We also �nd that export price index (XPI) growth varies considerably over time in response to favorable shocks; e.g., the response to XPI growth tripled in Chile and Peru in 1994-2009. Additionally, Fed rate movements create signi�cant and persistent shocks on monetary policy in the PA bloc, with a magni�ed impact during �nancial crises. Historical decomposition reveals a predominantly external in�uence in 2002-2011, in a context of surging commodity prices and high global growth. In contrast, in 1994-2001 the in�uence of domestic shocks surpassed that of external ones, in a context of high domestic volatility and idio- syncratic shocks. In line with IMF (2014), we �nd that external factors explained, on average, more than half of growth, in�ation, and interest rate deviations in PA countries over the sample period. Moreover, we perform four complementary exercises to validate the robustness of the baseline model. To achieve this, we: (i) estimate the model changing the di¤use priors for more informative ones (using a training sample); (ii) modify two external variables (Fed interest rate and XPI growth); (iii) assess low-dimensional models (4, 5, and 6 variables); and (iv) extend the baseline model by adding a �scal policy variable. The results do not change signi�cantly relative to those calculated for the baseline model. The article is divided as follows. Section 2 summarizes the literature on the relationship between external factors and economic performance in small open economies, with emphasis on the PA bloc. Section 3 describes the proposed methodology for estimating a family of TVP-VAR-SV models following Chan and Eisenstat (2018). Section 4 examines the results for the baseline model and discusses its economic interpretation. Section 5 suggests alternative exercises to validate the robustness of the proposed baseline model. Section 6 summarizes the conclusions. It should be noted that this article shows only the best-�tting models for each country. An appendix showing the �gures and results for other models, as well as the robustness exercises, is available on request. 2 Review of the Literature This section summarizes the main research on external shocks and their impact on EMEs�macroe- conomic performance, especially in Latin America. In the context of massive capital in�ows into Latin America at the end of the 1980s, Calvo et al. (1993) emphasize the role of external factors in Latin American countries�economic cycles (around 50% of the forecast error variance for the real exchange rate in most of them). However, these results contrast with Ahmed and Murthy (1994), Hausmann and Gavin (1995), and Ho¤maister and Roldós (1997), who conclude that, in general, external factors have a relatively limited role; and that aggregate supply shocks are the main driver of economic �uctuations in developing economies. Apart from methodological di¤erences, Mendoza (1995) uses a real-business-cycle (RBC) model to support Calvo et al. (1993), arguing that external shocks (terms of trade in particular) explain around 50% of output and exchange rate variability. Kose (2002) applies a dynamic stochastic general equilibrium (DSGE) model for a small open economy, �nding that global price shocks explain a signi�cant share of economic cycle variability in developing economies. Canova (2005) �nds that the transmission of U.S.-originated shocks explains 19%-56% of the variance of eight main macroeconomic variables in eight Latin American countries. The author underscores the role of the �nancial channel in magnifying external disturbances. Using a di¤er- ent identi�cation strategy, Mackowiak (2007) uses SVAR models to estimate that external shocks explain around 49% of the output variance in eight EMEs. Izquierdo et al. (2007) and Osterholm and Zettelmeyer (2007) model the transmission of in- ternational shocks to growth in Latin America via VECM and BVAR speci�cations, respectively, �nding that external factors explain 50%-60% of growth in PA countries. Cesa-Bianchi et al. (2011) estimate a global VAR (GVAR) model for 26 economies, including �ve Latin American countries, to capture possible heterogeneities in the transmission of shocks to EMEs. They �nd that the long-term impact of an output shock in China on a typical Latin American economy has tripled since the mid-1990s. In contrast, the long-term impact of a U.S. 1 growth shock halved over the same period. In the same line, Winkelried and Saldarriaga (2013) con�rm that China�s increased weight in the global economy has resulted in greater impacts on third-party countries, especially small open economies like Latin American countries. There is body of debate speci�cally about the relevance of external factors for PA countries. Using a VAR model with data for 1986-1997, Calvo and Mendoza (1998) identi�ed a Granger causality from terms of trade to economic activity in Chile. Following a similar strategy, a work by the IMF (2012) assesses the sensitivity of economic activity to external shocks; and veri�es that the latter (especially movements in copper price and changes in international �nancial conditions) have a signi�cant impact on production in Chile. Moreover, Fornero et al. (2016) con�rm that commodity price shocks are an important driver of business cycles in six commodity exporting countries (including Chile and Peru); and that such shocks a¤ect output signi�cantly through their impact on mining investment. Regarding Colombia, Abrego and Osterholm (2008) �nd that external factors explain around 40% of output dynamics. The main external factors are global output (17%) and foreign direct investment (14%); and, to a lesser extent, the U.S. interest rate (10%) and the EMBI (10%). Additionally, Mahadeva and Gómez (2009) identify a high participation of real export prices and capital �ows in Colombia�s output �uctuations. Echevarría et al. (2012) underscore that the relevance of external factors has not been stable over time, arguing that, during the GFC, they explained close to 75% of Colombia�s output dynamics, in contrast with 35% in 1998-1999. More recently, Melo-Becerra et al. (2020), using a more �exible empirical approach to the relationship between international conditions and output, estimated the impact of oil prices and output shocks; and identi�ed di¤erent SV patterns in the variables, suggesting the relevance of methodologies with time-varying parameters and heteroscedastic variance (TVP-VAR-SV). In the case of Mexico (an oil country like Colombia), Del Negro and Obiols-Homs (2001) conclude that changes in U.S. output, prices, and interest rates largely explain Mexico�s output variance, even to a greater extent than oil prices. Sosa (2008) and Blecker (2009) support these �ndings, un- derscoring that oil and U.S. shocks are the main drivers of output �uctuations in Mexico, especially since the enactment of the North American Free Trade Agreement (NAFTA). Recently Carrillo et al. (2020) examined these U.S.-Mexico co-movements, �nding that U.S. shocks explain around 75% of Mexico�s expected output �uctuations over a three-year horizon. In the case of Peru, an initial work by Dancourt et al. (1997) suggests that long-term macroeco- nomic performance is independent from development strategies and signi�cantly linked to external shocks. Moreover, Nolazco et al. (2016), Mendoza and Collantes Goicochea (2017), and Rodríguez et al. (2018) use di¤erent methodologies to verify that external drivers explain 50%-96% of domestic output �uctuations. In the same line, a research by MEF (2019) calculates a 55% contribution. Recent studies like Ojeda Cunya and Rodríguez (2022) and Rodríguez and Vassallo (2021) emphasize the advantages of using time-varying parameters and SV in discussing the role of external shocks in Peru�s economic performance. These studies �nd that the share of external shocks in the variance of growth forecasts has increased over time, from about 10% in the mid-1990s to over 80% around the GFC, suggesting Peru�s considerable dependence on, and vulnerability to, �uctuations in global variables. As mentioned above, a signi�cant body of global and regional literature points to external factors as the main driver of macroeconomic dynamics in EMEs like PA countries. However, recent studies, like Schmitt-Grohé and Uribe (2018), challenge this conclusion. Using speci�c SVAR models for 38 EMEs, they �nd that unanticipated terms-of-trade changes explain just around 10% of output variability on average. As their results contrast with the current standard approach, the authors suggest using commodity prices instead of aggregate indices for export/import unit values to improve the empirical model (a recommendation that we have considered in this study). 2 This work adheres to the methodology used initially by Cogley and Sargent (2005) and Primiceri (2005), who estimate TVP-VAR-SV models to assess monetary policy and its impact on the U.S. economy. Additionally, Primiceri (2005) uses recursion restrictions in the contemporaneous rela- tionship matrix to provide a structural interpretation of the overall dynamics. Moreover, Clark (2011) and D�Agostino et al. (2013) show the �t and forecasting advantages of using models with time-varying parameters and SV.1 At the same time, despite the improvements provided by �exible models, recent works like Chan et al. (2012), Nakajima and West (2013), and Belmonte et al. (2014) point out potential problems from overparameterization. In this context, we use a new estimation strategy suggested by Chan and Eisenstat (2018), who, in addition to the original TVP-VAR-SV model, implement six restricted versions based on di¤erent assumptions for time variability (or constancy) of intercepts, VAR coe¢ cients, and the variance matrix. This strategy seeks to isolate the role of time variability for di¤erent groups of parameters. In addition to addressing possible non-linearities in the relationship between external shocks and domestic macroeconomic dynamics, this study di¤ers from previous work in considering the three main channels for the transmission of shocks to PA economies: prices, trade, and �nancial conditions. Towards this end, we performed a set of estimations starting from a baseline model with seven variables (four external and three domestic) and later carried out robustness exercises to support our main �ndings. 3 Empirical Strategy 3.1 The Econometric Model We use a family of seven VAR models with di¤erent restrictions associated with the dynamics and nature of the parameters. First, we describe the TVP-VAR-SV model and then incorporate models identi�ed as restricted versions into the analysis. Following Chan and Eisenstat (2018), we de�ne an n�1 vector yt = (y1;t; :::; yn;t)0 of endogenous variables in period t. Therefore, the TVP-VAR-SV model can be expressed as: B0;tyt = �t +B1;tyt�1 + :::+Bp;tyt�p + �t; �t � N (0;�t); (1) where �t is an n�1 vector of time-varying intercepts, B1;t:::Bp;t are the n�n matrices of coe¢ cients associated with the vector of lagged endogenous variables, B0;t is the n�n lower triangular matrix of contemporary e¤ects with diagonal unit values, and �t = diag(exp(h1;t); :::; exp(hn;t)): The movement law for the logs of all variables ht = (h1;t; :::; hn;t)0 is speci�ed as an independent random walk: ht = ht�1 + �t; �t � N (0;�h); (2) where the initial conditions h0 are also parameters to be estimated. As the system in (1) is in structural form and the variance matrix �t is diagonal, the estimation can be carried out recursively. For this purpose, we rewrite the model. We consider the k��1 vector of intercepts and coe¢ cients associated with the lagged observations �t = vec((�t;B1;t; :::;Bp;t) 0). The second k �1 vector, containing the time-varying coe¢ cients that characterize contemporaneous relationships between variables, is denoted by t. It should be noted that k� = n(np + 1) and k = n(n� 1)=2. Therefore, equation (1) can be rewritten as: yt = eXt�t +Wt t + �t; �t � N (0;�t); 1For more details about stochastic volatility, see Harvey et al. (1994), Kim et al. (1998), and Chib et al. (2006). 3 where eXt = In (1;y0t�1; :::;y0t�p) and Wt is an n � k matrix that contains the appropriate elements of �yt2. If Xt = (eXt;Wt), we can simplify the above model to obtain a generic space- state representation: yt = Xt�t + �t; �t � N (0;�t); (3) where �t = (�0t; 0 t) 0 has a k� = k�+k dimension and the coe¢ cients have a random walk behavior: �t = �t�1 + �t; �t � N (0;��); (4) where the initial conditions �0 are also parameters to be estimated. A standard TVP-VAR-SV speci�cation takes all parameters in �t = (�0t; 0 t) 0 and the variance matrix �t to be time-varying. However, in order to assess the individual contribution of the two groups of parameters �t and t, we consider three variants of the general model, all with SV. Along these lines, we consider: (i) a TVP-VAR-R1-SV model, where the parameters associated with lagged observations and intercepts in the VAR remain constant (i.e., �t = �0); (ii) a TVP- VAR-R2-SV model, where the coe¢ cients that characterize contemporaneous relationships remain constant (i.e., t = 0), as proposed by Cogley and Sargent (2005); (iii) a TVP-VAR-R3-SV model, where only the intercepts �t are time-varying; (iv) a TVP-VAR model with time-varying coe¢ cients but no SV, to isolate the e¤ect of time variation, as suggested by Cogley and Sargent (2001); (v) a CVAR-SV model with constant VAR parameters and SV; and (vi) a traditional VAR (CVAR) model with neither time-varying parameters nor heteroscedastic variance. 3.2 Estimation and Criteria for Model Comparison We estimate the above models using Gibbs Sampling, where draws are based on the precision sampling proposed by Chan and Jeliazkov (2009). The authors modify the algorithm introduced by Primiceri (2005), as discussed by Del Negro and Primiceri (2015). Complete estimation details can be found in Section 4 and Appendix A of Chan and Eisenstat (2018). It is convenient to assume that the initial values of the coe¢ cients, covariances, log-volatilities, and hyperparameters are independent from each other. We assume that the priors for the initial states of the time-varying coe¢ cients and the logs of the standard errors follow a Normal distribution: �0 � N (a�;V�), h0 � N (ah;Vh). We also de�ne a diagonal matrix of error covariances for the state equations of the form �� = diag(�2�1 ; :::; � 2 �k� ), �h = diag(�2h1 ; :::; � 2 hn ). The diagonal elements in �� and �h are distributed independently as �2�i � IG(v�i ; S�i), �2hj � IG(vhj ; Shj ), i = 1; :::; k�, j = 1; :::; kh where IG denote the Inverse-Gamma distribution. Values for the hyperparameters are given in Section 4.2. We use two indicators to compare the models: marginal likelihood (estimated using the Cross- Entropy method) and the Deviation Information Criterion (DIC). A frequently used metric for comparing Bayesian models is the Bayes Factor (BF), calculated as the ratio of marginal likelihoods p(yjMi)=p(yjMj), where the numerator and denominator represent the marginal likelihoods of models i and j, respectively. The marginal likelihood is obtained by integrating the likelihood 2For example, when n = 3,Wt has the form: Wt = 264 0 0 0 �y1;t 0 0 0 �y1;t �y2;t 375 where yit is the ith element of yt for i = 1; 2. 4 function with respect to the prior distributions of the parameters; i.e., p(y) = Z p (yj�) p (�) d�. However, as this calculation method is time-consuming, we use the importance sampling approach proposed by Chan and Eisenstat (2015), which provides a more accurate and e¢ cient way to calculate the marginal likelihood. Complete details concerning integrated likelihood estimation may be found in Section 4 and Appendix B of Chan and Eisenstat (2018). Additionally, as a complementary indicator to the BF, we calculate the DIC, as originally proposed by Spiegelhalter et al. (2002). Using the notation suggested by Chan and Grant (2016), we de�ne the goodness of �t as D (�) = �2 log f (yj�)+2 log h(y), where f(yj�) is a function of the likelihood of the model and h(y) is a function of the data. We also use a measure of the complexity of the model through the e¤ective number of parameters, de�ned as pD = D (�) � D(e�), where D (�) = �2E� [log f (yj�) y]+2 log h(y) is the posterior mean deviation and e� is an estimator of �. Using the above de�nitions, we present the DIC as the sum of the posterior mean deviation and the actual number of parameters: DIC = D (�) + pD. After replacing some values and applying certain conditions, we obtain the following DIC version, which we use in this article: DIC = �4E� [log f (yj�) jy] + 2 log f(yj�̂): (5) We stress that we use the DIC based on the integrated likelihood, given the results obtained by Chan and Grant (2016), as other DIC forms are biased towards overparameterized models and show large standard errors. 4 Results This section assesses several models with/without time-varying parameters or SV for each PA country to identify a consistent, plausible, and well-�tting model that can be instrumental in estimating and analyzing the time variation of the interaction between external shocks and the main domestic macroeconomic variables (growth, in�ation, and interest rate). To achieve this, we use the standard instruments applied to VAR models: impulse-response functions (IRFs), historical decomposition (HD), and forecast error variance decomposition (FEVD). 4.1 Data The seven models proposed are estimated individually for each economy using quarterly data for 1994Q1-2019Q4. We focus mainly on the period following the 1990s, when signi�cant policy changes took place in PA countries (see Abiad et al. (2015)), notably the adoption of IT and rules-based �scal frameworks. The models are estimated using one lag (p = 1) selected via the Bayes Informa- tion Criterion (BIC) for the version of the model with constant parameters. The baseline model is made up of seven variables, which can be divided into two blocks consisting of four external and three domestic variables, respectively. The external block includes U.S. growth (yusat ), the Fed interest rate (i�t ), China�s growth (y chn t ), and XPI growth for each PA economy (p�t ). The series were obtained from Bloomberg and the Federal Reserve Bank of St. Louis, except for the XPIs, which were sourced from the IMF, as in Gruss and Kebhaj (2019). The domestic block includes growth (yt), in�ation (�t), and short-term interest rate (it) series obtained from the central bank and ministry of �nance websites of each country. Figure 1 shows the three global variables in the external block, while Figure 2 shows the variables for each PA economy. They are all expressed in annual growth rates, except the (international and domestic) short-term interest rates. 5 The identi�cation strategy is carried out using recursion restrictions à la Sims (1980), where the contemporaneous relationship matrix takes an inferior triangular form. This assumes that the variables are ordered from the most exogenous to the most endogenous; i.e., that the U.S. economy and monetary policy, China�s economic dynamics, and export prices have a contemporaneous in- �uence on the dynamics of economic variables in PA countries. However, the latter does not have a contemporaneous in�uence on external variables. On the external front, the proposed order assumes implicitly that Fed policy responds to move- ments in U.S. economic activity. Additionally, U.S.-originated real and �nancial movements have an in�uence on investment and trade decisions in China, which in turn have direct implications for commodity prices.3 On the domestic side, output �uctuations have direct implications for in�ation; and, based on the growth-in�ation dynamics (considering an implicit Taylor rule), the monetary authority responds by raising or cutting its policy rate. 4.2 Priors We establish non-informative priors for all models to add uncertainty around the information used to calculate the parameters. In particular, for the TVP-VAR-SV general model we consider a� = 0, V� = 10 � Ik� , ah = 0, Vh = 10 � In. Additionally, we assume that the parameters associated with the degrees of freedom are small: v�i = vhj = 5; that S�i = 0:01 2 for the lagged variables and S�i = 0:12 for the intercepts; and that Shj = 0:1 2. The priors for the restricted models follow the same rationale according to the restrictions imposed. Finally, we obtain the posterior distributions of the parameters using an MCMC (Monte Carlo Markov Chain) algorithm. We follow the method proposed by Chan and Eisenstat (2018), who use Gibbs Sampling to estimate marginal densities (which cannot be obtained analytically) from random samples with known distributions (see Section 3.2). 4.3 Evidence of Time Variation in Parameters and Volatility Prior to showing the results for the seven models, we provide support for using time-varying para- meters and SV as econometric strategy. Following Bijsterbosch and Falagiarda (2015), we performed three coe¢ cient variability tests: the Kolmogorov-Smirnov (K-S) test, the t�test, and the trace test. To implement them, we estimate the TVP-VAR-SV model and examine the distance between the prior and posterior distributions. Table 1 shows the three tests both for the whole sample and for two sub-samples with the same number of observations. The K-S and t�tests for the four economies suggests full variability of the coe¢ cients associated with the innovation variance matrix (matrix �t); i.e., the results support our preference for a speci�cation that considers SV. For the contemporaneous relationship coe¢ cients (matrix B0;t), the t�test con�rms full variability for all economies except Mexico (20/21 variable coe¢ cients); and the K-S test indicates 15-18 variable coe¢ cients out of 21. For the intercepts and coe¢ cients of lagged variables (matrix Bi;t), the K-S and t�tests yield the same result; i.e., more than 80% of the parameters should be considered time-varying, especially for Chile and Mexico. These results suggest that time variation may be related not only to innovation variance, but also to other parameters. The trace test, developed by Cogley and Sargent (2005), establishes whether the trace of the prior variance matrix is signi�cantly di¤erent from the trace of the posterior variance matrix. The results show that, in the cases of Chile and Peru, the trace of the prior variance matrix falls within the con�dence interval for the median of the trace of the posterior variance matrix; i.e., in these 3 It is worth noting that China and the U.S. together represent one-third of world demand for oil and more than 50% of the demand for industrial and precious metals. 6 cases there is no evidence of variance variability, which clashes with the previous tests. In contrast, for Colombia and Mexico, the trace of the prior variance matrix is signi�cantly smaller than that of the posterior variance matrix, which provides evidence of time variation in these parameters. 4.4 Model Selection Table 2 shows, for each PA economy, the two Bayesian selection criteria applied to all models: marginal likelihood (log-ML) and DIC, together with their standard deviations. For Chile and Peru, both criteria indicate that TVP-VAR-R3-SV is the best-�tting model. Besides including SV, the latter allows time variation for the intercepts in each equation (parameters associated with lags and contemporaneous e¤ects are constrained to remain constant). In the case of Peru, these results, which are consistent with Ojeda Cunya and Rodríguez (2022) and Rodríguez and Vassallo (2021), may be due to the fact that the system chosen includes variables, like in�ation and the policy interest rate, which were considerably volatile in the 1980s and 1990s; and abruptly became less �uctuating after the implementation of structural reforms. We underscore that, using the BF, we calculate that the TVP-VAR-R3-SV model is 3:3 � 103 times preferred over the second-best model (TVP-VAR-SV) in the case of Chile, and 2:5 � 102 times preferred over the second-best model (CVAR-SV) in the case of Peru, re�ecting the gains (in goodness of �t) from allowing time variation in the intercepts. In the case of Colombia, the results are not straightforward. On the one hand, the DIC indicates that TVP-VAR-R3-SV is the best-�tting model, as in the cases of Chile and Peru. On the other hand, the BF suggests that TVP-VAR-R2-SV, which allows time variation in both the intercepts and the coe¢ cients associated with the VAR�s lagged data, is the most appropriate; i.e., greater �exibility is introduced for the parameters that describe the inertia associated with each variable in the system. In this case, the TVP-VAR-R2-SV model is 3:3� 102 times preferred over the second- best model (TVP-VAR�R3-SV). Finally, the model chosen for Mexico is TVP-VAR-R1-SV, which only allows time variation in the contemporaneous relationship matrix. This model is 2:8 � 1032 times preferred over the second-best model (TVP-VAR-R3-SV), the largest distance between the selected and second-best models among PA countries. As discussed within the marginal likelihood analysis, the selected and second-best models have in common that both incorporate SV into their structures; i.e., SV plays a fundamental role in their performance. For instance, in the case of Chile, the TVP-VAR-R3-SV model is 4:7 � 1057 times preferred over the CVAR model and 9:4 � 1061 times preferred over the TVP-VAR model. In the case of Mexico, the TVP-VAR-R1-SV model is 3:1 � 10140 times preferred over the CVAR model and 3:5� 10132 times preferred over the TVP-VAR model. As the cases of Colombia and Peru are similar, the TVP-VAR and CVAR models are discarded for the four PA economies. We then examine the SV component, given its fundamental role in modeling PA economies. Figures 3 and 4 show the performance over time of the standard deviation of the errors for each equation in the models that consider SV. In general, the volatility derived from the CVAR-SV model tends to exceed that from the other estimations, especially in the equations for the Fed interest rate and domestic in�ation for each economy. Additionally, in most cases the deviations obtained from the TVP-VAR-SV and TVP-VAR-R2-SV models are in the lower range of the estimations (except for the XPI growth equation). This result may be due to the fact that, as time variation is allowed for a greater number of parameters (e.g., the TVP-VAR-SV model), the uncertainty captured via SV is lower compared to the models that restrict time variability (e.g., the CVAR-SV model); or, from a di¤erent perspective, not including time-varying intercepts seems to overestimate the time dynamics of the volatility of errors for each equation in the model. In particular, Figure 3 shows the volatilities of the global equations for each PA economy. We 7 underscore that the deviations associated with the equations for U.S. growth and the Fed interest rate reach relevant peaks in 2008 and 2009 (the Global Financial Crisis, GFC) and then moderate (except for the volatility of the error in the equation for the Fed rate, which increases over the last �ve years, probably due to the normalization of U.S. monetary policy after the GFC). For its part, volatility associated with the equation for China�s growth shows an increasing trend in 1994-2008, when China reduced trade barriers, inserted itself into the world economy, and became a global leader. Following the GFC, volatility dropped drastically, re�ecting a moderation probably associated with the structural changes introduced in the Chinese model in recent years. Figure 4 shows the median of the standard deviations of the innovations corresponding to each country�s equations for speci�c variables. As expected, deviations associated with XPI growth are the highest, with peaks in 2008-2010 (above 20 for Chile, Mexico, and Peru; and up to 18 for Colombia). Following the GFC, this variable became considerably less volatile: in the case of Chile, deviations dropped below 10; and diminished to turn-of-the-century levels (12-14) in the other PA countries. Regarding the domestic variable blocks for each country, although measured with di¤erent scales, the volatility dynamics are similar: widely unstable episodes in 1994-2000 translating into high and �uctuating deviations, followed by moderation in the last periods. The latter is likely associated with responsible and consistent �scal and monetary policy implementation since the turn of the new century. Castillo et al. (2016) examine the Great Moderation period for the case of Peru, emphasizing the key role of monetary policy in the signi�cant decline of output volatility over the last 30 years. At the same time, Chile shows a standard deviation upturn in the equation for output growth towards the end of the sample. 4.5 Impulse-Response Functions (IRFs) After estimating the parameters of the models, we calculate the IRFs for each point in time over the sample. Figure 5 shows the median of the responses of domestic variables to external shocks (yusat ; i�t ; y chn t ; p�t ) for the seven models. We underscore that these shocks are normalized so that the IRFs can be read as elasticities (not standard deviations). Against this backdrop, a positive real shock on U.S. growth results in a mixed output response in the four PA economies: the initial positive short-run response in economic activity reverts and becomes negative over time, notably in Chile and Peru, as re�ected in the IRF dynamics of the model selected for both countries (TVP-VAR-R3-SV). In the cases of Colombia and Mexico, most models suggest a positive response to a favorable U.S.-originated shock. For Colombia, non-SV models show short-run responses above those for the selected TVP-VAR-R2-SV model and later return to the initial path. For Mexico, the IRF for the selected TVP-VAR-R1-SV model lies on the middle range of the IRFs for the other models, with very similar impacts and persistence patterns. Results are also heterogenous for an unexpected raise in the Fed interest rate. In the cases of Chile and Colombia, the IRFs for the CVAR-SV and CVAR models suggest a positive output growth response, which is counterintuitive. In contrast, the IRFs for the TVP-VAR-SV and TVP- VAR-R3-SV models are more plausible. For Mexico and Peru, the results are clearer irrespective of the model (except for Mexico�s TVP-VAR model): these countries experience a fall in the pace of economic activity in response to a tightening of international �nancial conditions. We point out that, for all models, this kind of shock also implies an upward reaction in domestic interest rates; i.e., central banks raise their policy rates. We �nd that all PA economies bene�t from an increase in China�s growth in the short and medium run; i.e., this kind of shock has persistent e¤ects, with di¤erent magnitudes depending of the model used. For instance, the IRFs for the TVP-VAR-SV and TVP-VAR models are below all other estimations and show less lasting e¤ects (6-12 periods). In contrast, the CVAR-SV and 8 CVAR models show greater and more persistent e¤ects (12-20 periods). The intermediate models, particularly TVP-VAR-R1-SV and TVP-VAR-R3-SV, tend to yield more reasonable IRFs, with moderate impacts relative to the other models. Finally, in contrast with a shock on China�s growth, the impact from a positive shock on XPI growth has a short-run duration, dissipating in 2-5 periods, with the exception of Chile (7-15 periods). The following sections assess the results for the models selected using Bayesian criteria, as discussed in Section 4.4; i.e., TVP-VAR-R3-SV for Chile and Peru, TVP-VAR-R2-SV for Colombia, and TVP-VAR-R1-SV for Mexico. 4.5.1 Average Impact of External Shocks This section describes the average impact of the four external shocks mentioned above on the domestic variables of each PA economy, with the purpose of assessing whether the results are signi�cant across the sample. Figure 6 shows the median IRF and the associated credibility region (percentiles 16 and 84 of the distribution). Row 1 of each panel in Figure 6 shows the impact of a 1% increase in U.S. output growth. The output responses in Chile and Peru are very similar: a short-run expansion, to a 0.2% peak between quarters 2-3, followed by a gradual decline, to a 0.2%-0.3% contraction around quarter 10. The shock dissipates towards the fourth year of the forecast horizon. These mixed dynamics are due to the nature of U.S. growth changes, which are transmitted to PA economies via the external demand and �nancial channels. An increase in U.S. growth (Chile and Peru�s second major trading partner) stimulates exports to the U.S., in turn promoting domestic production. However, the results also show an upward Fed interest rate response to an increase in U.S. growth, which has a contractionary e¤ect on Chile and Peru�s growth. Moreover, both economies show an upward response of in�ation and the domestic interest rate, although Peru�s credibility region is wider than Chile�s. Colombia�s positive output growth reaction peaks at 0.2% in quarter 3. Thereafter, the credib- ility bands include a zero value; i.e., the impact on output (and in�ation) in the following periods is not signi�cant. Mexico shows a much clearer response: a 1% increase in U.S. growth raises Mexico�s growth by 0.7% towards quarter 3; and percentiles 16 and 84 are positive for close to eight quarters, re�ecting a moderate persistence resulting from this kind of shock. This behavior is associated with the role of U.S. business cycles in Mexico�s output �uctuations, given the considerable expansion of bilateral trade since the enactment of NAFTA (over 80% of Mexico�s exports and close to half of its imports are traded with the U.S., its main trading partner). These results are in line with Sosa (2008), who concludes that the impact of a U.S. growth shock on Mexico�s growth is very signi�cant, close to one-to-one as a general rule. Row 2 of each panel in Figure 6 shows the response of domestic variables to a 1% increase in the Fed interest rate. It is important to note that an upward Fed monetary shock results in a signi�cant and persistent fall in U.S. economic activity, in line with theory. The results show that an unexpected raise in the Fed rate results in a lagged deterioration in PA countries� economic activity; i.e., the contractionary e¤ect becomes more important after several months, especially in Chile, Mexico, and Peru; but is not signi�cant in Colombia. Again, the results for Chile and Peru are similar: a 1% increase in the Fed rate results in 0.4% fall in output growth in quarter 7 for Chile and in quarter 5 for Peru, with ample credibility regions including a zero value starting from quarter 12 for Chile and quarter 9 for Peru. Mexico experiences an important deterioration (around 0.7%) starting from the 10 �rst quarters after the shock, with persistent e¤ects beyond the 20 quarters considered. These results are in line with, and similar to, 9 those reported by Flores (2016). One way to understand these dynamics is considering that higher short-term rates translate into lower credit and, therefore, lower consumption and investment by U.S. households and �rms. In turn, the latter reduce their imports, thereby creating less income in PA economies. A main �nding is that, following a contractionary Fed shock, interest rates increase in all PA countries, notably Mexico and Peru, thus creating an additional negative e¤ects on economic activity. These empirical results provide evidence of the importance of U.S. monetary shocks; and might therefore contribute to enhancing the conduct of monetary policy in PA countries. For its part, a 1% increase in China�s growth (row 3 of each panel in Figure 6) results in positive and persistent e¤ects on the pace of economic activity in all PA economies. Growth in Chile, Colombia, and Mexico show a positive e¤ect of around 0.4% in quarters 5, 4, and 7 after the shock, respectively; and such gains persist until around the third year. In Chile, in�ation and the domestic interest rate show a signi�cant upward response, a result that is not as distinct in the cases of Colombia and Mexico. Peru shows the highest growth impact, peaking at 0.8% in quarter 4 and persisting beyond quarter 12; i.e., the impact of an increase in China�s growth is twice as large as for the other PA economies. In line with Bing et al. (2019), this considerable impact re�ects not only the real e¤ects from greater Chinese demand, but also an indirect e¤ect via commodity prices. These authors estimate that a 1% fall in China�s growth results in a 0.7%-1.4% contraction in Latin American growth. Moreover, using a GVAR model, the World Bank (2016) estimates that a 1% fall in China�s growth results in a 0.2% deceleration in Chile, Colombia and Mexico; and a 0.7% deceleration in Peru. These results are very similar to those obtained by Cesa-Bianchi et al. (2011). Row 4 of each panel in Figure 6 shows the IRFs for a shock on XPI growth for each economy. It is worth noting that commodity price volatility is important in explaining macroeconomic per- formance in PA countries, as the latter are mostly commodity exporters. World Bank information as of 2019 shows that copper exports are 50% of Chile�s total exports; copper and gold exports together are 47% of Peru�s total exports; and oil and coal exports together are 55% of Colombia�s total exports. In contrast, Mexico�s exports are more diversi�ed (commodities were around 12% of total exports in 2019). At the same time, commodity exports are important in Mexico due to their contribution to �scal revenues (20% from oil). Considering this common feature of PA economies, the results show a short-run impact on growth (in contrast with real shocks from China), except in Chile, where it is more persistent. For Colombia and Peru, a 10% increase in XPI growth induces a 1% expansion in the same period, which lasts until quarters 5-6 after the shock. For Mexico, there is a 2% response in the same period, which dissipates rather quickly (towards quarter 3). In Chile, the expansion lasts longer: a 10% increase in XPI growth results in a 0.8% growth increase in the same period, which moderates progressively until quarter 9. Lastly, with the exception of Colombia, policy interest rates respond in a contractionary manner to a positive export price shock (i.e., the monetary authorities raise them). 4.5.2 Evolution of the Impact of External Shocks Over Time An advantage of using TVP-VAR-SV models is the possibility to assess the impact of structural changes over time. Figure 7 shows the evolution over time of cumulative responses to the four shocks mentioned above for di¤erent horizons: the black, blue, and magenta lines show the cumulative responses toward the end of the �rst, second, and �fth year, respectively (we take the latter as the long-term response). The cumulative one-year impact from a 1% increase in U.S. growth (row 1 of each panel in 10 Figure 7) has a limited time variation and creates a 0.1%-0.2% short-term growth increase in Chile, Colombia, and Peru. In contrast, the impact is considerable in Mexico: by 1994, domestic growth would have increased by 0.65% in the �rst year, although it would have been closer to 0.8% in recent periods. The cumulative response by the second year suggests similar dynamics, although with greater impacts: in 1994 Mexico�s growth would have increased by 0.8% by the second year, but for 2019 the increase is estimated at 1%. These results re�ect greater U.S.-Mexico integration and synchronicity, with a signi�cant and immediate impact of U.S. shocks on Mexico�s growth. Row 2 of each panel in Figure 7 shows the cumulative responses to a 1% increase in the Fed rate. The two-year impacts on Chile, Mexico, and Peru have not �uctuated much over time, except under episodes like the U.S. crises of 2001 (the dot-com crash) and 2008. The fall in economic activity in these economies �uctuated, for the entire sample, between -0.5% and -0.2% by the second year after the shock. Additionally, in the four economies, the short-run monetary policy response was more important under international crisis episodes (2002 and 2009); and increased over time, re�ecting greater relative synchronicity between Fed movements and central bank decisions in PA countries. Regarding the impact from a 1% increase in China�s growth (row 3 of each panel in Figure 7), the results are heterogenous among PA countries. The cumulative impact on Chile�s growth does not vary considerably over time, with increases of around 0.3% in the �rst year. Towards the second year, the increase in growth, in�ation, and the interest rate is around 0.6%, 0.7%, and 0.2%-0.4%, respectively. In Colombia, the variation in the cumulative impact by the second year is greater: on average, growth would have increased by 0.6% in 1994-2001 and 0.7% in 2002-2011; and returned to around 0.6% in the last periods. The results also show a slight fall in the impact on the policy interest rate in 2002-2011. In Mexico, the growth response �uctuates between 0.4% in the �rst year and 0.8% in the second year, with limited evidence of time variation in these impacts. Finally, Peru shows the widest and most persistent impacts: in response to an unexpected increase in U.S. growth, Peru�s growth increases by around 0.8% in the �rst year, 1.2% in the second year, and 1.4% in the long run (�ve years). The evolution of the one-year cumulative impact in response to a positive shock on XPI growth over the last 25 years suggests considerable time variation in all PA countries (row 4 of each panel in Figure 7), especially during the GFC. In Chile and Peru, this impact has experienced sustained increases since the beginning of the sample, with peaks in 2009 and 2010, and then decelerated considerably. In 1994 the e¤ect from a 10% increase in XPI growth would have increased economic growth by around 0.5% in the �rst year in Chile and Peru; however, in 2009 this impact would have generated a response three times larger in these countries (1.5%), which is consistent with the high economic growth associated with the commodity boom. Over the last years, these impacts moderated towards pre-supercycle values (0.5%-1%). In Chile, the impact is more signi�cant beyond the �rst year: the increase in growth would have been close to 2% by the end of the second year in 2009; and would have moderated to 1% in 2019. In Colombia, the short-run e¤ect would have started with 0.2% growth increases in 1994; and would have reached 2.0% by 2019. In Mexico, the impact would have evolved from 0.7% to 2.2%, with an interruption in 2011-2012, when oil prices experienced an abrupt correction. The evidence also suggests that the impacts on in�ation and the interest rate increased over time. 4.6 Historical Decomposition (HD) The results have so far con�rmed that shocks originated in external demand, international prices, and �nancial conditions have signi�cant and time-varying implications for macroeconomic perform- ance in PA countries. At the same time, di¤ering economic structures and idiosyncratic policies in each country have contributed to o¤setting or magnifying such shocks. Along these lines, with the 11 purpose of decomposing the real growth, in�ation, and interest rate data into a trend (determin- istic) component and the cumulative e¤ects from structural shocks, we perform HDs on the models selected for each country. Figure 8 shows a predominant external in�uence in 2002-2011, a period associated with a commodity boom and high global growth. In contrast, the contribution of domestic shocks exceeds that of external shocks in 1994-2001, a high-volatility period with idiosyncratic shocks. There is also a limited contribution of external shocks in the last part of the sample (2012-2019), a period of moderation in global growth and international price correction. In this context, and in line with IMF (2014), we �nd that external factors explained, on average, more than half of the deviations in growth, in�ation, and interest rates in PA economies in 1994-2019. The HDs for growth in Chile and Peru share certain common features. For both countries, growth shocks originated in China are the most important external factor, as China is their main trading partner and copper (a key XPI component) is their main export commodity. Therefore, shocks on XPI growth are important in the decomposition of domestic growth in Chile (to a lesser extent than in Peru). In line with Rodríguez and Vassallo (2021), we �nd that around 70% of Peru�s average growth increase in 1994-2001 (4.2%) and 2002-2011 (6.2%) is explained by the four external factors identi�ed in the baseline model. Additionally, and mainly during �nancial crises, the contribution of U.S. growth shocks is neg- ative and reverts after each crisis for around �ve more quarters. In particular, external disturbances predominate in 2009, in the wake of the Lehman Brothers collapse and the impact of the GFC. For example, out of a fall of 8.1 percentage points in Peru�s growth in 2008-2009, 6.4 percentage points are explained by external factors. In Chile, out of a fall of 5.1 percentage points, 2.1 percentage points were explained by external factors. In the cases of Colombia and Mexico, growth variations are almost fully explained by external shocks, probably due to greater trade integration with the U.S. Regarding in�ation, external demand shocks (China) predominate in Chile, as well as magni�ed supply-side shocks during crisis periods. In Peru, in�ation has been considerably in�uenced by export price dynamics and U.S. economic activity. In Colombia, the contribution of growth shocks originated in China predominates in the periods close to the GFC, while in Mexico the relevant factor is the in�uence of U.S. growth disturbances. At the same time, the participation of Fed rate shocks is important in these economies for both the growth and in�ation HDs. However, in line with Carrillo-Maldonado and Díaz Cassou (2019), we �nd that U.S. monetary policy shocks have lost relevance over time, which should come as no surprise, considering that the Fed rate basically remained �at in 2009-2015, and later raises were considerably lower than in the past. We �nd that high interest rate volatility in the four economies in 1994-2001 was explained predominantly by domestic factors, mainly monetary and supply-side shocks. However, in later periods we identify an important moderation in this volatility, mainly associated with monetary structural reforms around the turn of the century; i.e., full IT adoption in 1999 in Chile, Colombia, and Mexico (Valdés (2007) and Urrutia et al. (2014)) and in 2002 in Peru (Rossini and Vega (2007)). By disaggregating the e¤ect of structural shocks we can build a counterfactual series to simulate a variable�s behavior in absence of external shocks. Figure 9 shows the results, where the black lines represent the observed values and the orange lines show the corresponding counterfactual series. The di¤erences become more pronounced in three sub-periods around the GFC: (i) in 2002-2008 (before the GFC), external disturbances enhanced average real growth in the four PA economies; (ii) in 2009, the external in�uence caused a deep fall in economic activity; and (iii) immediately after the GFC (2010-2011), external disturbances promoted recovery. That is, international conditions 12 magni�ed growth dynamics in PA economies, mainly during the commodity price boom. In absence of external shocks, macroeconomic �uctuations in PA countries would have followed a more moderate path without abrupt variations, mainly in crisis periods. For a more detailed examination of the sub-periods mentioned above, Table 3 compares observed vs. counterfactual growth �gures. We �nd that, without external shocks, the average growth in 2002-2008 (before the GFC) would have been 0.3 percentage points lower for Chile and Colombia. For Mexico and Peru, it would have been 1.0 and 1.7 percentage points lower, respectively. Additionally, in 2009 the average growth for PA economies would have been 3.1 percentage points higher; i.e., the losses from the GFC would have been substantially lower. Speci�cally, the fall in economic activity would have been 4.0, 3.0, 2.9, and 2.7 percentage points lower in Mexico, Chile, Peru, and Colombia, respectively. Finally, immediately after the GFC (2010-2011), the average recovery would have been 2.6, 2.2, 1.5, and 0.6 percentage points lower in Mexico, Peru, Chile, and Colombia, respectively. These results suggest that external in�uence on domestic output dynamics was greater in Mexico and Peru during the commodity boom. This in�uence has been more moderate, both in boom and crisis periods, in Chile and Colombia. At the same time, there are no signi�cant di¤erences between the observed and counterfactual data for in�ation and the interest rate in 1994-2001. As with output growth, the main divergences occur in 2002-2011. We con�rm that both the 2008-2009 general in�ation surge and the subsequent downward correction were in�uenced by an important external component. Additionally, the re- duction in interests rates after the GFC in the four PA economies would have been much more gradual and moderate in absence of external disturbances, especially in Colombia and Mexico. 4.7 Forecast Error Variance Decomposition (FEVD) Finally, we carry out an FEVD to identify the contributions of external shocks to long-term mac- roeconomic �uctuations in PA economies. Figure 10 shows the evolution over time of the FEVDs for domestic growth, in�ation, and the interest rate in the models selected for each country. We underscore that the FEVD is instrumental in dividing the forecast error variance for each variable into the components attributable to each shock. In particular, for each point in time we calcu- late the medians of the parameters; and use each set of parameters to forecast variables h periods ahead.4 The panels for the four PA economies in Figure 10 have a common feature: a limited parti- cipation of all external factors in the mid-1990s and the turn of the century (around 10%-40%), which grew steadily to peak values around 2009 (above 90% in Mexico) and moderated (and even fell slightly) in recent years. Additionally, the participation of monetary and supply-side shocks predominate within the domestic block, especially in the initial sample years; however, following IT adoption and central banks�greater use of a short-run interest rate as monetary instrument, this participation drops abruptly and even disappears in some cases. On the external front, XPI growth had a limited participation in the 1990s, but grew to a signi�cant FEVD share in all PA countries. Another key factor is China�s growth, which had an important participation, especially from 1994 to the GFC. U.S. growth shows a lower participation, but remains present in all FEVDs. Finally, Fed rate participation increased sporadically in crisis periods (2002 and 2008). Table 4 shows the average participation of external and domestic factors in growth within the baseline model. In 1994-2001, external factors explained 33% and 38% of growth �uctuations in 4The forecast horizon considered in this article is h = 20 quarters. 13 Colombia and Peru, respectively. In 2002-2011 this contribution doubled (73% and 79%, respect- ively). In the cases of Chile and Mexico, the participation of external factors was 48% and 50% in 1994-2001, respectively; and increased to 80% and 92% in 2002-2011. In all cases, the participation of international factors in output �uctuations increases signi�cantly during commodity booms. This participation moderates slightly towards the last part of the sample (2012-2019), except for Mexico, where external factors almost fully explain domestic growth variability (94% on average). Sorting PA countries according to their long-term vulnerability to external shocks, we obtain the following result: Mexico 93%, Colombia 88%, Peru 65%, and Chile 47%. At the same time, we emphasize that: (i) FEVD participations re�ect the uncertainty sources that determine forecasts for the relevant variables (in contrast with HD, which re�ects historic contributions); and (ii) FEVD results are sensitive to the speci�cation of the external variables used in the model, as discussed later in the section on robustness exercises. 5 Robustness Analysis With the purpose of validating the results in Section 4, we propose four complementary exercises, which imply the following changes in the baseline model: (i) using informative priors via a training sample; (ii) modifying two external variables (Fed Funds Rate and XPI growth); (iii) using low- dimensional models (4, 5, and 6 variables); and (iv) expanding the model by including public investment in the domestic block. For space reasons, the �gures for this sections have been grouped in an Appendix, which is available on request. 5.1 Changes in Priors We choose a training sample, as in Primiceri (2005), to obtain an informative prior that can provide more objective information compared with the di¤use prior used by Chan and Eisenstat (2018). We use the �rst 10 years of the sample (40 observations covering 1994Q1-2003Q4) to calibrate the prior distribution of the initial conditions. For example, in order to characterize the mean and variance of �0 we choose the OLS estimations (�̂OLS) and four times their variance in a constant VAR, estimated in the initial sub-sample. This prior captures the characteristics of the initial dynamics of the complete system and establishes a prior that is closer to, and more objective for, each parameter. Table 5 shows the values for the marginal likelihood and the DIC. The results con�rm the gains (in terms of goodness of �t) from considering SV. Additionally, TVP-VAR and CVAR continue to be the least-�tting models, thereby con�rming the preference for models that include SV. The models selected for Chile, Colombia, and Peru in the main section hold up; but, in the case of Mexico, the BF and the DIC indicate that the best-�tting model using informative priors is TVP-VAR-R3-SV (which includes time-varying intercepts). In general, the sign and magnitude of the impacts remain the same for all countries, thus con�rming the robustness of the baseline model using more restricted priors. The most important di¤erences are the following: (i) Chile shows a slightly higher output growth response to a Fed rate shock, but a lower response to a shock on China�s growth; (ii) Colombia�s output growth response to a U.S. growth shock becomes non-signi�cant; and (iii) Peru�s output growth response to a favorable XPI growth shock is more signi�cant (0.1% at the moment of the shock using the baseline model vs. 0.15% using informative priors). In general, we con�rm that Fed rate and XPI growth shocks create greater variability in cumu- lative domestic responses, in contrast with the more stable responses to shocks on U.S. and China�s growth. In particular, the short-term output growth response to a shock on XPI growth shows an 14 upward trend from 1994 to 2009 in Chile and Peru, with 0.2% and 0.25% peaks, respectively, and moderates towards the �nal periods. Colombia�s responses show peaks around 2009 (0.15%), but also a surge in the last part of the sample, with values close to 0.2% in 2019. In Mexico, cumulative responses are slightly lower than in the baseline model. Both HDs and FEVDs show that the higher domestic contribution to disturbances, identi�ed at the beginning of the sample (1994-2001), gives way to a greater relevance of international conditions in 2002-2011. In general, the results are consistent with those for the baseline model. 5.2 Changes in Variables This second exercise uses an alternative measure of the Fed interest rate, known as the Shadow Fed Fund Rate, introduced by Wu and Xia (2016); and replaces XPI growth for the terms-of-trade (TOT) index growth for each country to capture export/import movements. We note that we will continue to denote these variables as i�t and p � t in the HDs and FEVDs, respectively. The Bayesian criteria in Table 6 con�rm that the least-�tting models are those that do not consider SV modelling. Additionally, we use the models selected via marginal likelihood: TVP-VAR-R2-SV for Chile and Colombia, and TVP-VAR-R3-SV for Mexico and Peru. The IRFs di¤er very little from the results of the baseline model. The sign and signi�cance of the IRFs remain unchanged in response to an unexpected increase in the Shadow Rate for Chile, Colombia, and Peru (non-signi�cant for Colombia); but the magnitudes di¤er. For instance, output growth in Chile falls to a -0.25% low by quarter 7, while the baseline model estimates it at -0.4% by quarter 8. In Mexico, an increase in the Shadow Rate results in a maximum 0.5% fall in output growth in quarter 5, while the baseline model estimates it at -0.7% in quarter 8. In the case of Peru, inclusion of the Shadow Rate in the model moderates the impact on output growth relative to the baseline model. Substituting TOT growth for XPI growth also results in certain di¤erences: in Chile, a positive shock on TOT growth is more bene�cial to economic activity than a favorable shock on XPI growth. The results remain unchanged for Colombia; but in Mexico the response to a TOT growth shock decreases by half relative to the impact of an XPI growth shock estimated using the baseline model. In the case of Peru, the output growth response to a TOT growth shock is non-signi�cant. The FEVDs show greater di¤erences. The contribution of international conditions to output growth variability remains the same for Chile and Colombia (around 45% and 80% in 2019, re- spectively). In contrast, TOT growth inclusion slightly moderates this contribution in the cases of Mexico and Peru. In Mexico, the contribution of external shocks is around 75% in 2002-2011 and falls gradually to close to 60% in 2019. Similarly, in Peru this contribution rises to a peak of 75% in 2009 and moderates to 35% by 2019. 5.3 Smaller-Dimension Models 5.3.1 Four-Variable Model In this version, the external block is made up of one variable, XPI growth, for each PA economy. The domestic block shows the classic macroeconomic order (output growth, in�ation, and interest rate). The Bayesian criteria in Table 7 are instrumental in selecting the best-�tting model for each country: TVP-VAR-R3-SV for Chile and Peru; and TVP-VAR-R2-SV for Colombia and Mexico. The results indicate that a positive shock on XPI growth translates into a favorable and im- mediate output growth response in PA economies. In the period of the shock, Mexico shows the greater impact (a 0.4% increase, signi�cant until quarter 3), followed by Chile and Colombia (with 15 increases close to 0.2%, signi�cant until quarters 8 and 4, respectively). Finally, Peru shows a 0.1% increase in output growth, signi�cant until quarter 2. The cumulative one-, two-, and �ve-year responses of domestic variables are qualitatively similar to those described by the baseline model. The impact on output growth in Chile, Colombia, and Peru increases in the periods around the GFC (with an important surge towards the end of the sample in Colombia). In Mexico, the one-year cumulative response increases abruptly in 1994-2001 and later moderates. We point out that the impacts of XPI growth changes on output growth in the four-variable model tend to be larger that those estimated using the baseline model (except for Peru). These di¤ering results seem to be closely associated with the omission of relevant variables in the model speci�cation. The conclusions about the HDs and FEVDs for PA countries�domestic variables, even with one external variable, are basically the same as for the baseline model: a distinct predominance of external shocks in the con�guration of PA countries�macroeconomic �uctuations. In all cases, this predominance peaks during the GFC. At the same time, this vulnerability, as re�ected by the FEVD, receded in the last years of the sample: after peaking around 95% (Chile) and 80% (Peru) in 2009, there is evidence of an important moderation by 2019, with a 40% participation in both economies (a result that contrasts with the �ndings from the baseline model). 5.3.2 Five-Variable Model The external block includes the international interest rate channel (i�t ), leaving the Fed rate as the most exogenous variable in the system; i.e., Fed decisions a¤ect global �nancial and liquidity conditions, which have a contemporaneous impact on commodity prices. Both external variables have a direct e¤ect on PA economies, as characterized by the domestic blocks described above. Like in the four-variable model, the models selected for this robustness exercise are TVP-VAR- R3-SV for Chile and Peru; and TVP-VAR-R2-SV for Colombia and Mexico (Table 7). We note that, in the case of Peru, the DIC selects the TVP-VAR-R1-SV model, where the parameters for lagged observations and the intercepts remain constant; however, since the selection criteria provide di¤erent results, we choose the best model according to marginal likelihood. The IRFs for a Fed rate shock change substantially relative to the baseline model. Output growth responses in Mexico and Peru are statistically null (percentiles 16 and 84 include a zero value). Colombia shows a slightly positive reaction in quarter 1, which clashes with economic theory. In Chile, growth contracts persistently for almost 16 quarters (12 quarters in the baseline model). For their part, domestic macroeconomic responses to a shock on XPI growth maintain their sign and persistence relative to the baseline model. However, the magnitude of output growth responses is slightly higher in this robustness exercise; i.e., they are overestimated relative to the baseline model. Finally, time variability continues to be the di¤erentiating feature, especially regarding export price shocks. In addition, the involvement of external factors in variance decomposition continues to predominate, with a considerable contribution of international interest rate disturbances during the GFC and the dot-com crash. 5.3.3 Six-Variable Model The previous model included information on the �nancial and price channels. However, as for our purposes it is also necessary to consider the external demand channel, we include economic activity growth in China (ychnt ). We continue to take U.S. monetary policy as the most exogenous variable, 16 as it directly a¤ects �nancing costs in economies of global importance like China. In turn, we consider that the pace of economic activity in China has important implications for commodity indices. We use Bayesian criteria (Table 7) to select the best-�tting models: TVP-VAR-R3-SV for Chile, Colombia, and Mexico; and CVAR-SV for Peru. The latter is similar to the TVP-VAR-R3-SV model, although it does not include time-varying intercepts. The IRFs suggest that inclusion of China�s growth within the system contributes to correctly identifying the marginal impact of Fed rate shocks on Chile, Mexico, and Peru. Additionally, positive shocks on China�s growth have a favorable e¤ect on commodity indices and, in turn, on PA countries� growth, with peak impacts of 0.3% in Chile, 0.4% in Colombia and Mexico, and 0.8% in Peru by quarter 4. These responses last 8-12 quarters; i.e., the IRFs indicate a moderate persistence. The decompositions show that most of the variability attributable to commodity indices shifts to China�s growth, especially in 2002-2011, when Chinese expansion reached historic highs and propelled a global commodity boom. In sum, FEVD and HD results for the four-, �ve-, and six-variable models are qualitatively similar and consistent with the �ndings in Sections 4.6 and 4.7. 5.4 Inclusion of Fiscal Policy in the Baseline Model This exercise incorporates �scal policy into the baseline model in the form of real public investment growth (gpubt ). In this case, gpubt becomes the most exogenous domestic variable, as increasing the share of public investment in GDP is a �scal policy decision. We perform this exercise only for Chile and Peru, in view of limitations in accessing real public investment growth data for the other PA countries. The series were obtained from Chile�s Budget Directorate (DIPRES) and the Central Reserve Bank of Peru. We estimate the eight-variable model using the non-informative priors described in Section 4.2 for the seven models. Table 8 shows the Bayesian criteria, which point to TVP-VAR-R3-SV as the best-�tting model for both Chile and Peru, thus con�rming the robustness and relevance of this model for their economic structures. In general, gpubt inclusion into the model does not substantially modify the IRFs for the baseline model, and therefore the in�uence of external shocks on the domestic variables preserves its impact and signi�cance. On the domestic front, gpubt has a distinct positive e¤ect on domestic growth, evidencing the potential of �scal policy to propel economic activity. At the same time, the impacts on in�ation and the interest rate are not clear. In Chile, output growth increases by 0.1% in the initial period and returns gradually to the initial path (percentiles 16 and 84 are positive until quarter 8). In Peru, the impact on output growth at the moment of the shock is greater but of shorter duration (0.25% at the moment of the shock; and percentiles 16 and 84 are positive until quarter 6). These results re�ect a moderate persistence in response to a shock, probably associated with the fact that expanding the provision of public goods (e.g., infrastructure) stimulates employment in the short run and enhances medium- and long-run gains by increasing the capital endowment. Additionally, we �nd that the two-year cumulative impact (blue line) in Chile has not been constant over time: it was around 0.4% in 1994, increased gradually to 0.6% in 2015, and peaked at over 1.0% in the last four years. This impact has also grown signi�cantly in Peru since the beginning of the 2000s, implying that currently an increase in gpubt would yield higher returns on GDP that in the previous decade. Speci�cally, the response to a 1% increase in gpubt is an estimated 0.2% cumulative two-year output growth increase. However, in more recent periods, like 2019, such 17 a shock would increase output growth by 0.3%. Therefore, the results suggest that the impact of �scal policy on domestic economic activity has increased in Chile and Peru. These results are in line with Jiménez and Rodríguez (2019), who �nd that output growth responses to public capital expenditure shocks (associated with gpubt ) in Peru have increased over time. HD results con�rm that, historically, external shocks have been the main drivers of domestic �uctuations, particularly during commodity booms. Additionally, gpubt shocks on both economies have a greater participation in output growth decompositions. Chile shows a distinct positive im- pulse in periods prior to the GFC (2005-2008); however, following the 2009 fall, public investment contributes negatively to recovery (2010-2011). Peru shows a positive impulse from gpubt in key periods like 1998-1999, when the economy experienced both external and domestic shocks (inter- national crises and the El Niño Phenomenon, respectively), and to a lesser extent during the GFC (2009-2010). In sum, the inclusion of a �scal policy variable does not alter the IRFs for external shocks; and the HDs show that such shocks remain predominant. However, the inclusion of real public investment growth within the system changes the FEVD results signi�cantly. The FEVD analysis shows that gpubt contribution in both countries was 50% of output variation on average over the sample, surpassing external factors as main uncertainty source for long-run domestic growth. In particular, in the case of Chile, external conditions explained around 30% of output �uc- tuations in 1994-2001, peaked at 60% in 2009, and �nally fell to 10% in 2019. In�ation shows a similar pattern; but domestic factors remain predominant in interest rate behavior in 1994-2001 (around 80% of domestic interest rate variability). Regarding output growth variability in Peru, external factors explain around 20% in 1994-2001, peak at 50% in 2009, and decline to close to 30% in 2019. External factor participation in in�ation variability peaks at close to 70% in 2009 and declines to 40% in 2019; but, like in Chile, it remains limited in explaining interest rate variability in 1994-2001. While external factors continued to grow in in�uence during the commodity boom (especially China�s growth and XPI changes), their contribution decreased in favor of the �scal variable. In this regard, the literature indicates that the �scal multiplier of gpubt on output is greater than the unit, exceeding the multipliers for other �scal expenditure and revenue multipliers; see Végh et al. (2018). In addition to its impact, this variable shows considerable volatility relative to output: the standard deviation of gpubt is 5:7 times that of output over the sample (in line with the �ndings by Castillo et al. (2007) for Peru), which introduces further uncertainty in output growth behavior. The results con�rm that gpubt has considerable impact on output and is the greater source of un- certainty for output growth in Chile and Peru. Along these lines, Mendoza and Collantes Goicochea (2017) suggest that this variable is the best macroeconomic policy instrument for impacting eco- nomic activity. Therefore, while external factors have historically had a direct impact on domestic economic activity, we emphasize that domestic instruments like gpubt (which have experienced a growing impact over time) can be e¤ective stabilizing tools, precisely against unfavorable external shocks. 6 Conclusions This article seeks to examine and quantify the evolution of the impact of external shocks on the macroeconomic dynamics of PA countries. For this purpose, we asses jointly the main transmission channels through which these shocks propagate to small and open economies: the trade, �nancial, and price channels. Instead of using traditional estimation tools, we adopt a Bayesian approach to estimate a family of VAR models that allow time variance (or constancy) for certain groups of 18 parameters and the variance matrix (TVP-VAR-SV). The results for the four PA economies suggest that models that allow time variation for certain (not all) parameters, and include SV, perform better than traditional VAR models and models where all parameters are time-varying, as in Primiceri (2005) or Cogley and Sargent (2005). The impulse-response analysis throws three main �ndings. First, China�s output �uctuations create the most signi�cant and persistent impacts, reinforced by a positive chain reaction in export prices. Second, we identify considerable time variation in PA countries�macroeconomic responses to favorable XPI shocks. Third, unexpected Fed rate increases result in signi�cant increases in PA countries�monetary policy rates, an e¤ect that escalates during crisis periods and further deepens the negative impact on domestic output growth. Additionally, variance decompositions show that external factors explained over 50% of growth, in�ation, and interest rate deviations in PA economies, notably in a context of booming commodity prices, high global growth, and �nancial crisis (2002-2011). Speci�cally, we �nd that in 2009, in absence of external shocks, average growth in the PA bloc would have been 3.2 percentage points higher. In particular, the results show that external shock absorption over the sample is higher in Mexico and Peru. A counterfactual exercise suggests that, in absence of external disturbances, output dynamics would have changed the least in Chile and Colombia. On the contrary, external factors have led to important gains (and losses) in Mexico and Peru; i.e., they are highly vulnerable to changes in international conditions. These conclusions con�rm that small open commodity-exporting economies face considerable challenges from their exposure to changes in the international environment. Notably, strengthening the capacity to implement countercyclical policies should be a priority, as they are the main tool for attenuating macroeconomic volatility in the face of unfavorable external shocks. Speci�cally, build- ing �scal savings and foreign exchange reserves in boom times creates greater room for maneuver and enhances resources for withstanding such disturbances. Finally, we point out the following limitations: (i) the computational complexities in calculating Bayesian criteria and limitations in data availability hinder the estimation of larger models; and it would be useful to (ii) test the sensitivity of the results under a di¤erent identi�cation scheme (e.g., sign restrictions); and (iii) restrict the existence of domestic (in addition to contemporaneous) e¤ects of the external block by implementing an exogenous block. References [1] Abiad, A., Bluedorn, J., Guajardo, J., and Topalova, P (2015). The Rising Resilience of Emerging Market and Developing Economies. World Development 72, 1-26. doi: https:// doi.org/10.1016/j.worlddev.2015.02.005. [2] Abrego, L., and Osterholm, P. (2008). External Linkages and Economic Growth in Colombia: insights from a Bayesian VAR Model. IMF Working Papers 33(12), 1788-1810. doi: https: //doi.org/10.1111/j.1467-9701.2010.01288.x. [3] Aguirre, E. (2011). Business Cycles in Emerging Markets and Implications for the Real Ex- change Rate. Tesis Doctoral, Columbia University, New York. [4] Ahmed, S., and Murthy, R. (1994). Money, Output and Real Business Cycles in a Small Open Economy. The Canadian Journal of Economics 27(4), 982-993. 19 https://doi.org/10.1016/j.worlddev.2015.02.005 https://doi.org/10.1016/j.worlddev.2015.02.005 https://doi.org/10.1111/j.1467-9701.2010.01288.x https://doi.org/10.1111/j.1467-9701.2010.01288.x [5] Belmonte, M., Koop, G. and Korobilis, D. (2014). Hierarchical Shrinkage in Time-Varying Coe¢ cients Models. Journal of Forecasting 33(1), 80-94. doi: https://doi.org/10.1002/ for.2276. [6] Bijsterbosch, M., and Falagiarda, M. (2015). The Macroeconomic Impact of Financial Frag- mentation in the Euro Area: Which Role for Credit Supply?. Journal of International Money and Finance 54, 93-115. doi: https://doi.org/10.1016/j.jimonfin.2015.02.013. [7] Bing, X., Roth, M., and Santabárbara, D. (2019). Global Impact of a Slowdown in China. Economic Bulletin 1, 1-11. [8] Blecker, R. A. (2009). External Shocks, Structural Change, and Economic Growth in Mex- ico, 1979-2007. World Development 37(7), 1274-1284. doi: https://doi.org/10.1016/j. worlddev.2008.10.004. [9] Calvo, G. A., Leiderman, L., and Reinhart, C. M. (1993). Capital In�ows and Real Exchange Rate Appreciation in Latin America: The Role of External Factors. IMF Sta¤ Papers 40(1), 108-151. International Monetary Fund. doi: https://doi.org/10.5089/9781451964455.001. [10] Calvo, G. A., and Mendoza, E. G. (1998). Empirical Puzzles of Chilean Stabilization Policy. SSRN Electronic Journal 92(2). doi: https://doi.org/10.2139/ssrn.86749. [11] Canova, F. (2005). The Transmission of US Shocks to Latin America. Journal of Applied Econometrics 20(2), 229-251. doi: https://doi.org/10.1002/jae.837. [12] Carrillo, J. A., Elizondo, R., and Hernández-Román, L. G. (2020). Inquiry on the transmission of U.S. aggregate shocks to Mexico: a SVAR approach. Journal of International Money and Finance 104, article 102148. doi: https://doi.org/10.1016/j.jimonfin.2020.102148. [13] Carrillo-Maldonado, P., and Díaz Cassou, J. (2019). An Anatomy of External Shocks in the Andean Region. IDB Working Paper Series 1042. Inter-American Development Bank. doi: https://doi.org/10.18235/0001949. [14] Castillo, P., Montoro, C., and Tuesta, V. (2007). Hechos estilizados de la economía peruana. Revista de Estudios Económicos 14, 33-75. [15] Castillo, P., Montoya, J., and Quineche, R. (2016). From the �Great In�ation�to the �Great Moderation�in Peru: A Time Varying Structural Vector Autoregressions Analysis. Documento de Trabajo 003. Banco Central de Reserva del Perú. [16] Cesa-Bianchi, A., Pesaran, M. H., Rebucci, A., and Xu, T. (2011). China�s Emergence in the World Economy and Business Cycles in Latin America. IDB Working Paper Series 266. Inter-American Development Bank. doi: https://doi.org/10.2139/ssrn.1972109. [17] Chan, J. C. C., and Eisenstat, E. (2015). Marginal Likelihood Estimation with the Cross- Entropy Method. Econometric Reviews 34(3), 256�285. doi: https://doi.org/10.1080/ 07474938.2014.944474. [18] Chan, J. C. C., and Eisenstat, E. (2018). Bayesian Model Comparison for Time-Varying Para- meter VARs with Stochastic Volatility. Journal of Applied Econometrics 33(4), 509�532. doi: https://doi.org/10.1002/jae.2617. 20 https://doi.org/10.1002/for.2276 https://doi.org/10.1002/for.2276 https://doi.org/10.1016/j.jimonfin.2015.02.013 https://doi.org/10.1016/j.worlddev.2008.10.004 https://doi.org/10.1016/j.worlddev.2008.10.004 https://doi.org/10.5089/9781451964455.001 https://doi.org/10.2139/ssrn.86749 https://doi.org/10.1002/jae.837 https://doi.org/10.1016/j.jimonfin.2020.102148 https://doi.org/10.18235/0001949 https://doi.org/10.2139/ssrn.1972109 https://doi.org/10.1080/07474938.2014.944474 https://doi.org/10.1080/07474938.2014.944474 https://doi.org/10.1002/jae.2617 [19] Chan, J. C. C., and Grant, A. L. (2016). Fast Computation of the Deviance Information Criterion for Latent Variable Models. Computational Statistics and Data Analysis 100, 847� 859. doi: https://doi.org/10.1016/j.csda.2014.07.018. [20] Chan, J. C. C., and Jeliazkov, I. (2009). E¢ cient Simulation and Integrated Likelihood Estim- ation in State Space Models. International Journal of Mathematical Modelling and Numerical Optimisation 1(1-2), 101-120. doi: https://doi.org/10.1504/IJMMNO.2009.030090. [21] Chan, J. C. C., Koop, G., Leon-Gonzales, R., and Strachan, R. W. (2012). Time Varying Dimension Models. Journal of Business and Economic Statistics 30(3), 358-367. doi: https: //doi.org/10.1080/07350015.2012.663258. [22] Chávez, P. and Rodríguez, G. (2022). Time Changing E¤ects of External Shocks on Macroeco- nomic Fluctuations in Peru: Empirical Application Using Regime-Switching VAR Models with Stochastic Volatility. Manuscript. Department of Economics, Ponti�cia Universidad Católica del Perú. [23] Chib, S., Nardari, F., and Shephard, N. (2006). Analysis of High Dimensional Multivariate Stochastic Volatility Models. Journal of Econometrics 134(2), 341-371. doi: https://doi. org/10.1016/j.jeconom.2005.06.026. [24] Clark, T. E. (2011). Real-Time Density Forecast from Bayesian Vector Autoregressions with Stochastic Volatility. Journal of Business and Economic Statistics 29(3), 327-341. doi: https: //doi.org/10.1198/jbes.2010.09248. [25] Cogley, T., and Sargent, T. J. (2001). Evolving post-world war II US in�ation dynamics. NBER Macroeconomics Annual 16, 331-388. [26] Cogley, T., and Sargent, T. J. (2005). Drifts and volatilities: Monetary Policies and Outcomes in the Post WWII US. Review of Economic Dynamics 8(2), 262-302. doi: https://doi.org/ 10.1016/j.red.2004.10.009. [27] D�Agostino, A., Gambetti, L., and Giannone, D. (2013). Macroeconomic Forecasting and Structural Change. Journal of Applied Econometrics 28, 82-101. doi: https://doi.org/10. 1002/jae.1257. [28] Dancourt, O., Mendoza, W., and Vilcapoma, L. (1997). Fluctuaciones económicas, shocks externos, Perú 1950-1996. Working Paper 135, Ponti�cia Universidad Católica del Perú. [29] Del Negro, M., and Obiols-Homs, F. (2001). Has Monetary Policy Been so Bad that It Is Better to Get Rid of It? The Case of Mexico. Journal of Money, Credit and Banking 33(2), 404-433. doi: https://doi.org/10.2307/2673908. [30] Del Negro, M., and Primiceri, G. (2015). Time Varying Structural Vector Autoregressions and Monetary Policy: A Corrigendum. Review of Economic Studies 82(4), 1342-1345. doi: https://doi.org/10.1093/restud/rdv024. [31] Echavarría, J. J., González, A., López, E., and Rodríguez, N. (2012). International Finan- cial and Real Shocks and their Impact on the Colombian Economy. Ensayos sobre Política Económica 30(69), 13-66. doi: https://doi.org/10.32468/Espe.6901. [32] Flores, J. (2016). Transmisión de choques de política monetaria de Estados Unidos sobre América Latina: Un enfoque GVAR. Revista de Estudios Económicos 32, 35-54. 21 https://doi.org/10.1016/j.csda.2014.07.018 https://doi.org/10.1504/IJMMNO.2009.030090 https://doi.org/10.1080/07350015.2012.663258 https://doi.org/10.1080/07350015.2012.663258 https://doi.org/10.1016/j.jeconom.2005.06.026 https://doi.org/10.1016/j.jeconom.2005.06.026 https://doi.org/10.1198/jbes.2010.09248 https://doi.org/10.1198/jbes.2010.09248 https://doi.org/10.1016/j.red.2004.10.009 https://doi.org/10.1016/j.red.2004.10.009 https://doi.org/10.1002/jae.1257 https://doi.org/10.1002/jae.1257 https://doi.org/10.2307/2673908 https://doi.org/10.1093/restud/rdv024 https://doi.org/10.32468/Espe.6901 [33] Fornero, J., Kirchner, M., and Yany, A. (2016). Terms of Trade Shocks and Investment in Commodity-Exporting Economies. Working Paper 773, Banco Central de Chile. [34] Gruss, B., and Kebhaj, S. (2019). Commodity Terms of Trade: A New Database. IMF Working Paper 21. International Monetary Fund. doi: https://doi.org/10.5089/9781484393857. 001. [35] Guevara, B., Rodríguez, G. and Yamuca, L. (2022). External Shocks and Macroeconomic Fluctuations in Peru: Time-Varying E¤ects Using a Mixture Innovation TVP-VAR-SV Model. Manuscript. Department of Economics, Ponti�cia Universidad Católica del Perú. [36] Harvey, A., Ruiz, E., and Shephard, N. (1994). Multivariate Stochastic Variance Models. The Review of Economic Studies 61(2), 247-264. doi: https://doi.org/10.2307/2297980. [37] Hausmann, R., and Gavin, M. (1995). Overcoming Volatility: Economic and Social Progress in Latin America. Mimeo, Inter-American Development Bank. [38] Ho¤maister, A. W., and Roldós, J. E. (1997). Are Business Cycles Di¤erent in Asia and Latin America? IMF Working Paper 9, International Monetary Fund. [39] International Monetary Fund (2012). IMF Country Report 12/266, Chile Selected Issues. doi: https://doi.org/10.5089/9781513559858.002. [40] International Monetary Fund (2014). World Economic Outlook: Recovery Strengthens, Re- mains Uneven. Washington D.C. [41] Izquierdo, A., Romero, R., and Talvi, E. (2007). Booms and Busts in Latin America: The Role of External Factors. IDB Publications, Working Paper 1612, Inter-American Development Bank. doi: https://doi.org/10.2139/ssrn.1820920. [42] Jiménez, A., and Rodríguez, G. (2019). Time-Varying Impact of Fiscal Shocks over GDP Growth in Peru: An Empirical Application using Hybrid TVP-VAR-SV Models. Documento de Investigación del Consejo Fiscal 001. [43] Kim, S., Shephard, N., and Chib, S. (1998). Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models. Review of Economic Studies 65(3), 361-393. doi: https: //doi.org/10.1111/1467-937X.00050. [44] Kose, M. (2002). Explaining Business Cycles in Small Open Economies: How Much Do World Prices Matter? Journal of International Economics 56(2), 299-327. doi: https://doi.org/ 10.1016/S0022-1996(01)00120-9. [45] Lubik, T., and Teo, W. L. (2005). Do World Shocks Drive Domestic Business Cycles? Some Evidence from Structural Estimation. Working Paper 522, Johns Hopkins University. [46] Mackowiak, B. (2007). External Shocks, U.S. Monetary Policy and Macroeconomic Fluctu- ations in Emerging Markets. Journal of Monetary Economics 54(8), 2512-2520. doi: https: //doi.org/10.1016/j.jmoneco.2007.06.021. [47] Mahadeva, L., and Gómez, J. (2009). The International Cycle and Colombian Monetary Policy. Borradores de Economía 557. Banco de la República de Colombia. doi: https://doi.org/ 10.32468/be.557. 22 https://doi.org/10.5089/9781484393857.001 https://doi.org/10.5089/9781484393857.001 https://doi.org/10.2307/2297980 https://doi.org/10.5089/9781513559858.002 https://doi.org/10.2139/ssrn.1820920 https://doi.org/10.1111/1467-937X.00050 https://doi.org/10.1111/1467-937X.00050 https://doi.org/10.1016/S0022-1996(01)00120-9 https://doi.org/10.1016/S0022-1996(01)00120-9 https://doi.org/10.1016/j.jmoneco.2007.06.021 https://doi.org/10.1016/j.jmoneco.2007.06.021 https://doi.org/10.32468/be.557 https://doi.org/10.32468/be.557 [48] MEF (2019). Marco Macroeconómico Multianual 2020-2023. Ministerio de Economía y Finan- zas. [49] Melo-Becerra, L. A., Parrado-Galvis, L. M., Ramos-Forero, J. E., and Zarate-Solano, H. M. (2020). E¤ects of Booms and Oil Crisis on Colombian Economy: A Time-Varying Vector Autorregresive Approach. Revista de Economía del Rosario 23(1), 31-63. doi: https://doi. org/10.12804/revistas.urosario.edu.co/economia/a.8631. [50] Mendoza, E. G. (1995). The Terms of Trade, the Real Exchange Rate and Economic Fluc- tuations. International Economic Review 36(1), 101-137. doi: https://doi.org/10.2307/ 2527429. [51] Mendoza, W., and Collantes Goicochea, E. (2017). La economía de PPK. Promesas y resulta- dos: la distancia que nos separa. Documento de Trabajo 440, Ponti�cia Universidad Católica del Perú. [52] Nakajima, J., and West, M. (2013). Bayesian Analysis of Latent Threshold Dynamic Mod- els. Journal of Business and Economic Statistics 31(2), 151-164. doi: https://doi.org/10. 1080/07350015.2012.747847. [53] Nolazco, J. L., Lengua Lafosse, P., and Céspedes, N. (2016). Contribución de los choques externos en el crecimiento económico del Perú: un modelo semiestructural. Documento de Trabajo 006, Banco Central de Reserva del Perú. [54] Ojeda Cunya, J. A., and Rodríguez, G. (2022). Time-Varying E¤ects of External Shocks on Macroeconomic Fluctuations in Peru: Empirical Application Using TVP-VAR-SV Models. Manuscript. Department of Economics, Ponti�cia Universidad Católica del Perú. [55] Osterholm, P., and Zettelmeyer, J. (2007). The E¤ect of External Conditions on Growth in Latin America. IMF Sta¤ Papers 55(4), 595-623. doi: https://doi.org/10.1057/imfsp. 2008.20. [56] Primiceri, G. E. (2005). Time Varying Structural Vector Autoregressions and Monetary Policy. The Review of Economic Studies 72(3), 821-852. doi: https://doi.org/10.1111/ j.1467-937X.2005.00353.x. [57] Rodríguez, G., and Vassallo, R. (2021). Impacto de Choques Externos sobre la Economía Peruana: Aplicación Empírica usando Modelos TVP-VAR-SV. Documento de Investigación 001, Consejo Fiscal del Perú. [58] Rodríguez, G., Villanueva Vega, P., and Castillo Bardalez, P. (2018). Driving Economic Fluc- tuations in Peru: The Role of the Terms of Trade. Empirical Economics 53(3), 1089-1119. doi: https://doi.org/10.1007/s00181-017-1318-2. [59] Rossini, R., and Vega, M. (2007). El mecanismo de transmisión de la política monetaria en un entorno de dolarización �nanciera: el caso de Perú entre 1996 y 2006. Re