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 EXTERNAL SHOCKS AND ECONOMIC FLUCTUATIONS IN PERU: EMPIRICAL EVIDENCE USING MIXTURE INNOVATION TVP-VAR-SV MODELS Nº 529 Brenda Guevara, Gabriel Rodriguez and Lorena Yamuca Salvatierra DOCUMENTO DE TRABAJO N° 529 External Shocks and Economic Fluctuations in Peru: Empirical Evidence using Mixture Innovation TVP-VAR-SV Models Brenda Guevara, Gabriel Rodríguez and Lorena Yamuca Salvatierra Enero, 2024 DOCUMENTO DE TRABAJO 529 http://doi.org/10.18800/2079-8474.0529 http://doi.org/10.18800/2079-8474.0529 External Shocks and Economic Fluctuations in Peru: Empirical Evidence using Mixture Innovation TVP-VAR-SV Models Documento de Trabajo 529 @ Brenda Guevara, Gabriel Rodríguez and Lorena Yamuca Salvatierra (autores) Editado: © 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/ Encargado de la Serie: Gabriel Rodríguez Departamento de Economía – Pontificia Universidad Católica del Perú gabriel.rodriguez@pucp.edu.pe Primera edición – Enero, 2024 ISSN 2079-8474 (En línea) mailto:econo@pucp.edu.pe file:///d:/Users/mirtha.cornejo/Dropbox/cisepas%20(1)/Procesando-Documentos%20de%20Trabajo/jaleon@pucp.edu.pe External Shocks and Economic Fluctuations in Peru: Empirical Evidence using Mixture Innovation TVP-VAR-SV Models* Brenda Guevara� Pontificia Universidad Católica del Perú Gabriel Rodŕıguez� Pontificia Universidad Católica del Perú Leonela Yamuca Salvatierra§ Pontificia Universidad Católica del Perú This Version: November 27, 2023 Abstract We employ a family of mixture innovation, time-varying parameter VAR models with stochastic volatility (TVP-VAR-SV) to analyze the impact of external shocks on Peru’s GDP growth, inflation, and interest rate from 1998Q1 to 2019Q4. Our key findings are as follows: (i) the model best fitting the data features time-varying parameters and variances with a certain likelihood; (ii) impulse-response functions reveal that a 1% increase in the growth rate of Peru’s major trading partners (China and the U.S.) leads to a domestic GDP growth expansion of 0.65% and 0.21%, respectively; (iii) the forecast error variance decomposition shows that external shocks account for 65% of the long-term variability in output, 65% in inflation, and 67% in the interest rate; (iv) historical decomposition indicates that external shocks account for 50% of domestic GDP growth, particularly from 2002 onward. Lastly, we validate the results obtained in the primary specification through four robustness exercises. Classification JEL: C32, C52, E31, F41. Keywords: External Shocks, Macroeconomic Fluctuations, Time-Varying Parameter Vector Autoregressive Models, Stochastic Volatility, Mixture in Innovations, Peru. *This document is drawn from the Thesis submitted by Brenda Guevara and Leonela Yamuca Salvatierra to the Faculty of Social Sciences at Pontificia Universidad Católica del Perú (PUCP). We wish to express our gratitude for the valuable feedback provided by Paul Castillo (BCRP) and Fernando Pérez (BCRP) during the presentation of this document at the BCRP Economists’ Meeting in October 2023. Any remaining errors rest solely with the authors. �Department of Economics, Pontificia Universidad Católica del Perú, 1801 Universitaria Avenue, Lima 32, Lima, Perú. E-Mail Address: sofia.guevara@pucp.edu.pe. �Address for Correspondence: Gabriel Rodŕıguez, Department of Economics, Pontificia 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. §Department of Economics, Pontificia Universidad Católica del Perú, 1801 Universitaria Avenue, Lima 32, Lima, Peru. E-Mail Address: lorena.yamuca@pucp.edu.pe; leonelayamuca@bcp.com.pe. Choques Externos y Fluctuaciones Económicas en Perú: Evidencia Emṕırica utilizando Modelos TVP-VAR-SV con Mezcla en Innovaciones* Brenda Guevara� Pontificia Universidad Católica del Perú Gabriel Rodŕıguez� Pontificia Universidad Católica del Perú Leonela Yamuca Salvatierra§ Pontificia Universidad Católica del Perú Versión: Noviembre 27, 2023 Resumen Empleamos una familia de modelos VAR de parámetros cambiantes en el tiempo y volatilidad estocástica (TVP-VAR-SV) con mezcla en las innovaciones para analizar el impacto de los choques externos en el crecimiento del PIB, la inflación y la tasa de interés de Perú desde el primer trimestre de 1998 hasta el cuarto trimestre de 2019. Nuestros hallazgos importantes son los siguientes: (i) el modelo que mejor se ajusta a los datos presenta parámetros que vaŕıan en el tiempo y varianzas con cierta probabilidad; (ii) las funciones de impulso respuesta revelan que un aumento del 1% en la tasa de crecimiento de los principales socios comerciales del Perú (China y Estados Unidos) conduce a una expansión del crecimiento del PIB interno del 0.65% y 0.21%, respectivamente; (iii) la descomposición de la varianza del error de predicción muestra que los choques externos representan el 65% de la variabilidad a largo plazo del producto, el 65% de la inflación y el 67% de la tasa de interés; (iv) la descomposición histórica indica que los choques externos representan el 50% del crecimiento del PIB interno, particularmente a partir de 2002. Por último, validamos los resultados obtenidos en la especificación primaria mediante cuatro ejercicios de robustez. Clasificación JEL: C32, C52, E31, F41. Palabras Clave: Choques Externos, Fluctuaciones Macroeconómicas, Modelos VAR con Parámetros Cambiantes, Volatilidad Estocástica, Mezcla en Innovaciones, Perú. *Este documento está basado en la Tesis de Licenciatura presentada por Brenda Guevara y Leonela Yamuca Salvatierra ante la Facultad de Ciencias Sociales de la Pontificia Universidad Católica del Perú (PUCP). Deseamos expresar nuestro agradecimiento por la valiosos comentarios brindados por Paul Castillo (BCRP) y Fernando Pérez (BCRP) durante la presentación de este documento en el Encuentro de Economistas del BCRP en Octubre de 2023. Cualquier error restante es responsabilidad exclusiva de los autores. �Departamento de Economı́a, Pontificia Universidad Católica del Perú, Avenida Universitaria 1801, Lima 32, Lima, Perú. Correo Electrónico: sofia.guevara@pucp.edu.pe. �Dirección de Correspondencia: Gabriel Rodŕıguez, Departamento de Economı́a, Pontificia Universidad Católica del Perú, Avenida Universitaria 1801, Lima 32, Lima, Perú. Telephone: +511-626-2000 (4998), Correo Electrónico: gabriel.rodriguez@pucp.edu.pe. ORCID ID: https://orcid.org/0000-0003-1174-9642. §Departamento de Economı́a, Pontificia Universidad Católica del Perú, Avenida Universitaria 1801, Lima 32, Lima, Peru. Correo Electrónico: lorena.yamuca@pucp.edu.pe; leonelayamuca@bcp.com.pe. 1 Introduction The impact of external shocks on the domestic economy is a persistent concern in the field of macroeconomics and policy-making. Models related to international trade, such as the one proposed by Bussière et al. (2013), emphasize that a high degree of trade integration in the global economy leads to significant impacts on domestic output due the increased sensitivity of domestic demand to external conditions. Additionally, small, open, developing countries that have a higher degree of financial and trade integration, following the primary export model, are more susceptible to international developments than countries with a strong domestic market. In this context, it is crucial to analyze the extent and evolution of the impact of external shocks on Peru, a small, open economy specialized in commodity trade. The literature suggests that external shocks affect these economies through different channels. The first one is the financial channel, which impacts financing costs and capital flows through changes in foreign interest rates. Flores (2015) explains that an increase in the interest rate of the US Federal Reserve (Fed) generates capital outflows, resulting in reduced credit and investment, ultimately causing a significant and persistent decline in local economic activity. Furthermore, Contreras et al. (2017) explain that Peru is particularly exposed to this channel since private sector credit reached high levels of dollarization in the 1990s, making the country more sensitive to US monetary policy. Despite recent efforts to reduce financial dollarization, transactions in foreign currency persist at around 60%, meaning that a monetary shock in the federal funds rate can still have a significant impact on the Peruvian economy. The second one is the trade channel, which affects export incomes and capital flows through the demand from key trading partners, namely China and the US for Peru. Therefore, the level of trade openness is a critical factor in determining a country’s exposure to external shocks. As part of the reforms in the 1990s in Peru, foreign policy strategies, such as reducing and standardizing tariffs, increased the average level of trade openness1 from 30% between 1994-2006 to 50% between 2007-2019; see Dı́az-Cassou et al. (2020). These policies led to China and the US accounting for 29.4% and 12.3%, respectively, of Peru’s total exports in 2019, becoming Peru’s main trading partners. Finally, there is the nominal or price channel, which is activated by fluctuations in the terms of trade when prices of export commodities, such as copper and gold, change; see Nolazco et al. (2016) and Rodŕıguez et al. (2023). One characteristic that makes the Peruvian economy particularly sensitive to external shocks is its heavy reliance on exports of primary commodities. Mendoza and Collantes Goicochea (2017) highlight that, among external factors, terms of trade constitute the most critical component, explaining 25.6% of the variance in real GDP growth during the period 2001-2016. This finding is supported by Rodŕıguez et al. (2018), Florián et al. (2018), Rodriguez et al. (2023a, 2023b), and Chávez and Rodŕıguez (2023), who find that external shocks from the nominal channel explain between 30% and 60% of the variability in GDP growth. This document aims to provide further empirical evidence on the importance and evolution of external shocks on Peru’s economic activity between 1998Q1-2019Q4 using a family of time-varying parameter, mixture innovation VAR models with stochastic volatility (TVP-VAR-SV), as proposed by Koop et al. (2009). This approach has the advantage of estimating where, when, and how parameters change. The results obtained in this study contribute to the literature on the effects of external shocks on Peru by providing new stylized facts or reinforcing previous evidence. Firstly, the results suggest that the model incorporating time-varying parameters and stochastic volatility with a 99% probability is the best fit for the data, outperforming the traditional VAR model and 1The degree of average trade openness is measured as the average percentage of the value of exports relative to domestic output. 1 other restricted or unrestricted models. Secondly, favorable external shocks from China’s growth have the most substantial impact on domestic output, with an increase of up to 0.65%. Thirdly, external shocks explain between 60% and 65% of the forecast error variance decomposition (FEVD) for GDP growth, inflation, and interest rates. The remainder of the document is structured as follows: Section 2 offers a literature review; Section 3 outlines the methodology used to estimate the TVP-VAR-SV models proposed by Koop et al. (2009); Section 4 describes the data used and examines the impacts of external shocks on GDP growth, inflation, and interest rate; Section 5 provides an analysis of various robustness exercises; and Section 6 presents our conclusions. 2 Literature Review A considerable body of research suggests that external shocks have a significant impact on a coun- try’s domestic variables.2 Mendoza (1995) examines the relationship between the terms of trade and economic fluctuations, finding that external shocks explain approximately 50% of output vari- ability in G-7 countries. A similar result is found by Kose et al. (2003), who analyze economic fluctuations in North American countries, finding that external shocks explain 62.4% and 71.9% of growth variability in the US and Canada, respectively. Bergholt (2015) also finds that external shocks have a significant and persistent impact on the Canadian economy, increasing from 21.38% in the short term to 73.86% in the long term. In Russia, Simola (2019) concludes that external shocks play a significant role in the economy, arguing that a 10% increase in oil prices and a 1% increase in US output result in a 2% long-term increase in real GDP growth. In the UK, for the period 1997-2019, Cesa-Bianchi et al. (2021) show that global shocks explain 52% of output variability, with international financial shocks being the primary drivers. In Asia, Chua et al. (1999) analyze the influence of shocks from the US and Japan on output growth in Korea and Malaysia. They find that external shocks have a greater contribution than domestic shocks in the long term (64% for Korea and 56% for Malaysia). Similarly, Zaidi and Fisher (2010) estimate an SVAR model using Malaysian data and find that external shocks account for 65% of output variability in the long term, with commodity prices and foreign GDP having the most significant impact. Likewise, Zaim and Karim (2014) calculate that shocks from Singapore, the US, and Japan explain 48% and 86% of Malaysia’s inflation and interest rate variability, respectively, in the long term. Ruffer et al. (2007) estimate a VAR model and find that external shocks are more relevant than domestic shocks (68.7% for China, 81% for Malaysia, 75% for Singapore, and 52.4% for Thailand). Similar evidence is found by Allegret et al. (2012), who estimate an SVAR model and find that the contribution of these shocks is significant in the long term (58.58% for China, 82.91% for Japan, 63.11% for Indonesia, 69.20% for the Philippines, and 75.19% for Singapore). Of the four external shocks used, the most important for the five countries is oil price. In Latin America, studies indicate that external shocks play a significant role. Canova (2005) examines the impact of US shocks on output variability in eight countries (Mexico, Ecuador, Ar- gentina, Peru, Uruguay, Brazil, Chile, and Panama) and concludes that external shocks make a substantial average contribution of 58%. Österholm and Zettelmeyer (2008) obtain a similar result 2However, Ahmed and Murthy (1994) for Canada, Hoffmaister and Roldós (1997) for Latin America and Asia, and Boschi and Girardi (2011) for other Latin American countries, among other authors, suggest that output is primarily influenced by domestic supply and demand shocks, and that external shocks do not play a significant role in GDP growth variations. 2 using a Bayesian VAR model for the period 1994-2006 with data from Argentina, Brazil, Chile, Colombia, Mexico, and Peru, finding that external shocks account for 50-60% of output variability. In Bolivia, Jemio and Wiebelt (2003) find that a 10% drop in the terms of trade leads to a 2.5% reduction in GDP growth. In Colombia, Hernandez (2013) finds that shocks from commodities explain 30% of output variability. In Uruguay, Almada and Barreto (2017) estimate a Global Vector Autoregressive (GVAR) model and find that recessionary shocks of 1.34% and 3% on GDP growth in Argentina and Brazil, respectively, result in a 2% decline in domestic output growth. In Peru, the consensus among most authors is that external shocks are the primary drivers of economic fluctuations. Dancourt et al. (1997) highlight that out of the six recessions occurring between 1950-1996, five coincided with adverse external shocks, leading to the conclusion that external factors play a central role in the country’s economic oscillations. Castillo and Salas (2010) employed a VAR model with stochastic trends and determined that permanent terms-of-trade shocks account for 87% of output variability in the medium term. Similarly, Mendoza and Collantes Goicochea (2017) conclude that external factors (including US GDP growth, US inflation, 10- year US interest rates, China’s GDP growth, and terms-of-trade growth) explain 67.11% of real GDP growth variations during 2001-2016, with terms of trade growth being the most influential. Additionally, Rodŕıguez et al. (2018) suggest that terms of trade represent the primary source of uncertainty in GDP growth, contributing to 50% of the forecast error variance within one year. Florián et al. (2018) arrive at similar findings, noting that anticipated terms-of-trade shocks account for 57% of output variation over two years. Recent research in this field explores a range of TVP-VAR-SV models and Regime-Switching VAR models with stochastic volatility (RS-VAR-SV). Rodriguez et al. (2023a) present findings in- dicating that the growth of the S&P GCSI index explains 85% of the FEVD of output in the short term, while its influence on inflation hovers around 90%. Similarly, Rodŕıguez et al. (2023b) show that during the commodity boom period, external factors explained 80% of GDP growth fluctua- tions, thus confirming their pivotal role as the primary source of uncertainty. Additionally, Chávez and Rodŕıguez (2023) employ RS-VAR-SV models to demonstrate that, following the adoption of an inflation targeting (IT) regime in 2002, external shocks account for 70% of output variability. This research seeks to make a valuable contribution by offering additional empirical evidence for Peru, employing a distinct methodology. Following the approach of Koop et al. (2009), a family of TVP-VAR-SV models with mixture innovations is used, allowing for the estimation of when, where, and how variances and parameters change. Notably, this model shares a common feature with the works of Chávez and Rodŕıguez (2023) and Rodŕıguez et al. (2023) in specifying three channels for the transmission of external shocks to the Peruvian economy: cfinancial, ommercial, and nominal. 3 Methodology The econometric model is a mixture innovation TVP-VAR-SV model, as proposed by Koop et al. (2009), hereafter referred to as the Benchmark model, where both the transmission mechanism and the variance matrix can change over time. The model incorporates three blocks of parameters that can evolve differently over time: one is associated with the parameters of the VAR model coefficients, another with the error variance matrix, and the third with the contemporaneous effect coefficients. The advantage of the model is that it allows for estimating where, when, and how changes in parameters occur, rather than assuming a particular model in which all parameters change over time with a probability equal to 1, as in Primiceri (2005). 3 The reduced form of the TVP-VAR-SV model under a state-space form is: yt = XtBt + ut t = 1, 2, . . . , T (1) Bt+1 = Bt + vt t = 1, 2, . . . , T (2) where yt is an n × 1 vector of observations for the dependent variables; Bt is an m × 1 vector of states (VAR model coefficients); Xt is an n×m matrix containing explanatory variable data (each row of Xt contains lags of dependent variables and an intercept); ut ∼ N (0, Ht) and vt ∼ N (0, Qt) for t = 1, 2, ..., T. The errors in equations (1) and (2), ut and vs, are mutually independent for all t y s. The Gibbs sampler algorithm proposed by Carter and Kohn (1994) is used for drawing the state variables Bt = (B1, ..., BT ) ′.3 To allow the variance matrix of innovations and contemporaneous effect coefficients in the measurement equation to vary over time, a triangular decomposition is used, such that Ht = A−1 t ΣtΣ ′ t(A −1 t ) ′ , where Σt is a diagonal matrix with elements on the diagonal being σj,t for j = 1, ..., n and At is a lower triangular matrix: Σt =  σ1,t 0 · · · 0 0 σ2,t 0 . . . ... ... . . . . . . . . . σn−1,t 0 0 · · · 0 σn,t  , At =  1 0 · · · 0 α21,t 1 0 · · · ... ... . . . . . . . . . 1 0 αn1,t · · · αn(n−1),t 1  where Σt contains the variances and At contains the contemporaneous relationships. Additionally, the stochastic volatility framework is used for Σt, i.e., σt = (σ1,t, ..., σn,t) ′ where hi,t = ln(σi,t) and ht = (h1,t, ..., hp,t) ′. The elements of the ht vector evolve according to ht+1 = ht + ηt, where ηt ∼ N (0,W ) and exhibits no autocorrelation or correlation with the disturbance terms ut and vt. Koop et al. (2009) adapt the algorithm from Kim et al. (1998) and transform equation (1): y∗t = At(yt − Ztαt) = At(A −1 t Σtϵt) = Σtϵt, (3) where ϵt are independent and distributed as N (0, It). This system of measurement equations becomes a linear system through the following transformation of (3): y∗∗i,t = ln [ (y∗i,t) 2 + c ] , where c is a compensation constant that guarantees non-null values as proposed by Fuller (1996). This leads to the following state-space form: y∗∗t = 2ht + et, (4) ht = ht−1 + ηt, where et = ln(ϵ2t ), et, and ηt are uncorrelated, and et is distributed through a mixture of seven normal distributions according to Kim et al. (1998). For At, which contains the contemporaneous effect coefficients, Koop et al. (2009) stack the unrestricted elements by rows into a vector n(n−1) 2 as αt = (α21,t, α31,t, α32,t, ..., αn(n−1),t) ′ that evolves according to αt+1 = αt + ζt, where ζt ∼ N (0, S) and exhibits no autocorrelation or corre- lation with the disturbance terms ut, vt, and ηt. Koop et al. (2009) transform the measurement equation (1) so that the Carter and Kohn (1994) algorithm can be used for drawing the states: At(yt −X ′ tB̂t) = At(ŷt) = Σtϵt = ξt (5) 3For more details, see the Appendix of Koop et al. (2009). 4 where ξt ∼ N (0,ΣtΣ ′ t) and is independent of ζt. The structure of At is used to solve for ŷt on the left-hand side and obtain the following approximate state-space form: ŷt = Stαt + ξt, (6) αt+1 = αt + ζt, where St is detailed in Koop et al. (2009), and ŷi,t is the i-th element of ŷt. As for the mixture of innovations, the model allows for breakpoints in the VARmodel coefficients (Bt), and in the matrix of variances and contemporaneous effect coefficients Ht (Σt y At), where these breakpoints can occur at any time. Therefore, Kt = (K1t, K2t, K3t) ′ for t = 1, ..., T, where K1t ∈ {0, 1} controls the breakpoint in the VAR model coefficients, K2t ∈ {0, 1} controls the breakpoints in the variances, Σt; and K3t ∈ {0, 1} controls the breakpoints in the contemporaneous effect coefficients, At. Therefore, the state equations for Bt, ht and αt are reformulated as follows: Bt+1 = Bt +K1tvt, (7) ht+1 = ht +K2tηt, (8) αt+1 = αt +K3tζt, (9) where a Bernoulli distribution is used for the hierarchical order of the prior of Kjt; p(Kjt = 1) = pj for j = 1, 2, 3, i.e., pj is the probability of a breakpoint occurring at time t. Additionally, breakpoints occur independently in Bt, Σt y At. 3.1 Posterior Computation To estimate the posterior distributions of the parameters in the Benchmark model, a Markovian MCMC (Monte Carlo Markov Chain) algorithm is employed. Regarding the VAR model coefficients (Bt), a Wishart prior is used for Q−1 : Q−1 ∼ W(vQ, Q −1), where the posterior for Q−1 is a Wishart distribution: Q−1|Data ∼ W(vQ, Q −1 ). For Σt, a Wishart prior is used for W−1 : W−1 ∼ W(vw, W−1), where the posterior for W−1 is a Wishart distribution: W−1|Data ∼ W(vw, W −1 ). For At, a Wishart prior is employed for S−1 j :S−1 j ∼ W(vSj , S −1 j ), where S−1 j is a Wishart distribution: S−1 j |Data ∼ W(vSj , S −1 j ). Finally, concerning the hierarchical prior of Kjt, a conjugate Beta prior is used for pj : pj ∼ B(β 1j , β 2j ). Thus, the conditional posterior for pj es pj ∼ B(β1j , β2j), where β1j =β1j + T∑ t=1 Kjt y β2j =β2j + T − T∑ t=1 Kjt. Koop et al. (2009) combine the algorithm from Gerlach et al. (2000) with Carter and Kohn (1994) to obtain draws of K1t and Bt (conditioned on all other parameters of the model, including K2t and K3t). Subsequently, they combine the algorithm from Gerlach et al. (2000) with the extension by Kim et al. (1998) to obtain draws of K2t and Σt (conditioned on all other parameters of the model, including K1t and K3t). Finally, they combine the algorithm from Gerlach et al. (2000) with Carter and Kohn (1994) to obtain draws of K3t and A (conditioned on all other parameters of the model, including K1t and K2t). 3.2 Other Models Building upon the Benchmark model proposed by Koop et al. (2009), the following additional versions are considered: (i) the Primiceri model (2005) that imposes K1t = K2t = K3t = 1, i.e., all three blocks of parameters vary over time; (ii) a model that assumes that the coefficients of contemporaneous effects are constant over time (Benchmark At constant model) assuming K3t = 0, 5 similar to Cogley and Sargent (2005); (iii) a model that restricts both variances and coefficients of contemporaneous effects to be constant over time (Benchmark At and Σt constant model), imposing K2t = K3t = 0, akin to Cogley and Sargent (2001); (iv) the Benchmark At and Bt constant model, assuming only variances vary, i.e., K2t = 1; (v) the Benchmark Bt constant model, imposing that the coefficients of the VAR model are constant over time, i.e., K1t = 0; and (vi) the classic Constant VAR model (CVAR), assuming K1t = K2t = K3t = 0. 3.3 Model Performance Evaluation Following Carlin and Louis (2000), we use the expected value of the log-likelihood function as a conventional information criterion to compare the models described in 3.2. To obtain this value, let Y stack all the data in the dependent variables, and let λ denote all the model parameters except K1, K2 and K3 and the states themselves. Gerlach et al. (2000) describe how to calculate p(Y|Kt, λ). Therefore, we calculate p(Y|K1, λ), p(Y|K2, λ), and p(Y|K3, λ) and average these values. 4 Empirical Evidence In this Section, we begin by introducing the data used in the analysis. Subsequently, we delve into the empirical findings, which encompass insights into parameter evolution, error volatility in the employed variables, impulse-response functions (IRFs) of domestic variables to external shocks, forecast error variance decomposition (FEVD), and historical decomposition (HD) of domestic variables. 4.1 Data The data used in this study consists of quarterly time series expressed in annual growth rates, except for local and international interest rates. The sample period covers 1994Q1 to 2019Q4, and the data series have been sourced from the databases of the Central Reserve Bank of Peru (BCRP), Bloomberg, and the Federal Reserve Bank of St. Louis (FRED). The system comprises a total of seven variables categorized into two blocks: an external block, encompassing the first four variables, and a domestic block, encompassing the remaining variables. The external block comprises the US economic growth (yusat ), the Fed policy interest rate, (i∗t ), China’s economic growth (ychnt ), and the growth of the terms of trade (tott). The domestic block comprises the domestic GDP growth (ypert ),4 inflation (πt), and the local interest rate (it), which is constructed by combining the interbank interest rate until 2003Q3 and the reference interest rate from 2003Q4 until the end of the sample. Figure 1 presents the seven variables used in the base model. The ypert series reveals three significant declines: the first occurred in 1998, primarily attributed to the country’s recession resulting from the El Niño phenomenon and the global context, including the Asian, Russian, and Brazilian crises; the second one, in 2001, was due to reduced domestic demand and capital inflows; and the third one, in 2008, resulted from the onset of the Global Financial Crisis (GFC); see Winkelried (2017). During the period 1994-2001, πt decelerated due to weak domestic demand and the BCRP’s expansionary policy. Subsequently, during 2002-2013, πt decreased to 2.9%, primarily as a consequence of IT adoption, which strengthened Peru’s macroeconomic policy. The it series 4The domestic GDP series has been seasonally adjusted using the TRAMO/SEATS software developed by Gómez and Maravall (1996). 6 exhibited high levels in the pre-IT period, peaking in 1998 due to depreciatory expectations in the face of adverse economic conditions (i.e., El Niño phenomenon and international financial crises). On the external front, Figure 1 shows that yusat remained relatively stable throughout most of the sample, with sharp declines in 2001 and 2010. The 2001 decline was attributed to the bursting of the dot-com bubble5 and the terrorist attacks that occurred that year. The 2010 decline was a consequence of the global recession that began in 2008, triggered by the bursting of the housing bubble. The ychnt series exhibited higher volatility during the 1994-2010 period, primarily due to China’s industrial expansion, increased investments, and export demand. After 2008, the volatility of ychnt decreased due to the onset of the GFC that year. Moreover, after the Asian financial crisis in 1998 and the GFC in 2008, the i∗t series remained at levels below 2% to stabilize the financial system and prevent economic recession; see Recio and Egea (2015). Finally, in 2008, tott experienced a significant decline associated with the GFC. Its rapid recovery post-2009 was due to the macroeconomic stimulus emanating from China. 4.2 Prior Values To calibrate the hyperparameters, we estimate a CVAR model using fifteen quarters as a train- ing sample (1994Q1-1997Q3). This allows us to obtain the coefficients, β̂OLS , and the variance- covariance matrix can be decomposed to produce ÂOLS and σ̂0. We also obtain the variance- covariance matrices of β̂OLS and ÂOLS , denoted as V (β̂OLS) y V (ÂOLS), respectively. Using these values, the priors for the initial conditions of each of the state equations are:B0 ∼ N (B̂OLS , 4V (B̂OLS)), A0 ∼ N (ÂOLS , 4V (ÂOLS)), and log(σ̂0) ∼ N (log(σ̂0), 4In). The priors are then determined by the variances of the errors in the state equation, allowing these priors to depend on the priors that determine the number of breakpoints that can occur. It is important to note that the Beta prior we use for pj implies that E(pj) = β 1j β 1j +β 2j , where β 1j = 1 y β 2j = 1 for j = 1, 2, 3. Thus, E(pj) = 0.5, i.e., there is a 50% probability of a breakpoint occurring in the parameter block in any given time period. Therefore, the following prior is established for the error of the variances in the state equa- tion: vQ= 37, Q = (kQ) 2V (B̂OLS)(1/E(p1)), vQ= 5, W = 4(kW )2(I3)(1/E(p2)), vSj= j + 1, and Sj = (j + 1)(kS) 2V (Âm,OLS)(1/E(p3)) for j = 1, 2, 3. Finally, it is worth noting that kQ, kW and kS are the prior values for time variation; and k2Q= 0.5 x 10−4, k2W= 1 x 10−4 and k2S= 1 x 10−3 as in Canova and Pérez Forero (2015). 4.3 Empirical Results The estimates are based on 70,000 iterations of Gibbs sampling, discarding the first 20,000. The identification strategy is carried out through recursive restrictions (Sims, 1980), where the matrix of contemporaneous relationships adopts a lower triangular form, meaning the variables are ordered from the most exogenous to the most endogenous yt: [y usa t , i∗t , y chn t , tott, y per t , πt, it] ′ . In the external block, the proposed ordering assumes that i∗t responds to yusat . In turn, fluc- tuations in yusat and i∗t influence decisions about trade and investment in China, affecting ychnt . These global demand fluctuations directly impact tott through changes in commodity prices. In the domestic block, variations in ypert imply changes in πt, and depending on the dynamics of both variables, the monetary authority reacts by increasing or decreasing it. 5The dot-com bubble refers to the speculative phenomenon that took place between 1997 and 2001 in the tech- nology sector, specifically internet-related companies. The surge in stock prices for these firms, combined with speculation and ample capital availability, fostered a favorable environment. The bursting of the dot-com bubble marked the onset of a moderate and protracted recession in Western countries. 7 Each structural shock is identified as follows: the errors of the equations for yusat , i∗t , y chn t and tott represent external shocks; the error of the equation for ypert represents the aggregate demand (AD) shock; the error of the equation for πt represents the aggregate supply (AS) shock; and the error of the equation for it represents the monetary policy (MP) shock. This model is estimated using one lag, selected according to the Bayesian Information Criterion (BIC), so the results cover the period from 1998Q1 to 2019Q4. 4.3.1 Parameter Evolution To assess the evolution of parameters over time, we employ the Trace test, the Kolmogorov-Smirnov (K-S) test, and the t-test. These tests are directly applied to the coefficients, variances, and contemporaneous effect coefficients of the TVP-VAR-SV model. The results are summarized in Table 1. The Trace test examines the trace of the prior variance matrix, yielding a value of 0.28 in this case. This value falls below the mean bound of 0.30 but exceeds the lower bound of 0.22 (which is estimated for the trace of posterior variances), indicating the presence of changing volatility over time. The K-S test checks whether each parameter can be drawn from the same continuous distribution, while the t-test assesses if these distributions have the same mean at two different time points. Initially, we divide the sample into two regimes (1998Q1-2002Q4 and 2003Q1-2019Q4). The results for the variance matrix of innovations, Σt, indicate a 100% variability, supporting the inclusion of stochastic volatility for better model specification. However, the results for the remaining two parameter blocks yield different insights. For the coefficients of lagged variables, Bt, the K-S test reveals a variability range between 73% and 86%, while the t-test suggests a range of 71% to 84%. As for the contemporaneous effects, the K-S test points to variability between 62% and 76%, while the t-test suggests that the entire parameter block should vary over time. Similar results are obtained when these statistics are calculated by splitting the total sample in half. The empirical findings concerning breaks in all three parameter blocks and the model that gains the strongest support from the data are summarized in Table 2. The expected log-likelihood function value, denoted as E(logL), is used to gauge each model’s performance. In the Benchmark model, both expected probabilities of variability, E(p1|Data) and E(p2|Data), related to Bt and Σt, exceed 95%. This indicates a high likelihood that the coefficients of the SVAR model and error volatilities change over time. Conversely, the estimated probability of variability for E(p3|Data), associated with At, stands at 10%. This result suggests a low probability of the contemporaneous effect coefficients changing over time. As a result, the Benchmark At constant model (K3t = 0) outperforms the others, showing the highest expected log-likelihood function value, followed by the Benchmark and Primiceri (2005) models. The Benchmark At and Bt constant, Bt constant, and At and Σt constant models receive little support from the data, and the CVAR model receives the least support. Therefore, we conclude that the evolution of parameters over time is crucial, particularly for parameter blocks containing SVAR model coefficients and error variances. Consequently, the subsequent sections prioritize the analysis of the results from the Benchmark At constant model. 4.3.2 Volatilities Figure 2 shows how the standard deviation of errors changes over time for all the models. The results indicate that models considering time-varying Bt follow a similar pattern for both domestic and external shocks. It is important to note that the Primiceri (2005) model tends to estimate higher volatility compared to the other models. For the Benchmark and Benchmark At constant models, the standard deviations of errors are quite similar, which aligns with these models fitting 8 the data best. In the external block, there is a period of increased error volatility in ychnt (1998-2002), linked to the Asian financial crisis and China’s growing integration into the global economy. A similar pattern is seen in the volatility of errors in tott which reflects China’s role as the world’s largest consumer of commodities and its significant trade relationship with Peru. Additionally, the errors in yusat and i∗t show high volatility during 2008-2009, which coincides with the GFC triggered by Lehman Brothers’ bankruptcy. These findings are consistent with Rodriguez et al. (2023a), who found through a set of TVP-VAR-SV models that the standard deviation of external shocks increased until mid-2008 before leveling off. In the domestic block, the dynamics of standard deviations are similar: episodes of high volatility between 1998-2002, followed by a significant decline. Armas and Grippa (2006) explain that this decline is due to IT adoption by the BCRP to maintain price stability, enhance the effectiveness of monetary policy, and strengthen the role of the local currency. Additionally, in 2008, there is a slight increase in the volatility of domestic shocks, which was caused by the onset of the GFC. Portilla et al. (2022) suggest that while Peru experienced capital flow slowdowns and a significant decline in terms of trade during both the 1998 and 2008 international financial crises, the macroeconomic response during the latter was more effective due to the implementation of an expansionary policy by the BCRP, which helped alleviate the impact of the external context. Finally, in both the external and domestic blocks, it is evident that the CVAR model fails to capture the uncertainty in standard deviations of errors because it assumes constant variances. This aligns with the CVAR model ranking lowest in Table 2, indicating that it provides the poorest fit to the data. 4.3.3 Impulse Response Functions (IRFs) This section examines the IRFs for ypert , πt and it in response to various external shocks. We categorize the IRFs into two types: 3D IRFs, which illustrate the evolution of domestic variables’ responses to external shocks over time (from Figure 3 to Figure 6), and 2D IRFs, which present the median IRFs in response to positive external shocks along with their corresponding confidence intervals (from Figure 7 to Figure 10). In Figure 3 (positive shock to yusat ), we observe a positive impact on ypert lasting for three quarters. However, this effect diminishes over the years, declining from 0.37% in 2001 to 0.19% in 2019. Furthermore, both πt and it exhibit a positive response to the shock originating from yusat . Figure 4 (increase in i∗t ) demonstrates a negative impact on ypert , with a relatively stable effect over time, shifting from -0.53% in 2001 to -0.48% in 2019. Similarly, πt and it respond in alignment with US monetary policy. In Figure 5 (positive shock to ychnt ), the response of ypert is positive and grows over time. The impact in 2001 is 0.60%, rising to 0.87% in 2019. In the medium term, both πt and it display positive responses. Figure 6 (positive shock to tott) reveals a positive and transitory impact on ypert throughout all years, with a duration of two quarters. The magnitude displays moderate temporal variation, with the effect reaching 0.33% in 2001 and peaking at 0.39% in 2012. Figure 7 presents the median IRFs (black line) in response to a positive shock in yusat along with their 14% and 86% confidence intervals (shaded area). This visual indicates a positive and transitory response of ypert , with a magnitude of 0.24%. This response is attributed to the influence of the US economy on Peruvian trade.6 Studies by Chávez and Rodŕıguez (2023), and Rodŕıguez et 6An improvement in economic conditions in China and the US strengthens Peru’s economy through higher export revenues. See Urbina and Rodriguez (2023). 9 al. (2023a, 2023b) yield similar results, confirming the positive impact and transitory nature of the external shock. As for πt and it, their responses are also positive and transitory, with magnitudes of 0.2% and 0.1%, respectively. The increase in πt is due to the possibility that the shock from yusat may induce inflationary pressures through increased domestic demand resulting from higher export income and investment flows. The response of it aligns with the BCRP’s countercyclical stance against external shocks and its commitment to inflation stabilization. Figure 8 illustrates the response of domestic variables to a positive shock in i∗t . The impact on ypert is contractionary, with a magnitude of -0.15% in the third quarter. This is because a shock in i∗t negatively affects exchange rates, international reserves, and stock prices, leading to reduced credit, investment, and domestic demand. This, in turn, results in higher external financing costs for small, open economies like Peru; see Eichengreen and Gupta (2015), Flores (2015), Nolazco et al. (2016), and Quispe et al. (2017). Furthermore, the responses of πt and it are positive, with magnitudes of 0.14% and 0.6%, respectively, corroborating the synchronization of Peru’s monetary policy with Fed decisions. The increase in πt can be attributed to the exchange rate pass-through effect resulting from the depreciation of the domestic currency against the dollar, caused by capital outflows seeking higher returns in the US Likewise, the positive response of it results from the BCRP’s adoption of a countercyclical policy aimed at meeting the inflation target, indicating a pass-through effect from i∗t to it. Figure 9 showcases the response of domestic variables to a positive shock in ychnt . The impact on ypert is significant, with a magnitude of 0.65% and a duration of eight quarters. China, being one of the world’s largest consumers of raw materials, is a key factor in understanding why fluctuations in Peru’s economy are closely tied to China’s growth; see Xu et al. (2019). Furthermore, there is a 0.24% impact on πt in the second quarter, and a 0.12% impact on it in the fourth quarter. These results indicate an increase in the momentum of domestic demand due to higher exports, foreign direct investment, and portfolio flows. Figure 10 presents the impact of a positive shock in tott on domestic variables. The effect on ypert is positive and transitory, increasing by 0.28% in the first quarter, consistent with the findings of Ojeda Cunya and Rodŕıguez (2022). This reflects that tott is a source of prosperity for the Peruvian economy, as the globalization process reduces import and export restrictions, directly impacting ypert ; see Loser (2013). Furthermore, the impact on πt and it is -0.13% and 0.27%, respectively, attributable to the higher dynamism of exports, resulting in an appreciation of the local currency and a decrease in inflation due to the exchange rate pass-through effect. 4.3.4 Forecast Error Variance Decomposition (FEVD) Figure 11 shows the evolution of the FEVD over time for the domestic variables ypert , πt, and it in the short term (h = 2 quarters) and long term (h = 20 quarters). Additionally, Table 3 presents the FEVD results for ypert from the Benchmark At constant model. The results indicate that until the end of 2001, external shocks accounted for 34.8% of the long-term FEVD of ypert , relatively small share compared to domestic shocks. This aligns with Raddatz (2007), who suggests that external shocks explained only 11% of GDP growth in emerging economies. Chávez and Rodŕıguez (2023), and Rodŕıguez et al. (2023a, 2023b) also found that external shocks contributed between 17% and 38% to fluctuations in domestic output before IT adoption. During this period, the domestic shocks with the most substantial impact on the vari- ability of ypert were the AD and MP shocks, accounting for 25.6% and 34.1%, respectively. The limited contribution of the AS shock can be attributed to the macroeconomic policies implemented to address the adverse effects of the 1997 El Niño phenomenon and the international financial cri- 10 sis.7 Portilla et al. (2022) note that the BCRP responded more rapidly to external and AS shocks but more gradually to AD shocks. Based on the results in Table 3, it becomes evident that between 2002-2011, the contribution of external shocks increased compared to the previous period, accounting for around 57% of the variability of ypert . This was driven by greater trade openness, IT adoption, and elevated commodity prices, which reduced the volatility of domestic variables relative to external ones. Loser (2013) and Mendoza (2014) argue that trade openness, which began in 2003, was one of the primary factors contributing to the increased role of external shocks on ypert , as it allowed the domestic economy to benefit from the economic growth of its main trading partners. On the external side, the most significant factors were shocks originating from tott and global demand shocks, contributing an average of 27% and 19.7%, respectively. These results align with Souza and de Mattos (2022), who emphasize the importance of international commodity prices and external demand for economic growth uncertainty in South American countries following a primary-export model, such as Brazil and Chile. Additionally, the contribution of MP shocks decreased after IT adoption, averaging 7.2%, and ceased to be a major source of uncertainty due to changes in monetary policy. For the period 2012-2019, the share of external shocks in the variability of ypert increased from 57% in 2012 to 64.4% in 2019 (Table 3), despite a 5.2% decline in tot between 2012-2015 and global trade issues arising from trade tensions between the US and China. The increased uncertainty in ypert was associated with shocks originating from tott (averaging 31%) and ychnt (averaging 12%). Furthermore, Table 3 indicates that shocks from yusat and i∗t made a lower contribution of 11.5% and 10.6%, respectively, which is consistent with findings by Mendoza and Collantes Goicochea (2017). These results are also in line with Rodriguez et al. (2023a), who found that external shocks contributed between 65% and 85% to the variability of ypert . The results from the CVAR model suggest some differences. Firstly, they indicate that external shocks contribute 69% to the uncertainty of ypert over the entire sample period, which is 4 percentage points higher than the results from the Benchmark At constant model for 2012-2019. Secondly, they show that the external shocks contributing the most to the variability of ypert are shocks from tott (averaging 52%) and yusat (averaging 10%), whereas in the Benchmark At constant model, the shock from ychnt is the second most important. Thirdly, compared to the Benchmark At constant model, the results underestimate the contribution of the MP shock by 23.6 percentage points and 2.5 percentage points during the periods 1998-2001 and 2002-2019, respectively. Regarding πt, between 1998-2001, external shocks accounted for an average of 41% of its vari- ability. This is consistent with Canova (2005), who shows that in Latin American countries, external shocks contribute an average of 38% to the FEVD of πt. For the period 2002-2011, the contribution of external shocks increased to 58.2%, and between 2002-2019, it rose to 65.1%, on average. On the external side, shocks from tott had the largest share (averaging 33%), followed by shocks from yusat (averaging 14%), i∗t (averaging 10%), and ychnt (averaging 7.8%). Among domestic variables, the AS shock stood out (averaging 26.8%), which is in line with the findings of Armas and Grippa (2006), who argue that fluctuations in πt have been primarily driven by AS shocks and imported inflation. As for it, during 1998-2001, external shocks explained only 31.5% of its variability, with MP shocks being the most relevant, accounting for approximately 50%. This reflects the financing constraints faced by the domestic economy due to public sector deficits and high indebtedness relative to private sector capital. After IT adoption, the contribution of external shocks increased 7Between 1998-1999, Peru experienced capital outflows due to the Asian, Russian, and Brazilian crises. However, due to Peru’s strong macroeconomic stability, it was possible to mitigate their adverse effects via countercyclical policies. 11 significantly (from 38% in 2002 to 67% in 2019), with shocks from tott being the major source of uncertainty, contributing 30%. This finding is similar to that of Chávez and Rodŕıguez (2023). There are some differences when comparing the results for πt and it between the Benchmark At constant and CVAR models. For πt, the CVAR model underestimates the contribution of the trade and financial channels by 4 percentage points and 7 percentage points, respectively. Regarding it, the CVAR results underestimate contributions by 8 and 9 percentage points. Furthermore, models that do not allow volatility and contemporaneous effects coefficients to vary over time exhibit constant FEVD, which does not adequately approximate reality. 4.3.5 Historical Decomposition (HD) To quantify the contribution of external and domestic shocks to Peru’s economic fluctuations, Figure 12 presents the findings from the HDs of domestic variables. Additionally, Table 4 displays the results of the HD for ypert from the Benchmark At constant model. Between 1998-2002, domestic shocks made the largest contribution to ypert . According to the results, the average output growth (1.1%) is explained by external factors in 34%, while domes- tic factors contribute 59%. Recall that the low level of economic output during this period was primarily associated with internal factors, especially AD shocks due to a decrease in public and private investment, as well as AS shocks related to the El Niño phenomenon, which affected the fishing and agriculture sectors; see Velarde and Rodŕıguez (2001). The results in Table 4 show that during the 2002-2011 period, 57.8% of the increase in average output growth (6.2%) is explained by external shocks, with 30% attributed to tott, 15% to ychnt , 5% to yusat , and 8% to i∗t shocks. This predominance of external shocks is related to the surge in commodity prices experienced from 2002 to 2008, which led to annual economic growth of up to 9.2% during that period. These results align with Oladunni (2020), who argues that commodity price shocks and global demand shocks are the main sources of output growth for small open economies. On the other hand, during the GFC, external shocks largely explained the deceleration of ypert , which dropped to 1.1% in 2009. According to the results, 34.3% of the economic downturn was explained by tott and 15% by yusat shocks, as unfavorable conditions prevailed in financial markets, with contractions in developed countries and slowdowns in emerging economies. From 2012 onward, ypert experienced an average increase of 3.8%, with 46% of this increase attributed to external shocks. Shocks from tott contributed 30%, and shocks from the commercial channel (ychnt and yusat ) contributed 14% (Table 4). In that same year, the country went through an economic slowdown, primarily due to deteriorating terms of trade and trade tensions between the US and China. On the domestic front, AD, AS, and MP shocks explained 38%, 2%, and 9%, respectively, of the increase in ypert . These results were driven by a decrease in private investment, the impact of the El Niño Costero in 2017, and political uncertainty caused by the Lava Jato corruption scandal.8 When comparing the results with the CVAR model, 45% of the increase in ypert is attributed to external shocks, which is 4 percentage points lower than the results obtained with the Benchmark At constant model. Both models concur that shocks from tott are the primary contributors to the increase in ypert , but the CVAR model’s results emphasize that shocks from yusat (averaging 21%) constitute the second most significant source. This diverges from the Benchmark At constant model’s findings, which suggest that shocks from ychnt are the second most substantial contributors to the increase in ypert . 8The Lava Jato scandal refers to the corruption cases uncovered in 2017, involving companies accused of paying bribes to high-ranking public officials with the aim of winning tenders for public works. 12 Between 1998 and 2001, πt witnessed an average output growth of 4.1%, with 81% of this increase attributed to domestic shocks, particularly those related to MP and AS. In the subsequent period, the significance of domestic shocks declined in comparison to external shocks, which accounted for 58% of the average increase in πt (2.7%), with the shock from ychnt emerging as the most significant channel. These findings diverge from those of Rodŕıguez et al. (2023), who noted that from IT adoption until the end of the sample period, shocks from the nominal channel played the most substantial role. However, this discrepancy could be attributed to the use of a different external variable (global commodity price index). Regarding it, during the 1998-2001 period, MP shocks had the most significant impact, explaining 85% of the average increase in it. Subsequently, external shocks gained prominence, accounting for over 57%, with the tott channel being the most prominent contributor. Lastly, the CVAR model underestimated the influence of external shocks by 18 percentage points for πt and 19 percentage points for it, in comparison to the results of the Benchmark At constant model. 5 Robustness Exercises To validate the previous estimations, four robustness exercises are conducted, introducing changes to the baseline model: (i) an external variable from the nominal channel is modified; (ii) the baseline model is extended by adding the public investment variable in the domestic block; (iii) the baseline model is extended by adding the nominal exchange rate variable as the most endogenous variable in the domestic block; (iv) the model is estimated with four, five, and six variables. Figures are available in an Appendix upon request. 5.1 Change of External Variable The variable tott is replaced by the growth of the export price index (epit henceforth). Panel (a) of Table 5 indicates that the model that best fits the data is, once again, the Benchmark At constant model, and the models with the most support are those that incorporate stochastic volatility. On the other hand, the CVAR model is the one that fits the data the least. The results of the IRFs show that for the Benchmark At constant model, a positive shock from yusat expands ypert by 0.13% in the third quarter, while in the baseline model, the expansion is 0.2% for the same period. The response of ypert to a shock in i∗t is negative, with a magnitude of -0.16%, which is similar to the baseline model, where i∗t causes a drop of 0.15% in ypert . Likewise, the shock from ychnt and epit has a positive effect of 0.63% and 0.25%, respectively, on ypert , matching the baseline model’s result, which estimates that both external shocks generate an impact of 0.65% and 0.28%, respectively. The findings from the FEVD are in panel (a) of Table 6. First, during the period 2002-2019, the Benchmark At constant model shows a high contribution of external shocks to ypert , with epit and ychnt shocks being the greatest source of uncertainty (25% and 18%, respectively). Similarly, during the period 2012-2019, the shocks with the most influence are epit and ychnt , and the participation of all external shocks during that period is 55.1%, which coincides with the baseline model’s results. Finally, panel (a) of Table 7 shows that the results obtained for the HD are also similar to those obtained in the previous model. The Benchmark At constant model indicates that during 1998-2001, domestic shocks explained 49.5% of the increase in ypert (1.1%). Between 2002-2011, the contribution of external shocks increases, especially from ychnt (41.3%) and epit (13.2%), and between 2012-2019, external shocks explained 68.4% of the increase in ypert . 13 5.2 Extending the Baseline Model with Fiscal Policy The purpose of this section is to integrate Peru’s fiscal policy into the baseline model. To achieve this, we introduce the growth rate of public investment (gpubt ) as an exogenous domestic variable, as its increase is a result of public policy decisions. Furthermore, gpubt inmediately stimulates economic activity by positively affecting the country’s productive capacity, as outlined in Palacios Tovar (2018). In this case, once again, the Benchmark At constant model shows the best empirical fit, reaffirming the model’s robustness in capturing the dynamics of the Peruvian economy. Conversely, the CVAR model exhibits the weakest fit with the data, underscoring the significance of parameter evolution over time, as shown in panel (b) of Table 5. The time evolution of the IRFs suggests that the impact of a 1% change in gpubt on ypert has been steadily increasing, particularly since the 2000s when the National Public Investment System (SNIP) was established to optimize the utilization of public resources allocated to investment. According to the Benchmark At constant model, the effect of a gpubt shock on ypert has risen from 0.05% in 1998 to 0.15% in 2019, confirming the growing influence of public investment on economic activity since the SNIP’s inception. Concerning the median of the IRFs derived from the Benchmark At constant model, a positive gpubt shock exerts a favorable and sustained impact on ypert , with a magnitude of 0.15% in the first quarter. This outcome is linked to enhancements in healthcare and education, subsequently boosting labor productivity; see Mariátegui-Orbegozo (2019). Regarding the FEVD, as shown in panel (b) of Table 6, the inclusion of the gpubt variable results in a 50% reduction in the contribution of external factors to the variability of domestic variables. The Benchmark At constant model indicates that the contribution of gpubt accounts for 30% of the variability during the 2012-2019 period, becoming the primary source of uncertainty. These findings deviate from those obtained in the baseline model, where external shocks accounted for 62% of the variability in 2009, while in the model including gpubt it amounted to 32% in the same year. According to Rodŕıguez et al. (2023), this discrepancy can be attributed to the high volatility of gpubt , resulting in increased uncertainty in determining ypert . In terms of the Historical Decomposition (HD) results, panel (b) of Table 7 reveals that, in the Benchmark At constant model, the contribution of external shocks to ypert increases as the years progress. Consequently, external shocks explain 8.5% of the increase in ypert during 1998-2001 and 19.6% during 2002-2011. Additionally, gpubt accounts for approximately 31.2% of the increase in ypert , making it the second most significant variable contributing to growth. Finally, as in the baseline model, the HD presents an unclear and diffuse representation of the impact of both external and domestic shocks in the CVAR model. 5.3 Extending the Baseline Model with the Nominal Exchange Rate In this Section, we introduce the annual variation of the nominal exchange rate (et) as the primary domestic variable in our model, driven by the uncovered interest rate parity condition. This variable is also influenced by monetary policy and serves as a buffer against external shocks, affecting bond risk premiums in emerging markets and domestic competitiveness; see Nolazco et al. (2016). Our results indicate that the Benchmark model provides the best fit to the data, closely followed by the Benchmark At constant model, while the CVAR model exhibits the poorest fit (Table 5, panel c). The IRFs of the Benchmark model generally follow the patterns observed in our baseline model, with one noteworthy exception: the response of ypert to the tott shock. In this case, the initial impact is positive; however, economic output contracts starting in the third quarter before gradually recovering over the course of the second year. This complex behavior can be attributed to conflicting forces. On one hand, the expansion of tott has a positive effect on export income, while on the 14 other hand, it is influenced by the BCRP’s response to inflationary pressures and exchange rate fluctuations. Turning our attention to the FEVD, as shown in Table 6 (panel c), we observe a shift in the contribution of external shocks to the uncertainty surrounding ypert . Here, external shocks account for 26% of the uncertainty, demonstrating a decrease relative to domestic shocks. This trend aligns with our earlier findings when public spending was included in the model, indicating that the intervention of economic policymakers reduces the uncertainty arising from external shocks. Notably, the impact of the et shock appears relatively subdued compared to the influence of the gpubt shock in the previous model. This muted impact may be attributed to the indirect nature of et effects. Finally, the HD results in Table 7 (panel c) also emphasize the significant role of domestic shocks in explaining variations in ypert across the entire sample period. The largest external shock contribution occurred during 2002-2011, explaining 19% of the growth in ypert , with yusat having the most substantial impact at 6.8%, while i∗t had the smallest influence at 0.4%. 5.4 Lower-Dimensional Models To analyze the contribution of external shocks to the domestic block progressively, we present results with 4-variable, 5-variable, and 6-variable model specifications. 5.4.1 4-Variable Model In this model, the external block includes only one variable: epit. For the domestic block, we used the classic macroeconomic order: ypert , πt, and it. The results in Table 5 (panel d) show that the Benchmark At constant model fits the data best, consistent with our earlier findings. Conversely, the CVAR model is the least suitable. The FEVD results for ypert (Table 6, panel d) show that during 1998-2002, domestic factors contribute roughly 90%. However, their importance wanes as we move forward, with external shocks gradually becoming more prominent, eventually dominating variability in ypert with an 80% contribution, in line with Chávez and Rodŕıguez (2023). The HD findings for ypert indicate that during 1998-2001, domestic shocks account for about 57% of fluctuations. From 2002 onward, shocks related to epit gain importance, explaining 52.9% of growth in ypert during 2001-2019 (Table 7, panel d). 5.4.2 5-Variable Model In this model, we add two more variables, ychnt and tott, to the external block, while the domestic block retains ypert , πt, and it. Table 5 (panel e) underscores the Benchmark At constant model as the most empirically robust, with the CVAR model as the least supported. Reviewing the FEVD results for ypert variability, we find that external shocks dominate, con- tributing an average of 62.4% over the analysis period. This aligns with our prior findings. Specifi- cally, during 2002-2011, external shocks drive 77.3% of uncertainty, decreasing to 59.7% from 2012 onward (Table 6, panel e). Meanwhile, variations in the domestic block are mainly tied to tott shocks. Furthermore, the HD results (Table 7, panel e) reveal that external shocks explain the majority of the average 1.1% growth in ypert during 2002-2011 (45.4%). 5.4.3 6-Variable Model In this model, we expand the external block to include i∗t , ychnt and tott, while the domestic block still features ypert , πt, and it. Table 5 (panel f) confirms the Benchmark At constant model as the 15 most empirically supported, with the CVAR model receiving the least support. Much like the baseline model, the FEVD results indicate that external factors represent an average of 47% of the variation in ypert over the analysis period. Between 1998-2011, ychnt shocks are the primary source of external uncertainty (Table 6, panel f). The HD results (Table 7, panel f) show that approximately 45% of the average increase in ypert is attributed to external factors across the analysis period. Additionally, during 2012-2019, the contribution of tott shocks increases in comparison to other external factors, explaining 17.5%, in line with the baseline model. 6 Conclusions This research quantifies the importance and evolution of the effects of external shocks on the Peruvian economy during 1998Q1-2019Q4 using a family of mixture innovation TVP VAR models with SV (TVP-VAR-SV) following Koop et al. (2009). The model specification includes an external block comprising the trade, financial, and nominal channels, and a domestic block comprising output, inflation, and interest rates under recursive identification assumptions. The results suggest that the model with the best empirical fit is one where the coefficients associated with the SVAR model (Bt) and volatilities (Σt) vary over time, with probabilities of variability exceeding 95%. This indicates a high likelihood of gradual changes in these parameter blocks. Based on the findings from the IRFs, three conclusions can be drawn. Firstly, external shocks in the trade and nominal channels have positive short-term effects on the Peruvian economy, while financial shocks have a negative impact. Secondly, shocks related to fluctuations in the Chinese economy increase Peruvian output by 0.65%, making them the most impactful external shocks. Thirdly, the impacts of terms of trade growth and Chinese growth have increased in the post-IT period. Regarding the FEVD, the findings indicate that external shocks account for 56.5% of output variability between 2002-2011 and 64.4% between 2012-2019, with price-related external shocks being the primary source of uncertainty. In the HD results, external shocks play a significant role in driving economic cycle fluctuations, explaining 58% of Peruvian output growth during 2002-2011. In terms of robustness exercises, external shocks stemming from US monetary policy have a lower contribution to output growth uncertainty. Furthermore, the participation of global demand shocks in the HD of output growth has increased compared to price-related external shocks. Another critical result is that including fiscal policy (using public investment growth) and the nominal exchange rate reduces external factors’ uncertainty regarding output growth. The results of this study pose two challenges for Peruvian policymakers. The first challenge is to strengthen macroeconomic policies to mitigate the effects of external shocks on the domestic economy. This could involve promoting fiscal savings by the Ministry of Economy and accumulating international reserves by the BCRP. The second challenge is to diversify Peru’s economic structure, given its dependence on external nominal channels. While the primary sector plays a significant role in output growth, it has limited integration with other productive sectors. Lastly, it is worth noting potential extensions of this study for future research: (i) applying structural identification using sign restrictions, as in Canova (2005), or long-run restrictions, as in Blanchard and Quah (1993) and Gaĺı (1992); and (ii) imposing restrictions on the error variance decomposition, as proposed in Barsky and Sims (2011). 16 References [1] Allegret, J., Couharde, C. and Guillaumin, C. (2012). The impact of external shocks in East Asia: Lessons from a structural VAR model with block exogeneity. Économie Internationale 132, 35-89. doi: https://doi.org/10.3917/ecoi.132.0035 [2] Almada, L., and Barreto, P. (2017). Impactos de los cambios económicos recientes a nivel re- gional e internacional sobre el crecimiento económico uruguayo. Instituto de Economia-IECON 17-04, 6-50. [3] Armas, A. and Grippa, F. (2006). Metas de inflación en una economı́a dolarizada: La experi- encia del Perú. In A. Armas, A. Ize, and E. Levy Yeyati (Eds.). Dolarización Financiera: la Agenda de Poĺıtica, 135-162. Lima: BCRP y FMI. [4] Barsky, R. B., and Sims, E. R. (2011). News shocks and business cycles. Journal of Monetary Economics 58(3), 273-289. doi: https://doi.org/10.1016/j.jmoneco.2011.03.001 [5] Blanchard, O. J. and Quah, D. (1993). The Dynamic Effects of Aggregate Demand and Supply Disturbances. American Economic Review 83(3), 655-673. doi: https://www.jstor.org/ stable/2117540 [6] Bergholt, D. (2015). Foreign Shocks. Working Paper 15, Norges Bank. doi: https://doi. org/10.2139/ssrn.2695411 [7] Bussière, M., Callegari, G., Ghironi, F., Sestieri, G., and Yamano, N. (2013). Estimating trade elasticities: Demand composition and the trade collapse of 2008-2009. American Economic Journal: Macroeconomics 5(3), 118-151. doi: https://doi.org/10.1257/mac.5.3.118 [8] Canova, F. (2005). The transmission of US shocks to Latin America. Journal of Applied Econo- metrics 20(2), 229-251. doi: https://doi.org/10.1002/jae.837 [9] Canova, F., and Pérez Forero, F. J. (2015). Estimating overidentified, nonrecursive, time- varying coefficients structural vector autoregressions. Quantitative Economics 6(2), 359-384. doi: https://doi.org/10.3982/qe305 [10] Carlin, B. P., and Louis, T. A. (2000). Bayes and Empirical Bayes Methods for Data Analysis. Second ed. Chapman and Hall, Boca Raton. [11] Carter, C. K., and Kohn, R. (1994). On Gibbs sampling for state space models. Biometrika 81(3), 541-553. doi: https://doi.org/10.1093/biomet/81.3.541 [12] Castillo P., and Salas, J. (2010). The terms of trade as drivers of economic fluctuations in developing economies: An empirical study. Premio de Banca Central Rodrigo Gómez. [13] Cesa-Bianchi, A., Dickinson, R., Kösem, S., Lloyd, S., and Manuel, E. (2021). No economy is an island: how foreign shocks affect UK macrofinancial stability. Bank of England Quarterly Bulletin Q3, 1-21. [14] Chávez, P. and G. Rodŕıguez (2023). Time changing effects of external shocks on macroeco- nomic fluctuations in Peru: empirical application using regime-switching VAR models with stochastic volatility. Review of World Economics 159(2), 505-544. doi: https://doi.org/ 10.1007/s10290-022-00474-1 17 https://doi.org/10.3917/ecoi.132.0035 https://doi.org/10.1016/j.jmoneco.2011.03.001 https://www.jstor.org/stable/2117540 https://www.jstor.org/stable/2117540 https://doi.org/10.2139/ssrn.2695411 https://doi.org/10.2139/ssrn.2695411 https://doi.org/10.1257/mac.5.3.118 https://doi.org/10.1002/jae.837 https://doi.org/10.3982/qe305 https://doi.org/10.1093/biomet/81.3.541 https://doi.org/10.1007/s10290-022-00474-1 https://doi.org/10.1007/s10290-022-00474-1 [15] Chua, S. Y., Dibooglu, S., and Sharma, S. C. (1999). The impact of the US and Japanese economies on Korea and Malaysia after the Plaza Accord. Asian Economic Journal 13(1), 19-37. [16] Cogley, T., and Sargent, T. J. (2001). Evolving Post-World War II U.S. Inflation Dynamics. NBER Macroeconomics Annual 16, 331-373. doi: https://doi.org/10.1086/654451 [17] Cogley, T., and Sargent, T. J. (2005). Drifts and volatilities: Monetary policies and outcomes in the post WWII US. Review of Economic Dynamics 8, 262-302. doi: https://doi.org/10. 1016/j.red.2004.10.009 [18] Contreras, A. , Quispe, Z., Regalado, F. , and Martinez, M. (2017). Dolarización real en el Perú. Revista Estudios Económicos 33, 43-55. [19] Dancourt, O., Mendoza, W. and Vilcapoma, L. (1997). Fluctuaciones económicas, shocks externos, Perú 1950-1996. Economı́a 39-40(20), 63-101. [20] Dı́az-Cassou, J., Carrillo-Maldonado, P., and Moreno, K. (2020). Covid-19: El impacto del choque externo sobre las economıas de la región andina. Working Paper 779, InterAmerican Development Bank. [21] Eichengreen, B., and Gupta, P. (2015). Tapering talk: The impact of expectations of reduced Federal Reserve security purchases on emerging markets. Emerging Markets Review 25, 1-15. doi: https://doi.org/10.1016/j.ememar.2015.07.002 [22] Flores, J. (2015). Transmisión de choques de poĺıtica monetaria de Estados Unidos sobre América Latina: Un enfoque GVAR. Working Paper 779, Banco Central de Reserva del Perú. [23] Florián, D., Aguilar, J., Toma, H., and Velásquez, C. (2018). Impacto de los cambios antici- pados de los términos de intercambio en la economı́a. Revista Moneda 174, 21-25. [24] Fuller, W. A. (1996). Introduction to Time Series. John Wiley & Sons, New York. [25] Gaĺı, J. (1992). How Well Does the IS-LM Model Fit Postwar U.S. Data? Quarterly Journal of Economics 107(2), 709-738. doi: https://doi.org/10.2307/2118487 [26] Gerlach, R., Carter, C., and Kohn, R. (2000). Efficient bayesian inference for dynamic mixture models. Journal of the American Statistical Association 95(451), 819-828. doi: https://doi. org/10.1080/01621459.2000.10474273 [27] Gómez, V. and Maravall, A. (1996). Programs TRAMO and SEATS, Instruction for User. Working Paper 9628, Banco de España. [28] Hernández, G. (2013). Terms of trade and output fluctuations in Colombia. CEPAL Review 110, 109-131. [29] Jemio, L. C., and Wiebelt, M. (2003). ¿Existe espacio para poĺıticas anti-shock en Bolivia?: Lecciones de un análisis basado en un modelo de equilibrio general computable. Revista Lati- noamericana de Desarrollo Económico 1, 37-68. doi: https://doi.org/10.35319/lajed. 20031336 18 https://doi.org/10.1086/654451 https://doi.org/10.1016/j.red.2004.10.009 https://doi.org/10.1016/j.red.2004.10.009 https://doi.org/10.1016/j.ememar.2015.07.002 https://doi.org/10.2307/2118487 https://doi.org/10.1080/01621459.2000.10474273 https://doi.org/10.1080/01621459.2000.10474273 https://doi.org/10.35319/lajed.20031336 https://doi.org/10.35319/lajed.20031336 [30] Kim, S., Shephard, N., and Chib, S. (1998). Stochastic Volatility : Likelihood Inference and Comparison with ARCH Models. Review of Economic Studies 65, 361-393. doi: https:// doi.org/10.1111/1467-937X.00050 [31] Koop, G., Leon-Gonzalez, R., and Strachan, R. W. (2009). On the evolution of the monetary policy transmission mechanism. Journal of Economic Dynamics and Control 33(4), 997-1017. doi: https://doi.org/10.1016/j.jedc.2008.11.003 [32] Kose, M. A., Otrok, C., and Whiteman, C. H. (2003). International business cycles: World, region, and country-specific factors. American Economic Review 93(4), 1216-1239. doi: https://doi.org/10.1257/000282803769206278 [33] Loser, C. (2013). Commodity terms of trade in emerging markets: A fragile blessing. Global Journal of Emerging Market Economies 5(2), 99-115. doi: https://doi.org/10.1177/ 0974910113494538 [34] Mariátegui-Orbegozo, R. (2019). Efecto de la inversión pública en infraestructura económica y social sobre el ı́ndice de desarrollo humano en el Perú para el periodo 2007-2016. Manuscript, Universidad de Lima. [35] Meller, P., Poniachik, D., and Zenteno, I. (2012). El impacto de China en América Latina: ¿desindustrialización y no diversificación de exportaciones? Corporación de Estudios para Latinoamérica 5(42), 4-33. [36] 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 [37] Mendoza, W. (2014). Macroeconomı́a Intermedia para América Latina. Lima: Fondo Editorial de la Pontificia Universidad Católica del Perú. [38] Mendoza Bellido, W., and Collantes Goicochea, E. (2017). La economı́a de PPK. Promesas y resultados: la distancia que los separa. Working Paper 440, Department of Economics, Pontificia Universidad Católica del Perú. [39] Nolazco, J. L., Lengua Lafosse, P., and Céspedes, N. (2016). Contribución de los choques externos en el crecimiento económico del Perú: un modelo semi-estructural. Working Paper Series 6, Banco Central de Reserva del Perú. [40] Oladunni, S. (2020). External shocks and optimal monetary policy in oil exporting small open economies. Manuscript, University of Bath. [41] Österholm, P., and Zettelmeyer, J. (2008). The effect of external conditions on growth in Latin America. IMF Staff Papers 55(4), 595-623. doi: https://doi.org/10.1057/imfsp.2008.20 [42] Palacios Tovar, C. A. (2018). Efecto de la inversión pública en la infraestructura vial sobre el crecimiento de la economı́a peruana entre los años 2000 y 2016. Ingenieŕıa Industrial 36, 197-210. [43] Portilla, J., Rodŕıguez, G., and Castillo B., P. (2022). Evolution of Monetary Policy in Peru: An Empirical Application Using a Mixture Innovation TVP-VAR-SV Model. CESifo Economic Studies 68(1), 98-126. doi: https://doi.org/10.1093/cesifo/ifab013 19 https://doi.org/10.1111/1467-937X.00050 https://doi.org/10.1111/1467-937X.00050 https://doi.org/10.1016/j.jedc.2008.11.003 https://doi.org/10.1257/000282803769206278 https://doi.org/10.1177/0974910113494538 https://doi.org/10.1177/0974910113494538 https://doi.org/10.2307/2527429 https://doi.org/10.2307/2527429 https://doi.org/10.1057/imfsp.2008.20 https://doi.org/10.1093/cesifo/ifab013 [44] Primiceri, G. E. (2005). Time varying structural vector autoregressions and monetary policy. Review of Economic Studies 72(3), 821-852. doi: https://doi.org/10.1111/j.1467-937X. 2005.00353.x [45] Quispe, Z., Rodŕıguez, D., Toma, H., and Vásquez, C. (2017). Choques externos y coordinación de poĺıticas monetarias y macroprudenciales en las economı́as de la Alianza del Paćıfico. Revista Estudios Económicos 34, 31-53. [46] Raddatz, C. (2007). Are external shocks responsible for the instability of output in low-income countries? Journal of Development Economics 84(1), 155-187. doi: https://doi.org/10. 1016/j.jdeveco.2006.11.001 [47] Recio, L. and Egea, F. (2015). La eficacia de la poĺıtica monetaria durante la crisis económica mundial. Revista de Economı́a Mundial 41, 43-79. [48] Rodŕıguez, G., Castillo B., P., and Ojeda Cunya, J. A. (2023a). Time-Varying Effects of External Shocks on Macroeconomic Fluctuations in Peru: An Empirical Application using TVPVAR-SV Models. Forthcoming in Open Economies Review. [49] Rodŕıguez, G., Vassallo, R., and Castillo, P. (2023b). Effects of external shocks on macroe- conomic fluctuations in Pacific Alliance countries. Economic Modelling 124, 106302. doi: https://doi.org/10.1016/j.econmod.2023.10630 [50] Rodŕıguez, G., Villanueva Vega, P., and Castillo Bardalez, P. (2018). Driving economic fluc- tuations in Peru: the role of the terms of trade. Empirical Economics 55(3), 1089-1119. doi: https://doi.org/10.1007/s00181-017-1318-2 [51] Rüffer, R., Sanchez, M., and Shen, J. G. (2007). Emerging Asia’s growth and integration: how autonomous are business cycles? Working Paper 715, European Central Bank. [52] Simola, H. (2019). Effects of external shocks on Russian economy. Institute for Economies in Transition (4), 1-17. [53] Sims, C. A. (1980). Macroeconomics and Reality. Econometrica 48(1), 1-48. doi: https: //doi.org/10.2307/1912017 [54] Souza, R. D. S., and de Mattos, L. B. (2022). Oil price shocks, exchange rate and uncertainty: case of Latin American economies. Applied Economics Letters 29(10), 880-886. [55] Velarde, J., and Rodŕıguez, M. (2001). Efectos de la crisis financiera internacional en la economı́a peruana 1997-1998. Centro de Investigación de la Universidad del Paćıfico y Con- sorcio de Investigación Económica y Social. [56] Winkelried, D. (2017). Cronoloǵıa de los ciclos económicos en el Perú: 1992 a 2016. Revista Estudios Económicos 34, 55-76. [57] Xu, B., Roth, M. A., and Santabárbara Garćıa, D. (2019). Impacto global de una desaceleración en China. Working Paper 4/2019, Banco de España. [58] Zaidi, M. A., and Fisher, L. A. (2010). Monetary policy and foreign shocks: A SVAR analysis for Malaysia. Korea and the World Economy 11(3), 527-550. 20 https://doi.org/10.1111/j.1467-937X.2005.00353.x https://doi.org/10.1111/j.1467-937X.2005.00353.x https://doi.org/10.1016/j.jdeveco.2006.11.001 https://doi.org/10.1016/j.jdeveco.2006.11.001 https://doi.org/10.1016/j.econmod.2023.10630 https://doi.org/10.1007/s00181-017-1318-2 https://doi.org/10.2307/1912017 https://doi.org/10.2307/1912017 [59] Zaidi, M. A., and Karim, Z. A. (2014). Impact of Singapore, US and Japanese macroeconomic shocks on Malaysian economy: A sign-restricted SVAR analysis. Jurnal Pengurusan 41(1), 113-122. 21 Table 1. Tests for Time Variation in the Coefficients of VAR, Volatility and Contemporaneous Relations Tests Coefficients Sample 1998Q1-2002Q4 2003Q1-20190Q4 1998Q1-2008Q4 2008Q4-2019Q4 Bt 41/56 48/56 47/56 46/56 Kolgomorov-Smirnov Σt 7/7 7/7 7/7 7/7 At 13/21 16/21 16/21 14/21 Bt 40/56 47/56 47/56 42/56 t-test Σt 7/7 7/7 7/7 7/7 At 21/21 21/21 21/21 21/21 Trace Test Trace 16% perc. 50% perc. 84% perc. 0.28 0.22 0.30 0.42 The Table reports the number of time-varying parameters in each parameter block, according to the Kolgomorov-Smirnov test and the t-test. Bt contains the regression coefficients of VAR, Σt contains the volatilities of innovations and At contains the contemporaneously relations. In the Trace Test, the trace of the a priori variance matrix is reported, as well as the 16%, 50% and 84% percentiles of the trace of the posterior variance matrix T-1 Table 2. Results using Benchmark Priors for Mixture Innovation TVP-VAR-SV Models Model E(p1|Data) E(p2|Data) E(p3|Data) E(logL) Rank Benchmark 0.99 (0.01) 0.99 (0.02) 0.42 (0.07) −45.30 2 Primiceri (2005) 1.00 (0.01) 1.00 (0.01) 1.00 (0.01) −49.07 3 Benchmark At Constant 0.98 (0.02) 0.98 (0.02) 0.00 (0.01) −40.45 1 Benchmark At and Σt Constant 0.98 (0.02) 0.00 (0.01) 0.00 (0.01) −87.91 6 Benchmark At and Bt Constant 0.00 (0.01) 0.98 (0.02) 0.00 (0.01) −73.03 4 Benchmark Bt Constant 0.00 (0.01) 0.98 (0.02) 0.36 (0.23) −82.90 5 CVAR 0.00 (0.01) 0.00 (0.01) 0.00 (0.01) −90.10 7 Bt, Σt and At are the parameters blocks of VAR coefficients, volatilities and contemporaneously relations, respectively. E(p1|data), E(p2|data) and E(p3|data) are the posterior means of transition that break occurs at time t and are related to Bt, Σt and At, respectively. Standard deviations are in parenthesis. E(logL) is the expected value of the log-likelihood function. The simulations are based on 70,000 Gibbs Sampler iterations, discarding the first 20,000 by convergence. T-2 Table 3. FEVD of ypert at h = 20 quarters (mean values in %). Baseline Model - Benchmark At Constant Model. Sample Shock to: yusat i∗t ychnt tott External Domestic Total Sample 10.4 9.8 9.3 26.0 55.4 44.6 1998-2001 7.6 6.3 4.9 15.9 34.8 65.2 2002-2011 10.7 10.5 9.0 26.3 56.5 43.5 2012-2019 11.5 10.6 11.7 30.5 64.4 35.6 T-3 Table 4. HD Contribution of Shocks to ypert (mean values in %). Baseline Model - Benchmark At Constant Model. Sample Shock to: yusat i∗t ychnt tott External Domestic Deterministic Total Sample 6.7 4.8 10.4 27.1 49.0 43.8 7.3 1998-2001 6.8 2.1 10.3 14.7 33.9 59.3 6.9 2002-2011 5.2 8.4 14.5 29.7 57.8 33.9 8.3 2012-2019 8.6 1.6 5.3 30.0 45.4 48.3 6.3 T-4 T a b le 5 . R o b u st n es s C h ec k M o d el s E (p 1 |D a ta ) E (p 2 |D a ta ) E (p 3 |D a ta ) E (l og L ) R a n k E (p 1 |D a ta ) E (p 2 |D a ta ) E (p 3 |D a ta ) E (l og L ) R a n k (a ) 7 -V a ri a b le m o d el u si n g ep i t (b ) 8 -V a ri a b le m o d el in co rp o ra ti n g g p u b t B en ch m a rk 0. 99 (0 .0 1 ) 0 .9 9 (0 .0 2 ) 0 .1 0 (0 .0 7 ) -2 6 .7 0 1 0. 99 (0 .0 1 ) 0 .9 9 (0 .0 1 ) 0 .4 8 (0 .1 6 ) -6 7 .4 2 2 P ri m ic er i (2 0 0 5 ) 1. 0 0 (0 .0 1 ) 1 .0 0 (0 .0 1 ) 1 .0 0 (0 .0 1 ) -3 0 .2 7 2 1. 00 (0 .0 1 ) 1 .0 0 (0 .0 1 ) 1 .0 0 (0 .0 1 ) -8 9 .3 4 3 B en ch m a rk A t C o n st a n t 0. 99 (0 .0 1 ) 0 .9 8 (0 .0 2 ) 0 .0 0 (0 .0 1 ) -3 0 .6 3 3 0. 99 (0 .0 1 ) 0 .9 9 (0 .0 1 ) 0 .0 0 (0 .0 1 ) -5 6 .3 2 1 B en ch m a rk A t a n d Σ t C o n st a n t 0. 98 (0 .0 2 ) 0 .0 0 (0 .0 1 ) 0 .0 0 (0 .0 1 ) -3 1 .9 7 4 0. 99 (0 .0 1 ) 0 .0 0 (0 .0 1 ) 0 .0 0 (0 .0 1 ) -9 0 .6 7 4 B en ch m a rk A t a n d B t C o n st a n t 0. 00 (0 .0 1 ) 0 .9 6 (0 .0 2 ) 0 .0 0 (0 .0 1 ) -7 3 .0 3 7 0. 00 (0 .0 1 ) 0 .9 8 (0 .0 2 ) 0 .0 0 (0 .0 1 ) -1 0 6 .5 5 5 B en ch m a rk B t C o n st a n t 0. 00 (0 .0 1 ) 0 .9 8 (0 .0 2 ) 0 .1 1 (0 .2 3 ) -7 0 .9 3 5 0. 00 (0 .0 1 ) 0 .9 8 (0 .0 2 ) 0 .5 5 (0 .0 5 ) -1 1 1 .6 0 6 C V A R 0. 00 (0 .0 0 ) 0 .0 0 (0 .0 0 ) 0 .0 0 (0 .0 0 ) -7 1 .5 6 6 0. 00 (0 .0 1 ) 0 .0 0 (0 .0 1 ) 0 .0 0 (0 .0 1 ) -1 1 5 .8 2 7 (c ) 8 -V a ri a b le m o d el in co rp o ra ti n g e t (d ) 4 -V a ri a b le M o d el (e p i t , y p er t , π t, i t ) B en ch m a rk 0. 98 (0 .0 1 ) 0 .9 8 (0 .0 1 ) 0 .1 5 (0 .1 4 ) − 63 .3 1 0 .9 9 (0 .0 1 ) 0 .9 9 (0 .0 2 ) 0 .1 0 (0 .0 7 ) -3 1 .1 5 2 P ri m ic er i (2 0 0 5 ) 1. 0 0 (0 .0 1 ) 1 .0 0 (0 .0 1 ) 1 .0 0 (0 .0 1 ) − 66 .2 3 1 .0 0 (0 .0 1 ) 1 .0 0 (0 .0 1 ) 1 .0 0 (0 .0 1 ) -3 2 .5 7 3 B en ch m a rk A t C o n st a n t 0. 98 (0 .0 1 ) 0 .9 8 (0 .0 1 ) 0 .0 0 (0 .0 0 ) − 64 .5 2 0 .9 9 (0 .0 1 ) 0 .9 8 (0 .0 2 ) 0 .0 0 (0 .0 1 ) -3 1 .0 2 1 B en ch m a rk A t a n d Σ t C o n st a n t 0. 98 (0 .0 1 ) 0 .0 0 (0 .0 0 ) 0 .0 0 (0 .0 0 ) − 95 .5 6 0 .9 8 (0 .0 1 ) 0 .0 0 (0 .0 1 ) 0 .0 0 (0 .0 1 ) -5 6 .8 4 6 B en ch m a rk A t a n d B t C o n st a n t 0. 00 (0 .0 0 ) 0 .9 9 (0 .0 1 ) 0 .0 0 (0 .0 0 ) − 65 .7 3 4 0 .0 0 (0 .0 1 ) 0 .9 6 (0 .0 2 ) 0 .0 0 (0 .0 1 ) -4 6 .6 9 5 B en ch m a rk B t C o n st a n t 0. 0 0 (0 .0 0 ) 0 .9 8 (0 .0 2 ) 0 .1 2 (0 .1 0 ) − 67 .6 5 0 .0 0 (0 .0 1 ) 0 .9 8 (0 .0 2 ) 0 .1 1 (0 .2 3 ) -4 5 .5 8 4 C V A R 0. 0 0 (0 .0 0 ) 0 .0 0 (0 .0 0 ) 0 .0 0 (0 .0 0 ) − 10 0 .0 7 0 .0 0 (0 .0 1 ) 0 .0 0 (0 .0 1 ) 0 .0 0 (0 .0 1 ) -5 7 .7 8 7 B t, Σ t a n d A t a re th e p a ra m et er s b lo ck s o f V A R co effi ci en ts , v o la ti li ti es a n d co n te m p o ra n eo u sl y re la ti o n s, re sp ec ti v el y. E (p 1 |d a ta ), E (p 2 |d a ta ) a n d E (p 3 |d a ta ) a re th e p o st er io r m ea n s o f tr a n si ti o n th a t b re a k o cc u rs a t ti m e t a n d a re re la te d to B t, Σ t a n d A t, re sp ec ti v el y. S ta n d a rd d ev ia ti o n s a re in p a re n th es is . E (l o g L ) is th e ex p ec te d va lu e o f th e lo g -l ik el ih o o d fu n ct io n . T h e si m u la ti o n s a re b a se d o n 7 0 ,0 0 0 G ib b s S a m p le r it er a ti o n s, d is ca rd in g th e fi rs t 2 0 ,0 0 0 b y co n v er g en ce . T-5 T a b le 5 (C o n ti n u ed ). R o b u st n es s C h ec k M o d el s E (p 1 |D a ta ) E (p 2 |D a ta ) E (p 3 |D a ta ) E (l og L ) R a n k E (p 1 |D a ta ) E (p 2 |D a ta ) E (p 3 |D a ta ) E (l og L ) R a n k (e ) 5 -V a ri a b le M o d el (y ch n t , to t t , y p er t , π t, i t ) (f ) 6 -V a ri a b le M o d el (i ∗ t , y ch n t , to t t , y p er t , π t, i t ) B en ch m a rk 0. 99 (0 .0 1 ) 0 .9 9 (0 .0 1 ) 0 .4 8 (0 .1 6 ) -2 4 .3 3 2 0. 99 (0 .0 1 ) 0 .9 9 (0 .0 1 ) 0 .1 5 (0 .1 0 ) -2 6 .8 1 2 P ri m ic er i (2 0 0 5 ) 1. 0 0 (0 .0 1 ) 1 .0 0 (0 .0 1 ) 1 .0 0 (0 .0 1 ) -2 9 .1 6 3 1. 00 (0 .0 1 ) 1 .0 0 (0 .0 1 ) 1 .0 0 (0 .0 1 ) -3 5 .6 6 3 B en ch m a rk A t C o n st a n t 0. 99 (0 .0 1 ) 0 .9 9 (0 .0 1 ) 0 .0 0 (0 .0 1 ) -1 6 .1 5 1 0. 99 (0 .0 1 ) 0 .9 8 (0 .0 2 ) 0 .0 0 (0 .0 1 ) -2 0 .7 0 1 B en ch m a rk A t a n d Σ t C o n st a n t 0. 99 (0 .0 1 ) 0 .0 0 (0 .0 1 ) 0 .0 0 (0 .0 1 ) -4 1 .3 0 6 0. 98 (0 .0 2 ) 0 .0 0 (0 .0 1 ) 0 .0 0 (0 .0 1 ) -4 4 .8 9 4 B en ch m a rk A t a n d B t C o n st a n t 0. 00 (0 .0 1 ) 0 .9 8 (0 .0 2 ) 0 .0 0 (0 .0 1 ) -3 8 .5 3 4 0. 00 (0 .0 1 ) 0 .9 6 (0 .0 2 ) 0 .0 0 (0 .0 1 ) -5 4 .4 5 6 B en ch m a rk B t C o n st a n t 0. 0 0 (0 .0 1 ) 0 .9 8 (0 .0 2 ) 0 .5 5 (0 .0 5 ) 3 9 .1 1 5 0. 00 (0 .0 1 ) 0 .9 8 (0 .0 2 ) 0 .1 1 (0 .2 3 ) -5 1 .6 3 5 C V A R 0. 0 0 (0 .0 1 ) 0 .0 0 (0 .0 1 ) 0 .0 0 (0 .0 1 ) -4 7 .1 5 7 0. 00 (0 .0 0 ) 0 .0 0 (0 .0 0 ) 0 .0 0 (0 .0 0 ) -6 0 .4 1 7 B t, Σ t a n d A t a re th e p a ra m et er s b lo ck s o f V A R co effi ci en ts , v o la ti li ti es a n d co n te m p o ra n eo u sl y re la ti o n s, re sp ec ti v el y. E (p 1 |d a ta ), E (p 2 |d a ta ) a n d E (p 3 |d a ta ) a re th e p o st er io r m ea n s o f tr a n si ti o n th a t b re a k o cc u rs a t ti m e t a n d a re re la te d to B t, Σ t a n d A t, re sp ec ti v el y. S ta n d a rd d ev ia ti o n s a re in p a re n th es is . E (l o g L ) is th e ex p ec te d va lu e o f th e lo g -l ik el ih o o d fu n ct io n . T h e si m u la ti o n s a re b a se d o n 7 0 ,0 0 0 G ib b s S a m p le r it er a ti o n s, d is ca rd in g th e fi rs t 2 0 ,0 0 0 b y co n v er g en ce . T-6 Table 6. Robustness Check: FEVD of ypert at h = 20 quartes (mean values in %) Sample Shock to: yusat i∗t ychnt tott External Domestic (a) 7-Variable model using epit - Benchmark Model Total Sample 8.4 2.0 12.4 30.1 53.0 47.0 1998-2001 7.1 2.0 11.5 24.0 44.6 55.4 2002-2011 8.4 1.8 13.1 31.3 54.6 45.4 2012-2019 9.1 2.3 12.1 31.6 55.1 44.9 (b) 8-Variable model incorporating gpubt - Benchmark At Constant Model Total Sample 7.9 1.3 13.0 4.5 26.7 73.3 1998-2001 4.5 1.7 18.4 3.2 27.8 72.2 2002-2011 6.7 1.2 11.8 3.7 23.4 76.6 2012-2019 7.9 1.3 11.7 6.3 30.3 69.7 (c) 8-Variable model incorporating et- Benchmark Model Total Sample 8.2 0.7 5.0 12.0 26.0 74.0 1998-2001 8.7 0.7 10.9 14.3 34.8 65.2 2002-2011 8.0 0.7 5.5 11.3 25.5 74.5 2012-2019 8.1 0.7 1.5 11.8 22.1 77.9 (d) 4-Variable Model (epit, y per t , πt, it) - Benchmark At Constant Model Total Sample 62.8 62.8 37.2 1998-2001 20.4 20.4 79.6 2002-2011 68.2 68.2 31.8 2012-2019 78.6 78.6 21.8 (e) 5-Variable Model (ychnt , tott, y per t , πt, it) - Benchmark At Constant Model Total Sample 21.7 40.7 62.4 37.6 1998-2001 17.6 12.5 30.1 69.9 2002-2011 37.7 39.6 77.3 22.7 2012-2019 3.7 56.0 59.7 40.3 (f) 6-Variable Model (i∗t , y chn t , tott, y per t , πt, it) - Benchmark At Constant Model Total Sample 7.3 27.5 12.3 47.1 52.9 1998-2001 5.1 37.5 14.6 57.2 47.8 2002-2011 8.5 28.2 11.9 48.7 51.3 2012-2019 8.4 16.8 12.3 37.5 62.5 . T-7 Table 7. Robustness Check: HD Contribution of Shocks to ypert (mean values in %) Sample Shock to: yusat i∗t ychnt tott External Domestic Deterministic (a) 7-Variable model using epit - Benchmark Model Total Sample 4.9 1.6 42.2 12.9 61.6 33.5 5.0 1998-2001 2.6 0.3 35.7 10.8 49.5 33.9 16.6 2002-2011 4.8 1.7 41.3 13.2 60.9 37.2 1.9 2012-2019 6.1 2.2 46.5 13.6 68.4 28.7 3.0 (b) 8-Variable model incorporating gpubt - Benchmark At Constant Model Total Sample 4.3 1.3 5.1 4.6 15.4 82.8 1.8 1998-2001 1.5 0.5 3.2 3.2 8.4 87.3 4.3 2002-2011 3.8 1.4 6.2 5.3 16.7 82.3 1.0 2012-2019 6.2 1.7 4.8 4.5 17.2 81.2 1.6 (c) 8-Variable model incorporating et - Benchmark Model Total Sample 5.7 0.4 3.5 4.8 14.5 81.1 4.4 1998-2001 4.0 0.3 3.0 3.0 10.3 80.2 9.5 2002-2011 6.8 0.5 5.7 6.0 19.0 77.2 3.8 2012-2019 5.1 0.4 1.1 4.1 10.7 86.4 2.9 (d) 4-Variable Model (epit, y per t , πt, it) - Benchmark At Constant Model Total Sample 46.8 46.8 52.4 0.8 1998-2001 38.8 38.8 57.3 3.9 2002-2011 45.7 45.7 54.2 0.1 2012-2019 52.3 52.3 47.6 0.1 (e) 5-Variable Model (ychnt , tott, y per t , πt, it) - Benchmark At Constant Model Total Sample 23.6 9.6 45.1 49.0 5.9 1998-2001 15.6 5.7 21.3 76.0 2.7 2002-2011 33.4 9.7 53.7 42.1 4.1 2012-2019 23.8 22.3 46.1 44.1 9.8 (f) 6-Variable Model (i∗t , y chn t , tott, y per t , πt, it) - Benchmark At Constant Model Total Sample 13.9 16.7 14.5 45.1 52.7 3.2 1998-2001 5.7 13.0 6.7 25.4 66.2 8.4 2002-2011 15.9 20.9 14.9 51.8 46.9 1.3 2012-2019 15.3 12.3 17.5 45.1 51.9 3.0 T-8 1 9 9 4 1 9 9 8 2 0 0 2 2 0 0 6 2 0 1 0 2 0 1 4 2 0 1 8 -2024 y u s a t 1 9 9 4 1 9 9 8 2 0 0 2 2 0 0 6 2 0 1 0 2 0 1 4 2 0 1 8 -20246 i* t 1 9 9 4 1 9 9 8 2 0 0 2 2 0 0 6 2 0 1 0 2 0 1 4 2 0 1 8 68 1 0 1 2 1 4 y c h n t 1 9 9 4 1 9 9 8 2 0 0 2 2 0 0 6 2 0 1 0 2 0 1 4 2 0 1 8 -2 00 2 0 to t t 1 9 9 4 1 9 9 8 2 0 0 2 2 0 0 6 2 0 1 0 2 0 1 4 2 0 1 8 -505 1 0 y p e r t 1 9 9 4 1 9 9 8 2 0 0 2 2 0 0 6 2 0 1 0 2 0 1 4 2 0 1 8 68 1 0 1 2 1 4 t 1 9 9 4 1 9 9 8 2 0 0 2 2 0 0 6 2 0 1 0 2 0 1 4 2 0 1 8 5 1 0 1 5 2 0 2 5 i t F ig u re 1 . T im e S er ie s F-1 1 9 9 8 2 0 0 3 2 0 0 8 2 0 1 3 2 0 1 8 0 .1 0 .1 5 0 .2 0 .2 5 0 .3 0 .3 5 0 .4 y u s a t 1 9 9 8 2 0 0 3 2 0 0 8 2 0 1 3 2 0 1 8 0 0 .0 5 0 .1 0 .1 5 0 .2 0 .2 5 0 .3 i* t 1 9 9 8 2 0 0 3 2 0 0 8 2 0 1 3 2 0 1 8 0 0 .51 1 .52 2 .5 y c h n t 1 9 9 8 2 0 0 3 2 0 0 8 2 0 1 3 2 0 1 8 1 1 .52 2 .53 3 .54 to t t 1 9 9 8 2 0 0 3 2 0 0 8 2 0 1 3 2 0 1 8 1 1 .52 2 .53 3 .54 4 .5 y p e r t 1 9 9 8 2 0 0 3 2 0 0 8 2 0 1 3 2 0 1 8 1 1 .52 2 .53 3 .54 4 .5 t 1 9 9 8 2 0 0 3 2 0 0 8 2 0 1 3 2 0 1 8 0123456 i t B e n c h m a rk P ri m ic e ri ( 2 0 0 5 ) B e n c h m a rk A t C o n s ta n t B e n c h m a rk A t a n d t C o n s ta n t B e n c h m a rk A t a n d B t C o n s ta n t B e n c h m a rk B t C o n s ta n t C V A R F ig u re 2 . M ed ia n S ta n d a rd D ev ia ti o n o f th e In n ov a ti o n s in ea ch E q u a ti o n fo r a ll M o d el s F-2 F ig u re 3 . M ed ia n T im e- V a ry in g IR F s o f y p er t , π t, i t to a E x te rn a l S h o ck - y u sa t . T h e sh o ck s a re n o rm a li ze d to in cr ea se th e E x te rn a l S h o ck b y 1 % F-3 F ig u re 4 . M ed ia n T im e- V a ry in g IR F s o f y p er t , π t, i t to a E x te rn a l S h o ck - i∗ t . T h e sh o ck s a re n o rm a li ze d to in cr ea se th e E x te rn a l S h o ck b y 1 % F-4 F ig u re 5 . M ed ia n T im e- V a ry in g IR F s o f y p er t , π t, i t to a E x te rn a l S h o ck - y ch n t . T h e sh o ck s a re n o rm a li ze d to in cr ea se th e E x te rn a l S h o ck b y 1 % F-5 F ig u re 6 . M ed ia n T im e- V a ry in g IR F s o f y p er t , π t, i t to a E x te rn a l S h o ck - to t t . T h e sh o ck s a re n o rm a li ze d to in cr ea se th e E x te rn a l S h o ck b y 1 % F-6 F ig u re 7 . M ed ia n IR F s o f y p er t , π t, i t to a E x te rn a l S h o ck - y u sa t . T h e so li d b la ck li n e re p re se n ts th e re sp ec ti v e m o d el b y co lu m n s a n d th e sh a d ed a re a it s 6 8 % er ro r b a n d . F-7 F ig u re 8 . M ed ia n IR F s o f y p er t , π t, i t to a E x te rn a l S h o ck - i∗ t . T h e so li d b la ck li n e re p re se n ts th e re sp ec ti v e m o d el b y co lu m n s a n d th e sh a d ed a re a it s 6 8 % er ro r b a n d . F-8 F ig u re 9 . M ed ia n IR F s o f y p er t , π t, i t to a E x te rn a l S h o ck - y ch n t . T h e so li d b la ck li n e re p re se n ts th e re sp ec ti v e m o d el b y co lu m n s a n d th e sh a d ed a re a it s 6 8 % er ro r b a n d . F-9 F ig u re 1 0 . M ed ia n IR F s o f y p er t , π t, i t to a E x te rn a l S h o ck - to t t . T h e so li d b la ck li n e re p re se n ts th e re sp ec ti v e m o d el b y co lu m n s a n d th e sh a d ed a re a it s 6 8 % er ro r b a n d . F-10 F ig u re 1 1 . T im e E v o lu ti o n o f th e M ea n F E V D o f y p er t , π t, i t a t h = 2, 20 fo r a ll M o d el s. F-11 F ig u re 1 2 . H D o f D o m es ti c V a ri a b le s fo r a ll M o d el s. F-12 ÚLTIMAS PUBLICACIONES DE LOS PROFESORES DEL DEPARTAMENTO DE ECONOMÍA  Libros Adolfo Figueroa 2023 The Quality of Society, Volume III. Essays on the Unified Theory of Capitalism. New York, Palgrave Macmillan Efraín Gonzales de Olarte 2023 El modelo de Washington, el neoliberalismo y el desarrollo económico. El caso peruano 1990-2020. Lima, Fondo Editorial PUCP. Máximo Vega Centeno. 2023 Perú: desarrollo, naturaleza y urgencias Una mirada desde la economía y el desarrollo humano. Lima, Fondo Editorial PUCP. Waldo Mendoza 2023 Constitución y crecimiento económico: Perú 1993-2021. Lima, Fondo Editorial PUCP. Oscar Dancourt y Waldo Mendoza (Eds.) 2023 Ensayos macroeconómicos en honor a Félix Jiménez. Lima, Fondo Editorial PUCP. Carlos Contreras Carranza (ed.) 2022 Historia económica del Perú central. Ventajas y desafíos de estar cerca de la capital. Lima, Banco Central de Reserva del Perú e Instituto de Estudios Peruanos. Alejandro Lugon 2022 Equilibrio, eficiencia e imperfecciones del mercado. Lima, Fondo Editorial PUCP. Waldo Mendoza Bellido 2022 Cómo investigan los economistas. Guía para elaborar y desarrollar un proyecto de investigación. Segunda edición aumentada. Lima, Fondo Editorial PUCP. Elena Álvarez (Editor) 2022 Agricultura y desarrollo rural en el Perú: homenaje a José María Caballero. Lima, Departamento de Economía PUCP. Aleida Azamar Alonso, José Carlos Silva Macher y Federico Zuberman (Editores) 2022 Economía ecológica latinoamericana. Buenos Aires, México. CLACSO, Siglo XXI Editores. Efraín Gonzales de Olarte 2021 Economía regional y urbana. El espacio importa. Lima, Fondo Editorial PUCP. Alfredo Dammert Lira 2021 Economía minera. Lima, Fondo Editorial PUCP. Adolfo Figueroa 2021 The Quality of Society, Volume II – Essays on the Unified Theory of Capitalism. New York, Palgrave Macmillan. https://departamento.pucp.edu.pe/economia/libro/11996/ https://departamento.pucp.edu.pe/economia/libro/modelo-washington-neoliberalismo-desarrollo-economico-caso-peruano-1990-2020/ https://departamento.pucp.edu.pe/economia/libro/modelo-washington-neoliberalismo-desarrollo-economico-caso-peruano-1990-2020/ https://departamento.pucp.edu.pe/economia/libro/peru-desarrollo-naturaleza-urgencias-una-mirada-desde-la-economia-desarrollo-humano/ https://departamento.pucp.edu.pe/economia/libro/peru-desarrollo-naturaleza-urgencias-una-mirada-desde-la-economia-desarrollo-humano/ https://departamento.pucp.edu.pe/economia/libro/constitucion-crecimiento-economico-peru-1993-2021/ https://departamento.pucp.edu.pe/economia/libro/ensayos-macroeconomicos-honor-felix-jimenez/ https://departamento.pucp.edu.pe/economia/libro/agricultura-desarrollo-rural-peru-homenaje-jose-maria-caballero/ https://departamento.pucp.edu.pe/economia/libro/10743/ Carlos Contreras Carranza (Editor) 2021 La Economía como Ciencia Social en el Perú. Cincuenta años de estudios económicos en la Pontificia Universidad Católica del Perú. Lima, Departamento de Economía