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 PUBLIC DEBT DYNAMICS AND SUSTAINABILITY: A FRAMEWORK FOR ANALYSIS Nº 541 Waldo Mendoza, Marko Razzo and Rafael Vilca Public Debt Dynamics and Sustainability: A Framework for Analysis Documento de Trabajo 541 @ Waldo Mendoza, Marko Razzo and Rafael Vilca 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 https://departamento-economia.pucp.edu.pe/publicaciones/documentos Encargado de la Serie: Gabriel Rodríguez Departamento de Economía – Pontificia Universidad Católica del Perú gabriel.rodriguez@pucp.edu.pe Primera edición – Diciembre, 2024 ISSN 2079-8474 (En línea) mailto:econo@pucp.edu.pe file:///G:/Unidades%20compartidas/DECON%20-%20JEFATURA/Mirtha/MIS%20DOCUMENTOS/Documentos%20de%20Trabajo/DT´s%202024/gabriel.rodriguez@pucp.edu.pe DOCUMENTO DE TRABAJO N° 541 Public Debt Dynamics and Sustainability: A Framework for Analysis Waldo Mendoza, Marko Razzo and Rafael Vilca Diciembre, 2024 DOCUMENTO DE TRABAJO 541 http://doi.org/10.18800/2079-8474.0541 http://doi.org/10.18800/2079-8474.0541 Public Debt Dynamics and Sustainability: A Framework for Analysis Waldo Mendoza, Marko Razzo and Rafael Vilca1 ABSTRACT This paper presents a macro-fiscal model for examining the public sector primary surplus and the dynamics and sustainability of public debt in closed and open economies. The model simulates how changes in the primary surplus affect public debt, highlighting key differences between these economic contexts. Notably, open economies can finance fiscal deficits with foreign currency-denominated debt, introducing additional sources of instability in public debt dynamics. The analysis demonstrates how a permanent reduction in the primary surplus undermines public debt sustainability, with outcomes shaped by economic conditions and the features of open and closed economies. Furthermore, it confirms that delays in implementing fiscal adjustments following a destabilizing shock result in increasingly severe corrective measures over time. JEL Classification: E62, H62, H63 Keywords: Debt, Dynamic, Sustainability, Fiscal Adjustment RESUMEN En este trabajo, se presenta un modelo macro fiscal que permite abordar los conceptos de superávit primario, dinámica y sostenibilidad de la deuda pública en dos contextos: economía cerrada y una economía abierta. El modelo se ha construido para simular los efectos de una variación del superávit primario sobre la dinámica de la deuda pública. La principal diferencia entre ambas versiones del modelo radica en que, en el caso de la 1 Professor and teaching assistants, respectively, in the Department of Economics at the Pontificia Universidad Católica del Perú (PUCP). Waldo Mendoza https://orcid.org/0000-0001- 9422-7908. We thank Luis Mancilla, Rafael Velarde, Jesús Zavalaga, Juan Diego Goicochea, Luis Limas, Joseph Santisteban, and Piero Fernández Dávila, PUCP teaching assistants, as well as Marcelo Gallardo (PUCP mathematics program), for their valuable collaboration. We also appreciate the insights of a peer reviewer, whose suggestions encouraged us to explore the open economy framework. https://orcid.org/0000-0001-9422-7908 https://orcid.org/0000-0001-9422-7908 economía abierta, el déficit fiscal también puede financiarse con deuda pública en moneda extranjera, lo cual introduce nuevos mecanismos de desestabilización de la trayectoria estable de la deuda pública. Los resultados muestran que, bajo una serie de condiciones, una reducción permanente del superávit primario tiene efectos significativos en la sostenibilidad de la deuda pública. Asimismo, se muestra que, en ambos casos, los ajustes fiscales son más grandes, conforme más tiempo transcurre desde el shock desestabilizador original. Clasificación JEL: E62, H62, H63 Palabras clave: Deuda, dinámica, sostenibilidad, ajuste fiscal INTRODUCTION Fiscal policy, implemented by the government—in Peru’s case, the Ministry of Economy and Finance (MEF)—involves managing public spending, tax rates, and public debt to maintain output near potential without jeopardizing public debt sustainability. In macroeconomic literature, particularly in the study of business cycles, public spending and tax rates are frequently discussed as tools to guide aggregate demand toward potential output. These analyses typically assume the sustainability of public debt, as it is a prerequisite for the discretionary use of public spending and tax rates. A country’s public debt is considered sustainable if: “[...] the government is able to meet all its current and future payment obligations without exceptional financial assistance or going into default.” (Hakura, 2020, p. 60) That is, public debt is sustainable when: "[...] the government has a high likelihood of solvency, meaning it can meet its current and future financial obligations without resorting to unfeasible or undesirable policies. Additionally, the government must also have sufficient liquidity." (Hakura, 2020, p. 60). For the purposes of this text, designed for undergraduate students, we adopt a more straightforward definition. Public debt will be considered sustainable if the government can maintain it at a constant level, as a percentage of GDP, that is deemed appropriate. Along with sustainability, this analysis explores how public debt evolves over time—a concept referred to as public debt dynamics. 1. MACRO-FISCAL MODEL OF A CLOSED ECONOMY 1.1 Public Debt Dynamics2 The fiscal deficit (𝐷𝐹𝑡), though an imperfect measure,3 is a key indicator of fiscal policy. In any given period 𝑡, it can be defined in two complementary ways. First, it represents the difference between public sector spending and revenue. Second, since the deficit must be financed, it is equal to the net borrowing flow, or the change in the public debt stock. This flow accounts for disbursements received net of repayments made during the same period. Borrowing can occur through bond issuance, bilateral agreements, or loans from multilateral organizations such as the International Monetary Fund (IMF), the World Bank (WB), or the Inter-American Development Bank (IDB). Under the first definition, the fiscal deficit reflects the difference between total public spending and revenue. Spending includes primary (non-financial) spending in real terms (𝐺𝑡) and financial spending, which consists of interest payments on public debt—the real interest rate multiplied by the previous period’s debt stock (𝑟𝐵𝑡−1 𝑔 ). Revenue comes from tax collection, equal to the tax rate multiplied by real GDP (𝑡𝑌𝑡). Abstracting from international considerations, the real fiscal deficit can be expressed as: 𝐷𝐹𝑡 = 𝐺𝑡 + 𝑟𝐵𝑡−1 𝑔 − 𝑡𝑌𝑡 (1) Debt is measured as of the previous period for two reasons. First, this approach reflects the reality that interest payments result from past borrowing. Second, it facilitates the development of a dynamic model in discrete time to examine debt behavior over time. A model is considered dynamic when variables span multiple time periods. Using the primary surplus (𝑆𝑃𝑡 = 𝑡𝑌𝑡 − 𝐺𝑡), which excludes interest payments, this equation can be rewritten as: 𝐷𝐹𝑡 = 𝑟𝐵𝑡−1 𝑔 − 𝑆𝑃𝑡 (2) 2 For a general overview, see Blanchard (2023). 3 This result reflects not only fiscal policy but also the state of the economic cycle—whether expansionary or contractionary—as well as the interest rate cycle and international commodity price trends in an open economy. The second definition of the fiscal deficit focuses on financing. Under this approach, the deficit is equal to the net borrowing flow, or the change in the public debt stock between periods 𝑡 and 𝑡 − 1: 𝐵𝑡 𝑔 − 𝐵𝑡−1 𝑔 = 𝐷𝐹𝑡 (3) Combining these definitions yields: 𝐵𝑡 𝑔 − 𝐵𝑡−1 𝑔 = 𝐷𝐹𝑡 = 𝑟𝐵𝑡−1 𝑔 − 𝑆𝑃𝑡 (4) To facilitate international comparisons, it is useful to express these variables as percentages of GDP. Dividing both sides of equation (4) by real GDP (𝑌𝑡) and applying standard algebraic transformations leads to: 𝐵𝑡 𝑔 𝑌𝑡 − 𝐵𝑡−1 𝑔 𝑌𝑡 𝑌𝑡−1 𝑌𝑡−1 = 𝐷𝐹𝑡 𝑌𝑡 = 𝑟 𝐵𝑡−1 𝑔 𝑌𝑡 𝑌𝑡−1 𝑌𝑡−1 − 𝑆𝑃𝑡 𝑌𝑡 (5) Expressing growth as: 𝑌𝑡−𝑌𝑡−1 𝑌𝑡−1 = 𝑔 (6) or equivalently: 𝑌𝑡 𝑌𝑡−1 = 1 + 𝑔 (7) provides the basis for reformulating equation (5) as: 𝑏𝑡 𝑔 − 𝑏𝑡−1 𝑔 1+𝑔 = 𝑑𝑓𝑡 = 𝑟 𝑏𝑡−1 𝑔 1+𝑔 − 𝑠𝑝𝑡 (8) This formulation underpins the equation that describes the dynamics of public debt: 𝑏𝑡 𝑔 = 1+𝑟 1+𝑔 𝑏𝑡−1 𝑔 − 𝑠𝑝𝑡 (9) Equation (9) shows that public debt, as a percentage of GDP, is determined by the previous period’s debt (adjusted for interest and growth) minus the primary surplus. This framework captures the dynamics of debt accumulation over time, assuming the absence of borrowing constraints—a point discussed further below. Plotted as the relationship between current (𝑏𝑡 𝑔 ) and previous (𝑏𝑡−1 𝑔 ) debt levels, both expressed as percentages of GDP, equation (9) forms the 𝑏𝑏 line. The slope of this line varies under different conditions, which will be explored in subsequent sections. 1.2 Public Debt Sustainability In discrete-time dynamic equations, a steady-state (long-run) equilibrium is reached when the dynamic endogenous variable stabilizes—that is, when it stops changing. The concept of public debt sustainability is closely tied to the idea of steady-state equilibrium. In equation (9), the dynamic endogenous variable is the public debt stock as a percentage of GDP. Achieving steady-state equilibrium means that the debt-to-GDP ratio no longer changes, implying that public debt in one period is equal to that of the previous period. This represents the most fundamental concept of public debt sustainability: the government’s ability to stabilize public debt as a percentage of GDP. The condition for public debt sustainability, or steady-state equilibrium, is expressed in equation (10): 𝑏𝑡 𝑔 = 𝑏𝑡−1 𝑔 (10) Graphically, this condition is represented by the 𝑒𝑒 line, which has a positive slope of one, in the (𝑏𝑡−1 𝑔 , 𝑏𝑡 𝑔 ) plane. Figure 1 Public Debt Sustainability What is required for an economy to achieve steady-state equilibrium—that is, to keep the public debt stock constant as a percentage of GDP? Combining equation (9), which describes debt dynamics, with equation (10), which defines the sustainability condition, yields the equation for the primary surplus needed to stabilize public debt: 𝑠𝑝𝑒𝑒 = 𝑟−𝑔 1+𝑔 𝑏𝑡−1 𝑔 (11) Equation (11) has significant implications for macroeconomic policy. Highly indebted governments—those with very high public debt-to-GDP ratios and/or those where the real interest rate significantly exceeds the GDP growth rate (𝑟 − 𝑔 > 0)—must allocate substantial resources to debt interest payments. Consequently, they are required to maintain large primary surpluses, which can only be achieved through significant reductions in primary spending and/or major increases in revenue, both as percentages of GDP. It is important to note that the assumption of a constant interest rate is highly concessive. In practice, as public debt increases, interest rates tend to rise as well. 𝑏𝑡 𝑔 𝑒𝑒0 𝑏𝑡−1 𝑔 𝑏1 𝑔 𝑏0 𝑔 𝐴 To summarize, the framework includes the debt dynamics equation (9), the steady-state equilibrium condition (10), and the primary surplus required to stabilize public debt at equilibrium, expressed in equation (11): 𝑏𝑡 𝑔 = 1+𝑟 1+𝑔 𝑏𝑡−1 𝑔 − 𝑠𝑝𝑡 (9) 𝑏𝑡 𝑔 = 𝑏𝑡−1 𝑔 (10) 𝑠𝑝𝑒𝑒 = 𝑟−𝑔 1+𝑔 𝑏𝑡−1 𝑔 (11) 1.3 Public Debt Dynamics and Sustainability If a government disregards or downplays the importance of public debt sustainability in fiscal policy—perhaps due to confidence in its ability to finance fiscal deficits without difficulty—it operates solely under equation (9). In contrast, a government concerned with sustainability also considers equation (10). Fiscal balance, referred to here as intertemporal fiscal balance, results from combining equations (9) and (10).4 Solving these equations leads to three possible scenarios. To graph these cases, it is essential to first determine the initial steady-state equilibrium point and the slope of the 𝑏𝑏 line in each case. Using the primary surplus at steady-state equilibrium (equation 11) and the slope of the 𝑏𝑏 line (equation 9), we identify three cases:5 Case 1: 𝒓 = 𝒈 𝑠𝑝𝑒𝑒 = 𝑟−𝑔 1+𝑔 𝑏𝑒𝑒 𝑔 = 0 (12.1) Slope of 𝑏𝑏 = slope of 𝑒𝑒. Case 2: 𝒓 > 𝒈 𝑠𝑝𝑒𝑒 = 𝑟−𝑔 1+𝑔 𝑏𝑒𝑒 𝑔 > 0 (12.2) 4 Given the values of public debt and the primary surplus, the fiscal deficit can be determined. 5 In the steady-state equilibrium, 𝑏𝑡 𝑔 = 𝑏𝑡−1 𝑔 = 𝑏𝑒𝑒 𝑔 . From this, the expressions for the steady-state surplus in the different cases can be derived. Slope of 𝑏𝑏 > slope of 𝑒𝑒. Case 3: 𝒓 < 𝒈 𝑠𝑝𝑒𝑒 = 𝑟−𝑔 1+𝑔 𝑏𝑒𝑒 𝑔 < 0 (12.3) Slope of 𝑏𝑏 < slope of 𝑒𝑒. Figures 2, 3, and 4 illustrate these cases. Figure 2 Public Debt Dynamics and Sustainability – Case 1: 𝒓 = 𝒈 Figure 3 Public Debt Dynamics and Sustainability – Case 2: 𝒓 > 𝒈 𝑏𝑡 𝑔 𝑏1 𝑔 𝑏𝑡−1 𝑔 𝑏0 𝑔 𝑏𝑏0(𝑠𝑝 = 0) = 𝑒𝑒0 𝐴 𝑏𝑡−1 𝑔 𝑏𝑡 𝑔 𝑒𝑒0 𝑏𝑏0(𝑠𝑝 > 0) 𝑏1 𝑔 𝑏0 𝑔 𝐴 Figure 4 Public Debt Dynamics and Sustainability – Case 3: 𝒓 < 𝒈 In these figures, the public debt dynamics line (equation 9, 𝑏𝑏), the steady-state equilibrium line (equation 10, 𝑒𝑒), and their slopes are compared. The 𝑏𝑏 line represents how public debt evolves over time, while the 𝑒𝑒 line indicates the condition where public debt in one period equals that of the previous period. In Figure 2, the 𝑏𝑏 and 𝑒𝑒 lines overlap, as their slopes are identical; in Figure 3, the slope of the 𝑏𝑏 line exceeds that of the 𝑒𝑒 line; and in Figure 4, the slope of the 𝑏𝑏 line is less than that of the 𝑒𝑒 line. At point 𝐴, intertemporal fiscal balance is achieved. At this point, public debt remains constant because interest payments on debt are fully supported by the existing primary surplus (𝑠𝑝0). If this level of primary surplus is maintained over time, and no shocks occur to the interest rate or GDP growth rate, public debt sustainability is ensured. In such a case, the public debt-to-GDP ratio remains constant across periods. 1.4. Primary Surplus, Public Debt Dynamics, and Sustainability This section examines the effects of a permanent increase in public spending as a share of GDP, which reduces the primary surplus below the level required to stabilize public 𝑏𝑡−1 𝑔 𝑏𝑡 𝑔 𝑏𝑏0(𝑠𝑝 < 0) 𝑒𝑒0 𝑏0 𝑔 𝑏1 𝑔 𝐴 debt as a percentage of GDP (𝑠𝑝1 < 𝑠𝑝0). The response of public debt dynamics depends on the specific case: 𝑟 = 𝑔, 𝑟 > 𝑔, or 𝑟 < 𝑔. Assuming an initial steady-state equilibrium, public debt is constant at its steady-state level, and the primary surplus is sufficient to stabilize public debt as a percentage of GDP. Public debt in period 1 equals that in period 0 (𝑏1 𝑔 = 𝑏0 𝑔 ) and the primary surplus is 𝑠𝑝0. This analysis considers three phases: the short-term impact, the transition toward a new equilibrium, and the long-term outcome (if a new steady-state equilibrium exists). Case 1: 𝒓 = 𝒈 When the real GDP growth rate equals the real interest rate, equation (9) implies: 1 + 𝑟 1 + 𝑔 = 1 Short-Term Impact Differentiating equation (9) to determine the short-term effects gives: 𝑑𝑏1 𝑔 = −𝑑𝑠𝑝1 > 0 This indicates that a reduction in the primary surplus during the first period increases public debt by the same amount. Transition to Steady State In subsequent periods, public debt increases by the same magnitude as in the first period. This occurs because the condition 1+𝑟 1+𝑔 = 1 implies that the debt increment remains constant across periods. In period 2, the increase in public debt from period 1 causes a further increase in debt by the same amount.6 This pattern repeats in period 3 and subsequent periods. Each increase in public debt equals the initial reduction in the primary surplus, and the debt-to-GDP ratio continues to rise indefinitely. 6 This is because, in the public debt dynamics equation, the public debt from the previous period is multiplied by a coefficient equal to 1. Differentiating equation (9) yields: 𝑑𝑏2 𝑔 = −𝑑𝑠𝑝1 > 0 𝑑𝑏3 𝑔 = −𝑑𝑠𝑝1 > 0 Generalizing for any period 𝑛: 𝑑𝑏𝑛 𝑔 = −𝑑𝑠𝑝1 > 0 Steady-State Equilibrium To analyze the long-term behavior of public debt, equation (9) is expressed as: 𝑏𝑛 𝑔 = 𝑏0 𝑔 + ∑ 𝑑𝑏𝑡 𝑔𝑛 𝑡=1 (13) Since 1+𝑟 1+𝑔 = 1, the debt increment is constant (𝑑𝑏𝑛 𝑔 = −𝑑𝑠𝑝1, ∀𝑛 ≥ 1). Substituting into the equation gives: 𝑏𝑛 𝑔 = 𝑏0 𝑔 − ∑ 𝑑𝑠𝑝1 𝑛 𝑡=1 (13.1) Taking the limit as 𝑛 → ∞: lim 𝑛→∞ 𝑏𝑛 𝑔 = ∞+ > 0 This confirms that a permanent reduction in the primary surplus7 leads to a divergent trajectory for public debt. Figure 5 illustrates this case. Initially, the 𝑏𝑏0 and 𝑒𝑒0 lines overlap, representing the steady-state equilibrium at point 𝐴, where public debt is stable at 𝑏𝑒𝑒 𝑔 . In period 1, when the primary surplus is reduced, the 𝑏𝑏0 line shifts upward to 𝑏𝑏1, and public debt increases to point 𝐵. In subsequent periods, the economy moves to points 𝐶, 𝐷,…, with public debt increasing indefinitely. This dynamic system is linearly unstable, and public debt becomes unsustainable. 7 That is, the primary surplus as a percentage of GDP decreases from its initial level, 𝑠𝑝0, to a lower level, 𝑠𝑝1 , and remains at that new level indefinitely. Figure 5 Reduction in the Primary Surplus: Case 𝒓 = 𝒈 Case 2: 𝒓 > 𝒈 When the real interest rate exceeds the GDP growth rate, equation (9) implies: 1 + 𝑟 1 + 𝑔 > 1 Short-Term Impact Differentiating equation (9) to determine the short-term effects gives: 𝑑𝑏1 𝑔 = −𝑑𝑠𝑝1 > 0 This result indicates that public debt increases by the same magnitude as the reduction in the primary surplus. Transition to Steady State In period 2, public debt increases again, but by a multiple of the increment observed in period 1. This pattern arises because, under the condition 𝑟 > 𝑔, the numerator in the 𝑏1 𝑔 𝑏2 𝑔 𝑏3 𝑔 𝑏𝑏0(𝑠𝑝 = 0) = 𝑒𝑒0 𝑏𝑏1(𝑠𝑝 < 0) 𝑏𝑡−1 𝑔 𝑏𝑡 𝑔 𝑏𝑒𝑒 𝑔 𝑏0 𝑔 𝑏1 𝑔 𝑏2 𝑔 𝑏3 𝑔 𝐴 𝐵 𝐶 𝐷 debt dynamics equation exceeds the denominator.8 In period 3, the debt rises again, magnified by the same factor applied to the increase from period 2. This compounding process continues in subsequent periods, with public debt growing at an accelerating rate. Differentiating equation (9) for subsequent periods yields: 𝑑𝑏2 𝑔 = − ( 1 + 𝑟 1 + 𝑔 ) 𝑑𝑠𝑝1 > 0 𝑑𝑏3 𝑔 = − ( 1 + 𝑟 1 + 𝑔 ) 2 𝑑𝑠𝑝1 > 0 Generalizing for any period 𝑛: 𝑑𝑏𝑛 𝑔 = − ( 1 + 𝑟 1 + 𝑔 ) 𝑛−1 𝑑𝑠𝑝1 > 0 Steady-State Equilibrium In this case, where 1+𝑟 1+𝑔 > 1, the change in public debt is given by: 𝑑𝑏𝑛 𝑔 = − ( 1 + 𝑟 1 + 𝑔 ) 𝑛−1 𝑑𝑠𝑝1 > 0, ∀𝑛 ≥ 1 From this expression, the total public debt in period 𝑛 is given by: 𝑏𝑛 𝑔 = 𝑏0 𝑔 − ∑ ( 1+𝑟 1+𝑔 ) 𝑡−1 𝑑𝑠𝑝1 𝑛 𝑡=1 (13.2) Taking the limit as 𝑛 → ∞: lim 𝑛→∞ 𝑏𝑛 𝑔 = ∞+ > 0 This confirms that a permanent reduction in the primary surplus leads to a divergent trajectory for public debt. Figure 6 illustrates this case. At the initial steady-state equilibrium, the public debt dynamics line (𝑏𝑏0) intersects with the steady-state equilibrium line (𝑒𝑒0) at point 𝐴. The 8 In equation (9), public debt from the previous period is multiplied by a factor greater than one. slope of 𝑏𝑏 is steeper than that of 𝑒𝑒, reflecting the greater weight of interest payments relative to GDP growth. Public debt at this initial equilibrium is 𝑏𝑒𝑒 𝑔 . In period 1, the reduction in the primary surplus shifts the public debt dynamics line upward, from, from 𝑏𝑏0 to 𝑏𝑏1. Debt increases to point 𝐵, above the previous level. In subsequent periods, as the debt and fiscal deficit grow, the economy moves to points 𝐶, 𝐷 ,…, with debt increasing indefinitely. Without changes to the primary surplus, the economy fails to reach a new steady-state equilibrium. Figure 6 Reduction in the Primary Surplus: Case 𝒓 > 𝒈 Case 3: 𝒓 < 𝒈 When the GDP growth rate exceeds the real interest rate, equation (9) implies: ( 1 + 𝑟 1 + 𝑔 ) < 1 Short-Term Impact Differentiating equation (9) to determine the short-term effects gives: 𝑑𝑏1 𝑔 = −𝑑𝑠𝑝1 > 0 This result indicates that public debt increases by the same magnitude as the reduction in the primary surplus during the first period. Transition to Steady State 𝑏1 𝑔 𝑏2 𝑔 𝑏𝑡−1 𝑔 𝑏0 𝑔 𝑏𝑒𝑒 𝑔 𝑏1 𝑔 𝑏2 𝑔 𝑏3 𝑔 𝑏𝑡 𝑔 𝐴 𝐵 𝐶 𝐷 𝑒𝑒0 𝑏𝑏1(𝑠𝑝1) 𝑏𝑏0(𝑠𝑝0) In period 2, the increase in public debt from period 1 causes a further increase, but by a fraction of the initial rise.9 In period 3, the debt increases again, but only by a fraction of the rise in period 2. In subsequent periods, this periodic increase in public debt continues, with the increments becoming progressively smaller until the debt-to-GDP ratio stabilizes. At the new steady-state equilibrium, public debt is higher than in the initial equilibrium. Differentiating equation (9) for subsequent periods yields: 𝑑𝑏2 𝑔 = − ( 1 + 𝑟 1 + 𝑔 ) 𝑑𝑠𝑝1 > 0 𝑑𝑏3 𝑔 = − ( 1 + 𝑟 1 + 𝑔 ) 2 𝑑𝑠𝑝1 > 0 Generalizing for any period 𝑛: 𝑑𝑏𝑛 𝑔 = − ( 1 + 𝑟 1 + 𝑔 ) 𝑛−1 𝑑𝑠𝑝1 > 0 Steady-State Equilibrium For this case, where ( 1+𝑟 1+𝑔 ) < 1, the change in public debt is given by: 𝑑𝑏𝑛 𝑔 = − ( 1 + 𝑟 1 + 𝑔 ) 𝑛−1 𝑑𝑠𝑝1 > 0, ∀𝑛 ≥ 1 From this expression, the total public debt in period 𝑛 is given by: 𝑏𝑛 𝑔 = 𝑏0 𝑔 − ∑ ( 1+𝑟 1+𝑔 ) 𝑛−1 𝑑𝑠𝑝1 𝑛 𝑡=1 (13.3) Taking the limit as 𝑛 → ∞: lim 𝑛→∞ 𝑏𝑛 𝑔 = 𝑏0 𝑔 − 𝑑𝑠𝑝1 lim 𝑛→∞ ∑ ( 1 + 𝑟 1 + 𝑔 ) 𝑛−1𝑛 𝑡=1 = 𝑏0 𝑔 − 𝑑𝑠𝑝1 ( 1 + 𝑔 𝑔 − 𝑟 ) > 0 9 When 𝑔 > 𝑟, 1+𝑟 1+𝑔 is a fraction. This confirms that, although a permanent reduction in the primary surplus leads to an increase in public debt, it eventually stabilizes at a new steady-state level. Figure 7 illustrates this case. At the initial steady-state equilibrium, the public debt dynamics line (𝑏𝑏0) intersects the steady-state equilibrium line (𝑒𝑒0) at point 𝐴, with the slope of 𝑏𝑏 being less steep than that of 𝑒𝑒. Public debt at this equilibrium is 𝑏𝑒𝑒 𝑔 . In period 1, the reduction in the primary surplus shifts the public debt dynamics line upward, from 𝑏𝑏0 to 𝑏𝑏1, causing public debt to rise above its previous level, reaching point 𝐵. In subsequent periods, the rate of debt growth slows, and the economy transitions through points 𝐶, 𝐷,…, until public debt stabilizes at point 𝑍, the new steady- state equilibrium, characterized by a higher debt level. Figure 7 Reduction in the Primary Surplus: Case 𝒓 < 𝒈 In Case 3, where the real GDP growth rate exceeds the real interest rate, a permanent reduction in the primary surplus leads to a convergent trajectory for public debt. Public debt stabilizes at a new steady-state equilibrium, which is higher than the initial equilibrium. This outcome highlights the stabilizing influence of GDP growth exceeding the real interest rate, even under conditions of fiscal expansion. If real-world economies behaved as described in Cases 1 and 2, we would observe widespread explosive debt trajectories among governments. However, this is not the case. A continuous growth of public debt over time, as outlined in these cases, presupposes economies with unlimited borrowing capacity—a condition that is unrealistic. In reality, all countries face borrowing constraints, typically expressed as a maximum public debt-to-GDP ratio. Developed economies, benefiting from stronger reputations, generally have higher debt limits compared to emerging or developing nations. 𝑏1 𝑔 𝑏2 𝑔 𝑏𝑒𝑒1 𝑔 𝑏0 𝑔 𝑏𝑡−1 𝑔 𝑏𝑒𝑒0 𝑔 𝑏1 𝑔 𝑏2 𝑔 𝑏3 𝑔 𝑏𝑒𝑒1 𝑔 𝐴 𝐵 𝐶 𝐷 𝑍 𝑏𝑡 𝑔 𝑒𝑒0 𝑏𝑏1(𝑠𝑝1 ≪ 0) 𝑏𝑏0(𝑠𝑝0 < 0) A key observation is that countries neglecting sustainability by maintaining a primary surplus below the level needed to stabilize debt often enter a phase of annual debt accumulation. This trend is eventually interrupted when access to credit is curtailed, both in financial markets—preventing the issuance of public debt—and through multilateral or bilateral lenders, such as the IMF, WB, or IDB.10 When these borrowing limits are reached, and fiscal deficits can no longer be financed, governments face two choices: 1. Immediate Fiscal Adjustment: Governments without international support—either because assistance is unavailable or, more commonly, because they choose not to seek it for ideological reasons—must undertake abrupt fiscal adjustments. This requires immediate expenditure cuts and tax increases to raise the primary surplus. Public debt is frozen at its current level, the fiscal deficit is eliminated, and the primary surplus stabilizes debt. 2. Gradual Adjustment with IMF Support: Governments anticipating the consequences of reaching their borrowing limit may turn to the IMF preemptively. The IMF facilitates a more gradual fiscal adjustment, allowing deficits to narrow progressively rather than being eliminated at once. Expenditures are reduced, and revenues are increased incrementally, slowing the growth of public debt until it stabilizes at its upper limit. While this approach still entails social and political costs, these are often less severe than those of an abrupt adjustment. No fiscal adjustment is cost-free. Hendrik (2022) highlights that IMF programs often extend beyond direct financial assistance, providing a “catalytic effect.” Agreements with the IMF frequently act as a signal to other multilateral institutions, such as the WB or IDB, of a country’s commitment to meeting its debt obligations. 10 We exclude the option of central bank financing of the government through primary issuance. In such cases, the debt explosion could be accompanied by hyperinflation. 1.5 The Stabilizing Shock When a fiscal deficit can no longer be financed, governments face no alternative but to adjust public spending and revenue. This section examines a scenario in which the government implements an abrupt stabilization of public debt—a shock treatment. The analysis focuses on Case 2, where the real interest rate exceeds the real GDP growth rate ( 1+𝑟 1+𝑔 > 1), a particularly relevant scenario for economies with low growth rates and high interest rates. The starting point is an initial steady-state equilibrium where the primary surplus is sufficient to maintain public debt stability. In period 1, a permanent reduction in the primary surplus occurs, falling below the level required to stabilize debt. This is assumed to result from a permanent increase in public spending as a percentage of GDP. The immediate consequence is an increase in public debt during that period. This rise, driven by the dynamics described in equation (9), leads to further increases in public debt in period 2, at a faster rate than in period 1. In period 3, debt rises again, growing even more rapidly, until it reaches the maximum limit imposed by financial markets and international institutions.11 At this point, public debt cannot increase further, and the fiscal deficit must be eliminated. Achieving a zero deficit requires a sharp increase in the primary surplus through spending cuts and revenue increases, raising it to the level necessary to freeze debt at its upper limit. The new primary surplus must cover total interest payments on the debt in period 3. In the absence of external shocks, this would represent a new steady-state equilibrium. If the economy can sustain the required primary surplus each year and avoid adverse changes to interest rates or GDP growth, the debt level in period 3 can be considered sustainable. However, the primary challenge with this “market-driven” adjustment is the size of the primary surplus needed to stabilize public debt at its new, elevated level (𝑟𝑏3 𝑔 ).12 The 11 The government may also choose not to seek IMF support for ideological reasons or other considerations. 12 Stabilizing public debt at its original level, 𝑏0 𝑔 , would require a significantly greater fiscal effort. During the adjustment period, the primary surplus would need to be substantially higher than 𝑟𝑏3 𝑔 , an unrealistic objective. With such a surplus, the model’s dynamics would allow public debt to gradually decrease over time, and upon higher debt volume can result in a significantly larger primary surplus requirement, with severe social and political implications. Figure 8 illustrates this situation. In period 1, a permanent reduction in the primary surplus, below the level required to stabilize public debt, shifts the debt dynamics line upward from 𝑏𝑏0 to 𝑏𝑏1, increasing debt from 𝑏0 𝑔 to 𝑏1 𝑔 . The increase in debt during period 1 leads to further growth in period 2, reaching 𝑏2 𝑔 , and again in period 3, reaching 𝑏3 𝑔 , which we assume represents the debt limit beyond which debt cannot increase. To stabilize debt at 𝑏3 𝑔 , the primary surplus must increase from 𝑠𝑝0 to 𝑠𝑝3, causing the debt dynamics line to shift downward from 𝑏𝑏1 to 𝑏𝑏2. The intercept of this new line reflects the new primary surplus, which is significantly higher than the initial level. The new steady-state equilibrium is reached at point 𝑍, where the debt dynamics line (𝑏𝑏2) intersects the sustainable debt line (𝑒𝑒0). reaching its initial level, the government could maintain the exact primary surplus needed to stabilize debt at that level. This analysis focuses on the more realistic and feasible scenario of stabilizing public debt at a new, higher level. Figure 8 The Stabilizing Shock in a Closed Economy The analysis assumes that the country has lost access to credit from financial markets and international institutions. Additionally, the possibility of the central bank acting as the government’s lender of last resort is excluded. Under these conditions, the country would need to implement a drastic fiscal adjustment, potentially exacerbating challenges beyond the economic sphere. The scale of spending cuts and tax increases required could lead to significant social unrest. 𝑏3 𝑔 𝑍 𝑏𝑡−1 𝑔 𝑏0 𝑔 𝑏𝑒𝑒 𝑔 𝑏1 𝑔 𝑏2 𝑔 𝑏3 𝑔 𝑏𝑡 𝑔 𝐴 𝐵 𝐶 𝐷 𝑒𝑒0 𝑏𝑏1(𝑠𝑝 1 ) 𝑏𝑏0(𝑠𝑝0) 𝑏1 𝑔 𝑏2 𝑔 −𝑠𝑝1 −𝑠𝑝0 −𝑠𝑝2 𝑏𝑏2(𝑠𝑝2) 2. MACRO-FISCAL MODEL FOR AN OPEN ECONOMY13 2.1. Public Debt Dynamics In an open economy, the macro-fiscal model introduces two key changes. On the revenue side, the government may receive income from taxes on export earnings, particularly from commodities. On the expenditure side, access to external borrowing introduces foreign-denominated debt and associated interest payments. Therefore, equation (4) in Section 1, which combines the two definitions of the fiscal deficit—as the change in public debt and as the difference between government expenditures and revenues—becomes: 𝐵𝑡 𝑔 − 𝐵𝑡−1 𝑔 + 𝑒𝑡(𝐵𝑡 𝑔∗ − 𝐵𝑡−1 𝑔∗ ) = 𝐷𝐹𝑡 = 𝑟𝐵𝑡−1 𝑔 + 𝑒𝑡𝑟∗𝐵𝑡−1 𝑔∗ − 𝑆𝑃𝑡 (15) Where: 𝑒𝑡 is the real exchange rate in period 𝑡 𝐵𝑡 𝑔∗ is public debt in foreign currency in period 𝑡 𝐵𝑡−1 𝑔∗ is public debt in foreign currency in period 𝑡 − 1 𝑟∗ is the international interest rate on foreign-denominated debt 𝑆𝑃𝑡 is the primary surplus The primary surplus (𝑆𝑃𝑡) now also includes revenues from commodity exports, which depend on international prices (𝑃∗) and export volumes (𝑋0). 14 𝑆𝑃𝑡 = 𝑡𝑌𝑡 + 𝑡𝑒𝑡𝑃∗𝑋0 − 𝐺𝑡 (16) Applying the algebraic transformations outlined in Section 1 and expressing the variables in equation (15) as percentages of GDP results in: 𝐵𝑡 𝑔 𝑌𝑡 − 𝐵𝑡−1 𝑔 𝑌𝑡 𝑌𝑡−1 𝑌𝑡−1 + 𝑒𝑡𝐵𝑡 𝑔∗ 𝑌𝑡 − 𝑒𝑡𝐵𝑡−1 ∗𝑔 𝑌𝑡 𝑌𝑡−1 𝑌𝑡−1 𝑒𝑡−1 𝑒𝑡−1 = 𝐷𝐹𝑡 𝑌𝑡 = 𝑟 𝐵𝑡−1 𝑔 𝑌𝑡 𝑌𝑡−1 𝑌𝑡−1 + 𝑒𝑡𝑟∗𝐵𝑡−1 ∗𝑔 𝑌𝑡 𝑌𝑡−1 𝑌𝑡−1 𝑒𝑡−1 𝑒𝑡−1 − 𝑆𝑃𝑡 𝑌𝑡 (17) 13 Jiménez (2008). 14 Income tax on exporters. We denote 𝑥𝑡 as the share of 𝑋𝑡 in GDP (𝑥𝑡 = 𝑋𝑡 𝑌𝑡 ). Additionally, the growth rate of the real exchange rate is defined as: 𝑒𝑡−𝑒𝑡−1 𝑒𝑡−1 = 𝑔𝑒 (18) or equivalently: 𝑒𝑡 𝑒𝑡−1 = 1 + 𝑔𝑒 (19) Building on equation (17), and converting the variables into percentages of GDP using equations (7) and (19), we arrive at equation (20), which summarizes the two ways of expressing the fiscal deficit, now as percentages of GDP: 𝑏𝑡 𝑔 − 1 1+𝑔 𝑏𝑡−1 𝑔 + 𝑏𝑡 𝑔∗ − (1+𝑔𝑒) (1+𝑔) 𝑏𝑡−1 𝑔∗ = 𝑑𝑓𝑡 = 𝑟 1 1+𝑔 𝑏𝑡−1 𝑔 + 𝑟∗ (1+𝑔𝑒) (1+𝑔) 𝑏𝑡−1 𝑔∗ − 𝑠𝑝𝑡 (20) From equation (20), we derive the equation describing the behavior of public debt over time—the public debt dynamics equation, which is central to our analysis: 𝑏𝑡 𝑔 + 𝑏𝑡 𝑔∗ = 1+𝑟 1+𝑔 𝑏𝑡−1 𝑔 + (1+𝑟∗)(1+𝑔𝑒) 1+𝑔 𝑏𝑡−1 𝑔∗ − 𝑠𝑝𝑡 (21) To graphically represent the relationship between current and previous-period domestic public debt, the equation can be rearranged as follows: 𝑏𝑡 𝑔∗ = (1+𝑟∗)(1+𝑔𝑒) 1+𝑔 𝑏𝑡−1 𝑔∗ − 𝑏𝑡 𝑔 + 1+𝑟 1+𝑔 𝑏𝑡−1 𝑔 − 𝑠𝑝𝑡 (22) Equation (22), which is plotted in terms of current foreign-denominated public debt (𝑏𝑡 𝑔∗ ) and previous-period foreign-denominated public debt (𝑏𝑡−1 𝑔∗ ), defines the 𝑏𝑏∗ line. This line has a positive slope, but for different slope values, three cases arise, which will be discussed later. Figure 9 depicts this relationship. Figure 9 Public Debt Dynamics in an Open Economy The open economy model is represented by equation (21), which characterizes the dynamics of public debt. This model incorporates two endogenous variables: domestic public debt and external public debt, both expressed as percentages of GDP. 2.2 Public Debt Sustainability As in the closed economy model, steady-state or long-term equilibrium is achieved when the dynamic endogenous variables stabilize and no longer change. In equation (21), these variables—domestic public debt and external public debt, both expressed as percentages of GDP—reach equilibrium when their levels remain constant over time, meaning the debt in one period equals the debt in the previous period. This condition reflects the concept of public debt sustainability used in this analysis: the government’s ability to stabilize public debt as a percentage of GDP. This relationship is expressed in equation (23): 𝑏𝑡 𝑔 + 𝑏𝑡 𝑔∗ = 𝑏𝑡−1 𝑔 + 𝑏𝑡−1 𝑔∗ (23) For consistency with the closed economy model, equation (23) can be rearranged as: 𝐴 𝑏𝑡−1 𝑔∗ 𝑏1 𝑔∗ 𝑏0 𝑔∗ 𝑏𝑏∗(𝑠𝑝 < 0) 𝑏𝑏∗(𝑠𝑝 = 0) 𝑏𝑡 𝑔∗ 𝑏𝑏∗(𝑠𝑝 > 0) 𝑏𝑡 𝑔 = (𝑏𝑡−1 𝑔∗ − 𝑏𝑡 𝑔∗ ) + 𝑏𝑡−1 𝑔 (24) In this form, the 𝑒𝑒 line, shown in Figure 10, represents the condition for public debt sustainability in the (𝑏𝑡 𝑔∗ , 𝑏𝑡−1 𝑔∗ ) plane. The line has a positive slope of one and passes through the origin, reflecting the assumption of an initial steady-state equilibrium where 𝑏𝑡−1 𝑔∗ − 𝑏𝑡 ∗𝑔 = 0. Figure 10 Public Debt Sustainability in an Open Economy The primary surplus required to stabilize both domestic and external public debt as percentages of GDP can be determined by combining the debt dynamics equation (21) with the sustainability condition in equation (24). This yields the steady-state fiscal surplus: 𝑠𝑝𝑒𝑒 = 𝑟−𝑔 1+𝑔 𝑏𝑡−1 𝑔 + 𝑟∗(1+𝑔𝑒)+(𝑔𝑒−𝑔) 1+𝑔 𝑏𝑡−1 𝑔∗ (25) Similar to equation (11) in the closed economy model, equation (25) has significant implications for macroeconomic policy. Governments with high debt-to-GDP ratios, real interest rates far exceeding GDP growth (𝑟 − 𝑔 > 0), or exchange rate depreciation 𝐴 𝑏1 𝑔∗ 𝑏0 𝑔∗ 𝑏𝑡 𝑔∗ 𝑏𝑡−1 𝑔∗ 𝑒𝑒0 ∗ surpassing GDP growth,15 face substantial interest obligations. Such governments must maintain large primary surpluses, achievable only through significant reductions in primary expenditures or substantial increases in revenue, both as percentages of GDP. To summarize, the open economy model16 is characterized by:  The debt dynamics equation (21)  The condition for steady-state equilibrium or debt sustainability (equation 24)  The steady-state primary surplus required to stabilize public debt (equation 25) 𝑏𝑡 𝑔 + 𝑏𝑡 𝑔∗ = 1+𝑟 1+𝑔 𝑏𝑡−1 𝑔 + (1+𝑟∗)(1+𝑔𝑒) 1+𝑔 𝑏𝑡−1 𝑔∗ − 𝑠𝑝𝑡 (21) 𝑏𝑡 𝑔 = (𝑏𝑡−1 𝑔∗ − 𝑏𝑡 𝑔∗ ) + 𝑏𝑡−1 𝑔 (24) 𝑠𝑝𝑒𝑒 = 𝑟−𝑔 1+𝑔 𝑏𝑡−1 𝑔 + 𝑟∗(1+𝑔𝑒)−(𝑔−𝑔𝑒) 1+𝑔 𝑏𝑡−1 𝑔∗ (25) When external borrowing is absent (𝑏𝑡−1 𝑔∗ , 𝑏𝑡 𝑔∗ = 0), the equations governing public debt dynamics in an open economy become identical to those of a closed economy. 2.3 Debt Dynamics and Sustainability Building on this framework, three cases can be identified, similar to those discussed in the closed economy model.17 However, in the open economy context, in addition to the relationship between the domestic interest rate (𝑟) and the GDP growth rate (𝑔), it is necessary to account for the relationship between the international interest rate, (𝑟∗), the real depreciation rate of the domestic currency (𝑔𝑒), and the GDP growth rate (𝑔). Case 1: (𝒊) 𝒓 = 𝒈, o 15 The transmission mechanism operates as follows: when a country’s currency depreciates faster than its GDP grows, its domestic-currency revenues (which depend on GDP growth, 𝑌) are insufficient to offset exchange rate risk. This necessitates a higher primary surplus. This is the 'balance sheet effect' applied to public debt. 16 This model assumes imperfect capital mobility, following Mendoza (2019) and Mendoza and Vilca (2024). Consequently, domestic and foreign interest rates are determined independently, and the uncovered interest rate parity equation is not applied. 17 In an open economy, additional cases may arise. (𝒊𝒊) 𝒓∗ + 𝒈𝒆 = 𝒈18 𝑠𝑝𝑒𝑒 = 0 𝑏𝑏∗ slope = 𝑒𝑒∗ slope Case 2: (𝒊) 𝒓 > 𝒈, o (𝑖𝑖) 𝒓∗ + 𝒈𝒆 > 𝒈 𝑠𝑝𝑒𝑒 > 0 𝑏𝑏∗ slope > 𝑒𝑒∗ slope Case 3: (𝒊) 𝒓 < 𝒈, o (𝒊𝒊) 𝒓∗ + 𝒈𝒆 < 𝒈 𝑠𝑝𝑒𝑒 < 0 𝑏𝑏∗ slope < 𝑒𝑒∗ slope Figures 11, 12, and 13 illustrate Cases 1, 2, and 3, respectively. The choice of axes depends on the type of debt used to finance the fiscal deficit. If external public debt is used, the axes will be 𝑏𝑡−1 𝑔∗ and 𝑏𝑡 𝑔∗ , allowing an analysis of the trajectory of external public debt in response to deviations from the initial primary surplus equilibrium. In this scenario, the relationship between entre 𝑟∗, 𝑔𝑒 and 𝑔 is central. Conversely, if the fiscal deficit is financed through domestic public debt, the axes will be the same as in the closed economy model (𝑏𝑡−1 𝑔 , 𝑏𝑡 𝑔 ). In this case, the relevant relationship is between 𝑟 and 𝑔. 18 To ensure that the steady-state primary surplus equals zero, we consider the relationship (1 + 𝑔𝑒)(1 + 𝑟∗) = (1 + 𝑔). Since the values of 𝑔𝑒 , 𝑟∗, and 𝑔 are typically small, a linear approximation can be applied. Taking natural logarithms and using Taylor's approximation around 𝑥 = 0, where ln(1 + 𝑥) ≈ 𝑥, the original equation, (1 + 𝑟∗)(1 + 𝑔𝑒) = (1 + 𝑔), simplifies to the following linearized expression: 𝑟∗ + 𝑔𝑒 = 𝑔. Hereafter, we will adopt this linearized version. Figure 11 Public Debt Dynamics and Sustainability in an Open Economy 𝒓 = 𝒈 or 𝒓∗ + 𝒈𝒆 = 𝒈 𝑏𝑡 𝑔∗ 𝑏1 𝑔∗ 𝑏𝑡−1 𝑔∗ 𝑏0 𝑔∗ 𝑏𝑏0 ∗(𝑠𝑝 = 0) = 𝑒𝑒0 ∗ 𝐴 Figure 12 Public Debt Dynamics and Sustainability in an Open Economy 𝒓 > 𝒈 or 𝒓∗ + 𝒈𝒆 > 𝒈 𝑏𝑡−1 𝑔∗ 𝑏𝑡 𝑔∗ 𝑒𝑒0 ∗ 𝑏𝑏0 ∗(𝑠𝑝 > 0) 𝑏1 𝑔∗ 𝑏0 𝑔∗ 𝐴 Figure 13 Public Debt Dynamics and Sustainability in an Open Economy 𝒓 < 𝒈 or 𝒓∗ + 𝒈𝒆 < 𝒈 In these figures, the public debt dynamics line (𝑏𝑏∗), defined by equation (22), and the steady-state equilibrium line (𝑒𝑒∗), defined by equation (24), are combined. The 𝑏𝑏∗ line, with a positive slope, illustrates the evolution of public debt over time, while the 𝑒𝑒∗ line, with a slope of one, represents the condition for public debt sustainability, where public debt remains unchanged between periods. The main difference between these figures and those in the closed economy model lies in the intercepts of the public debt dynamics line. These intercepts now include components of external public debt, both from the dynamics equation and the steady- state analysis. However, the slopes of the lines remain unchanged, preserving the fundamental similarity to the closed economy model. Finally, at point 𝐴, intertemporal fiscal balance is achieved. At this point, public debt remains constant because interest payments on both domestic and external public debt are fully covered by the existing primary surplus (𝑠𝑝0). If this level of primary surplus is sustained over time, public debt sustainability is ensured, as public debt remains constant as a percentage of GDP across periods. 𝑏𝑡−1 𝑔∗ 𝑏𝑡 𝑔∗ 𝑏𝑏0 ∗(𝑠𝑝 < 0) 𝑒𝑒0 ∗ 𝑏0 𝑔∗ 𝑏1 𝑔∗ 𝐴 2.4. Primary Surplus, Debt Dynamics, and Sustainability in an Open Economy In an open economy at intertemporal fiscal equilibrium, a shock that reduces the primary surplus below the level required to stabilize public debt as a percentage of GDP (𝑠𝑝1 < 𝑠𝑝0) can have significant effects. This analysis considers a permanent reduction in the primary surplus resulting from a decline in export prices (𝑑𝑃∗ < 0), under the assumption that the fiscal deficit is financed entirely through external public debt as a percentage of GDP (𝑏𝑡 𝑔∗ ). 19 The outcomes depend on the relationships among 𝑟, 𝑔, 𝑟∗, and 𝑔𝑒. Since external public debt is the model’s endogenous variable, the relationship between 𝑟 and 𝑔 is excluded from this analysis. Case 1: 𝒓∗ + 𝒈𝒆 = 𝒈 When the sum of the international interest rate and the real depreciation rate equals the GDP growth rate, equation (21) simplifies to (1+𝑟∗)(1+𝑔𝑒) (1+𝑔) = 1. In this scenario, a reduction in the primary surplus caused by lower export prices increases external public debt in period 1 by the same magnitude as the reduction in the surplus. This analysis examines the effects across three periods: short-term (period 1), transition to steady state (subsequent periods), and steady-state equilibrium. The reduction in the primary surplus is defined as 𝑑𝑠𝑝1 < 0, 𝑑𝑠𝑝𝑛 = 0, ∀𝑛 > 1, under the condition 𝑟∗ + 𝑔𝑒 ≅ 𝑔. Short-Term Impact From equation (21): 𝑏𝑡 𝑔 + 𝑏𝑡 𝑔∗ = (1 + 𝑟∗)(1 + 𝑔𝑒) 1 + 𝑔 𝑏𝑡−1 𝑔∗ − 𝑠𝑝𝑡 + 1 + 𝑟 1 + 𝑔 𝑏𝑡−1 𝑔 Differentiating: 𝑑𝑏1 𝑔∗ = −𝑑𝑠𝑝1 > 0 19 Alternatively, the deficit could be financed through the stock of domestic public debt as a percentage of GDP (𝑏𝑡 𝑔 ) or even through a combination of both. However, financing with external debt requires an adequate supply of dollars in the economy. Thus, the reduction in the primary surplus immediately increases external public debt in period 1. Transition to Steady State Differentiating equation (21) to analyze changes in subsequent periods yields the following results: 𝑑𝑏2 𝑔∗ = −𝑑𝑠𝑝1 > 0 𝑑𝑏3 𝑔∗ = −𝑑𝑠𝑝1 > 0 Generalizing for any period 𝑛: 𝑑𝑏𝑛 𝑔∗ = −𝑑𝑠𝑝1 > 0 Steady-State Equilibrium To determine the long-term outcome, we simulate the case where 𝑛 → ∞. Using a similar approach to equation (13) in the closed economy model, we derive the following expression: 𝑏𝑛 𝑔∗ = 𝑏0 𝑔∗ + ∑ 𝑑𝑏𝑡 𝑔∗ 𝑛 𝑡=1 Given that the change in external public debt is constant across all periods, this simplifies to: 𝑏𝑛 𝑔∗ = 𝑏0 𝑔∗ − ∑ 𝑑𝑠𝑝1 𝑛 𝑡=1 Taking the limit as 𝑛 → ∞: lim 𝑛→∞ 𝑏𝑛 𝑔∗ = ∞+ > 0 Thus, as in the closed economy model, a permanent reduction in 𝑠𝑝𝑡 generates an explosive trajectory for external public debt, increasing indefinitely without reaching a steady-state equilibrium. It is also worth noting that if the lower primary surplus were financed through domestic public debt or a combination of domestic and external public debt, the same divergent trajectory would be observed, precluding a new steady-state equilibrium. Case 2: 𝒓∗ + 𝒈𝒆 > 𝒈 When the sum of the international interest rate and the real depreciation rate exceeds the GDP growth rate, equation (21) implies: (1+𝑟∗)(1+𝑔𝑒) (1+𝑔) > 1 As in Case 1, a reduction in the primary surplus in period 1—resulting from a decline in export prices—causes an increase in external public debt during that period, equal to the reduction in the surplus. Short-Term Impact Differentiating equation (21) to assess the short-term to assess the short-term impact yields the following result: 𝑑𝑏1 𝑔∗ = −𝑑𝑠𝑝1 > 0 This indicates an immediate increase in external public debt as a result of the lower primary surplus. Transition to Steady State In period 2, external public debt increases further, rising by a multiple of the previous period's increment. This pattern continues in subsequent periods, with debt growth accelerating because the numerator in the debt dynamics equation exceeds the denominator under the condition 𝑟∗ + 𝑔𝑒 > 𝑔. Differentiating equation (21) for subsequent periods yields: 𝑑𝑏2 𝑔∗ = − ( (1 + 𝑟∗)(1 + 𝑔𝑒) (1 + 𝑔) ) 𝑑𝑠𝑝1 > 0 𝑑𝑏3 𝑔∗ = − ( (1 + 𝑟∗)(1 + 𝑔𝑒) (1 + 𝑔) ) 2 𝑑𝑠𝑝1 > 0 Generalizing for any period 𝑛: 𝑑𝑏𝑛 𝑔∗ = − ( (1 + 𝑟∗)(1 + 𝑔𝑒) (1 + 𝑔) ) 𝑛−1 𝑑𝑠𝑝1 > 0 Because (1+𝑟∗)(1+𝑔𝑒) (1+𝑔) > 1, the increments in external public debt grow progressively larger, preventing convergence to a steady-state equilibrium. Steady-State Equilibrium In this case, where (1+𝑟∗)(1+𝑔𝑒) (1+𝑔) > 1, the change in external public debt is given by: 𝑑𝑏𝑛 𝑔 = − ( (1 + 𝑟∗)(1 + 𝑔𝑒) (1 + 𝑔) ) 𝑛−1 𝑑𝑠𝑝1 > 0, ∀𝑛 ≥ 1 From this, we derive the following equation: 𝑏𝑛 𝑔∗ = 𝑏0 𝑔∗ − ∑ ( (1 + 𝑟∗)(1 + 𝑔𝑒) (1 + 𝑔) ) 𝑡−1 𝑑𝑠𝑝1 𝑛 𝑡=1 Since (1+𝑟∗)(1+𝑔𝑒) (1+𝑔) > 1 when 𝑟∗ + 𝑔𝑒 > 𝑔, taking the limit as 𝑛 → ∞ yields: lim 𝑛→∞ 𝑏𝑛 𝑔∗ = ∞+ > 0 This result confirms that a permanent reduction in the primary surplus (𝑠𝑝𝑡) results in a divergent trajectory for external public debt (𝑏𝑡 𝑔∗ ). Case 3: 𝒓∗ + 𝒈𝒆 < 𝒈 In an open economy, the desirable scenario for fiscal policy arises when the sum of the international interest rate and the depreciation rate is lower than the real GDP growth rate. From equation (21), this condition is expressed as: (1 + 𝑟∗)(1 + 𝑔𝑒) (1 + 𝑔) < 1 In this scenario, a reduction in the primary surplus, caused by a decline in export prices, leads to an increase in external public debt during the same period, equal to the magnitude of the surplus reduction. Short-Term Impact Differentiating equation (21) to assess the short-term impact yields: 𝑑𝑏1 𝑔∗ = −𝑑𝑠𝑝1 > 0 This result indicates that external public debt rises in direct proportion to the reduction in the primary surplus during the first period. Transition to Steady State In period 2, external public debt increases again but by only a fraction of the increment observed in period 1. This pattern arises because, under the condition 𝑟∗ + 𝑔𝑒 < 𝑔, the numerator in the debt dynamics equation is smaller than the denominator. Differentiating equation (21) for subsequent periods yields: 𝑑𝑏2 𝑔∗ = − ( (1 + 𝑟∗)(1 + 𝑔𝑒) (1 + 𝑔) ) 𝑑𝑠𝑝1 > 0 𝑑𝑏3 𝑔∗ = − ( (1 + 𝑟∗)(1 + 𝑔𝑒) (1 + 𝑔) ) 2 𝑑𝑠𝑝1 > 0 Generalizing for any period 𝑛: 𝑑𝑏𝑛 𝑔∗ = − ( (1 + 𝑟∗)(1 + 𝑔𝑒) (1 + 𝑔) ) 𝑛−1 𝑑𝑠𝑝1 > 0 Steady-State Equilibrium For this case, where (1+𝑟∗)(1+𝑔𝑒) (1+𝑔) < 1, the change in external public debt is given by: 𝑑𝑏𝑛 𝑔 = − ( (1 + 𝑟∗)(1 + 𝑔𝑒) (1 + 𝑔) ) 𝑛−1 𝑑𝑠𝑝1 > 0, ∀𝑛 ≥ 1 From this, the total external public debt in period 𝑛 can be expressed as: 𝑏𝑛 𝑔∗ = 𝑏0 𝑔∗ − ∑ ( (1 + 𝑟∗)(1 + 𝑔𝑒) (1 + 𝑔) ) 𝑡−1 𝑑𝑠𝑝1 𝑛 𝑡=1 Since (1+𝑟∗)(1+𝑔𝑒) (1+𝑔) < 1 when 𝑟∗ + 𝑔𝑒 < 𝑔, taking the limit as 𝑛 → ∞ yields: lim 𝑛→∞ 𝑏𝑛 𝑔∗ = 𝑏0 𝑔∗ − 𝑑𝑠𝑝1 lim 𝑛→∞ ∑ ( (1 + 𝑟∗)(1 + 𝑔𝑒) (1 + 𝑔) ) 𝑡−1𝑛 𝑡=1 = 𝑏0 𝑔 − 𝑑𝑠𝑝1 ( 1 + 𝑔 (1 + 𝑔) − (1 + 𝑟∗)(1 + 𝑔𝑒) ) > 0 This result confirms that, although a permanent reduction in the primary surplus (𝑠𝑝𝑡) leads to an increase in external public debt, it eventually stabilizes at a new steady-state level. 2.5 The Stabilizing Shock This section examines the possibility of halting an explosive trajectory of external public debt, similar to the analysis conducted for a closed economy. In this context, adjustments must occur through either expenditure reductions or revenue increases. The analysis begins with an initial steady-state equilibrium in which the primary surplus is sufficient to maintain external public debt at a stable level. The focus is on Case 2, where the international interest rate, combined with the real depreciation rate of the domestic currency, exceeds the real GDP growth rate, (1+𝑟∗)(1+𝑔𝑒) 1+𝑔 > 1. In this scenario, as previously demonstrated, the trajectory of public debt does not naturally converge to a new equilibrium but instead grows at an increasingly rapid pace. During period 1, a permanent reduction in the primary surplus occurs, driven by a decline in export prices, which reduces government revenues as a percentage of GDP. This leads to an immediate increase in external public debt during the same period. According to the dynamics outlined in equation (21), the debt rises further in period 2 at a greater rate than in period 1. In period 3, external public debt grows again, surpassing the prior increase and reaching the maximum level allowed by markets and international organizations. Consequently, debt can no longer grow, making it impossible to continue financing fiscal deficits as in previous periods. At this point, the fiscal deficit must be eliminated entirely. To achieve this, the primary surplus must increase to a level sufficient to cover interest payments on the external public debt at its new upper limit in period 3. Absent any adverse external shocks, this marks a new steady-state equilibrium. If the economy can sustain the described primary surplus annually and no unfavorable shocks occur to the international interest rate, the domestic currency's depreciation rate, or the real GDP growth rate, the external debt level in period 3 becomes sustainable. However, the primary surplus required to stabilize external public debt at this higher level, 𝑟𝑏3 𝑔∗ , is significant due to the elevated debt volume. This implies substantial social and political costs. This dynamic is depicted in Figure 14. In period 1, a permanent reduction in the primary surplus below the level required to stabilize public debt shifts the debt dynamics line 𝑏𝑏0 ∗ to 𝑏𝑏1 ∗, raising external debt from 𝑏0 𝑔∗ to 𝑏1 𝑔∗ . The increased debt in period 1 drives further growth in period 2 to 𝑏2 𝑔∗ , which, in turn, leads to a further increase in period 3 to 𝑏3 𝑔∗ , the debt ceiling. As noted earlier, debt cannot grow beyond this level. To stabilize debt at 𝑏3 𝑔∗ , the primary surplus must increase from 𝑠𝑝0 to 𝑠𝑝3, shifting the debt dynamics line from 𝑏𝑏1 ∗ to 𝑏𝑏2 ∗. The new steady-state equilibrium is represented by point 𝑍, where the debt dynamics line, 𝑏𝑏2 ∗, intersects the public debt sustainability line, 𝑒𝑒0 ∗. Figure 14 The Stabilizing Shock in an Open Economy 3. CONCLUSIONS AND IMPLICATIONS This paper presents a model in two versions—closed economy and open economy—to analyze the dynamics and sustainability of public debt. The model was used to examine how an economy responds when public debt reaches a critical threshold, leading to the closure of all credit markets. In such a scenario, where the deficit must be eliminated, the only option is to implement a fiscal adjustment that stabilizes public debt as a percentage of GDP. 𝑏3 𝑔∗ 𝑍 𝑏𝑡−1 𝑔∗ 𝑏0 𝑔∗ 𝑏𝑒𝑒 𝑔∗ 𝑏1 𝑔∗ 𝑏2 𝑔∗ 𝑏3 𝑔 𝑏𝑡 𝑔∗ 𝐴 𝐵 𝐶 𝐷 𝑒𝑒0 ∗ 𝑏𝑏1 ∗(𝑠𝑝1) 𝑏𝑏0 ∗(𝑠𝑝0) 𝑏1 𝑔∗ 𝑏2 𝑔∗ −𝑠𝑝1 −𝑠𝑝0 −𝑠𝑝2 𝑏𝑏2 ∗(𝑠𝑝2) In the closed economy version, public debt sustainability depends primarily on the relationship between the real interest rate (𝑟) and the GDP growth rate (𝑔). In the open economy version, the fiscal deficit can be financed through domestic public debt or external public debt. If the deficit is financed domestically, the situation mirrors the closed economy case, where sustainability depends on the relationship between 𝑟 and 𝑔. In the open economy model, a key distinction emerges when the deficit is financed through external public debt, in which case debt dynamics depend on the relationship between the international interest rate (𝑟∗), the depreciation rate of the domestic currency (𝑔𝑒), and the GDP growth rate (𝑔). Simulations were conducted in both versions to examine the impact of a permanent reduction in the primary surplus (𝑠𝑝𝑡). The results indicate that when 𝑟 > 𝑔 in the closed economy and 𝑟∗ + 𝑔𝑒 > 𝑔 in the open economy, public debt follows an explosive trajectory, failing to reach a new steady-state equilibrium. However, this trajectory is constrained by limits imposed by markets and multilateral organizations. At this point, achieving a new equilibrium requires a sufficiently large primary surplus to freeze public debt at its upper limit. 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Washington, BID. José D. Gallardo Ku 2019 Notas de teoría para para la incertidumbre. Lima, Fondo Editorial de la Pontificia Universidad Católica del Perú. Úrsula Aldana, Jhonatan Clausen, Angelo Cozzubo, Carolina Trivelli, Carlos Urrutia y Johanna Yancari 2018 Desigualdad y pobreza en un contexto de crecimiento económico. Lima, Instituto de Estudios Peruanos. Séverine Deneulin, Jhonatan Clausen y Arelí Valencia (Eds.) 2018 Introducción al enfoque de las capacidades: Aportes para el Desarrollo Humano en América Latina. Flacso Argentina y Editorial Manantial. Fondo Editorial de la Pontificia Universidad Católica del Perú. Mario Dammil, Oscar Dancourt y Roberto Frenkel (Eds.) 2018 Dilemas de las políticas cambiarias y monetarias en América Latina. Lima, Fondo Editorial de la Pontificia Universidad Católica del Perú. http://departamento.pucp.edu.pe/economia/libro/las-alianzas-publico-privadas-app-en-el-peru-beneficios-y-riesgos/ http://departamento.pucp.edu.pe/economia/libro/las-alianzas-publico-privadas-app-en-el-peru-beneficios-y-riesgos/ http://departamento.pucp.edu.pe/economia/libro/las-alianzas-publico-privadas-app-en-el-peru-beneficios-y-riesgos/  Documentos de trabajo No. 540 “Efecto de los bonos sobre el consumo de bienes durante la crisis económica de la pandemia de Covid 19”. Luis García. Diciembre 2024. No. 539 “Regime-Switching, Stochastic Volatility, Fiscal Policy Shocks and Macroeconomic Fluctuations in Peru”. Gabriel Rodríguez and Joseph Santisteban. Octubre 2024. No. 538 “Flotación cambiaria, precio materias primas y fluctuaciones macroeconómicas: un modelo para el Perú”. Waldo Mendoza y Rafael Vilca Romero. Setiembre 2024. No. 537 “Regime-Switching, Stochastic Volatility and Impacts of Monetary Policy Shocks on Macroeconomic Fluctuations in Peru”. Paola Alvarado Silva, Moisés Cáceres Quispe and Gabriel Rodríguez. Agosto 2024 No. 536 “La dinámica de la inversión en una economía primario exportadora: un modelo”. Waldo Mendoza. Julio 2024. No. 535 “Perú 1895-2019: Continuidad de la Dependencia Externa y Desindustrialización Prematura”. Félix Jiménez. Junio 2024. No. 534 “‘Bonos’: Lecciones de las transferencias monetarias no condicionadas durante la pandemia de COVID-19 en Perú”. Pedro Francke y Josue Benites. Abril 2024. No. 533 “Modeling the Trend, Persistence, and Volatility of Inflation in Pacific Alliance Countries: An Empirical Application Using a Model with Inflation Bands”. Gabriel Rodríguez and Luis Surco. Febrero 2024. No. 532 “Regional Financial Development and Micro and Small Enterprises in Peru”. Jennifer de la Cruz. Enero 2024. No. 531 “Time-Varying Effects of Financial Uncertainty Shocks on Macroeconomic Fluctuations in Peru”. Mauricio Alvarado and Gabriel Rodríguez. Enero 2024. No. 530 “Experiments on the Different Numbers of Bidders in Sequential Auctions”. Gunay, Hikmet and Ricardo Huamán-Aguilar. Enero 2024. No. 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. No. 528 “COVID-19 y el mercado laboral de Lima Metropolitana y Callao: Un análisis de género”. Tania Paredes. Noviembre, 2023. No. 527 “COVID-19 y el alza de la inseguridad alimentaria de los hogares rurales en Perú durante 2020-2021”. Josue Benites y Pedro Francke. Noviembre, 2023. No. 526 “Globalización Neoliberal y Reordenamiento Geopolítico”. Jorge Rojas. Octubre, 2023. No. 525 T”he effects of social pensions on mortality among the extreme poor elderly”. Jose A. Valderrama and Javier Olivera. Setiembre, 2023. https://repositorio.pucp.edu.pe/browse/author?startsWith=Rodr%C3%ADguez,%20Gabriel No. 524 “Jane Haldimand Marcet: Escribir sobre economía política en el siglo XVIII”. Cecilia Garavito. Setiembre, 2023. No. 523 “Impact of Monetary Policy Shocks in the Peruvian Economy Over Time”. Flavio Pérez Rojo and Gabriel Rodríguez. Agosto, 2023. No. 522 “Perú 1990-2021: la causa del “milagro” económico ¿Constitución de 1993 o Superciclo de las materias primas?” Félix Jiménez, José Oscátegui y Marco Arroyo. Agosto, 2023. No. 521 “Envejeciendo desigualmente en América Latina”. Javier Olivera. Julio, 2023. No. 520 “Choques externos en la economía peruana: un enfoque de ceros y signos en un modelo BVAR”. Gustavo Ganiko y Álvaro Jiménez. Mayo, 2023 No. 519 “Ley de Okun en Lima Metropolitana 1970 – 2021”. Cecilia Garavito. Mayo, 2023 No. 518 “Efectos ‘Spillovers’ (de derrame) del COVID-19 Sobre la Pobreza en el Perú: Un Diseño No Experimental de Control Sintético”. Mario Tello. Febrero, 2023 No. 517 “Indicadores comerciales de la Comunidad Andina 2002-2021: ¿Posible complementariedad o convergencia regional?” Alan Fairlie y Paula Paredes. Febrero, 2023. No. 516 “Evolution over Time of the Effects of Fiscal Shocks in the Peruvian Economy: Empirical Application Using TVP-VAR-SV Models”. Alexander Meléndez Holguín and Gabriel Rodríguez. Enero, 2023. No. 515 “COVID-19 and Gender Differences in the Labor Market: Evidence from the Peruvian Economy”. Giannina Vaccaro and Tania Paredes. Julio, 2022. No. 514 “Do institutions mitigate the uncertainty effect on sovereign credit ratings?” Nelson Ramírez-Rondán, Renato Rojas-Rojas and Julio A. Villavicencio. Julio 2022. No. 513 “Gender gap in pension savings: Evidence from Peru’s individual capitalization system. Javier Olivera and Yadiraah Iparraguirre”. Junio 2022. No. 512 “Poder de mercado, bienestar social y eficiencia en la industria microfinanciera regulada en el Perú. Giovanna Aguilar y Jhonatan Portilla”. Junio 2022. No. 511 “Perú 1990-2020: Heterogeneidad estructural y regímenes económicos regionales ¿Persiste la desconexión entre la economía, la demografía y la geografía?” Félix Jiménez y Marco Arroyo. Junio 2022. No. 510 “Evolution of the Exchange Rate Pass-Throught into Prices in Peru: An Empirical Application Using TVP-VAR-SV Models”. Roberto Calero, Gabriel Rodríguez and Rodrigo Salcedo Cisneros. Mayo 2022. No. 509 “ Time Changing Effects of External Shocks on Macroeconomic Fluctuations in Peru: Empirical Application Using Regime-Switching VAR Models with Stochastic Volatility”. Paulo Chávez and Gabriel Rodríguez. Marzo 2022. No. 508 “ Time Evolution of External Shocks on Macroeconomic Fluctuations in Pacific Alliance Countries: Empirical Application using TVP-VAR-SV Models”. Gabriel Rodríguez and Renato Vassallo. Marzo 2022. No. 507 Time-Varying Effects of External Shocks on Macroeconomic Fluctuations in Peru: An Empirical Application using TVP-VARSV Models. Junior A. Ojeda Cunya and Gabriel Rodríguez. Marzo 2022. No. 506 “ La Macroeconomía de la cuarentena: Un modelo de dos sectores”. Waldo Mendoza, Luis Mancilla y Rafael Velarde. Febrero 2022. No. 505 “ ¿Coexistencia o canibalismo? Un análisis del desplazamiento de medios de comunicación tradicionales y modernos en los adultos mayores para el caso latinoamericano: Argentina, Colombia, Ecuador, Guatemala, Paraguay y Perú”. Roxana Barrantes Cáceres y Silvana Manrique Romero. Enero 2022. No. 504 “Does the Central Bank of Peru Respond to Exchange Rate Movements? A Bayesian Estimation of a New Keynesian DSGE Model with FX Interventions”. Gabriel Rodríguez, Paul Castillo B. and Harumi Hasegawa. Diciembre, 2021 No. 503 “La no linealidad en la relación entre la competencia y la sostenibilidad financiera y alcance social de las instituciones microfinancieras reguladas en el Perú”. Giovanna Aguilar y Jhonatan Portilla. Noviembre, 2021. No. 502 “Approximate Bayesian Estimation of Stochastic Volatility in Mean Models using Hidden Markov Models: Empirical Evidence from Stock Latin American Markets”. Carlos A. Abanto-Valle, Gabriel Rodríguez, Luis M. Castro Cepero and Hernán B. Garrafa-Aragón. Noviembre, 2021. No. 501 “El impacto de políticas diferenciadas de cuarentena sobre la mortalidad por COVID-19: el caso de Brasil y Perú”. Angelo Cozzubo, Javier Herrera, Mireille Razafindrakoto y François Roubaud. Octubre, 2021. No. 500 “Determinantes del gasto de bolsillo en salud en el Perú”. Luis García y Crissy Rojas. Julio, 2021. No. 499 “Cadenas Globales de Valor de Exportación de los Países de la Comunidad Andina 2000-2015”. Mario Tello. Junio, 2021. No. 498 “¿Cómo afecta el desempleo regional a los salarios en el área urbana? Una curva de salarios para Perú (2012-2019)”. Sergio Quispe. Mayo, 2021. No. 497 “¿Qué tan rígidos son los precios en línea? Evidencia para Perú usando Big Data”. Hilary Coronado, Erick Lahura y Marco Vega. Mayo, 2021. No. 496 “Reformando el sistema de pensiones en Perú: costo fiscal, nivel de pensiones, brecha de género y desigualdad”. Javier Olivera. Diciembre, 2020. No. 495 “Crónica de la economía peruana en tiempos de pandemia”. Jorge Vega Castro. Diciembre, 2020. No. 494 “Epidemia y nivel de actividad económica: un modelo”. Waldo Mendoza e Isaías Chalco. Setiembre, 2020. No. 493 “Competencia, alcance social y sostenibilidad financiera en las microfinanzas reguladas peruanas”. Giovanna Aguilar Andía y Jhonatan Portilla Goicochea. Setiembre, 2020. No. 492 “Empoderamiento de la mujer y demanda por servicios de salud preventivos y de salud reproductiva en el Perú 2015-2018”. Pedro Francke y Diego Quispe O. Julio, 2020. No. 491 “Inversión en infraestructura y demanda turística: una aplicación del enfoque de control sintético para el caso Kuéalp, Perú”. Erick Lahura y Rosario Sabrera. Julio, 2020. No. 490 “La dinámica de inversión privada. El modelo del acelerador flexible en una economía abierta”. Waldo Mendoza Bellido. Mayo, 2020. No. 489 “Time-Varying Impact of Fiscal Shocks over GDP Growth in Peru: An Empirical Application using Hybrid TVP-VAR-SV Models”. Álvaro Jiménez and Gabriel Rodríguez. Abril, 2020. No. 488 “Experimentos clásicos de economía. Evidencia de laboratorio de Perú”. Kristian López Vargas y Alejandro Lugon. Marzo, 2020. No. 487 “Investigación y desarrollo, tecnologías de información y comunicación e impactos sobre el proceso de innovación y la productividad”. Mario D. Tello. Marzo, 2020. No. 486 “The Political Economy Approach of Trade Barriers: The Case of Peruvian’s Trade Liberalization”. Mario D. Tello. Marzo, 2020. No. 485 “Evolution of Monetary Policy in Peru. An Empirical Application Using a Mixture Innovation TVP-VAR-SV Model”. Jhonatan Portilla Goicochea and Gabriel Rodríguez. Febrero, 2020. No. 484 “Modeling the Volatility of Returns on Commodities: An Application and Empirical Comparison of GARCH and SV Models”. Jean Pierre Fernández Prada Saucedo and Gabriel Rodríguez. Febrero, 2020. No. 483 “Macroeconomic Effects of Loan Supply Shocks: Empirical Evidence”. Jefferson Martínez amd Gabriel Rodríguez. Febrero, 2020. No. 482 “Acerca de la relación entre el gasto público por alumno y los retornos a la educación en el Perú: un análisis por cohortes”. Luis García y Sara Sánchez. Febrero, 2020. No. 481 “Stochastic Volatility in Mean. Empirical Evidence from Stock Latin American Markets”. Carlos A. Abanto-Valle, Gabriel Rodríguez and Hernán B. Garrafa- Aragón. Febrero, 2020. No. 480 “Presidential Approval in Peru: An Empirical Analysis Using a Fractionally Cointegrated VAR2”. Alexander Boca Saravia and Gabriel Rodríguez. Diciembre, 2019. No. 479 “La Ley de Okun en el Perú: Lima Metropolitana 1971 – 2016.” Cecilia Garavito. Agosto, 2019. No. 478 “Peru´s Regional Growth and Convergence in 1979-2017: An Empirical Spatial Panel Data Analysis”. Juan Palomino and Gabriel Rodríguez. Marzo, 2019.  Materiales de Enseñanza No. 10 “Boleta o factura: el impuesto general a las ventas (IGV) en el Perú”. Jorge Vega Castro. Abril, 2023 No. 9 “Economía Pública. Segunda edición”. Roxana Barrantes Cáceres, Silvana Manrique Romero y Carla Glave Barrantes. Febrero, 2023. No. 8 “Economía Experimental Aplicada. Programación de experimentos con oTree”. Ricardo Huamán-Aguilar. Febrero, 2023 No. 7 “Modelos de Ecuaciones Simultáneas (MES): Aplicación al mercado monetario”. Luis Mancilla, Tania Paredes y Juan León. Agosto, 2022 No. 6 “Apuntes de Macroeconomía Intermedia”. Felix Jiménez. Diciembre, 2020 No. 5 “Matemáticas para Economistas 1”. Tessy Váquez Baos. Abril, 2019. No. 4 “Teoría de la Regulación”. Roxana Barrantes. Marzo, 2019. No. 3 “Economía Pública”. Roxana Barrantes, Silvana Manrique y Carla Glave. Marzo, 2018. No. 2 “Macroeconomía: Enfoques y modelos. Ejercicios resueltos”. Felix Jiménez. Marzo, 2016. No. 1 “Introducción a la teoría del Equilibrio General”. Alejandro Lugon. Octubre, 2015. Departamento de Economía - Pontificia Universidad Católica del Perú Av. Universitaria 1801, San Miguel, 15008 – Perú Telf. 626-2000 anexos 4950 – 4951 https://departamento-economia.pucp.edu.pe/ https://departamento-economia.pucp.edu.pe/