## wp1770 — 1. Introduction ## Source details **Canonical URL:** [wp1770 — 1. Introduction](https://www.imf.org/-/media/files/publications/wp/2017/wp1770.pdf) ## Other formats - [Markdown version](/-/media/files/publications/wp/2017/wp1770.pdf.md) - [Structured JSON version](/-/media/files/publications/wp/2017/wp1770.pdf.json) --- ### Context and problem - Small open economies face recurrent fluctuations in their terms of trade. - During episodes of positive terms of trade shocks, the equilibrium response of the economy is a real exchange rate appreciation. - When this appreciation induces a contraction of the manufacturing sector, an economy is usually diagnosed as experiencing a Dutch disease. - The reduction in manufacturing production does not necessarily reduce welfare, as it reflects the natural adjustment of an economy to higher wealth and the optimal response of the economy is to shift resources from the tradable to the non-tradable sector. - Policymakers are typically concerned when the decline of manufacturing production is more persistent than warranted by higher commodity prices; this persistence can arise when learning-by-doing externalities (LBD) are present in the production process of manufactured goods. - The term "Dutch Disease" originated with the Netherlands in the 1960s after the discovery of gas deposits; the term is also used to describe negative export effects induced by foreign aid, remittances, capital inflows or an improvement in the terms of trade. ### Research question and approach - Key policymaker question: What is the optimal policy response to a Dutch disease episode? - This paper analyzes the macroeconomic benefits from relying on Foreign Exchange (FX) intervention to cope with Dutch disease symptoms during a boom in commodity prices. - The paper compares welfare gains from conducting optimal FX intervention policy against the benefits from relying only on monetary policy. ### Empirical motivation and stylized facts - Figure 1 illustrates a recent episode of a boom in commodity prices in six Latin American economies. - Most of these economies responded to higher commodity prices as predicted by the standard textbook model: an improvement in the terms of trade and higher export revenue led to exchange rate appreciation and, with a stronger currency, loss of competitiveness and a decline in manufacturing production as a share of Gross Value Added (GVA). - Most of these economies accumulated FX reserves during this episode, motivated partly by precautionary motives but also to counteract the adverse effects of large exchange rate movements on tradable output. - A relevant policy question is whether the observed accumulation of FX reserves was welfare-improving, or whether central banks should have refrained from intervening and allowed the exchange rate to absorb the positive terms of trade shock. ### Model, calibration, and experiment - Multi-sector small open economy DSGE model with nominal rigidities and learning-by-doing externalities. - Learning-by-doing externalities generate an inefficient decline in tradable production in response to a boom in commodity prices. - The central bank uses two instruments to stabilize the economy during the commodity boom: the policy rate and FX reserves. - The study evaluates welfare gains from using each instrument individually and the optimal combination of both. - Baseline calibration and experiments are illustrated with a calibration to the Brazilian economy. ### Key quantitative findings - A 10 percent increase in commodity prices elicits a reallocation and macroeconomic response that, under the baseline calibration, corresponds to approximately a two standard deviations shock. - Optimal reliance on FX reserves during a commodity boom yields welfare gains of 0.04 percent of lifetime (permanent) consumption. - Relying exclusively on using the policy rate yields welfare gains of 0.02 percent of lifetime consumption. - The combined optimal monetary and FX intervention rules yield a welfare gain of 0.05 percent of lifetime consumption. - An exchange rate peg implemented via the policy rate produces a welfare loss of 0.55 percent of permanent consumption (Table 2). - 1.5 percent of GDP in response to a 10 percent increase in commodity prices. ### Model structure and mechanisms - Model features preserved exactly: - Nominal rigidities (Calvo price/wage stickiness). - Learning-by-doing (LBD) externalities in the tradable sector via organizational capital Ht (equations (7)-(8)), with 1ϵT + μT = 1 (constant returns to scale). - Large commodity sector with exogenous commodity exports Xt and commodity price Px_t processes (equations (14)-(15)). - Sterilized FX intervention where purchases of foreign bonds Et·F̃t are matched by issuance of domestic bonds ΔBt (Et·F̃t = ΔBt) and central bank budget constraint in equation (18). - Monetary policy follows a Taylor-type rule (equation (16)), and FX intervention follows a policy rule (equation (17)) with weights θy, θπN, θe; in the baseline scenario θy = θπN = θe = 0 (no FX intervention). - LBD mechanism: lower tradable production reduces organizational capital Ht, which lowers tradable productivity and further depresses tradable output—amplifying the initial shock and generating additional negative spillovers. ### Calibration highlights (quarterly, Brazil) - Discount factor ϕ = 0:99 - Habit formation h = 0:74 - 1/Frisch = 1 - Share of tradable inputs in final good βY = 0:30; elasticity of substitution ηY = 1 - Elasticities: εN = 11; εL = 11 - Calvo parameters: ξN = 0:75; ξW = 0:75 - Capital shares: βN = 0:30; βT = 0:30 - Depreciation rate δ = 0:02 - Investment adjustment cost parameter μS = 3:4 - Share of organizational capital μT = 0:25; depreciation of organizational capital 1ϵT = 0:37 - Taylor rule coefficients: ψy = 0:2; ψπ = 1:7; ψe = 0:7 - FXI rule baseline coefficients: θy = 0; θπN = 0; θe = 0 - Foreign risk premium elasticity % = 0:4 - Steady-state foreign debt B̃t/Y = 0:6 - Commodity sector processes (estimated 1990:Q1-2014:Q4): - pXt = 0:95 pXt1 + εPXt ; εPXt ~ N(0; σ2PX); σPX = 0:06 - x t = 0:97 xt1 + εXt ; εXt ~ N(0; σ2X); σX = 0:13 - Commodity sector shares 10 percent of GDP. ### Policy experiments and welfare evaluation - Welfare measured as fraction of lifetime consumption following Lucas (1987) and Schmitt-Grohé and Uribe (2007); welfare gain ϑ solved by equating baseline and alternative discounted utilities (equations (27)-(28)). - Policies evaluated and outcomes: - Baseline: estimated Taylor-type rule (de Castro et al., 2011), no FX intervention. - Fixed exchange rate (peg) implemented via policy rate: welfare loss of -0.55 percent. - Optimal monetary policy rule (alone): welfare gain 0.02 percent; reduces GDP volatility relative to baseline. - Optimal FX intervention (with calibrated Taylor rule): welfare gain 0.04 percent; largely stabilizes real exchange rate, tradable output, trade balance, domestic demand, and inflation. - Jointly optimal monetary and FX intervention rules: welfare gain 0.05 percent; FX intervention magnitude is smaller than in the FX-only optimum because the policy rate also stabilizes the cycle. - Interpretation: FX reserves act as a second instrument that—via Tinbergen’s principle—permits simultaneous stabilization of tradable and non-tradable sectors; monetary policy alone faces trade-offs. ### Sensitivity analysis (robustness and comparative statics) - Welfare gains from optimal FX intervention, given a calibrated Taylor-type rule, lie in the range 0.02 to 0.06 percent of lifetime consumption across parameter variations. - Main sensitivities: - Share of organizational capital μT: larger μT → larger optimal accumulation of FX reserves. - Presence vs. absence of LBD: even without LBD, optimal FX accumulation is positive but smaller; role shifts from correcting externalities to business-cycle smoothing. - Sticky prices ξN and sticky wages ξW: reducing nominal rigidities (lower ξN or ξW) leads the central bank to optimally accumulate more FX reserves because LBD externalities become relatively more important and FXI is more effective. - Degree of imperfect asset substitution ζ: lower ζ reduces the effectiveness of FXI → requires larger optimal FX reserve accumulation. - Qualitative result: across parameterizations, commodity shocks cause tradable balance deterioration and optimal policy involves FX reserve accumulation to smooth external adjustment. ### Conclusions and policy implications - Under LBD externalities, the optimal central bank response to a commodity price boom is a large and persistent accumulation of FX reserves to correct tradable-sector externalities. - Even absent LBD, FX reserves play an important role in smoothing the commodity cycle via saving in good times, though at a more modest accumulation pace. - Choice of instruments matters: FX reserves are a superior instrument relative to the policy rate alone for counteracting Dutch disease effects; combining instruments yields the largest welfare gains with smaller required FX intervention. - Suggested avenues for future research: inclusion of fiscal instruments or sovereign wealth funds, and multi-country models to study spillovers of LBD externalities and FX reserve policies. *Source: wp1770 - 1. Introduction* ### 1. Introduction ....................................................................................................... ### 1. Introduction ### Context and problem - Small open economies face recurrent fluctuations in their terms of trade. - During episodes of positive terms of trade shocks, the equilibrium response of the economy is a real exchange rate appreciation. - When this appreciation induces a contraction of the manufacturing sector, an economy is usually diagnosed as experiencing a Dutch disease. - By itself, the reduction in manufacturing production does not necessarily reduce welfare, as it reflects the natural adjustment of an economy to higher wealth and the optimal response of the economy is to shift resources from the tradable to the non-tradable sector. - Policymakers are typically concerned when the decline of manufacturing production is more persistent than warranted by higher commodity prices; this persistence can arise when learning-by-doing externalities (LBD) are present in the production process of manufactured goods. - The term "Dutch Disease" was introduced to describe the situation experienced in the Netherlands in the 1960s after the discovery of gas deposits in the North Sea. The discovery of natural resources was followed by an appreciation of the real exchange rate and a crowding out of the manufacturing exports. More recently, the term is also used to describe the negative effects on exports induced by foreign aid, remittances, capital inflows or an improvement in the terms of trade. ### Research question and approach - Key policymaker question: What is the optimal policy response to a Dutch disease episode? - This paper analyzes the macroeconomic benefits from relying on Foreign Exchange (FX) intervention to cope with Dutch disease symptoms during a boom in commodity prices. - The paper compares welfare gains from conducting optimal FX intervention policy against the benefits from relying only on monetary policy. ### Empirical motivation and stylized facts - Figure 1 (referenced) illustrates a recent episode of a boom in commodity prices in six Latin American economies. - Most of these economies responded to higher commodity prices as predicted by the standard textbook model: an improvement in the terms of trade and higher export revenue led to exchange rate appreciation and, with a stronger currency, loss of competitiveness and a decline in manufacturing production as a share of Gross Value Added (GVA). - Most of these economies accumulated FX reserves during this episode, motivated partly by precautionary motives but also to counteract the adverse effects of large exchange rate movements on tradable output. - A relevant policy question related to this episode is whether the observed accumulation of FX reserves was welfare-improving, or whether central banks should have refrained from intervening and allowed the exchange rate to absorb the positive terms of trade shock. ### Model, calibration, and experiment - The authors develop a multi-sector small open economy model with nominal rigidities and learning-by-doing externalities. - Learning-by-doing externalities generate an inefficient decline in tradable production in response to a boom in commodity prices. - In the model, the central bank relies on two instruments to stabilize the economy during the commodity boom: the policy rate and FX reserves. - The study evaluates welfare gains derived from using each instrument individually and the optimal combination of both. - To illustrate mechanisms, the model is calibrated to the Brazilian economy, which like other Latin American economies experienced a loss of competitiveness during the commodity price boom. ### Key findings and policy implications - Quantitative simulations find that during a boom in commodity prices, the optimal policy consists of a large and sustained accumulation of FX reserves. - The central bank accumulation of FX reserves is presented as a welfare-improving response in the presence of learning-by-doing externalities that otherwise make the decline in manufacturing persist. *Source: wp1770 - 1. Introduction* ### 1.5 percent of GDP in response to a 10 percent increase in commodity prices. ### wp1770 - 1.5 percent of GDP in response to a 10 percent increase in commodity prices. ### Key quantitative findings - A 10 percent increase in commodity prices elicits a reallocation and macroeconomic response that, under the baseline calibration, corresponds to approximately a two standard deviations shock. - Optimal reliance on FX reserves during a commodity boom yields welfare gains of 0.04 percent of lifetime (permanent) consumption. - Relying exclusively on using the policy rate yields welfare gains of 0.02 percent of lifetime consumption. - The combined optimal monetary and FX intervention rules yield a welfare gain of 0.05 percent of lifetime consumption. - An exchange rate peg implemented via the policy rate produces a welfare loss of 0.55 percent of permanent consumption (Table 2). ### Model structure and mechanisms - The paper develops a small open economy DSGE model with: - Nominal rigidities (Calvo price/wage stickiness). - Learning-by-doing (LBD) externalities in the tradable sector via organizational capital Ht (equations (7)-(8)), with 1ϵT + μT = 1 (constant returns to scale). - A large commodity sector with exogenous commodity exports Xt and commodity price Px_t processes (equations (14)-(15)). - Sterilized FX intervention where purchases of foreign bonds Et·F̃t are matched by issuance of domestic bonds ΔBt (Et·F̃t = ΔBt) and central bank budget constraint in equation (18). - Monetary policy follows a Taylor-type rule (equation (16)), and FX intervention follows a policy rule (equation (17)) with weights θy, θπN, θe; in the baseline scenario θy = θπN = θe = 0 (no FX intervention). - The LBD mechanism: lower tradable production reduces organizational capital Ht, which lowers tradable productivity and further depresses tradable output—amplifying the initial shock and generating additional negative spillovers. ### Calibration highlights - Model calibrated to Brazil; quarterly frequency. - Key parameter values preserved exactly: - Discount factor ϕ = 0:99 - Habit formation h = 0:74 - 1/Frisch = 1 - Share of tradable inputs in final good βY = 0:30; elasticity of substitution ηY = 1 - Elasticities: εN = 11; εL = 11 - Calvo parameters: ξN = 0:75; ξW = 0:75 - Capital shares: βN = 0:30; βT = 0:30 - Depreciation rate δ = 0:02 - Investment adjustment cost parameter μS = 3:4 - Share of organizational capital μT = 0:25; depreciation of organizational capital 1ϵT = 0:37 - Taylor rule coefficients: ψy = 0:2; ψπ = 1:7; ψe = 0:7 - FXI rule baseline coefficients: θy = 0; θπN = 0; θe = 0 - Foreign risk premium elasticity % = 0:4 - Steady-state foreign debt B̃t/Y = 0:6 - Commodity sector processes (estimated 1990:Q1-2014:Q4): - pXt = 0:95 pXt1 + εPXt ; εPXt ~ N(0; σ2PX); σPX = 0:06 - x t = 0:97 xt1 + εXt ; εXt ~ N(0; σ2X); σX = 0:13 - Commodity sector shares 10 percent of GDP. ### Policy experiments and welfare evaluation - Welfare measured as fraction of lifetime consumption following Lucas (1987) and Schmitt-Grohé and Uribe (2007); welfare gain ϑ solved by equating baseline and alternative discounted utilities (equations (27)-(28)). - Policies evaluated: - Baseline: estimated Taylor-type rule (de Castro et al., 2011), no FX intervention. - Fixed exchange rate (peg) implemented via policy rate: large volatility increases in consumption and labor; welfare loss of -0.55 percent. - Optimal monetary policy rule (alone): welfare gain 0.02 percent; reduces GDP volatility relative to baseline. - Optimal FX intervention (with calibrated Taylor rule): welfare gain 0.04 percent; largely stabilizes real exchange rate, tradable output, trade balance, domestic demand, and inflation. - Jointly optimal monetary and FX intervention rules: welfare gain 0.05 percent; FX intervention magnitude is smaller than in the FX-only optimum because the policy rate also stabilizes the cycle. - Interpretation: FX reserves act as a second instrument that—via Tinbergen’s principle—permits simultaneous stabilization of tradable and non-tradable sectors; monetary policy alone faces trade-offs. ### Sensitivity analysis (robustness and comparative statics) - Welfare gains from optimal FX intervention, given a calibrated Taylor-type rule, lie in the range 0.02 to 0.06 percent of lifetime consumption across parameter variations. - Main sensitivities: - Share of organizational capital μT: larger μT → larger optimal accumulation of FX reserves (more gains from stimulating tradable sector). - Presence vs. absence of LBD: even without LBD, optimal FX accumulation is positive but smaller; role shifts from correcting externalities to business-cycle smoothing. - Sticky prices ξN and sticky wages ξW: reducing nominal rigidities (i.e., lower ξN or ξW) leads the central bank to optimally accumulate more FX reserves because LBD externalities become relatively more important and FXI is more effective. - Degree of imperfect asset substitution ζ: lower ζ (less substitutability) reduces the effectiveness of FXI → requires larger optimal FX reserve accumulation to attain similar welfare outcomes. - Qualitative result: across parameterizations, commodity shocks cause tradable balance deterioration and optimal policy involves FX reserve accumulation to smooth external adjustment. ### Conclusions and policy implications - Under LBD externalities, the optimal central bank response to a commodity price boom is a large and persistent accumulation of FX reserves to correct tradable-sector externalities. - Even absent LBD, FX reserves play an important role in smoothing the commodity cycle via saving in good times, though at a more modest accumulation pace. - Choice of instruments matters: FX reserves are a superior instrument relative to the policy rate alone for counteracting Dutch disease effects; combining instruments yields the largest welfare gains with smaller required FX intervention. - Suggested avenues for future research: inclusion of fiscal instruments or sovereign wealth funds, and multi-country models to study spillovers of LBD externalities and FX reserve policies. *Source: wp1770 - 1.5 percent of GDP in response to a 10 percent increase in commodity prices.* ### References ### wp1770 - References ### References - [1]Adolfson, M., S. LasÈen, J. LindÈ, and M. Villani, (2007), "Bayesian Estimation of an Open Economy DSGE model with Incomplete Pass-Through,"Journal of International Economics, 72, 481-511. - [2]Bayoumi, T., J. E. Gagnon and C. Saborowski, (2015), ìO¢ cial Financial Flows, Capital Mobility, and Global Imbalances,îJournal of International Money and Finance. - [3]Benes, J., A. Berg, R. Portillo, D. Vavra, (2015), "Modeling Sterilized Interventions and Balance Sheet E§ects of Monetary Policy in a New-Keynesian Framework,"Open Economies Review, 26, 81-108. - [4]Blanchard, O. and J. GalÌ, 2007, ìReal Wage Rigidities and the New Keynesian Model,îJournal of Money, Credit and Banking39(s1): 35-65. - [5]Caballero, R. and G. Lorenzoni, (2014), "Persistent Appreciations and Overshooting: A Normative Analysis," IMF Economic Review, 62, 1-47. - [6]Calvo, G., (1983), " Staggered Prices in a Utility-Maximizing Framework,"Journal of Monetary Economics, 12, 383-398. - [7]Canzoneri, M. and R. Cumby, (2014), "Optimal Foreign Exchange Intervention in an Ináation Targeting Regime: Some Cautionary Tales" Open Economies Review, 45, 429-450. - [8]Christiano, L. J., M. Eichenbaum, and C. L. Evans, (2005), "Nominal Rigidities and the Dynamic E§ects of a Shock to Monetary Policy," Journal of Political Economy, 113, 1-45. - [9]Cooper, R. and A. Johri, (2002), "Learning-by-doing and Aggregate Fluctuations,"Journal of Monetary Economics, 49, 1539-1566. - [10]de Castro, M. R., S. N. Gouvea, A. Minella, R.C. Santos, and N. F. Souza-Sobrinho, (2011), "SAMBA: Stochastic Analytical Model with a Bayesian Approach," Central Bank of Brazil Working Paper No. 239. - [11]Erceg, C. J., D.W. Henderson, and A.T. Levin (2000), "Optimal Monetary Policy with Staggered Wage and Price Contracts,"Journal of Monetary Economics, 46, 281-313. - [12]GarcÌa-Cicco, J. and E. Kawamura, (2015), "Dealing with the Dutch Disease: Fiscal Rules and Macroprudential Policies,"Journal of International Money and Finance, 55,205-239. - [13]Krugman, P., (1987), "The Narrow Moving Band, the Dutch Disease, and the Competitive Consequences of Mrs. Thatcher,"Journal of Development Economics, 27, 41-55. - [14]Lama, Ruy, and J.P. Medina, (2012), "Is Exchange Rate Stabilization an Appropriate Cure for the Dutch Disease?"International Journal of Central Banking, 8, 5-46. - [15]Lev, B. and S. Radharkrishnan, (2003), "The Measurement of Firm-SpeciÖc Organization Capital,"NBER Working Paper9581 (Cam- bridge, Mass.: National Bureau of Economic Research). - [16]Liu Z. , and M. Spiegel, (2015), ìOptimal Monetary Policy and Capital Account Restrictions in a Small Open Economy,îIMF Economic Review,63, 298-324. - [17]Lucas, R., (1987),Models of Business Cycles, New York: Basil Black- well. - [18]Ostry, J. D., A. R. Ghosh, and M. Chamon, (2016), "Two Targets, Two Instruments: Monetary and Exchange Rate Policies in Emerging Market Economies,"Journal of International Money and Finance, 60, 172 -196. - [19]Schmitt-GrohÈ, S. and M. Uribe, (2001), ìStabilization Policy and the Costs of Dollarization,îJournal of Money, Credit, and Banking, vol. 33, 482-509. - [20]Schmitt-GrohÈ, S. and M. Uribe, (2003), "Closing Small Open Economy Models,"Journal of International Economics, 61, 163-185. - [21]Schmitt-GrohÈ, S. and M. Uribe (2007), ìOptimal simple and implementable monetary and Öscal rules,îJournal of Monetary Economics, 54, 1702-1725. - [22]Smets, F. and R. Wouters, (2007), "Shocks and Frictions in the US Business Cycles: A Bayesian DSGE Approach,"American Economic Review, 97, 586-606. - [23]Tinbergen, J., (1952), "On the Theory of Economic Policy" Second edition (1952) Volume 1 of Contributions to Economic Analysis, Amsterdam: North-Holland. - [24]Van Wijnbergen, S., (1984), "The Dutch Disease: A Disease After All?," Economic Journal, 94, 41-55. ### Appendix: Equilibrium conditions — structure and key equations - Theme: Equilibrium conditions that characterize the small open economy model. - Households: - Euler equation for domestic bonds (equation (29)): - E_t [ (1 + i_t) P_t / P_{t+1} ( C_t - h C_{t-1} ) / ( C_{t+1} - h C_t ) ] = 1; (29) - Euler equation for international bonds (equation (30)): - E_t [ (1 + i^*_t) (B^*_t) P_t / P_{t+1} E_{t+1} / E_t ( C_t - h C_{t-1} ) / ( C_{t+1} - h C_t ) ] = 1: (30) - Labor supply and wage setting: - Optimal wage condition (equation (31)) (expectational condition involving consumption, inflation target , labor L_{t+ijt}, wage W^*_t, wage stickiness parameter _L, and convexity parameter ): - E_t [ sum_{i=0}^X ( _W)^i ( (C_{t+ijt} - h C_{t+i-1|t})^{-1} / P_{t+i} ) L_{t+ijt} ( W^*_t - _L / (_L -1) (L_{t+ijt})^{1+} ) ] = 0; (31) - Aggregate wage (equation (32)): - (W_t)^{1-_L} = _W (W_{t-1})^{1-_L} + (1-_W) (W^*_t)^{1-_L} (32) - Final good producers: - Demand for tradable and non-tradable inputs (equations (33) and (34)): - P_t [ _Y Y^F_t / Y_DT_t ]^{1=_Y} = P^T_t; (33) - P_t [ (1- _Y) Y^F_t / Y_DN_t ]^{1=_Y} = P^N_t; (34) - Intermediate good producers — first-order conditions: - Non-tradable sector (equations (35) and (36)): - (1- _N) A^N_t ( K^N_t / L^N_t )^{ _N} = W_t / P_{WN,t}; (35) - _N A^N_t ( L^N_t / K^N_t )^{1- _N} = R^N_{K;t} / P_{WN,t}; (36) - Tradable sector (equations (37) and (38)): - (1-_T)(1- _T) A^T_t ( H_t L^T_t )^{_T} ( K^T_t L^T_t )^{ _T} (1-_T) = W_t / P^T_t; (37) - (1-_T) _T A^T_t ( H_t K^T_t )^{_T} ( L^T_t / K^T_t )^{(1- _T)(1-_T)} = R^T_{K;t} / P^T_t; (38) - Retailers: - First-order condition for non-tradable sector retailers (equation (39)): - E_t [ sum_{i=0}^X ( _N)^i (C_t - h C_{t-1})(C_{t+i} - h C_{t+i-1}) P_t / P_{t+i} Y_{DN,t}(j) ( P^N_t - _N / (_N -1) P_{WN,t+i} ) ] = 0; (39) - Aggregate non-tradable price with Calvo pricing (equation (40)): - P^N_t = ( _N (P^N_{t-1})^{1-_N} + (1-_N) (P^{N*}_t)^{1-_N} )^{1/(1-_N)} (40) - Capital producers (sector-specific J = H,N): - Investment Euler-type condition (equation (41)): - 1 = Q^J_t / P_t [ S( I^J_t / I^J_{t-1} ) + S'( I^J_t / I^J_{t-1} ) I^J_t / I^J_{t-1} ] - E_t [ (C_t - h C_{t-1})/(C_{t+1}-h C_t) Q^J_{t+1}/P_{t+1} S'( I^J_{t+1}/I^J_t ) ( I^J_{t+1}/I^J_t )^2 ]; (41) - Real price of capital (equation (42)): - Q^J_t / P_t = E_t [ (C_t - h C_{t-1})/(C_{t+1} - h C_t) ( R^J_{K;t+1} / P_{t+1} + Q^J_{t+1} / P_{t+1} (1-) ) ]; (42) - Monetary policy and foreign exchange intervention: - Taylor-type rule (equation (43)) — notation preserved exactly: -  (1 + i_t)/(1 + i) = _{Y_t}/Y y ( _ N_t  ) _N ( e_t e ) e (43) - where i_t, Y_t, _N_t = P^N_t / P^N_{t-1}, e_t = E_t / E_{t-1}, are the nominal interest rate, GDP, non-tradable inflation, and the depreciation rate, respectively. - FX intervention policy rule (equation (44)): -  (F^*_t / F^* ) = _{Y_t}/Y _y ( _ N_t  ) _ N ( e_t e ) _e . (44) - Market clearing conditions and accounting identities: - Labor and wages dispersion (equation (45)): - L^N_t + L^T_t = L_t = Z_1^0 L_t(h) dh 1  W_t; (45) - Non-tradable output clearing (equation (46)): - Y_{DN,t}  N_t = Y^N_t; (46) - Final goods identity (equation (47)): - Y^F_t = C_t + I^T_t + I^N_t; (47) - Wage dispersion (equation (48)) and price dispersion (equation (49)): -  W_t = _W (W_{t-1}/W_t)^{-_L}  W_{t-1} + (1-_W) (W^*_t / W_t)^{-_L}; (48) -  N_t = _N (P^N_{t-1} / P^N_t)^{-_N}  N_{t-1} + (1-_N) (P^{N*}_t / P^N_t)^{-_N}; (49) - Law of one price for tradables (equation (50)): - P^T_t = E_t P^*_t; (50) - Balance of payments identity (equation (51)): - E_t (B^*_t + F^*_t) = (1 + i^*_t-1) -  B^*_t-1 E_t B^*_t-1 + E_t F^*_{t-1}  + P^T_t Y^T_t - P^T_t Y_{DT,t} . (51) - Real GDP definition (equation (52)): - Y_t = P^N_0 Y^N_t + P^T_0 Y^T_t + P^x_0 X_t (52) ### Figures and empirical/analytical displays (as labeled in source) - Figure 1. Commodity Cycle and Foreign Exchange Intervention - Panels include country-specific time series for Argentina, Brazil, Chile, Colombia, Mexico, Peru with series labeled: - "REER and Terms of Trade (100 = 2004:Q1)" (or 2000:Q1/2003:Q1 depending on country) - "Manufacturing Production (Percent of GVA)" - "Foreign Exchange Reserves (Percent of GDP)" - Source: Haver Analytics. - Figure 2. Effects of Learning-by-Doing - Panels A–H display impulse-response style series titled: - A. Commodity Prices - B. Real Exchange Rate - C. Tradable Production - D. Non-tradable Production - E. Trade Balance/GDP - F. Domestic Demand - G. Foreign Exchange Reserves/GDP - H. Inflation - Subsequent page continues with macro aggregates: - A. GDP, B. Investment, C. Consumption, D. Employment, E. Policy Rate, F. Real Wages, G. Nominal Depreciation, H. Non-tradable Inflation - Series compared labeled "LBD" and "No LBD". - Figure 3. Dutch Disease and Policy Rules - Panels mirror Figure 2 structure with series labeled: - "%DVHOLQH", "PegOptimal MPOptimal FXOptimal FX and MP" across panels A–H. - Macro aggregate panels include GDP, Investment, Consumption, Employment, Policy Rate, Real Wages, Nominal Depreciation, Non-tradable Inflation. - Figure 4. Sensitivity Analysis - Panels A–H show sensitivity to parameters: - A/B: Learning by Doing (6_T values: 0.01, 0.25, 0.50) - C/D: Sticky Prices (3_N values: 0.01, 0.75, 0.83) - E/F: Sticky Wages (3_w values: 0.01, 0.75, 0.83) - G/H: Risk Premium (; values: 0.001, 0.40, 10) - Outcome variables include Trade Balance / GDP and FX Reserves / GDP. - Figure 5. Welfare Gains and Sensitivity Analysis - Panels plot welfare gains (percent) across parameter sweeps for: - A. Learning by Doing (6_T from 0.2 to 0.8) - B. Sticky Prices (3_N from 0.2 to 0.8) - C. Sticky Wages (3_w from 0.2 to 0.8) - D. Risk Premium (; from 0 to 1) - Vertical axis values shown from 0 to 0.1 (and finer ticks 0.01, 0.02, ... 0.1) as plotted in source. *Source: wp1770 - References (appendix and figures) as provided in the PDF content unit.* --- _Source: https://www.imf.org/-/media/files/publications/wp/2017/wp1770.pdf_