## wpiea2023235-print-pdf ## Source details **Canonical URL:** [wpiea2023235-print-pdf](https://www.imf.org/-/media/files/publications/wp/2023/english/wpiea2023235-print-pdf.pdf) ## Other formats - [Markdown version](/-/media/files/publications/wp/2023/english/wpiea2023235-print-pdf.pdf.md) - [Structured JSON version](/-/media/files/publications/wp/2023/english/wpiea2023235-print-pdf.pdf.json) --- ### 2.1 Internal balance - FINEX links a disaggregated IS curve, a set of Phillips curves, and an explicit production function to determine output and inflation via internal balance. - IS curve (domestic market clearing) specification: - Y_R_t = C_R_t( r_R_t ;  ) + I_R_t( r_R_t ;  ) + G_R_t + X_R_t( Z_t ; Y_R;_t ;  ) M_R_t( Z_t ; Y_R_t ;  ) (1) - Y_R_t depends on real exchange rate Z_t, real interest rate r_R_t, and external demand. - Price dynamics: - Prices evolve according to a set of Phillips curves (see Section 3) tied to output gaps and other terms; price dynamics treated via gap relationships in this section. - Production and capital accumulation: - Potential output: Y_R_t( K_R_{t-1} ). - Capital accumulation: K_R_t = (1 _K_R) K_R_{t-1} + I_R_t (2), where _K_R is the depreciation rate. - Implications: - Fiscal policy can affect trend growth directly via public capital stock. - Public debt levels can affect UIP premia, affecting long-run outcomes. - Policies affecting reserves and NFA (e.g., FXI and CFMs) can influence long-run real interest rates and private capital accumulation. ### 2.2 External balance - BoP identity (trend and gaps): - 0 = X^Y_t( Z_t; Y^R,_t; α ) − M^Y_t( Z_t; Y^R_t; α ) + FA^{Exo;Y}_t + FA^{O;Y}_t( τ_t − ~τ_t( (+) B^Y_t; (−) FXR^Y_t; (−) NFA^{O;Y}_t ) − "τ_t ) − FXI^Y_t. - Variables with superscript “Y” are ratios to nominal GDP. - Endogenous financial inflows and UIP premium: - UIP premium: τ_t = r^R_t − r^{R;US}_t − ∆z_{t+1}. (4) - Investors’ required return includes exogenous risk-on/off term "τ_t and state-contingent ~τ_t. - ~τ_t rises with higher B^Y, falls with higher FXR^Y and higher NFA^{O;Y}; nonlinear/exponential functions capture sudden-stop behavior. - ∂FA^{O;Y}/∂τ measures capital mobility / depth of FX markets. - Supply–demand framing for endogenous flows: - Demand: FA^{O;D}_t = M^Y_t( Z_t; Y^R_t; α ) − X^Y_t( Z_t; Y^R,∗_t; α ) + FXI^Y_t − FA^{Exo;Y}_t. (6) - Supply slopes up in (τ; FA^{O;Y}) space; demand slopes down. - Shocks: - Quantity shocks shift demand laterally. - Negative supply shocks or increases in "τ_t shift supply up. - Capital mobility implications: - Open account (flat supply): lateral demand shifts absorbed with little change in τ. - Closed account (steep supply): large τ adjustments. - Policy interactions: - Monetary policy assumes IT regime: r_t = F_r( π^C_{t+1} − π^C; α ). (7) - Free float: FXI^Y_t = 0; pegged/managed regimes use FXI rule FXI^Y_t = F_{FXI}^Y( ∆s_{US}; α ). (8) - CFMs: - Administrative CFMs reduce ∂FA^{O;Y}_t/∂τ_t (slope effect). - Price-based CFMs (taxes) enter via ζ^{FAO}_t in BoP modification (9). - Fiscal block (simplified): - GD_t = G_t + r^G_{t−1} 100^{-1} B_{t−1} − GR_t( Y_t; C_t; M_t; α ). (10) - B_t = GD_t + B_{t−1}. (11) - GD_t = F_{GD}( Y_t; B^Y; ^B^Y_t; ^y^R_t; α ). (12) - FINEX distinguishes LCY and FCY debt and does not assume Ricardian equivalence. - Trends, gaps, steady state: - Decomposition into trend (bar) and gap (hat) components; 100×ln notation used. - Trends converge to a balanced-growth steady state; typical closure: - Gaps to trends in 3–5 years. - Trends to steady state in 10–15 years. - Permanent shocks (e.g., permanent drop in Y^R,∗) require permanent real depreciation Z and permanent τ increase, raising r^R and reducing potential GDP Y^R. ### 3.1 Internal balance: demand, prices, production - Aggregate demand decomposition: - Five components: C_Rt, I_Rt, G_Rt, X_Rt (split X_R;NR_t and X_R;NNR_t), M_Rt (split M_R;OIL_t and M_R;NOIL_t). (23) - Output gap ^y_R_t is weighted sum of component gaps with trend nominal expenditure shares. (24) - Potential real GDP growth ∆y_R_t is weighted sum of trend growth rates of components. (25) - Generic gap and trend structures: - Component gap: ^x_t = _x * ^x_{t-1} + (1-_x) * ^x_{t+1} + determinants^x_t + " ^x_t. (A1) - Component trend growth: ∆x_t = _1 * ∆x_{t-1} + (1- _1)*(∆y_R_t + ∆p_R;Y_t - ∆p_R;X_t) - _2*(X_Y_t - (X_Y;SS - determinants ∆x_t)) + " ∆x_t. (A2) - Prices and Phillips curves: - p_X_t = 100 * log(P_X_t). (A3) - p_R;X_t = p_X_t - p_C_t. (A4) - Inflation _X_t = p_X_t - p_X_{t-1}. (A6) - For C_R, I_R, G_R: hybrid NK Phillips curve with RM C_X_t. (A7a) - For traded components: inflation driven by domestic relative price trend, foreign price _X;* _t, ∆s_US_t, and relative price gap. (A7b) - RM C_X_t = b_1;X * ^x_t + b_2;X * (^p_R;M_NOIL_t - ^p_R;X_t) + b_3;X * (^p_R;M_OIL_t - ^p_R;X_t). (A8) - Baseline: small open economy price-taker, foreign prices in USD; framework consistent with DCP; can accommodate PCP and LCP. - Component-specific determinants (high-level): - Private consumption gap drivers include ^r_R_t, ^y_R_t, tax timing, remittances, transfers. (26)-(27) - Private investment gap driven by ^r_R_t, expected consumption and exports, cost of imported capital / REER. (28)-(29) - Non-natural resource exports respond to competitiveness (^z_Xw_t - ^p_R;X_NNR_t) and foreign demand. (30)-(32) - Non-oil imports respond to demand components, relative import prices, fiscal timing of import duties. (33)-(35) - Government absorption G_R_t modeled via fiscal policy (section 3.3.2) and differs from generic block. - Production function and investment–growth nexus: - Cobb-Douglas potential GDP with private capital K_R_t, public capital K_R;G_t, and TFP A_R_t. - ∆y_R_t = c_∆yR1 * ∆k_R_t + c_∆yR2 * ∆k_R;G_t + ∆a_R_t. (36) - Private capital accumulation: I_R_t = K_R_t - (1 - _K_R) * K_R_{t-1}. (37) - Public capital accumulation with multi-year lags; public investment becomes fully productive after three years. (38) - TFP: ∆a_R_t = ∆a_R;g_t + " ∆a_R_t; ∆a_R;g_t follows AR(1) toward ∆a_R;SS. (42)-(43) - Investment–debt tradeoffs: - Higher real interest rates reduce private investment and potential GDP during transition. - Higher interest costs can force fiscal consolidation and reduce public investment. - Public investment can raise potential GDP but may increase premia via debt; net effect depends on productivity of public investment and premium sensitivity. ### 3.2 External balance: BoP, financial account, UIP supply - BoP and current account: - 0 = CAYt + FAYt. (44)-(45) - CAYt specification includes trade balance, REM_Y_t, NR profit repatriation, interest on FCY debt, interest income on private NFA, and other flows. (46)-(47) - Financial account decomposition: - FAYt = FAO;Y t − FXI Y t − FXA Y t + (GF F CY;Y t + " B F CY;Y t). (48) - FAO;Y t builds NF A O;Y t via NF A O;Y t = −FAO;Y t + NF A O;Y t−1 * (1 + ∆s US t =100) / (1 + ∆y t =100). (50) - Net interest income on private NFA: I NF A O;Y t = r NF A O t−1 =100 * NF A O;Y t−1 * (1 + ∆s US t =100) / (1 + ∆y t =100). (51) - UIP premium and endogenous flows: - τ t = r R t − r R;US t − ∆z t+1. (52) - FAO;Y t responds to UIP gap: FAO;Y t = FAO;Y t + c FAO;Y 1 * (1 − ξ FAO;adm ) * (^ t − " ^ t). (54) - Trend FAO;Y t determinants: FAO;Y t = S(FAO;Y) + FAO;Exo;Y t + c FAO;Y 1 * (1 − ξ FAO;adm ) * ( τ t − ( SS + B t + FXR t + NF A O t + ( ξ FAO t − ξ FAO;SS ) + " t ) ). (55) - Trend risk-appetite terms modeled as exponentials to capture sudden-stop nonlinearities: (56)–(58). - Supply curve for financial flows (combined): - FAO;Y t = S(FAO;Y) + FAO;Exo;Y t + c FAO;Y 1 * ( τ t − ( ~ t + " t ) ). (59) - Rearranged into domestic rate: r R t = r R;US t + ∆z t+1 + ( FAO;Y t − S(FAO;Y) − FAO;Exo;Y t ) / c FAO;Y 1 + ~ t + " t. (62) - Extremes: - c FAO;Y 1 → 1: r R t = r R;US t + ∆z t+1 + ~ t + " t. (63) - c FAO;Y 1 = 0: price-based shocks do not affect supply (closed capital account). - Practical implications: - Can use either quantity or price formulations depending on context; equivalence breaks down at extremes of capital mobility. ### 3.3 Macroeconomic policies - Monetary policy instruments: - Taylor-type rule: runc_t = c_r1 * r_{t-1} + (1 - c_r1) * (r^R_t + π^C_t + c_r2*(π^C_{t+1} - π^C_t) + c_r3 * ^y^R_t) + ε^r_t. (64) - ELB: r_t = max(runc_t; r). (65) - Inflation target path π^C_t is a random walk (c_{π^C1} = 1); shocks ε^{π^C}_t implement disinflation or target revisions. (66) - r^R_t = r_t - π^C_t. (68) - Reserves and FXI: - Reserve law of motion: FXR^Y_t = FXI^Y_t + FXA^Y_t + (1 + r^US_{t-1}/100) * FXR^Y_{t-1} * (1 + ∆s^US_t/100)/(1 + ∆y_t/100) + ε^{FXR}_t. (71) - FXI rule: FXI^Y;unc_t = c_{FXI^Y1} * FXI^Y_{t-1} - c_{FXI^Y2}*(∆s^US_t - ∆s^US_t^*) + ε^{FXI^Y}_t. (72) - ELB on FXR via FXI^Y_t = max(FXI^Y;unc_t; FXR_min - (FXA^Y_t + ...)). (73) - Systematic FXA^Y_t targets desired FXR^Y_t (AR(1) with c_{FXR^Y1}). (74)–(76) - CFMs: - Administrative CFMs: change ϕ_{F_A^O;adm} to reduce responsiveness of FAO;Y_t to UIP. - Capital-inflow taxes: policy variable ϕ_{F_A^O_t} (AR(1) rule-of-thumb: ϕ_{F_A^O_t} = c_{ϕ_{F_A^O1}} * ϕ_{F_A^O_{t-1}} + (1 - c_{ϕ_{F_A^O1}}) * ϕ_{F_A^O;SS} + ε^{ϕ_{F_A^O}}_t). (78) - Policy regime calibrations (examples): - IT with free float: - c_{F_A^O;Y1} ≈ 1000 for advanced economy; for EMDEs suggest c_{F_A^O;Y1}*(1 - ϕ_{F_A^O;adm}) ≈ 1. - FXR;max = 0 if FXR has little effect on required return. - IT with managed float and partially-closed capital account: - c_{FXI^Y2} > 0 (example c_{FXI^Y2} = 2.0). - FXR^Y;SS set to 15 percent in baseline calibration for EMDE example. - Peg with open capital account: - ∆s^US_t pinned exogenously; very large c_{F_A^O;Y1}*(1 - ϕ_{F_A^O;adm}) makes FXI ineffective. - Fixed exchange rate with partially closed capital account: - c_{F_A^O;Y1}*(1 - ϕ_{F_A^O;adm}) = 0.1 in baseline calibration. - Fully closed capital account: - c_{F_A^O;Y1}*(1 - ϕ_{F_A^O;adm}) = 0. - Fiscal block (non-Ricardian): - Revenues: GR^Y_t = GR^Y;Y_t + GR^C;Y_t + GR^M;NOIL;Y_t + GR^M;OIL;Y_t + GR^NR;Y_t + GR^O;Y_t. (79) - Revenue rules: GR^X;Y_t = ϕ^X_t/100 * (1/(1 + ϕ^X_t/100)) * X^Y_t. (A9/A10) - Natural resource royalties: GR^NR;Y_t = ϕ^{NR}_t/100 * G^{NR;Y}_t. (80) - Expenditures: GE^Y_t = G^Y_t + GE^B;Y_t + GE^O;Y_t + GE^{Tr};Y_t. (84) - Public investment GE^{IG};Y_t is fully endogenous and the fiscal adjustment margin. - Interest payments split by currency and include term premia responsive to debt gaps. (86)–(94) - Fiscal targets and reaction functions: - Debt target AR(1): B^Y_t = c_{B^Y1} * B^Y_{t-1} + (1 - c_{B^Y1}) * B^Y;SS + ε^{B^Y}_t. (95) - Structural deficit reaction function: GD^{S;Y}_t = c_{GD^{S;Y}1} * GD^{S;Y}_{t-1} + (1 - c_{GD^{S;Y}1}) * GD^{S;Y}_t - c_{GD^{S;Y}2} * ^B^Y_t + c_{GD^{S;Y}3} * ^y^R_t + ε^{GD^{S;Y}}_t. (107) - Foreign-currency financing rule includes expected deviation of FCY debt share from target. (109) - Model use and baseline calibration notes: - FINEX is a forecasting/semi-structural model used to interpret historical data and generate policy-contingent forecasts. - Baseline simulation calibration assumes EMDE with pure float IT, fiscal policy targets a predefined debt level via public investment, strong Phillips-curve persistence, substantial imported-price pass-through, active monetary response, and imperfect capital mobility. - Policy reaction parameters not optimized in presented simulations. ### 4.1 Effects of a fiscal expansion (experiment and six cases) - Experiment setup: - Government raises transfers by five percent of GDP in the first two years. - Government relaxes long-term fiscal objectives to allow debt-to-GDP to increase permanently by ten percentage points. - From year three, government adjusts consumption spending while keeping investment-to-GDP ratio fixed to steer debt to objective. - Until last scenario, increased spending financed through domestic debt issuance. - Six calibrated cases and key outcomes: - Case 1 — Baseline (solid black line) - Real GDP increases. - Current account deficit widens; higher financial inflows attracted by a small UIP premium rise finance the deficit. - Inflation rises; central bank raises interest rates; exchange rate appreciates. - Long run: higher public debt raises investor required return; in case (1) long-run real interest rates remain stable because reduced current account and financial inflows offset premium effect. - Case 2 — High capital mobility (c_FAO;Y_1 = 1000) (solid green line) - Larger current account deficit since financial inflows finance imports with no UIP premium increase. - Slightly larger real appreciation, lower inflation, smaller nominal rate increase versus case (1). - Long run: higher public-debt premium raises long-term real interest rates, reducing steady-state investment and real GDP. - Case 3 — IT with limited capital mobility (c_FAO;Y_1 = 0:1) (solid blue line) - Short run: output and inflation rise; foreigners reluctant to finance imports so UIP premium increases. - Interest rates rise to fight inflation but not enough for UIP, so exchange rate depreciates. - Depreciation raises inflation further; short-run debt-to-GDP lower due to higher nominal GDP from inflation. - Long run: real GDP barely falls; closed account insulates from long-run costs of higher UIP premium. - Case 4 — IT with managed exchange rate, limited capital mobility (solid red line) - Authorities sell reserves per FXI rule to reduce demand for financial inflows, mitigating UIP premium increase. - Stabilizes exchange rate, inflation, and policy rate. - Cost: bigger current account deficit financed by reserve sales rather than financial inflows. - Short-run GDP effect similar to case (3); depreciation in case (3) stimulates exports more than in case (4), offset by higher interest rates. - Case 5 — IT with managed exchange rate, limited capital mobility, low reserves and high public debt (dotted red line) - Initial reserves 6 percent of GDP (vs 13 percent in case (4)); FXR lower bound at 5 percent. - Debt-to-GDP 80 percent (vs 50 percent in case (4)). - Low reserves and high debt erode management benefits: reserve depletion and higher debt increase UIP premium. - UIP premium rise induces weaker exchange rate, higher inflation, contractionary monetary policy, reducing fiscal expansion impact on consumption. - Long run: real GDP declines substantially due to permanently higher UIP premium raising rates and depressing investment and potential output; current account rises sharply. - Case 6 — Foreign currency-financed deficit (dotted black line) - Same as baseline except spending financed by dollar-denominated foreign borrowing (treated as exogenous capital flows). - Official inflows over-finance imports, causing significant exchange rate appreciation—more than in case (2). - Appreciation triggers endogenous capital outflows, reduces UIP premium and inflation. - Real GDP growth lower because appreciation compresses net exports, but consumption is higher. - Mechanisms emphasized: - Exchange rate response depends on capital mobility and central bank reaction. - UIP premium dynamics and reserve buffers critically shape short- vs long-run outcomes. - Financing currency composition matters for appreciation/depreciation and distributional outcomes between consumption and net exports. ### 4.5 Monetary policy instruments: drop in external demand - Transitory shock: - 2 percent transitory drop in external demand for exports produces contraction in output gap and increase in current account deficit across configurations. - Restoring equilibrium requires real exchange rate depreciation to enable expenditure switching. - Policy configuration responses: - Fully flexible exchange rate (baseline, solid black line): - Depreciation passes through to inflation; central bank raises policy rate despite output fall. - Managed exchange rate (solid red line): - Smaller depreciation allows central bank to pursue countercyclical policy, but smaller expenditure-switching implies a somewhat larger fall in output gap. - Managed float with low reserves (dotted red line): - Low reserves that raise investors’ required return make managed float perform worse; higher UIP premium reduces investment and potential GDP. - Closed capital account via administrative CFMs (solid blue line): - Reduces FAO;Y sensitivity to UIP; requires larger depreciation, higher inflation, and higher interest rate to attract needed flows. - More adjustment falls on current account; greater expenditure switching helps buffer output gap, but consumption volatility increases. - Role of reserves and UIP premium: - Low reserves that raise UIP premium lead to persistently higher required returns, fall in investment, and worse macro outcomes under managed regimes. - FINEX application example (Israel, Box 4): - IFM is a modified FINEX used for short- and long-run fiscal issues; does not feature FXI, CFM, commodity blocks, or NFA effects on UIP premia; includes CPI-linked debt. - Historical decompositions show large output-gap swings (5 percent in 2000 to −4 percent in 2003) and government debt peaking at 90 percent in 2003. - Fiscal reforms (2004–2019) reduced debt to about 60 percent and raised public investment; counterfactual without reforms implies real GDP about 6 percent lower in 2019. ### Box 5. The calibration of FINEX - Calibration approach: - Parsimonious, judgment-based calibration similar to IMF TA practice rather than full likelihood estimation. - DSGE models may guide calibration or provide priors; caution that DSGE restrictions can be rejected by data. - Calibration criteria and stages: - Criteria: empirical fit, forecasting performance, economic coherence, ability to explain historical data, consistency with econometric estimates. - Stages: model structure definition, data collection, parameter selection, iterative adjustment. - Data and preprocessing: - Domestic sources: Statistical Office, Central Bank, Ministry of Finance. - External sources: WEO, Consensus Forecast, World Bank ‘Pink-Sheet’. - Data transformed for FINEX structure (flows vs stocks, frequency). - Parameter taxonomy and steady state: - Parameters set for steady state, gap/trend decomposition, and transmission/policy responses. - Steady-state calibration aligns with observed long-term values (growth, prices, interest rates, expenditure shares). - Trend/cycle decomposition: - Kalman smoother applied using FINEX structure as state equation and subset of variables as measurement equation (zero measurement noise). - Relative variances of cyclical vs trend disturbances determine decomposition (example: investment gap variance four times trend shock variance). - Persistence calibrated so cyclical half-life < trend half-life (examples: cyclical private investment half-life < 1 year; trend private investment growth half-life ~1.5 years). - Transmission and policy parameter calibration: - Includes substitution between domestic and foreign assets, capital mobility, monetary/fiscal-rule parameters, sensitivity of trade flows to REER, import content, pass-through to inflation. - Calibration tailored to country characteristics (capital mobility, Phillips-curve persistence, central bank behavior, fiscal-rule aversion to debt). - Iteration, validation, application: - Calibration is iterative and case-specific; benchmarks include empirical fit, forecast performance, and historical-data explanation. - FINEX suited for economies with imperfect capital mobility and hybrid policy regimes; simpler models may be preferable where appropriate. *Source: wpiea2023235-print-pdf* ### 2.1 Internal balance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 ### 2.1 Internal balance ### Overview - FINEX places internal balance at the center of macroeconomic dynamics, linking a disaggregated IS curve, a set of Phillips curves, and an explicit production function. - Internal balance determines output and inflation through the interaction of demand and supply represented by: - an extended IS curve (domestic market clearing), and - associated Phillips curves (price dynamics as a function of the output gap and other terms). ### IS curve and demand components - The domestic market clearing condition (IS curve) is stated as: Y_R_t = C_R_t( r_R_t ;  ) + I_R_t( r_R_t ;  ) + G_R_t + X_R_t( Z_t ; Y_R;_t ;  ) M_R_t( Z_t ; Y_R_t ;  ) (1) - Key functional relationships in the IS curve: - Private consumption C_R_t and private investment I_R_t are functions of the real interest rate r_R_t and other factors denoted by ‘’. - Exports X_R_t and imports M_R_t depend on the real exchange rate Z_t. - Exports also depend on real foreign output Y_R;_t. - Imports depend on domestic output Y_R_t. - In sum, Y_R_t depends on the real exchange rate Z_t, the real interest rate r_R_t, and external demand. ### Price setting and Phillips curves - A set of Phillips curves determines the evolution of prices as a function of the output gap and other terms (Phillips curves are described in Section 3 in the source). - The model treats price dynamics as tied to gap relationships rather than imposing microfoundations on price setting in this section. ### Production function and capital accumulation - Trend (potential) output is determined by a production function that depends explicitly on the capital stock: Y_R_t( K_R_{t-1} ) - Capital accumulation follows: K_R_t = (1 _K_R) K_R_{t-1} + I_R_t (2) - where _K_R is the depreciation rate. - The explicit dependence of potential output on capital stocks implies: - Fiscal policy can affect trend growth directly through the public capital stock. - Public debt levels can affect UIP premia, with implications for long-run outcomes. - Policies affecting reserves and NFA (e.g., FXI and CFMs) can influence long-run real interest rates and thus private capital accumulation and potential output. ### Implications for policy analysis - The disaggregated treatment of exports, imports, and components of absorption enables richer analysis of fiscal policy instruments (e.g., the distinction between government consumption and investment). - By connecting trends to economic relationships (production function, UIP effects), FINEX captures both business-cycle and equilibrium effects of fiscal and external policies. - The model’s structure makes fiscal policy relevant for equilibrium outcomes via: - direct effects on the public and total capital stock, and - indirect effects through UIP premia linked to debt, reserves, and NFA. *Source: wpiea2023235-print-pdf — 2.1 Internal balance.* ### 2.2 External balance ### 2.2 External balance ### Balance of payments (BoP) representation - The BoP constraint is modeled explicitly via the BoP identity (3): 0 = X^Y_t( Z_t; Y^R,_t; α ) − M^Y_t( Z_t; Y^R_t; α ) + FA^{Exo;Y}_t + FA^{O;Y}_t( τ_t − ~τ_t( (+) B^Y_t; (−) FXR^Y_t; (−) NFA^{O;Y}_t ) − "τ_t ) − FXI^Y_t. - Variables with superscript “Y” are ratios to nominal GDP. - Exports (X^Y) and imports (M^Y) depend on the real exchange rate (Z) and foreign/domestic demand (Y^R and Y^R,∗). Exogenous flows (FA^{Exo;Y}) can include foreign aid, remittances, or FDI. - FXI (foreign exchange intervention) and CFMs (capital flow measures) act directly on the BoP constraint. ### Endogenous financial inflows and the UIP premium - Endogenous private financial inflows FA^{O;Y} (portfolio flows, cross-border bank lending) are modeled as a supply function for endogenous capital flows (equation (5)). - The UIP premium τ_t is defined in (4): τ_t = r^R_t − r^{R;US}_t − ∆z_{t+1}. - Investors compare the UIP premium to their required rate of return, which includes an exogenous risk-on/off term "τ_t and a state-contingent component ~τ_t. - The state-contingent component ~τ_t: - Rises with higher public-debt-to-GDP ratio (B^Y). - Falls with higher reserves (FXR^Y) and higher private NFA (NFA^{O;Y}). - Is modeled with exponential functions to capture nonlinearities and sudden-stop behavior. - The derivative ∂FA^{O;Y}/∂τ captures responsiveness of capital flows to the UIP premium and is a measure of capital mobility (or depth of FX markets). ### Supply–demand framing for endogenous capital flows - Demand for endogenous flows is given implicitly by (6): FA^{O;D}_t = M^Y_t( Z_t; Y^R_t; α ) − X^Y_t( Z_t; Y^R,∗_t; α ) + FXI^Y_t − FA^{Exo;Y}_t. - Graphical interpretation (Figure 1): - Supply (FA^{O;S}) slopes up in (τ; FA^{O;Y}) space because higher UIP premium attracts portfolio flows. - Demand (FA^{O;D}) slopes down because a higher premium (via policy rates and exchange rate) improves the trade balance. - Types of shocks and their effects: - Quantity shocks (e.g., changes in imports, FXI sales, FA^{Exo;Y}_t) shift the demand curve laterally. - Negative shocks to supply (or declines in risk appetite, i.e., increases in "τ_t) shift the supply curve up, raising the UIP premium and reducing financial inflows. - Capital mobility matters: - With open capital account (flat supply curve), lateral demand shifts are absorbed with little change in τ. - With closed capital account (steep supply curve, e.g., extensive administrative CFMs), the same shifts induce large τ adjustments. - Vertical shifts of the supply curve (e.g., declines in risk appetite or capital-inflow taxes) require large premium changes even with an open capital account. - The model uses a hybrid flow-and-stock specification: τ depends on portfolio flows and stocks (debt, NFA, reserves) to match EMDE behavior where modest flow changes relative to NFA stocks can generate strong exchange rate pressures. ### Interaction with policy instruments - Monetary policy: - Baseline assumes an IT regime. The central bank sets the short-term nominal policy rate r_t per rule (7): r_t = F_r( π^C_{t+1} − π^C; α ). - Under free float FXI^Y_t = 0. Pegged/managed regimes use an FXI rule (8): FXI^Y_t = F_{FXI}^Y( ∆s_{US}; α ). - FXI affects the exchange rate and the UIP premium by changing the required quantity of capital inflows to close the BoP. - Capital flow measures (CFMs): - Administrative CFMs reduce responsiveness of capital inflows: lower ∂FA^{O;Y}_t/∂τ_t. - Price-based CFMs (e.g., taxes) enter the BoP via modification (9), where ζ^{FAO}_t is the tax rate on capital inflows: 0 = X^Y_t − M^Y_t + FA^{Exo;Y}_t + FA^{O;Y}_t( τ_t − ~τ_t( B^Y_t; FXR^Y_t; NFA^{O;Y}_t ) − ζ^{FAO}_t − "τ_t ) − FXI^Y_t. - In Figure 1 terms: administrative CFMs change the slope of supply; capital-inflow taxes shift supply vertically. - Fiscal policy: - Simplified fiscal block: - Deficit identity (10): GD_t = G_t + r^G_{t−1} 100^{-1} B_{t−1} − GR_t( Y_t; C_t; M_t; α ). - Debt accumulation (11): B_t = GD_t + B_{t−1}. - Fiscal reaction function (12): GD_t = F_{GD}( Y_t; B^Y; ^B^Y_t; ^y^R_t; α ). - FINEX distinguishes LCY and FCY debt and does not assume Ricardian equivalence. - Fiscal rules in FINEX ensure fiscal sustainability in the long term; the model identifies but does not quantitatively analyze unsustainable policies beyond flagging them. ### IS-MP-BP intuition (Box 1) - A static simplification reproduces IS-MP-BP intuition: - IS: Y^R = C^R(r^R) + I^R(r^R) + G^R + X^R(Z; Y^R,∗) − M^R(Z; Y^R) (13). - MP: r^R = F_{r^R}( Y^R − Y^R ) (14). - BP (simplified): 0 = X^R(Z; Y^R,∗) − M^R(Z; Y^R) + FA^{O;Y}( τ ) (15). - Key insights: - Fiscal expansion shifts IS right; monetary policy raises r; capital inflows finance imports depending on BP steepness. - Administrative CFMs steepen BP; capital-inflow taxes shift BP vertically; FXR sales shift BP right. - Effectiveness of FXI and CFMs depends on capital account openness. ### Trends, gaps, and the steady state - Most variables are decomposed into trend (bar) and gap (hat) components; 100×ln notation (lowercase) is used for logged variables (Box 2). - Example decomposition for real output (16): Y^R_t = Y^R_t( K^R_t; α )( 1 + ^y^R/100 ). - Trends converge to a balanced-growth steady state where ratios of trending variables are constant. - FINEX allows: - Convergence of gaps to trends (business-cycle closure, typically 3–5 years). - Convergence of trends to the steady-state balanced growth path (typically 10–15 years). - Multiple, time-varying trends and slow or permanent deviations in trends. - Trend-level counterparts of key equations are specified (17)–(22), linking trend external balance, real exchange rate (Z), UIP premium (τ), trend interest rates, potential GDP (Y^R), structural deficit (GD), and debt (B^Y). Examples: - Trend BoP (17): 0 = X^Y_t( Z_t; Y^R,∗_t; α ) − M^R^Y_t( Z_t; Y^R_t; α ) + FA^{Exo;Y}_t + FA^{O;Y}_t( τ_t − ~τ_t( B^Y_t; FXR^Y_t; NFA^{O;Y}_t )). - Trend UIP (18): τ_t = r^R_t − r^{R;US}_t − ∆z_{t+1}. - Trend goods market (19): Y^R_t( K^R_{t−1}; α ) = C^R_t( r^R_t; α ) + I^R_t( r^R_t; α ) + G^R_t + X^R_t( Z_t; Y^R,∗_t; α ) − M^R_t( Z_t; Y^R_t; α ). - Permanent shocks example: a permanent drop in foreign demand (Y^R,∗) requires a permanent real depreciation (Z) and a permanent increase in τ, leading to permanently higher real and nominal interest rates (r^R and r) and a gradual permanent drop in potential GDP (Y^R). *Source: 2.2 External balance (from wpiea2023235-print-pdf - 2.2 External balance).* ### 3.1 Internal balance ### wpiea2023235-print-pdf - 3.1 Internal balance ### Overview - FINEX decomposes real aggregate demand into five main components: private consumption (C_Rt), private investment (I_Rt), government absorption (G_Rt), exports (X_Rt), and imports (M_Rt). Exports are further split into natural resource (X_R;NR_t) and non-natural resource (X_R;NNR_t); imports into oil (M_R;OIL_t) and non-oil (M_R;NOIL_t). (equation (23)) - The aggregate real output gap ^y_R_t is the weighted sum of component gaps (^c_R_t, ^i_R_t, ...), with weights given by trend nominal expenditure shares to GDP (C_Y_t, I_Y_t, ...). (equation (24)) - Potential real GDP growth ∆y_R_t is the weighted sum of trend growth rates of expenditure components. (equation (25)) - Trend dynamics for non-stationary variables (including potential GDP) are modeled in growth rates; these growth rates are stationary. (footnote 25) ### Demand components: generic structure (sections 3.1.1) - Representative gap equation for a component X (A1): - ^x_t = _x * ^x_{t-1} + (1-_x) * ^x_{t+1} + determinants^x_t + " ^x_t - Captures real rigidities (lag ^x_{t-1}), forward-looking expectations (^x_{t+1}), and component-specific determinants (determinants^x_t). All gaps close in equilibrium. - Representative trend equation for component X (A2): - ∆x_t = _1 * ∆x_{t-1} + (1- _1)*(∆y_R_t + ∆p_R;Y_t - ∆p_R;X_t) - _2*(X_Y_t - (X_Y;SS - determinants ∆x_t)) + " ∆x_t - Trend growth ∆x_t follows AR(1); adjustment term ensures convergence of the component share X_Y_t to the balanced growth path share X_Y;SS. ### Price setting: generic structure (section 3.1.2) - Price deflator and relative price definitions: - p_X_t = 100 * log(P_X_t). (A3) - p_R;X_t = p_X_t - p_C_t. (A4) - Trend growth of relative price ∆p_R;X_t converges to ∆p_R;X;SS; export/import relative price trends are influenced by changes in component-specific equilibrium real exchange rate ∆z_X_t. (A5) - Inflation definitions and NK Phillips curve structure: - _X_t = p_X_t - p_X_{t-1}. (A6) - For C_R, I_R, G_R: _X_t follows hybrid New Keynesian Phillips curve with forward- and backward-looking terms and real marginal costs RM C_X_t. (A7a) - For traded components (X_R;NNR, X_R;NR, M_R;NOIL, M_R;OIL): _X_t driven by domestic relative price trend, foreign price _X;* _t, exchange rate ∆s_US_t, and relative price gap ^p_R;X_t. (A7b) - Real marginal costs formulation: - RM C_X_t = b_1;X * ^x_t + b_2;X * (^p_R;M_NOIL_t - ^p_R;X_t) + b_3;X * (^p_R;M_OIL_t - ^p_R;X_t). (A8) - Baseline assumption: small open economy price-taker; foreign prices quoted in U.S. dollars and adjusted by local currency/USD exchange rate; framework consistent with dominant currency pricing (DCP); FINEX can accommodate PCP and LCP. (footnote 31) ### Demand components: determinants (section 3.1.3) - Private consumption (equations (26)-(27)): - Business-cycle gap equation (26) drivers: - Forward/backward components: c^c_R1 * ^c_R_{t-1} + c^c_R2 * ^c_R_{t+1} - Real interest rate gap: - c^c_R3 * ^r_R_t - Output gap: c^c_R4 * ^y_R_t - Consumption tax timing effect: - c^c_R5 * (_C_t - _C_{t+1}) - Cyclical remittances: c^c_R6 * ^REM_Y_t - Government transfers: c^c_R7 * cGETr;Y_t - Trend consumption dynamics (27): - Converges to potential real GDP growth adjusted by trend relative price (∆p_R;Y_t + ∆y_R_t) - Converges to steady-state consumption share C_Y;SS; affected by trend remittances (REM_Y_t) and trend government transfers (GETr;Y_t) - Permanent increases in consumption tax (_C_t - S(_C)) reduce C_Y_t relative to C_Y;SS - Exchange rate does not directly affect private consumption; import substitution captured in imports equation. - Private investment (equations (28)-(29)): - Business-cycle gap equation (28) drivers: - Lag and lead investment gaps: c^i_R1 * ^i_R_{t-1} + c^i_R2 * ^i_R_{t+1} - Real interest rate gap: - c^i_R3 * ^r_R_t - Expected private consumption: c^i_R4 * ^c_R_{t+1} - Expected non-natural resource exports: c^i_R6 * ^x_R;NNR_{t+1} - Cost of imported capital goods / REER: - c^i_R5 * (^z_Mw_t - ^p_R;I_t) - Trend investment dynamics (29): - Trend real interest rates r_R_t and corporate income tax rates _Y_t above steady state discourage ∆i_R_t and reduce I_Y_t. - Non-natural resource exports (equations (30)-(32)): - Cyclical drivers (30): - Lag/lead export gaps, competitiveness via export-weighted REER gap (^z_Xw_t - ^p_R;X_NNR_t), foreign demand ^y_R;*_t. - Trend export growth (31)-(32): - Depends on trend foreign demand X_R;NNR;S_t, which increases with ∆y_R;*_t and improvements in competitiveness (∆p_R;X_NNR_t). - Sustained rise in X_R;NNR;S_t raises trend export-to-GDP share X_NNR;Y_t. - Non-oil imports (equations (33)-(35)): - Cyclical drivers (33): - Demand from consumption ^c_R_t, investment ^i_R_t, government absorption ^g_R_t, and NNR exports ^x_R;NNR_t - Relative import prices ^p_R;M_NOIL_t and relative price to investment (^p_R;M_NOIL_t - ^p_R;I_t) - Fiscal policy: timing of import duties (_M_NOIL_t - _M_NOIL_{t+1}) can induce front-loading of imports - Government absorption gap ^g_R_t enters with coefficient c^m_R;NOIL7 - Trend imports (34)-(35): - Converge to M_NOIL;Y;SS; adjust for demand M_R;NOIL;D_t (35), relative price trends, persistent shifts in other expenditure shares (C_Y_t, I_Y_t, X_NNR;Y_t, X_NR;Y_t), and permanent changes in import duties _M_NOIL_t. - Government absorption: - Government absorption G_R_t is modeled as a function of fiscal policy decisions and follows a different process (see section 3.3.2); it does not have the generic behavioral block used for other components. ### Production function and investment–growth nexus (section 3.1.4) - Potential GDP is determined by a Cobb-Douglas function of private capital K_R_t, public capital K_R;G_t, and total factor productivity A_R_t. Growth in potential GDP ∆y_R_t is driven by ∆k_R_t, ∆k_R;G_t, and ∆a_R_t. (equation (36)) - ∆y_R_t = c_∆yR1 * ∆k_R_t + c_∆yR2 * ∆k_R;G_t + ∆a_R_t. (36) - Private capital accumulation (37): - I_R_t = K_R_t - (1 - _K_R) * K_R_{t-1}. (37) - Public capital accumulation with multi-year implementation lags (38): - K_R;G_t = (1 - _K_R;G) * K_R;G_{t-1} + (1 - c_KR;G2 - c_KR;G3 - c_KR;G4) * GE_R;IG_t + c_KR;G2 * GE_R;IG_{t-1} + c_KR;G3 * GE_R;IG_{t-2} + c_KR;G4 * GE_R;IG_{t-3}. - Public investment becomes fully productive after three years (implementation lags reflected by GE_R;IG_{t-1}, GE_R;IG_{t-2}, GE_R;IG_{t-3}). - TFP process (equations (42)-(43)): - ∆a_R_t = ∆a_R;g_t + " ∆a_R_t. (42) - ∆a_R;g_t = c_∆aR;g1 * ∆a_R;g_{t-1} + (1 - c_∆aR;g1) * ∆a_R;SS + ∆a_R;g_t. (43) - TFP growth rate is stationary but subject to transitory and persistent shocks (" ∆a_R_t and " ∆a_R;g_t). - Investment–debt tradeoffs and channels: - Private investment is dampened by higher real interest rates, reducing private capital accumulation and thus potential GDP growth during transition to steady state. - Higher interest rates raise government borrowing costs and interest payments, possibly forcing fiscal consolidation and reducing public investment, which can further reduce potential GDP growth depending on calibration. - Public investment, even if debt-financed, can boost potential GDP by raising public capital and demand; however, higher indebtedness can increase UIP and term premia, raising interest rates and reducing potential GDP growth. - Net effect depends on productivity of public investment and responsiveness of premia to additional borrowing, which may depend on initial debt level. - Alternative formulation for calibration (equations (39)-(41) and note): - Define adjusted quasi-TFP ∆~a_R_t = ∆a_R_t + c_∆yR1 * S(∆k_R) + c_∆yR2 * S(∆k_R;G). - Rewritten system used in model code: - ∆y_R_t = c_∆yR1*(∆k_R_t - S(∆k_R)) + c_∆yR2*(∆k_R;G_t - S(∆k_R;G)) + ∆~a_R_t. (39) - ∆~a_R_t = ∆~a_R;g_t + " ∆~a_R_t. (40) - ∆~a_R;g_t = c_∆~aR;g1 * ∆~a_R;g_{t-1} + (1 - c_∆~aR;g1)*∆~a_R;SS + " ∆~a_R;g_t. (41) - Steady-state potential GDP growth is ∆~a_R;SS. (footnote 37) - Crowding-in and crowding-out possibilities along convergence path: - Higher public investment raises demand and can spur private investment (crowding in) and raise trend GDP via public capital accumulation. - Higher demand may induce tighter monetary policy to control inflation, reducing private investment (crowding out). *Source: wpiea2023235-print-pdf - 3.1 Internal balance* ### 3.2 External balance ### 3.2 External balance ### BoP identity and current account (equations (44)–(47)) - The BoP identity holds in both levels (44) and trends (45): net cross-border flows of goods and services—the current account—must be matched by net flows of financial claims—the financial account. - (44) 0 = CAYt + FAYt - (45) 0 = CAYt + FAYt - The current account balance, CAYt, is specified in (46) and includes: - trade balance: X Y t − M NOIL;Y t =(1 + ξ M NOIL t =100) − M OIL;Y t =(1 + ξ M OIL t =100) - remittances: REM Y t - natural resource sector profits paid abroad net of royalty revenues: −(G NR;Y t − GR NR;Y t) - interest payments on foreign currency-denominated debt: −GE B F CY;Y t - interest income on private NFA: I NF A O;Y t - other current account flows: CA O;Y t - (46) CAYt = X Y t − M NOIL;Y t =(1 + ξ M NOIL t =100) − M OIL;Y t =(1 + ξ M OIL t =100) + REM Y t − (G NR;Y t − GR NR;Y t) − GE B F CY;Y t + I NF A O;Y t + CA O;Y t - Trend (equilibrium) current account is defined in (47), analogous to (46). - (47) CAYt = X Y t − M NOIL;Y t =(1 + ξ M NOIL t =100) − M OIL;Y t =(1 + ξ M OIL t =100) + REM Y t − (G NR;Y t − GR NR;Y t) − GE B F CY;Y t + I NF A O;Y t + CA O;Y t ### Financial account decomposition and reserve management (equations (48)–(50)) - Financial account inflows are decomposed in (48): - (48) FAYt = FAO;Y t − FXI Y t − FXA Y t + (GF F CY;Y t + " B F CY;Y t) - Endogenous financial inflows: FAO;Y t - Reserve accumulation: FXA Y t - Interventions: FXI Y t - Net foreign currency borrowing: change in foreign currency debt ratio captured by GF F CY;Y t with idiosyncratic error " B F CY;Y t (see (104) in section 3.3.2) - Trend financial account inflows (49) assume planned trend reserve accumulation and target foreign currency debt ratio: - (49) FAYt = FAO;Y t − FXA Y t + GF F CY;Y t - FAO;Y t gives rise to a stock of private NFA (50), with exchange rate and output revaluation terms: - (50) NF A O;Y t = −FAO;Y t + NF A O;Y t−1 * (1 + ∆s US t =100) / (1 + ∆y t =100) - Net interest income on private NFA is given by (51): - (51) I NF A O;Y t = r NF A O t−1 =100 * NF A O;Y t−1 * (1 + ∆s US t =100) / (1 + ∆y t =100) ### UIP premium, decomposition, and endogenous financial inflows (equations (52)–(55)) - UIP premium defined (52) as interest rate differential adjusted by expected exchange rate depreciation: - (52) τ t = r R t − r R;US t − ∆z t+1 - UIP premium decomposed into trend and gap (53): - (53) τ t = τ t + ^ t - where ^ t is the gap (business-cycle/transitory), and τ t is the trend (secular) component - When cyclical pressures force FAO;Y t to deviate from trend, a UIP premium gap ^ t opens according to (54): - (54) FAO;Y t = FAO;Y t + c FAO;Y 1 * (1 − ξ FAO;adm ) * (^ t − " ^ t) - " ^ t is a UIPpremium shock; a positive value of " ^ t implies a decline in investor appetite and requires a larger UIP premium for a given financial inflow - The responsiveness of FAO;Y t to UIPpremium changes is governed by c FAO;Y 1 * (1 − ξ FAO;adm ): - c FAO;Y 1 reflects structural features (e.g., depth of domestic financial markets) - ξ FAO;adm reflects strength of administrative CFMs - Determinants of trend endogenous flows FAO;Y t are specified in (55): - (55) FAO;Y t = S(FAO;Y) + FAO;Exo;Y t + c FAO;Y 1 * (1 − ξ FAO;adm ) * ( τ t − ( SS + B t + FXR t + NF A O t + ( ξ FAO t − ξ FAO;SS ) + " t ) ) - FAO;Exo;Y t captures permanent shifts in the quantity of financial flows (e.g., long-term risk appetite cycles) - Increases in capital inflow tax ξ FAO t relative to steady state increase investors’ required excess return (policy variable discussed in section 3.3.1) - Trend risk appetite depends on government debt, foreign reserves (for managed/peg regimes), and private NFA (B t, FXR t, NF A O t), modeled in (56)–(58): - (56) B t = exp(c^ B 1 * (B Y t − B Y;SS )) − 1 - (57) FXR t = c^ FXR 4 * ( FXR;max + min(c^ FXR 1 + c^ FXR 3 * exp( − c^ FXR 2 * FXR Y t ) − FXR;max , 1e−8 ) ) - (58) NF A O t = exp( − c^ NF A O 1 * ( NF A O;Y t − S(NF A O;Y) ) ) − 1 - Nonlinearities capture ‘sudden stops’: small changes in debt, net foreign liabilities, and reserves can have explosive effects on capital flows when risks are high ### Risk appetite, capital mobility, and equilibrium interactions - The trend risk appetite shock " t in (55) captures trend risk-off shocks - Equations (54) and (55) together represent a supply function for endogenous capital flows: - International investors supply financial flows as an increasing function of the gap and trend UIP premia (^ t and τ t) - FAO;Exo;Y t and S(FAO;Y) represent short-run and long-run shifts in supply of financial flows - Risk-appetite terms B t, FXR t, NF A O t capture influence of stocks of public debt, reserves, and NFA on required rates of return - Demand for FAO;Y t is a declining function of the UIP premium: high interest rates and a depreciated exchange rate reduce the need for endogenous capital inflows to close the BoP; UIP premium and endogenous flows are equilibrium outcomes determining the equilibrium exchange rate (given policy interest rate) - Degree of capital mobility shaped by parameters c FAO;Y 1 and ξ FAO;adm: - Small product c FAO;Y 1 * (1 − ξ FAO;adm ) ⇒ financial flows unresponsive to UIP premium and to changes in investors’ required returns (including debt sustainability and reserves adequacy) - Shallow domestic financial markets (small c FAO;Y 1) and/or tight capital account regulation (ξ FAO;adm close to 1) reduce effect of price-based CFMs - If capital mobility is low, changes in other BoP components or exogenous shifts in quantity of financial flows have large impacts on equilibrium UIP premium ### The supply of financial flows (Box 3) — combined supply curve and implications (equations (59)–(63)) - With no CFMs (ξ FAO;adm = 0, ξ FAO t = ξ FAO;SS) and same capital mobility in equilibrium and business cycle (c FAO;Y 1 = c FAO;Y 1 ), combining (54) and (55) yields: - (59) FAO;Y t = S(FAO;Y) + FAO;Exo;Y t + c FAO;Y 1 * ( τ t − ( ~ t + " t ) ) - with state-dependent risk appetite term: - (60) ~ t ≡ SS + B t + FXR t + NF A O t - and idiosyncratic risk appetite shock: - (61) " t ≡ " t + " ^ t - Rearranging using (52) gives supply curve expression with domestic interest rate on left-hand-side: - (62) r R t = r R;US t + ∆z t+1 + ( FAO;Y t − S(FAO;Y) − FAO;Exo;Y t ) / c FAO;Y 1 + ~ t + " t - Extremes: - Perfect capital mobility (c FAO;Y 1 → 1) gives UIP-like condition with state-dependent premium: - (63) r R t = r R;US t + ∆z t+1 + ~ t + " t - Two types of supply-shift terms: - exogenous quantity-based component: S(FAO;Y) + FAO;Exo;Y t - price-based component: investors’ risk appetite (~ t + " t) - Redundancy and limits: - Price-based shocks can be expressed as quantity shocks via conversion factor c FAO;Y 1, but equivalence breaks down at extremes: - Closed capital account (c FAO;Y 1 = 0): price-based shocks do not affect supply of financial flows - Fully open capital account (c FAO;Y 1 → 1): quantity shifters no longer matter, price-based shocks move UIP premium one-for-one - Practical implication: may consider either quantity or price formulation depending on context; yield/spread information often used to represent price-based shocks _Italic: Source — wpiea2023235-print-pdf — 3.2 External balance_ ### 3.3 Macroeconomic policies ### 3.3 Macroeconomic policies ### Monetary policy - FINEX accommodates a wide range of monetary and fiscal policies across exchange rate regimes from hard pegs to pure floats with IT. - Available monetary instruments: - Policy interest rate (rt) governed by a Taylor-type rule (equation (64)): - runc_t = c_r1 * r_{t-1} + (1 - c_r1) * (r^R_t + π^C_t + c_r2*(π^C_{t+1} - π^C_t) + c_r3 * ^y^R_t) + ε^r_t - Policy rate subject to an ELB(r) via r_t = max(runc_t; r) (equation (65)). - Planned purchases and sterilized foreign exchange intervention (FXI) to accumulate reserves and target exchange rate. - Price-based and regulatory capital controls (CFMs). - Inflation targeting specifics: - Inflation target path π^C_t is a policy variable specified as a random walk with c_{π^C1} = 1; shocks ε^{π^C}_t can implement disinflation or target revisions (equation (66)). - Trend nominal exchange rate ∆s^US_t is pinned down by domestic and foreign inflation targets and changes in the equilibrium REER: π^C_t = π^C;US;SS + ∆s^US_t - ∆z^US_t (equation (67)). - Real interest rate definitions: - r^R_t = r_t - π^C_t (equation (68)). - Equilibrium trend real interest rate r^R_t determined by trend UIP condition (equation (69)); cyclical gap ^r^R_t enters private consumption and investment (equation (70)). ### Foreign reserves management - Stock of reserves FXR^Y_t (dollars, ratio to nominal GDP) follows law of motion (equation (71)): - FXR^Y_t = FXI^Y_t + FXA^Y_t + (1 + r^US_{t-1}/100) * FXR^Y_{t-1} * (1 + ∆s^US_t/100)/(1 + ∆y_t/100) + ε^{FXR}_t - FXI (sterilized intervention) specification (equation (72)): - FXI^Y;unc_t = c_{FXI^Y1} * FXI^Y_{t-1} - c_{FXI^Y2}*(∆s^US_t - ∆s^US_t^*) + ε^{FXI^Y}_t - c_{FXI^Y2} controls response to exchange rate misalignment; c_{FXI^Y1} controls persistence; discretionary shock ε^{FXI^Y}_t allows ad-hoc interventions. - ELB on FXR can constrain interventions via FXI^Y_t = max(FXI^Y;unc_t; FXR_min - (FXA^Y_t + (1 + r^US_{t-1}/100)*FXR^Y_{t-1}*(1 + ∆s^US_t/100)/(1 + ∆y_t/100))) (equation (73)). - Systematic reserve accumulation FXA^Y_t targets desired FXR^Y_t: - Desired FXR^Y_t follows AR(1) with persistence parameter c_{FXR^Y1} (equation (74)). - Target FXA path satisfies equation (75) (implicit). - FXA actual dynamics include correction term -c_{FXA^Y2} * dFXR^Y_t (equation (76)); dFXR^Y_t defined in (77). ### Capital flow management (CFMs) - Two broad CFM types modeled: - Administrative restrictions: reduce responsiveness of endogenous capital flows F_A^O;Y_t to UIP premium by changing parameter ϕ_{F_A^O;adm} in equations (54) and (55). - Capital inflow tax (market-based measures): captured by policy variable ϕ_{F_A^O_t} in equation (55) that increases excess return demanded by investors. - No explicit optimized reaction functions specified; instead rules-of-thumb AR(1) for ϕ_{F_A^O_t} (equation (78)): - ϕ_{F_A^O_t} = c_{ϕ_{F_A^O1}} * ϕ_{F_A^O_{t-1}} + (1 - c_{ϕ_{F_A^O1}}) * ϕ_{F_A^O;SS} + ε^{ϕ_{F_A^O}}_t - Shocks ε^{ϕ_{F_A^O}}_t represent idiosyncratic policy adjustments; with c_{ϕ_{F_A^O1}} = 1 shocks are essentially permanent. - Model can be extended to richer CFM reaction functions (e.g., leaning against foreign borrowing) for country-specific applications. ### Monetary and exchange rate policy frameworks - FINEX allows coherent choices among three policy dimensions (Mundell-Fleming trilemma): control over domestic interest rates, exchange rate flexibility, openness of capital account. - Standard regime calibrations illustrated: - IT with free-floating exchange rate: - Full control over domestic interest rates via Taylor rule (equation (64)). - Inflation target path exogenous (equation (66)). - Broadly open capital account: for advanced economy c_{F_A^O;Y1} ≈ 1000 and ϕ_{F_A^O;adm} = 0; for EMDEs suggested c_{F_A^O;Y1}*(1 - ϕ_{F_A^O;adm}) ≈ 1. - If FXR has little effect on required return, set FXR;max = 0 so FXR = 0. - Exchange rate adjusts to expectations and interest rates; equilibrium REER and inflation targets determine trend nominal exchange rate. - IT with managed exchange rate and partially-closed capital account: - Set c_{FXI^Y2} > 0 to lessen exchange rate volatility (calibration example uses c_{FXI^Y2} = 2.0). - Capital account less than fully open: c_{F_A^O;Y1}*(1 - ϕ_{F_A^O;adm}) ≈ 1 for EMDEs. - Low reserves may increase UIP premium via FXR contribution when FXR^Y below threshold FXR^Y;SS (set to 15 percent in baseline calibration). - Exchange rate peg with open capital account: - Target path for ∆s^US_t set exogenously (equation (66′)). - With very large c_{F_A^O;Y1}*(1 - ϕ_{F_A^O;adm}), FXI is ineffective; monetary policy loses control over domestic interest rates, which become endogenous. - Tax-based CFM could remain effective even with open capital account. - Fixed exchange rate with partially closed capital account: - Lower c_{F_A^O;Y1}*(1 - ϕ_{F_A^O;adm}) to 0.1 in baseline calibration: FXI more effective and scope for independent monetary policy increases, though low reserves can still render FXI ineffective. - Fully closed capital account: - Set c_{F_A^O;Y1}*(1 - ϕ_{F_A^O;adm}) = 0: cross-border financial flows not influenced by UIP premium. In pure float with no FXI, exchange rate adjusts to close BoP through trade flows; under fixed exchange rate FXI sustains the peg. ### Fiscal policy — overview - Fiscal block is non-Ricardian and allows analysis of: - Macroeconomic effects of expenditure and revenue policies with plausible fiscal multipliers. - Public debt projections and fiscal adjustments for sustainability. - Macroeconomic implications of financing choices (official vs private; foreign vs domestic). - Long-term implications of public investment for debt and growth. - Fiscal/monetary interactions. - FINEX includes fiscal targets and reaction functions: fiscal targets (e.g., debt-to-GDP) and fiscal reaction functions adjust fiscal instruments to achieve targets and stabilize the economy in a forward-looking framework. ### Government revenues - Overall government revenues decomposed (equation (79)): - GR^Y_t = GR^Y;Y_t + GR^C;Y_t + GR^M;NOIL;Y_t + GR^M;OIL;Y_t + GR^NR;Y_t + GR^O;Y_t - Tax revenue for each main source follows (equations (A9) and (A10)): - GR^X;Y_t = ϕ^X_t/100 * (1/(1 + ϕ^X_t/100)) * X^Y_t (equation (A9) form) - X^Y_t = 100 * (1 + ϕ^X_t/100) * P^X_t * X_t / (P^Y_t * Y^R_t) for X in {C_R; M_R;NOIL; M_R;OIL; Y_R} (equation (A10) form) - Natural resource royalties: - GR^NR;Y_t = ϕ^{NR}_t/100 * G^{NR;Y}_t (equation (80)). - Other revenues follow AR(1) (equation (81)): - GR^O;Y_t = c_{GR^O;Y1} * GR^O;Y_{t-1} + (1 - c_{GR^O;Y1}) * GR^O;Y_t + ε^{GR^O;Y}_t - Tax rates ϕ^X_t follow AR(1) (equation (A11)), typically random walk (ζ = 1) so policy shocks are perceived as permanent. - Revenue decomposition into trend and gap (equation (82)): - GR^Y_t * (1 + c_{GR^Y1} * ^y^R_t/100) = GR^Y_t + c_{GR^Y_t} - Trend revenue share is given by product of tax rates and trend bases (equation (83)). ### Government expenditures - Total expenditures GE^Y_t (equation (84)): - GE^Y_t = G^Y_t + GE^B;Y_t + GE^O;Y_t + GE^{Tr};Y_t - Government absorption G^Y_t decomposed (equation (85)): - G^Y_t = GE^C;Y_t + GE^{IG};Y_t (government consumption + public investment) - Interest expenditures split into local- and foreign-currency components (equation (86)): - GE^B;Y_t = GE^{B;LCY};Y_t + GE^{B;FCY};Y_t - Government consumption, transfers, and other expenditures follow AR(1) processes (exogenous), while public investment GE^{IG};Y_t is modeled as the only fully endogenous fiscal component and is the adjustment margin to meet fiscal targets. - Interest payments on foreign currency debt (equation (87)): - GE^{B;FCY};Y_t = r^{G;FCY}_{t-1}/100 * B^{FCY;Y}_{t-1} * (1 + ∆s^US_t/100)/(1 + ∆y_t/100) - Interest payments on local currency debt (equation (88)): - GE^{B;LCY};Y_t = (r^{G;LCY}_{t-1}/100) * B^{LCY;Y}_{t-1}/(1 + ∆y_t/100) - Government borrowing costs include compounded short-term rates and term premia: - Foreign currency rate r^{G;FCY}_t = r^{G;Comp;FCY}_t + κ^{G;FCY}_t + ε^{r^{G;FCY}}_t (equation (89)) - Compounded foreign rate r^{G;Comp;FCY}_t defined recursively with IN_FCY as inverse of average maturity (equation (90)): r^{G;Comp;FCY}_t = IN_FCY * r^US_t + (1 - IN_FCY) * r^{G;Comp;FCY}_{t+1} - Term premium κ^{G;FCY}_t responds to public debt gap (equation (91)): κ^{G;FCY}_t = c_{κ^{G;FCY}1} * κ^{G;FCY}_{t-1} + (1 - c_{κ^{G;FCY}1})*(κ^{G;FCY} + c_{κ^{G;FCY}2}*(B^Y_t - B^Y;SS)) + ε^{κ^{G;FCY}}_t - Local currency rates analogous with inclusion of both local and foreign currency term premia (equations (92)-(94)). - Currency composition of public debt is an important policy choice given impacts on borrowing costs. ### Fiscal targets and reaction functions - Debt targets: - Public debt-to-GDP target B^Y_t evolves via AR(1) with steady-state B^Y;SS (equation (95)): B^Y_t = c_{B^Y1} * B^Y_{t-1} + (1 - c_{B^Y1}) * B^Y;SS + ε^{B^Y}_t - Target share of foreign-currency-denominated debt B^{FCY;B}_t evolves via AR(1) with steady-state B^{FCY;B;SS} (equation (96)): B^{FCY;B}_t = c_{B^{FCY;B}1} * B^{FCY;B}_{t-1} + (1 - c_{B^{FCY;B}1}) * B^{FCY;B;SS} + ε^{B^{FCY;B}}_t - Identities determine stock shares (equations (97)-(98)): - B^Y_t = B^{FCY;Y}_t + B^{LCY;Y}_t - B^{FCY;Y}_t = B^{FCY;B}_t/100 * B^Y_t - Fiscal deficit decomposition: - GD^Y_t = GE^Y_t - GR^Y_t (equation (99)) - GD^Y_t = GD^{S;Y}_t + GD^{C;Y}_t (equation (100)): structural and cyclical components - Cyclical deficit GD^{C;Y}_t = -c_{GR^Y_t} - c_{GD^{C;Y}1} * ^y^R_t (equation (101)) - Deficit financing split and debt accumulation: - GD^Y_t = GF^{LCY;Y}_t + GF^{FCY;Y}_t (equation (102)) - B^{LCY;Y}_t = GF^{LCY;Y}_t + B^{LCY;Y}_{t-1}/(1 + ∆y_t/100) + ε^{B^{LCY;Y}}_t (equation (103)) - B^{FCY;Y}_t = GF^{FCY;Y}_t + B^{FCY;Y}_{t-1} * (1 + ∆s^US_t/100)/(1 + ∆y_t/100) + ε^{B^{FCY;Y}}_t (equation (104)) - Implicit definitions to link structural deficit and foreign financing to debt targets: - B^Y_t = GD^{S;Y}_t + (B^{FCY;Y}_t * (1 + (∆z^{SS;US} - π^{C;US;SS} + π^C_t)/100) + B^{LCY;Y}_t)/(1 + ∆y_t/100) (equation (105)) - GF^{FCY;Y}_t = (1 - (1 + (∆z^{SS;US} - π^{C;US;SS} + π^C_t)/100)/(1 + ∆y_t/100)) * B^{FCY;Y}_t (equation (106)) - Fiscal reaction functions: - Structural deficit reaction function (equation (107)): - GD^{S;Y}_t = c_{GD^{S;Y}1} * GD^{S;Y}_{t-1} + (1 - c_{GD^{S;Y}1}) * GD^{S;Y}_t - c_{GD^{S;Y}2} * ^B^Y_t + c_{GD^{S;Y}3} * ^y^R_t + ε^{GD^{S;Y}}_t - ^B^Y_t includes forward-looking component per (108): ^B^Y_t = (1 - c_{^B^Y1})*(B^Y_t - B^Y_t^*) + c_{^B^Y1} * ^B^Y_{t+1} - c_{GD^{S;Y}3} < 0 allows countercyclical structural deficit. - Foreign-currency financing reaction function (equation (109)): - GF^{FCY;Y}_t = c_{GF^{FCY;Y}1} * GF^{FCY;Y}_{t-1} + (1 - c_{GF^{FCY;Y}1})*(GF^{FCY;Y}_t - c_{GF^{FCY;Y}2}*(100 * B^{FCY;Y}_{t+1}/B^Y_{t+1} - B^{FCY;B}_t)) + c_{GF^{FCY;Y}3}*(GD^Y_t - GD^{S;Y}_t) + ε^{GF^{FCY;Y}}_t - Larger expected deviations of foreign-currency debt share from target reduce foreign-currency financing share via the -c_{GF^{FCY;Y}2} term. - If overall deficit exceeds structural target, authorities may increase foreign-currency financing via c_{GF^{FCY;Y}3} term. - Implications: - Reaction function parameter configurations determine probabilities of adherence to fiscal rules and macro outcomes, interacting with monetary regime, countercyclicality, and currency composition of debt. - Model can explore hypotheses such as fiscal procyclicality when UIP premia correlate negatively with GDP. ### Model applications and baseline calibration notes - FINEX is fundamentally a forecasting model used to provide structural interpretation of historical data and policy-contingent forecasts. - Section 4 demonstrates applications: fiscal expansion under different regimes, public investment vs consumption effects, use of FXI and pre-emptive CFMs in response to shocks to foreign risk appetite, benefits and costs of pre-emptive CFMs when private external debt is high, and differences in responses to real vs financial external shocks. - Baseline calibration for simulations assumes an EMDE with pure float IT regime, fiscal policy targets a predefined public debt level using public investment as fiscal instrument, and further assumes: - strong persistence in the Phillips curve, - substantial pass-through from imported prices to inflation, - relatively active monetary policy response, - imperfect capital mobility. - Policy reaction function parameters are not optimized in the presented simulations; optimization could be undertaken but results depend on calibrations, shock distributions, and regime specifics. *Source: wpiea2023235-print-pdf - 3.3 Macroeconomic policies* ### 4.1 Effects of a fiscal expansion ### 4.1 Effects of a fiscal expansion ### Setup and experiment - Government raises transfers to households by five percent of GDP in the first two years. - Government relaxes its long-term fiscal objectives to allow the debt-to-GDP ratio to increase permanently by ten percentage points. - Starting from the third year, government adjusts consumption spending while keeping investment spending-to-GDP ratio fixed to steer the debt level towards its debt objective. - Until the last scenario, increased spending is financed through domestic debt issuance. ### Six cases and key outcomes - Case 1 — Baseline (solid black line) - Real GDP increases with higher aggregate demand. - Current account deficit increases with higher imports. - Higher financial capital inflows, attracted by a small rise in the UIP premium, finance the current account deficit. - Higher demand pushes up inflation, inducing the central bank to raise interest rates, leading to an exchange rate appreciation. - Long-run: higher public debt ratio raises foreign investors’ required return; in case (1) long-run real interest rates remain stable because a reduction in the current account and financial inflows offsets the premium effect. - Case 2 — High capital mobility (c_FAO;Y_1 = 1000) (solid green line) - Larger increase in current account deficit than case (1) because deficit is more easily financed by financial inflows, with no increase in the UIP premium. - Slightly larger real exchange rate appreciation, lower inflation, and thus a smaller increase in the nominal interest rate compared to case (1). - Long-run: with much higher capital mobility, higher public debt premium translates directly into higher long-term real interest rates, decreasing steady-state investment and reducing long-term real GDP. - Case 3 — IT with limited capital mobility (c_FAO;Y_1 = 0:1) (solid blue line) - Short run: higher aggregate demand raises output and inflation; foreigners are reluctant to finance the import increase so the UIP premium increases. - Interest rates rise to fight inflation, but not enough to generate required UIP premium increase, so the exchange rate depreciates (instead of appreciating as in case (1)). - Depreciation raises inflation more—and interest rates respond more—than in case (1). - Debt-to-GDP ratio is lower in the short run because higher inflation increases nominal GDP more than the fiscal deficit. - Long run: real GDP barely falls. Capital flows are less sensitive to the UIP premium, so debt-related premium increases do not lead to substantial financial outflows; current account and investment are little changed. A closed capital account insulates the economy from long-run costs of a higher UIP premium (and also from benefits of a fiscal consolidation). - Case 4 — IT with managed exchange rate, limited capital mobility (solid red line) - Authorities follow foreign exchange intervention rule and sell reserves to reduce demand for financial inflows, mitigating the UIP premium increase. - This helps stabilize the exchange rate, inflation, and the policy rate. - Cost: bigger current account deficit financed by selling foreign exchange reserves rather than by financial capital inflows. - Short-run GDP effect about the same as case (3): depreciated real exchange rate in case (3) stimulates exports more than in case (4), but higher interest rates offset. - Case 5 — IT with managed exchange rate, limited capital mobility, low reserves and high public debt (dotted red line) - Initial reserves-to-GDP is 6 percent here, compared to 13 percent in case (4), just above the FXR lower bound of 5 percent where the central bank stops intervening. - Debt-to-GDP ratio is 80 percent here, compared to 50 percent in case (4). - With low reserves and high debt, benefits from managing the exchange rate are lost: depletion of reserves and rise in government debt increase the UIP premium firmly. - UIP premium increase induces a weaker exchange rate (even more than in case (3)), driving inflation up and requiring a more contractionary monetary policy that reduces the positive fiscal expansion impact on private consumption. - Short run: weaker exchange rate more than offsets effects of higher real interest rates on real GDP. - Long run: real GDP declines much more because permanently higher UIP premium increases interest rates, depressing private investment and potential output; weak real exchange rate drives large increase in the current account balance. - Case 6 — Foreign currency-financed deficit (dotted black line) - Same as baseline except increase in government spending financed by dollar-denominated foreign borrowing (treated as part of exogenous capital flows). - Official inflows over-finance imports generated by higher aggregate demand, causing significant exchange rate appreciation—more than even with an open capital account (case (2)). - Appreciation results in endogenous capital outflows, drops in the UIP premium and inflation. - Real GDP growth is lower because appreciation compresses net exports, but consumption is higher. ### Mechanisms and interactions emphasized - Exchange rate response depends critically on degree of capital mobility and central bank interest rate response. - UIP premium dynamics: higher public debt raises required returns; the pass-through of this to long-term real rates depends on capital mobility and reserve buffers. - Reserve usage: using reserves to manage the exchange rate can stabilize inflation and the policy rate but at the cost of reserve depletion that may raise UIP premium if reserves fall near a lower bound. - Financing currency composition matters: foreign currency-financed deficits can cause large appreciation and different distributional outcomes between consumption and net exports. - Short-run vs long-run trade-offs: many scenarios show short-run GDP gains from fiscal expansion, with potential long-run costs to investment and potential output depending on capital mobility, UIP premium response, and reserve/debt levels. *Source: 4.1 Effects of a fiscal expansion — IMF Working Paper (wpiea2023235-print-pdf).* ### 4.5 Monetary policy instruments: drop in external demand ### 4.5 Monetary policy instruments: drop in external demand ### Effects of a transitory drop in external demand - The analysis examines a 2 percent transitory drop in external demand for exports. - In all policy configurations, the reduction in external demand generates: - a contraction in the output gap, and - an increase in the current account deficit. - Restoring external equilibrium calls for a real exchange rate depreciation to activate expenditure switching. ### Policy configurations and central bank response - Fully flexible exchange rate (baseline, solid black line): - Exchange rate depreciation passes through to inflation. - The pass-through induces the central bank to raise the policy interest rate despite the fall in output. - Managed exchange rate (solid red line): - Reduces the size of the depreciation and allows the central bank to pursue a countercyclical policy. - The smaller expenditure-switching effect outweighs the policy benefit, and the fall in the output gap is somewhat larger. - Managed float with low reserves (dotted red line): - If reserves are low such that a further decline raises investors’ required return, the managed float performs worse. - Persistently higher UIP premium induces a decline in investment and potential GDP. ### Role of reserves and the UIP premium - Low reserve levels that raise the UIP premium: - Lead to persistently higher required returns on foreign investment. - Induce declines in investment and potential GDP, worsening macroeconomic outcomes under managed regimes. ### Closing the capital account with administrative CFMs - Closing the capital account through ex ante administrative CFMs (solid blue line): - Reduces the sensitivity of endogenous financial flows to changes in the UIP premium. - Requires a larger exchange rate depreciation, higher inflation, and a higher interest rate to attract financial flows to replace lost foreign export demand and close the BoP. - More of the adjustment falls on the current account. - Greater expenditure switching helps buffer the impact on the output gap. - The lack of countercyclical capital inflows makes consumption more volatile. ### FINEX in action: an Israel example (Box 4) - IFM: the Israel Forecasting Model is a somewhat modified version of the canonical FINEX model focused on short- and long-run fiscal issues. - IFM does not feature FXI, CFM, commodity blocks, or NFA effects on the UIP premium. - IFM includes CPI-linked debt, which represents about half of Israel government debt. - Historical/model-based decompositions and calibration: - The output gap went from 5 percent in 2000 to around -4 percent in 2003, driven initially by export demand and later by consumption and investment declines. - Government debt reached 90 percent of GDP in 2003. - From 2004 the government embarked on fiscal reforms that brought government debt down to around 60 percent of GDP over the next 12 years. - The decline in government absorption had a persistent negative effect on the output gap over the 2005-2008 period. - COVID-19 episode: - The COVID-19 shock drove down private consumption and investment, and hence the output gap. - Government absorption responded counter-cyclically, and transfers increased, which spurred private consumption. - Model-based estimates show the whole ‘COVID-19’ fiscal package significantly mitigated the impact on output and CPI inflation. - Counterfactual scenario without the 2004–2019 fiscal reforms: - Real GDP would have been consistently lower from 2009 onwards—by about 6 percent in 2019—absent the reforms. - Positive long-term impacts of the reforms are driven mainly by the increase in public investment and a decrease in the UIP premium in response to government debt consolidation. *Source: wpiea2023235-print-pdf - 4.5 Monetary policy instruments: drop in external demand* ### Box 5.The calibration of FINEX ### Box 5.The calibration of FINEX ### Calibration approach - Calibration is described as “more of an art than a science,” requiring expertise, intuition, and judgment to balance theoretical assumptions and empirical evidence. - FINEX follows the approach used in IMF technical assistance projects for semi-structural models rather than likelihood-maximizing estimation (for example, Bayesian methods). Parameters are calibrated parsimoniously and gradually to: - allow deeper understanding of model properties; - acknowledge that no model captures all economic characteristics; - reduce biases from breaks in time series, including policy-regime breaks. - A supporting DSGE model may be used to guide calibration (or to provide priors for Bayesian estimation), for example by suggesting cross-equation restrictions. Example: the parameter in front of lagged inflation in the Phillips curve for private consumption c′C1 in a DSGE model is a function of a discount factor β such that c′C1 = 1/(1+β); because discount factor must be smaller than one, c′C1 must be less than 1/2. Caution: DSGE-derived restrictions may be rejected by the data. ### Calibration criteria and stages - Criteria used to ensure accurate and reliable results: - empirical fit; - forecasting performance; - economic coherence; - ability to explain historical data; - consistency of parameter values with econometric estimates; - assessments of trends, cyclical components, and shocks consistent with economic intuition and common wisdom. - The calibration process is iterative and involves these stages: - Definition of the FINEX structure. - Data collection. - Determination of parameters to be calibrated. - Modification of parameter values to meet the previously-defined criteria. ### Data sources and preprocessing - Domestic data (national accounts, fiscal accounts, prices, balance of payments) typically from each country’s Statistical Office, Central Bank, and Ministry of Finance. - External variables (GDP of trading partners, interest rates, exchange rates, price index, commodity prices) from external sources such as the IMF’s WEO, Consensus Forecast, and the World Bank ‘Pink-Sheet.’ - Data must be transformed to be consistent with FINEX’s structure (e.g., adjust frequency for annual model, distinguish flows and stocks). - Transformed data are used for model filtering and computing long-term relationships that determine parameter calibration. ### Parameter taxonomy and steady state calibration - Parameters are divided into three types: - Parameters determining the steady state. - Parameters determining the decomposition between gaps and trends. - Parameters governing transmission mechanisms and policy responses. - Steady state in FINEX: long-term equilibrium where variables follow their balanced growth path. - Steady-state parameters are calibrated so long-term values to which FINEX converges align with observed data (growth rate, price level growth, relative prices, interest rates and risk premium, depreciation of the real exchange rate, GDP ratios of aggregate demand components, fiscal variables, balance of payments). - Although parameter values generally replicate historical means, they also incorporate expert judgment about long-term prospects. - Some long-term relationships are endogenous and only some steady-state aspects can be directly adjusted (example: steady-state fiscal deficit is determined endogenously by debt target, inflation, output growth, interest rates, and exchange rates). ### Trend and cycle decomposition - Kalman smoother is used to estimate unobserved variables (cyclical and trend decomposition) and make forecasts. State-space representation uses FINEX structure as the state equation and a subset of available variables as the measurement equation, assuming zero measurement noise. - Decomposition depends on relative variances of disturbances in cyclical vs trend components: - Usual practice: variance of shocks affecting cyclical components > variance of shocks affecting trend components. - Example: for private investment, variance of the investment gap disturbance is four times greater than the variance of the trend-component disturbance in trend growth of private investment. - Persistence parameters are calibrated so half-life of cyclical processes < half-life of trend processes: - Example: persistence of the cyclical component of private investment has a half-life of less than a year. - Example: half-life of the trend component of real private investment growth is close to 1.5 years. - The trend growth equation for each aggregate-demand component includes a correction mechanism ensuring the trend level converges to the steady state characterized by a constant share of nominal expenditure in GDP. Parameters governing this correction are chosen to guarantee faster convergence of variables in levels than of trend variables. ### Transmission mechanisms and policy parameters - Calibrated transmission parameters include: - substitution between domestic and foreign assets and degree of capital mobility; - monetary policy and fiscal-rule parameters; - sensitivity of exports and imports to the real exchange rate; - import content in components of aggregate demand; - parameters governing transmission of economic activity and relative prices to inflation. - Calibration aims to reflect specific economy characteristics: - degree of capital mobility adjusted to illustrate FX market depth; - persistence in Phillips curve reflects anchoring of inflation expectations; - persistence of nominal interest rates and coefficient on inflation deviations in the monetary rule reflect central bank operation; - fiscal-rule parameters reflect fiscal policy’s aversion to debt deviations from target; - produce reasonable and empirically plausible set of fiscal multipliers. - For external-block dynamics, external data and multivariate estimates used for persistence coefficients and standard deviations. ### Iteration, validation, and practical application - Calibration is an iterative, hands-on, case-by-case process requiring careful attention to detail and repeated adjustments to meet empirical and policy-relevant criteria. - Benchmarks for model performance include empirical fit, forecast performance, economic consistency, historical-data explanation, and comparison with previous econometric estimates. - FINEX is designed for application to countries with imperfect capital mobility and hybrid monetary policy regimes, where monetary/fiscal/reserves interactions matter; it is more complex than traditional gap-trend models but aims to better address pressing policy issues. - Simpler subsets (e.g., traditional ‘four-equation’ QPM) may be preferable for institutions with simple policy regimes or low capacity. *Source: Box 5. The calibration of FINEX, FINEX - A New Workhorse Model for Macroeconomic Forecasting and Policy Analysis (Working Paper No. WP/2023/235).* --- _Source: https://www.imf.org/-/media/files/publications/wp/2023/english/wpiea2023235-print-pdf.pdf_