## wpiea2020295-print-pdf — appendix B and related sections

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### External sector treatment and foreign variables
- The foreign interest rate is approximated by the US rate; this is the only foreign rate included in the Rwanda QPM in the UIP equation.
- Equations for foreign variables are specified in univariate reduced form (not structural).
- Forecasts for foreign variables and commodity prices are exogenized in BNR applications and taken from external sources (WEO and others); domestic projections are conditioned on these external projections.
- Model uses a limited number of countries to approximate the effective external sector to limit practical forecasting burden.

### Money demand block (M3 and reserve money)
- Structure and role:
  - Describes demand for M3 aggregate (m3) and reserve money (rm).
  - Reserve and broad money growth are used as indicator variables about monetary stance.
- Key equations (as presented):
  - Nominal broad money demand: m3_t = m3_t + cpi_t.  (Equation (34) as presented)
  - Real broad money demand decomposed into trend (m3_eq) and gap (m3_gap).
  - Real money gap dynamics: m3_gap_t = c_1 m3_gap_{t-1} + (1−c_1)(c_2 y_gap_nonag_t − c_3 r_hat_t) + ε_t_m3_gap.  (Equation (35) as presented)
  - Equilibrium real broad money growth: Δm3_eq_t = ρ_m3_trend Δm3_eq_{t-1} + (1−ρ_m3_trend)[Δy_trend_t − Δv_t − c_4(r̅_t − r̅_{t-1})] + ε_t_m3_trend.  (Equation (36) as presented)
  - Velocity AR: Δv_t = ρ_Δv Δv_{t-1} + (1−ρ_Δv) Δv_00 + ε_t_Δv.  (Equation (37) as presented)
  - Reserve money: rm_t = m3_t + mult_t.  (Equation (38) as presented)
  - Money multiplier modeled as trend and gap with AR dynamics (Equations (39)–(40) as presented).
- Shocks:
  - ε broad money demand shock and ε velocity shock are formally included.

### Model calibration and parameterization
- Calibration aims to match policy transmission and Rwandan economy particularities.
- Parameter subsets:
  - Steady state parameters (informed by in-sample averages, judgment, forecasting performance, policy objectives).
  - Structural equation coefficients and reduced-form foreign-variable/trend equation coefficients.
  - Standard deviations of shocks calibrated to observed variances; trend components are calibrated to be generally less volatile than gaps.
- Calibration sources and availability:
  - Uses other published models, historical data, and impulse response analysis.
  - Calibrated steady-state parameter values and structural coefficients provided in Annex B; remaining parameters including standard deviations of shocks can be provided upon request.
- Important caution:
  - An excessively high standard deviation for the cost-push shock in the inflation equation can produce an output gap estimate largely uninformed by inflation developments.

### Impulse response experiments and model properties
- Comparison:
  - Impulse responses compare Rwanda QPM (exchange rate management as in BNR framework) with FlexER (floating exchange rate). Responses are deviations from steady state.
- Cost-push shock (1 p.p. increase in core inflation):
  - Headline inflation rises; central bank raises policy interest rate and initially keeps nominal depreciation unchanged.
  - Real exchange rate appreciates → negative real exchange rate gap → tighter real monetary conditions.
  - Non-agricultural output gap turns negative; inflation gradually declines below target.
  - Central bank ultimately allows higher nominal depreciation to mitigate undershooting of the inflation target.
- Demand shock (1 p.p. increase in non-agricultural output gap):
  - Inflation rises; central bank increases policy rate and allows marginally slower nominal depreciation.
  - Real exchange rate temporarily overvalued; real interest rate above equilibrium tightens conditions and restores capacity utilization.
  - Overvalued currency and subsiding cost pressures slow inflation back to target.
- Agricultural (good harvest) shock (1 p.p. increase in agricultural production):
  - Food prices fall; headline inflation drops below target.
  - Central bank cuts policy rate while initially keeping nominal depreciation unchanged.
  - Real exchange rate depreciates (temporarily undervalued), non-agricultural capacity utilization rises; domestic and imported costs pick up, returning inflation to target.
- Fiscal impulse (simulated):
  - Simulated as a 1 percent increase of structural budget deficit and 1 percent increase of exceptional expenditures over 1 year; fiscal impulse peaks at 2 percent at the start of simulation.
  - Boosts non-agricultural output gap and inflationary pressures; central bank tightens policy.
  - Nominal exchange rate appreciates initially then depreciates as domestic price level rises.
  - Fiscal impulse (change of structural deficit/GDP) becomes negative in the second year; negative impulse enforces monetary tightening and pushes non-agricultural output gap negative.
  - Total GDP effects remain positive assuming a positive fiscal multiplier.
  - Government deficit/GDP widens consistent with the positive fiscal impulse.
  - Model does not endogenously model debt stabilization; simulations assume external fiscal projections and planned deficits are sustainable. Simulating a debt-threatening path would require combining fiscal impulse with a shock raising the country risk premium.
- Aid inflows shock:
  - Aid inflows reaching 1 percent of GDP for 1 year boost domestic demand; transmission and monetary response similar to fiscal impulse.
  - Inflation variability is lower under float compared to current regime because a free float allows accommodation via exchange rate depreciation.
- Exchange rate management trade-off:
  - BNR interventions to smooth exchange rate volatility plus use of policy interest rate as operational target make policy transmission differ from a flexible exchange rate framework.
  - Limited exchange rate variability reduces exchange rate role in macro stabilization and increases variability of inflation, real output, and interest rates.
  - Increasing exchange rate flexibility or making depreciation target respond only to inflation deviation could increase macro stabilization role of exchange rate; similar effects arise if exchange rate responds more to interest rate differential.

### Model simulations, in-sample performance, and historical decomposition
- Applications:
  - (i) In-sample simulations to check ex-post forecasting ability.
  - (ii) Filtration/decomposition of historical data into structural shocks.
- In-sample simulation setup:
  - Start from 2009Q1.
  - All external variables are assumed known over forecasting horizon.
  - All other observed variables are known only until the quarter preceding each forecast over the next 8 quarters.
  - No expert judgments added.
- In-sample findings (2009Q1–2019Q4):
  - Model-based forecasts broadly do not deviate systematically from data; model matches actual data reasonably well, notably for 2009-2013.
  - In 2014-2016 model predicted higher headline and core inflation and higher nominal interest rate than actual.
  - Inflationary bias in 2014-2016 arose from faster predicted nominal depreciation driven by a higher predicted country risk premium; the unobserved risk premium peaked in early 2015 and sharply declined afterwards, a drop not predicted in-sample.
  - Conditioning nominal exchange rate dynamics and the premium (treating them as known) removes the upward bias in headline and core inflation projections for 2014-2015.
  - Remaining upward bias after conditioning is attributable to a more accommodative policy stance the model predicts for 2012-2013 than actually occurred; counterfactual without the 2012-2013 rate hikes would bring actual inflation closer to model projections and the 5 percent benchmark.

### Forecasting performance: QPM versus Random Walk (RW)
- Overall: QPM outperforms RW for majority of key variables and horizons (1 to 8 quarters), with exceptions.
- Selected QPM/RW ratios by horizon:
  - Policy Interest Rate: 1Q: 1.34, 2Q: 1.32, 3Q: 1.14, 4Q: 1.04, 5Q: 0.97, 6Q: 0.91, 7Q: 0.83, 8Q: 0.71.
  - Nominal Depreciation RWF/USD, YoY: 1Q: 1.13, 2Q: 1.10, 3Q: 1.05, 4Q: 1.05, 5Q: 1.24, 6Q: 1.40, 7Q: 1.50, 8Q: 1.57.
- Table 1 (in-sample forecasting performance QPM vis-à-vis RW, 2009Q1–2019Q4) — QPM/RW ratios by horizon:
  - Headline CPI Inflation, YoY: 0.49, 0.50, 0.49, 0.53, 0.49, 0.46, 0.41, 0.40
  - Core Inflation, YoY: 0.51, 0.50, 0.48, 0.52, 0.49, 0.50, 0.51, 0.54
  - Food Inflation, YoY: 0.56, 0.57, 0.54, 0.60, 0.55, 0.48, 0.41, 0.40
  - Policy Interest Rate: 1.34, 1.32, 1.14, 1.04, 0.97, 0.91, 0.83, 0.71
  - Nominal Depreciation RWF/USD, YoY: 1.13, 1.10, 1.05, 1.05, 1.24, 1.40, 1.50, 1.57
  - Real GDP Growth, YoY: 0.57, 0.49, 0.43, 0.42, 0.54, 0.57, 0.63, 0.60
  - Real Non-agricultural GDP Growth, YoY: 0.40, 0.34, 0.31, 0.33, 0.39, 0.45, 0.48, 0.50
- Interpretative notes:
  - Interest rate and nominal depreciation are policy variables; in-sample simulations set them endogenously to deliver inflation to the benchmark, complicating direct comparison to historical policy actions.
  - Conditioning nominal exchange rate path as known improves in-sample forecasts of non-agricultural GDP growth.

### Drivers of actual inflation outcomes (2017–2019) and model shortfalls
- Observed deviations:
  - Predicted high food and core inflation did not materialize.
  - Food prices declined at end-2018 due to good domestic harvests despite rising world food prices.
  - Core inflation was surprisingly low in 2018-2019 while the model predicted rising inflation.
- Identified forces:
  - Disinflationary shocks identified in filtration exercises.
  - Limited food inflation constrained core inflation via relative prices.
  - Actual monetary policy was tighter than the model predicted starting 2017, contributing to lower-than-predicted inflation.
- Historical counterfactual:
  - From ex-post perspective, had there been no hike in interest rates in 2012-2013, inflation would have been closer to target in 2014–2015.

### Historical data filtration, real marginal costs, and inflation decomposition
- Methodology:
  - Kalman filtration used to identify unobserved variables and structural shocks; historical decomposition attributes variable dynamics to shocks.
- Timing and drivers:
  - Real marginal cost developments precede inflation dynamics for both core and food inflation.
  - Non-agricultural output gap was mostly disinflationary over 2012-2019, reflecting moderate GDP growth.
  - A positive real exchange rate gap sometimes offset low demand; on average total costs constrained core inflation.
  - Food inflation driven mainly by local supply fluctuations and world food prices; world food prices and good local harvests produced strong disinflationary pressures during 2016-2017.
  - World food prices became inflationary in 2018 but domestic food inflation remained subdued until a below-average harvest in H2 2019 which contributed to food price acceleration.

### Structural shock decomposition insights
- Core inflation:
  - Substantially impacted by external shocks; world food and oil prices sharply declined in 2009-2010, reducing inflation despite accommodative policy.
  - External developments relatively neutral for core inflation in 2011-2015.
  - Deviations driven mostly by cost-push shocks: inflationary in most of 2011-2013 and disinflationary in 2014-2016.
  - During 2017-2019 foreign developments (mainly oil) and low domestic demand constrained core inflation; tight monetary policy in 2017-2018 helped prevent core inflation rises.
- Food inflation:
  - Mostly shaped by external factors (world food prices) and supply shocks; domestic agricultural shocks had milder effects compared to external factors.
  - High share of supply shocks indicates agricultural output gap may capture only part of local supply effects on food prices.

### Policy implications and recommended model and capacity improvements
- Institutional progress:
  - Tangible progress in modeling capacity at BNR; forecasting team clearer responsibilities; model-based analysis gained prominence in MPC discussions.
- Recommended model and data improvements:
  - Develop satellite models for: (i) agricultural sector, (ii) fiscal sector, (iii) banking sector and credit.
  - Obtain near-term projections for agricultural sector to better capture volatile agricultural output and food supply.
  - Conduct agricultural producer surveys and evaluate weather–harvest relationships for better current/expected output gauges.
  - Elaborate the external sector by:
    - (i) specifying relationships in more structural form,
    - (ii) expanding coverage of countries and commodities.
  - Prioritize introducing structural foreign-sector relationships to enable alternative macro scenarios (e.g., Global VARs or IMF GPM prototypes).
  - Clarify UIP relationship and make country risk premium a function of trade flows and terms-of-trade to link global commodity outlooks with Rwanda’s trade balance and QPM projections.
- Policy strategy and implementation improvements:
  - Expand FPAS modeling capacity alongside advances in policy strategy, implementation, and external communications.
  - Greater exchange rate flexibility typically strengthens policy transmission and macro stabilization under price-based frameworks.
  - Improve open market operations and liquidity management to align announced policy rate, marginal rate in OMOs, and short-term interbank rate.
  - Publish macroeconomic projections and conditional forecasts of the interest rate and exchange rate to communicate BNR policy intentions.
  - Publishing a forecast of the policy rate over the policy horizon (benchmark forward yield curve) would aid commercial banks in pricing longer-term financial products, improving transmission to market rates.
  - Use concerted FPAS, policy strategy, operations, and communications to inform demand for further technical assistance.

### Selected calibrated parameter values (from Appendix C)
- Real GDP – Agriculture Block:
  - w_ag = 0.3
  - ρ_ag_trend = 0.75
  - b_11 = 0.4
  - Δy_trend_00^ag = 8.158
- Real GDP – Non-agriculture Block:
  - b_12 = 0.75
  - b_22 = 0.1
  - b_32 = 0.3
  - b_42 = 0.1
  - b_52 = 0.1
- Real interest rate:
  - ρ_rbar = 0.8
  - r̅_00 = 2
- Real exchange rate:
  - ρ_z_trend = 0.8
  - ρ_Δzbar = 0.85
  - b_15 = 0.035
  - b_15_alt = 0.5
  - Δz̅_00 = 0
- Relative prices:
  - ρ_rp_trend = 0.8
  - Δrp_trend_00_core = -1
  - Δrp_trend_00_food = 1
- Inflation – Core:
  - a_11 = 0.5
  - a_21 = 0.2
- Inflation – Food:
  - a_12 = 0.5
  - a_23 = 0.3
  - a_25 = 0.7
  - a_33 = 1.6
- Inflation – Energy:
  - a_13 = 0.2
  - a_34 = 0.3
  - a_35 = 0.7
- Money demand block:
  - c_1 = 0.5
  - c_2 = 1.5
  - c_3 = 0.5
  - c_4 = 0.5
  - ρ_m3_trend = 0.8
  - ρ_Δv = 0.95
  - Δv_00 = -8
  - Δmult_eq_00 = 3
  - ρ_mult_trend = 0.9
  - ρ_mult_eq = 0.5
- World oil and food price processes:
  - ρ_rp_oil_trend = 0.75
  - ρ_rp_oil_gap = 0.9
  - Δrp_oil_00 = 0
  - ρ_rp_food_trend = 0.75
  - ρ_rp_food_gap = 0.9
  - Δrp_food_00 = 0
- Monetary policy – exchange rate and interest rates:
  - w_uip = 0.5
  - f_15 = 0.3
  - f_23 = 0.85
  - e_1 = 0.8
  - g_1 = 0.8
  - g_2 = 0.25
  - g_3 = 0.2
- External sector and market interest rates:
  - w_ext = 0.6
  - ρ_rbar_star = 0.9
  - r̅_00^* = 1
  - ρ_prem = 0.6
  - prem_00_dom = 1.5
  - prem_00_foreign = 1.5

*Source: wpiea2020295-print-pdf - appendix B). The foreign interest rate is approximated by the US rate this is the only foreign rate, (authors’ calculations as provided in the source content).*

### appendix B). The foreign interest rate is approximated by the US rate this is the only foreign rate,

### wpiea2020295-print-pdf - appendix B). The foreign interest rate is approximated by the US rate this is the only foreign rate,

### External sector treatment and foreign variables
- The foreign interest rate is approximated by the US rate; this is the only foreign rate included in the Rwanda QPM in the UIP equation.
- Equations for foreign variables are specified in univariate reduced form (not structural).
- Forecasts for foreign variables and commodity prices are not produced endogenously by these equations when the QPM is applied in macroeconomic and policy projections by the BNR; instead, forecasts from external sources like WEO and others are exogenized and used.
- Domestic projections are therefore “conditioned” on external projections from these sources.
- The model uses a limited number of countries to approximate the effective external sector by design because practical application requires collecting forecasts for all external variables; expanding the model requires trading off increased coverage with the practical burden of collecting external forecasts.

### Money demand block (M3 and reserve money)
- Money demand block describes demand for M3 aggregate (푚3) and reserve money (푟푚).
- Reserve and broad money growth are used by authorities as indicator variables about monetary stance.
- Nominal broad money demand equation:
  - 푚3 ௧ = 푚3 ௧ + 푐푝푖 ௧.  (Equation (34) as presented)
- Real broad money demand decomposition:
  - Real demand split into trend (푚3 തതതത) and gap (푚3 ෢).
  - Real money holding depends on the real non-agricultural output gap and the real interest rate gap:
    - 푚3 ෢ ௧ = 푐 ଵ 푚3 ෢ ௧ିଵ + (1−푐 ଵ)(푐 ଶ 푦ො ௧ ௡௔௚௥ − 푐 ଷ 푟̂ ௧) + 휀 ௧ ௠ଷ ෢.  (Equation (35) as presented)
    - 휖 ௠ଷ ෢ is the broad money demand shock.
- Equilibrium changes in real broad money demand align with country fundamentals (potential GDP growth) adjusted by changes in velocity, Δ푣:
  - Δ푚3 തതതത ௧ = 휌 ௠ଷ തതതതത Δ푚3 തതതത ௧ିଵ + (1−휌 ௠ଷ തതതതത)[Δ푦ത ௧ − Δ푣 ௧ − 푐 ସ(푟̅ ௧ − 푟̅ ௧ିଵ)] + 휀 ௧ ഑௠ଷ തതതതത.  (Equation (36) as presented)
  - 휖 ഑௠ଷ തതതതത is the shock to equilibrium real broad money demand growth.
- Changes in velocity follow an AR process:
  - Δ푣 ௧ = 휌 ഑௩ Δ푣 ௧ିଵ + (1−휌 ഑௩) Δ푣 ௦௦ + 휀 ௧ ഑௩.  (Equation (37) as presented)
  - 휖 ഑௩ is a velocity shock.
- Reserve money derived from broad money and money multiplier:
  - 푟푚 ௧ = 푚3 ௧ + 푚푢푙푡 ௧.  (Equation (38) as presented)
- Money multiplier modeled as trend and gap:
  - Δ푚푢푙푡 തതതതതതത ௧ = 휌 ௠௨௟௧ തതതതതതത Δ푚푢푙푡 ௧ିଵ + (1−휌 ௠௨௟௧ തതതതതതത) Δ푚푢푙푡 തതതതതതത ௦௦ + 휀 ௧ ഑௠௨௟௧ തതതതതതத.  (Equation (39) as presented)
  - 푚푢푙푡 ෣ ௧ = 휌 푚푢푙푡 ෣ ௧ିଵ + 휀 ௧ ௠௨௟௧ ෣.  (Equation (40) as presented)

### Model calibration and parameterization
- Calibration aims to match the policy transmission mechanism and Rwandan economy particularities.
- Parameter subsets:
  - Steady state parameters (informed by in-sample averages, judgments about changes/breaks, in-sample forecasting performance, and policy objectives like inflation target).
  - Equation coefficients in structural equations for domestic variables and reduced-form foreign-variable/trend equations (guided by matching observed data and smooth long-term trends).
  - Standard deviations of shocks (calibrated accounting for observed variance; ensure unobserved/estimated trends are generally less volatile than gaps and observed variables).
- Calibration also uses other published models, historical data, and impulse response analysis.
- Calibrated steady-state parameter values and structural coefficients are provided in Annex B; remaining parameters including standard deviations of shocks can be provided upon request.
- Note on standard deviation calibration: an excessively high standard deviation for the cost-push shock in the inflation equation can lead to an output gap estimate that is largely uninformed by inflation developments, contradicting macroeconomic priors.

### Impulse response experiments and model properties
- Impulse responses compare the Rwanda QPM (exchange rate management as in BNR framework) with a FlexER model variant (floating exchange rate). Responses are deviations from steady-state.
- Cost-push shock:
  - A 1 p.p. increase in core inflation pushes up headline inflation.
  - Central bank raises policy interest rate and initially keeps nominal exchange rate depreciation unchanged.
  - Stable nominal exchange rate plus higher domestic prices causes real exchange rate appreciation and a negative real exchange rate gap, tightening real monetary conditions.
  - Non-agricultural output gap turns negative; disinflationary pressures appear on domestic and imported costs; inflation gradually declines below target.
  - Central bank eventually allows higher nominal exchange rate depreciation to mitigate undershooting of the inflation target.
- Demand shock:
  - A 1 p.p. increase of the non-agricultural output gap raises inflation.
  - Central bank increases monetary policy rate and allows marginally slower nominal depreciation.
  - Temporarily overvalued real exchange rate and real interest rate above equilibrium lead to tight monetary conditions, counteracting demand pressures and restoring capacity utilization.
  - Overvalued real domestic currency and subsiding domestic cost pressures help slow inflation back to target.
- Agricultural (good harvest) shock:
  - A 1 p.p. increase in agricultural production pushes down food prices; headline inflation drops below target.
  - Central bank cuts policy rate while initially keeping nominal exchange rate depreciation unchanged.
  - Domestic price decline causes real exchange rate depreciation (temporarily undervalued), creating inflationary pressures; non-agricultural sector capacity utilization rises above normal.
  - Domestic and imported costs pick up and help bring inflation back to target.
- Fiscal impulse (positive fiscal shock):
  - Simulated as a 1 percent increase of structural budget deficit and a 1 percent increase of exceptional expenditures, both over the 1 year horizon; fiscal impulse peaks at 2 percent at the start of simulation.
  - Positive fiscal impulse boosts non-agricultural output gap and generates inflationary pressures; central bank tightens monetary policy.
  - Nominal exchange rate appreciates initially then depreciates as domestic price level rises.
  - The fiscal impulse (defined as change of structural deficit/GDP) becomes negative in the second year of simulation; negative impulse enforces monetary tightening and pushes the non-agricultural output gap negative.
  - Total GDP effects remain positive given the assumption of a positive fiscal multiplier.
  - Government deficit/GDP widens consistently with the positive fiscal impulse.
  - Model does not endogenously model debt and its stabilization; simulations assume external fiscal projections from Ministry of Finance and Economic Planning and assume planned deficits are sustainable.
  - To simulate a debt path threatening sustainability would require combining the fiscal impulse with a shock increasing the country risk premium.
- Aid inflows shock:
  - Aid inflows reaching 1 percent of GDP for 1 year boost domestic demand (non-agricultural gap); transmission and monetary policy response are similar to the fiscal impulse.
  - Variability of inflation is lower under the float compared to the current regime because a free float allows accommodation through exchange rate depreciation.
- Exchange rate management trade-off:
  - BNR’s market interventions to smoothen exchange rate volatility plus use of policy interest rate as operational target make Rwanda’s policy transmission differ from a flexible exchange rate framework.
  - Limited exchange rate variability under current framework reduces exchange rate’s role in macro stabilization and increases variability of inflation, real output, and interest rates.
  - The trade-off between stabilizing inflation and stabilizing the exchange rate is implied by the exchange rate targeting rule (equation (18)); an illustration is given with the demand shock where exchange rate smoothing limits depreciation that could stabilize the economy faster.
  - Increasing exchange rate flexibility or making the depreciation target respond only to inflation deviation could increase the macro stabilization role of the exchange rate; qualitatively similar effects arise if exchange rate responds more to the interest rate differential.

### Model simulations, in-sample performance, and historical decomposition
- Applications:
  - (i) In-sample simulations to check ex-post forecasting ability.
  - (ii) Filtration/decomposition of historical data into structural shocks to assess historical macroeconomic developments.
- In-sample simulation setup:
  - Start from 2009Q1.
  - All external (foreign) variables are assumed known over the forecasting horizon.
  - All other observed variables are known only until the quarter preceding every forecast realization over the next 8-quarters.
  - No expert judgments are added in these exercises.
- In-sample findings:
  - Model-based forecasts broadly do not deviate systematically from data; model matches actual data reasonably well, notably for 2009-2013.
  - Model-based forecasts in 2014-2016 predict higher than actual headline and core inflation and correspondingly higher nominal interest rate.
  - Inflationary bias in 2014-2016 arises from faster predicted nominal exchange rate depreciation driven by a higher predicted country risk premium.
  - The unobserved risk premium (estimated/filtered with Kalman Filter) peaked in early 2015 and sharply declined afterwards; the drop was not predicted in in-sample simulations and led to faster predicted depreciation relative to actual.
  - Conditioning the nominal exchange rate dynamics and the premium (i.e., treating them as known) removes the upward bias in headline and core inflation projections for 2014-2015.
  - Remaining upward bias in 2014-2015 inflation projections after conditioning is attributable to a more accommodative policy stance (lower interest rate) that the model predicts compared to the actual stance in 2012-2013; had interest rates in 2012-2013 stayed lower, actual inflation in 2014–2015 would have been closer to model projections and the 5 percent benchmark.
- Simulation details and notes:
  - Impulse responses presented compare solid line = Rwanda QPM and dashed line = FlexER variant; bars (right axis) show differences between IRs for the QPM and FlexER.
  - All IRs are authors’ calculations.
  - The model’s calibrated values of steady-state parameters and coefficients are in Annex B; remaining parameters including standard deviations of shocks available upon request.

*Source: wpiea2020295-print-pdf - appendix B). The foreign interest rate is approximated by the US rate this is the only foreign rate, (authors’ calculations as provided in the source content).*

### 2019. This is driven by the predicted high food and core inflation which did not take place actually.

### wpiea2020295-print-pdf - 2019

### Forecasting performance of the QPM versus Random Walk (RW)
- QPM outperforms the RW benchmark for the majority of key variables and forecasting horizons (1 to 8 quarters), with notable exceptions:
  - Policy Interest Rate: QPM/RW ratios greater than 1 at short horizons (1Q: 1.34, 2Q: 1.32, 3Q: 1.14, 4Q: 1.04) before falling below 1 at longer horizons (5Q: 0.97, 6Q: 0.91, 7Q: 0.83, 8Q: 0.71).
  - Nominal Depreciation RWF/USD, YoY: QPM underperforms RW at all horizons (1Q: 1.13, 2Q: 1.10, 3Q: 1.05, 4Q: 1.05, 5Q: 1.24, 6Q: 1.40, 7Q: 1.50, 8Q: 1.57).
- Table 1: In-sample forecasting performance of the QPM vis-à-vis Random Walk (RW) benchmark during 2009Q1 – 2019Q4
  - Headline CPI Inflation, YoY: 0.49, 0.50, 0.49, 0.53, 0.49, 0.46, 0.41, 0.40
  - Core Inflation, YoY: 0.51, 0.50, 0.48, 0.52, 0.49, 0.50, 0.51, 0.54
  - Food Inflation, YoY: 0.56, 0.57, 0.54, 0.60, 0.55, 0.48, 0.41, 0.40
  - Policy Interest Rate: 1.34, 1.32, 1.14, 1.04, 0.97, 0.91, 0.83, 0.71
  - Nominal Depreciation RWF/USD, YoY: 1.13, 1.10, 1.05, 1.05, 1.24, 1.40, 1.50, 1.57
  - Real GDP Growth, YoY: 0.57, 0.49, 0.43, 0.42, 0.54, 0.57, 0.63, 0.60
  - Real Non-agricultural GDP Growth, YoY: 0.40, 0.34, 0.31, 0.33, 0.39, 0.45, 0.48, 0.50
- Interpretative notes from the source:
  - Both interest rate and nominal depreciation are policy variables; in-sample simulations assume they are set by the model to deliver inflation back to the benchmark (target), which may make direct comparison with actual monetary policy settings inappropriate if the historical policy framework relied less on interest rate steering.
  - Assuming the nominal exchange rate path is known improves in-sample forecasts of non-agricultural GDP growth, moving them closer to actual data over the whole range.

### Drivers of actual inflation outcomes (2017–2019) and model shortfalls
- Observed deviations:
  - Predicted high food and core inflation did not materialize in practice.
  - Food prices in Rwanda significantly declined at the end of 2018 on the back of relatively good domestic harvests despite rising world food prices.
  - Core inflation was surprisingly low during 2018-2019 while the model predicted rising inflation.
- Identified macroeconomic forces and shocks:
  - Disinflationary shocks during this period were identified by the model in the filtration exercise.
  - Limited food inflation constrained core inflation via the effect of relative prices.
  - Starting from 2017, the model predicted a more accommodative monetary policy than actually took place; the tighter actual monetary policy contributed to lower-than-predicted inflation.
- Historical context and counterfactual:
  - From the ex-post perspective, had there been no hike in interest rates in 2012-2013, inflation would have been closer to the target in 2014–2015.

### Historical data filtration, real marginal costs, and inflation decomposition
- Methodology:
  - Kalman filtration (KF) is used to match actual data with the model and identify unobserved variables including structural shocks.
  - Filtration outcomes present unobserved variables driving inflation, the output gap, and the real exchange rate gap.
  - Historical decomposition to shocks uses the filtration to show which structural shocks affected variable dynamics.
- Findings on real marginal costs and timing:
  - Real marginal cost developments precede inflation dynamics for both core and food inflation.
  - Figure V.3 (as described): Non-agricultural output gap (approximating domestic cost pressures) was mostly disinflationary over 2012-2019, reflecting relatively moderate GDP growth compared to earlier periods.
  - Positive real exchange rate gap at times offset low demand and domestic cost pressures, but on average total costs constrained core inflation.
  - In 2018-2019 the output turned above neutral while a positive real exchange rate gap persisted, leading to a gradual increase in core Q-o-Q inflation toward the end of the sample.
- Food inflation specifics (Figure V.4 narrative):
  - Fluctuations in local supply of agricultural products together with world food prices were the main drivers of highly volatile food price inflation.
  - World food prices and a good local harvest produced substantial disinflationary pressures on food prices during 2016-2017, pushing food inflation down from its end-2016 peak.
  - World food prices switched from disinflationary to inflationary pressures in 2018, but domestic food inflation remained subdued, bringing headline inflation close to the two percent lower bound of the interval around the inflation target.
  - Drag on costs diminished starting from the second half of 2018, and food price inflation started to accelerate in 2019.

### Structural shock decomposition insights
- Decomposition general points:
  - Decomposition should show that variable dynamics are not driven solely by their “own” shock and that the macroeconomic story matches experts’ intuition.
  - Core and food inflation are analyzed as deviations from their respective implicit targets.
- Core inflation decomposition (Figure V.5 narrative):
  - Dynamics of core inflation were substantially impacted by external shocks.
  - World food and oil prices sharply declined in 2009-2010, pushing down inflation globally and in Rwanda despite accommodative monetary policy.
  - External developments were relatively neutral for Rwandan core inflation in 2011-2015.
  - Core inflation deviations were driven mostly by cost-push (supply) shocks: inflationary in most of 2011-2013 and disinflationary in 2014-2016.
  - During 2017-2019 foreign developments (mainly oil prices) and low domestic demand created constrained inflation; these were only partly offset by pro-inflationary cost-push shocks.
  - Tight monetary policy stance during 2017-2018 started to prevent increases in core inflation.
- Food inflation decomposition (Figure V.6 narrative):
  - Food price inflation was mostly shaped by external factors, particularly world food prices, and supply shocks together with shocks to domestic agricultural production.
  - Domestic agricultural shocks had relatively mild effects compared to external factors.
  - High share of supply shocks reflects the high volatility of food price inflation and suggests the agricultural output gap may capture only part of local supply effects on food prices.
  - World food prices declined significantly in 2009-2010, slowing food price inflation in Rwanda despite domestic inflationary cost-push shocks and monetary policy accommodation.
  - World food prices had an inflationary impact during 2011-2013 and a disinflationary effect in 2014-2015.
  - Above-average harvests and disinflationary supply reduced food inflation despite moderate rises in world food prices.
  - Below-average harvest in the second half of 2019 contributed to acceleration of food price inflation.

### Policy implications and recommended model and capacity improvements (Conclusion and way ahead)
- Institutional and capacity progress:
  - Tangible progress in developing modeling capacity at the BNR to support decision making in the modernized price-based policy framework.
  - The forecasting team’s contours and responsibilities became clearer; the forecasting cycle is better organized.
  - BNR staff acquired and continue to develop the core QPM and near-term forecasting and nowcasting tools that inform medium-term macroeconomic projections.
  - Model-based analysis and forecasting gained a more prominent role in staff policy presentations and policy discussions at MPC meetings.
- Suggested avenues for further FPAS development:
  - Develop a set of satellite models to support sectoral experts and cover:
    - (i) agricultural sector,
    - (ii) fiscal sector,
    - (iii) banking sector and credit.
  - Obtain near-term projections for the agricultural sector to better capture volatile agricultural output and food supply, given their major implications for price dynamics.
  - Conduct surveys of agricultural producers and evaluate relationships between weather conditions and harvests to better gauge current and expected output.
  - Further elaborate the external sector in the model by:
    - (i) specifying relationships in a more structural form (as opposed to reduced form AR processes),
    - (ii) expanding coverage in terms of number of countries and commodities.
  - Prioritize introducing structural relationships to enable formulation of alternative macroeconomic scenarios of global developments because structural relationships deliver responses of all foreign variables to structural shocks in the foreign sector.
  - Consider developing a joint satellite model for the external sector (e.g., Global VARs (GVAR) or IMF’s Global Projection Model (GPM) as prototypes) potentially undertaken jointly by central banks from the EAC to share costs.
  - Clarify the UIP relationship and make the country risk premium a function of trade flows and terms-of-trade to link global commodity outlooks with Rwanda’s trade balance and QPM projections of the country risk premium and the exchange rate.
- Policy strategy and implementation recommendations:
  - Expanding modelling capacity and FPAS should be accompanied by advances in policy strategy, policy implementation framework, and external communications.
  - Greater exchange rate flexibility typically strengthens policy transmission and macroeconomic stabilization under price-based frameworks and moves focus to price stability.
  - Improve conduct of open market operations and liquidity management to ensure alignment among announced policy rate, the marginal rate in OMOs, and the short-term interbank market rate to eliminate conflicting policy signals.
  - Publish macroeconomic projections and conditional forecasts of the interest rate and exchange rate to communicate BNR policy intentions to market participants.
  - Publishing the forecast of the policy rate over the policy horizon (benchmark forward yield curve) would provide critical input for commercial banks to price longer-term financial products, improving transmission of policy expectations to market rates for bonds, loans, and deposits.
  - Concerted efforts across FPAS work, policy strategy, operations, and communications should inform demand for further technical assistance, including from the IMF.

*Source: wpiea2020295-print-pdf - 2019*

### APPENDIX A. Model Variables

### APPENDIX A. Model Variables

### Variable definitions — Real activity and output
- y : Real GDP, 100*ln  
- Δy : Real GDP growth, annualized q-o-q, percent  
- y_gap (푦ො) : Output gap, percent  
- y_trend (푦ത) : Potential GDP, 100*ln  
- y_ag (푦
௔௚௥) : Real agricultural GDP, 100*ln  
- Δy_ag (Δ푦
௔௚௥) : Real agricultural GDP growth, annualized q-o-q, percent  
- y_gap_ag (푦ො
௔௚௥) : Agricultural output gap, percent  
- y_trend_ag (푦ത
௔௚௥) : Potential agricultural GDP, 100*ln  
- y_nonag (푦
௡௔௚௥) : Real non-agricultural GDP, 100*ln  
- Δy_nonag (Δ푦
௡௔௚௥) : Real non-agricultural GDP growth, annualized q-o-q, percent  
- y_gap_nonag (푦ො
௡௔௚௥) : Non-agricultural output gap, percent  
- y_trend_nonag (푦ത
௡௔௚௥) : Potential non- agricultural GDP, 100*ln  
- disc : GDP discrepancy, 100*ln  
- Δdisc : GDP discrepancy growth, annualized q-o-q, percent

### Monetary, exchange rate, and interest rate variables
- rmci (푟푚푐푖) : Real monetary condition index, percent  
- z : Real exchange rate, 100*ln  
- z_bar (푧̅) : Equilibrium real exchange rate, 100*ln  
- Δz_bar (Δ푧̅) : Equilibrium real exchange rate depreciation, annualized q-o-q, percent  
- z_hat (푧̂) : Real effective exchange rate gap, percent  
- E_t Δz_t+1 (퐸
௧
Δ푧
௧ାଵ) : Expected equilibrium real exchange rate depreciation at t for t+1, annualized q-o-q, percent  
- r : Real interest rate, percent  
- r_bar (푟̅) : Equilibrium real interest rate, percent  
- r_hat (푟̂) : Real interest rate gap, percent  
- i_policy (푖
ெ௉) : Nominal policy interest rate, percent p.a.  
- i_neutral (푖
ே௘௨௧௥௔௟) : Nominal neutral interest rate, percent p.a.  
- i_interbank (푖) : Nominal interbank interest rate, percent p.a.  
- prem_interbank (푝푟푒푚
ூ஻) : Premium of interbank rate above the policy interest rate, percent p.a.  
- prem (푝푟푒푚) : Country risk premium, percent

### Prices and inflation (CPI components and related)
- cpi : Headline CPI, 100*ln  
- cpi_core (푐푝푖
஼) : Core CPI, 100*ln  
- cpi_food (푐푝푖
ி) : Food CPI, 100*ln  
- cpi_energy (푐푝푖
ா) : Energy CPI, 100*ln  
- π : Headline CPI inflation, annualized q-o-q, percent  
- π_core (휋
஼) : Core CPI inflation, annualized q-o-q, percent  
- π_food (휋
ி) : Food CPI inflation, annualized q-o-q, percent  
- π_energy (휋
ா) : Energy CPI inflation, annualized q-o-q, percent  
- π4 : Headline CPI inflation, y-o-y, percent  
- E_t π4_t+1 (퐸
௧
휋4
௧ାଵ) : Expected headline CPI inflation in time t for t+1, y-o-y, percent  
- π4_target (휋4
்௔௥) : Inflation target for headline inflation, y-o-y, percent  
- π4_dev (휋4
஽௘௩) : Inflation deviation from the target, p.p.  
- rmc_core (푟푚푐
஼) : Real marginal costs – core inflation, percent  
- rmc_food (푟푚푐
ி) : Real marginal costs – food inflation, percent  
- rmc_energy (푟푚푐
ா) : Real marginal costs – energy inflation, percent

### Relative prices (component to headline and world prices)
- rp_core (푟푝
஼) : Relative price of core to headline, 100*ln  
- rp_core_eq (푟푝തതത
஼) : Equilibrium relative price of core to headline, 100*ln  
- Δrp_core_eq (Δ푟푝തതത
஼) : Equilibrium relative price growth – core to headline, annualized q-o-q, percent  
- rp_core_gap (푟푝ෞ
஼) : Relative price gap – core to headline, percent  
- rp_food (푟푝
ி) : Relative price of food to headline, 100*ln  
- rp_food_eq (푟푝തതത
ி) : Equilibrium relative price of food to headline, 100*ln  
- Δrp_food_eq (Δ푟푝തതത
ி) : Equilibrium relative price growth – food to headline, annualized q-o-q, percent  
- rp_food_gap (푟푝ෞ
ி) : Relative price gap – food to headline, percent  
- rp_energy (푟푝
ா) : Relative price of energy to headline, 100*ln  
- rp_energy_eq (푟푝തതത
ா) : Equilibrium relative price of energy to headline, 100*ln  
- Δrp_energy_eq (Δ푟푝തതത
ா) : Equilibrium relative price growth – energy to headline, annualized q-o-q, percent  
- rp_energy_gap (푟푝ෞ
ா) : Relative price gap – energy to headline, percent  
- rp_world_oil (푟푝
௪௢௜௟) : Relative price of world oil to US CPI, 100*ln  
- rp_world_oil_eq (푟푝තതത
௪௢௜௟) : Equilibrium relative price of world oil to US CPI, 100*ln  
- Δrp_world_oil_eq (Δ푟푝തതത
௪௢௜௟) : Equilibrium relative price growth – world oil to US CPI, annualized q-o-q, percent  
- rp_world_oil_gap (푟푝ෞ
௪௢௜௟) : Relative price gap – world oil to US CPI, percent  
- rp_world_food (푟푝
௪௙௢௢ௗ) : Relative price of world food to US CPI, 100*ln  
- rp_world_food_eq (푟푝തതത
௪௙௢௢ௗ) : Equilibrium relative price of world food to US CPI, 100*ln  
- Δrp_world_food_eq (Δ푟푝തതത
௪௙௢௢ௗ) : Equilibrium relative price growth – world food to US CPI, annualized q-o-q, percent  
- rp_world_food_gap (푟푝ෞ
௪௙௢௢ௗ) : Relative price gap – world food to US CPI, percent

### Exchange rates and nominal variables
- s : Nominal exchange rate FRW to USD, 100*ln  
- Δs : Nominal ER depreciation of FRW to USD, annualized q-o-q, percent  
- Δs_uip (Δ푠
௎ூ௉) : Nominal ER depreciation of FRW to USD – UIP implied, annualized q-o-q, percent  
- Δs_target (Δ푠
்௔௥) : Nominal ER depreciation of FRW to USD – target, annualized q-o-q, percent  
- USD_per_EUR (푠
௎ௌ஽
ா௎ோ) : USD per EUR exchange rate, 100*ln

### Fiscal and aid variables
- famp (푓푖푚푝) : Fiscal impulse, p.p.  
- df2y : Deficit to nominal GDP, percent. Excludes project grants (aid) and exceptional expenditure.  
- df2y_cyc (푑푓2푦
௖) : Cyclical component of the deficit to nominal GDP, percent  
- df2y_caa (푑푓2푦
௖௔ௗ௝) : Cyclically adjusted deficit to nominal GDP, percent  
- Δdf2y_caa (Δ푑푓2푦
௖௔ௗ௝) : Change of cyclically adjusted deficit to nominal GDP, percent  
- Δee2y : Change of exceptional expenditures on nominal GDP, percent  
- a2y : Ratio of aid to nominal GDP, percent  
- a2y_eq (푎2푦
തതതതത) : Equilibrium ratio of aid to nominal GDP, percent  
- a2y_gap (푎2푦
෢) : Ratio of aid to nominal GDP gap, percent

### Money and liquidity
- m3_nom (푚3
ே) : Nominal M3 money, 100*ln  
- m3 (푚3) : Real M3 money, 100*ln  
- m3_eq (푚3
തതതത) : Equilibrium real M3 money, 100*ln  
- Δm3_eq (Δ푚3
തതതത) : Equilibrium real M3 money rate of growth, annualized q-o-q, percent  
- m3_gap (푚3
෢) : Real M3 money gap, percent  
- rm (푟푚) : Reserve money, 100*ln  
- mult : Money multiplier, 100*ln  
- mult_eq (푚푢푙푡
തതതതതതത) : Equilibrium money multiplier, 100*ln  
- Δmult_eq (Δ푚푢푙푡
തതതതതതത) : Equilibrium money multiplier growth, annualized q-o-q, percent  
- mult_gap (푚푢푙푡
෣) : Money multiplier gap, percent

### Foreign variables and external sector
- π4_star (휋4
∗) : Foreign effective inflation, annualized q-o-q, percent  
- cpi_star (푐푝푖
∗) : Foreign effective CPI, 100*ln  
- i_star (푖
∗) : Foreign effective interest rate, percent  
- cpi_us (푐푝푖
௎ௌ) : US CPI, 100*ln  
- π_us (휋
௎ௌ) : US CPI inflation, annualized q-o-q, percent  
- cpi_ez (푐푝푖
ா௓) : Eurozone CPI, 100*ln  
- π_ez (휋
ா௓) : Eurozone CPI inflation, annualized q-o-q, percent  
- r_star (푟
∗) : Foreign effective real interest rate, percent  
- r_bar_star (푟̅
∗) : Equilibrium foreign effective real interest rate, percent  
- r_hat_star (푟̂
∗) : Foreign effective real interest rate gap, percent  
- y_gap_star (푦ො
∗) : Foreign effective output gap, percent  
- y_gap_ez (푦ො
ா௓) : Eurozone output gap, percent  
- y_gap_us (푦ො
௎ௌ) : US output gap, percent

### Shocks and measurement errors
- ε_ag_gap_dom (휀
௬
ො
ೌ೒ೝ) : Shock to domestic agricultural output gap, percent  
- ε_nonag_gap_dom (휀
௬
ො
೙ೌ೒ೝ) : Shock to domestic non-agricultural output gap (aggregate demand shock), percent  
- ε_pot_growth_ag (휀
௱௬
ೌ೒ೝ) : Shock to the potential growth in agricultural sector, percent  
- ε_pot_growth_nonag (휀
௱௬
೙ೌ೒ೝ) : Shock to the potential growth in non-agricultural sector, percent  
- ε_core_inf (휀
గ
஼) : Shock to core subcomponent of inflation, percent  
- ε_food_inf (휀
గ
ி) : Shock to food subcomponent of inflation, percent  
- ε_energy_inf (휀
గ
ா) : Shock to energy subcomponent of inflation, percent  
- ε_meas_headline (휖
௧
௖௣௜) : Measurement error in equation for headline CPI as a weighted average of CPI subcomponents, percent  
- ε_inflation_target (휀
గ
்஺ோ) : Shock to inflation target, percent  
- ε_nom_eff_exrate (휀
௦) : Shock to the nominal effective exchange rate, percent  
- ε_nom_eff_exrate_target (휀
୼௦
೅ಲೃ) : Shock to the nominal effective exchange rate target, percent  
- ε_long_run_reer (휀
௱௭) : Shock to the long-term rate of change in real effective exchange rate, percent  
- ε_policy_rate (휀
௧
௜
ಾು) : Shock to the domestic policy interest rate (monetary policy shock), percent  
- ε_prem_overnight (휖
௧
௣௥௘௠
಺ಳ) : Shock to the premium of the overnight interbank money market rate over the policy rate, percent  
- ε_foreign_output_gap (휀
௬
ො
೎೚ೠ೙೟ೝ೤_೎೚೏೐) : Shock to foreign (country_code=EZ or US) output gap, percent  
- ε_foreign_inflation (휀
గ
೎೚ೠ೙೟ೝ೤_೎೚೏೐) : Shock to foreign (country_code=EZ, or US) inflation, percent  
- ε_us_interest (휀
௧
௜
ೆೄ) : Shock to the US interest rate, percent  
- ε_us_rbar (휀
௥
̅
ೠೞ) : Shock to the US equilibrium real interest rate, percent  
- ε_trend_core_rel (휀
௱௥௣
಴) : Shock to the rate of growth of trend in domestic core CPI subcomponent relative to headline CPI, percent  
- ε_trend_energy_rel (휀
௱௥௣
ಶ) : Shock to the rate of growth of trend in domestic energy CPI subcomponent relative to headline CPI, percent  
- ε_trend_real_money (휀
୼௠ଷ
തതതതത) : Shock to the trend of real money balances, percent  
- ε_gap_real_money (휀
௠ଷ
෢) : Shock to the gap of real money balances, percent  
- ε_velocity (휀
௱௩) : Shock to the velocity of money, percent  
- ε_gap_real_money_alt (휀
୼௠௨௟௧
തതതതതതത) : Shock to the trend of real money balances, percent  
- ε_trend_real_money_alt (휀
௠௨௟௧
෣) : Shock to the gap of real money balances, percent  
- ε_oil_gap_cycle (휀
௥௣
ෞ
೚೔೗) : Shock to the cyclical component (gap) in relative oil prices, percent  
- ε_oil_trend (휀
୼௥௣
തതതത
೚೔೗) : Shock to the trend in relative oil prices, percent  
- ε_food_gap_cycle (휀
௥௣
ෞ
೑೚೚೏) : Shock to the cyclical component (gap) in world food prices relative to US CPI, percent  
- ε_food_trend (휀
୼௥௣
തതതത
೑೚೚೏) : Shock to the trend in world food prices relative to US CPI, percent  
- ε_usdeur (휀
௱௦
ೠೞॽ) : Shock to the USDEUR nominal exchange rate, percent  
- ε_df2y_caa_ratio (휀
௧
ௗ௙ଶ௬
೎ೌ೏ೕ) : Shock to the ratio of cyclically-adjusted deficit to GDP, percent  
- ε_a2y_gap (휀
௧
௔ଶ௬
෣) : Shock to the gap of the ratio of aid to GDP, percent  
- ε_a2y_trend (휀
௧
௔ଶ௬
തതതതതത) : Shock to the trend of the ratio of aid to GDP, percent  
- ε_excep_exp_ratio (휀
௧
௘௫௖௘௫௣) : Shock to the ratio of exceptional expenditures to GDP, percent  
- ε_meas_var_weights (휖
௧
ௗ௜௦௖) : Measurement error due to varying weights of agricultural and non-agricultural production in total output, percent

---

### APPENDIX B. Model Equations — Key dynamic relations (selected)
- Real GDP aggregate:
  - Δy_t = w_ag Δy_t^ag + (1−w_ag) Δy_t^nonag + Δdisc_t  (B.1)  
  - disc_t = disc_t^{00} + ε_t^{measurement}  (B.2)  
  - y_gap_t = w_ag y_gap_t^ag + (1−w_ag) y_gap_t^nonag  (B.3)  
  - y_t = y_gap_t + y_trend_t  (B.4)
- Agricultural block:
  - y_t^ag = y_gap_t^ag + y_trend_t^ag  (B.5)  
  - y_gap_t^ag = b_11 y_gap_{t-1}^ag + ε_t^{ag_gap}  (B.6)  
  - Δy_trend_t^ag = ρ_x Δy_trend_{t-1}^ag + (1−ρ_x) Δy_trend_{00}^ag + ε_t^{ag_trend}  (B.7)
- Non-agricultural block:
  - y_t^{nonag} = y_gap_t^{nonag} + y_trend_t^{nonag}  (B.8)  
  - y_gap_t^{nonag} = b_12 y_gap_{t-1}^{nonag} − b_22 rmci_t + b_32 y_gap_t^* + b_42 fimpt_t + b_52 (a2y_eq_t − a2y_eq_{t-1}) + ε_t^{nonag_gap}  (B.9)  
  - Δy_trend_t^{nonag} = ρ Δy_trend_{t-1}^{nonag} + (1−ρ) Δy_trend_{00}^{nonag} + b_15 (a2y_trend_t − a2y_trend_{00}) + ε_t^{nonag_trend}  (B.10)
- Monetary conditions and exchange rate:
  - rmci_t = −b_15 z_hat_t + (1−b_15) r_hat_t  (B.11)  
  - Δs_t = w_uip Δs_t^{uip} + (1−w_uip) Δs_t^{target}  (B.19)  
  - Δs_t^{target} = (Δz̅_t + π4_t^{target} − π4_t^*) − f_15 E_t π4_{t+1}^{dev} − f_23 z_hat_t + ε_t^{exrate_target}  (B.20)
- Inflation (aggregates and components):
  - cpi_t = w_core cpi_t^{core} + w_food cpi_t^{food} + (1−w_core−w_food) cpi_t^{energy} + ε_t^{meas_cpi}  (B.12)  
  - π_core_t = a_11 E_t π_{t+1}^{core} + (1−a_11) π_{t-1}^{core} + a_21 rmc_t^{core} + ε_t^{core_shock}  (B.13)  
  - rmc_core_t = a_25 y_gap_t^{nonag} + (1−a_25) (z_hat_t − rp_core_trend_t)  (B.14)  
  - Analogous forms for food and energy inflation with respective rmc and relative price terms (B.15–B.18)
- Monetary policy rule (interest rates):
  - i_policy_t = g_1 i_{t-1}^{policy} + (1−g_1) (i_neutral_t + g_2 E_t π4_{t+1}^{dev} + g_3 y_gap_t^{nonag}) + ε_t^{mp_shock}  (B.22)
- Real interest and UIP:
  - r_t = i_t − E_t π4_{t+1}  (B.34)  
  - prem_t = r̅_t − r̅_t^* − E_t Δz̅_{t+1}  (B.40)
- Money demand and multiplier:
  - m3_real_t = m3_trend_t + m3_gap_t  (B.50)  
  - m3_gap dynamics and money velocity equations include Δm3_trend processes and Δv dynamics (B.52–B.54, B.56–B.58)
- External sector and world prices:
  - rp_world_oil_t = p_world_oil_t − p_us_t  (B.58)  
  - rp_world_oil_gap and rp_world_food_gap follow AR processes with specified ρ coefficients (B.60–B.65)
- Fiscal and aid blocks:
  - fimpt_t = Δdf2y_caa_t + Δee2y_t  (B.27)  
  - df2y_t = df2y_cyc_t + df2y_caa_t  (B.28)  
  - df2y_cyc_t = d_1 y_gap_t^{nonag}  (B.29)  
  - a2y dynamics split into trend, gap, and equilibrium components with AR processes (B.31–B.33)

(Equations are reported in the source as numbered relations (B.1)–(B.71); only dynamic equations and definitions for trends and gaps are included here as in the source. Δ indicates q-o-q annualized growth rates, Δ4 indicates y-o-y growth rates. All variables are in natural logs unless noted otherwise.)

### APPENDIX C. Calibration of the Model Coefficients — Selected coefficient values
- Real GDP – Agriculture Block
  - w_ag (푤
௔௚௥) = 0.3  
  - ρ_ag_trend (휌
ௗ௙ଶ௬
೎ೌ೏ೕ) = 0.75  
  - b_11 (푏
ଵଵ) = 0.4  
  - Δy_trend_00^ag (Δ푦ത
௦௦
௔௚௥) = 8.158
- Real GDP – Non-agriculture Block
  - b_12 (푏
ଵଶ) = 0.75  
  - b_22 (푏
ଶଶ) = 0.1  
  - b_32 (푏
ଷଶ) = 0.3  
  - b_42 (푏
ସଶ) = 0.1  
  - b_52 (푏
ହଶ) = 0.1
- Real interest rate
  - ρ_rbar (휌
௥
̅) = 0.8  
  - r̅_00 (푟̅
௦௦) = 2
- Real exchange rate
  - ρ_z_trend (휌
୼௬
ത
ೌ೒ೝ) = 0.8  
  - ρ_Δzbar (휌
୼௭̅) = 0.85  
  - b_15 (푏
ଵଷ) = 0.035  
  - b_15_alt (푏
ଵସ) = 0.5
  - Δz̅_00 (Δ푧̅
௦௦) = 0
- Relative prices
  - ρ_rp_trend (휌
௥௣
തതതത
಴) = 0.8  
  - Δrp_trend_00_core (Δ푟푝തതത
௦௦
஼) = -1  
  - Δrp_trend_00_food (Δ푟푝തതത
௦௦
ி) = 1
- Inflation – Core inflation
  - a_11 (푎
ଵଵ) = 0.5  
  - a_21 (푎
ଶଵ) = 0.2
- Inflation – Food price inflation
  - a_12 (푎
ଵଶ) = 0.5  
  - a_23 (푎
ଶଶ) = 0.3  
  - a_25 (푎
ଷଶ) = 0.7  
  - a_33 (푎
ସଶ) = 1.6
- Inflation – Energy price inflation
  - a_13 (푎
ଵଷ) = 0.2  
  - a_34 (푎
ଶଷ) = 0.3  
  - a_35 (푎
ଷଷ) = 0.7
- Money demand block
  - c_1 (푐
ଵ) = 0.5  
  - c_2 (푐
ଶ) = 1.5  
  - c_3 (푐
ସ) = 0.5  
  - c_4 (푐
ଷ) = 0.5  
  - ρ_m3_trend (휌
௠ଷ
തതതതത) = 0.8  
  - ρ_Δv (휌
୼௩) = 0.95  
  - Δv_00 (Δ푣
௦௦) = -8
  - Δmult_eq_00 (Δ푚푢푙푡
തതതതതതത
௦௦) = 3
  - ρ_mult_trend (휌
௠௨௟௧
തതതതതതത) = 0.9  
  - ρ_mult_eq (휌
௠௨௟௧
෣) = 0.5
- World oil and food price processes
  - ρ_rp_oil_trend (휌
௥௣
ෞ
ೢ೚೔೗) = 0.75  
  - ρ_rp_oil_gap (휌
௱௥௣
തതതത
ೢ೚೔೗) = 0.9  
  - Δrp_oil_00 (훥푟푝തതത
௦௦
௪௢௜௟) = 0
  - ρ_rp_food_trend (휌
௥௣
ෞ
ೢ೑೚೚೏) = 0.75  
  - ρ_rp_food_gap (휌
௱௥௣
തതതത
ೢ೑೚೚೏) = 0.9  
  - Δrp_food_00 (훥푟푝തതത
௦௦
௪௙௢௢ௗ) = 0
- Monetary policy – exchange rate and interest rates
  - w_uip (푤
௎ூ௉) = 0.5  
  - f_15 (푓
ଵଶ) = 0.3  
  - f_23 (푓
ଶଶ) = 0.85  
  - e_1 (푒
ଵ) = 0.8  
  - g_1 (푔
ଵ) = 0.8  
  - g_2 (푔
ଶ) = 0.25  
  - g_3 (푔
ଷ) = 0.2
- External sector and market interest rates
  - w_ext (푤
௎ௌ) = 0.6  
  - ρ_rbar_star (휌
௥
̅
∗) = 0.9  
  - r̅_00^* (푟̅
௦௦
∗) = 1  
  - ρ_prem (휌
௣௥௘௠
಺ಳ) = 0.6  
  - prem_00_dom (푝푟푒푚
௦௦
்஻) = 1.5  
  - prem_00_foreign (푝푟푒푚
௦௦
ூ஻) = 1.5

*Source: APPENDIX A–C (Model Variables, Model Equations, Calibration of the Model Coefficients) as provided in the supplied content.*

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_Source: https://www.imf.org/-/media/files/publications/wp/2020/english/wpiea2020295-print-pdf.pdf_