## wpiea2024126-print-pdf — Executive Summary & Appendices (DRCMOD)

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---

### Semi-structural Quarterly Projection Model (QPM / DRCMOD) — Overview
- Introduces a semi-structural Quarterly Projection Model (QPM) tailored for the Democratic Republic of the Congo (DRC), called DRCMOD.
- Purpose:
  - Capture key features of the DRC economy (resource richness, high degree of dollarization).
  - Provide a framework for joint and systematic analysis of economic variables and policy scenarios within the Forecasting and Policy Analysis System (FPAS).
  - Serve as a structural tool to contextualize and structure policy discussions rather than merely generating forecasts.
- Model features:
  - Semi-structural, grounded in canonical QPM (aggregate demand IS, aggregate supply/forward-looking Phillips curve, UIP, monetary policy rule) with DRC-specific extensions.
  - Explicit representation of high dollarization, strong exchange rate pass-through to inflation, dependence on commodity exports, public debt dynamics, and the BCC’s Monetary Policy Framework (MPF) including exchange rate interventions.
  - Calibrated with available data to reproduce monetary policy transmission mechanisms and relevant historical events for the DRC.

### Key Characteristics of the DRC Economy (findings)
- Resource dependence and fiscal/growth drivers:
  - Mining sector dominated by copper and cobalt production.
  - Mining sector accounts for about 35% of GDP in 2022.
  - Historically, prior to 1990s the mining sector contributed over 70% of budget revenues; it remains a significant source of domestic revenues.
- Dollarization and financial structure:
  - More than 90 percent of the banking system's deposits and lending are denominated in US dollars.
  - Shallow financial system and large informal sector constrain monetary policy options.
- Vulnerabilities and policy constraints:
  - High exposure to global commodity price shocks and external demand.
  - Strong impact of exchange rate fluctuations and commodity prices on inflation.
  - History of fiscal dominance and monetary financing of fiscal deficits has contributed to hyperinflation episodes and entrenched dollarization.
  - Gross foreign reserves have been below 3 months of imports for several years; around 6 weeks of imports on average between 2016-2022.
  - Net international reserves as of December 2022: USD 4.72 billion, representing 2.56 months of imports.
- Legal and institutional context:
  - Law No. 18/027 enacted on December 13, 2018, entrusting the BCC with exclusive responsibility for monetary policy.
  - Ordonnance – Law n°18/027 of December 13, 2018, formally prohibits monetary financing of the fiscal deficit.

### Monetary Policy Framework and Operational Instruments (description)
- Exchange rate arrangement and operations:
  - Official arrangement: floating; CDF exchange rate dictated by supply and demand; BCC interventions via auctions; de facto classified as crawl-like in IMF AREAER.
- BCC Monetary Policy Framework (MPF):
  - Three liquidity windows: short-term loans, standing facilities, special loans.
  - Variable mandatory reserve coefficients differentiated by deposit currency and maturity.
  - Issuance of BCC Bonds ("Bon de la Banque Centrale du Congo") — short-term debt securities to stabilize bank liquidity.
  - Monetary targeting system: money supply of domestic currency as intermediate objective; monetary base as operational objective.
  - Since 2016, BCC adopted a medium-term inflation target of 7 percent.
- Operational constraints:
  - Monetary targets often implemented flexibly; frequent misses make stance undetermined.
  - Foreign exchange interventions constrained by low reserves and commitments to build reserves, limiting effectiveness.

### Nowcasting, Quarterly GDP Interpolation, and Near-Term Forecasts (methods & findings)
- Importance:
  - High-frequency indicators and quarterly GDP are essential for real-time assessment (nowcasting) and medium-term forecasts using the QPM.
  - Nowcasting and Near-Term Forecast (NTF) models complement DRCMOD in FPAS.
- Interpolating quarterly GDP (Chow-Lin approach):
  - Annual GDP is the only official release; quarterly GDP constructed using interpolation methods (Chow-Lin, 1971).
  - Candidate monthly indicators: Copper Production (start 2004, BCC), Cobalt Production (start 2004, BCC), Broad Money (monthly, start 2004, BCC), Copper Price (monthly, start 2004, IMF/WB), Cobalt Price (monthly, start 2004, IMF/WB), Foreign Reserves (monthly, start 2004, BCC).
  - Final selected indicators: copper and cobalt production for mining GDP; broad money for non-mining GDP. Monthly CPI used to convert annual GDP deflator to quarterly series via Chow-Lin.
- Nowcasting ensemble:
  - Ensemble mean of Bridge Model, MIDAS, and Unrestricted MIDAS (U-MIDAS).
  - Empirical findings:
    - Change in copper production is an important driver for mining GDP (significant).
    - Broad money is positive and statistically significant for non-mining GDP.
    - One period lag of mining GDP included to capture persistence.
    - Limited spillovers from mining to non-mining sector (coefficients positive but not statistically significant).
  - Adjusted R Squared:
    - Mining: Bridge 0.59, MIDAS 0.63, U-MIDAS 0.62.
    - Non-mining: Bridge 0.56, MIDAS 0.48, U-MIDAS 0.48.
- Near-Term Forecasts (NTF) for CPI components:
  - Single-equation autoregressions and VARs augmented with exogenous variables (domestic: nominal exchange rates; external: primary goods prices, trade-partner inflation).
  - NTFs tend to outperform structural QPM in one- to two-quarter horizons; outputs integrated into QPM scenarios via expert judgment.

### Model Structure, Calibration, and Database (high-level)
- Two-sector aggregate demand block: mining and non-mining, each decomposed into trend and gap.
- Monetary condition index (MCI) incorporates real exchange rate gap and effective real interest rates to reflect dollarization channels.
- UIP and FX intervention block: exchange rate determined as weighted average of policy target and UIP-implied depreciation; FX intervention can affect reserves and an intervention-related risk premium.
- Monetary policy reaction allows two branches:
  - Monetary-target branch where money growth targets imply a consistent short-term interest rate.
  - Inflation-targeting branch that mixes UIP and Taylor-type rule; parameter k1 regulates sterilization vs pass-through.
- Fiscal block: debt-to-GDP decomposed into local and foreign currency components; structural deficit, cyclical components, and fiscal impulse enter non-mining demand.
- Database: domestic data from BCC; foreign variables from IMF WEO and Fed; multiple frequencies converted to quarterly.

### Key calibration parameters and steady states (selected exact values)
- Shares and structural parameters:
  - w_NMIN = 0.70
  - w_CPIE = 0.09
  - w_CPIF = 0.47
- Dollarization / MCI weights:
  - h1 = 0.70
  - h2 = 0.20
- Aggregate demand coefficients:
  - b11 = 0.50; b12 = 0.20; b13 = 0.10; b15 = 0.10; b16 = 0.10
  - b21 = 0.50; b22 = 0.10; b23 = 0.28; b231 = 0.24; b24 = 0.10; b241 = 0.19
- Phillips and inflation coefficients:
  - a11 = 0.50; a12 = 0.30; a13 = 0.50
  - a21 = 0.50; a22 = 0.30; a23 = 0.50
  - a31 = 0.50; a32 = 0.01
- UIP / exchange parameters:
  - k1 = 0.10; k2 = 0.90; k3 = 0.09; k4 = 0.10; k5 = 0.12
  - e1 = 0.40
- FX intervention and reserves:
  - gamma = 1.00; theta = 0.00; rho_RES_BAR = 0.80; ss_RES_BAR = 7.00
- Policy rule and smoothing:
  - g1 = 0.70; g2 = 0.50; g3 = 0.50; mpr = 0.75; f1 = 0.50
- Selected steady-state scalars:
  - ss_DLA_RWOIL_BAR = 3.00; ss_DLA_RWCOP_BAR = 4.70
  - ss_DLA_Prod_copper_BAR = 8.47; ss_DLA_prod_cobalt_BAR = 3.82
  - ss_D4L_CPI_TAR = 7.00; ss_RR_BAR = 3.00; ss_DLA_NGDP = 12.50
  - ss_DEF_RAT = 0.50; ss_DEB_RAT_TAR = 4.50; ss_DEB_LC_RAT = 0.90; ss_DEB_FC_RAT = 3.60
- Fiscal coefficients:
  - p1 = 0.05; p2 = 0.50; p3 = 0.10; p4 = 0.10
  - s1 = 0.89; s2 = 0.01; s3 = 0.89; s4 = 0.03; s5 = 0.03
  - q1 = 0.89; q2 = 0.03; q3 = 0.04

### Model shocks (selected standard deviations, exact values)
- Real activity shocks:
  - ε^{y_NMIN}_t StDev = 2.39
  - ε^{y_MIN}_t StDev = 14.34
  - SHK_RS StDev = 14.34
  - ε^{s}_t StDev = 5.98
- Price-component shocks:
  - SHK_DLA_CPIXFE StDev = 7.17
  - SHK_DLA_CPIF StDev = 11.95
  - SHK_DLA_CPIE StDev = 4.78
- World commodity and production shocks:
  - SHK_L_RWOIL_GAP StDev = 21.51
  - SHK_L_RWCOP_GAP StDev = 15.54
  - SHK_L_RWCOB_GAP StDev = 20.32
  - SHK_L_Prod_copper_GAP StDev = 19.12
  - SHK_L_prod_cobalt_GAP StDev = 16.73
- Money and velocity shocks:
  - SHK_DLA_RM StDev = 7.17
  - SHK_L_V_GAP StDev = 3.59
  - SHK_DLA_V StDev = 2.39

### Test-driving the model — Impulse responses, filters, and forecast performance
- Representative impulse responses:
  - Positive non-mining output shock: short-term increase in overall inflation via core and non-food inflation; energy unchanged; central bank raises interest rate; currency appreciates; gap closes gradually.
  - Positive copper production gap shock: raises mining output, spillovers to non-mining; core and food inflation increase, mitigated by nominal exchange rate appreciation; energy inflation turns negative; central bank increases policy rate.
  - Core price shock: central bank raises nominal rate; nominal appreciation and negative RER gap; short-term decline in non-mining output; mining output unaffected.
  - Exchange rate (UIP) depreciation shock: nominal and real depreciation raise headline inflation via core and food; central bank raises short-term rate; initial RIR gap slightly negative then turns positive; initial positive non-mining output gap.
  - Contractionary monetary policy shock: hump-shaped negative non-mining output gap; subdued effects due to high dollarization; maximum declines in food and core inflation of 0.05 percent (quarterly annualized); nominal appreciation and only slightly negative RER gap.
- Multivariate filter / Kalman filter results (selected diagnostics):
  - Output gap decomposition: post-civil war (2005–08) negative gap driven by both sectors; mining gap severely negative after the Great Financial Crisis 2008–09; robust growth early 2010s until 2016; fluctuations thereafter driven by mining.
  - Real monetary conditions index (RMCI): accommodative 2005–08; tightened in early 2010s; highly accommodative in 2016–17 (negative real interest rate); mostly accommodative in past four years.
  - Inflation decomposition (2013Q1–2023Q3): three large inflationary periods—2016–2017, 2020, and since 2022Q3—driven primarily by food inflation with significant core increases.
- Recursive (in-sample) forecast RMSE ratios vs random walk (selected exact ratios, 8-quarter horizon from 2013Q1):
  - Real GDP growth (%, YoY): 1.13 (1Q), 0.83 (2Q), 0.69 (3Q), 0.65 (4Q), 0.61 (5Q), 0.61 (6Q), 0.59 (7Q), 0.56 (8Q).
  - Non-mining output growth (%, YoY): 0.50 (1Q), 0.40 (2Q), 0.36 (3Q), 0.38 (4Q), 0.48 (5Q), 0.56 (6Q), 0.64 (7Q), 0.72 (8Q).
  - Headline inflation rate (%, YoY): 0.44 (1Q), 0.43 (2Q), 0.46 (3Q), 0.52 (4Q), 0.54 (5Q), 0.56 (6Q), 0.59 (7Q), 0.64 (8Q).
  - Food inflation rate (%, YoY): 0.48 (1Q), 0.44 (2Q), 0.45 (3Q), 0.49 (4Q), 0.51 (5Q), 0.54 (6Q), 0.57 (7Q), 0.61 (8Q).
  - Policy interest rate (%, YoY): 3.44 (1Q), 1.81 (2Q), 1.12 (3Q), 0.77 (4Q), 0.52 (5Q), 0.42 (6Q), 0.49 (7Q), 0.60 (8Q).
  - Exchange rate CDF/USD: 0.79 (1Q), 0.75 (2Q), 0.75 (3Q), 0.77 (4Q), 0.79 (5Q), 0.82 (6Q), 0.84 (7Q), 0.86 (8Q).

### Policy-Relevant Exercise (pseudo-forecast for 2023 — design and results)
- Design and assumptions:
  - Data cut-off: 2022Q4.
  - External assumptions: commodity price forecasts from World Bank Pink Sheet December 2022; US, Eurozone, Chinese GDP and inflation from IMF WEO October 2022; Fed Funds projections from end-2022 dot plot.
  - Domestic assumption: mining sector production increase of 15.7 percent year-on-year in 2023 (expert judgement).
  - Starting conditions end-2022: exchange rate ~2000 CDF per USD; BCC policy rate 7.75 percent (average 2022Q4); headline CPI 10.8 percent (average 2022Q4) on increasing trend.
- Baseline (model-based) vs realized outcomes:
  - Realized 2023 ex-post: franc reached 2600 per USD on average by end-2023 (30 percent year-on-year depreciation); inflation reached 32 percent by 2023Q4; BCC policy rate tightened to 25 percent in second half 2023.
  - Model baseline prediction: 15 percent depreciation by end-2023; inflation accelerates to above 15 percent due to high pass-through; model suggests policy rate increase to 12.5 percent, rising earlier than actual BCC policy.
- Alternative scenario (fixing realized exchange rate path):
  - Fixing realized 30 percent year-on-year depreciation by end-2023: model forecasts higher inflation close to 20 percent by 2023Q4 and more pronounced tightening in policy rate closely following realized path (but starting earlier, from 2023Q1).
  - GDP growth higher in alternative scenario than baseline due to competitiveness effects of depreciation.
- Purpose and caveats:
  - Designed to showcase scenario-making and reporting capabilities; results are not official IMF or Congolese authorities’ projections.
  - Emphasizes exchange rate’s key role and high exogeneity via commodity price exposure.

### Conclusions and Guidance on FPAS Use
- The DRCMOD is proposed as a structural tool for the Banque Central du Congo’s FPAS.
- Model capabilities:
  - Reflects DRC characteristics: high dollarization, strong exchange rate pass-through to inflation, dependence on commodity exports, public debt dynamics, monetary aggregate targeting and FX interventions.
  - Calibrated to reproduce transmission mechanisms and historical events; useful for analysis and forecasting within the BCC.
- Usage guidance:
  - Intended to contextualize and structure policy discussions rather than be a purely predictive tool.
  - Successful FPAS implementation requires institutional teams, systematic processes for discussion and communication of staff analyses and macroeconomic projections to policymakers.
  - Complement DRCMOD with nowcasting, NTFs, and data interpolation methods for real-time inputs and short-term accuracy.

_International Monetary Fund — Executive Summary, Appendix A, Annex I, and Annex IV of wpiea2024126-print-pdf_

### Executive Summary ......................................................................................................

### Executive Summary

### Document structure and major sections
- Executive Summary ............................................................................................................................................ 4
- I.Introduction .................................................................................................................................................. 5
- II.Key Characteristics and Monetary Policy Framework of the DRC ................................................... 6
- III.Assessing the DRC’s Economy in Real-time ...................................................................................... 9
  - A.Interpolating Quarterly GDP Data ......................................................................................................... 9
  - B.Nowcasting Quarterly GDP ................................................................................................................ 12
  - C.Inflation Near Term Forecast .............................................................................................................. 14
- IV.The DRC QPM Model ........................................................................................................................... 16
  - A.Aggregate Demand: mining and non-mining output ........................................................................... 16
  - B.Aggregate Supply – Relative prices and CPI decomposition ............................................................. 18
  - C.The Uncovered Interest Rate Parity and Foreign Exchange Intervention .......................................... 21
  - D.Monetary Policy Reaction Function .................................................................................................... 22
  - E.The Fiscal Block ................................................................................................................................. 25
- V.Model Calibration and Database ........................................................................................................ 26
  - A.Calibration .......................................................................................................................................... 26
  - B.Test Driving the Model ........................................................................................................................ 27
- VI.A Policy-Relevant Exercise ................................................................................................................ 36
  - A.Assumptions ....................................................................................................................................... 36
  - B.The Results ........................................................................................................................................ 37
- VII.Conclusion ........................................................................................................................................... 38
- Reference ........................................................................................................................................................... 40

### Annexes and technical appendices
- Annex I. Interpolating Quarterly GDP .............................................................................................................. 42
- Annex II. Nowcasting ........................................................................................................................................ 42
- Annex III. Near Term Forecast ......................................................................................................................... 44
- Annex IV. Summary of the DRCMOD Model ................................................................................................... 47

### Glossary (selected acronyms and definitions as listed)
- ARMA Auto-Regression Moving Average
- ARMAX Auto-Regression Moving Average with Exogenous Variables
- BCC Banque Central du Congo
- CPI Consumer Price Index
- DFM Dynamic Factor Model
- GDP Gross Domestic Product
- FPAS Forecasting and Policy Analysis System
- MIDAS Mixed Frequency Data Sampling
- NTF Near-term forecasting
- OLS Ordinary Least Squared
- U-MIDAS Unrestricted Mixed Frequency Data Sampling
- VAR Vector Auto-Regression
- VARX Vector Auto-Regression with Exogenous Variables
- WEO World Economic Outlook

*Source: wpiea2024126-print-pdf - Executive Summary (IMF).*

### Executive Summary

### Executive Summary

### Semi-structural Quarterly Projection Model (QPM / DRCMOD) — Overview
- Introduces a semi-structural Quarterly Projection Model (QPM) tailored for the Democratic Republic of the Congo (DRC), referred to as DRCMOD.
- Purpose:
  - Capture key features of the DRC economy (resource richness, high degree of dollarization).
  - Provide a framework for joint and systematic analysis of economic variables and policy scenarios within the Forecasting and Policy Analysis System (FPAS).
  - Serve as a structural tool to contextualize and structure policy discussions rather than merely generating forecasts.
- Model features:
  - Semi-structural, grounded in canonical QPM (aggregate demand IS, aggregate supply/forward-looking Phillips curve, UIP, monetary policy rule) with extensions for DRC-specific features.
  - Explicit representation of: high dollarization, strong exchange rate pass-through to inflation, dependence on commodity exports, public debt dynamics, and the BCC’s Monetary Policy Framework (MPF) including exchange rate interventions.
  - Calibrated with available data to reproduce monetary policy transmission mechanisms and relevant historical events for the DRC.

### Key Characteristics of the DRC Economy (findings)
- Resource dependence and growth drivers:
  - Mining sector dominated by copper and cobalt production.
  - The mining sector accounts for about 35% of GDP in 2022.
  - Historically, prior to 1990s the mining sector contributed over 70% of budget revenues; it remains a significant source of domestic revenues.
- Dollarization and financial structure:
  - Dollarization is pronounced: more than 90 percent of the banking system's deposits and lending are denominated in US dollars.
  - Shallow financial system and large informal sector constrain monetary policy options.
- Vulnerabilities and policy constraints:
  - High exposure to global commodity price shocks and external demand.
  - Strong impact of exchange rate fluctuations and commodity prices on inflation.
  - History of fiscal dominance and monetary financing of fiscal deficits has contributed to hyperinflation episodes and entrenched dollarization.
  - Gross foreign reserves have been below 3 months of imports for several years, at around 6 weeks of imports on average between 2016-2022.
  - As of December 2022, net international reserves stand at USD 4.72 billion, representing only 2.56 months of imports.
- Legal and institutional context:
  - Modernization process governed by Law No. 18/027, enacted on December 13, 2018, which entrusts the BCC with exclusive responsibility for independently defining and implementing monetary policy.
  - Ordonnance – Law n°18/027 of December 13, 2018, formally prohibits monetary financing of the fiscal deficit.

### Monetary Policy Framework and Operational Instruments (description)
- Official exchange rate arrangement:
  - Designated as floating; CDF exchange rate dictated by supply and demand in the foreign exchange market.
  - BCC interventions are conducted through auctions; de facto arrangement classified as crawl-like in IMF AREAER.
- Monetary Policy Framework (MPF) at the BCC — instruments and operations:
  - Various interest rates on refinancing providing banks with three liquidity windows: short-term loans, standing facilities, and special loans.
  - Variable mandatory reserve coefficients adjusted in response to structural shocks, differentiated by deposit currency and maturity.
  - Issuance of BCC Bonds ("Bon de la Banque Centrale du Congo") — short-term debt securities to stabilize bank liquidity.
  - Monetary targeting system: money supply of domestic currency serves as an intermediate objective and the monetary base as the operational objective.
  - Since 2016, BCC adopted a medium-term inflation target of 7 percent.
- Operational constraints:
  - Monetary targets often implemented flexibly in LICs; frequent misses make stance of policy undetermined.
  - Foreign exchange interventions have been constrained by low reserves and/or commitments to build reserves, limiting effectiveness in stabilizing the CDF and controlling inflation.

### Nowcasting, Quarterly GDP Interpolation, and Near-Term Forecasts (complementary tools)
- Importance:
  - High-frequency indicators and quarterly GDP are essential for real-time assessment (nowcasting) and medium-term forecasts using the QPM.
  - Nowcasting and Near-Term Forecast (NTF) models complement DRCMOD in the FPAS.
- Interpolating quarterly GDP (methodology and indicators):
  - Annual GDP is the only official release; quarterly GDP constructed using interpolation methods (Chow-Lin, 1971).
  - Candidate high-frequency indicators evaluated: Copper Production (monthly, start 2004, BCC), Cobalt Production (monthly, start 2004, BCC), Broad Money (monthly, start 2004, BCC), Copper Price (monthly, start 2004, IMF/WB), Cobalt Price (monthly, start 2004, IMF/WB), Foreign Reserves (monthly, start 2004, BCC).
  - Final selected indicators: copper and cobalt production for mining GDP; broad money for non-mining GDP. Monthly CPI used as indicator to convert annual GDP deflator to quarterly series via Chow-Lin.
  - Cross-checked with BCC expertise to ensure alignment with key economic events.
- Nowcasting models:
  - Ensemble mean of Bridge Model, MIDAS, and Unrestricted MIDAS (U-MIDAS) used for nowcasting quarterly GDP.
  - Bridge Model: linear regressions linking high-frequency indicators (transformed to quarterly) to quarterly GDP.
  - MIDAS: tightly parameterized mixed-frequency regression using distributed lag polynomials.
  - U-MIDAS: unrestricted variant, generally performs better when mixing quarterly and monthly data; higher-frequency indicators converted with split-sampling.
  - Key empirical findings:
    - Change in copper production is an important driver for mining GDP (significant at conventional levels across models).
    - Broad money is positive and statistically significant for non-mining GDP.
    - One period lag of mining GDP included to capture persistence.
    - Limited spillovers from mining to non-mining sector (coefficients positive but not statistically significant).
    - Adjusted R Squared reported for models: mining (Bridge 0.59, MIDAS 0.63, U-MIDAS 0.62); non-mining (Bridge 0.56, MIDAS 0.48, U-MIDAS 0.48).
- Near-Term Forecast (NTF) models for inflation:
  - Single-equation autoregressions and VARs augmented with exogenous variables to forecast CPI components (core, food, energy) one or two quarters ahead.
  - Models include domestic variables (e.g., nominal exchange rates) and exogenous variables (e.g., primary goods prices, inflation in trade partners).
  - NTFs tend to outperform structural QPM in one- to two-quarter horizons; NTF outputs are integrated into QPM scenarios via expert judgment.

### Model Application, Calibration, and Policy Analysis (use and scenario)
- Model calibration:
  - DRCMOD calibrated with available data to plausibly reproduce transmission mechanisms of monetary policy and historical events in the DRC economy.
  - Extensions to the canonical model include two-sector aggregate demand block (mining and non-mining) to reflect the importance of commodity exports.
  - Model allows monetary targets (consistent with BCC MPF) rather than pure inflation-targeting rule; allows exchange rate interventions; accounts for dollarization via transmission channels and high pass-through of exchange rate to prices.
  - Informality not explicitly modeled but its effects are incorporated via calibration of transmission parameters.
- Practical application:
  - DRCMOD used to generate medium-term forecasts, assess counterfactual policy scenarios, and provide monetary policy advice.
  - Paper demonstrates a counterfactual scenario comparing DRCMOD policy prescriptions with actual BCC responses to exchange rate and inflation pressures in 2023 (application illustrated in Section V).
  - QPM integrates forward-looking expectations and endogenous monetary policy, making it suitable for prospective policy recommendations and risk assessment.
- FPAS institutional requirements for effective use:
  - Formation of internal teams to discuss and analyze recent economic developments using the model.
  - Systematic process for communicating staff analyses and macroeconomic projections to policymakers to ensure substantial influence on policy decisions.
  - Coherent framework for policy implementation and operations, and effective external policy communications.
  - Complement DRCMOD with nowcasting, NTFs, and data interpolation methods for real-time inputs and short-term accuracy.

### Key quantitative and legal facts (preserved values)
- Law No. 18/027 enacted on December 13, 2018, entrusting the BCC with exclusive responsibility for monetary policy.
- Mining sector accounts for about 35% of GDP in 2022.
- More than 90 percent of the banking system's deposits and lending are denominated in US dollars.
- BCC adopted a medium-term inflation target of 7 percent in 2016.
- Gross foreign reserves: below 3 months of imports for several years; around 6 weeks of imports on average between 2016-2022.
- Net international reserves as of December 2022: USD 4.72 billion, representing 2.56 months of imports.
- Interpolation method referenced: Chow-Lin (1971).

_International Monetary Fund — Executive Summary of wpiea2024126-print-pdf_

### Appendix A.

### Appendix A.

### A. Aggregate Demand: mining and non-mining output
- Model structure
  - Two sectors: mining and non-mining. Both decomposed into unobserved components: gap and trend.
  - Overall output gap (푦푦̂푡) and annualized QoQ real GDP growth rate (Δ푦푦𝑡) are linear combinations of sectoral gaps and growth rates with weight 푤푁푁푁푁 (share of non-mining output in total GDP) and a discrepancy term Δ푦푡𝑫𝑫𝑫𝑫𝑫𝑫𝑫𝑫 to allow for changes in sectoral weights.
- Non-mining sector drivers (equation (3))
  - Short-term drivers: foreign output gap (푦̂푡𝑟𝑟𝑟𝑟), real monetary condition index (M M I𝑡), fiscal impulse (fiscal imp𝑡), spillovers from mining (푦̂𝑡𝑁), and demand shock ε𝑡𝑦𝑁𝑁𝑁𝑁.
  - Monetary condition index M M I𝑡 defined in (3a) as a weighted average including real exchange rate gap (−ẑ𝑡) and effective real interest rate components with weights c1 and c2.
- Dollarization channels
  - Two channels: limited ability of the central bank to affect aggregate demand through monetary policy stance, and valuation effects of public debt denomination on public finances.
  - Monetary condition index composed of weighted average of the real exchange rate gap (ẑ𝑡) and effective real interest rate (combination of domestic real interest rate gap rirr̂𝑡 and foreign currency interest rate gap rirr̂𝑡𝐹𝐷).
- Mining sector specification (equations (4), (4a), (4b))
  - Mining output gap (푦̂𝑡𝑁) has autoregressive persistence (b21) and is affected by global demand (푦̂𝑡𝑟𝑟𝑟𝑟), and gaps in copper and cobalt production (prpr̂𝑡𝑐opper, prpr̂𝑡𝑐obalt) driven by relative world prices rp̂𝑡.
  - Relative commodity price definition: rp𝑡 = p𝑡commodity − p𝑡reff (equation (5)) and decomposed into trend and gap (equation (6)).

### B. Aggregate Supply – Relative prices and CPI decomposition
- CPI decomposition (equation (7))
  - Headline CPI p𝑡 is weighted average: weights w𝐷𝐶𝐷𝐶energy and w𝐷𝐶𝐷𝐹food for energy (p𝐶) and food (p𝐹), and remainder is core CPI (p𝐷); measurement error ε𝑡𝑐𝐷𝐷𝐷𝐷𝑫 included.
  - Assumption: 0 < w𝐷𝐶𝐷𝐶energy, w𝐷𝐶𝐷𝐹food < 1.
- Core inflation (equation (8))
  - Core Phillips curve: core inflation π𝑡𝐷 depends on backward- and forward-looking expectations, real marginal cost index rfc𝑡𝐷, and cost-push shock ε𝑡π𝐷. Persistence parameter a11 measures core inflation persistence.
  - Real marginal costs for core (equation (9)): rfc𝑡𝐷 = a13·ŷ𝑡𝑁𝑁𝑁𝑁 + (1−a13)·(ẑ𝑡 − rpr̂𝑡𝐷).
  - Relative price gap for core: rpr𝑡𝐷 = p𝑡𝐷 − p𝑡 (equation (10)) and decomposed into trend and gap (equation (11)).
- Food inflation (equation (12), (13), (14), (15))
  - Food Phillips curve includes a21, a22 and real marginal cost for food rfc𝑡𝐹 = a23·ŷ𝑡𝑁𝑁𝑁𝑁 + (1−a23)·ẑ𝑡 + rp̂𝑡ʷ𝑓𝑜𝑜𝑑 − rp̂𝑡𝐹.
  - World food relative price rp𝑡ʷ𝑓𝑜𝑜𝑑 = p𝑡ʷ𝑓𝑜𝑜𝑑 − p𝑡reff (equation (14)); decomposed into trend and gap (equation (15)).
  - Parameter assumption: 0 < a21 < 1 and 0 < a23 < 1.
- Energy inflation (equations (16), (17), (18))
  - Energy Phillips curve similar in form, real marginal cost rfc𝑡𝐶 = ẑ𝑡 + rp̂𝑡ʷ𝑜𝑖𝑙 − rp̂𝑡𝐶 where rp̂𝑡ʷ𝑜𝑖𝑙 = p𝑡ʷ𝑜𝑖𝑙 − p𝑡reff (equation (18)).
  - Domestic demand assumed not influential for energy prices; energy driven by global prices and relative PPP.

### C. The Uncovered Interest Rate Parity and Foreign Exchange Intervention
- Exchange rate equation (equation (19))
  - Exchange rate s𝑡 is weighted average of implicit policy target exchange rate s𝑇 and UIP-implied depreciation s𝑼𝑰𝑷 with weight k2; exchange rate shock ε𝑡s included.
- Policy target dynamics (equations (20), (21))
  - s𝑇 evolves with previous exchange rate, neutral depreciation Δs𝑁, and cyclical/global factors including global demand ŷ̂𝑡𝑟𝑟𝑟𝑟 and commodity price gaps rp̂𝑡.
  - Neutral depreciation Δs𝑁 depends on inflation differential (π𝑡4T − π̂𝑟𝑟𝑟𝑟) and equilibrium depreciation Δz𝑡.
- Modified UIP (equation (22))
  - Expected exchange rate partly forward- and partly backward-looking with parameter e1 regulating backward-looking behavior; UIP includes country risk premium prref and endogenous FXI-related risk premium prref𝐶.
- Alternative FXI specification (equation (23))
  - FXI-related risk premium prref𝐶 = θ·|R R R 2Y 𝑡 − R R R 2Y 𝑡^| (depends on deviation of international reserves from long-run level).

### D. Monetary Policy Reaction Function
- Observed nominal interest rate (equation (24))
  - f𝑡 = fpr·f𝑡𝐷𝑇 + (1−fpr)·f𝑡𝑁𝑇 where 0 < fpr < 1 allows partial adherence to monetary targeting.
- Monetary-target branch (equations (25)–(29))
  - Money-interest rate relationship (equation (25)) links real money growth target Δrf𝑇 to real GDP growth Δy𝑡, change in short-term interest rates (f𝑡 − f𝑡−1), real money gap rf̂𝑡−1, change in velocity Δv𝑡, and shock ε𝑡Δrc.
  - Real money gap rf̂ defined in (26).
  - Nominal money growth target Δf𝑇 defined in (27); real money growth target Δrf𝑇 in (28).
  - Monetary-target consistent short-term interest rate f𝑁𝑇 given in (29).
  - Central bank can allow partial adherence to money targets to stabilize market interest rates.
- Inflation-targeting branch and interaction with exchange rate (equations (30)–(32))
  - Inflation-targeting rate f𝑡𝐷𝑇 = k1·f𝑈𝑰𝑷 + (1−k1)·f𝑇𝑇𝑇𝑦 (equation (30)); k1 = 0 implies sterilized FX interventions (full control of interest rate), k1 = 1 implies loss of rate control (peg).
  - UIP interest rate f𝑈𝑰𝑷 given in (31).
  - Canonical Taylor rule part f𝑇𝑇𝑇𝑦 follows (32) with smoothing parameter g1 and weights g2 (inflation deviation) and g3 (output gap).
- Regime mapping (Table 3)
  - Parameter combinations of k1 = 0, 0<k1<1, k1 = 1 and fpr = 0, 0<fpr<1, fpr =1 correspond to Money targeting vs Hybrid vs Inflation targeting and Floating vs Managed vs Peg exchange rate regimes.

### E. The Fiscal Block
- Debt dynamics and decomposition (equations (33)–(38))
  - Debt to GDP composed of local currency D2Y𝑡𝑳𝐷 and foreign currency D2Y𝑡𝐹𝐷.
  - Debt update equation (33) adds current overall deficit D2Y𝑡 and adjusts previous-period local and foreign debt for nominal GDP growth (ΔP Y𝑡 − ΔP Y𝑠𝑠) and exchange rate depreciation (Δs𝑡 − Δs𝑠𝑠), with coefficients s1..s5 and shock ε𝑡𝐷𝐶𝐷2Y.
  - Debt target D2Y𝑡𝑇 follows (34) with persistence ρ and shock ε𝑡𝐷𝐶𝐷2Y𝑇.
  - Debt deviation D2Ŷ𝑡 smoothed across periods (35).
  - Overall deficit D2Y𝑡 decomposed into structural deficit RRDDR D2Y𝑡 and cyclical component −p1·ŷ̂𝑡 (36).
  - Structural deficit evolves per (37) with persistence, cyclical adjustment (−p4·ŷ̂𝑡), debt deviation adjustment (−p2·D2Ŷ𝑡), and shock ε𝑡𝐷𝐷𝐶𝐹2Y.
  - Fiscal impulse that enters non-mining demand (equation (3)) defined as fiscal_imp𝑡 = ε𝑡RRDDR𝑤 2Y + p3·ε𝑡𝐷𝐶𝐷2Y𝑇 (equation (38)).

### V. Model Calibration and Database
- Database and calibration
  - Domestic variables from BCC and foreign variables from IMF WEO and Fed; raw data in annual, quarterly, monthly frequencies converted to quarterly.
  - Long-term calibration based on historical averages and policy targets for growth rates, interest rates, exchange rates, relative prices, debt, and fiscal ratios; external steady states calibrated for foreign interest rate, foreign inflation, and international prices of oil, copper, cobalt, and food.
  - Parameter calibration used time series with filtering and forecasting capacity analysis; aligned with BCC staff views.
- Key calibration implications
  - High informality and high dollarization reduce monetary policy effectiveness.
  - High exchange rate pass-through amplifies transmission through prices.

### V.B Test Driving the Model — Impulse Responses, Filters, and Forecasts
- Impulse response highlights
  - Positive non-mining output shock: short-term increase in overall inflation via core and non-food inflation; energy unchanged; central bank raises interest rate; currency appreciates; gradual closure of positive output gap.
  - Positive copper production gap shock: raises mining output, spillovers to non-mining; core and food inflation increase, mitigated by nominal exchange rate appreciation; energy inflation turns negative; central bank increases policy rate.
  - Core price shock: central bank raises nominal rate; nominal appreciation and negative RER gap; short-term decline in non-mining output; mining output unaffected; model implies central bank tightens despite trade-off because inflation objective is weighted more heavily.
  - Exchange rate (UIP) depreciation shock: nominal and real depreciation raise headline inflation through core and food via imported costs; central bank raises short-term rate; initial RIR gap slightly negative then turns positive; initial positive non-mining output gap due to accommodative real conditions.
  - Monetary policy shock (contractionary): hump-shaped negative non-mining output gap; subdued effect due to high dollarization; maximum declines in food and core inflation of 0.05 percent (quarterly annualized); nominal appreciation and only slightly negative RER gap.
- Multivariate filter / Kalman filter results
  - Output gap decomposition (Figure 22): post-civil war (2005–08) negative output gap driven by both sectors; mining cyclical position severely negative after Great Financial Crisis 2008–09; robust growth in early 2010s until 2016; fluctuations thereafter driven by mining.
  - Real monetary conditions index (RMCI): accommodative 2005–08; tightened in early 2010s; highly accommodative in 2016–17 (negative real interest rate); mostly accommodative in past four years.
  - Non-mining output gap decomposition shows RMCI effects cooling economy in early 2010s and accommodative periods in 2016; mining gap driven by foreign demand and copper/cobalt production.
  - Inflation decomposition (2013Q1–2023Q3): three large inflationary periods—2016–2017, 2020, and since 2022Q3—driven primarily by food inflation with significant core increases.
  - Structural decomposition attributes inflation spikes to world copper and cobalt price declines (post-2008 and 2012–16) leading to exchange rate depreciation and large inflation increases due to high pass-through.
- Recursive (in-sample) forecast performance
  - In-sample forecasts (8-quarter horizon from 2013Q1) generally match data; model failed to predict the large 2016–17 franc depreciation and consequent inflation spike but outperformed thereafter.
  - RMSE ratios vs random walk (Table 4): for horizons above two quarters the QPM outperforms random walk across key variables. Selected ratios from Table 4:
    - Real GDP growth (%, YoY): 1.13 (1Q), 0.83 (2Q), 0.69 (3Q), 0.65 (4Q), 0.61 (5Q), 0.61 (6Q), 0.59 (7Q), 0.56 (8Q).
    - Non-mining output growth (%, YoY): 0.50 (1Q), 0.40 (2Q), 0.36 (3Q), 0.38 (4Q), 0.48 (5Q), 0.56 (6Q), 0.64 (7Q), 0.72 (8Q).
    - Headline inflation rate (%, YoY): 0.44 (1Q), 0.43 (2Q), 0.46 (3Q), 0.52 (4Q), 0.54 (5Q), 0.56 (6Q), 0.59 (7Q), 0.64 (8Q).
    - Food inflation rate (%, YoY): 0.48 (1Q), 0.44 (2Q), 0.45 (3Q), 0.49 (4Q), 0.51 (5Q), 0.54 (6Q), 0.57 (7Q), 0.61 (8Q).
    - Policy interest rate (%, YoY): 3.44 (1Q), 1.81 (2Q), 1.12 (3Q), 0.77 (4Q), 0.52 (5Q), 0.42 (6Q), 0.49 (7Q), 0.60 (8Q).
    - Exchange rate CDF/USD: 0.79 (1Q), 0.75 (2Q), 0.75 (3Q), 0.77 (4Q), 0.79 (5Q), 0.82 (6Q), 0.84 (7Q), 0.86 (8Q).

### VI. A Policy-Relevant Exercise
- Pseudo-forecast design for 2023 (two scenarios)
  - Data cut-off: 2022Q4.
  - External assumptions: commodity price forecasts from World Bank Pink Sheet December 2022; US, Eurozone, Chinese GDP and inflation from IMF WEO October 2022; Fed Funds projections from end-2022 dot plot.
  - Domestic assumption: mining sector production increase of 15.7 percent year-on-year in 2023 (expert judgement).
  - Starting conditions end-2022: exchange rate ~2000 CDF per USD; BCC policy rate 7.75 percent (average 2022Q4); headline CPI 10.8 percent (average 2022Q4) on increasing trend.
- Baseline scenario (model-based)
  - Realized 2023 outcomes (ex-post): franc reached 2600 per USD on average by end-2023 (30 percent year-on-year depreciation); inflation reached 32 percent by 2023Q4; BCC policy rate tightened to 25 percent in second half 2023.
  - Model baseline prediction: 15 percent depreciation by end-2023; inflation accelerates to above 15 percent due to high pass-through; model suggests policy rate increase to 12.5 percent, rising earlier than actual BCC policy.
- Alternative scenario (fixed realized exchange rate path)
  - Fixing realized 30 percent year-on-year depreciation by end-2023: model forecasts higher inflation close to 20 percent by 2023Q4 and more pronounced tightening in policy rate closely following realized path (but starting earlier, from 2023Q1).
  - GDP growth higher in alternative scenario than baseline due to competitiveness effects of depreciation (imports more expensive, exports more competitive).
- Exercise purpose and caveats
  - Designed to showcase scenario-making and reporting capabilities; results are not official IMF or Congolese authorities’ projections.
  - Emphasizes the exchange rate’s key role and high exogeneity via commodity price exposure.

### VII. Conclusion
- The DRCMOD (Quarterly Projection Model) is proposed as a structural tool for the Banque Central du Congo’s Forecasting and Policy Analysis System (FPAS).
- Model capabilities
  - Reflects DRC characteristics: high dollarization, strong exchange rate pass-through to inflation, dependence on commodity exports, public debt dynamics, monetary aggregate targeting and FX interventions.
  - Calibrated to reproduce transmission mechanisms and historical events; useful for analysis and forecasting within the BCC.
- Usage guidance
  - The model is a structural framework to contextualize and structure policy discussions rather than a purely predictive tool.
  - Successful FPAS implementation requires institutional teams, systematic processes for discussion and communication of staff analyses and macroeconomic projections to policymakers.

*Source: Appendix A, "A Projection Model for Resource-rich and Dollarized Economy — The Democratic Republic of the Congo", IMF Working Paper (source PDF: wpiea2024126-print-pdf - Appendix A).*

### Annex I.  Interpolating Quarterly GDP

### Annex I.  Interpolating Quarterly GDP

### Methodology: Chow-Lin approach
- The Chow-Lin procedure uses a statistical relationship between low frequency data (i.e., annual GDP) and higher frequency indicator variables (i.e., export of copper) through a regression equation.
- The approach assumes a linear relationship between high frequency variables (not causation):
  - 푦푦ℎ푤푤 = 푋푋푋푋 + 푢푢
- It then imposes the constraint relating high frequency data y (e.g., quarterly GDP) to low frequency data Y (e.g., annual GDP):
  - 푌푌표표푤푤 = 푀푀푦푦ℎ푤푤 = 푀푀(푋푋푋푋 + 푢푢) = 푀푀푋푋푋푋 + 푀푀푢푢
- Example: C (sum) 푛푛 × 4푛푛 matrix converts 4n quarterly observations into n annual observations:
  - 푀푀푠푠푠푠푐푐 =
    �
    11 00
    11 00
    00 11
    00 11  ⋯  00 00
    00 00 ⋱ 00 00
    ⋯     11 11
    �

### Implementation notes and software
- Latest version of EViews has a built-in Chow-Lin function (copy-paste special) which can be used to convert a low frequency series to a high frequency one using multiple indicator series.
- First, check correlations to select potential indicators. Based on these correlations and visual inspection of charts, use selected indicators in the Chow-Lin procedure to estimate quarterly GDP.
- The interpolated quarterly GDP are then checked with insights from the BCC team.

### Indicator selection (empirical guidance)
- For Mining GDP, high correlation observed with:
  - production of copper
  - cobalt
  - M2
- For Non-mining GDP, potential indicators:
  - mining GDP
  - M2

### Correlation matrix (percent change of Variables)
- Correlation matrix among listed variables:
  - Variables: GDP_MINING | GDP_NM | PROD_COPPER | RM2 | WCOPPER
  - Row: GDP_MINING — 1.000 .10 .780 .160 .17
  - Row: GDP_NM — 0.10 1.000 .10 .72 -0.50
  - Row: PROD_COPPER — 0.780 .10 1.000 .21 .17
  - Row: RM2 — 0.160 .72 .21 1.00 -0.12
  - Row: WCOPPER — 0.17 -0.50 .17 -0.12 1.00

### Relationship to nowcasting and higher-frequency models (context)
- MIDAS: tightly parameterized reduced-form regressions with variables sampled at different frequencies; response of dependent variable (e.g., GDP) to HF explanatory variable is modeled using distributed lag polynomials with coefficients depending on a small number of parameters (see Ghysels et al (2004) referenced).
- U-MIDAS: estimated in LF (as MIDAS and Bridge), uses HF regressors (as MIDAS, not as Bridge), and can be re-estimated each month within the quarter (see Foroni, Marcellino and Schumacher (2015) referenced).
- Bridge model specification (textual form preserved):
  - 푦푦푡푡푞푞 = α + �푋푋표표(퐿퐿)푥푥표표푡푡푞푞푗푗표표=1 + 푢푢푡푡푞푞
  - where y = quarterly GDP growth of mining and non-mining sectors, xi are HF indicators such as copper production, cobalt production, copper price, and broad Money.
  - βi(L) are polynomials in lag operator L: βi(L)= β0i + β1i L + ⋯ + βpi L^pi, one for each HF indicator, where pi is number of lags.
  - utq is an i.i.d. error term.

### Validation and diagnostic practice
- Select indicators based on correlation checks and chart inspection before applying Chow-Lin.
- After interpolation, validate interpolated quarterly GDP against qualitative and expert insights (BCC team).
- Use MIDAS/Bridge/U-MIDAS frameworks when integrating higher-frequency indicators and when re-estimation within the quarter is needed.

*International Monetary Fund — Annex I. Interpolating Quarterly GDP (from provided document content).*

### Annex IV . Summary of the DRCMOD Model

### Annex IV . Summary of the DRCMOD Model

### Model Equations — Aggregate Demand
- Aggregate demand decomposed into non-mining and mining components and includes lags, monetary conditions, foreign output gap, mining output gap, fiscal impulse, and shocks:
  - Equation (1): ŷ_t_NMIN = b11 ŷ_{t-1}_NMIN − b12 MCI_t + b13 ŷ_t_RW + b15 ŷ_t_MIN + b16 fisp_t + ε_{t}^{y_NMIN}
  - Output level identity: y_t_NMIN = y_t_NMIN_bar + ŷ_t_NMIN (equations (2), (4))
  - Mining and non-mining gap dynamics with autoregressive terms and interest/relative price influences (equations (3), (10), (11))
  - Quarterly growth and gap definitions given by 4⋅(level − previous level) (equations (12)–(17))
- Fiscal divergence/statistical discrepancy treated as random walk: y_t_D = y_{t-1}_D + ε_{t}^{y_D} (equation (16))

### Model Equations — Phillips Curve and Inflation
- Aggregate price index is weighted average across underlying components and foreign/domestic items (equation (18)):
  - p_t = w_C ⋅ p_t_C + w_F ⋅ p_t_F + (1 − w_C − w_F) ⋅ p_t_D + ε_{t}^{c_D}
- Component inflation processes (domestic underlying, food, energy) follow AR(1) with expected inflation and real marginal cost terms:
  - π_t_D = a11 ⋅ π_{t-1}_D + (1 − a11) ⋅ Rπ_t_D + a12 ⋅ rfc_t_D + ε_{t}^{π_D} (equation (19))
  - Similar forms for π_t_F (equation (25)) and π_t_C (equation (31))
- Real marginal cost and relative price definitions: rrp_t_D = p_t_D − p_t_RW (equation (21)); rp definitions and gaps (equations (32)–(36))
- Inflation annualization and forecasting relations: π_t = 4(p_t − p_{t-1}) and Rπ_t = π_{t+1} (equations (37)–(45))
- Quarterly-to-annual transformations and AR(1) of inflation innovations (equations (46)–(49))

### Model Equations — Relative Prices
- Relative price levels, gaps and trend dynamics defined for various components (underlying, energy, food, world commodity prices):
  - rp_t_{component} = p_t_{component} − p_t_{reference} with rp_t = rp_t_bar + rp'_t (equations (50)–(66))
  - Quarterly differences and AR(1)/smoothed processes for gaps and trends (equations (51)–(69))

### Model Equations — Uncovered Interest Parity (UIP)
- Exchange rate s_t dynamics include inertia, expected change in neutral exchange rate, output gap, relative price gaps, expected interest differentials, inflation terms, and shocks:
  - Equation (70) specifies s_t as function of s_{t-1}, Δs_{t}_N, ŷ_t_RW, rrp'_t_MIN, rrp'_t_NMIN, expectations term (1−k2)(1−e1)s_{t+1}+e1(s_{t-1}), inflation/term structure, and ε_{t}^{s}
- Δs_t_N specified as π_{t}_4T − sss Δπ_{rrr} + Δz_t (equation (71))
- Quarterly and annual differences defined (equations (78)–(79))

### Model Equations — Foreign Exchange Intervention
- Reserves and intervention rules:
  - RES_t = RES_{t-1} + γ ⋅ (Δs_{t}_N − Δs_t) + ε_t^{RES} (equation (72))
  - RES_t follows AR(1) toward a steady-state with rho_RES_BAR = 0.80 (equation (73))
  - p_r_e_f_t_RES = θ (RES_t − RES_t_bar) (equation (74))
- Real exchange gap definitions: z_t = s_t + p_t_RW − p_t (equation (75)); z_hat_t = z_t − z_t_bar (equation (76))

### Model Equations — Monetary Policy
- Monetary policy instrument (policy rate or monetary target) mixes exchange-rate-influenced terms, inflation deviations, output gap, persistence and shocks:
  - f_t_DTT given by a comprehensive rule mixing k1, e1, s_t expectations, inflation targets, Δz_t, past policy rate, neutral rates, and shock ε_t^{policy} (equation (80))
- Nominal interest rate decomposition and Fisher relation:
  - f_t_N = rrr_t + π_{t+1}/4 (equation (81))
  - rrr_t = f_t − π_{t+1}/4 (equation (82))
  - Persistence of real rate innovations rrr_t = rrr_t + rrr'_t (equation (83))
- Money demand and velocity dynamics: v_t = v_t_bar + v'_t with v'_t AR(1) (equations (95)–(97)), and Δv definitions (equations (98)–(99))
- Multiple quarterly averaging and transformation definitions for policy rates and yields (equations (86)–(94))

### Model Equations — Trend and Equilibrium Processes
- Trend growth and potential output processes specified as AR(1) with stochastic innovations and smoothing parameters (equations (100)–(111))
  - Δy_t_NMIN etc. follow rho parameters toward steady-state ss_ values
- Trend inflation and trend real rates follow AR(1) (equations (108)–(111))
- External price shock/premium relations: p_r_e_f_t = rrr_t − rrr_t_rrr − Δz_{t+1} (equation (112))

### Model Equations — External Sector
- World output gap, foreign interest rates and foreign inflation follow AR(1) with shocks:
  - ŷ_t_RW = ρ_{ŷ_RW} ŷ_{t-1}_RW + ε_{t}^{ŷ_RW} (equation (113))
  - f_t_RW = ρ_{f_RW} f_{t-1}_RW + (1 − ρ_{f_RW}) ⋅ (f_RW_t + Δπ_{t}_RW) + ε_t^{f_RW} (equation (114))
  - Δπ_t_RW AR(1) with shock (equation (115))

### Model Equations — Fiscal Block
- Debt dynamics and fiscal targets:
  - Debt-to-GDP processes with persistence toward targets and shocks (equations (117)–(125))
  - Debt decomposition into local-currency and foreign-currency components; interactions with reserves, exchange rate changes, commodity price and production gaps (equations (121)–(124))
  - Price-level and nominal GDP relations: ΔPPY_t = Δy_t + π_t (equations (125)–(126))
  - Fiscal impulse fisp_t specified as linear combination of fiscal shock series (equation (127))

### Model Equations — Dollarization and Related Blocks
- Dollarization index MCI_t defined as weighted combination of foreign-currency rates and real exchange misalignment:
  - MCI_t = h1 ⋅ (h2 ⋅ rrr'_t + (1 − h2) ⋅ rrr'_t_FXD) + (1 − h1) ⋅ (− ẑ_t) (equation (128))
- Foreign-currency interest and Fisher relations and growth differencing spelled out (equations (129)–(138))

### Model Variables (selection)
- Notation mapping (variable / model name / description) includes, among others:
  - ŷ: L_GDP_GAP — Écart de production
  - ŷ_NMIN: L_NMIN_GAP — Écart de production non-minière
  - ŷ_MIN: L_MIN_GAP — Écart de production minière
  - MCI: MCI — Indice des Conditions Monétaires
  - ŷ_RW: L_GDP_RW_GAP — Écart de production pour le reste du monde
  - rrr': RR_GAP — Écart de taux d’intérêt réel
  - ẑ: L_Z_GAP — Écart de taux de change réel
  - π: DLA_CPI — Taux d’inflation trimestriel annualisé (en %)
  - p: L_CPI — Indice des prix domestiques (niveau, 100*log)
  - rrfc_D, rrfc_F, rrfc_C: RMC_XFE, RMC_F, RMC_E — Coûts marginaux réels des composantes IPC
  - A broad set of world commodity price logs and gaps: L_WCOP, L_WCOB, L_WFOOD, and their relative price gaps and trends
  - Fiscal and debt variables: DEB_RAT_TAR, DEB_RAT, DEF_RAT, DEF_S_RAT, etc.
  - Monetary aggregates and velocity: rrf (L_RM), v (L_V), growth rates DLA_M, DLA_V, and targets (DLA_M_TAR, DLA_RM_TAR)

### Model Parameters (selected values)
- Dollarization and MCI weights:
  - h1 = 0.70
  - h2 = 0.20
- Aggregate demand coefficients:
  - b11 = 0.50
  - b12 = 0.20
  - b13 = 0.10
  - b15 = 0.10
  - b16 = 0.10
  - b21 = 0.50
  - b22 = 0.10
  - b23 = 0.28
  - b231 = 0.24
  - b24 = 0.10
  - b241 = 0.19
- Shares and Phillips coefficients:
  - w_NMIN = 0.70
  - a31 = 0.50
  - a32 = 0.01
  - a11 = 0.50
  - a12 = 0.30
  - a13 = 0.50
  - a21 = 0.50
  - a22 = 0.30
  - a23 = 0.50
  - w_CPIE = 0.09
  - w_CPIF = 0.47
- UIP / exchange parameters:
  - k1 = 0.10
  - k2 = 0.90
  - k3 = 0.09
  - k4 = 0.10
  - k5 = 0.12
- FX intervention and related:
  - gamma = 1.00
  - theta = 0.00
  - rho_RES_BAR = 0.80
- Persistence and smoothing parameters (selected):
  - rho_DLA_RPXFE_BAR = 0.80
  - rho_DLA_RPF_BAR = 0.80
  - rho_DLA_RWOIL_BAR = 0.80
  - rho_DLA_RWFOOD_BAR = 0.80
  - rho_DLA_RWCOP_BAR = 0.80
  - rho_DLA_RWCOB_BAR = 0.80
  - rho_DEB_RAT_TAR = 0.99
  - rho_DEF_S_RAT = 0.70
  - g1 = 0.70; g2 = 0.50; g3 = 0.50
  - e1 = 0.40
  - c1 = 0.60; c2 = 0.30
  - f1 = 0.50
  - mpr = 0.75
  - p1 = 0.05; p2 = 0.50; p3 = 0.10; p4 = 0.10
- Steady-state and long-run scalars (selected ss_ values):
  - ss_DLA_RWOIL_BAR = 3.00
  - ss_DLA_RWCOP_BAR = 4.70
  - ss_RES_BAR = 7.00
  - ss_DLA_Prod_copper_BAR = 8.47
  - ss_DLA_prod_cobalt_BAR = 3.82
  - ss_D4L_CPI_TAR = 7.00
  - ss_RR_BAR = 3.00
  - ss_DLA_NGDP = 12.50
  - ss_DEF_RAT = 0.50
  - ss_DEB_RAT_TAR = 4.50
  - ss_DEB_LC_RAT = 0.90
  - ss_DEB_FC_RAT = 3.60
  - s1 = 0.89; s2 = 0.01; s3 = 0.89; s4 = 0.03; s5 = 0.03
  - q1 = 0.89; q2 = 0.03; q3 = 0.04

### Model Shocks (standard deviations)
- Real activity shocks:
  - ε^{y_NMIN}_t (SHK_L_NMIN_GAP) StDev = 2.39
  - ε^{y_MIN}_t (SHK_L_MIN_GAP) StDev = 14.34
  - SHK_RS StDev = 14.34
  - ε^{s}_t (SHK_L_S) StDev = 5.98
- Potential/productivity shocks:
  - SHK_DLA_NMIN_BAR StDev = 2.03
  - SHK_DLA_MIN_BAR StDev = 5.98
- Inflation, interest-rate, external shocks:
  - SHK_D4L_CPI_TAR StDev = 2.39
  - SHK_RR_RW_BAR StDev = 2.39
  - SHK_DLA_Z_BAR StDev = 1.79
  - SHK_L_GDP_RW_GAP StDev = 1.00
  - SHK_RS_RW StDev = 1.00
  - SHK_RS_FC StDev = 4.78
  - SHK_DLA_CPI_RW StDev = 2.00
  - SHK_RR_BAR StDev = 2.39
- Money and velocity shocks:
  - SHK_DLA_RM StDev = 7.17
  - SHK_L_V_GAP StDev = 3.59
  - SHK_DLA_V StDev = 2.39
- Price-component shocks (CPI subcomponents):
  - SHK_L_CPI_DISC StDev = 1.20
  - SHK_DLA_CPIXFE StDev = 7.17
  - SHK_DLA_CPIF StDev = 11.95
  - SHK_DLA_CPIE StDev = 4.78
- Relative price trend shocks and world commodity price shocks:
  - SHK_DLA_RPXFE_BAR StDev = 0.60
  - SHK_DLA_RPF_BAR StDev = 0.60
  - SHK_DLA_RWOIL_BAR StDev = 3.59
  - SHK_L_RWOIL_GAP StDev = 21.51
  - SHK_DLA_RWFOOD_BAR StDev = 1.20
  - SHK_L_RWFOOD_GAP StDev = 7.17
  - SHK_DLA_RWCOP_BAR StDev = 3.59
  - SHK_L_RWCOP_GAP StDev = 15.54
  - SHK_DLA_RWCOB_BAR StDev = 4.06
  - SHK_L_RWCOB_GAP StDev = 20.32
- Fiscal and reserves shocks:
  - SHK_DEB_RAT_TAR StDev = 5.98
  - SHK_DEF_S_RAT StDev = 2.39
  - SHK_DEB_RAT StDev = 8.96
  - SHK_RES StDev = 2.39
  - SHK_RES_BAR StDev = 2.39
- Statistical discrepancy, production shocks:
  - SHK_L_GDP_DISC StDev = 2.39
  - SHK_BCC_INS_DISC StDev = 9.56
  - SHK_L_prod_cobalt_GAP StDev = 16.73
  - SHK_L_Prod_copper_GAP StDev = 19.12
  - SHK_DLA_prod_cobalt_BAR StDev = 4.78
  - SHK_DLA_Prod_copper_BAR StDev = 5.98

*International Monetary Fund — Working Paper No. WP/2024/126 — Annex IV . Summary of the DRCMOD Model*

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_Source: https://www.imf.org/-/media/files/publications/wp/2024/english/wpiea2024126-print-pdf.pdf_