## Preface

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---

### Mission context and participants
- TA mission on “Further strengthening the nowcasting framework at the National Bank of Rwanda” (NBR) took place during October 9–18, 2023.
- The mission was part of the IMF Monetary and Capital Markets Department (MCM) and AFRITAC East (AFE) technical assistance (TA) project on Forecasting and Policy Analysis System (FPAS).
- Mission team comprised:
  - Messrs. Eilert Husabø and Pål Bergset Ulvedal Short-Term Experts (STXs), the Norges Bank.
  - Jianping Zhou (Senior Economist, MCM) provided support from the IMF HQ.
- Daily technical sessions were attended by staff from the forecasting teams of the Monetary Policy & Research Directorate.
- Mr. Thierry Mihigo Kalisa (Chief Economist of the NBR) joined a concluding session.

### Acknowledgements
- The mission thanks the NBR staff and management for the engaging and productive discussions.

### Executive Summary — objectives and accomplishments
- Mission objectives:
  - (i) further strengthen the understanding and use of nowcasting frameworks for Gross Domestic Product (GDP) and Consumer Price Index (CPI) inflation at the NBR;
  - (ii) analyze the effects of weather shocks on food crop production and fresh food prices.
- Tasks completed:
  - Improved forecast evaluation by fixing problems with using different Core CPI definitions for the medium-term Quarterly Projection Model (QPM) and the nowcasting models.
  - Provided hands-on training to NBR staff on using CPI nowcasting tools for monitoring monthly inflation outcomes and on creating and interpreting uncertainty fan charts for GDP and CPI projections.
  - Enhanced NBR staff’s understanding of how high-frequency real sector indicators are constructed in the GDP nowcasting models.
  - Established a system for analyzing weather shocks (in particular rainfall) on food crop production and fresh food prices.
- Forward-looking needs:
  - GDP and CPI nowcasting frameworks need further refinement to support deeper analysis at a disaggregated level to improve understanding of current developments and storytelling.
  - Nowcasting model systems need integration with the new in-house database currently under construction at the NBR.
  - NBR staff plan to create one or more diffusion indexes using the Food Price Expectations Survey; further technical support may be needed in constructing these indexes and understanding their use in the FPAS.
- Terminology note (preserved from source):
  - "In this report, nowcasting and near-term forecasting are used interchangeably. Strictly speaking, nowcasting GDP refers to the process of predicting the current state and near-term forecasting (NTF) refers to the process of predicting future GDP using real-time economic data."

### Key recommendations (Table 1: Key Recommendations)
- NBR should organize the data from the Food Price Expectations Survey as time series, develop diffusion indexes and start to use them systematically in the FPAS.
  - Priority: High
  - Timeframe: Medium-term
- NBR should adapt the Quarterly Projection Model and Near-Term Forecasting systems to collect input data from the new in-house database system that is currently being established.
  - Priority: High
  - Timeframe: Medium-term
- NBR should continue refining the models in the nowcasting system for the twelve main CPI Classification of Individual Consumption by Purpose (COICOP) groups, with a view to increase understanding of inflation dynamics, and with a goal to move from forecasting core, energy, and food inflation directly, to forecasting these three groups bottom-up.
  - Priority: Medium
  - Timeframe: Medium-term
- Timeframe definitions (from source):
  - Near term: < 12 months
  - Medium term: 12 to 24 months

*IMF Technical Assistance Report*

### The NBR price-based monetary policy framework and FPAS development
- The NBR started implementing a price-based monetary policy framework (MPF) in January 2019.
- The FPAS framework generates model-based forecasts, presented to the Monetary Policy Committee (MPC) and published in the quarterly monetary policy reports (MPRs).
- Since 2020, AFE supported the development of this framework through regular TA missions and bilateral and multilateral workshops.
- An FPAS framework includes three technical elements: frameworks for analyzing and forecasting foreign developments (external assumptions, EAs), the nowcasting framework (initial conditions, IC), and the QPM. At the start of the TA project, the nowcasting framework and external frameworks were less developed than the QPM at the NBR.

### Focus on nowcasting development and key deficiency
- Recent TA missions emphasized:
  - Expert sector teams responsible for monitoring, tools/models, forecast error analysis, judgments, narrative inputs for MPRs, and drafting internal memos.
  - Separation of nowcasting team expertise and core model team.
- Key deficiency identified:
  - Nowcasting systems for GDP and CPI perform well in many respects but lack relevant indicators and mechanisms for agricultural production and food prices.
  - NBR requested TA to develop a framework for analyzing effects of weather shocks on agricultural production and food prices — the main focus of this mission.

### The Nowcasting System — CPI and GDP (mission chronology and outputs)
- CPI nowcasting developments:
  - September 2021: Developed tools for deeper disaggregate analysis of inflation and underlying measures for MPRs.
  - March 2022: Built nowcasting models with out-of-sample forecast error calculations and model averaging; covered headline, core, food, energy; refined system outperformed ARMA and existing VAR up to six months.
  - December 2022: Extended system to forecast headline and core CPI from 12 COICOP groups; developed Inflation Dashboard and forecast error framework.
  - Current mission: Strengthened monthly-to-quarterly transformations, recommended updating nowcasting with every new inflation outcome, unified Core CPI definition across QPM and nowcasting, and trained on uncertainty fan charts.
- GDP nowcasting developments:
  - Original framework included bridge equations and a Dynamic Factor Model (DFM) used to backcast monthly GDP; lacked out-of-sample evaluations.
  - March 2022: Built EViews-based GDP nowcasting with bivariate bridge equations, indicator selection via out-of-sample performance, and model averaging; outperformed autoregressive benchmark at one- and two-quarter horizons.
  - December 2022: Provided disaggregate forecasts for Agriculture, Industry, Services, and Net Taxes.
  - Current mission: Ensured updated nowcasts with incomplete indicators by forecasting missing monthly indicators via autoregressive models; revisited uncertainty band construction and visualization.

### Analysis of the Effects of Rainfall

### Motivation and scope
- Previous missions identified shortcomings forecasting agricultural production and fresh food price inflation; recent weather shocks caused shortfalls in agricultural production and increases in fresh food prices not captured by existing systems.
- This mission established a framework to analyze weather shocks on food crop production and food price inflation using daily rainfall data from weather stations across Rwanda.
- Focus: identify dry-spells and heavy rainfall periods and estimate effects on crop production; estimate the effect of crop production variations on fresh food prices.

### Data collection and processing
- Data sources and formats:
  - Daily rainfall data from 14 weather stations across Rwanda, measured in millimeters per day.
  - Semi-annual food crop production from the Seasonal Agricultural Survey (National Institute of Statistics Rwanda) for seasons A, B, and C from 2013 to 2023; season C negligible, analysis focused on seasons A and B.
  - Due to extreme outliers in 2013, data from 2013 excluded—resulting in only 20 data points of crop production for each single crop for estimation.
  - Disaggregate fresh food price data starts in January 2019.
  - Aggregate price of imported fertilizer and back-casting of CPI based on actual price levels also collected.
- Data handling:
  - Untransformed data stored in Excel; EViews programs used for transforms and aggregation.
  - EViews programs designed to allow easy changes to group definitions, time periods, and threshold values.
  - Manual for updating system included in appendix 3.
- Rain indicators and thresholds:
  - Rainfall for each crop aggregated as the average across relevant stations on a daily basis.
  - Dry spell (DS) defined as seven consecutive days without rainfall.
  - Heavy rainfall (HR) defined as a day when it rained more than four standard deviations above average level for the relevant region.
  - A day with less than 0.85 mm rain counts as a day with no rainfall.

### A. Agricultural Production — modeling approach and key empirical findings
- Modeling challenges and constraints:
  - Relationship between rainfall and production is complex; crop-specific water needs vary by stage; tolerance to rainfall differs; production influenced by fertilizer availability/cost, seeds, storage weather, market access.
  - Analysis focused solely on rainfall due to lack of data on other explanatory variables.
  - Short sample length: only 20 semi-annual observations per crop.
- Model structure:
  - Panel data methods used to exploit cross-sectional variation across crops and time variation.
  - Crop production gaps constructed as log-deviations from a linear trend to capture levels rather than growth rates.
  - Rain indicators linked to relevant months/areas per crop.
  - Parsimonious pooled least squares (panel) model estimated in EViews with cross-section identifiers for crops and relevant geographic rainfall.
- Estimated regression (parsimonious notation preserved):
  - y_{i,t} = C + β0 y_{i,t−1} + β1 DS_{i,t}^{P} + β2 HR_{i,t}^{P} + β3 HR_{i,t}^{H} + β4 TR_{i,t} + ε_{i,t}
    - y_{i,t} (productiongap): gap measure of crop production (log deviation from linear trend).
    - DS_{i,t}^{P} (dryspell_planting): dummy = dry-spell during planting period in relevant areas.
    - HR_{i,t}^{P} (heavyrain_planting), HR_{i,t}^{H} (heavyrain_harvesting): dummies for heavy rainfall during planting and harvesting.
    - TR_{i,t} (sum): average amount of rainfall during growing and harvesting periods.
- Rules of thumb identified (stable, theory-consistent results):
  - Dry spells during the planting season are expected to lower crop production by around 7 percent.
  - Heavy rainfall during the harvesting season is expected to lower crop production by around 5 percent.
  - Total amount of rainfall during the growing season (sum) does not have a significant effect on crop production after controlling for unusual weather events.
- Caveats:
  - Some evidence of a negative effect of heavy rainfall during planting, but this is less robust across specifications.
  - Estimates may lack robustness due to the short sample size and should be cross-checked against other studies when available.
- Operational recommendation:
  - Use the framework to inform judgement in nowcasting but not integrate the estimated model formally into the nowcasting system yet.
  - Start monitoring daily rainfall data and use the rules of thumb together with other sources (news, surveys) to inform judgements.
  - Update the estimated model bi-annually when new crop production data become available.

### B. Fresh Food Prices — modeling approach and specification
- Data and modelling constraints:
  - Disaggregate fresh food prices available from January 2019 — a short series for robust inference.
  - Panel data models used to exploit cross-sectional variation across 11 food groups.
  - Food groups linked to the most relevant crops; crop production for seasons A and B added as deviation from normal level.
  - Model includes the effect of variations in the price of imported fertilizer.
- Estimated model (preserved notation):
  - Δp_{i,t} = C + β0 Δp_{i,t−1} + β1 Δp_{i,t−2} + β2 Δp_{i,t−3} + β3 y_{i,t} + β3 Δf_{t−2} + ε_{i,t}
    - p_{i,t} (cpi): log level of CPI for fresh food crop i in period t; Δ denotes first difference.
    - y_{i,t} (production): gap measure for crop production.
    - f_{t−2} (bnr_fertilizer_rwf): log level of fertilizer prices in Rwandan Francs in period t−2.
- Timing assumption:
  - CPI models assume production variations affect CPI food prices in the first month following the growing season (Season A → January; Season B → June). Effects on intermediate months assumed not captured, but level effect in January and June fully captured.

### Key quantitative findings and rules of thumb
- A 10 percent decline in crop production relative to its normal level is associated with a 5 percent increase in fresh food prices, and vice versa.
- Normal level of crop production is defined as the linear trend of crop production over time (the model therefore assumes that crop production is increasing over time for most foods).
- A 10 percent increase in the RWF price of imported fertilizer is associated with a 1 percent increase in fresh food prices.
- Model caution: "It is important to stress that these estimates might not be robust because of the small sample size. The estimates should be cross-checked against other relevant studies if available."

### Estimation results (pooled least squares for DLOG(CPI?))
- Sample (adjusted): 2019M02 2023M09
- Included observations: 56 after adjustments
- Cross-sections included: 11
- Total pool (balanced) observations: 616
- Estimated coefficients and inference:
  - C = 0.012957; Std. Err. = 0.004457; t-Statistic = 2.907046; Prob. = 0.0038
  - DLOG(CPI?(-1)) = 0.042451; Std. Err. = 0.040253; t-Statistic = 1.054604; Prob. = 0.2920
  - DLOG(CPI?(-2)) = -0.247794; Std. Err. = 0.038866; t-Statistic = -6.375563; Prob. = 0.0000
  - DLOG(CPI?(-3)) = 0.080673; Std. Err. = 0.040365; t-Statistic = 1.998588; Prob. = 0.0461
  - PRODUCTION? = -0.482844; Std. Err. = 0.115149; t-Statistic = -4.193190; Prob. = 0.0000
  - DLOG(BNR_FERTILIZER_RWF(-2)) = 0.081804; Std. Err. = 0.032874; t-Statistic = 2.488387; Prob. = 0.0131
- Model fit and diagnostics:
  - R-squared = 0.103197
  - Adjusted R-squared = 0.095846
  - Mean dependent var = 0.013088
  - S.D. dependent var = 0.113016
  - S.E. of regression = 0.107463
  - Akaike info criterion = -1.613646
  - Schwarz criterion = -1.570562
  - Log likelihood = 503.0028
  - Hannan-Quinn criter. = -1.596894
  - Sum squared resid = 7.044477
  - F-statistic = 14.03882
  - Prob(F-statistic) = 0.000000
  - Durbin-Watson stat = 2.024918

### Additional quantitative results referenced in slides
- A dry spell during planting season is expected to reduce crop production by 6.5 percent.
- Heavy rainfall during harvesting season is expected to reduce crop production by 5 percent.
- Quantitative summary restated: "A reduction(increase) in production of a crop by 10% is expected to give an increase(reduction) of the price of that crop by 5%."
- Note: "These estimates are based on a short sample, and are uncertain."

### Policy and operational recommendations (Next Steps)
- Establish monitoring of daily rainfall data:
  - NBR should start monitoring data on rainfall to detect weather events that could affect crop production.
  - Procedures for obtaining and analyzing daily rainfall data from the relevant weather stations should be established.
  - The framework developed during the mission could be used for this purpose.
- Use identified rules of thumb to inform nowcasting:
  - The rule of thumb (10 percent production ⇄ 5 percent price change; fertilizer price effects) should be used to inform judgement in the nowcasting process.
  - It could be used together with results from crop production models and other information regarding developments in agricultural output.
  - The estimated model should be updated bi-annually when new crop production data is available.
- Use and formalize the Food Price Expectations Survey:
  - The Food Price Expectations Survey should be used actively in the nowcasting process.
  - Historical results from the survey should be organized as time series and a diffusion index created from the data for different crops.
  - Such diffusion indices could be valuable indicators for variations in fresh food production and prices.
- Continue refining the nowcasting framework and integrate tools:
  - The nowcasting framework should be refined to support deeper monetary policy analysis, using disaggregated-level analysis for better storytelling and policy communication.
  - CPI and GDP NTF tools should be used monthly as part of the forecasting process and FPAS work at the NBR going forward; CPI NTF includes monthly forecasts of ten subgroups of the core CPI and two subgroups of food inflation.
  - The GDP NTF-system should replace the current DFM for improved sectoral production forecasts.
  - Integrate QPM and NTF systems into the in-house database currently being constructed; make necessary changes to existing forecasting systems once the new database is finalized.
  - The NBR may benefit from technical assistance during the migration to a more robust database system.

### Data and model caveats emphasized
- Short sample lengths and limited historical availability:
  - Crop production data starts in 2013; price data is only available since 2019 (5 years).
  - The impact from weather to crop production is complex and varies across crops and regions; no simple stable relationship between rainfall and crop production.
  - Other factors (diseases, fertilizer availability, acreage) matter and current data may not be granular enough.
- Empirical approach and robustness:
  - Estimates rely on both cross-section and time variation (panel regression) over 11 years (22 seasons) of data.
  - The rule-of-thumb and model estimates should be cross-checked against other relevant studies and treated as inputs to judgement-based nowcasting.

_Italic: Source: IMF and NBR staff, IMF Technical Assistance Report (section: fresh food prices and corresponding crop production data as shown in Table 5)._

### Preface ................................................................................................................

### Preface

### Mission context and participants
- TA mission on “Further strengthening the nowcasting framework at the National Bank of Rwanda” (NBR) took place during October 9–18, 2023.
- The mission was part of the IMF Monetary and Capital Markets Department (MCM) and AFRITAC East (AFE) technical assistance (TA) project on Forecasting and Policy Analysis System (FPAS).
- Mission team comprised:
  - Messrs. Eilert Husabø and Pål Bergset Ulvedal Short-Term Experts (STXs), the Norges Bank.
  - Jianping Zhou (Senior Economist, MCM) provided support from the IMF HQ.
- Daily technical sessions were attended by staff from the forecasting teams of the Monetary Policy & Research Directorate.
- Mr. Thierry Mihigo Kalisa (Chief Economist of the NBR) joined a concluding session.

### Acknowledgements
- The mission thanks the NBR staff and management for the engaging and productive discussions.

### Executive Summary — objectives and accomplishments
- Mission objectives:
  - (i) further strengthen the understanding and use of nowcasting frameworks for Gross Domestic Product (GDP) and Consumer Price Index (CPI) inflation at the NBR;
  - (ii) analyze the effects of weather shocks on food crop production and fresh food prices.
- The mission built on progress from the December 2022 FPAS mission, which focused on improving the nowcasting framework for key domestic variables (including CPI and GDP) and building tools for analyzing new data releases and assessing the nowcasting systems.
- Tasks completed:
  - Improved forecast evaluation by fixing problems with using different Core CPI definitions for the medium-term Quarterly Projection Model (QPM) and the nowcasting models.
  - Provided hands-on training to NBR staff on using CPI nowcasting tools for monitoring monthly inflation outcomes and on creating and interpreting uncertainty fan charts for GDP and CPI projections.
  - Enhanced NBR staff’s understanding of how high-frequency real sector indicators are constructed in the GDP nowcasting models.
  - Established a system for analyzing weather shocks (in particular rainfall) on food crop production and fresh food prices.
- Forward-looking needs:
  - GDP and CPI nowcasting frameworks need further refinement to support deeper analysis at a disaggregated level to improve understanding of current developments and storytelling.
  - Nowcasting model systems need integration with the new in-house database currently under construction at the NBR.
  - NBR staff plan to create one or more diffusion indexes using the Food Price Expectations Survey; further technical support may be needed in constructing these indexes and understanding their use in the FPAS.

- Terminology note preserved from source:
  - "In this report, nowcasting and near-term forecasting are used interchangeably. Strictly speaking, nowcasting GDP refers to the process of predicting the current state and near-term forecasting (NTF) refers to the process of predicting future GDP using real-time economic data."

### Key recommendations (Table 1: Key Recommendations)
- NBR should organize the data from the Food Price Expectations Survey as time series, develop diffusion indexes and start to use them systematically in the FPAS.
  - Priority: High
  - Timeframe: Medium-term
- NBR should adapt the Quarterly Projection Model and Near-Term Forecasting systems to collect input data from the new in-house database system that is currently being established.
  - Priority: High
  - Timeframe: Medium-term
- NBR should continue refining the models in the nowcasting system for the twelve main CPI Classification of Individual Consumption by Purpose (COICOP) groups, with a view to increase understanding of inflation dynamics, and with a goal to move from forecasting core, energy, and food inflation directly, to forecasting these three groups bottom-up.
  - Priority: Medium
  - Timeframe: Medium-term

- Timeframe definitions (from source):
  - Near term: < 12 months
  - Medium term: 12 to 24 months

*IMF Technical Assistance Report*

### Introduction

### Introduction

### The NBR price-based monetary policy framework and FPAS development
- The NBR started implementing a price-based monetary policy framework (MPF) in January 2019.
- The FPAS framework generates model-based forecasts, presented to the Monetary Policy Committee (MPC) and published in the quarterly monetary policy reports (MPRs).
- Since 2020, AFE supported the development of this framework through regular TA missions and bilateral and multilateral workshops.
- An FPAS framework includes three technical elements: frameworks for analyzing and forecasting foreign developments (external assumptions, EAs), the nowcasting framework (initial conditions, IC), and the QPM. At the start of the TA project, the nowcasting framework and external frameworks were less developed than the QPM at the NBR.

### Focus on nowcasting development
- The last four TA missions focused on developing the NBR’s nowcasting framework, emphasizing:
  - Expert sector teams (one to three staff per key variable/sector) responsible for monitoring, tools/models, forecast error analysis, judgments, narrative inputs for MPRs, and drafting internal memos.
  - Separation of nowcasting team expertise and core model team; often hosted in different divisions within the Research department or from the Monetary Policy and Research Directorate (MPRD).

### Key deficiency identified
- Nowcasting systems for GDP and CPI perform well in many respects but lack relevant indicators and mechanisms for agricultural production and food prices.
- The NBR requested TA to develop a framework for analyzing effects of weather shocks on agricultural production and food prices — the main focus of this mission.

---

### The Nowcasting Framework (high level)
- Nowcasting team composition and roles:
  - Responsible variables/sectors: inflation, real sector activity/GDP, fiscal performance, labor market, and other primary sectors.
  - Tasks: develop/run analytical tools and models (aggregate and disaggregate), perform forecast error analysis, provide judgement and interpretation for near and medium-term forecasts, supply MPR text and internal memos.

---

### A. The Nowcasting System for CPI — mission chronology and outputs
- September 2021 mission:
  - Developed tools for deeper disaggregate analysis of inflation to improve understanding of inflation dynamics and underlying pressures.
  - Tools provide up-to-date, high frequency data and charts/measures of underlying inflation used in MPRs.
- March 2022 mission:
  - Built a system of nowcasting models based on different indicators/explanatory variables with out-of-sample forecast error calculations and model averaging.
  - Covered headline, core, food, and energy inflation.
  - Refined system outperformed benchmark ARMA and existing VAR on horizons up to six months.
- December 2022 mission:
  - Extended system to forecast headline and core CPI from the 12 main COICOP groups.
  - Developed a framework (Inflation Dashboard) to bridge nowcasting-system results to the policy model.
  - Emphasized regular forecast error analysis and developed a framework for it.
- This mission (current):
  - Revisited the nowcasting system to strengthen understanding of monthly-to-quarterly transformations and allow monthly comparisons to actual outcomes.
  - Recommended updating inflation nowcasting and the Inflation Dashboard with every new inflation outcome.
  - Assisted in unifying the Core CPI definition used in the QPM and nowcasting systems.
  - Provided hands-on training for creating and interpreting uncertainty fan charts for CPI.

---

### B. The Nowcasting System for GDP — mission chronology and outputs
- Original framework limitations:
  - Included bridge equations and a Dynamic Factor Model (DFM) used to backcast a monthly GDP variable (quarterly GDP divided by 3).
  - Lacked out-of-sample evaluations and were based on annual changes.
- March 2022 mission:
  - Built an EViews-based system for GDP nowcasting similar to CPI system.
  - System: simple bivariate bridge equations with indicators selected for out-of-sample performance and model averaging.
  - Produces backcast and nowcast for previous and current quarter; outperforms a simple autoregressive benchmark at one- and two-quarter horizons.
- December 2022 mission:
  - Refined the system and provided disaggregate forecasts for main sectors: Agriculture, Industry, Services, and Net Taxes.
  - Disaggregate GDP nowcasts help provide a story behind the aggregate nowcast.
- This mission (current):
  - Ensured system can produce updated nowcasts at any point even with incomplete high-frequency indicators by using forecasts from autoregressive models to fill missing monthly indicators.
  - Revisited uncertainty band construction and visualization to communicate ranges and confidence in forecasts.

---

### Analysis of the Effects of Rainfall

### Motivation and scope
- Previous missions identified shortcomings forecasting agricultural production and fresh food price inflation; recent weather shocks caused shortfalls in agricultural production and increases in fresh food prices not captured by existing systems.
- This mission established a framework to analyze weather shocks on food crop production and food price inflation using daily rainfall data from weather stations across Rwanda.
- Focus: identify dry-spells and heavy rainfall periods and estimate effects on crop production; estimate the effect of crop production variations on fresh food prices.

### Data collection and processing
- Data sources and formats:
  - Daily rainfall data from 14 weather stations across Rwanda, measured in millimeters per day.
  - Semi-annual food crop production from the Seasonal Agricultural Survey (National Institute of Statistics Rwanda) for seasons A, B, and C from 2013 to 2023; season C negligible, analysis focused on seasons A and B.
  - Due to extreme outliers in 2013, data from 2013 excluded—resulting in only 20 data points of crop production for each single crop for estimation.
  - Disaggregate fresh food price data starts in January 2019.
  - Aggregate price of imported fertilizer and back-casting of CPI based on actual price levels also collected.
- Data handling:
  - Untransformed data stored in Excel; EViews programs used for transforms and aggregation.
  - EViews programs designed to allow easy changes to group definitions, time periods, and threshold values.
  - Manual for updating system included in appendix 3.
- Rain indicators and thresholds:
  - Rainfall for each crop aggregated as the average across relevant stations on a daily basis.
  - Dry spell (DS) defined as seven consecutive days without rainfall.
  - Heavy rainfall (HR) defined as a day when it rained more than four standard deviations above average level for the relevant region.
  - A day with less than 0.85 mm rain counts as a day with no rainfall.

---

### A. Agricultural Production — modeling approach and key empirical findings
- Modeling challenges and constraints:
  - Relationship between rainfall and production is complex: crop-specific water needs vary by stage; tolerance to rainfall differs; production influenced by other factors (fertilizer availability/cost, seeds, storage weather, market access).
  - The analysis focused solely on rainfall due to lack of data on other explanatory variables.
  - Short sample length: only 20 semi-annual observations per crop.
- Model structure:
  - Panel data methods used to exploit cross-sectional variation across crops and time variation.
  - Crop production gaps constructed as log-deviations from a linear trend to capture levels rather than growth rates.
  - Rain indicators linked to relevant months/areas per crop (see Table 2 and Table 3 definitions).
  - Parsimonious pooled least squares (panel) model estimated in EViews with cross-section identifiers for crops and relevant geographic rainfall.
- Estimated regression (parsimonious notation preserved):
  - y_{i,t} = C + β0 y_{i,t−1} + β1 DS_{i,t}^{P} + β2 HR_{i,t}^{P} + β3 HR_{i,t}^{H} + β4 TR_{i,t} + ε_{i,t}
    - y_{i,t} (productiongap): gap measure of crop production (log deviation from linear trend).
    - DS_{i,t}^{P} (dryspell_planting): dummy = dry-spell during planting period in relevant areas.
    - HR_{i,t}^{P} (heavyrain_planting), HR_{i,t}^{H} (heavyrain_harvesting): dummies for heavy rainfall during planting and harvesting.
    - TR_{i,t} (sum): average amount of rainfall during growing and harvesting periods.
- Rules of thumb identified (stable, theory-consistent results):
  - Dry spells during the planting season are expected to lower crop production by around 7 percent.
  - Heavy rainfall during the harvesting season is expected to lower crop production by around 5 percent.
  - Total amount of rainfall during the growing season (sum) does not have a significant effect on crop production after controlling for unusual weather events.
- Caveats:
  - Some evidence of a negative effect of heavy rainfall during planting, but this is less robust across specifications.
  - Estimates may lack robustness due to the short sample size and should be cross-checked against other studies when available.
- Operational recommendation:
  - Use the framework to inform judgement in nowcasting but not integrate the estimated model formally into the nowcasting system yet.
  - Start monitoring daily rainfall data and use the rules of thumb together with other sources (news, surveys) to inform judgements.
  - Update the estimated model bi-annually when new crop production data become available.

---

### B. Fresh Food Prices — modeling approach and specification
- Data and modelling constraints:
  - Disaggregate fresh food prices available from January 2019 — a short series for robust inference.
  - Panel data models used to exploit cross-sectional variation across 11 food groups.
  - Food groups linked to the most relevant crops; crop production for seasons A and B added as deviation from normal level.
  - Model includes the effect of variations in the price of imported fertilizer.
- Estimated model (preserved notation):
  - Δp_{i,t} = C + β0 Δp_{i,t−1} + β1 Δp_{i,t−2} + β2 Δp_{i,t−3} + β3 y_{i,t} + β3 Δf_{t−2} + ε_{i,t}
    - p_{i,t} (cpi): log level of CPI for fresh food crop i in period t; Δ denotes first difference.
    - y_{i,t} (production): gap measure for crop production.
    - f_{t−2} (bnr_fertilizer_rwf): log level of fertilizer prices in Rwandan Francs in period t−2.
- Timing assumption:
  - CPI models assume production variations affect CPI food prices in the first month following the growing season (Season A → January; Season B → June). Effects on intermediate months assumed not captured, but level effect in January and June fully captured.

---

*Source: IMF TA mission team and NBR staff (Introduction section of tarea2025006-print-pdf).*

### section identifiers are fresh food prices and corresponding crop production data as shown in Table 5.

### section identifiers are fresh food prices and corresponding crop production data as shown in Table 5

### Key quantitative findings and rule of thumb
- A 10 percent decline in crop production relative to its normal level is associated with a 5 percent increase in fresh food prices, and vice versa.  
- Normal level of crop production is defined as the linear trend of crop production over time (the model therefore assumes that crop production is increasing over time for most foods).
- A 10 percent increase in the RWF price of imported fertilizer is associated with a 1 percent increase in fresh food prices.
- Model caution: "It is important to stress that these estimates might not be robust because of the small sample size. The estimates should be cross-checked against other relevant studies if available."

### Estimation results (pooled least squares for DLOG(CPI?))
- Sample (adjusted): 2019M02 2023M09  
- Included observations: 56 after adjustments  
- Cross-sections included: 11  
- Total pool (balanced) observations: 616
- Estimated coefficients and inference:
  - C = 0.012957; Std. Err. = 0.004457; t-Statistic = 2.907046; Prob. = 0.0038
  - DLOG(CPI?(-1)) = 0.042451; Std. Err. = 0.040253; t-Statistic = 1.054604; Prob. = 0.2920
  - DLOG(CPI?(-2)) = -0.247794; Std. Err. = 0.038866; t-Statistic = -6.375563; Prob. = 0.0000
  - DLOG(CPI?(-3)) = 0.080673; Std. Err. = 0.040365; t-Statistic = 1.998588; Prob. = 0.0461
  - PRODUCTION? = -0.482844; Std. Err. = 0.115149; t-Statistic = -4.193190; Prob. = 0.0000
  - DLOG(BNR_FERTILIZER_RWF(-2)) = 0.081804; Std. Err. = 0.032874; t-Statistic = 2.488387; Prob. = 0.0131
- Model fit and diagnostics:
  - R-squared = 0.103197
  - Adjusted R-squared = 0.095846
  - Mean dependent var = 0.013088
  - S.D. dependent var = 0.113016
  - S.E. of regression = 0.107463
  - Akaike info criterion = -1.613646
  - Schwarz criterion = -1.570562
  - Log likelihood = 503.0028
  - Hannan-Quinn criter. = -1.596894
  - Sum squared resid = 7.044477
  - F-statistic = 14.03882
  - Prob(F-statistic) = 0.000000
  - Durbin-Watson stat = 2.024918

### Additional quantitative results referenced in slides
- A dry spell during planting season is expected to reduce crop production by 6.5 percent.
- Heavy rainfall during harvesting season is expected to reduce crop production by 5 percent.
- Quantitative summary restated: "A reduction(increase) in production of a crop by 10% is expected to give an increase(reduction) of the price of that crop by 5%."
- Note: "These estimates are based on a short sample, and are uncertain."

### Policy and operational recommendations (Next Steps)
- Establish monitoring of daily rainfall data:
  - NBR should start monitoring data on rainfall to detect weather events that could affect crop production.
  - Procedures for obtaining and analyzing daily rainfall data from the relevant weather stations should be established.
  - The framework developed during the mission could be used for this purpose.
- Use identified rules of thumb to inform nowcasting:
  - The rule of thumb (10 percent production ⇄ 5 percent price change; fertilizer price effects) should be used to inform judgement in the nowcasting process.
  - It could be used together with results from crop production models and other information regarding developments in agricultural output.
  - The estimated model should be updated bi-annually when new crop production data is available.
- Use and formalize the Food Price Expectations Survey:
  - The Food Price Expectations Survey should be used actively in the nowcasting process.
  - Historical results from the survey should be organized as time series and a diffusion index created from the data for different crops.
  - Such diffusion indices could be valuable indicators for variations in fresh food production and prices.
- Continue refining the nowcasting framework and integrate tools:
  - The nowcasting framework should be refined to support deeper monetary policy analysis, using disaggregated-level analysis for better storytelling and policy communication.
  - CPI and GDP NTF tools should be used monthly as part of the forecasting process and FPAS work at the NBR going forward; CPI NTF includes monthly forecasts of ten subgroups of the core CPI and two subgroups of food inflation.
  - The GDP NTF-system should replace the current DFM for improved sectoral production forecasts.
  - Integrate QPM and NTF systems into the in-house database currently being constructed; make necessary changes to existing forecasting systems once the new database is finalized.
  - The NBR may benefit from technical assistance during the migration to a more robust database system.

### Data and model caveats emphasized
- Short sample lengths and limited historical availability:
  - Crop production data starts in 2013; price data is only available since 2019 (5 years).
  - The impact from weather to crop production is complex and varies across crops and regions; no simple stable relationship between rainfall and crop production.
  - Other factors (diseases, fertilizer availability, acreage) matter and current data may not be granular enough.
- Empirical approach and robustness:
  - Estimates rely on both cross-section and time variation (panel regression) over 11 years (22 seasons) of data.
  - The rule-of-thumb and model estimates should be cross-checked against other relevant studies and treated as inputs to judgement-based nowcasting.

_Italic: Source: IMF and NBR staff, IMF Technical Assistance Report (section: fresh food prices and corresponding crop production data as shown in Table 5)._

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_Source: https://www.imf.org/-/media/files/publications/tar/2025/english/tarea2025006-print-pdf.pdf_