## wpiea2019179-print-pdf

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---

### Introduction: context, motivation, and scope
- Agriculture accounts for 29.5 percent of global employment and 68.5 percent of employment in low-income countries.
- Close to 800 million (or 78 percent) of the world’s poor live in rural areas and rely on agriculture for their livelihoods.
- Cross-country productivity disparities:
  - GDP per worker of the richest 5 percent of countries is 34 times that of the bottom 5 percent.
  - In the agricultural sector this ratio is 78.
- Prior literature emphasizes input use and technology adoption (fertilizers, pesticides, seeds, machinery) as key drivers of low yields; alternative mechanisms include crop selection and market/infrastructure constraints affecting crop choice and aggregate productivity.
- Contribution and data scope:
  - Uses crop-specific global spatial datasets to produce geographically attainable potential yields and measure agricultural productivity gaps, with a decomposition to identify the quantitative relevance of mechanisms (crop selection, inputs, geography).
  - Spatial resolution: 5 arc-minute cells (~10 x 10 km) aggregated to 2,423 states (admin 1) in 127 countries.
  - Full M3 dataset contains information on 175 crops; this study focuses on 25 crops.
  - M3 data: circa 2000 (average of censuses from 1997-2003). Country-specific crop prices: average for 2003-2007. GAEZ high-input reference: based on 1961-1990.
- State-level gap counts:
  - 749 states have a negative gap (more observed than potential production).
  - 1,534 states have a positive gap (less observed than potential production).
  - 140 states have zero observed or potential production.

### Data and methods
- Primary data sources:
  - Observed harvested land area and observed yield: Monfreda et al. (2008) (M3), downscaled to 5 arc-minute resolution using Ramankutty et al. (2008) cropland map.
  - Potential yields: Global Agro-Ecological Zones (GAEZ) (IIASA and FAO) under low, medium, high input assumptions and rainfed/irrigated agriculture.
  - Country-specific crop prices: FAOSTAT (average 2003-2007); missing prices interpolated using ratios of international prices.
  - Country-level explanatory variables: World Bank WDI (GDP per capita, fertilizer use), Vollrath (2007) average farm size, Canning road density (paved roads in 2005), CHAT tractors (Comin and Hobijn 2010), government effectiveness.
- Crop selection (25 crops; perishability categories H/M/L) — exact harvested area (1,000 Ha) and country counts (selected entries):
  - Banana — High — 80 — 3,536
  - Barley — Low — 91 — 50,788
  - Maize — Medium — 108 — 122,232
  - Rice — Low — 91 — 137,460
  - Wheat — Low — 98 — 197,657
  - (full 25-crop list preserved in source)
- Potential yield construction and assumptions:
  - Uses GAEZ high-input assumptions (commercial, mechanized, improved seed, optimal fertilizer and pest control) based on 1961-1990.
  - Potential yield = max(rainfed, irrigated) under high-input assumptions.
  - Potential is an agro-ecological attainable yield measure; observed yields can exceed potential in some cells.
- Price interpolation example:
  - p_A_wheat = p_A_maize * p_Intl_wheat / p_Intl_maize
- Spatial aggregation and measurement treatment:
  - Cell-level potential yields converted to potential production by multiplying by harvested area from M3; observed production = M3 yield × harvested area.
  - Aggregation to sub-national state (admin 1) to mitigate downscaling measurement error.
  - For cells with positive observed yield and zero potential, production from zero-potential cells redistributed equally among positive-potential cells within the country.

### Empirical framework and decomposition approach
- Objective: Decompose the gap between observed and potential yields into components due to input choice and crop selection.
- Yield measures calculated:
  - Observed yield within a state (y_s): y_s = (1 / L_s) ∑_{i=1}^{N} ∑_{c=1}^{C} p_c q_{i}^c
  - Mid-potential yield holding crop choice fixed (y_{s}^{mid}): y_{s}^{mid} = ∑_{i=1}^{N} ∑_{c=1}^{C} ω_{i}^c p_c \bar{q}_{i}^c
  - Overall potential yield (y_{s}^{pot}): y_{s}^{pot} = (1 / L_s) ∑_{i=1}^{N} max_{c} { p_c \bar{q}_{i}^c }
- Decomposition identity:
  - y_{s}^{pot} − y_s = (y_{s}^{pot} − y_{s}^{mid}) + (y_{s}^{mid} − y_s)
  - Interpretations:
    - (y_{s}^{pot} − y_{s}^{mid}) = gap due to crop selection.
    - (y_{s}^{mid} − y_s) = gap due to inputs/technology relative to high-input potential.
- Gaps as percentages of potential:
  - gap = 100 × (y_{s}^{pot} − y_s) / y_{s}^{pot}
  - gap_{crop} = 100 × (y_{s}^{pot} − y_{s}^{mid}) / y_{s}^{pot}
  - gap_{in} = 100 × (y_{s}^{mid} − y_s) / y_{s}^{pot}
- Cross-country regressions:
  - ln(gap_k) = γ ln(X_k) + θ_r + ε_k
  - Covariates X_k: GDP per capita, road density, fertilizer use, tractor use, average farm size. Regional fixed effects for seven regions.

### Results — geography, crop selection, and yields
- Geography and crop-specific potential:
  - Potential yields vary significantly across space for each crop; spatial patterns differ by crop (e.g., wheat vs sugarcane).
  - Potential yields of different crops can be negatively correlated across space.
- Variances (logs) — spatial and country-level:
  - Potential yields (sub-national): 0.99
  - Observed yields (sub-national): 1.13
  - Country-level variances (log yields): Overall potential 0.73; Observed yields 1.25
  - Regional variances in log potential yields:
    - Sub-Saharan Africa: 0.51
    - Latin America & the Caribbean: 0.58
    - Middle East & North Africa: 0.95
    - North America: 1.22
    - East Asia & Pacific: 0.75
    - Europe & Central Asia: 0.44
  - Correlation (logs) between observed and potential yields: 0.35
  - Potential yield explains 13 percent of cross-sectional variation in observed yields.
- Role of crop selection:
  - Mid-potential yield variance: 0.88
  - Comparison: Potential 0.99; Mid-potential 0.88; Observed 1.13
  - Crop selection mitigates geographic variation; high-input usage explains the right-hand fat-tail of observed yields.
- Regional means (tons per hectare and mean log gaps) — Table 2 regional means:
  - East Asia & Pacific: Observed 3,995; Mid-Potential 1,883; Overall Potential 3,838; Mean Gap due to Crops 0.505; Mean Gap due to Inputs 0.138; Mean Overall Gap 0.468
  - Europe & Central Asia: Observed 1,722; Mid-Potential 969; Overall Potential 2,962; Mean Gap due to Crops 0.628; Mean Gap due to Inputs 0.140; Mean Overall Gap 0.630
  - North America, Latin America & the Caribbean: Observed 3,370; Mid-Potential 1,676; Overall Potential 6,243; Mean Gap due to Crops 0.643; Mean Gap due to Inputs 0.086; Mean Overall Gap 0.432
  - Middle East & North Africa: Observed 1,364; Mid-Potential 1,137; Overall Potential 2,499; Mean Gap due to Crops 0.504; Mean Gap due to Inputs 0.244; Mean Overall Gap 0.592
  - South Asia: Observed 559; Mid-Potential 928; Overall Potential 2,211; Mean Gap due to Crops 0.546; Mean Gap due to Inputs 0.170; Mean Overall Gap 0.716
  - Sub-Saharan Africa: Observed 2,310; Mid-Potential 1,048; Overall Potential 2,981; Mean Gap due to Crops 0.579; Mean Gap due to Inputs 0.228; Mean Overall Gap 0.762
  - World: Observed 2,399; Mid-Potential 1,267; Overall Potential 3,710; Mean Gap due to Crops 0.591; Mean Gap due to Inputs 0.167; Mean Overall Gap 0.642
- Explanatory power (R-squared) of overall potential yield (Table 3):
  - World: Obs. Yield 0.321; Mid-Pot. Yield 0.525
  - By region (Obs. Yield / Mid-Pot. Yield):
    - East Asia & Pacific: 0.390 / 0.659
    - Europe & Central Asia: 0.430 / 0.290
    - North America, Latin America & the Caribbean: 0.579 / 0.718
    - Middle East & North Africa: 0.203 / 0.330
    - South Asia: 0.324 / 0.748
    - Sub-Saharan Africa: 0.040 / 0.413
- Agricultural productivity gaps — magnitudes and decomposition:
  - Cross-country patterns: yield often falls short of potential; exceptions include desert-dominated countries and small islands/states.
  - Average total gaps (regional averages reported):
    - Sub-Saharan Africa: average gap 0.73
    - East Asia and Pacific: average gap 0.56
    - Latin America and the Caribbean: average gap 0.55
  - Decomposition in logs:
    - Log gap from inputs: average -2.09; variance 1.28
    - Log crop selection gaps: average -0.57; variance 0.15
    - Overall gap in logs: average -0.54; variance 0.49
  - Interpretation: Crop-selection gap is similar to the overall gap; input-driven gaps are smaller on average and more dispersed; input-driven gaps appear larger in many Sub-Saharan African countries.
- Income-group comparisons and counterfactuals (top vs bottom 10%):
  - By GDP per capita:
    - Top 10%: Observed 2,750; Mid-Potential 1,350; Potential 3,834
    - Bottom 10%: Observed 610; Mid-Potential 1,138; Potential 2,874
    - Ratio: Observed 4.51; Mid-Potential 1.19; Potential 1.33
  - Road density, Fertilizer, Technology top/bottom 10% comparisons provided (see source for full table entries).
  - Counterfactuals: Mid-potential reduces richest-poorest observed-yield ratio from 4.5 to 1.2; Potential ratio = 1.3.
- Regressions and correlations (selected coefficients and significance; full tables in source):
  - Bivariate regressions (Table 5) — ln(total gap):
    - ln GDP pc: -0.046* (t-stat -1.80)
    - ln Road Density: -0.059** (t-stat -2.21)
    - ln Fertilizer: -0.080*** (t-stat -2.71)
  - ln(gap_crop): ln GDP pc: 0.015** (t-stat 2.57)
  - ln(gap_inputs): ln GDP pc: -0.094** (t-stat -2.33); ln Road Density -0.098**; ln Fertilizer -0.129**
  - Correlations (Table 6) — conditional (controlling for GDP pc) and unconditional:
    - Total Gap — Road density: Cond. -0.056**; Uncond. -0.059**
    - Gap due to Inputs — Fertilizer use: Cond. -0.112**; Uncond. -0.129**
  - Cross-country regressions (Table 7):
    - Unconditional ln(total gap): ln Road density -0.043*; ln Fertilizer -0.066**; Observations 88; R-squared 0.324
    - Conditional (including ln GDP pc): ln(total gap) — ln GDP pc -0.025 (t-stat -1.45); ln Road density -0.037*; ln Fertilizer -0.062**; Observations 88; R-squared 0.333
  - Notes: log gaps calculated as ln(gap+2). Robust t-statistics; significance levels: *** 1%, ** 5%, * 10%.

### Key implications and policy-relevant conclusions
- Geography explains a substantial share of cross-regional yield variation, but geography alone does not fully explain aggregate productivity gaps: large residual gaps remain after accounting for geography and crop-specific potentials.
- Crop selection is quantitatively important and often comparable to the overall gap; changing crop mix is necessary to close total yield gaps in many contexts.
- Input usage (fertilizer, machinery) is more strongly correlated with GDP per capita and explains part of the high yields in top-performing countries.
- Infrastructure (road density) and input access (fertilizer) are negatively correlated with total and input-driven gaps, indicating potential policy levers.
- Policy recommendations:
  - Do not focus solely on improving input usage in current crops; also facilitate crop diversification.
  - Facilitate crop diversification directly (policies that influence crop choice) and indirectly (infrastructure, market access, investments in technology).
  - State- and subnational-level spatially-explicit analyses can better target where input subsidies, infrastructure improvements, market interventions, or technology adoption will be most effective.
- Caveats:
  - Measurement limitations: national statistics are downscaled to 5-arcmin cells; plot-level observed yields and land allocation would be preferable but unavailable.
  - Cross-country associations are correlations; causal inference is beyond the scope of this paper.

*Source: wpiea2019179-print-pdf — IMF Working Paper (excerpts: 1. Introduction; 2. Data and methods; 3. Empirical Framework; 4. Results; 5. Conclusion).*

### 1. Introduction ........................................................................................................

### 1. Introduction

### Context and motivation
- Agriculture accounts for 29.5 percent of global employment and 68.5 percent of employment in low-income countries.
- Close to 800 million (or 78 percent) of the world’s poor live in rural areas and rely on agriculture for their livelihoods.
- Cross-country productivity disparities: GDP per worker of the richest 5 percent of countries is 34 times that of the bottom 5 percent; in the agricultural sector this ratio is 78.
- Prior literature emphasizes input use and technology adoption (fertilizers, pesticides, seeds, machinery) as key drivers of low yields in low-income countries; crop selection and market/infrastructure constraints are alternative mechanisms that can affect crop choice and aggregate productivity.
- This paper uses crop-specific global spatial datasets to produce geographically attainable potential yields and measure agricultural productivity gaps, with a decomposition to identify the quantitative relevance of mechanisms (crop selection, inputs, geography).

### Main findings (as stated in the Introduction)
- Geographical variation plays a substantial role in explaining cross-regional variation in aggregate yields, but substantial gaps remain even after controlling for crop- and region-specific measures of potential.
- When decomposing the within-country gap between observed and potential production, differences in crop selection are most important; gaps in inputs play a lesser role.
- Measured gaps and yields vary systematically across income levels and across countries with different infrastructure and input availability, highlighting the importance of understanding crop selection decisions given geographic constraints.

### Organization of the paper (excerpt)
- Section 2: data sources and variable construction.
- Section 3: empirical framework.
- Section 4: main findings and correlations of yields and gaps with income, inputs, technology and infrastructure.
- Section 5: conclusion.

### Key references (mentioned)
- Uses and compares approaches in Adamopoulos and Restuccia (2018), Gollin, Lagakos and Waugh (2014), Duflo, Kremer, and Robinson (2008, 2011), Beaman, Karlan, Thuysbaert, and Udry (2013), Asad (2014), Emran et al. (2012), among others.

### Policy relevance (implicit in motivation)
- Understanding the relative importance of crop selection versus input gaps can inform policies that aim to raise aggregate agricultural productivity: interventions that correct market failures affecting crop choice (e.g., market access, post-harvest loss reduction, risk sharing) may be as important as input provision and technology adoption.

### Empirical scope and contribution
- Uses exceptionally rich, crop-specific global datasets at 5 arc-minute resolution (~10 x 10 km), aggregated to subnational (state, admin 1) level.
- Replicates and extends Adamopoulos and Restuccia (2018) using different production and price datasets and a more granular, state-level approach across 2,423 states in 127 countries.

### Numerical and quantitative summary from the Introduction
- Full M3 dataset contains information on 175 crops; this study focuses on 25 crops.
- Geographic unit: 5 arc-minute cells aggregated to 2,423 states (admin 1) in 127 countries.
- Dataset time coverage and references:
  - M3 data: circa 2000, the average of censuses from 1997-2003.
  - Country-specific crop prices: average for 2003-2007.
  - GAEZ high-input reference: based on 1961-1990.
- State-level gap counts:
  - 749 states have a negative gap (more observed than potential production).
  - 1,534 states have a positive gap (less observed than potential production).
  - 140 states have zero observed or potential production.

---

### 2. Data and methods

### Primary data sources
- Observed harvested land area and observed yield: Monfreda et al. (2008) (M3), downscaled to 5 arc-minute resolution using Ramankutty et al. (2008) cropland map.
- Potential yields: Global Agro-Ecological Zones (GAEZ) (IIASA and FAO), which compiles climatic, soil, and land cover data to estimate potential production under low, medium, high input assumptions and under rainfed and irrigated agriculture.
- Country-specific crop prices: FAOSTAT (average 2003-2007); missing prices interpolated using ratios of international prices.
- Country-level explanatory variables: World Bank World Development Indicators (GDP per capita, fertilizer use), Vollrath (2007) average farm size, Canning (1998, 2007 update) road density (kilometers of road per square kilometer of land, paved roads in 2005), CHAT database tractors (Comin and Hobijn 2010), and a measure of government effectiveness.

### Crop selection in this study (Table 1 summary)
- The study focuses on 25 crops chosen from the M3 “major crops” list and supplemented by more perishable commercial crops, with perishability categorization (High, Medium, Low) guided by field tests in Pakistan (Asad 2014) and authors’ judgment.
- Selected crops with their perishability ranking, number of countries where grown, and harvested area (1,000 Ha) include (exact entries from Table 1):
  - Banana — High — 80 — 3,536
  - Barley — Low — 91 — 50,788
  - Cabbage — High — 109 — 2,593
  - Carrot — High — 102 — 915
  - Cassava — Medium — 61 — 11,014
  - Citrus — High — 70 — 798
  - Cotton — Low — 76 — 25,813
  - Groundnut — Low — 84 — 18,957
  - Maize — Medium — 108 — 122,232
  - Millet — Low — 76 — 31,398
  - Oil palm — High — 33 — 8,903
  - Onion — Medium — 112 — 2,498
  - Potato — Medium — 106 — 17,937
  - Rapeseed — Medium — 69 — 23,875
  - Rice — Low — 91 — 137,460
  - Rye — Low — 60 — 9,197
  - Sorghum — Low — 96 — 36,026
  - Soybean — Medium — 95 — 72,702
  - Sugar beet — Medium — 61 — 5,865
  - Sugarcane — High — 70 — 17,387
  - Sunflower — Medium — 77 — 18,797
  - Sweet potato — Medium — 81 — 7,991
  - Tomato — High — 116 — 3,212
  - Wheat — Low — 98 — 197,657
  - Yam — Medium — 46 — 3,249

### Potential yield construction and assumptions
- GAEZ provides attainable yields under three input assumptions (low, medium, high) for rainfed and irrigated agriculture.
- This analysis relies on high-input assumptions (commercial, mechanized, improved seed, optimal fertilizer and pest control) based on the 1961-1990 reference.
- Potential yield is defined as the maximum of rainfed and irrigated amounts under high-input assumptions.
- The potential measure does not consider profit-maximization; it captures achievable yields under high-input agro-ecological conditions; observed yields can be higher than potential in some cells.

### Price interpolation method (as used)
- For missing country-crop prices, the ratio between crop prices is assumed constant; example formula provided in the source:
  p_A_wheat = p_A_maize * p_Intl_wheat / p_Intl_maize
  (Equation (1) in the source, where p_s_c is the price of crop c in country s.)

### Spatial aggregation and treatment of measurement issues
- Cell-level potential yields converted to potential production by multiplying by harvested area from M3; observed production equals M3 yield times harvested area.
- Geographic unit of analysis: sub-national state (admin 1 in GADM). Aggregation to state level used to mitigate measurement error from downscaling.
- For cell-level cases with positive observed yield and zero potential, production values from zero-potential cells were redistributed equally among positive-potential cells within the country to minimize measurement error.

---

### 3. Empirical framework and analytic approach (summary)
- Empirical focus on measuring agricultural productivity gaps: differences between observed production and potential production (under high-input GAEZ estimates).
- Decomposition of within-country aggregate gaps into components attributable to crop selection versus inputs/technology.
- Cross-country analysis: aggregate state-level database to country level and regress agricultural gap measures on country characteristics (GDP per capita, road density, fertilizer use, tractors, average farm size, subsidies, government effectiveness).

---

### 4. Key statistics, sample sizes, and data coverage
- Full M3 dataset: 175 crops; study uses 25 crops (see list above).
- Spatial resolution: 5 arc-minute cells (~10 x 10 km); aggregated to 2,423 states (admin 1) in 127 countries for which price data were available.
- Time references:
  - M3 data circa 2000 (average of censuses from 1997-2003).
  - Crop prices averaged 2003-2007.
  - GAEZ high-input reference 1961-1990.
- State-level gap distribution:
  - 749 states have observed production greater than potential production (negative gap).
  - 1,534 states have observed production less than potential production (positive gap).
  - 140 states have zero observed or potential production.

---

### 5. Implications for research and policy (as framed by the paper)
- Geographic factors account for a substantial fraction of cross-regional yield variation, but cannot fully explain aggregate productivity gaps: policy and research should focus on mechanisms beyond geography.
- Crop selection decisions (market access, risk, post-harvest losses, price formation) are quantitatively important in explaining within-country gaps and merit policy attention alongside input and technology interventions.
- State- and subnational-level analysis using spatially-explicit potential yields can refine understanding of where input subsidies, infrastructure improvements, market interventions, or technology adoption will be most effective.

*Source: wpiea2019179-print-pdf — 1. Introduction; Data description (excerpts).*

### 3. Empirical Framework

### 3. Empirical Framework

### Overview
- Objective: Decompose the gap between observed and potential yields into the portion due to input choice and the portion due to crop selection.
- Approach: Calculate three yield measures—(i) average observed yield within a state, (ii) ‘mid-potential’ yield obtained from using high inputs while holding crop choice fixed, and (iii) overall potential yield obtained from using high inputs and growing the crop with the highest value using all available cropland.

### Yield measures
- Observed yield within a subnational state (y_s):
  - Formula: y_s = (1 / L_s) ∑_{i=1}^{N} ∑_{c=1}^{C} p_c q_{i}^c
  - Definitions:
    - L_s is the total harvested land in state s.
    - p_c is the price of crop c in the country where s is located (country subscripts suppressed).
    - q_{i}^c is the production of crop c in grid cell i.
- Mid-potential yield holding crop choice fixed (y_{s}^{mid}):
  - Formula: y_{s}^{mid} = ∑_{i=1}^{N} ∑_{c=1}^{C} ω_{i}^c p_c \bar{q}_{i}^c
  - Definitions:
    - \bar{q}_{i}^c is the potential production of crop c in grid cell i if high inputs are used.
    - ω_{i}^c is the share of harvested area allocated to crop c (i.e. ω_{i}^c = l_{i}^c / L_i, where l_{i}^c is harvested land of crop c and L_i = ∑_{c} l_{i}^c).
  - Interpretation: Differences between y_s and y_{s}^{mid} are attributed to differences between crop-specific observed yields and corresponding high-input crop-specific potential.
- Overall potential yield (y_{s}^{pot}):
  - Formula: y_{s}^{pot} = (1 / L_s) ∑_{i=1}^{N} max_{c} { p_c \bar{q}_{i}^c }
  - Definitions:
    - L_s is the total harvested land within state s.
  - Interpretation: A measure of revenue maximizing potential across all crops, driven solely by geographical differences between regions and not affected by any choice on the ground.

### Decomposition of the agricultural productivity gap
- Identity:
  - y_{s}^{pot} − y_s = (y_{s}^{pot} − y_{s}^{mid}) + (y_{s}^{mid} − y_s)
- Interpretation:
  - First component (y_{s}^{pot} − y_{s}^{mid}): gap due to crop selection.
  - Second component (y_{s}^{mid} − y_s): gap due to differences between the high input assumption of the database and inputs actually used.
- Gaps expressed as a percentage of potential production:
  - gap = 100 × (y_{s}^{pot} − y_s) / y_{s}^{pot}
  - gap_{crop} = 100 × (y_{s}^{pot} − y_{s}^{mid}) / y_{s}^{pot}
  - gap_{in} = 100 × (y_{s}^{mid} − y_s) / y_{s}^{pot}
  - Definitions:
    - gap, gap_{crop}, and gap_{in} are the total gap, gap due to crop choice, and gap due to inputs, respectively.

### Cross-country aggregation and regression analysis
- Aggregation: Data are aggregated to the country level to document correlations of yields and gaps with economic characteristics.
- Regression specification:
  - ln(gap_k) = γ ln(X_k) + θ_r + ε_k
  - Definitions:
    - gap_k is the gap for country k.
    - X_k is a vector of available cross-country measures informative of mechanisms from the agricultural productivity literature.
    - θ_r are regional fixed effects.
- Covariates included in X_k:
  - GDP per capita (measure of a country’s level of income).
  - Road density (indicator of a country’s connectivity and infrastructure development).
  - Use of fertilizer (proxy for key inputs determining agricultural production).
  - Tractor use (indicator of machinery use in agriculture).
  - Average farm size (scale of production indicator).
- Regional fixed effects (θ_r) included for:
  - East Asia and Pacific; Europe and Central Asia; Latin America and the Caribbean; Middle East and North Africa; North America; South Asia; and Sub-Saharan Africa.

*Source: wpiea2019179-print-pdf - 3. Empirical Framework*

### 4. Results

### 4. Results

### The role of geography in crop-specific yield potentials
- Potential yields vary significantly across space for each crop; geographical patterns vary significantly by crop.
- Example: Wheat and sugarcane potential-yield maps (5 arc-minute resolution) are nearly mirror images:
  - Wheat: higher potential in temperate regions of Europe and North America.
  - Sugarcane: favors tropical areas in South America, Africa, and Asia.
- Potential yields of different crops can be negatively correlated across space, underscoring the importance of crop-selection optimization to exploit geographical comparative advantages.
- Source datasets cited: IIASA and GAEZ; maps depict agro-climatically attainable yield for high-input, rainfed crops, under baseline (1961-1990) assumptions.

### The role of geography in cross-country yield variation
- Aggregating across crops, geography-driven potential variation is substantial and comparable in magnitude to observed-yield variation.
- Variances (log yields):
  - Potential yields (sub-national): 0.99
  - Observed yields (sub-national): 1.13
- Country-level variances (log yields):
  - Overall potential: 0.73
  - Observed yields: 1.25
- Regional variances in log potential yields:
  - Sub-Saharan Africa: 0.51
  - Latin America & the Caribbean: 0.58
  - Middle East & North Africa: 0.95
  - North America: 1.22
  - East Asia & Pacific: 0.75
  - Europe & Central Asia: 0.44
- Observed and potential yields are positively correlated:
  - Correlation (logs): 0.35
  - Potential yield explains 13 percent of cross-sectional variation in observed yields.

### The role of crop selection in cross-country variation
- Mid-potential yield (high-input across all regions and crops, holding crop selection fixed) variance: 0.88.
- Comparison of variances:
  - Potential: 0.99
  - Mid-potential: 0.88
  - Observed: 1.13
- Interpretation:
  - Crop selection mitigates geographic variation because countries respond to geography-specific comparative advantages.
  - Combined crop selection and geography still do not explain the right-hand fat-tail of observed yields, which is attributed to high-input usage in high-yield countries.

### Mean yields, potentials, and decomposed gaps (regional averages, tons per hectare and log gaps)
- Table 2 regional means (Observed Yield, Mid-Potential Yield, Overall Potential Yield, Mean Gap due to Crops, Mean Gap due to Inputs, Mean Overall Gap):
  - East Asia & Pacific: Observed 3,995; Mid-Potential 1,883; Overall Potential 3,838; Mean Gap due to Crops 0.505; Mean Gap due to Inputs 0.138; Mean Overall Gap 0.468
  - Europe & Central Asia: Observed 1,722; Mid-Potential 969; Overall Potential 2,962; Mean Gap due to Crops 0.628; Mean Gap due to Inputs 0.140; Mean Overall Gap 0.630
  - North America, Latin America & the Caribbean: Observed 3,370; Mid-Potential 1,676; Overall Potential 6,243; Mean Gap due to Crops 0.643; Mean Gap due to Inputs 0.086; Mean Overall Gap 0.432
  - Middle East & North Africa: Observed 1,364; Mid-Potential 1,137; Overall Potential 2,499; Mean Gap due to Crops 0.504; Mean Gap due to Inputs 0.244; Mean Overall Gap 0.592
  - South Asia: Observed 559; Mid-Potential 928; Overall Potential 2,211; Mean Gap due to Crops 0.546; Mean Gap due to Inputs 0.170; Mean Overall Gap 0.716
  - Sub-Saharan Africa: Observed 2,310; Mid-Potential 1,048; Overall Potential 2,981; Mean Gap due to Crops 0.579; Mean Gap due to Inputs 0.228; Mean Overall Gap 0.762
  - World: Observed 2,399; Mid-Potential 1,267; Overall Potential 3,710; Mean Gap due to Crops 0.591; Mean Gap due to Inputs 0.167; Mean Overall Gap 0.642
- Note: Observed and Potential averages are calculated based on the raw values and are measured in tons per hectare.

### Explanatory power of overall potential yield (Table 3: R-squared values)
- Share of variance explained by overall potential yield (R2) for observed yield and mid-potential yield:
  - East Asia & Pacific: Obs. Yield 0.390; Mid-Pot. Yield 0.659
  - Europe & Central Asia: Obs. Yield 0.430; Mid-Pot. Yield 0.290
  - North America, Latin America & the Caribbean: Obs. Yield 0.579; Mid-Pot. Yield 0.718
  - Middle East & North Africa: Obs. Yield 0.203; Mid-Pot. Yield 0.330
  - South Asia: Obs. Yield 0.324; Mid-Pot. Yield 0.748
  - Sub-Saharan Africa: Obs. Yield 0.040; Mid-Pot. Yield 0.413
  - World: Obs. Yield 0.321; Mid-Pot. Yield 0.525
- Notes: (1) R2 calculated based on OLS regressions of observed on potential yield. (2) R2 calculated based on OLS regressions of mid-potential on overall potential yield.

### Agricultural productivity gaps: magnitude and decomposition
- Cross-country patterns:
  - Yield falls short of potential for most countries (points below 45-degree line in country-level comparisons).
  - Exceptions: countries dominated by deserts, and small islands and states.
- Average total gaps (by region) reported in text (average gap values):
  - Sub-Saharan Africa: average gap 0.73
  - East Asia and Pacific: average gap 0.56
  - Latin America and the Caribbean: average gap 0.55
  - Note: North America has a large gap at country level but includes only two countries; sub-regional average gap is 54 (footnote text).
- Decomposition statistics (log gaps):
  - Log gap from inputs: average -2.09; variance 1.28
  - Log crop selection gaps: average -0.57; variance 0.15
  - Overall gap in logs: average -0.54; variance 0.49
- Interpretation:
  - Gap due to crop choice is very similar to the overall gap, suggesting changing crop mix is necessary to close total yield gap.
  - Gaps from inputs are smaller on average and more dispersed.
  - Input-driven gaps appear larger in many Sub-Saharan African countries, but this pattern does not hold for crop selection gaps.
  - Both the higher means in crop selection gaps and heterogeneity across economies indicate crop selection differences must be studied alongside inputs to understand aggregate productivity gaps.

### Aggregate yields and gaps across income groups
- Observed differences between richest and poorest countries (by GDP per capita):
  - Richest 10% have yields 4.5 times larger than poorest 10%.
- Effects of counterfactual measures:
  - Mid-potential (crop-selection variation only) reduces the richest-poorest ratio from 4.5 to 1.2.
  - Potential (geography alone) ratio: 1.3
- Table 4 highlights production by yield measure for top and bottom 10% by characteristics (selected entries):
  - By GDP per capita:
    - Top 10%: Observed 2,750; Mid-Potential 1,350; Potential 3,834
    - Bottom 10%: Observed 610; Mid-Potential 1,138; Potential 2,874
    - Ratio: Observed 4.51; Mid-Potential 1.19; Potential 1.33
  - By Road Density:
    - Top 10%: Observed 4,815; Mid-Potential 2,050; Potential 7,868
    - Bottom 10%: Observed 810; Mid-Potential 911; Potential 3,337
    - Ratio: Observed 5.94; Mid-Potential 2.25; Potential 2.36
  - By Fertilizer:
    - Top 10%: Observed 5,468; Mid-Potential 1,784; Potential 5,079
    - Bottom 10%: Observed 561; Mid-Potential 697; Potential 2,676
    - Ratio: Observed 9.75; Mid-Potential 2.56; Potential 1.90
  - By Technology:
    - Top 10%: Observed 7,024; Mid-Potential 2,156; Potential 7,298
    - Bottom 10%: Observed 1,520; Mid-Potential 1,224; Potential 4,284
    - Ratio: Observed 4.62; Mid-Potential 1.76; Potential 1.70
- Table 5 (bivariate regressions between gap measures and market characteristics; coefficients shown with significance):
  - Panel A: ln(total gap) — Market Characteristic coefficients:
    - ln GDP pc: -0.046* (t-stat -1.80)
    - ln Road Density: -0.059** (t-stat -2.21)
    - ln Fertilizer: -0.080*** (t-stat -2.71)
    - ln Farm Size: 0.019 (t-stat 1.43)
    - ln Tech use: 0.001 (t-stat 0.13)
    - Observations vary: 121, 117, 114, 100, 111; R-squared range 0.039–0.230 depending on regression.
  - Panel B: ln(gap_crop) — ln GDP pc: 0.015** (t-stat 2.57); other coefficients small or insignificant.
  - Panel C: ln(gap_inputs) — ln GDP pc: -0.094** (t-stat -2.33); ln Road Density: -0.098**; ln Fertilizer: -0.129**.
  - Note: Regional dummies included; robust t-statistics; significance: *** 1%, ** 5%, * 10%.

### Correlations of yields and gaps with infrastructure and inputs
- Negative relationships between gaps and GDP per capita are largely accounted for by technology use and road infrastructure; relationship weakens once these factors are included.
- Documented correlations between gap measures and:
  - Road density
  - Fertilizer use
  - Use of modern technology in agriculture
  - Average farm size
- Table 6: Correlations between gap measures and market characteristics (Conditional = controlling for GDP per capita; Unconditional = bivariate)
  - A. Total Gap:
    - Road density: Cond. -0.056**; Uncond. -0.059**
    - Fertilizer use: Cond. -0.076**; Uncond. -0.080***
    - Farm size: Cond. 0.026*; Uncond. 0.019
    - Tractor use: Cond. 0.022; Uncond. 0.001
  - B. Gap due to Crop Selection:
    - Road density: Cond. -0.005; Uncond. 0.002
    - Fertilizer use: Cond. -0.009*; Uncond. 0.000
    - Farm size: Cond. 0.000; Uncond. 0.003
    - Tractor use: Cond. -0.005; Uncond. 0.000
  - C. Gap due to Inputs:
    - Road density: Cond. -0.085**; Uncond. -0.098**
    - Fertilizer use: Cond. -0.112**; Uncond. -0.129**
    - Farm size: Cond. 0.046*; Uncond. 0.030
    - Tractor use: Cond. 0.047; Uncond. 0.007
  - Note: Conditional refers to multivariate regression including GDP per capita as control. Significance: *** 1%, ** 5%, * 10%.
- Table 7: Cross-country regressions of agricultural gap on market characteristics
  - 7a. Unconditional (omitting GDP per capita):
    - ln(total gap): ln Road density -0.043*; ln Fertilizer -0.066**; ln Farm size 0.015; ln Tech use 0.011; Observations 88; R-squared 0.324
    - ln(gap, crops): ln Road density 0.001; ln Fertilizer -0.001; Observations 89; R-squared 0.267
    - ln(gap, inputs): ln Road density -0.069**; ln Fertilizer -0.106**; Observations 88; R-squared 0.264
  - 7b. Conditional (including GDP per capita):
    - ln(total gap): ln GDP pc -0.025 (t-stat -1.45); ln Road density -0.037*; ln Fertilizer -0.062**; ln Farm size 0.020; ln Tech use 0.015; Observations 88; R-squared 0.333
    - ln(gap, crops): ln GDP pc 0.030***; ln Road density -0.006; ln Fertilizer -0.005; ln Farm size -0.001; ln Tech use -0.005; Observations 89; R-squared 0.414
    - ln(gap, inputs): ln GDP pc -0.078***; ln Road density -0.050; ln Fertilizer -0.097**; ln Farm size 0.034; ln Tech use 0.035*; Observations 88; R-squared 0.289
  - Note: log gaps calculated as ln(gap+2). Robust t-statistics in parenthesis. Significance: *** 1%, ** 5%, * 10%.

### Key implications from results
- Geography is a major driver of cross-country and within-country variation in agricultural yields; potential yield variance is of similar magnitude to observed-yield variance.
- Crop selection responds to geography and mitigates some geographic variation, but crop-selection differences alone do not explain high observed yields in top-performing countries—high input use is important there.
- Decomposed gaps show crop-selection gaps are substantial and comparable to overall gaps, while input gaps are on average smaller but more dispersed.
- Infrastructure (road density) and input use (fertilizer) are negatively correlated with total and input-driven gaps, suggesting these market characteristics are systematically associated with smaller yield gaps.

*Source: IMF Working Paper — 4. Results (wpiea2019179-print-pdf)*

### 5. Conclusion

### 5. Conclusion

### Main findings
- Differences in geographically-induced, crop-specific comparative advantages can explain a substantial share of the variation in yields across the world.
- Large gaps between potential and actual yields indicate large potential gains from improving crop and input choices.
- When decomposing these gaps:
  - Crop selection plays a relatively larger role in explaining gaps as compared to input usage.
  - Input usage is more strongly correlated with GDP per capita levels.
- The interaction of crop selection and market accessibility is quantitatively important in explaining aggregate yield variation.

### Caveats and measurement limitations
- Results are subject to measurement limitations:
  - Ideally, the analysis would use observed yields and land allocation at the plot level; such a precise dataset was not available.
  - The analysis relies on modeled data whereby national statistics are downscaled to the 5-arcmin cell level following assumptions described in section 2, which might miss important features of within-country land allocation and introduce biases in country-level potential yield measures.
- Cross-country associations:
  - Road infrastructure and access to better inputs such as fertilizer are associated with lower agricultural yield gaps.
  - These are simple correlations; drawing causal implications is beyond the scope of this paper.

### Policy implications and recommendations
- Policies should not focus solely on improving input usage in current crops but also facilitate crop diversification.
- Facilitation of crop diversification can be pursued:
  - Directly through policies that influence crop choice.
  - Indirectly through infrastructure and investments in new technologies that improve market accessibility and input access.
- Further work is encouraged on policies that jointly address crop selection and market accessibility to better uncover macro-relevant sources of aggregate productivity gaps and formulate appropriate interventions.

*Source: wpiea2019179-print-pdf - 5. Conclusion*

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_Source: https://www.imf.org/-/media/files/publications/wp/2019/wpiea2019179-print-pdf.pdf_