## wp1926 — References (content unit summary)

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### I. Scope, data, and objective
- Objective: understand cross-country variations in agricultural total factor productivity (TFP) and its growth by focusing on two factors — imported intermediate inputs and weather shocks.
- Sample and period: data from 162 countries during the period 1991-2015; growth accounting restricted to 135 countries with complete data 1991–2015 (25 LICs, 35 lower-middle-income, 34 upper-middle-income, 41 high-income).
- Key data sources: FAO (2018), World Bank (2018a,b), EORA (Lenzen et al., 2012, 2013), IMF Commodity Price Index, authors’ calculations.

### II. Main empirical findings — levels and growth
- Effect of imported intermediate inputs on TFP:
  - Baseline IV estimates (Table 2): Column (3) 8.863*** (1.093); preferred specification (column (4)) 4.399*** (1.290); other specifications 4.023** (1.677) and 3.995*** (1.114).
  - Stated interpretation: "A one percentage point increase in the share of imported inputs to total value of intermediate goods raises TFP by 3-4 percent." (paper summary)
  - First-stage evidence: a 10 percentage point decline in tariffs increases imported-inputs share by 3 percentage points; combined with second-stage implies a 10 percentage point tariff decrease associates with 12 percent increase in TFP (comparison to Amiti and Konings (2007): 12 percent).
- Weather shocks on TFP growth:
  - Baseline growth regression (Table 4) — heterogeneous effects by income:
    - Linear combination for LICs: a 1°C rise reduces TFP growth rate by 2.7 percent (−2.697*** (0.666) reported).
    - Middle-income countries: −0.618 (0.633), not statistically significant.
  - Rainfall effects for LICs: linear combinations show positive coefficients in some specifications (e.g., 5.850** (3.385); 6.092** (2.648)), indicating heterogenous rainfall responses.
- Interaction: imported inputs mitigate weather sensitivity
  - LIC-specific interaction (Table 6): in LICs with lower imported-inputs shares (below 50th percentile in 1991):
    - Lower share × d.Temp: −4.915*** (0.977); linear combination for these LICs: −4.284*** (0.850) — a 1°C increase reduces TFP growth by 4.284 percent.
    - Lower share × d.Rainfalls: 11.96*** (4.563); linear combination: 13.56*** (3.943) — a 100 mm/month increase raises TFP growth by 13.56 percent in these LICs.
  - Robustness (Table 7): imported-inputs interaction remains significant after controlling for aggregate imports-to-GDP, initial GDP per capita, and initial TFP; reported linear combinations include examples such as −5.620** (2.853), −3.334*** (1.283), rainfall effects 24.23*** (5.155), 22.86*** (5.922), 13.82*** (4.797).
  - Robustness checks (Table A9) show consistent sign patterns across samples and alternative constructions of the imported-inputs indicator; selected coefficients include d.Temperature values (e.g., −2.903***, −2.831***) and Lower share × d.Temperature values (e.g., −3.458**, −5.321***, −4.409***), with linear combinations for temperature effects ranging from −3.985*** to −6.177*** depending on specification.

### III. Methodology — TFP measurement, regressions, and identification
- Production function and TFP:
  - Cobb-Douglas CRS: Y_it = A_it (K_it)^{α^K_it} (L_it)^{α^L_it} (T_it)^{α^T_it}, with α^K_it + α^L_it + α^T_it = 1.
  - TFP residual: A_it = Y_it / [K_it^{α^K_it} L_it^{α^L_it} T_it^{α^T_it}].
  - Alternative TFP^b: log-linearized Cobb-Douglas assuming identical factor shares across countries; TFP^b sample coverage 144 countries.
- Growth decomposition (annualized long-run growth, 1991–2015 = 24 years):
  - g^{TFP}_{i,1991−2015} = 100×[ln(A_{i,2015}) − ln(A_{i,1991})]/24.
  - Capital, employment, land growth decomposed analogously using factor shares.
- Regression specifications:
  - Level regression: ln(TFP_{i,t}) = β_i + β_1 ImInputs_{i,t} + X_{i,t} β_2 + e_{i,t}, where ImInputs_{i,t} = 100 × Imported intermediate inputs / Total intermediate inputs; controls include fertilizer & pesticides, capital-to-labor ratio, taxes, subsidies, political instability index, R&D share, temperatures, and rainfalls.
  - Growth regression: g^{TFP}_{i,t} = 100 × (TFP_{i,t} − TFP_{i,t−1})/TFP_{i,t−1} with d.Temp and d.Rain variables as year-to-year changes and interactions by income groups.
- Identification and instruments:
  - Instrumenting ImInputs with weighted average tariffs on all products and share of inward FDI to agricultural value-added; alternative instrument in robustness: real effective exchange rate.
  - Diagnostics reported: Cragg-Donald Wald F-statistic = 15.73 (column (4)); Sargan statistic = 0.021, p-value = 0.885; Hausman statistic = 8.20, p-value = 0.004.
  - Hariss-Tzavalis unit-root test for ln(TFP) on balanced panel (135 countries, 1991-2015): test statistic = 0.8429, p-value = 0.000 (reject unit root at 1 percent).

### IV. Growth accounting and stylized magnitudes
- Group averages (annualized 1991–2015):
  - Low-income countries: Value-added 3.32; TFP 1.87; Capital stock 0.86; Labor 0.69; Land 0.30.
  - Lower-middle income countries: Value-added 3.42; TFP 2.29; Capital stock 1.43; Labor -0.03; Land 0.26.
  - Upper-middle income countries: Value-added 3.01; TFP 2.16; Capital stock 1.49; Labor -1.27; Land 0.42.
  - High-income countries: Value-added 1.08; TFP 1.93; Capital stock 0.39; Labor -1.22; Land -0.02.
- Selected country-level examples (LICs, 1991–2015 annualized rates):
  - Mali: Value-added 7.7 percent; TFP 3.5 percent (Table A2 lists TFP 7.69 in decomposition table — preserve source entries accordingly).
  - Chad: Value-added 6.8 percent; TFP 3.6 percent.
  - Liberia: Value-added 6.2 percent; capital growth explains 3.5 percent of value-added growth.
  - Low-end LICs: Central African Republic 0 percent; Burundi −0.14 percent; Haiti −0.27 percent — all with non-positive TFP growth and negative capital growth.
- Factor shares (Table A6 averages):
  - Low income countries (1990): Capital 0.397; Labor 0.338; Land 0.265. (2015): Capital 0.417; Labor 0.307; Land 0.276.
  - High income countries (1990): Capital 0.376; Labor 0.510; Land 0.114. (2015): Capital 0.387; Labor 0.499; Land 0.114.
- Alternative estimated factor shares (Table A7):
  - α_K = 0.378*** (0.062); α_T = 0.521*** (0.097); implied labor share by CRS = 0.100* (0.056); Observations 4,114; Countries 170; R-squared 0.585.

### V. Counterfactual magnitudes and economic impacts
- Contribution of imported inputs to observed TFP:
  - An increase in the share of imported inputs explains at most 60 percent of agricultural TFP in high-income countries and 20 percent of agricultural TFP in low-income and middle-income countries (paper summary).
- Counterfactuals: no change in imported-inputs share since 1991 (textual results from Figure 7):
  - 2002 example: Upper-middle income countries would have had 20 percent higher agricultural TFP if share stayed at 1991 level; low-income and lower-middle income countries would have had 10 percent greater TFP.
  - By 2014: LICs and middle-income countries would have about 20 percent lower TFP if the share of imported inputs stayed at 1991 level; high-income countries’ increase in imported inputs contributed to about 60 percent increase in TFP by 2014.
- Weather counterfactuals for LICs (Scenarios in Figure 8 and Table 8):
  - Scenario 1 (no change in temperatures since 1991) and Scenario 3 (no change in temperatures and rainfalls) yield similar results; temperature effects dominate rainfall effects.
  - Aggregate LICs: collecting largest damages during the sample, 3.2 percent of agricultural value-added lost due to a rise in temperatures, equivalent to 1.4 billion USD (explicit aggregate figure reported).
  - Country examples (Scenario 1, year of largest difference shown):
    - Afghanistan (AFG) 2010: Actual 2,639 million USD; Hypothetical 2,772 million USD; Difference 133 million USD; Percentage difference 5.0%
    - Madagascar (MDG) 2009: Actual 1,053 million USD; Hypothetical 1,122 million USD; Difference 69 million USD; Percentage difference 6.6%
    - Mali (MLI) 2010: Actual 3,583 million USD; Hypothetical 3,719 million USD; Difference 136 million USD; Percentage difference 3.8%
    - Aggregate (listed LICs in table): Actual total 44,223 million USD; Hypothetical total 45,636 million USD; Difference 1,413 million USD; Percentage difference 3.2%

### VI. Theory and mechanisms
- Formalization:
  - A_{it} = A(Temp_{it}, Rain_{it}, φ_{it}), with input quality φ_{it} = ω_{it}^D φ_{it}^D + ω_{it}^{Im} φ_{it}^{Im}, ω_{it}^{Im} = share of imported inputs.
- Three mechanisms by which imported inputs mitigate weather sensitivity (authors’ interpretation):
  1. Imported inputs embed better technologies/higher quality, reducing producers’ sensitivity to weather shocks.
  2. A greater share of imported inputs delinks input quality from local climate (imported inputs unaffected by local weather).
  3. Sectoral linkages: imported-inputs-driven productivity gains for final-good producers benefit domestic intermediate goods producers, reducing domestic input climate-sensitivity.

### VII. Robustness and validation
- Endogeneity addressed via IV (tariffs, inward FDI); diagnostics reported (e.g., Cragg-Donald F-statistics across tables: values include 15.73, 7.45, 11.40, 7.78, 5.95, 12.90).
- Weather identification exploits year-to-year fluctuations; Hariss-Tzavalis unit-root test rejects unit root for ln(TFP): statistic = 0.8429, p-value = 0.000.
- Robustness checks:
  - Alternative dependent variables: Value-added (effect 5.408*** (1.334) per 1 percentage point increase in imported inputs), TFP^b (3.871*** (1.115)).
  - Samples excluding high-income countries, excluding oil producers, excluding commodity price-hike years, alternate instruments (real effective exchange rate) — results qualitatively similar.
  - Robustness of interaction results: dropping extreme weather observations, alternative constructions of imported-inputs dummy (1995 point-in-time, 1991-1995 mean), and using continuous imported-inputs share — baseline findings hold (Table A9 summaries report consistent linear combinations and significance).

### VIII. Conclusions and policy implications
- Three major conclusions:
  1. Increase in usage of imported intermediate inputs has a significant and sizable impact on the level of agricultural TFP.
  2. Rising temperatures and rainfall shortages negatively influenced agricultural TFP growth rates, particularly in LICs.
  3. Within LICs, a greater share of imported inputs reduces the negative effects of weather shocks on agricultural TFP.
- Policy-relevant magnitudes:
  - The paper quantifies that accumulated weather damages in warmest years imply a 3.2 percent loss of agricultural value-added across LICs in the sample, equivalent to 1.4 billion USD.
  - Imported-inputs-driven changes can explain up to 60 percent of agricultural TFP in high-income countries and up to 20 percent in low- and middle-income countries.
- Caution: results are from reduced-form regressions using historical short-run weather-TFP relationships; the paper is silent about impacts of future climate change, which may be more severe than historical variability and so historical mitigation via imported inputs does not guarantee adaptation to future changes.

*Source: IMF Working Paper wp1926 (content unit: wp1926 - References).*

### References .............................................................................................................

### wp1926 - References

### I. Introduction — scope and purpose
- Objective: understand cross-country variations in agricultural total factor productivity (TFP) and its growth by focusing on two factors — imported intermediate inputs and weather shocks.
- Sample and period: data from 162 countries during the period 1991-2015.
- Key framing points:
  - Trade in intermediate inputs covered 64 percent of world trade in 2014 (World Input-Output Table references).
  - Climate-related weather variations are an ongoing issue and may increasingly harm agricultural productivity.

### II. Main empirical claims and magnitudes
- Independent effects:
  - Imported intermediate inputs boost agricultural productivity because they tend to be higher quality and less expensive than domestic equivalents.
  - Weather shocks affect agricultural TFP: higher temperatures and rainfall shortages reduce agricultural TFP in low-income countries (LICs).
- Interaction effect:
  - Within LICs, stronger weather effects are observed in countries employing less imported inputs.
  - Higher temperatures and rainfall shortages do not seem to have significant effects on countries employing greater imported inputs.
- Estimated causal magnitude for imported inputs:
  - "A one percentage point increase in the share of imported inputs to total value of intermediate goods raises TFP by 3-4 percent."
- Interpretation of mechanisms (authors’ three reasons):
  - Imported inputs embed better technologies and higher quality, reducing producers’ sensitivity to weather shocks.
  - A greater share of imported inputs makes overall input quality less sensitive to local weather because local climate does not affect imported input quality.
  - Sectoral linkages: productivity gains for local final-good producers (via imported inputs) benefit domestic intermediate goods producers, reducing domestic input climate-sensitivity.

### III. Agricultural TFP — methodology and sample details
- Production structure:
  - Cobb-Douglas production function with constant returns to scale (CRS): Y_it = A_it (K_it)^{α^K_it} (L_it)^{α^L_it} (T_it)^{α^T_it}, with α^K_it + α^L_it + α^T_it = 1.
- Inputs used:
  - Value-added (Y_it), capital stock (K_it), employment (L_it), land area (T_it).
  - Income shares: capital and labor shares from EORA (payments to capital, payments to labor, value-added); land share by residual.
- TFP calculation:
  - TFP as a residual: A_it = Y_it / [K_it^{α^K_it} L_it^{α^L_it} T_it^{α^T_it}].
- Growth decomposition (annualized long-run growth, 1991–2015 = 24 years):
  - TFP growth: g^TFP_{i,1991−2015} = 100×[ln(A_{i,2015}) − ln(A_{i,1991})]/24.
  - Capital: g^K_{i,1991−2015} = 100×α^K_it [ln(K_{i,2015}) − ln(K_{i,1991})]/24.
  - Employment: g^L_{i,1991−2015} = 100×α^L_it [ln(L_{i,2015}) − ln(L_{i,1991})]/24.
  - Land: g^T_{i,1991−2015} = 100×α^T_it [ln(T_{i,2015}) − ln(T_{i,1991})]/24.
- Data coverage for growth accounting:
  - Initial sample: 162 countries.
  - Growth accounting restricted to countries with complete data 1991–2015: 135 countries = 25 LICs, 35 lower-middle-income, 34 upper-middle-income, 41 high-income.
- Alternative productivity measure:
  - TFP^b: derived from a log-linearized Cobb-Douglas assuming identical factor shares across countries.
  - TFP^b sample coverage: 144 countries = 27 LICs, 37 lower-middle, 38 upper-middle, 42 high-income.

### IV. Growth accounting results — group averages (1991–2015)
- Simple averages of annualized growth rates, by income group (24-year period):
  - Value-added and decomposition (as reported in the main text and Table 1):
    - Low-income countries: Value-added 3.32; TFP 1.87; Capital stock 0.86; Labor 0.69; Land 0.30.
    - Lower-middle income countries: Value-added 3.42; TFP 2.29; Capital stock 1.43; Labor -0.03; Land 0.26.
    - Upper-middle income countries: Value-added 3.01; TFP 2.16; Capital stock 1.49; Labor -1.27; Land 0.42.
    - High-income countries: Value-added 1.08; TFP 1.93; Capital stock 0.39; Labor -1.22; Land -0.02.
- Cross-country notes:
  - TFP grew most in lower-middle income countries: annual average growth rate 2.3 percent (2.29% in table).
  - LICs: agricultural value-added growth 3.32 percent, but smaller TFP contribution due to relatively higher input growth.
  - High-income countries: lower value-added growth 1.08 percent but relatively high TFP growth 1.93 percent because of input declines (labor -1.22%; land -0.02%).
- Country examples among LICs (1991–2015 annualized average growth rates):
  - Highest value-added growth: Mali 7.7 percent; Chad 6.8 percent; Liberia 6.2 percent.
  - TFP contributions: Mali TFP 3.5 percent; Chad TFP 3.6 percent; Liberia capital growth explains 3.5 percent of value-added growth.
  - Lowest value-added growth: Central African Republic 0 percent; Burundi -0.14 percent; Haiti -0.27 percent — all with non-positive TFP growth and negative capital growth.

### V. Stylized facts on imported inputs, temperatures, and rainfalls
- Imported inputs:
  - Figure 3 summary: high-income countries consistently have higher share of imported inputs after 1995; LICs have the lowest share except year 2000.
  - Time trends: slight decline in share during the 1990s, increase since early 2000s, sharp declines in 2008-2010 associated with the 2008-09 global financial crisis.
- Temperatures and rainfalls (Figures 4 and 5):
  - Panel A (temperature): lower income countries tend to have higher average temperatures; average temperatures are rising over 1991-2015.
  - Panel B (rainfall): middle-income countries have greater average rainfalls; LICs and high-income countries have similar rainfall levels.

### VI. Contributions to the literature and novelty
- Novel contributions:
  - First large-panel, cross-country analysis showing imported intermediate inputs increase agricultural TFP.
  - First panel-dataset demonstration that weather shocks (higher temperatures, rainfall shortages) negatively affect agricultural TFP in LICs, with a time-varying identification strategy addressing time-invariant omitted variables.
  - New finding of interaction: prevalence of imported inputs reduces countries’ vulnerability of agricultural TFP to weather shocks.
- Relation to prior work:
  - Extends literature on productivity gains from imported inputs (previously focused on manufacturing; examples: Amiti and Konings, 2007; Topalova and Khandelwal, 2011).
  - Aligns with literature finding stronger weather effects in lower-income contexts (e.g., Dell et al., 2012; Cattaneo and Peri, 2016), but adds agricultural TFP as the outcome.

### VII. Empirical and methodological notes relevant for interpretation
- Identification / robustness:
  - Imported input share instrumented by tariff cuts and inward FDI in the empirical strategy.
  - Weather effect identification exploits plausibly exogenous year-to-year fluctuations in temperatures and rainfalls.
  - Robustness checks include alternative TFP measure (TFP^b) and other specifications (referenced in the paper).
- Data sources cited in methods:
  - FAO (2018) for agricultural value-added, capital stock, land area.
  - World Bank (2018a) for agricultural employment.
  - EORA (Lenzen et al., 2012, 2013) for payments to capital and labor and value-added.

*Source: IMF Working Paper wp1926 (content unit: wp1926 - References).*

### Part I: Distribution of Average Temperatures and Long-Run Changes

### Part I: Distribution of Average Temperatures and Long-Run Changes

### Scope
- Distribution of Average Temperatures and Long-Run Changes

### Structure
- Part I: Distribution of Average Temperatures and Long-Run Changes

_Implied source: wp1926 - Part I: Distribution of Average Temperatures and Long-Run Changes_

### Part II: Distribution of Average Rainfalls and Long-Run Changes

### Part II: Distribution of Average Rainfalls and Long-Run Changes

### Distributional patterns of temperatures and rainfalls (1990–2015)
- Kernel density estimates use data from World Bank (2018b).
- Panel A (2015):
  - Average temperatures in LICs and middle-income countries are right-skewered; modes are above 25 degrees Celsius.
  - Average temperatures for high-income countries are almost normally distributed; mode is about 10 degrees Celsius.
- Panel B (1990–2015 long-run changes):
  - Long-run changes in average temperatures: modes are above zero for all country groups (most countries experienced a rise in temperatures).
  - Long-run changes in monthly rainfalls are almost symmetrically distributed with mean zero.

---

### IV. Regression analysis — Overview and specification
- Baseline regression (equation (2)):
  - ln(TFP_{i,t}) = β_i + β_1 ImInputs_{i,t} + X_{i,t} β_2 + e_{i,t}
  - ImInputs_{i,t} = 100 × Imported intermediate inputs / Total intermediate inputs
  - X_{i,t} includes: consumption of fertilizers and pesticides, capital-to-labor ratio, production taxes-to-value added ratio, production subsidies-to-value added ratio, political instability index (1–7), expenditure share on R&D, temperatures, and rainfalls.
- Endogeneity concern: reverse causality between TFP and imported inputs.
- Instruments used: weighted average tariffs on all products, share of inward FDI to agricultural value-added (and in some robustness checks, real effective exchange rate).
- Hariss-Tzavalis unit-root test for ln(TFP) on balanced panel of 135 countries over 1991-2015: test statistic = 0.8429, p-value = 0.000 (reject unit root at 1 percent).

---

### A. Imported inputs and agricultural TFP level — Main findings
- OLS (columns (1)–(2) of Table 2):
  - Imported inputs-to-total inputs ratio: insignificant coefficients; zero point estimates likely due to endogeneity bias.
- 2SLS (columns (3)–(6) of Table 2):
  - Column (3): a one percentage point increase in share of imported inputs raises TFP by 8.9 percent (8.863***, standard error 1.093).
  - Column (4) (preferred specification, includes controls): point estimate = 4.399*** (standard error 1.290).
  - Columns (5) and (6): point estimates 4.023** (1.677) and 3.995*** (1.114), respectively.
- Selected control coefficients from column (4):
  - Fertilizer & pesticides: 4.122*** (1.304)
  - Capital-labor ratio: 0.344*** (0.096)
  - Taxes: -1.606 (1.241)
  - Subsidies: 0.475 (0.593)
  - Political instability index: -7.596*** (2.520)
- Diagnostics (column (4)):
  - Cragg-Donald Wald F-statistic = 15.73
  - Sargan statistic = 0.021, p-value = 0.885
  - Hausman statistic = 8.20, p-value = 0.004
- Interpretation:
  - After instrumenting, a one percentage point increase in the share of imported inputs raises agricultural TFP by about 4 percent (baseline).

---

### Robustness checks on imported inputs (Table 3)
- Alternative dependent variables:
  - Value-added: a one percentage point increase in share of imported inputs raises value-added by 5.408*** (1.334).
  - TFP^b: effect = 3.871*** (1.115).
- Additional specifications:
  - Excluding high-income countries, excluding oil producers, excluding commodity price-hike years, and adding real effective exchange rate as instrument — results remain qualitatively similar.
- First-stage and overidentification:
  - Cragg-Donald Wald F-statistics reported across columns: e.g., 7.45, 11.40, 7.78, 5.95, 12.90, 12.90.
  - Sargan p-values generally indicate instruments pass exclusion restriction tests in reported specifications.
- Comparison with firm-level literature:
  - First-stage: a 10 percentage point decline in tariffs increases imported-inputs share by 3 percentage points (first-stage evidence).
  - Combined with second-stage (1 pp increase → 4 percent TFP), implies a 10 percentage point tariff decrease associates with 12 percent increase in TFP (comparable to Amiti and Konings (2007): 12 percent).

---

### B. Weather shocks and agricultural TFP growth — Specification and baseline estimates
- Baseline growth regression (equation (3)):
  - g^{TFP}_{i,t} = 100 × (TFP_{i,t} − TFP_{i,t−1})/TFP_{i,t−1}
  - d.Temp_{i,t} = Temp_{i,t} − Temp_{i,t−1} (degrees Celsius)
  - d.Rain_{i,t} = Rain_{i,t} − Rain_{i,t−1} (units of 100 mm per month)
  - Interactions: income-level dummies (Low, Middle) interacted with d.Temp and d.Rain to capture heterogeneous responses.
  - Income-level dummies interacted with year fixed effects: D_i^{Low} θ_t and D_i^{Middle} θ_t.
- Table 4 baseline results:
  - Column (1) (no heterogeneity): d.Temperature coefficient = -0.606 (0.447), not statistically significant.
  - Column (2) (interactions by income level):
    - d.Temperature: -0.215 (0.614)
    - Low-income dummy × d.Temperature: -2.482** (1.121)
    - Middle-income dummy × d.Temperature: -0.404 (0.296)
    - Linear combination (Low-income countries): -2.697*** (0.666) — a 1°C rise reduces TFP growth rate by 2.7 percent in LICs.
    - Linear combination (Middle-income countries): -0.618 (0.633) — not statistically significant.
  - Rainfall interactions:
    - d.Rainfalls (base): -2.069 (7.648), not significant.
    - Low-income dummy × d.Rainfalls: 7.919 (9.131) — linear combination for LICs: 5.850** (3.385).
- Robustness (columns (3)–(5) and Table 5):
  - Results robust to adding hot-country dummy, agriculture-based dummy, alternative dependent variables (value-added growth, TFP^b growth), excluding oil producers, excluding commodity price-hike years, different income-group definitions, and adding controls (capital-labor, taxes, subsidies).
  - Table 5 linear combinations examples:
    - Low-income countries temperature effect (baseline specification & sample): -2.586** (1.044)
    - Middle-income countries temperature effect: -0.702 (0.521)
    - Low-income countries rainfall effect: 6.092** (2.648)

---

### C. Theory: imported inputs reduce sensitivity to weather shocks
- Production setup:
  - Y_{it} = A_{it} (K_{it})^{α_{it}^K} (L_{it})^{α_{it}^L} (T_{it})^{α_{it}^T}
  - A_{it} = A(Temp_{it}, Rain_{it}, φ_{it})
  - Input quality φ_{it} = ω_{it}^D φ_{it}^D + ω_{it}^{Im} φ_{it}^{Im}
  - ω_{it}^{Im} = share of imported inputs; ω_{it}^D = 1 − ω_{it}^{Im}
- Mechanisms for ∂^2 A_{it} / (∂Temp ∂ω^{Im}) > 0 (i.e., imported inputs mitigate negative temperature effects):
  1. Direct productivity effect: imported inputs embody better technologies that reduce temperature sensitivity.
  2. Diversification effect: higher imported-inputs share de-localizes inputs not affected by local shocks (∂φ^D/∂Temp < 0 → reduces sensitivity).
  3. Synergies between domestic and imported inputs: productivity gains in domestic intermediates amplify resilience (positive cross-derivative in φ^D).

---

### D. Evidence: imported inputs mitigate weather shocks in LICs (Tables 6–7, Figures)
- Estimation on LIC sample (equation (4)):
  - D_i^{LowIm} = 1 if country's imported-inputs-to-total-inputs share < 50th percentile of LICs in 1991.
  - Interact D_i^{LowIm} with d.Temp and d.Rain.
- Table 6 (baseline LIC results):
  - Column (1) (TFP growth rate):
    - d.Temp: 0.631 (0.849)
    - Lower share of imported inputs × d.Temp: -4.915*** (0.977)
    - d.Rainfalls: 1.593 (2.465)
    - Lower share of imported inputs × d.Rainfalls: 11.96*** (4.563)
    - Linear combination (Lower share of imported inputs, temperature effect): -4.284*** (0.850) — a 1°C increase reduces TFP growth by 4.284 percent in LICs with lower imported-inputs shares.
    - Linear combination (Lower share of imported inputs, rainfall effect): 13.56*** (3.943) — a 100 mm/month increase raises TFP growth by 13.56 percent in those LICs.
  - Columns (2)–(6): robustness to dependent variable (value-added growth, TFP^b growth), excluding oil producers, excluding commodity price-hike years, and controlling for other determinants — results remain robust.
- Addressing alternative explanations (Table 7):
  - Tests control for:
    - Aggregate imports-to-GDP ratio (D_i^{LowAggIm})
    - Initial GDP per capita (D_i^{LowGDPpc})
    - Initial TFP level (D_i^{LowTFP})
  - Key findings:
    - The interaction with imported-inputs-to-total-inputs remains significant when controlling for aggregate imports-to-GDP (Columns (1)–(3)).
    - Lower initial income level × d.Temp shows significant negative interaction in some specifications, but the imported-inputs effect remains after controlling for initial income and initial TFP.
    - Linear combinations (selected):
      - Lower share of imported inputs, temperature effects: examples include -5.620** (2.853) and -3.334*** (1.283) across specifications.
      - Lower share of imported inputs, rainfall effects: 24.23*** (5.155), 22.86*** (5.922), 13.82*** (4.797).
- Visual evidence (Figure 6):
  - Panel A: TFP growth rates vs annual changes in temperatures — steeper negative temperature effects for LICs with lower imported-inputs shares.
  - Panel B: similar pattern for rainfalls.

---

### V. Counterfactuals — Magnitudes of impacts
- Counterfactual without change in share of imported inputs since 1991:
  - Procedure: use IV baseline coefficients (column (4) of Table 2), set ImInputs_{i,t} = ImInputs_{i,1991}, include residuals, compute percentage gap Gap_{i,t}^{1991} = 100 × [ŷ_{i,t}^{1991} − ln(TFP_{i,t})].
  - Figure 7 summary (textual):
    - Changes in share of imported inputs in the 1990s worked to reduce agricultural TFP in lower income countries.
    - 2002 example: if share stayed at 1991 level:
      - Upper-middle income countries would have had 20 percent higher agricultural TFP.
      - Low-income and lower-middle income countries would have had 10 percent greater TFP than actual.
    - Around 2004 and 2010 gaps turn negative for some groups; in 2014:
      - LICs and middle-income countries would have about 20 percent lower TFP if the share of imported inputs stayed at 1991 level.
    - High-income countries: continuous increase in share of imported inputs contributed to about 60 percent increase in TFP by 2014.
- Counterfactuals without weather shocks (LICs only), three scenarios:
  - Scenario 1: No change in temperatures since 1991 (d.Temp_{i,t} = 0).
  - Scenario 2: No change in rainfalls since 1991 (d.Rain_{i,t} = 0).
  - Scenario 3: No change in temperatures and rainfalls since 1991.
  - Procedure: estimate equation (3), generate counterfactual TFP growth rates, iterate TFP levels from 1991 baseline, compute Gap_{i,t}^{1991} = 100 × [ln(TFP̂_{i,t}^{1991}) − ln(TFP_{i,t})].
  - Figure 8 summary:
    - Weather shocks reduced agricultural TFP in LICs.
    - About 2 percent agricultural TFP were lost in 2005 and 2010 (noted as warmest average-temperature years).
    - Temperature effects are much more sizable than rainfall effects; Scenario 1 and Scenario 3 imply similar results; Scenario 2 yields smaller differences.
- Scenario 1 counterfactual agricultural value-added (Table 8) — selected entries (year shown is year with largest difference):
  - Afghanistan AFG 2010: Actual = 2,639 million USD; Hypothetical = 2,772 million USD; Difference = 133 million USD; Percentage difference = 5.0%
  - Burundi BDI 2005: Actual = 45 million USD; Hypothetical = 47 million USD; Difference = 1 million USD; Percentage difference = 3.2%
  - Madagascar MDG 2009: Actual = 1,053 million USD; Hypothetical = 1,122 million USD; Difference = 69 million USD; Percentage difference = 6.6%
  - Mali MLI 2010: Actual = 3,583 million USD; Hypothetical = 3,719 million USD; Difference = 136 million USD; Percentage difference = 3.8%
  - Syria SYR 2010: Actual = 5,219 million USD; Hypothetical = 5,479 million USD; Difference = 260 million USD; Percentage difference = 5.0%
  - Tanzania TZA 2010: Actual = 6,421 million USD; Hypothetical = 6,569 million USD; Difference = 148 million USD; Percentage difference = 2.3%
  - Aggregate (listed LICs in table): Actual total = 44,223 million USD; Hypothetical total = 45,636 million USD; Difference = 1,413 million USD; Percentage difference = 3.2%
- Interpretation:
  - Temperature-driven weather shocks have measurable negative effects on agricultural TFP and value-added in LICs, with notable country-level losses in both absolute and percentage terms.
  - Imported intermediate inputs can mitigate negative weather impacts, especially in LICs with higher shares of imported inputs.

*Source: "Part II: Distribution of Average Rainfalls and Long-Run Changes" (wp1926) — IMF working paper content supplied.*

### 3.2 percent of total agricultural value-added, which is equivalent to 1.4 billion USD, were lost if

### 3.2 percent of total agricultural value-added, which is equivalent to 1.4 billion USD, were lost if

### Conclusions
- This paper has estimated agricultural TFP for 162 countries from 1990 to 2015 and examined the determinants of TFP by focusing on the role of imported inputs and weather shocks.
- Three major findings:
  - (1) An increase in usage of imported inputs has a significant impact on the level of TFP;
  - (2) rising temperatures and rainfall shortages negatively influenced the agricultural TFP growth rate;
  - (3) within LICs, a greater share of imported inputs works to reduce the negative effects of weather shocks.
- Caveat on interpretation:
  - Results come from reduced-form regressions relating annual TFP growth rates with short-run fluctuations in weather.
  - The paper is silent about the impact of future climate change, which is projected to lead to more severe rises in temperatures and more radical changes in precipitation patterns compared with historical variations in the last two decades.

### Counterfactual analyses and economic magnitudes
- An increase in the share of imported inputs explains at most:
  - 60 percent of agricultural TFP in high-income countries;
  - 20 percent of agricultural TFP in low-income and middle-income countries.
- The economic magnitude of weather shocks:
  - Collecting the cumulative losses in the warmest years during the sample period, in total 3.2 percent of agricultural value-added, which is equivalent to 1.4 billion USD, were lost due to a rise in temperatures in LICs as a whole.
- Supporting statement earlier in the text:
  - 3.2 percent of total agricultural value-added, which is equivalent to 1.4 billion USD, were lost if we collect the largest damages throughout the sample period 1991-2015. These results suggest that rising temperatures have economically sizable effects on agricultural value-added.

### Implications for policy and resilience
- Imported inputs can play a role in mitigating short-run negative weather impacts on agricultural TFP, especially within LICs.
- However, reliance on historical short-run weather-TFP relationships does not by itself justify optimistic conclusions about adaptation to projected future climate changes, which may be more severe than past variability.

*Source: Excerpt from IMF working paper (estimates of agricultural TFP, determinants, and counterfactual analyses, 1990–2015).*

### 44. World Bank (2018b) Climate Change Knowledge Portal, available at

### wp1926 - 44. World Bank (2018b) Climate Change Knowledge Portal

### A. List of Countries and Income Classification
- Uses the World Bank’s classification of income-level of countries.
- Lower-middle income and upper-middle countries are collectively considered middle-income under a broader definition.
- Country lists: detailed enumerations of Low-income countries (LICs), Lower-middle-income countries, Upper-middle-income countries, and High-income countries are provided (country names and ISO codes listed in the source).

### B. Data Sources and Summary Statistics
- Main data sources:
  - FAOSTAT, WDI, EORA Database, Freedom House, World Bank’s Climate Change Knowledge Portal, IMF Commodity Price Index, authors’ calculations based on EORA.
- Variables, units, and sources (selected examples as presented):
  - Agricultural value-added: Value USD, 2005 prices, millions — FAOSTAT
  - Gross Production Value (Agriculture, PIN): Value USD, Constant 2004-2006, millions — FAOSTAT
  - Net Capital Stocks (Agriculture, Forestry and Fishing): Value US$, 2005 prices, millions — FAOSTAT
  - Population, total: Persons — WDI
  - Temperatures: Degree Celsius — World Bank’s Climate Change Knowledge Portal
  - Rainfalls: mm — World Bank’s Climate Change Knowledge Portal
  - Other sectoral values and taxes/subsidies: Current USD — EORA Database
- Table A1 (summary statistics, exact figures preserved):
  - Dependent variables:
    - ln(TFP): Obs. 3,914; Mean -0.02; Std. Dev. 1.06; Min. -3.89; Max. 3.72
    - ln(TFP_b): Obs. 4,114; Mean -0.52; Std. Dev. 0.88; Min. -3.79; Max. 2.02
    - ln(Value-added): Obs. 4,774; Mean 7.02; Std. Dev. 2.16; Min. -0.35; Max. 12.94
    - TFP growth rate: Obs. 3,751; Mean 2.44; Std. Dev. 14.02; Min. -80.03; Max. 384.96
    - TFP_b growth rate: Obs. 3,943; Mean 1.85; Std. Dev. 10.32; Min. -71.17; Max. 197.92
    - Value-added growth rate: Obs. 4,747; Mean 2.35; Std. Dev. 10.91; Min. -80.78; Max. 167.06
  - Explanatory variables and instruments (selected):
    - Imported inputs/Total inputs×100: Obs. 4,420; Mean 16.62; Std. Dev. 16.62; Min. 0.00; Max. 99.96
    - Fertilizer & Pesticide: Obs. 1,957; Mean 0.31; Std. Dev. 0.52; Min. 0.00; Max. 5.25
    - Capital-to-labor ratio: Obs. 4,152; Mean 26.23; Std. Dev. 55.44; Min. 0.02; Max. 561.62
    - Tariffs for all products: Obs. 2,919; Mean 7.36; Std. Dev. 10.62; Min. 0.42; Max. 421.50
    - ln(Effective exchange rate/100 + 1): Obs. 2,030; Mean 0.69; Std. Dev. 0.11; Min. 0.27; Max. 1.82
  - Climate variables:
    - Average temperature (degree Celsius): Obs. 4,160; Mean 19.26; Std. Dev. 8.35; Min. -7.06; Max. 29.75
    - Average monthly rainfalls in 100 mm: Obs. 4,134; Mean 1.00; Std. Dev. 0.73; Min. 0.01; Max. 3.75
    - Yearly change in average temperature: Obs. 4,160; Mean 0.03; Std. Dev. 0.55; Min. -3.64; Max. 2.93
    - Yearly change in average monthly rainfalls: Obs. 4,134; Mean 0.00; Std. Dev. 0.22; Min. -1.35; Max. 1.99
  - Country dummies:
    - Hot country dummy: Obs. 4,160; Mean 0.50; Std. Dev. 0.50; Min. 0; Max. 1
    - Agricultural country dummy: Obs. 4,758; Mean 0.25; Std. Dev. 0.43; Min. 0; Max. 1
    - Oil producer dummy: Obs. 4,186; Mean 0.10; Std. Dev. 0.30; Min. 0; Max. 1
  - Dummies for LICs (selected counts and means reported in table)

### C. Growth Accounting Results (1991-2015)
- Growth accounting tables provide annualized average growth rates of components (TFP, Capital stock, Employment, Land area) over 24 years (1991-2015), by income group and country.
- Selected country-level decompositions (TFP, Capital stock, Employment, Land area) — examples preserved as in source:
  - LICs (Table A2), selected entries:
    - Mali MLI: TFP 7.69; Capital stock 3.49; Employment 2.21; Land area 1.71; Value-added decomposition 0.29
    - Chad TCD: TFP 6.85; Capital stock 3.60; Employment 2.06; Land area 1.15; Value-added decomposition 0.04
    - Burundi BDI: TFP -0.04; Capital stock -0.14; Employment -0.36; Land area 0.51; Value-added decomposition -0.05
    - Haiti HTI: TFP -0.80; Capital stock -0.27; Employment -0.84; Land area 0.14; Value-added decomposition 0.17
  - Lower-middle income (Table A3), selected entries:
    - Angola AGO: TFP 6.65; Capital stock 4.50; Employment 0.36; Land area 1.76; Value-added decomposition 0.03
    - Nigeria NGA: TFP 6.24; Capital stock 4.24; Employment 1.63; Land area 0.22; Value-added decomposition 0.15
    - India IND: TFP 3.01; Capital stock 1.68; Employment 1.60; Land area -0.26; Value-added decomposition 0.00
  - Upper-middle income (Table A4), selected entries:
    - China CHN: TFP 7.07; Capital stock 3.52; Employment 5.04; Land area -1.50; Value-added decomposition 0.01
    - Brazil BRA: TFP 3.61; Capital stock 4.51; Employment 0.01; Land area -1.20; Value-added decomposition 0.29
    - Libya LBY: TFP -3.80; Capital stock -5.30; Employment -0.23; Land area 1.73; Value-added decomposition -0.01
  - High income (Table A5), selected entries:
    - Kuwait KWT: TFP 10.68; Capital stock 8.92; Employment 0.90; Land area 0.84; Value-added decomposition 0.02
    - United States USA: TFP 2.17; Capital stock 1.80; Employment 1.07; Land area -0.70; Value-added decomposition 0.00
    - Germany DEU: TFP -2.72; Capital stock -0.66; Employment 0.31; Land area -2.38; Value-added decomposition 0.00
    - Hong Kong SAR, China HKG: TFP -4.87; Capital stock -0.99; Employment -0.18; Land area -3.43; Value-added decomposition -0.27

### D. Estimating Agricultural TFP
- D.1 Factor Shares:
  - Labor compensation and capital compensation from EORA database.
  - Capital share formula: 훼_{i,t}^K = payments to capital_{i,t} / value-added_{i,t}
  - Labor share formula: 훼_{i,t}^L = payments to labor_{i,t} / value-added_{i,t}
  - Land share: 훼_{i,t}^T = 1 − 훼_{i,t}^K − 훼_{i,t}^L (CRS assumption).
  - Table A6: Average factor shares (1990 and 2015):
    - Low income countries: 1990 — Capital share 0.397; Labor share 0.338; Land share 0.265. 2015 — Capital share 0.417; Labor share 0.307; Land share 0.276.
    - Lower-middle income countries: 1990 — Capital share 0.300; Labor share 0.416; Land share 0.284. 2015 — Capital share 0.305; Labor share 0.399; Land share 0.297.
    - Upper-middle income countries: 1990 — Capital share 0.298; Labor share 0.408; Land share 0.294. 2015 — Capital share 0.316; Labor share 0.379; Land share 0.305.
    - High income countries: 1990 — Capital share 0.376; Labor share 0.510; Land share 0.114. 2015 — Capital share 0.387; Labor share 0.499; Land share 0.114.
- D.2 Cobb-Douglas Production Function and Alternative TFP (TFP_b):
  - Production function: Y_{i,t} = A_{i,t} K_{i,t}^{α_K} L_{i,t}^{α_L} T_{i,t}^{α_T}, CRS so α_K + α_L + α_T = 1.
  - Intensive-form and log-linearization used to estimate α_K and α_T; α_L obtained by CRS.
  - Table A7 (estimation results, exact coefficients preserved):
    - Capital share (α_K): 0.378*** (standard error 0.062)
    - Land share (α_T): 0.521*** (standard error 0.097)
    - Labor share by assuming CRS: 0.100* (standard error 0.056)
    - Observations: 4,114
    - Countries: 170
    - R-squared: 0.585
    - F-statistic: 211.15
    - p-value of F-statistic: 0.000

### E. Level Effects and Growth Effects of Regressors on TFP
- E.1 Effect on the level of TFP:
  - Structural specification: A_{i,t} = exp(X_{i,t} β + a_i + ε_{i,t}), yielding ln(A_{i,t}) = X_{i,t} β + a_i + ε_{i,t} as the regression equation (Equation (A.1)).
  - Regression framework follows literature on determinants of TFP (Alene, 2010; Craig et al., 1997; Amiti and Konings, 2007; Olper et al., 2017).
- E.2 Effect on the growth rate of TFP:
  - TFP evolution: A_{i,t} = A_{i,t−1} exp(D_{i,t}), where D_{i,t} is a damage function of weather shocks.
  - Linear damage function: D_{i,t} = γ_0 + γ_1 d.Temp_{i,t} + γ_2 d.Rainfalls_{i,t} + u_{i,t}.
  - Leads to growth equation: ln(A_{i,t}) − ln(A_{i,t−1}) = γ_0 + γ_1 d.Temp_{i,t} + γ_2 d.Rainfalls_{i,t} + u_{i,t} (Equation (A.2)), which is the baseline regression model in Section V.
  - The empirical approach parallels studies on climate effects on GDP growth (Dell et al., 2012; Hsiang and Jina, 2014; Moore and Diaz, 2015; IMF, 2017).

### F. Correlation between Temperatures and Rainfalls
- Multicollinearity concern between changes in temperatures and changes in rainfalls examined.
- Correlation coefficients (exact as reported):
  - All countries, 1970-2015: correlation coefficient -0.0860
  - All countries, 1990-2015: correlation coefficient -0.0885
- Restricting the sample to LICs yields correlation coefficients reported in the source (continued beyond the supplied excerpt).

*Source: wp1926 - 44. World Bank (2018b) Climate Change Knowledge Portal (excerpted content provided).*

### 0.1512 and -0.0959, for 1970-2015 and 1990-2015, respectively, which are quite low. Therefore,

### wp1926 - 0.1512 and -0.0959, for 1970-2015 and 1990-2015, respectively, which are quite low. Therefore,

### Robustness Checks on the Interactive Effects
- Purpose: Present robustness checks on the climate change mitigation effect of imported inputs using equation (3) in the main text and the sample of LICs only.
- Sample coverage and summary statistics:
  - Correlation coefficient: -0.0860 (All countries), -0.0885 (Low-income countries), -0.1512 (1970-2015), -0.0959 (1990-2015).
  - Observations: 7,110 (All countries), 3,950 (Low-income countries), 1,170 (1970-2015), 650 (1990-2015).

### Experimental variations and treatments (columns (1)–(6) in Table A9)
- Column (1): Drops observations with extreme temperature changes defined as d.Temp > 95th percentile or < 5th percentile of d.Temp among observations from LICs after 1991.
- Column (2): Drops observations with extreme rainfall changes defined analogously for d.Rainfalls.
- Column (3): Drops observations with both extreme temperature and extreme rainfall changes.
  - Outcome: None of columns (1)-(3) change results qualitatively.
- Columns (4)–(6): Change construction of imported input indicator.
  - Column (4): Imported inputs dummy constructed from data in 1995 using the 50th percentile threshold.
  - Column (5): Dummy constructed based on the country mean of Imported inputs / Total inputs during 1991-1995.
  - Column (6): Introduces a continuous variable Imported inputs / Total inputs and its interaction term with weather changes.
  - Expected signs for coefficients:
    - d.Temp × Imported inputs / Total inputs: positive (countries with higher share of imported inputs are less sensitive to weather shocks).
    - d.Temp: negative.
    - d.Rainfalls × Imported inputs / Total inputs: negative.
    - d.Rainfalls: positive.
  - Outcome: Results in columns (4)-(6) are similar to baseline and as expected.

### Key coefficient estimates from Table A9 (columns (1)–(6))
- d.Temperature:
  - (1) -2.720
  - (2) 1.337
  - (3) -2.903***
  - (4) 0.158
  - (5) 0.302
  - (6) -2.831***
  - Standard errors (in parentheses): (1.764), (0.872), (1.100), (0.829), (1.021), (0.657)
- Lower share of imported inputs × d.Temperature:
  - (1) -3.458**
  - (2) -5.321***
  - (3) -2.586**
  - (4) -4.405***
  - (5) -4.409***
  - (6) 0.055*
  - Standard errors: (1.586), (0.926), (1.261), (1.017), (0.979), (0.029)
- d.Rainfalls:
  - (1) 0.698
  - (2) 16.91***
  - (3) 18.71***
  - (4) 3.877***
  - (5) 4.383***
  - (6) 6.136
  - Standard errors: (2.343), (6.417), (4.453), (0.735), (0.553), (3.982)
- Lower share of imported inputs × d.Rainfalls:
  - (1) 12.00***
  - (2) 3.769
  - (3) 3.930
  - (4) 3.072
  - (5) 1.500
  - (6) -0.025
  - Standard errors: (3.777), (10.150), (7.929), (6.892), (5.501), (0.228)
- Lower share of imported inputs dummy:
  - (1) -0.053
  - (2) 0.125
  - (3) 0.357
  - (4) -0.993
  - (5) -0.991
  - (6) -0.013
  - Standard errors: (0.408), (0.849), (0.495), (0.833), (0.838), (0.015)

### Sample sizes, fit, and derived linear combinations
- Observations by column: (1) 499, (2) 513, (3) 459, (4) 557, (5) 557, (6) 557
- Countries: 24 (all columns)
- R-squared by column: 0.095, 0.110, 0.122, 0.079, 0.080, 0.072
- Linear combination of coefficients — Temperature effects (Lower share of imported inputs):
  - (1) -6.177*** (1.247)
  - (2) -3.985*** (0.792)
  - (3) -5.489*** (1.238)
  - (4) -4.247*** (1.003)
  - (5) -4.107*** (0.819)
- Linear combination of coefficients — Rainfall effects (Lower share of imported inputs):
  - (1) 12.70*** (3.080)
  - (2) 20.68*** (5.266)
  - (3) 22.64*** (4.906)
  - (4) 6.949 (7.188)
  - (5) 5.883 (5.666)

### Interpretation and conclusion
- The robustness checks indicate the baseline finding that countries with lower shares of imported inputs are more sensitive to temperature and rainfall shocks is robust to:
  - Dropping observations with extreme weather changes.
  - Alternative constructions of the imported-inputs dummy (1995 point-in-time, 1991-1995 mean).
  - Using a continuous imported-inputs share and interaction terms.
- Sign patterns conform to expectations:
  - Temperature shocks have negative effects overall; interaction with imported-inputs share mitigates negative temperature effects.
  - Rainfall shocks have positive coefficients in some specifications; interaction with imported-inputs share tends to amplify sensitivity when imported-inputs share is lower.
- Overall: Baseline results are robust across the presented checks.

*Source: wp1926, Table A9 and accompanying text.*

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_Source: https://www.imf.org/-/media/files/publications/wp/2019/wp1926.pdf_