## wpiea2021238-print-pdf — 6.2 Sensitivity analysis / RESULTS

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---

### Adjusted elasticities and main drivers of undernourishment
- Adjustment method:
  - Coefficients multiplied by ratio of standard deviations to adjust for different spreads of regressors: food inflation coefficient multiplied by 1.5; social protection coefficient multiplied by 8.
- Adjusted effects:
  - A typical change in food inflation is associated with an increase in undernourishment of 0.175 percent.
  - A typical change in social protection expenditure leads to a reduction in undernourishment of 0.237 percent.
- Relative importance:
  - Economic growth is the largest driver of improvements in undernourishment.
  - The effect of social transfers expansions is four time smaller than that of income, making them just enough to offset the effects of rising prices.
- Conditional convergence:
  - Countries with higher initial undernourishment exhibit a higher reduction rate.
  - The speed of convergence is about 0.4 percentage point per year for a typical low-income country that starts with a 20 percent share of population undernourished.
  - The catch-up effect disappears in the FD-IV approach; conclusion: the race to close the undernourishment gap between the developing and the developed world has currently come to a halt.

### Estimation results for Prevalence of Undernourishment (PoU) — key coefficients (Table 3)
- FD estimates (column labelled FD):
  - H0: -0.013*** (0.001)
  - Δln GDP pc: -0.310*** (0.061)
  - ΔFood inflation: 0.032 (0.024)
  - Δln Social transfers: -0.010*** (0.003)
  - _cons: -0.043*** (0.004)
  - N: 2232
- FD-IV estimates (column labelled FD-IV):
  - H0: -0.004 (0.003)
  - Δln GDP pc: -0.748*** (0.172)
  - ΔFood inflation: 0.116* (0.064)
  - Δln Social transfers: -0.030** (0.013)
  - _cons: -0.007 (0.012)
  - N: 2083
- First-stage F statistics (last column of Table 3):
  - H0: 15.55 (0.000)
  - Δln GDP pc: 14.02 (0.000)
  - ΔFood inflation: 57.78 (0.000)
  - Δln Social transfers: 5.28 (0.000)
- Overidentification test: 1.56 (P value)(0.46)
- Note on significance markers: *** ? <0.01, ** ? <0.05, * ? <0.1.

### Diet composition: cereals (staples) and animal protein (Table 4) — key coefficients
- FD estimates (CER = energy share from starchy staples; PROT = average animal protein supply):
  - H0: CER -0.008*** (0.002); PROT -0.010*** (0.001)
  - Δln GDP pc: CER -0.073*** (0.020); PROT 0.239*** (0.035)
  - ΔFood inflation: CER 0.001 (0.007); PROT -0.030 (0.019)
  - Δln Social transfers: CER 0.002 (0.002); PROT -0.003 (0.003)
  - _cons: CER -0.007*** (0.002); PROT 0.038*** (0.005)
  - N: CER 2139; PROT 2139
- FD-IV estimates:
  - H0: CER 0.006 (0.004); PROT -0.002 (0.003)
  - Δln GDP pc: CER -0.227*** (0.070); PROT 0.812*** (0.249)
  - ΔFood inflation: CER 0.030 (0.023); PROT -0.173*** (0.045)
  - Δln Social transfers: CER -0.010 (0.010); PROT -0.002 (0.019)
  - _cons: CER 0.008** (0.003); PROT -0.006 (0.016)
  - N: CER 1975; PROT 1975
- First-stage F statistics (identical for the two outcome variables except for initial conditions):
  - H0: 48.48 (0.000) and 96.75 (0.000)
  - Δln GDP pc: 18.43 (0.000) and 18.43 (0.000)
  - ΔFood inflation: 58.3 (0.000) and 58.3 (0.000)
  - Δln Social transfers: 4.6 (0.000) and 4.6 (0.000)
- Overidentification tests:
  - CER: 5.12 (P value)(0.08)
  - PROT: 1.56 (P value)(0.46)
- Interpretation:
  - Income is the key determinant of dietary habits: a 1 percent increase in GDP leads to a 0.07 percent reduction in cereals/roots/tubers consumption (FD) and a 0.24 percent increase in animal products (FD).
  - FD-IV magnifies these effects: a 1 percent increase in income leads to a 0.23 percent reduction in staple share and a 0.82 percent increase in proteins from meat and fish.
  - Food inflation does not increase cereals consumption but reduces meat and fish consumption (price-responsiveness differs by food type).
  - Social transfers do not show statistically significant effects on diet composition in these country-level estimates.

### Heterogeneity of effects of growth (FD-IV focus)
- Variation with country characteristics:
  - Growth reduces undernourishment more at early stages of development; effect weakens as countries become richer and PoU reaches low levels.
  - Growth effectiveness is 25 percent higher in a country where the bottom 20 percent holds 15 percent of national income relative to a country where the bottom 20 percent holds 5 percent of income.
  - Growth substitutes for social protection: growth reduces hunger when social protection expenditure (% of GDP) is small, but becomes irrelevant when social protection reaches considerable levels.
  - Growth is more effective when food import dependency is low; as food import dependency rises, growth loses effectiveness in reducing undernourishment.
- Diet composition heterogeneity (with caveats on instrument exogeneity for cereals):
  - Reduction in cereals consumption with income growth happens at early development stages and stops around I$ 15000.
  - Meat and fish consumption increases with income up to around I$ 50000.
  - Inclusiveness (share held by bottom 20 percent) does not affect cereals response, but lower inequality strengthens the effect of growth on animal protein consumption.

### Sensitivity analysis and robustness checks
- Instrument set variation (Table 5):
  - Alternative instrument sets (overidentified and just-identified) produce broadly similar results to benchmark FD-IV.
  - FD-IV (alternative instruments) key coefficients include:
    - H0: -0.004 (0.003) and -0.010*** (0.002)
    - Δln GDP pc: -0.748*** (0.172) and -0.776*** (0.187)
    - ΔFood inflation: 0.116* (0.064) and 0.234** (0.100)
    - Δln Social transfers: -0.030** (0.013) and -0.030** (0.013)
  - First-stage F statistics reported (e.g., H0: 90.51 (0.000)).
  - Overidentification test: 1.56 (P value)(0.46).
  - Conclusion: overidentified models that pass validity tests are preferred; overall picture remains unchanged.
- Parameter stability over time (structural break test around 2013; Table 6):
  - Chow-like test including time dummy for years after 2013; similar results for 2012 and 2014.
  - FD-IV with interactions show coefficients of income, food prices and social transfers do not change significantly over the two periods.
  - Key coefficients (Table 6 FD-IV):
    - H0: -0.003 (0.005)
    - Δln GDP pc: -0.866** (0.436)
    - ΔFood inflation: 0.055 (0.126)
    - Δln Social transfers: -0.021 (0.177)
  - First-stage F statistics reported; Overidentification test: 3.23 (P value)(0.66).
  - Conclusion: no strong evidence that effects changed across the two subperiods; IV estimates remain consistent.
- Additional robustness notes:
  - First-stage tests generally reject null that excluded instruments are jointly zero.
  - Hansen tests of overidentifying restrictions generally fail to reject exogeneity for key specifications, supporting instrument validity (with exception warnings for cereals where exogeneity is weaker).

### Sensitivity to controlling for social unrest (Table 7)
- Approach:
  - Controlled for number of social unrest events per country-year using Barret et al. (2020) composite indicator; range of the social unrest variable is [0,12].
  - Civil unrest indicator entered as changes and instrumented by its first and second lagged levels.
- FD-IV estimates (Table 7):
  - H0: -0.007* (0.004)
  - Δln GDP pc: -0.894*** (0.280)
  - ΔFood inflation: 0.1032 (0.077)
  - Δln Social transfers: -0.001 (0.055)
  - ΔSocial unrest: 0.009* (0.005)
  - _cons: -0.013 (0.018)
  - N: 1386
  - Overidentification test: 4.4 (P value)(0.22)
- First-stage diagnostics:
  - H0: 88.16 (0.000)
  - Δln GDP pc: 8.81 (0.000)
  - ΔFood inflation: 1.04 (0.000)
  - Δln Social transfers: 3.9 (0.000)
  - ΔSocial unrest: 82.72 (0.000)
- Interpretation:
  - Income growth remains statistically significant and slightly larger than the benchmark.
  - Food inflation effect similar in magnitude to benchmark but imprecisely estimated.
  - Effect of social transfers disappears in this specification.
  - ΔSocial unrest coefficient: 0.009* (0.005) — one extra social unrest event increases the share of undernourished by a very small amount on average.
  - Conclusion: Civil unrest affects undernourishment mainly indirectly via income and food price channels and has only a limited direct effect.

### Jackknife (leave-one-country-out) sensitivity
- Procedure:
  - Systematically omit one country at a time to assess influence of individual countries, outliers, or data irregularities.
- Findings:
  - Jackknife estimates of the income elasticity of undernourishment are close to the full sample value; outlying omitted-country estimates lie within the full-sample confidence interval.
  - Greater variability across omitted countries for food inflation and initial conditions.
  - Social transfers effects show a small range around negative effects.

### Semi-parametric fixed effects (relaxing linearity) — (Table 8)
- Model:
  - Semi-parametric fixed effects where one covariate at a time is modeled non-parametrically; estimation via spline approximation and local–constant Epanechnikov kernel regression.
- SP-FE estimates (Table 8):
  - H0: -0.000 (0.000)
  - Δln GDP pc: -0.234*** (0.031)
  - ΔFood inflation: 0.015*** (0.003)
  - Δln Social transfers: -0.009*** (0.000)
  - N: 2229
- Interpretation:
  - Semi-parametric average derivatives are very close in magnitude to linear FE estimates.
  - Linearity assumption appears appropriate for these data.

### Key quantitative sensitivities and robustness takeaways
- Income growth:
  - Robust negative effect on undernourishment across specifications.
  - FD-IV (with social unrest): Δln GDP pc coefficient -0.894*** (0.280).
  - SP-FE: Δln GDP pc coefficient -0.234*** (0.031).
  - Narrative summary reported: "a one percent increase in GDP per capita cutting the share of undernourished population by 0.75 percent".
- Food inflation:
  - Smaller influence than real income on undernourishment.
  - FD-IV: ΔFood inflation 0.1032 (0.077) (imprecise).
  - SP-FE: ΔFood inflation 0.015*** (0.003).
  - Narrative summary reported: "A typical change in food inflation will raise the prevalence of undernourishment by 0.17 percent".
- Social protection (social transfers):
  - SP-FE: Δln Social transfers -0.009*** (0.000).
  - Narrative summary reported: "a typical change in social protection spending leads to a 0.24 percent reduction in the prevalence of undernourished".
  - In FD-IV with social unrest included, the direct effect disappears: Δln Social transfers -0.001 (0.055), indicating sensitivity to specification and potential indirect channels.
- Social unrest:
  - Direct FD-IV effect small but positive: ΔSocial unrest 0.009* (0.005).
  - Concluded to exert most influence indirectly through income and food price channels.

### Appendix — selected interaction and sectoral results (Tables A1–A3)
- Table A1 (FD-IV interaction equation for PoU, selected coefficients and diagnostics):
  - H0: -0.002 (0.006) ; First stage F: 146.52 (0.000)
  - Δln GDP pc: -0.601 (0.433) ; First stage F: 9.85 (0.000)
  - Δln Social transfers: -0.021*** (0.007) ; First stage F: 7.82 (0.000)
  - Share of SP: 0.279 (0.232) ; First stage F: 152.29 (0.000)
  - Δln GDP pc × Share of SP: 3.178 (2.647) ; First stage F: 9.81 (0.000)
  - Δln GDP pc × Bottom 20: -5.489 (3.905) ; First stage F: 7.5 (0.000)
  - N: 1696
  - Overidentification test: 69.9 (P value)(0.28)
- Table A2 (FD-IV interaction for diet composition, CER and PROT, selected coefficients and diagnostics):
  - H0: CER -0.001 (0.009) ; PROT -0.004 (0.006) ; First stage F: 80.27 (0.000) and 143 (0.000)
  - Δln GDP pc: CER -0.077 (0.184) ; PROT 0.834*** (0.270) ; First stage F: 11.02 (0.000)
  - ΔFood inflation: CER -0.009 (0.026) ; PROT -0.095*** (0.037) ; First stage F: 7.08 (0.000)
  - Δln Social transfers: CER -0.000 (0.005) ; PROT -0.001 (0.008) ; First stage F: 1.81 (0.000)
  - Food imp ratio: CER 0.050** (0.024) ; PROT 0.005 (0.028) ; First stage F: 8.08 (0.000)
  - Overidentification tests: CER 88.91 (P value)(0.02) ; PROT 71.39 (P value)(0.25)
  - N: 1662 for both CER and PROT
- Table A3 (Effects of sectoral composition of growth):
  - NonAg growth: FD -0.268*** (0.066) ; FD-IV -0.648*** (0.214) ; First stage F: 18.59 (0.000)
  - Agr. growth: -0.025 (0.019) reported (first-stage diagnostics shown in table)
  - ΔFood inflation: FD 0.042* (0.025) ; FD-IV 0.115 (0.079)
  - Δln Social transfers: FD -0.012*** (0.003) ; FD-IV -0.029** (0.013)
  - Sample sizes: N1994 and 1723
  - Overidentification test: 4.87 (P value)(0.30)

*Source: wpiea2021238-print-pdf — 6.2 Sensitivity analysis / RESULTS*

### 0.03 percent in the FD-IV approach. When it comes to gauging the relative strength of the

### wpiea2021238-print-pdf - 0.03 percent in the FD-IV approach. When it comes to gauging the relative strength of the

### Adjusted elasticities and main drivers of undernourishment
- To adjust for different spreads of regressors, coefficients are multiplied by the ratio of standard deviations: food inflation coefficient multiplied by 1.5; social protection coefficient multiplied by 8.
- After adjustment:
  - A typical change in food inflation is associated with an increase in undernourishment of 0.175 percent.
  - A typical change in social protection expenditure leads to a reduction in undernourishment of 0.237 percent.
- Economic growth is the largest driver of improvements in undernourishment.
  - The effect of social transfers expansions is four time smaller than that of income, making them just enough to offset the effects of rising prices.
- Conditional convergence:
  - Countries with higher initial undernourishment exhibit a higher reduction rate.
  - The speed of convergence is about 0.4 percentage point per year for a typical low-income country that starts with a 20 percent share of population undernourished.
  - The catch-up effect disappears in the FD-IV approach; conclusion: the race to close the undernourishment gap between the developing and the developed world has currently come to a halt.

### Estimation results for Prevalence of Undernourishment (PoU) — key coefficients (Table 3)
- FD estimates (column labelled FD):
  - H0: -0.013*** (0.001)
  - Δln GDP pc: -0.310*** (0.061)
  - ΔFood inflation: 0.032 (0.024)
  - Δln Social transfers: -0.010*** (0.003)
  - _cons: -0.043*** (0.004)
  - N: 2232
- FD-IV estimates (column labelled FD-IV):
  - H0: -0.004 (0.003)
  - Δln GDP pc: -0.748*** (0.172)
  - ΔFood inflation: 0.116* (0.064)
  - Δln Social transfers: -0.030** (0.013)
  - _cons: -0.007 (0.012)
  - N: 2083
- First-stage F statistics (last column of Table 3) (F test statistics and corresponding p value shown):
  - H0: 15.55 (0.000)
  - Δln GDP pc: 14.02 (0.000)
  - ΔFood inflation: 57.78 (0.000)
  - Δln Social transfers: 5.28 (0.000)
- Overidentification test: 1.56 (P value)(0.46)
- Note on significance markers in tables:
  - *** ? <0.01, ** ? <0.05, * ? <0.1.

### Diet composition: cereals (staples) and animal protein (Table 4) — key coefficients
- FD estimates (CER = energy share from starchy staples; PROT = average animal protein supply):
  - H0: CER -0.008*** (0.002); PROT -0.010*** (0.001)
  - Δln GDP pc: CER -0.073*** (0.020); PROT 0.239*** (0.035)
  - ΔFood inflation: CER 0.001 (0.007); PROT -0.030 (0.019)
  - Δln Social transfers: CER 0.002 (0.002); PROT -0.003 (0.003)
  - _cons: CER -0.007*** (0.002); PROT 0.038*** (0.005)
  - N: CER 2139; PROT 2139
- FD-IV estimates:
  - H0: CER 0.006 (0.004); PROT -0.002 (0.003)
  - Δln GDP pc: CER -0.227*** (0.070); PROT 0.812*** (0.249)
  - ΔFood inflation: CER 0.030 (0.023); PROT -0.173*** (0.045)
  - Δln Social transfers: CER -0.010 (0.010); PROT -0.002 (0.019)
  - _cons: CER 0.008** (0.003); PROT -0.006 (0.016)
  - N: CER 1975; PROT 1975
- First-stage F statistics (identical for the two outcome variables except for initial conditions):
  - H0: 48.48 (0.000) and 96.75 (0.000)
  - Δln GDP pc: 18.43 (0.000) and 18.43 (0.000)
  - ΔFood inflation: 58.3 (0.000) and 58.3 (0.000)
  - Δln Social transfers: 4.6 (0.000) and 4.6 (0.000)
- Overidentification tests:
  - CER: 5.12 (P value)(0.08)
  - PROT: 1.56 (P value)(0.46)
- Interpretation and substantive findings:
  - Income is the key determinant of dietary habits: a 1 percent increase in GDP leads to a 0.07 percent reduction in cereals/roots/tubers consumption (FD) and a 0.24 percent increase in animal products (FD).
  - FD-IV magnifies these effects: a 1 percent increase in income leads to a 0.23 percent reduction in staple share and a 0.82 percent increase in proteins from meat and fish.
  - Food inflation does not increase cereals consumption but reduces meat and fish consumption (price-responsiveness differs by food type).
  - Social transfers do not show statistically significant effects on diet composition in these country-level estimates, despite micro-level evidence to the contrary.

### Heterogeneity of effects of growth (FD-IV focus)
- Growth effect varies with country characteristics (FD-IV estimates used for figures and Table A1 referenced):
  - Growth reduces undernourishment more at early stages of development; effect weakens as countries become richer and PoU reaches low levels.
  - Growth effectiveness is 25 percent higher in a country where the bottom 20 percent holds 15 percent of national income relative to a country where the bottom 20 percent holds 5 percent of income.
  - Growth substitutes for social protection: growth reduces hunger when social protection expenditure (% of GDP) is small, but becomes irrelevant when social protection reaches considerable levels.
  - Growth is more effective when food import dependency is low; as food import dependency rises, growth loses effectiveness in reducing undernourishment.
- Diet composition heterogeneity (FD-IV, with caveats on instrument exogeneity for cereals):
  - Reduction in cereals consumption with income growth happens at early development stages and stops around I$ 15000 (stopping earlier than some S-shape hypotheses).
  - Meat and fish consumption increases with income up to around I$ 50000 (saturation of animal products occurs much later than staple reduction).
  - Inclusiveness (share held by bottom 20 percent) does not affect cereals response, but lower inequality strengthens the effect of growth on animal protein consumption.

### Sensitivity analysis and robustness checks
- Instrument set variation (Table 5):
  - Alternative instrument sets (overidentified and just-identified) produce broadly similar results to benchmark FD-IV.
  - FD-IV (alternative instruments) key coefficients:
    - H0: -0.004 (0.003) and -0.010*** (0.002)
    - Δln GDP pc: -0.748*** (0.172) and -0.776*** (0.187)
    - ΔFood inflation: 0.116* (0.064) and 0.234** (0.100)
    - Δln Social transfers: -0.030** (0.013) and -0.030** (0.013)
  - First-stage F statistics and p values shown (e.g., H0: 90.51 (0.000)).
  - Overidentification test: 1.56 (P value)(0.46).
  - Conclusion: overidentified models that pass validity tests are preferred; overall picture remains unchanged.
- Parameter stability over time (structural break test around 2013; Table 6):
  - Chow-like test including time dummy for years after 2013 (also tested for 2012 and 2014 with similar results).
  - FD-IV estimates with interactions show coefficients of income, food prices and social transfers do not change significantly over the two periods.
  - Key coefficients (Table 6 FD-IV):
    - H0: -0.003 (0.005)
    - Δln GDP pc: -0.866** (0.436)
    - ΔFood inflation: 0.055 (0.126)
    - Δln Social transfers: -0.021 (0.177)
    - Additional interaction terms (1, 2, 3) reported with standard errors and first-stage diagnostics.
  - First-stage F statistics reported; Overidentification test: 3.23 (P value)(0.66).
  - Conclusion: no strong evidence that effects changed across the two subperiods; IV estimates remain consistent.
- Additional robustness notes:
  - First stage tests generally reject null that excluded instruments are jointly zero.
  - Hansen tests of overidentifying restrictions generally fail to reject exogeneity for key specifications, supporting instrument validity (with exception warnings for cereals where exogeneity is weaker).

*Source: https://www.imf.org/-/media/files/publications/wp/2021/english/wpiea2021238-print-pdf.pdf*

### 6.2  Sensitivity analysis6  RESULTS

### 6.2  Sensitivity analysis — RESULTS

### Sensitivity to controlling for social unrest
- Approach:
  - Controlled for the number of social unrest events per country-year using the Barret et al. (2020) composite indicator (an event is flagged when both indices exceed thresholds: above 0.1 for the first index and top 2% for the second).
  - Civil unrest indicator entered as changes and instrumented by its first and second lagged levels.
  - Note: The range of the social unrest variable is [0,12]. (A specification adding 1 before logs did not change results substantially.)

- FD-IV estimates (Table 7, FD-IV column; standard errors in parentheses):
  - H0: -0.007* (0.004)
  - Δln GDP pc: -0.894*** (0.280)
  - ΔFood inflation: 0.1032 (0.077)
  - Δln Social transfers: -0.001 (0.055)
  - ΔSocial unrest: 0.009* (0.005)
  - _cons: -0.013 (0.018)
  - N: 1386
  - Overidentification test: 4.4 (P value)(0.22)

- First-stage diagnostics (last column of Table 7: F test statistics and p values for each regressor):
  - H0: 88.16 (0.000)
  - Δln GDP pc: 8.81 (0.000)
  - ΔFood inflation: 1.04 (0.000)
  - Δln Social transfers: 3.9 (0.000)
  - ΔSocial unrest: 82.72 (0.000)

- Interpretation:
  - After controlling for social unrest, income growth remains statistically significant and slightly larger than the benchmark specification.
  - Food inflation effect similar in magnitude to benchmark but imprecisely estimated.
  - The effect of social transfers disappears both statistically and substantially in this specification.
  - ΔSocial unrest coefficient: 0.009* (0.005) — one extra social unrest event in year t in a given country increases the share of undernourished by a very small amount on average.
  - Conclusion: Civil unrest affects undernourishment mainly indirectly via income and food price channels and has only a limited direct effect.

### Jackknife (leave-one-country-out) sensitivity
- Procedure:
  - Systematically omit one country at a time to assess influence of individual countries, outliers, or data irregularities (e.g., revisions to FAO undernourished numbers).
  - Country-specific effects in the baseline equation help net out some country-specific shocks.

- Findings (Figure 4, Jackknife effects):
  - Jackknife estimates of the income elasticity of undernourishment are close to the full sample value; even estimates further away lie within the full-sample confidence interval.
  - Other covariates also broadly robust, though jackknife effects for food inflation and initial conditions show greater variability (higher cross-country heterogeneity).
  - Jackknife results for:
    - Growth effects: individual omitted-country estimates cluster near full-sample effect.
    - Food inflation effects: more wobbly across omitted countries.
    - Social transfers effects: small range around negative effects.
    - Initial conditions: greater dispersion across omitted countries.

### Semi-parametric fixed effects (relaxing linearity)
- Model:
  - Estimate a semi-parametric fixed effects specification where one covariate at a time (Δln GDP pc, ΔFood inflation, or Δln Social transfers) is modeled non-parametrically via an unknown function 5(.), while other covariates enter linearly.
  - Estimation via spline approximation followed by local–constant Epanechnikov kernel regression; intermediate OLS step used to obtain residuals.

- SP-FE estimates (Table 8; standard errors in parentheses):
  - H0: -0.000 (0.000)
  - Δln GDP pc: -0.234*** (0.031)
  - ΔFood inflation: 0.015*** (0.003)
  - Δln Social transfers: -0.009*** (0.000)
  - N: 2229

- Interpretation:
  - Semi-parametric average derivatives are very close in magnitude to linear FE estimates (first column of table 3 in the source).
  - The linearity assumption appears appropriate for these data (no substantive departure from linear FE results when relaxing linearity).

### Key quantitative sensitivities and robustness takeaways
- Income growth:
  - Robust negative effect on undernourishment across specifications.
  - FD-IV: Δln GDP pc coefficient -0.894*** (0.280) when controlling for social unrest.
  - SP-FE: Δln GDP pc coefficient -0.234*** (0.031) in semi-parametric specification.
  - Narrative summary: "a one percent increase in GDP per capita cutting the share of undernourished population by 0.75 percent" (as reported in the conclusion).

- Food inflation:
  - Smaller influence than real income on undernourishment.
  - FD-IV: ΔFood inflation 0.1032 (0.077) (imprecise).
  - SP-FE: ΔFood inflation 0.015*** (0.003).
  - Narrative summary: "A typical change in food inflation will raise the prevalence of undernourishment by 0.17 percent" (as reported in the conclusion).

- Social protection (social transfers):
  - SP-FE: Δln Social transfers -0.009*** (0.000).
  - Narrative summary: "a typical change in social protection spending leads to a 0.24 percent reduction in the prevalence of undernourished" (as reported in the conclusion).
  - In FD-IV with social unrest included, the direct effect disappears (Δln Social transfers -0.001 (0.055)), suggesting sensitivity to specification and potential indirect channels.

- Social unrest:
  - Direct FD-IV effect small but positive: ΔSocial unrest 0.009* (0.005).
  - Concluded to exert most influence indirectly through income and food price channels.

### Implications for interpretation of robustness checks
- Instruments and first-stage diagnostics indicate instruments are well correlated with endogenous regressors and plausibly exogenous (overidentification test reported).
- Jackknife checks indicate no single country unduly drives the main growth elasticity result; greater heterogeneity exists for food inflation and initial conditions.
- Semi-parametric checks indicate linear FE estimates are not driven by restrictive linearity — results largely consistent when allowing nonparametric shapes.

*Italic: Source: wpiea2021238-print-pdf — 6.2 Sensitivity analysis / RESULTS*

### References

### wpiea2021238-print-pdf - References

### References (bibliography themes)
- Bibliographic coverage includes empirical and theoretical studies on:
  - Measurement and validity of food security indicators (e.g., Barrett, 2010; Cafiero et al., 2014; Coates, 2013; Webb et al., 2006).
  - Impacts of food price volatility and food crises on food insecurity and social unrest (e.g., Bellemare, 2015; Headey, 2013; Laborde et al., 2016; Verpoorten et al., 2013).
  - Social protection, cash transfers, and safety nets effects on food security and consumption smoothing (e.g., Bitler et al., 2020; Hidrobo et al., 2018; Miller et al., 2011; Tiwari et al., 2016).
  - Nutrition, undernourishment trends and long-term human capital consequences (e.g., Victora et al., 2008; Fogel, 2004; Eini-Zinab et al., 2020).
  - Macro determinants of food security: economic growth, inflation, trade, and sectoral composition (e.g., Timmer, 2000; Gouel, 2013; Soriano & Garrido, 2016; Shahne et al., 2000).
- The reference list contains multiple methodological sources on panel data, treatment effects, identification, and instrumentation (e.g., Abrevaya et al., 2015; Ai & Li, 2008; Anderson & Hsiao, 1981; Baltagi & Li, 2002; Reed, 2015).

### Appendix — Estimation tables and key statistics

- Table A1: Estimation results of interaction equation for PoU (FD-IV)
  - Reported coefficients (column labeled H0 and First stage F-statistics with p values in parentheses):
    - H0: -0.002 (0.006) ; First stage F: 146.52 (0.000)
    - Δln GDP pc: -0.601 (0.433) ; First stage F: 9.85 (0.000)
    - ΔFood inflation: 0.035 (0.061) ; First stage F: 6.35 (0.000)
    - Δln Social transfers: -0.021*** (0.007) ; First stage F: 7.82 (0.000)
    - GDP pc: -0.000 (0.000) ; First stage F: 140.78 (0.000)
    - Share of SP: 0.279 (0.232) ; First stage F: 152.29 (0.000)
    - Food imp ratio: 0.031 (0.081) ; First stage F: 7.59 (0.000)
    - Bottom 20: 0.017 (0.033) ; First stage F: 16.49 (0.000)
    - Δln GDP pc × GDP pc: 0.008 (0.008) ; First stage F: 9.14 (0.000)
    - Δln GDP pc × Share of SP: 3.178 (2.647) ; First stage F: 9.81 (0.000)
    - Δln GDP pc × Food imp ratio: 1.032 (0.753) ; First stage F: 4.98 (0.000)
    - Δln GDP pc × Bottom 20: -5.489 (3.905) ; First stage F: 7.5 (0.000)
    - _cons: -0.033** (0.016)
  - Sample size: N1696
  - Overidentification test: 69.9 (P value)(0.28)
  - Note on significance: *** ? <0.01, ** ? <0.05, * ? <0.1. The last column shows the F test statistics from the first stage of each regressor and its p value.

- Table A2: Estimation results of interaction equation for diet composition (CER, PROT — FD-IV and First stages)
  - Reported coefficients and first-stage F-statistics (with p values):
    - H0: CER -0.001 (0.009) ; PROT -0.004 (0.006) ; First stage F: 80.27 (0.000) and 143 (0.000)
    - Δln GDP pc: CER -0.077 (0.184) ; PROT 0.834*** (0.270) ; First stage F: 11.02 (0.000) and 11.02 (0.000)
    - ΔFood inflation: CER -0.009 (0.026) ; PROT -0.095*** (0.037) ; First stage F: 7.08 (0.000) and 7.08 (0.000)
    - Δln Social transfers: CER -0.000 (0.005) ; PROT -0.001 (0.008) ; First stage F: 1.81 (0.000) and 1.8 (0.000)
    - GDP pc: CER -0.000 (0.000) ; PROT -0.000 (0.000) ; First stage F: 136.47 (0.000) and 136.47 (0.000)
    - Share of SP: CER 0.042 (0.039) ; PROT 0.028 (0.048) ; First stage F: 156.15 (0.000) and 156.15 (0.000)
    - Food imp ratio: CER 0.050** (0.024) ; PROT 0.005 (0.028) ; First stage F: 8.08 (0.000) and 8.08 (0.000)
    - Bottom 20: CER -0.023 (0.079) ; PROT -0.018 (0.112) ; First stage F: 14.04 (0.000) and 14.04 (0.000)
    - Δln GDP pc × GDP pc: CER 0.008 (0.006) ; PROT 0.000 (0.006) ; First stage F: 8.47 (0.000) and 8.47 (0.000)
    - Δln GDP pc × Share of SP: CER -0.658 (1.210) ; PROT -2.446* (1.426) ; First stage F: 8.89 (0.000) and 8.89 (0.000)
    - Δln GDP pc × Food imp ratio: CER -0.717 (0.436) ; PROT -0.217 (0.645) ; First stage F: 6.23 (0.000) and 6.23 (0.000)
    - Δln GDP pc × Bottom 20: CER -0.679 (1.453) ; PROT -0.683 (2.015) ; First stage F: 8.37 (0.000) and 8.37 (0.000)
    - _cons: CER -0.006 (0.010) ; PROT 0.008 (0.016)
  - Sample sizes: N1662 for both CER and PROT
  - Overidentification tests: CER 88.91 (P value)(0.02) ; PROT 71.39 (P value)(0.25)
  - Note on significance: *** ? <0.01, ** ? <0.05, * ? <0.1. The last column shows the F test statistics from the first stage of each regressor and its p value.

- Table A3: Effects of sectoral composition of growth (FD, FD-IV)
  - Reported coefficients and first-stage F-statistics:
    - H0: FD -0.000 (0.000) ; FD-IV -0.000 (0.000)
    - Agr. growth: -0.025 (0.019) ; First stage F: 0.0809.72 (0.075) (0.000)  [table shows Agr. growth -0.025 (0.019) and 0.0809.72 (0.075) (0.000)]
    - NonAg growth: -0.268*** (0.066) ; FD-IV -0.648*** (0.214) ; First stage F: 18.59 (0.000)
    - ΔFood inflation: 0.042* (0.025) ; FD-IV 0.115 (0.079) ; First stage F: 18.53 (0.000)
    - Δln Social transfers: -0.012*** (0.003) ; FD-IV -0.029** (0.013) ; First stage F: 8.76 (0.000)
    - _cons: -0.007*** (0.002) ; FD-IV 0.005 (0.005)
  - Sample sizes: N1994 and 1723
  - Overidentification test: 4.87 (P value)(0.30)
  - Note on significance: *** ? <0.01, ** ? <0.05, * ? <0.1. The last two columns show the F test statistics from the first stage of each regressor and its p value.

*wpiea2021238-print-pdf - References*

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_Source: https://www.imf.org/-/media/files/publications/wp/2021/english/wpiea2021238-print-pdf.pdf_