## _wp05127

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### Summary and main contributions
- Research question: whether foreign aid helps countries grow; motivated by Millennium Declaration commitments.
- Two main contributions:
  - Construction of plausibly exogenous instruments for aid to isolate the exogenous component of aid flows.
  - Systematic testing of the robustness of the aid–growth relationship across time horizons (1960–2000; 1960–80; 1970–2000; 1980–2000; 1990–2000), periods, sources (multilateral, bilateral), types (economic, social, food), timing (short-term vs long-term), specifications (cross-section and panel), and samples.
- Core empirical summary:
  - Little evidence of a robust positive impact of aid on growth.
  - Cross-sectional: some negative association in long run (1960–2000) that loses significance after instrumentation; some positive evidence for 1980–2000 only when outliers included.
  - Panel: positive and negative significant relationships appear but are fragile to small specification changes.
  - Aid–policy, aid–institution, and aid–geography interactions generally do not yield robust positive effects.

### Instrumentation strategy and first-stage diagnostics
- Identification approach:
  - Exploit non-economically-motivated donor–recipient determinants (STRAT, USISEG, COMCOL, COMCOLUK, COMCOLFRA, COMCOLSPA, COMCOLPOR, CURCOL, COMLANG) to estimate donor–recipient shares θ̂drt (equation 1).
  - Aggregate donor-share predictions into an instrumented aid-to-GDP ratio Ârt via Ârt = Σd (θ̂drt * Adt * GDPdt) / GDPrt (equation 2).
  - Alternative instrument exploiting donor macro conditions (fiscal balance and unemployment) also constructed (equations 3–4).
- First-stage performance:
  - Instrumenting variables jointly account for between 20 and 23 percent of variation in donor allocation (donor-allocation equation).
  - First-stage coefficient on fitted aid about 0.44 with t-statistic > 5 (reported first-stage coefficients in Table 4B include 0.270, 0.176, 0.264, 0.211, 0.164).
  - First-stage F-values reported: 13.44, 8.47, 23.62, 14.52, 3.43 (Table 4B); Staiger and Stock (1997) weak-instrument threshold of ten exceeded in four out of five cross-section cases.

### Cross-section evidence (OLS and IV)
- OLS (Table 2) baseline:
  - In four of five horizons, OLS aid coefficient is negative; only significant estimate for 1960–2000.
  - Long-run OLS magnitude (1960–2000): increase in aid of 1 percentage point of GDP would lower long-run growth by about 0.07 percentage points per year (coefficients should be divided by 100 to obtain percentage point increase in annual growth).
  - Representative OLS Aid/GDP coefficients across periods include -7.276, -5.900, -5.852, -4.159, 9.446.
- IV (Table 4A) core results:
  - R-squares high in longer horizons: 0.73 (1960–2000) and 0.70 (1970–2000) in core IV specifications.
  - IV Aid/GDP coefficients: -2.551, 1.353, -0.829, 1.313, -13.514 (Table 4A).
  - Aid coefficient negative in three out of five cases and significant in none.
  - Including outliers yields a significant positive aid coefficient in 1980–2000 driven by two observations (Cape Verde and Guinea-Bissau).
  - IV estimates generally less negative or more positive than OLS, interpreted as correcting negative endogeneity bias (donors giving more to countries faring poorly).
- Disaggregation by aid category (Table 6):
  - No sub-category (social, economic, food; multilateral vs bilateral; short-impact vs long-impact) shows any robust significant impact on growth.
  - Example IV coefficients: Social aid/GDP examples -4.717, 7.664, -84.776; Economic aid/GDP examples -16.511, 16.030, 895.087; Food aid/GDP examples -19.015, -5.433, -206.035.
- Non-linear and conditional effects (Table 7 and Appendix Table 2):
  - Including squared aid term: level terms often positive and squared terms negative, but neither significant.
  - Interactions aid*policy (Sachs-Warner, CPIA) and aid*geography generally not robustly positive; interaction coefficients unstable and sometimes negative.
  - Evidence consistent with substantial fungibility: economic, social and food aid have similar (non-robust) effects; bilateral and multilateral aid show similar effects.

### Panel evidence (GMM: difference- and system-GMM)
- Estimation methods and considerations:
  - Use Arellano-Bond (difference-GMM) and Blundell-Bond (system-GMM) with many researcher choices (lag lengths, endogenous vs predetermined variables), making results sensitive to specification.
- GMM findings (Tables 9 and 10; Table 10 summarized in Appendix 1):
  - Mixed results across estimators and specifications:
    - Total aid: negative and significant in one variant (examples Aid/GDP: -0.231, -3.781 in Table 9).
    - Short-impact aid: negative and significant in difference-GMM variant (examples: -7.794, -23.937, -7.888).
    - Economic aid: positive and significant in some specifications (examples: 43.347, 44.773, 9.746, 59.185).
  - Fragility illustrated:
    - Positive economic-aid effects disappear when reducing lag instruments (e.g., moving to three lags removes significance and can reduce magnitude by three-quarters).
    - Negative short-impact aid effect breaks down if government consumption is excluded as regressor.
  - Diminishing returns (aid-squared) generally insignificant.
  - Aid–policy and aid–geography interactions yield some significant coefficients in select specifications (e.g., Aid/GDP * area in tropics: -14.137 (1.71)* in Table 10 Column (1); Economic aid/GDP: 70.304 (1.90)* in Column (5)), but results are estimator- and specification-sensitive.
  - Diagnostics (Table 10): Chi-Square (Hansen over-id test) values often reported as 1.000 or near 1.000; AR(2) test statistics reported (e.g., 0.166, 0.243, 0.066, 0.497, 0.621, 0.495, 0.685).
- Conclusion on panel evidence:
  - Significant impacts of aid on growth can be found but are not robust across alternative GMM specifications; difficult to discern systematic effect.

### Theory, quantitative benchmark, and comparison with empirical magnitudes
- Theoretical derivation (Cobb–Douglas framework) leads to:
  - γy = (Aid/Y) * (αβ / (Y/K + δ))  (relationship presented in Appendix).
- Numerical illustrative benchmark under optimistic assumptions:
  - Parameters: β = 1; α = 0.35; Y/K = 0.45 → theoretical regression coefficient = 0.16.
  - Interpretation: "a 1 percentage point increase in the ratio of aid to GDP should raise the growth rate by 0.16 percent" under optimistic assumptions (reported regression coefficients should be divided by 100 to obtain percentage point increase in annual growth).
  - If only half of aid invested (β = 0.5), coefficient ≈ 0.08 ("close to 0.1").
- Empirical magnitudes in literature and reconciliation:
  - Clemens et al. (2004): coefficient of gross aid on growth about 0.9.
  - Hansen and Tarp (2000) and Dalgaard et al. (2004): coefficient on net aid varies between 0.6 and 1.3 (GMM estimations).
  - Many coefficients in this paper, when positively signed, are in the range about 0.01 to 0.2 (noting the division-by-100 convention).
  - Reconciliation: high empirical coefficients (0.6–1.3 and 0.9) would require large TFP impacts—e.g., a 1 percentage point increase in aid/GDP raising annual average TFP growth by 0.5 to 1.0 percent—an implausibly large effect comparable to the "IT-revolution in the United States in the 1990s."

### Selected key summary statistics (Table 1 excerpts)
- Real annual average per capita GDP growth (PPP): Mean 1.435, Std. Dev. 1.756, Min -3.373, Max 26.794 (1980-00, 83 Obs. panel shown among others).
- Aid to GDP: Mean 0.069, Std. Dev. 0.081, Min 0.000, Max 0.423.
- Fitted aid to GDP: Mean 0.095, Std. Dev. 0.171, Min 0.000, Max 0.927.
- Initial per capita (PPP) GDP: Mean 7.375, Std. Dev. 0.696, Min 5.944, Max 18.967.
- Initial life expectancy at birth: Mean 47.443, Std. Dev. 9.664, Min 32.380, Max 71.680.
- Institutional quality: Mean 0.525, Std. Dev. 0.119, Min 0.225, Max 0.859.
- Geography: Mean -0.599, Std. Dev. 0.724, Min -1.040, Max 1.528.
- Initial government consumption to GDP: Mean 13.595, Std. Dev. 9.510, Min 1.376, Max 65.041.
- Average no. of revolutions: Mean 0.233, Std. Dev. 0.201, Min 0.000, Max 0.829.
- Average level of the terms of trade: Mean 113.332, Std. Dev. 22.922, Min 66.665, Max 176.213.
- Standard deviation of the terms of trade: Mean 26.237, Std. Dev. 18.430, Min 1.681, Max 94.323.
- Initial level of trade policy: Mean 0.013, Std. Dev. 0.114, Min 0.000, Max 1.000.

### Policy-relevant implications and recommendations
- Main conclusion: No robust positive relationship between aid and growth in cross-section after instrumenting; panel-GMM results are inconsistent and fragile.
- Policy implications:
  - Re-examine policy prescriptions that rely solely on cross-country regression evidence about aid effectiveness because of possible data noise and lack of robustness.
  - Rethink aid delivery mechanisms: how aid is delivered, to whom, in what form, and under what conditions.
  - Focus further research on direct evidence of channels (e.g., human capital accumulation, policy change, TFP effects) through which aid might affect growth.
  - Support ongoing national and international efforts to improve aid effectiveness and identify hindrances that offset potential growth-enhancing effects of transfers.
- Caveat: Absence of detected robust effects in cross-country regressions does not imply aid cannot be beneficial; noise or offsetting mechanisms may mask real effects.

*Source: _wp05127 - 1.    Summary Statistics (IMF PDF content unit).*

### 1.    Summary Statistics................................................................................................

### 1.    Summary Statistics

### Main sections (by heading and page number)
- 1.    Summary Statistics............................................................................................................20
- 2.    Impact of Total Aid on Growth, OLS Estimations ...........................................................21
- 3.    Estimation of Exogenous in the Allociation of Aid by Donors Across Recipients ..........22
- 4A. Impact of Total Aid on Growth, IV Estimation ................................................................23
- 4B. Impact of Total Aid on Growth, First-Stage Regression, 1960–00 ..................................23
- 5.    Impact of Total Aid on Growth, OLS Estimations using Lagged Aid .............................24
- 6.    Impact of Different Categories of Aid on Growth, IV Estimations...................................25
- 7.    Aid and Growth: Disminishing Returns and Impact of Policies and Institution, IV Estimations ..................................................................................................................26
- 8.    Aid and Growth: Impacat of Geography, IV Estimations ................................................27
- 9.    Impact of Different Aid Measures on Growth, GMM Estimations ..................................28
- 10.  Impact of Aid Conditional on Policies and geography, GMM Estimations .....................29

### Charts (by number and title)
- Chart 1. Conditional Relationship Between Aid and its Instrument, 1960–00..................................30
- Chart 2. Conditional Correlation Between Growth and Total Aid, 1960–00 ....................................31
- Chart 3. Conditional Correlation Between Growth and Total Aid, 1960–00 ....................................32

### Appendixes (by Roman numeral and title)
- I. Data Description and Sources...............................................................................................33
- II. Issues Relating to the Instrumentation Strategy ..................................................................36
- III. Sample of Countries...........................................................................................................39
- IV. Prediction of the Standard Growth Model of the Quantitative Impact of Aid ..................40

### Appendix Tables (by number and title)
- 1. Impact of Aid on Growth Using Alternative Instrument .....................................................42
- 2. Impact of Aid on Growth Conditional on Policy and Institutions, IV Estimations .............43
- 3. Impact of Aid on Growth: Does Donor Type Matter? IV Estimations................................44
- 4. Estimating the Exogenous Variation in Donors’ Allocation of Social Aid Across Recipients................................................................................................................45

*Source: _wp05127 - 1.    Summary Statistics (IMF PDF content unit).*

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

### _wp05127 - References..............................................................................................................

### I. INTRODUCTION
- Research question: whether foreign aid helps countries grow; motivation includes Millennium Declaration commitments to “grant more generous development assistance, especially to countries that are genuinely making an effort to apply their resources to poverty reduction.”
- Two main contributions claimed by the paper:
  - Construction of plausibly exogenous instruments for aid to isolate the exogenous component of aid flows.
  - Systematic testing of the robustness of the aid–growth relationship across time horizons (long and medium run), periods (1960s–1990s), sources (multilateral, bilateral), types (economic, social, food), timing (short-term vs long-term), specifications (cross-section and panel), and samples.
- Core empirical findings summarized:
  - Little evidence of a robust positive impact of aid on growth.
  - Cross-sectional: some evidence for a negative relationship in the long run (40 year horizon), but not significant after instrumentation; some positive evidence for 1980–2000 only when outliers included.
  - Panel: both positive and negative significant relationships appear but are fragile to small specification changes.
  - Aid–policy, aid–institution, and aid–geography interactions generally do not yield robust positive effects.
- Interpretation and implications:
  - Predicted positive effects of aid may be too small to detect against data noise using standard cross-sectional techniques.
  - Effects of other interventions (such as good policies) are discernible and robust.
  - If noise is not the entire explanation, further research is needed to identify mechanisms that offset transfers and subsidized credit inherent in aid.

### II. TACKLING ENDOGENEITY: AN INSTRUMENTATION STRATEGY
- Methodological context:
  - Cross-sectional regressions suffer from endogeneity, outliers, model uncertainty, measurement error, and omitted-variable bias; panel estimations partially address unobservable heterogeneity via fixed effects.
  - For cross-sections, long horizons are preferred; paper reports five time periods: 1960-2000; 1960-80; 1970-2000; 1980-2000; 1990-2000 (covering 40-, 30-, 20-, and 10-year horizons as applicable).
- Controls used in cross-sectional specifications:
  - initial income; initial life expectancy; institutional quality (Hall and Jones (1999)); policy quality (Wacziarg and Welch (2003)); geography (frost days and area in the tropics); external shocks (average growth and variability of terms of trade); government consumption; revolutions (Banks (2004)).
- Outlier treatment:
  - Outliers dropped using Hadi (1992) procedure for each time horizon.
- Instrument construction:
  - Main identification: exploit non-economically-motivated aid determinants; assume such aid is unaffected by economic outcomes.
  - Model of donor allocation (equation 1) uses bilateral donor-recipient covariates (STRAT, USISEG, COMCOL, COMCOLUK, COMCOLFRA, COMCOLSPA, COMCOLPOR, CURCOL, COMLANG).
  - Predicted donor share θ̂drt from equation (1) is aggregated into an instrumented aid-to-GDP ratio Ârt via equation (2): Ârt = Σd (θ̂drt * Adt * GDPdt) / GDPrt (notation as in source).
  - Instruments derived along Frankel and Romer (1999) lines but starting from bilateral relationships and aggregating up.
- First-stage and instrument strength:
  - Instrumenting variables jointly account for between 20 and 23 percent of variation in donor allocation.
  - First-stage relationship between actual and fitted aid: coefficient about 0.44 with t-statistic > 5.
  - First-stage F-values exceed Staiger and Stock (1997) weak-instrument threshold of ten in four out of five cross-section cases.

### III. AID AND GROWTH: REVISITING THE CROSS-SECTION EVIDENCE
- OLS cross-section baseline (Table 2) (no endogeneity correction):
  - In four of five horizons, OLS estimate of aid coefficient is negative; only significant estimate for 1960-2000 horizon.
  - Long-run OLS magnitude (1960-2000): increase in aid of 1 percentage point of GDP would lower long-run growth by about 0.07 percentage points per year (coefficients should be divided by 100 to obtain percentage point increase in annual growth).
- IV (instrumented) core results (Table 4A):
  - Core IV specifications yield high explanatory power: R-squares typically greater in longer horizons—73 percent (1960-2000) and 70 percent (1970-2000).
  - Aid coefficient negative in three out of five cases and significant in none.
  - Retaining outliers yields a significant positive aid coefficient in 1980-2000 driven by two observations (Cape Verde and Guinea-Bissau), illustrating fragility.
  - IV estimates generally less negative or more positive than OLS estimates, suggesting correction for negative endogeneity bias (donors giving more to countries faring poorly).
  - Aid coefficient magnitudes are small.
- Instrument validity and robustness:
  - First-stage coefficients on instrument significant at 1 percent; F-values generally exceed 10.
  - Alternative endogeneity corrections (initial/lagged aid, alternative instrument exploiting exogenous variation in donor aggregate aid – described in Appendix 2) produce similar aid coefficients.
- Disaggregation by aid category (Table 6):
  - Categories tested: by sector (social, economic, food), timing (short-impact vs long-impact), donor type (multilateral vs bilateral).
  - No sub-category shows any significant impact—positive or negative—on growth.
- Non-linear and conditional effects (Table 7):
  - Including squared aid term renders level terms positive and squared terms negative but neither level nor squared aid term significant.
  - Interactions of aid with policy (Sachs-Warner / Wacziarg and Welch (2003) and World Bank CPIA) yield no positive and significant aid–policy interaction; underlying policy variable often significant, interaction term unstable and sometimes negative.
- Aid effectiveness conditional on geography (Table 8):
  - Interaction of aid with geography (Bosworth and Collins (2003) measure) yields aid–geography coefficient significant in only one of five horizons despite geography itself usually significant.

### IV. AID AND GROWTH: REVISITING THE PANEL EVIDENCE
- Estimation methods and caveats:
  - Use of panel GMM: Arellano-Bond (difference-GMM) and Blundell-Bond (system-GMM) to address endogeneity and incorporate fixed effects.
  - GMM confers many researcher choices (which lags, which variables treated as endogenous/predetermined, number of lags), making robustness claims sensitive to specification choices.
- GMM empirical findings (Table 9 and Table 10):
  - Mixed/fragile results across estimators and specifications:
    - Total aid: negative and significant in one variant.
    - Short-impact aid: negative and significant in difference-GMM variant.
    - Economic aid: positive and significant in both variants in some specifications.
  - Fragility demonstrated:
    - Positive economic-aid effects disappear when reducing lags used as instruments (e.g., moving to three lags removes significance and can reduce magnitude by three-quarters).
    - Negative short-impact aid effect breaks down if government consumption is excluded as a regressor.
  - Diminishing/increasing returns: aid-square term generally insignificant.
  - Aid–policy interaction:
    - One specification shows positive and significant interaction for short-impact aid (appearing to confirm Burnside and Dollar (2000)), but the term loses significance under difference-GMM.
    - Replacing short-impact with economic aid and using three-lag instrumentation can produce a near-significant interaction with the opposite (negative) sign.
  - Aid–geography interaction:
    - One specification finds aid more effective outside tropics using fraction of land area in tropics; result sensitive to estimator choice and inflation measurement (log vs level).
- Overall panel conclusion:
  - GMM results are inconsistent and fragile; degrees of freedom in GMM mean robustness claims must be scrutinized.
  - Authors conclude it is difficult to discern robust effects of aid—positive or negative—using panel GMM methods.

### V. QUANTITATIVE IMPACT OF AID: THEORY AND EMPIRICS
- Theoretical benchmark assuming aid increases public investment:
  - Derived relationship (notation per source): γy = (Aid/Y) * (αβ / (Y/K + δ))  (presented in source text as a functional relationship; see Appendix 4 for details).
  - Symbols: γy is rate of growth of output per worker; Aid/Y is ratio of aid to GDP; α is capital share in income; β is fraction of aid invested; Y/K is output-capital ratio; δ is depreciation (notation as in source).
- Numerical example under optimistic assumptions:
  - Set β = 1 (all aid invested); α = 0.35 (capital share in income, Bosworth and Collins (2003)); Y/K = 0.45 (average developing country in regression sample).
  - The magnitude of the regression coefficient suggested by theory is 0.16; i.e., a 1 percentage point increase in the ratio of aid to GDP should at most raise the long-run growth rate by 0.16 (coefficients reported in the paper should be divided by 100 to obtain percentage point increase in annual growth—consistent with cross-section reporting practice described earlier).
- Interpretation:
  - Even under optimistic assumptions, theoretical impact of aid on long-run growth is positive but relatively small, consistent with difficulty of detecting robust empirical effects given data noise.

*Italic source attribution: _wp05127 - References..............................................................................................................*

### 0.16 percent, even on the most optimistic assumption that all aid is usefully invested. More

### _wp05127 - 0.16 percent, even on the most optimistic assumption that all aid is usefully invested. More

### Theoretical estimate of aid’s effect on growth and comparison with empirical magnitudes
- Theoretical estimate: 0.16 percent (even on the most optimistic assumption that all aid is usefully invested).  
- More realistic theoretical coefficient if half of all aid is wasted or consumed: "close to 0.1."  
- Empirical magnitudes reported in the literature:
  - Clemens et. al. (2004): coefficient of gross aid on growth of about 0.9.
  - Hansen and Tarp (2000) and Dalgaard et. al. (2004) (GMM estimations): coefficient on net aid varies between 0.6 and 1.3.
  - Many coefficients in the paper: when positively signed (Table 4A, columns 2 and 4, and Table 10, columns 5-7), magnitudes in the range of about 0.01 and 0.2. (Note: "the coefficient estimate has to be divided by 100 to get the effects of a percentage point increase in aid to GDP on annual growth.")
- Interpretation: Theory suggests the high GMM values (0.6–1.3 and 0.9) are about 6–10 times greater than theoretical predictions; coefficients in this paper (0.01–0.2 before dividing by 100) are much closer to theory.

### Reconciling high empirical coefficients with theory
- To reconcile Clemens et. al. (2004) and Dalgaard et. al. (2004) high estimates with theory, aid would need to have a substantial impact on total factor productivity (TFP), for example via:
  - human capital accumulation, or
  - promotion of better policies.
- Required TFP impact implied by those empirical estimates: a one percentage point increase in the aid to GDP ratio should increase annual average TFP growth by between 0.5 percent and 1 percent.
- Contextual comparison: This would imply that an additional 1 percentage point of aid to GDP in the post-war period produced productivity growth in developing countries roughly equivalent to "the IT-revolution in the United States in the 1990s."

### Central conclusions and robustness
- Main conclusion: There is no robust positive relationship between aid and growth in the cross-section, despite instrumenting strategies that correct bias in OLS.
- This conclusion holds across:
  - time horizons;
  - time periods;
  - types of aid distinguished by:
    - what they are used for (economic, social, food, etc.);
    - who gives it (multilateral donors, bilateral donors);
    - who it is given to (those with good policies and institutions and others);
    - who it is given to (those in the tropics and outside);
    - how long it takes to impact (short and long impact).
- Fungibility finding: Results are reasonably uniform across sub-categories of aid, suggesting a high degree of fungibility—economic, social and food aid have similar effects on growth, as do bilateral and multilateral aid.
- Panel-GMM findings: Significant impacts of aid on growth can be found (positive and negative) but they do not hold up to robustness checks across the considerable choice of specifications; difficult to discern any systematic effect of aid on growth in panel context.
- Possible explanations:
  - Noise in cross-country data could obscure real relationships—making strong claims about aid effectiveness or ineffectiveness based on cross-country evidence unwarranted.
  - If noise is not the entire explanation, research must shift from cross-sectional analysis to direct evidence on channels through which aid affects growth to identify aspects of aid that offset growth-enhancing effects of resource transfers.
- Implications:
  - Past findings do not imply aid cannot be beneficial in the future.
  - For future effectiveness, aid delivery mechanisms (how, to whom, in what form, under what conditions) will have to be rethought.
  - Understanding hindrances to aid effectiveness is essential; findings support efforts under way at national and international levels to improve aid effectiveness.

### Selected key summary statistics (Table 1 excerpts)
- Real annual average per capita GDP growth (PPP): Mean 1.435, Std. Dev. 1.756, Min -3.373, Max 26.794 (1980-00 (83 Obs.) panel shown among others).
- Aid to GDP: Mean 0.069, Std. Dev. 0.081, Min 0.000, Max 0.423.
- Fitted aid to GDP: Mean 0.095, Std. Dev. 0.171, Min 0.000, Max 0.927.
- Initial level of per capita (PPP) GDP: Mean 7.375, Std. Dev. 0.696, Min 5.944, Max 18.967.
- Initial level of life expectancy at birth: Mean 47.443, Std. Dev. 9.664, Min 32.380, Max 71.680.
- Institutional quality: Mean 0.525, Std. Dev. 0.119, Min 0.225, Max 0.859.
- Geography: Mean -0.599, Std. Dev. 0.724, Min -1.040, Max 1.528.
- Initial level of government consumption to GDP: Mean 13.595, Std. Dev. 9.510, Min 1.376, Max 65.041.
- Average no. of revolutions: Mean 0.233, Std. Dev. 0.201, Min 0.000, Max 0.829.
- Average level of the terms of trade: Mean 113.332, Std. Dev. 22.922, Min 66.665, Max 176.213.
- Standard deviation of the terms of trade: Mean 26.237, Std. Dev. 18.430, Min 1.681, Max 94.323.
- Initial level of trade policy: Mean 0.013, Std. Dev. 0.114, Min 0.000, Max 1.000.

### Representative regression results and diagnostics (selected tables)
- Table 2 (OLS, dependent = average annual growth rate of per capita GDP):
  - Aid/GDP coefficients across periods: -7.276, -5.900, -5.852, -4.159, 9.446 (with various t-statistics and specification details).
  - R-square values: 0.77, 0.57, 0.72, 0.59, 0.52 across columns.
- Table 4A (IV estimations):
  - Aid/GDP coefficients: -2.551, 1.353, -0.829, 1.313, -13.514.
  - R-square values: 0.73, 0.55, 0.70, 0.59, 0.52.
- Table 4B (first-stage fitted aid to GDP, 1960-00):
  - Fitted aid to GDP coefficient on instruments: 0.270, 0.176, 0.264, 0.211, 0.164.
  - R-square values: 0.74, 0.69, 0.78, 0.74, 0.80.
  - F-values: 13.44, 8.47, 23.62, 14.52, 3.43.
- Table 6 (IV by category of aid):
  - Social sector aid/GDP coefficients (examples): -4.717, 7.664, -84.776.
  - Economic aid/GDP coefficients (examples): -16.511, 16.030, 895.087.
  - Food aid/GDP coefficients (examples): -19.015, -5.433, -206.035.
- Table 7 (Aid and diminishing returns; aid interacted with policy):
  - Examples: Aid/GDP coefficients include 2.885, 2.922, 25.649, 6.774, 140.408, -4.093, 1.522, 1.365, 2.089, -13.395.
  - Aid/GDP-squared examples: -17.683, -5.788, -95.526, -22.755, -786.286.
  - Policy (Sachs-Warner) coefficients include values such as 2.001, 1.538, 2.634, 2.375, 0.397, 1.731, 2.031, 2.442, 0.523, 0.774.
- Table 9 (GMM estimations, selected):
  - Aid/GDP examples: -0.231, -3.781.
  - Short-term aid/GDP examples: -7.794, -23.937, -7.888.
  - Economic Aid/GDP examples: 43.347, 44.773, 9.746, 59.185.
  - Log Inflation coefficients: values include -1.742, -1.947, -1.677, -1.810, -1.623, -1.544, -1.744, -1.020, -1.566.
  - Institutional quality examples: 7.152, 7.259, 4.013, 0.017, 6.025.
  - Diagnostics reported: Chi-Square (Hansen over-id test) values include 1.000, 1.000, 1.000, 0.959, 1.000, 0.936, 0.952, 0.419, 0.866; AR(2) test statistics include 0.481, 0.352, 0.254, 0.067, 0.179, 0.121, 0.246, 0.484, 0.288.
  - GMM methods: System and Difference GMM used in different specifications.

### Policy-relevant implications and recommendations
- Re-examine policy prescriptions that rely solely on cross-country regression evidence about aid effectiveness due to possible data noise and lack of robustness.
- For aid to be effective in the future, rethink the aid apparatus: how aid is delivered, to whom, in what form, and under what conditions.
- Focus further research on direct evidence of channels (e.g., human capital accumulation, policy change, TFP effects) through which aid might help or hinder growth.
- Support ongoing national and international efforts to improve aid effectiveness and to identify hindrances that offset the potential growth-enhancing effects of resource transfers.

*Source: _wp05127 - 0.16 percent, even on the most optimistic assumption that all aid is usefully invested. More*

### Appendix 1.

### _wp05127 - Appendix 1.

### GMM Estimation Results (Table 10: Impact of Aid Conditional on Policies and geography)
- Dependent variable: average annual growth rate of per capita GDP.
- Selected coefficient estimates and reported t-statistics (as presented in the table):
  - Aid/GDP:
    - Column (1): 11.406 (1.36)
    - Column (2): 20.179 (1.25)
    - Column (3): 9.377 (1.15)
  - Area in tropics:
    - Column (2): -0.227 (0.39)
    - Column (3): -0.319 (0.55)
  - Aid/GDP * area in tropics:
    - Column (1): -14.137 (1.71)*
    - Column (2): -24.601 (1.51)
    - Column (3): -11.810 (1.48)
  - Economic aid/GDP:
    - Column (5): 70.304 (1.90)*
    - Column (6): 83.924 (1.85)*
  - Economic aid/GDP Square:
    - Column (6): -144.278 (0.59)
  - Initial level of policy:
    - Column (1): 0.564 (1.08)
    - Column (2): 0.149 (0.22)
    - Column (3): -2.079 (1.57)
    - Column (4): 0.098 (0.09)
    - Column (5): 0.634 (1.32)
    - Column (6): -0.642 (0.69)
    - Column (7): 0.612 (1.25)
  - Economic aid/GDP * Policy:
    - Column (5): -112.193 (1.65)
  - Short-term aid/GDP:
    - Column (1): -0.096 (1.43)
    - Column (2): -0.226 (2.42)**
  - Short-term aid/GDP * Policy:
    - Column (1): 0.146 (1.76)*
    - Column (2): 0.083 (0.93)
  - Log Inflation:
    - Column (1): -1.595 (4.85)***
    - Column (2): -1.587 (4.91)***
    - Column (3): -1.878 (3.76)***
    - Column (4): -1.080 (1.24)
    - Column (5): -0.957 (3.50)***
  - Inflation (percent):
    - Column (6): -0.001 (2.97)***
    - Column (7): -0.001 (1.76)*
  - Institutional quality:
    - Column (1): 3.967 (0.97)
    - Column (2): 6.533 (1.69)*
    - Column (3): 11.185 (3.14)***
    - Column (4): 11.036 (3.16)***
  - Geography:
    - Column (1): 0.681 (2.18)**
    - Column (2): 0.313 (1.12)
  - Initial per cap. GDP:
    - Column (1): -0.554 (0.79)
    - Column (2): -1.488 (2.27)**
    - Column (3): -6.062 (6.59)***
    - Column (4): -6.429 (4.77)***
    - Column (5): -1.529 (2.89)**
    - Column (6): -3.138 (4.83)***
    - Column (7): -1.488 (2.77)***
  - Revolutions:
    - Column (1): -1.165 (1.56)
    - Column (2): -1.814 (2.29)**
    - Column (3): -2.759 (3.15)***
    - Column (4): -4.844 (4.09)***
    - Column (5): -1.560 (2.34)**
    - Column (6): -2.243 (2.65)**
    - Column (7): -1.370 (1.96)*
  - Initial government consumption:
    - Column (1): -0.080 (2.31)**
    - Column (2): -0.026 (0.92)
    - Column (3): 0.062 (1.14)
    - Column (4): -0.054 (0.74)
    - Column (5): -0.078 (2.54)**
    - Column (6): -0.040 (1.19)
    - Column (7): -0.071 (2.31)**
- Sample, diagnostics, and estimation:
  - Observations by column: 423, 417, 329, 332, 512, 431, 512
  - Number of Groups: 88, 87, 83, 85, 81, 80, 81
  - Chi-Square (Hansen over-id test): 1.000, 1.000, 0.999, 0.752, 1.000, 1.000, 1.000
  - AR(2) (test for serial correlation): 0.166, 0.243, 0.066, 0.497, 0.621, 0.495, 0.685
  - GMM estimation method: System, System, Difference, Difference, System, Difference, System
  - Endogenous variables instrumented (listed): Initial income, aid, aid-square, aid*policy, gov. cons., policy, inflation (varies by specification)
  - Number of lags used in instrumentation: unrestricted or three (varies by column)
  - Exogenous instrumenting variable: Geography or Tropics (varies by column)
- Notes:
  - All standard errors are robust. T-statistics reported below coefficient estimates.
  - ***, **, and * denote significance at 1, 5, and 10 percent, respectively.
  - Details of the GMM choices appear in the table footnotes.

### Charts: First-stage and conditional correlations
- Chart 1: Conditional Relationship between Aid and its Instrument, 1960-00
  - Plots the first-stage relationship between actual aid and the instrument (fitted aid), conditional on all covariates in the second-stage growth regression.
  - The slope is the coefficient on fitted aid in the first-stage regression (also shown in Table 4B).
  - For presentational purposes, two countries included in Table 4 are excluded from the chart.
- Chart 2: Conditional Correlation between Growth and Total Aid, 1960-00 (OLS estimation)
  - Reported line fit: Coefficient = -7.28; t-statistic = 2.79
  - Plots the relationship between growth and actual aid, conditional on covariates; slope equals coefficient on aid in the OLS regression in column 1 of Table 2.
- Chart 3: Conditional Correlation Between Growth and Total Aid, 1960-00 (IV Estimations)
  - Reported line fit: Coefficient value = -2.55; t-statistic = 1.08
  - Plots the relationship between growth and aid, conditional on covariates; slope equals coefficient on aid in the instrumental variable regression in column 1 of Table 4A.

### Data description and variable definitions (Appendix I)
- Primary data sources cited:
  - Heston, Alan, Robert Summers and Bettina Aten, Penn World Table Version 6.1, Center for International Comparisons at the University of Pennsylvania (CICUP), October 2002.
  - OECD, DAC (Development Assistance Committee) database on Aid, 2002.
  - World Bank, 2004. World Development Indicators, Washington, D.C.: World Bank.
  - IMF (International Monetary Fund), 2004, World Economic Outlook, Washington, D.C.: IMF.
  - Bosworth, B., and S. Collins, 2003, “The Empirics of Growth: An Update,” mimeo, Brookings Institution, Washington D.C.
  - Barro and Lee, 1994: Data Set for a Panel of 138 Countries (Revised January 1994).
  - Arthur S. Banks, CROSS-NATIONAL TIME SERIES, 1815-2002 [Computer file]. Databanks International, 2002.
  - Wacziarg, Romain and Karen Horn Welch (2003) “Trade Liberalization and Growth: New Evidence,” Mimeo, Stanford University.
  - Correlates of War 2, Correlates of War Project, 2002, University of Michigan.
  - Rose, A.K., “Do we really know that the WTO increases trade?” 2004, American Economic Review.
- Key variables and sources (as listed):
  - Rgdpchg: Annual growth rate of real GDP per capita — PWT
  - aid_gdp: The ratio of aid to GDP — OECD, DAC
  - FaN_gdp: The ratio of fitted aid to GDP based on exploiting exogenous variation in the allocation of aid by donors across recipients — Authors' calculations
  - bilat_gdp: The ratio of bilateral aid to GDP — OECD, DAC
  - multi_gdp: The ratio of multilateral aid to GDP — OECD, DAC
  - social_gdp: The ratio of social sector aid to GDP — OECD, DAC
  - Fsocial_gdp: The ratio of fitted social sector aid to GDP — Authors' calculations
  - economic_gdp: The ratio of economic aid to GDP — OECD, DAC
  - Feconomic_gdp: The ratio of fitted economic aid to GDP — Authors' calculations
  - food_gdp: The ratio of food aid to GDP — OECD, DAC
  - Ffood_gdp: The ratio of fitted food aid to GDP — Authors' calculations
  - yc_penn: Initial period per capita (PPP) GDP — PWT, 6.1
  - le_wdi: Initial period life expectancy at birth — WDI
  - gadp6099: Institutional Quality — Bosworth & Collins, 2003
  - geog6099: Geography — Bosworth & Collins, 2003
  - cg: Government consumption as share of GDP — PWT, 6.1
  - cg_i: Initial period government consumption as share of GDP — PWT, 6.1
  - revol: No. of revolutions — Arthur S. Banks
  - tot_av: Terms of trade — WDI
  - tot_stdev: Standard deviation of terms of trade — WDI
  - sw1: Trade policy — Wacziarg & Welch, 2003
  - aid_gdpsq: The ratio of aid to GDP squared — Authors' calculations
  - Tropicar: The fraction of a country’s land area in the tropics — Doppelhoffer et. al. (2004)
  - aid_sw1: The ratio of aid to GDP * Trade policy — Authors' calculations
  - sw1_i: Initial level of trade policy — Wacziarg & Welch, 2003
  - aid_sw1_i: The ratio of aid to GDP * Initial trade policy — Authors' calculations
  - cpia: Policy and institutional rating — World Bank
  - aid_cpia: The ratio of aid to GDP * cpia — Authors' calculations
  - cpia_i: Initial level of policy and institutional rating — World Bank
  - aid_cpia_i: The ratio of aid to GDP * initial policy — Authors' calculations
  - ggb_gdp: The ratio of donor country's general government balance to GDP — WEO
  - lurn: Donor country's natural rate of unemployment — WEO
  - aid_shr: Donor country's aid share to recipient country — Authors' calculations
  - allidum_3: Dummy that takes a value of 1 if donor and recipient country are part of the same entente alliance — Correlates of War, 2
  - egy_isr_dum: Dummy that takes a value of 1 if donor is US and recipient is Egypt or Israel — Authors' calculations
  - Colony: Dummy that takes a value of 1 if donor and recipient country were ever in colonial relationship — Rose, 2004
  - Curcol: Dummy that takes a value of 1 if donor and recipient country enjoy a current colonial relationship — Rose, 2004

### Instrumentation strategy and related issues (Appendix II)
- Main concerns discussed:
  - Exclusion restriction:
    - Instruments (strategic variables, colonial relationships, proximity to donors) may be correlated with aid but could affect growth directly, violating exclusion.
    - Difficulty testing exclusion restriction formally when instrumenting a single endogenous regressor and when instruments are constructed from donor-recipient dyads while the growth regressions use recipient observations.
    - Heuristic checks: introducing share of aid from Scandinavian countries (perceived “good donors”) did not significantly change the aid coefficient nor show an independent positive effect.
    - Comparison with literature: lagged aid and policy variables as instruments are likely invalid if shocks to growth persist.
  - Bias:
    - Strategic variables may be endogenous if donors lend to “bad leaders,” potentially biasing IV estimates toward negative impacts of aid.
    - Authors note mixed historical evidence on recipients of strategic aid and growth outcomes; multilateral and bilateral aid showing similar effects (Table 6, Panel C) suggests strategic motives do not straightforwardly map into bad usage of aid.
    - Instrumenting tended to increase the size of the aid coefficient relative to OLS (compare Table 2 with Table 4), interpreted as correcting a negative endogeneity bias (donors giving more aid to countries doing poorly).
    - Similar first-stage determinants for total aid and “good” (social) aid (Appendix Table 4) suggest strategic covariates explain both types similarly.
  - Extracting exogenous donor-side variation:
    - Authors propose exploiting donor macroeconomic/budgetary conditions (fiscal balance and unemployment) as more neutral determinants of total aid:
      - Regression notation reported in the text:
        - 012 ' d tdtdtdtd td t AFBUN Xα  ααα=+   +    +∈=   +∈                                    -------(3)
        - Predicted value: ˆ' dtd t AXα= 
        - Instrument constructed as:
          - ˆˆ . dtdtdrt d rt rt GDP  A A GDP θ = ∑ -----(4)
      - Explanation: use predicted donor-level generosity (from macro conditions) and donor allocation patterns to form recipient-level instruments.
      - Authors acknowledge cyclical donor factors could affect recipient cyclical growth but argue their influence on long-run trend growth is likely limited when measuring over 20–40 year spans.
  - Other concerns:
    - Fitted aid is correlated with recipient country size (inverse relation to economic size), but the first-stage relationship between actual and fitted aid remains significant after controlling for second-stage regressors (including level of GDP), as shown in Chart 1 and Table 4B.

### Country coverage table notes (Appendix III excerpt)
- The appendix lists country inclusion flags for panels “1960_00” and “1980_00” and a Panel indicator (yes/no) for each country. Examples excerpted in the table (formatted as Country | 1960_00 | 1980_00 | Panel):
  - Albania | no | no | yes
  - Algeria | yes | yes | yes
  - Angola | yes | yes | yes
  - Argentina | yes | yes | yes
  - Bangladesh | yes | yes | yes
  - Brazil | yes | yes | yes
  - China | yes | yes | yes
  - India | yes | yes | yes
  - Korea, Rep. | yes | yes | yes
  - Mexico | yes | yes | yes
  - Nigeria | yes | yes | yes
  - South Africa | yes | yes | yes
  - (Table continues for a wide set of countries; entries are presented as in the source table.)

*Appendix content and tables reproduced from _wp05127 - Appendix 1.*

### Appendix III. Sample of Countries

### _wp05127 - Appendix III. Sample of Countries

### Prediction of the Standard Growth Model of the Quantitative Impact of Aid
- Model framework and key equations:
  - Cobb-Douglas production: Y = A K^α L^(1−α)  ---(1)
  - Per worker form: y = A k^α  (where y = Y/L and k = K/L)
  - Capital accumulation (sectoral): .( ) G P G P I I I K K K δ δ = − = + − +  ---(2)  [as printed in source]
  - Assuming fraction β of aid is invested: .( ) P K Aid I K β δ = + − and .( ) ( ) P I Aid knk LL β δ = + − +  ---(3)
  - Growth of output per worker related to capital per worker: γ_y = .( ) y = ykA ykA α = +  ---(4)  [as printed in source]
  - Substituting (3) into (4) yields: .( ) ( ) P y I Aid A n kL kLA β γ α α δ α = + − + +  ---(5)
  - Re-writing in terms of aid/GDP: .( ) P y I Aid YA n YK kLA α α β γ α δ α = + − + +  ---(6)
  - Differentiating with respect to aid-to-GDP: () y Y Aid K Y δ γ α β δ =  ---(7)  [as printed in source]
- Interpretations from equation (7):
  - The coefficient of aid in cross-country growth regressions should be related to:
    - capital share in income (α),
    - fraction of aid that is invested (β),
    - output-capital ratio (Y/K),
    - depreciation rate (δ) appears in denominator.
- Numerical illustrative magnitudes (using assumptions from the source):
  - If β = 1, α = 0.35 (Bosworth and Collins (2003) value), Y/K ≈ 0.45 (sample average), then the magnitude of the regression coefficient = 0.16. Interpretation: "a 1 percentage point increase in the ratio of aid to GDP should raise the growth rate by 0.16 percent" under the optimistic assumption that all aid is usefully invested.
  - If only half of all aid is invested (β = 0.5), the coefficient value should be 0.08 (noted as "close to 0.1" in the source).

### Appendix Table 1: Impact of Aid on Growth Using Alternative Instrument (dependent variable is average annual growth rate of per capita GDP)
- Sample columns: (1) 1960_00, (2) 1960_80, (3) 1970_00, (4) 1980_00, (5) 1990_00
- Key coefficient: Aid/GDP:
  - (1) -2.513  (t-statistic (1.08))
  - (2) 1.725  (0.42)
  - (3) -0.951  (0.22)
  - (4) 1.528  (0.27)
  - (5) -14.284  (0.89)
- Selected additional coefficients (with t-statistics below):
  - Initial per cap. GDP: (1) -1.124 (4.40)***; (2) -1.070 (1.75)*; (3) -1.475 (4.62)***; (4) -1.284 (2.90)***; (5) -1.157 (1.54)
  - Initial level of life expectancy: (1) 0.038 (2.13)**; (2) 0.065 (1.42); (3) 0.044 (1.86)*; (4) 0.062 (1.44); (5) -0.009 (0.08)
  - Institutional quality: (1) 4.035 (2.32)**; (2) 7.934 (3.15)***; (3) 3.359 (1.48); (4) 2.384 (0.77); (5) 5.331 (1.25)
  - Geography: (1) 0.430 (3.25)***; (2) -0.181 (0.77); (3) 0.406 (2.55)**; (4) 0.603 (3.15)***; (5) 0.310 (0.86)
  - Initial level of government consumption: (1) -0.008 (0.39); (2) -0.016 (0.45); (3) -0.020 (1.00); (4) -0.047 (2.35)**; (5) -0.030 (0.96)
  - Revolutions: (1) -1.257 (2.52)**; (2) 1.109 (1.05); (3) -1.358 (2.75)***; (4) -0.343 (0.55); (5) -1.772 (2.20)**
  - Terms of trade growth: (1) 0.015 (1.79)*; (2) 0.011 (1.82)*; (3) 0.030 (2.46)**; (4) 0.011 (0.59); (5) -0.042 (1.00)
  - St. deviation of TOT growth: (1) -0.014 (1.36); (2) 0.002 (0.21); (3) -0.033 (2.22)**; (4) -0.013 (0.53); (5) -0.120 (1.96)*
  - Initial level of policy (Sachs-Warner): (1) 1.933 (3.48)***; (2) 1.551 (1.58); (3) 2.217 (4.02)***; (4) 2.343 (3.11)***; (5) 0.774 (1.31)
- Sample size and fit:
  - Observations: (1) 74; (2) 61; (3) 80; (4) 81; (5) 79
  - R-square: (1) 0.73; (2) 0.55; (3) 0.70; (4) 0.59; (5) 0.52
- Notes (as in source):
  - All standard errors are robust. T-statistics reported below coefficient estimates. ***, **, and * denote significance at 1, 5, and 10 percent, respectively.
  - The instrument for aid is discussed in Appendix 2. Outliers identified using the Hadi (1992) procedure. All specifications include dummies for sub-Saharan African and East Asian countries.

### Appendix Table 2: Impact of Aid on Growth Conditional on Policy and Institutions, IV Estimations (dependent variable is average annual growth rate of per capita GDP)
- Columns / periods: (1) 1980_00, (2) 1990_00, (3) 1980_00, (4) 1990_00 (note: source lists as (1)(2)(3(4))
- Key coefficients:
  - Aid/GDP: (1) -4.591 (0.30); (2) -9.529 (0.32); (3) 3.280 (0.48); (4) -13.415 (0.78)
  - Policy (Sachs-Warner): 0.556 (0.48) and 0.779 (0.94) in relevant columns
  - Aid/GDP*policy (Sachs-Warner): 107.860 (1.58) and -0.202 (0.02)
  - Policy (World Bank's CPIA ratings): 0.239 (0.86) and 1.071 (1.72)*
  - Aid/GDP*policy (World Bank's CPIA ratings): 0.741 (0.21) and -1.008 (0.12)
- Sample size and fit:
  - Observations: (1) 80; (2) 76; (3) 80; (4) 76
  - R-square: (1) 0.54; (2) 0.53; (3) 0.62; (4) 0.50
- Notes (as in source):
  - Table reproduces results in Table 7 with CPIA substituting for Sachs-Warner-Wacziarg-Welch measure. Estimation for sample common across two measures of policy. All standard errors are robust. T-statistics reported below coefficient estimates. ***, **, and * denote significance at 1, 5, and 10 percent, respectively. Instrument for aid corresponds to equation 2 in Section II of the paper. All specifications include dummies for sub-Saharan African and East Asian countries. Other covariates and first-stage omitted for presentational simplicity.

### Appendix Table 3: Impact of Aid on Growth: Does Donor Type Matter? IV Estimations (dependent variable is average annual growth rate of per capita GDP)
- Columns: (1) 1960_00, (2) 1960_80, (3) 1970_00, (4) 1980_00, (5) 1990_00
- Key coefficients:
  - Aid/GDP:
    - (1) -2.489 (1.04)
    - (2) 3.241 (0.81)
    - (3) -0.823 (0.19)
    - (4) 1.197 (0.20)
    - (5) -12.799 (0.72)
  - Aid share of Scandinavian countries:
    - (1) -0.670 (0.30)
    - (2) -4.108 (1.59)
    - (3) -1.101 (0.38)
    - (4) -0.233 (0.08)
    - (5) 0.630 (0.16)
- Sample size and fit:
  - Observations: (1) 74; (2) 61; (3) 80; (4) 81; (5) 79
  - R-square: (1) 0.73; (2) 0.57; (3) 0.7; (4) 0.59; (5) 0.52
- Notes (as in source):
  - Scandinavian countries include Denmark, Finland, Netherlands, Norway, and Sweden. All standard errors robust; t-statistics reported below coefficient estimates. Instrument for aid discussed in Appendix 2. Outliers identified using Hadi (1992). All specifications include dummies for sub-Saharan African and East Asian countries.

### Appendix Table 4: Estimating the Exogenous Variation in Donors’ Allocation of Social Aid Across Recipients (dependent variable is share of donor i’s social aid to recipient j)
- Period columns: (2) 1970_00, (3) 1980_00, (4) 1990_00
- Selected coefficients (with t-statistics):
  - Dummy for common membership in Entente Alliance (Alliance Dummy): (2) 0.126 (3.14)***; (3) 0.475 (5.87)***; (4) 0.283 (6.39)***
  - Dummy for Egypt and Israel after Camp David (Egypt Israel Dummy): (2) 0.233 (10.30)***; (3) 0.226 (10.58)***; (4) 0.189 (10.02)***
  - Dummy for pairs that ever had a colonial relationship: (2) 0.101 (10.86)***; (3) 0.086 (9.91)***; (4) 0.064 (7.99)***
  - Dummy for pairs currently in a colonial relationship: (2) 0.006 (0.17); (3) -0.038 (1.02); (4) -0.025 (0.56)
  - Dummy for pairs that have common language: (2) 0.006 (2.90)***; (3) 0.005 (2.74)***; (4) 0.003 (1.85)*
  - Dummy for country that ever had a colonial relationship with UK: (2) -0.089 (8.60)***; (3) -0.076 (7.75)***; (4) -0.061 (6.88)***
  - Dummy for country that ever had a colonial relationship with France: (2) -0.091 (8.11)***; (3) -0.078 (7.42)***; (4) -0.054 (5.69)***
  - Dummy for country that ever had a colonial relationship with Spain: (2) -0.074 (5.92)***; (3) -0.058 (4.92)***; (4) -0.034 (3.20)***
  - Dummy for country that ever had a colonial relationship with Portugal: (2) 0.040 (2.49)**; (3) 0.056 (3.73)***; (4) 0.083 (6.12)***
- Sample size and fit:
  - Observations: (2) 2,315; (3) 2,302; (4) 2,213
  - R-squared: (2) 0.15; (3) 0.16; (4) 0.16
- Notes (as in source):
  - Estimation is by ordinary least squares. The estimated equation corresponds to equation 1 in Section II. Dependent variable is the share of social sector aid given by donor i to recipient j. All standard errors are robust. T-statistics reported below coefficient estimates. ***, **, and * denote significance at 1, 5, and 10 percent, respectively.

*Source: _wp05127 - Appendix III. Sample of Countries (PDF content provided).*

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