## The Effect of Foreign Aid on Sub-national Development

|# 5. Empirical Results

## Texte intégral

1I begin this investigation by first replicating the results obtained by Briggs (2018) and challenging the findings with additional specifications. Maintaining the same cross-sectional structure as in the original study, I estimate a model with spatial fixed effects as opposed to country fixed effects. In other words, I transform the data to deviations with respect to group means, which are composed by the neighbouring grid cells, using a spatial weight matrix similar to that described in the previous section. I then compute the estimated parameters using a standard linear model, with standard errors clustered at the country-level to allow for spatial correlation beyond the contiguous neighbours.

2I examine both the individual and joint effects of all poverty proxies used in Briggs (2018) on the three foreign aid indicators. In all cases, the inclusion of spatial fixed effects did not significantly change the author’s original results, which suggest that more prosperous grid cells are associated with higher values of aid.

3I also carried out the above estimations using panel data, and controlling for unobserved heterogeneity at the grid cell level. For the model with the logarithm of total disbursements as a dependent variable, I find the coefficient associated with night-time luminosity to be statistically insignificant. What’s more, once I include the log of total commitments as a covariate, the relationship between nightlights and disbursements becomes negative, thus suggesting a pro-poverty allocation of aid (Appendix C).

4In the next section, I discuss the main findings on the effects of foreign aid using the two estimation strategies described in Section 4.

# 5.1 Main results

## Quantile fixed effects results

5Table 2 below summarises the results for quantile regressions of the baseline model, using each of the four foreign aid indicators. The results suggest that, *ceteris paribus*, foreign aid generally has a positive and significant effect on night-time luminosity, although the effect is not particularly large in economic terms. The lagged terms consistently display a greater effect, which is in line with the notion that any effect would require time to translate into an observable economic impact. For instance, looking at the median effect, an increase in the number of projects by one unit would lead to a 2.2% increase in nightlights in subsequent periods.

6The analyses using the presence or number of active projects as indicators show a much greater impact than the two using annual financial flows. This may simply be a result of the infrequency of project-specific flows, or it may be an indication of an underlying mechanism obstructing the full impact (e.g. misuse of aid funds).

- 1 Unfortunately, due to computational constraints, it was not possible to perform a formal test for t (...)

7In addition, the results reveal the existence of heterogeneity in the effect of aid at different levels of development, confirming the merits of the chosen identification strategy.1 The coefficients display a positive trend with respect to the quantiles, with the smallest values consistently observed at the 95^{th }percentile.

8Given the right-skewness of the night-time luminosity distribution, it is likely that the 75% percentile represents grid cells with low economic activity; therefore, the results would indicate that the marginal effect of foreign aid is greatest within a country’s poorest regions.

- 2 The authors estimate a quadratic production function for the logarithm of night lights
*m*(*.*) such th (...)

9For more intuitive interpretations, I also calculate the effects of aid on real GDP per capita, using estimated “exchange rates” between night-time lights and GDP by Hu & Yao (2019).2 Unlike previous studies, they find that the elasticity varies with respect to the level of income. For instance, in the case of Equatorial Guinea - with one of the highest GDP per capita in 2017 (constant 2011 Intl$22,214) - the elasticity of GDP with respect to nightlights would equal approximately 0.96, while in the case of grid cells in Burundi (GDP per capita of Intl$668), the elasticity would be 0.36. Taking these two cases as examples, the presence of an active project within a grid cell in Equatorial Guinea could increase real GDP per capita up to 15.3%, while for a corresponding grid cell in Burundi, the same treatment would translate into a 5.7% increase in per capita GDP.

10It should be noted that the above results are quite sensitive to the inclusion of year or country-year fixed effects. In fact, once I include them in the analysis, all coefficients of interest become insignificant. I also carry out a standard fixed effects regression of night luminosity on the year dummy variables. Surprisingly, I find that almost all of the within-grid variation in nightlights is explained by the year fixed effects (*R*^{2 }= 0*.*957). This would explain the very small or insignificant coefficients, as there would be no room left for any of the remaining variables to have an observable impact. As such, all following regressions are estimated without the year fixed effects.

11To further examine other forms of heterogeneous effects, I repeat each of the above regressions and include an interaction term between the respective aid indicator and the log of total population. As expected, the coefficients on the interactions are statistically significant, suggesting that the effect of aid differs depending on population density. However, the differential effect is not observed at the highest end of the distribution, particularly with regards to the contemporaneous effect.

12Interestingly, the sign of the coefficients is not consistent across the model specifications, nor across the quantiles for some instances. For the majority of indicators, the estimates are positive, indicating that aid projects are more impactful within more densely populated grid cells, all other things being equal. However, an increase in the number of active projects would actually lead to a decrease in the effect on night luminosity with respect to the grid cell-level population.

13Table 3 instead displays the findings from the quantile regressions of the spatial lag model. As expected, the coefficients on the aid indicators are considerably smaller compared to the baseline model, as the spatial lag of the dependent variable explains most of the variation.

14In the case of the regressions with the binary indicator, the estimates still suggest a positive effect on night-time luminosity, though there is no longer a clear trend in the marginal returns with respect to the quantiles. One important implication from this model is that the spill-over effects appear to have a greater economic impact than the within-cell treatment. For a given grid cell, the presence of an aid project in at least one of its neighbours leads to a 7.5% increase in nightlights.

15On the other hand, when using the log of total commitments as the aid indicator, the estimated coefficients are often statistically insignificant, especially those associated with the spatial lag operators. In addition, all the effects are arguably negligible in economic terms, where the largest observed impact to a 1% increase in total commitment flows is equal to 0.002.

## Instrumental variable results

16Table 4 reports the findings from the 2SLS estimation of the baseline model, in which the instrument is a binary variable indicating whether a country is below the IDA’s income threshold, interacted with a grid cell’s probability of receiving aid.

17These results diverge substantially from the OLS estimates, showing a negative and significant effect for all four aid indicators. In addition, these effects are all much larger in economic terms. The first-stage coefficients also go against initial predictions, as they suggest that, for a given probability, a grid cell in an IDA-eligible country would receive less aid than one in a non-eligible country.

18These unusual findings are likely driven by the weakness of the instrument, as a result of the majority of observations either having a probability of zero or having no variation in the binary indicator, leading to very low predictive power. In fact, the cluster-robust Kleibergen-Paap F-statistic is consistently below Stock & Yogo (2005)’s critical value of 16.38 across all specifications, which allows for a maximum Wald test size of 10%.

19The results remain very similar even when using the distance from the IDA threshold as the time-varying component of the instrument. Despite providing relatively more variation in the instrument, the first-stage F-statistics also remain very low. This may again be the result of the instrument being equal to zero throughout the sample period for most observations.

20Table 5 below repeats the 2SLS estimations on a sub-sample of grid cells located within the countries that have crossed the IDA threshold at one point during the sample period. The results do not offer further inference compared to the estimations on the complete sample, as the coefficients are again all negative and significant, and of a similar magnitude. The results also remain unchanged when using a data sample averaged over three-year periods.

21All the above findings would suggest that, for this particular context, the interaction is not an appropriate instrument to identify the causal impact of foreign aid at the grid cell level. Aside from the issue of low variation, the weakness of the instrument may simply be signalling that a country’s position relative to the operational cut-off does not determine their aid inflows. For instance, it may be the case that most of the projects in this AidData sample are funded by the IBRD rather than the IDA, and as such, the distribution of aid projects would be less responsive to changes in IDA eligibility, contrary to the results found by Galiani *et al. *(2017).

22Moreover, the construction of the instrument relies on values of per capita GNI expressed in current prices, which are regularly revised by the World Bank. Consequently, even a small change from historical values may result in a different implication with regards to a country’s position in relation to the IDA threshold, introducing bias in the instrumental variable due to measurement error.

23Another potential reason for the bias in the results could be that the exclusion restriction does not strictly hold. Given that the exogeneity of the instrument cannot be confirmed directly, a next step would be to relax the exclusion restriction and test for plausible exogeneity, as per the methodology by Conley *et al. *(2012).

**Table 5: **Panel 2SLS regressions of night-time luminosity on aid with grid fixed effects for sub-sample

# 5.2 Robustness checks

24As a first exercise, I evaluate the robustness of the main findings to a specification in which the dependent variable is defined as the growth in night-time lights. The baseline reduced-form model would in this case be defined by the following equation,

25where ∆ln(*Light*_{ic,t}) represents annual logarithmic growth of night-time lights in grid cell *i *of country *c *in year *t*, and ln(*Light*_{ic,t}_{−1}) accounts for the conditional convergence effect. The remaining variables all maintain the same definitions as in the original specification.

26Table 6 reports the results for the quantile regressions using the binary aid indicator. The direction of the coefficient associated with the term controlling for conditional convergence is as expected. For instance, looking at the lower end of the distribution, an increase in night-time lights would result in a subsequent decrease in growth of 0.19 percentage points.

27The estimates for the effect of the presence of an aid project are robust to this specification, demonstrating a positive effect on the growth of night-time lights. In addition, the results again display a trend in the marginal return of aid across the quantiles, with the largest impact observed at the lower end of the distribution. An interesting point is that countries at lower stages of development usually display higher growth. Applying this concept, the findings would suggest that the impact of aid is strongest within “richer” grid cells. On the other hand, it is also likely that the lower end of the night-time luminosity distribution still represents poor grid cells, especially when considering that night-time lights do not change substantially from year to year.

**Table 6: **Quantile fixed effect regressions of growth of night-time luminosity on binary aid indicator

28I then repeat the baseline estimations on a sample which includes project locations that have been geo-referenced up to the level of second-order administrative regions (i.e. precision code 3), which corresponds to 72.5% of the full AidData sample size. The results remain consistent with those reported in Table 2 in both direction and magnitude, indicating no bias arising from the choice of the precision cut-off.

- 3 Early-impact aid sectors include: agriculture, forestry, fishing; energy; industry; mining; trade p (...)

29Following Clemens *et al. *(2012), I also estimate the baseline model on a subsample which differentiates aid projects according to the expected impact, namely “early-impact” and “late-impact”. Early-impact projects are predicted to affect development in the short-run, while late-impact projects would only produce an effect in the long-run.3 In general, the main findings remain qualitatively unchanged by this specification. The coefficients associated with the early-impact indicator suggest a larger contemporaneous effect of aid on night-time lights, while the effect of late-impact aid is largest after a one-year lag.

30Finally, I test the sensitivity of the results to a different variable transformation. As mentioned in Section 3.1, a small constant of 0.01 is added to the dependent and monetary aid variables when adopting the logarithmic transformation. This may create bias in the estimations, especially when considering that the night luminosity variable is standardized between 0 and 1. I therefore repeat the baseline regressions using the inverse hyperbolic sine (IHS) transformation instead, which can be expressed as follows:

31Compared to the natural log, the IHS transformation offers several benefits beyond adjusting for skewness. Most importantly, it retains zero and negative values, thus mitigating potential biases arising from adding an arbitrary number to the variables of interest. In addition, it is more sensitive to changes in the underlying variable, and performs similarly to the log transformation in terms of interpretation.

32Table 7 shows that the underlying implications are maintained, as the estimated coefficients show a positive and significant effect of aid, with a few exceptions. However, these coefficients are considerably smaller compared to those reported previously. For instance, the largest observable effect for the presence of an active project is 0.013, as opposed to 0.159 for the corresponding coefficient in Table 2.

33This would suggest that the potential bias from the inclusion of an arbitrary constant is not negligible, and that past studies making use of the logarithmic transformation are overstating the effects of aid on development.

## Notes

1 Unfortunately, due to computational constraints, it was not possible to perform a formal test for the joint significance of the quantiles.

2 The authors estimate a quadratic production function for the logarithm of night lights *m*(*.*) such that: *m*(*y*) = 0*.*398+1*.*234*y*−0*.*244*y*^{2}, where *y *denotes the real GDP per capita in logarithm. The data was re-centred around the mean, namely 9.62.

3 Early-impact aid sectors include: agriculture, forestry, fishing; energy; industry; mining; trade policy; finance; transport; and communications. Late-impact sectors include: education; water and sanitation; health; social infrastructure; environmental protection; and public administration.

## Table des illustrations

Titre | Table 2: Quantile fixed effects regressions of night-time luminosity on aid indicators |
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Titre | Table 3: Quantile spatial fixed effects regression of night-time luminosity on aid indicators |

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Titre | Table 4: Panel 2SLS regressions of night-time luminosity on aid variables with grid fixed effects |

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Titre | Table 5: Panel 2SLS regressions of night-time luminosity on aid with grid fixed effects for sub-sample |

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Titre | Table 6: Quantile fixed effect regressions of growth of night-time luminosity on binary aid indicator |

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URL | http://books.openedition.org/iheid/docannexe/image/7838/img-7.png |

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Titre | Table 7: Quantile fixed effect regressions of transformed night-time luminosity on binary aid indicator |

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© Graduate Institute Publications, 2020