Other than fragility of BD results as a result of extreme sample dependency as shown, Dalgaard and Hansen (2001) further asserts that BD results may have suffered from mis- specification of the empirical econometric model. BD estimate a non-linear specification, however with their explicit emphasis on the impact of macro policy on aid effectiveness, they explore policy selectivity effects by using an aid-policy interaction term to capture non-linearities in their specification.
BD motivate their choice of policy selectivity by arguing that unlike the proposition from neoclassical growth model that poor countries should have higher returns to capital and a faster transition to the steady state, poor infrastructure and production technology, imperfect capital markets and most crucially institutions and policy distortions tend to lower the returns to capital and reduce the transition to the steady state. They thus argue that aid will have a greater impact on growth rates in an environment with the least policy distortions, and there-in lies the motivation for interacting aid with a policy index.
relationship between aid and growth; these studies explore the possibility that aid inflows have diminishing returns on the recipient economy. Dalgaard et al. (2004) and Lensink and White (1999) provide theoretical analysis that explains why beyond a certain threshold of aid, it may become detrimental rather than beneficial to recipient economy’s growth. The- oretical arguments for possibility of diminishing returns proposed in aid-growth literature include negative effects of aid-financed public capital (Griffin and Enos (1970)), Dutch disease problems and capacity constraints (Durbarry et al. (1998)), absorptive capacity constraints (Ghura et al. (1995)) and inappropriate technology as well as institutional de- struction (encourage inward-looking and/or corrupt government policies) from aid inflows (Lensink and White (1999) ).
An easy way to capture diminishing returns in econometric modeling is adding quadratic term of the variable of interest, which results in the parabolic shape for non-linear rela- tionship between two variables (Wooldridge (2013)). Adding a quadratic term is similar to including an interaction (as in BD with aid*policy), the coefficient of the quadratic term interpreted as the interaction effect of a variable on itself. In aid-growth studies, it captures the idea that the effect of additional units of aid decreases (just as diminishing returns) such that beyond some level, it would have negative effects on growth. Empirical results from Ghura et al. (1995), Durbarry et al. (1998) and Hansen and Tarp (2001) among others find evidence that when a quadratic term is included in the empirical spec- ification, the estimated model finds significant effects of aid, even without taking into account interaction with policy.
There is no conclusive theoretical basis on the choice between using policy selectivity through an interactive term or diminishing returns using a polynomial effect or indeed a combination of both in the same model, thus the preferred specification is a hypothesis that can be tested empirically and chosen at the researcher’s discretion. Hansen and Tarp (2000) argue that a complete model must include the following five terms: aid,
aid squared, policy, policy squared and the interaction term (aid policy)24 which make
a complete, second order, polynomial response space in the policy dependent aid growth relationship. Thus a more complete specification would look like:
24BD actually include a further variable; the interaction between aid squared and policy. Perhaps a fuller model would include six variables rather than the five included in Hansen and Tarp (2000).
gi(t) =α+ϑXi(t) +β1Ai(t) +β2Ai(t)2+β3Pi(t) +β4Pi(t)2
+β5Ai(t)Pi(t) +β6Ai(t)2Pi(t) +i(t) (3.4.1)
where all variables are as already defined, Pi(t) is a policy index and β denotes constant
parameters estimated. BD set β2 = β4 = 0 and in their preferred specification β6 = 0
while Hansen and Tarp (2000) set β6 = 0. When Hansen and Tarp (2000) tested the
model using the full specification (albeit excludingβ6Ai(t)2Pi(t)) and they find statistical
evidence to support diminishing returns i.e. β4 = β5 = 0 and β1 6= 0, β2 6= 0, β3 6= 0.
To assess empirically the effect of the choice between either the policy interaction term or a polynomial effect of aid, on the estimated impact of aid on growth, we estimate the empirical model expressed in equation 5 using our full sample. The results of this estimation are reported in table 3.4.1.
All regressions do not include influential observations (outliers). In all estimations, vari- ables that are functions of aid are modeled as endogenous regressors. The first three columns in the table give results for the full sample with all 81 countries, while the last three have results for sample with low income countries only. Equations 1 and 4 use the full model specification with all 6 variables in equation (3.4.1) above included; as the results reveal policy squared, aid-policy interaction and aid squared-policy interaction are all found to be statistically insignificant, in contrast to the findings of BD but in support of the findings of Hansen and Tarp (2001) and Dalgaard and Hansen (2001).
In equations 2 and 5 we omit the three statistically insignificant policy variables (and their interaction with aid) from regressions 1 and 4. It is evidently clear that omitting the three variables, aid-policy, aid square-policy and policy squared, does not affect the regression 1 and 4 results; both aid and aid squared remain statistically significant. Furthermore, the Wald test for joint exclusion of the three variables has p-values that are very high, thus we cannot reject the null that the omitted variables do not have significant effect on the growth model estimated.
Finally, in equations 3 and 6 we omit aid square and aid square-policy interaction term, we get contrasting results. The coefficient for aid becomes statistically insignificant while the aid policy interaction term is only weakly significant, being statistically significant only
Table 3.4.1: 2SLS regressions with different specifications using reconstructed dataset
Dependent variable: Annual real per capita GDP growth rate All developing countries Low income countries
1 2 3 4 5 6 Aid 1.9871* 1.2164** -0.3775 0.9624* 0.4342* -0.3793 (1.0825) (0.4853) (0.2442) (0.4403) (0.1553) (0.1455) Policy 0.5448*** 0.9532*** 0.7139*** 1.7888** 0.9512*** 0.9463*** (0.2105) (0.1057) (0.1304) (0.8198) (0.1307) (0.2342) Aid square -0.2774*** -0.1663** -0.2024** -0.1083** (0.0682) (0.0668) (0.0966) (0.0511) Policy square 0.0851 -0.045 (0.0524) (0.0928) Aidpolicy 0.6185 0.1393* -0.8714 -0.1022* (0.3903) (0.0825) (1.2905) (0.0649) Aidsq.policy -0.0914 -0.1255 (0.0673) (0.1942) Initial GDP -0.7011 -0.5838 -0.5314 -0.9419* -0.851 -0.8447 (0.4322) (0.3941) (0.3802) (0.5667) (0.5304) (0.5319) Ethnic fractionalization -0.8188 -0.6205 -0.4507 1.1581 0.6426 0.6625 (0.7542) (0.7280) (0.6677) (1.2068) (0.8689) (0.8382) Assassinations -0.3498** -0.3697** -0.3289** -0.5292 -0.6177 -0.6203 (0.1606) (0.1580) (0.1489) (0.4626) (0.3978) (0.3967) Ethnassass 0.467 0.5385* 0.4668 0.4846 0.4411 0.4453 (0.3035) (0.2975) (0.2862) (0.8339) (0.7834) (0.7822) ICRGE 0.1979 0.1815 0.3001*** 0.3128* 0.3551** 0.3592** (0.1231) (0.1244) (0.1004) (0.1669) (0.1488) (0.1447) M2 lagged 2.5188** 1.9602* 1.9254** -0.6269 0.115 0.1232 (0.9864) (1.0106) (0.9376) (1.8580) (1.5794) (1.6318) SSA -0.6414 -0.6766 -1.1309** -2.3020*** -2.0939*** -2.1127*** (0.7188) (0.7191) (0.5683) (0.7152) (0.6353) (0.6303) E.Asia 0.4979 0.2368 0.6804 0.2057 0.731 0.7594 (0.5357) (0.5482) (0.4889) (0.9381) (0.6385) (0.6384) Observations 397 397 397 221 221 221 R-squared 0.2723 0.2487 0.3389 0.2854 0.362 0.3636 No. of countries 81 81 81 48 48 48 AR F-test (p-value) 0.0005 0.0009 0.0008 0.11 0.121 0.231 KP Wald F-Stat 9.64 10.95 11.27 8.097 11.02 9.93
Wald test (p-values) 0.921 0.013 0.986 0..017
Hansen J (p-value) 0.104 0.117 0.083 0.414 0.222 0.229
Notes: The table presents instrumental variable growth regression results for estimation using the full sample covering the period from 1997 to 2013 over 81 countries, 48 of which are low income countries. Dependent variable is annual growth rate of per capita GDP, all regresions include time dummies for each period in the sample; Results reported in columns 1-3 are for sample with all developing countries while in columns 4-6 are results for sample with only low-income countries. Instruments used in all regressions are listed in table 1 in the main text. Robust standard errors in parentheses, *** p<0.01, ** p<0.05, * p<0.1
at 10% level, and the magnitude of the coefficient diminishes substantially. Moreover, the Wald test p-values imply strong inclination to reject the null that the omitted variables are not significant. This result too conforms to the findings of Dalgaard and Hansen (2001).
Additionally, note in the table that in all specifications that includes aid squared, the coefficient is not only significant but also that it is always negative, which also gives
evidence to the notion of diminishing returns with respect to levels of aid. It is also worth noting that in all regressions, the coefficient for policy is strongly significant at any conventional level of significance. Thus while there may be a heated debate in the literature on the rationale and significance of interacting aid with policy index, there is
no question as to the importance of good policies on growth25.