Policy, Aid and Growth: A Threshold
Hypothesis
Philip Denkabe
New York University, Department of Economics
269 Mercer Street, New York, NY 10003
This Draft: December 3rd, 2003
Abstract
This study examines the contribution of foreign aid to economic
growth in the context of macroeconomic policy.
Using certain macroeconomic indicators as policy variables, I construct a dynamic growth equation which is estimated by way of Generalized Method of Moments. In undertaking the estimation, attention is focused on country-specific effects and the non-linearity in the
contribution of aid to economic growth arising from the interaction
between aid and macroeconomic policy. I construct a simple growth
model in a bid to analyse the empirical results.
Findings suggest the existence of a threshold value of aid, defined
by macroeconomic policy, below which aid tends to have a positive
effect on economic growth and beyond which diminishing returns to
aid may generate a non-positive impact on growth. For two economies
characterized by different macroeconomic policies, similar aid inflows
will have different effects on economic growth. As compared to a relatively ’good’ policy environment, a relatively ’bad’ policy environment
experiences diminishing returns to aid relatively more quickly.This
could be attributed to the inability to effectively absorb aid.
1
1
Introduction
A major objective of foreign aid is to spur economic growth in the recipient
nation through various channels. Despite the high aid inflows to developing
economies and the numerous econometric studies, the various conclusions
about the relationship between foreign aid and economic growth are not
without controversy.
Over the years, the literature on the aid-growth link has evolved from
Harrod-Domar based, linear, cross section studies using single equation estimation techniques to the use of panel data studies inspired by new growth
theory with particular attention on nonlinearity. Early investigations of the
contribution of aid to growth have yielded contrasting results. It has been
argued that the ambiguity of these studies may be due in part to the poor
quality of data during those periods.
More recently, a new generation of aid-growth studies have emerged,
breaking novel ground in terms of data coverage and modelling of the aidgrowth link. Hadjicmichael et al (1995) using a sample of 41 countries for
the period 1986 - 1992 and including terms to capture nonlinearity in aid and
other policy variables, find that aid impacts positively on economic growth.
A much more sophisticated attempt to incorporate aid and policy variables
in investigating the aid-growth link comes from Dollar and Burnside (2000).
Using a model, that includes a variety of policy variables, they find that
though the ratio of aid to GDP does not significantly affect growth in LDCs,
aid interacted with policy produces a positive effect on growth. Hansen and
Tarp(1999) also establish a positive impact of aid on growth. Easterly and
Levine (2003) argues that the Burnside and Dollar outcome is not robust to
additional data. Updating the data, their study suggests that an ambiguity about the effectiveness of aid in a good policy environment. Dalgaard,
Hansen and Tarp(2002), using theoretical and empirical models, suggest that
aid can be effective in a ’bad’ policy environment. Guillaumont and Chauvet
(2001) also establish that in a ’bad’ policy environment larger amounts of
aid are required to ensure a beneficial impact on growth.
2
In this study, I seek to re-examine this aid-growth nexus in the context
of macroeconomic policy. In particular, by employing a dynamic panel data
estimation technique, I critically analyze, among others, the contribution
of foreign aid to economic growth and the role of macroeconomic policy in
augmenting this contribution. Drawing from recent modelling techniques in
the literature, I investigate this relationship with particular attention on the
consistency of our estimators.
In studying the aid-growth relationship, the exogeneity of some determinants of growth as well as the negligence of country specific effects can bring
the estimators into question. I undertake the analysis of the aid-growth link
using a dynamic growth equation which includes a lagged dependent variable, policy variable, foreign aid, the interaction between macroeconomic
policy and foreign aid as well as a quadratic term in aid. The interaction
and quadratic terms are meant to capture the non-linearity in the contribution of aid to growth. By classifying variables according to their level
of exogeneity, we employ instrumental variables in estimating our parameters. Overall, findings suggest a remarkable role for macroeconomic policy in
the effectiveness of aid, albeit not ruling out aid effectiveness without good
macroeconomic policy.
The paper is organized as follows: section 2 presents the empirical model
while section 3 and 4 respectively discuss variables and data sources. Section
5 presents the estimation and results. Section 6 presents a theoretical model.
Section 7 is the conclusion.
2
The Model
Consider the following growth equation
ln Yi,t − ln Yit−1 = θ ln Yi,t−1 + xit β + git γ + µi + λt +
it
(1)
where Yi,t is GDP per capita for country i in period t , xit is a 1 × W
vector of determinants of economic growth, which includes foreign aid, policy
3
variables, the interaction between aid and policy. The vector git is a 1 × P
vector of institutional and political factors that affect economic growth.
These factors include a measure of financial development, institutional quality, ethnic fractionalization and assassinations. The term µi is a permanent
but unobservable country-specific effect that captures the existence of other
determinants of an economy’s growth rate that are not already controlled
for by xit . It is time invariant and generally captures such cross sectional
heterogeneity as differences in technology between countries, it is an error
term such that it ∼ IID (0, σ 2 ).
It is worth noting that a less than zero coefficient on lagged output per
capita (θ < 0) will be consistent with the conditional convergence theory of
the neoclassical model. In this regard, variables in vector xit and µi will be
proxies for the long run level that the economy is converging to. However,
if θ = 0, there is no convergence and the other right handside variables will
measure differences in the steady state growth rate.
The growth equation in (1) can be expressed as
yi,t = αyi,t−1 + xit β + git γ + µi + λt +
(2)
i,t
where α = 1 + θ and yit = ln Yit . It can be observed that equation (2) is
a dynamic equation with a lagged dependent variable.
In the presence of any correlation between the right hand side variables
and the country specific effect (µi ), estimation methods such as Ordinary
Least squares will not be consistent. This is evident from the fact that
E(µi yi,t−1 ) = E [µi (αyi,t−2 + xit−1 β + git γ + µi + λt−1 +
i,t−1 )]
6= 0
Secondly, the determinants of growth in the vectors xit and git can be
classified according to whether they are strictly exogenous, predetermined or
endogenous. For a variable zit that belongs to the 1 × W vector x0it , zit is
said to be endogenous if it is correlated with it and earlier shocks but uncorrelated with it+1 and subsequent shocks. For example, a macroeconomic
shock to the growth rate of an economy could have a contemporaneous effect
4
on foreign aid inflows or the level of openness of a country, thus compromising the strict exogeneity of these variables. Alternatively, it is reasonable to
infer that a positive shock to economic growth in period t − 1 will result in
a higher level of openness or positively affect the budget surplus in period t.
Thus, the possibility of endogeneity together with the presence of country
specific effects (µi ) and its subsequent correlation with some of the explanatory variables results in a violation of the assumption of strict exogeneity
of the explanatory variables. Consequently, the inconsistency of estimation
methods such as Ordinary Least Squares cannot be overemphasized.
In this regard, it is appropriate to use an estimation procedure which
simultaneously addresses the issues of correlation and endogeneity. An application of Generalized Method of Moments(GMM) proposed by Arellano and
Bond(1991) is employed in this endeavor. This GMM estimator optimally
exploits all the linear restrictions implied by a dynamic panel data model.
As is common in the literature, one way of eliminating country specific
effects is by taking deviations with respect to individual country means1 .
Eventhough this eliminates the country specific effect, for panels where the
time dimension is small, the transformation results in a non-negligible correlation between the transformed lagged dependent variable and the transformed error term. Therefore, direct estimation of such a regression in the
context of dynamic panel data would lead to inconsistent estimators.
Consequently, following Arellano and Bond (1991), Holtz-Eakin, Newey,
and Rosen(1988), a first step towards obtaining a consistent estimator is
to eliminate the country-specific effects via first difference transformation of
1
Specifically, the mean values of yit , yit−1 , xit , git , µi and it across the t−1 observations
for each country i are obtained and the original observations are expressed as deviations
from these individual means. Oridinary Least Squares(OLS) is then used to estimate
these transformed equations. Since the mean of the time invariant effect µi is itself µi , the
individual effects are removed from the transformed equations.
5
equation (2)
yit − yit−1 = α (yit−1 − yit−2 ) + (xit − xit−1 ) β +
(git − git−1 ) γ +
it
−
(3)
it−1
However, eliminating the country specific effect introduces a correlation between the lagged dependent variable and the new error term. From
(3) ,because of the correlation between yit−1 and it−1 , it can be observed that
E (yit−1 − yit−2 ) (
it
−
it−1 )
6= 0
(4)
In addition, as discussed above, the contemporaneous effects of growth
shocks on the determinants of growth will result in the presence of endogeneity. This arises mainly due to the correlation between xit and it where
E (xit − xit−1 ) (
it
−
it−1 )
6= 0
(5)
Due to the presence of correlation and endogeneity, a preferred approach
for estimating equation (3) will be to use instrumental variables. An appropriate instrument for (yit−1 − yit−2 ) is yit−2 .This is because (yit−1 − yit−2 ) is
correlated with yit−2 and
E[yit−2 (
it
−
it−1 )]
= 0.
In this study, in order to address the issue of endogeneity, I impose the
identifying restriction that the variables that constitute the vector xit are
predetermined where predeterminacy refers to the case that elements of xit
could be correlated with i,t−1 and earlier shocks but uncorrelated with it .In
particular, I assume that shocks to economic growth in period t − 1 could affect foreign aid, openness, fiscal balance or their interaction terms in period t.
This could arise because of policy implementation lags. By this assumption I
rule out a contemporaneous effect of growth shocks on these variables. Consequently, by the assumption of predeterminacy, an appropriate instrument
for (xit − xit−1 ) is xt−1 , since
E[xit−1 (
it
−
6
it−1 )]
=0
Note that git is assumed to contain only strictly exogenous covariates and
therefore 4git will serve as its own instrument. The set of instruments can be
expressed as M x T matrix, qi where T denotes the number of time periods
and M is the number of variables. Let ∆ i be the vector of differenced
0
errors. Thus qi ∆ i (δ) is a set of M functions satisfying the orthogonality
0
conditions E(qi ∆ i ) = 0 from which a consistent estimate of parameters can
be obtained2 .
However, before proceeding with the generalized method of moments,
the following identifying assumption is necessary. We assume that there is
no second order serial correlation in the first differences of the error term,
E (∆ it ∆ it−2 ) = 0. The consistency of the resulting Generalized Method of
Moments(GMM) estimator requires that this condition be satisfied3 . Given
the construction of the instruments as lagged variables, the presence of second order serial correlation will render such instruments invalid. Since the
consistency of the results critically depend on the above mentioned identifying assumption , we make use of various specification tests to ascertain the
veracity of the assumption and therefore the consistency of the resulting
estimators. One such test is the Sargan test of overidentifying restrictions.
This test is based on the sample analog of the moment conditions used in
2
Arellano & Bond(1991) suggest two types of estimators: the one-step estimator and
the two-step estimator. In the one-step estimator, it is assumed that it are indepen¡ ¢
dently identically distributed with a constant variance σ 2 while in the latter case, the
assumption of homoscedasticity is relaxed and consistent estimates of the first differenced residuals, ∆ i , are obtained from a preliminary consistent estimator. The ∆ i so
obtained are used to construct a consistent estimate of the variance-covariance matrix of
the moment conditions.
In this study, I use the one-step estimator. Simulation studies suggest very modest
efficiency gains from using the two-step version even in the presence of considerable heteroskedasticity. Also, the two-step weight matrix ( WN2 ) depends on estimated parameters
and this makes the usual asymptotic distribution approximations less reliable. Furthermore, simulation studies have shown that the asymptotic standard errors tend to be much
too small, or the asymptotic t-ratios much too big, for the two-step estimator, in sample
sizes where the equivalent tests based on the one-step estimator are quite accurate.
3
See Arellano & Bond (1991)
7
the estimation process and evaluates the validity of the set of instruments
and therefore determines the validity of the assumptions of predeterminacy,
endogeneity and exogeneity. .
3
The Variables
The set of explanatory variables that constitute the vector xit include; foreign
aid as a percentage of GDP, policy index, the interaction effects between
policy and aid and a quadratic term in aid.
The policy variables are openness, inflation and fiscal balance. Openness,
a measure of international trade, is believed to affect growth through several channels, such as access to technology from abroad, greater access to
a variety of inputs for production and access to broader markets that raise
the efficiency of domestic production through increased specialization. Various measures of openness have been proposed with no resulting single best
measure4 . Frequently used measures include the dummy variable definition
by Sachs and Warner (1995), ratio of total trade to GDP, Terms of trade
(TOT). In this study, I use the Sachs and Warner(1995) definition as the
measure of openness.Use of the other variables does not affect the results in
any significant way.
As suggested by Easterly and Rebelo (1993) and following Dollar and
Burnside (2000), budget surplus (Fiscal Balance) as a % of GDP is included
as a measure of fiscal policy. The budget surplus is believed to be an indicator
of the stabilizing role of government. In line with Fischer (1993) inflation is
taken as a measure of monetary policy.
The interaction effect between foreign aid and macroeconomic policy is
captured by the term aid/GDP ×policy. The policy index used in this study
is an updated version of that constructed by Burnside and Dollar(2000). This
index is constructed as a weighted average of budget balance, inflation and
4
For example, see Harrison (1996)
8
openness5 . I also include a quadratic term in aid to capture the possible presence of diminishing returns to aid. The interaction terms are meant to capture the non-linearity in the contribution of foreign aid to economic growth.
Theoretically, interaction terms and quadratic terms can be obtained from a
second order Taylor approximation of a standard Solow growth model with
convergence effects. Hansen and Tarp (2000) also show that by specifying
policy as a function of aid, one can obtain the interaction effects and the
quadratic term6 . All of the above mentioned variables( foreign aid, interaction effect, quadratic term) are assumed to be predetermined for period
t. In particular, I assume that a shock to economic growth in period t − 1
can affect any of the above mentioned policy variables and their interaction
effects in period t. As already discussed, a shock to an economy’s growth
rate in period t − 1 can affect the level of openness in period t and therefore the policy index, or the aid inflows and the interaction between policy
and aid inflows in period t. In this regard, I consider all these variables as
predetermined and not strictly exogenous.
As discussed earlier, the 1 × P vector git consists of institutional and
political factors that might affect growth. I consider the measure of financial development as predetermined while the other institutional variables are
considered to be strictly exogenous and are not affected by shocks to the
economy’s growth rate. These variables are ethnic fractionalization and assassinations, which is a measure of civil unrest and the interaction between
assassinations and ethnic fractionalization.
4
Data
The data used in estimating the model is basically the same as that used by
Dollar and Burnside (2000) with the relevant variables updated.
This is panel data for 56 countries. Aside from making it possible for one
5
6
See Burnside and Dollar (2000)
See Hansen & Tarp (2000)
9
to exploit a much larger sample or to pool more panels, the use of unbalanced
panels may lessen the impact of self selection in the sample. The time periods
are four year averages from 1970-2000. The countries consist of 21 SubSaharan African Countries, 21 Latin American Countries, 6 from the middle
east and north Africa, 5 from East Asia and 3 from South Asia. The choice of
countries reflects economies which are remarkable aid recipients. As noted in
most empirical work, for robust results, it is essential to have good coverage
of poor countries. The dependent variable in this study is the average growth
rate of real GDP per capita.
5
Estimation and Results
The basic specification as in equation (1) is estimated by OLS and the results
are as shown in Table 1. The first column is without interaction terms whilst
the other two columns include interaction effects.
In all of the three different formulations, the coefficient on initial GDP
is negative, and statistically significant, which, according to the classical
theory suggest some convergence. Institutional quality, Sub-Saharan African
Dummy and the East Asian dummy are all statistically significant. Aid/GDP
has a negative and statistically significant coefficient in all the formulations.
As regards interaction effects, the first order interaction between aid/GDP
and policy does not have a statistically significant impact on growth.
Table 2 illustrates the results of the preferred method of estimation (GMM)
as discussed above. However for table 2, I assume that the right handside
variables involving aid, policy index and interaction effect are strictly exogenous, which is the assumption underlying the use of OLS. Thus, the results
from Table 2 help evaluate the appropriateness of the assumption that all
the right handside variables are strictly exogenous. This is achieved by using the Sargan Test which tests the null hypothesis that the overidentifying
restrictions (exogeneity of right handside variables) are valid.
From the results of the Sargan test, at the 5 percent level of significance,
10
the null hypothesis that all right hand side variables are strictly exogenous
is rejected. These results suggest the possibility of different assumptions
characterizing the right hand side variables.
Taking cue from the above, table 3 presents results, once again, by using
the preferred method of estimation in which I now assume that aid, policy
variables and the interaction effect between aid and policy are predetermined
for period t, while the institutional variables are considered to be strictly
exogenous.
In table 3, it can be observed that the Sargan test gives p-values which
are much bigger than those obtained in table 2 when we assumed strict
exogeneity of all right handside variables. The increase in the p-values of
the Sargan test indicate that treating foreign aid, policy and the interaction
effect as predetermined makes it more difficult to reject the null hypothesis
that the over-identifying restrictions are valid. This increase in the Sargan
statistic provides some evidence that these variables are better modeled as
predetermined variables. It can also be observed that the p-values in the
test for second order serial correlation results in the acceptance of the null
hypothesis that there is no second order serial correlation in the differenced
residuals suggesting consistency of our estimators.
The results in table 3 also indicate that aid and aid interacted with policy
all have positive and statistically significant coefficients suggesting a positive
impact on economic growth. A positive coefficient on lagged growth is in conformity with the neoclassical theory of convergence as observed earlier. The
quadratic term in (Aid/GDP )2 has a negative and statistically significant
coefficient.
The favored specification in table 3 is column (3) which includes the first
order interaction and the quadratic term. Figs 1 and 2 present a simulation of
the preferred estimation which gives the effect of changes in aid on economic
growth with different policy indices. It can be observed from both charts
that the marginal impact of aid on economic growth is generally higher in
a good policy environment. It can be established that there exist a certain
11
threshold value of aid (aid∗ ), which is a function of macroeconomic policy,
such that below this value, changes in aid tend to have a positive effect on
economic growth and above which diminishing returns to aid may generate
a non positive effect on economic growth. That is,
aid∗ = f (policy)
0
where f (policy) > 0. Thus the better the policy, the higher this threshold value of aid and the higher the likelihood of observing a positive impact
of aid on growth. This suggest that two economies characterized by different macroeconomic policies and consequently, different threshold values
of aid(aid∗ ), will experience a dissimilar impact of aid on growth given the
same aid inflows. This result is in conformity with a number of earlier studies, as discussed in the introduction, that have established that aid is more
effective in a ’good’ policy environment and could be effective in a bad policy environment. However, in this study, using the threshold hypothesis, it
is established that diminishing returns to aid sets in relatively more quickly
in a ’bad’ policy environment and there is no guarantee that more aid can
actually change policy.
6
A Theoretical Model
In this section I consider a theoretical model in line with the results of the
empirical model obtained above. The model consists of households, producers
and a government sector.
6.1
Households
The representative household’s instantaneous utility function is given as
u(c) =
c(1−θ) − 1
(1 − θ)
12
where θ > 0, the elasticity of marginal utility is given as −θ.and the
elasticity of substitution is σ = 1θ .
Consider foreign aid inflows which is normalized to have value one. A
proportion F is used by government in the production of relevant services
for development. A fraction 1 − F is transferred to households. Households
hold assets a with a rate of return r. It is assumed that the transfer 1 − F
is used to complement their asset holdings. Consequently, the flow budget
constraint is given as
ȧ = a(1 − F )r + w − c
(6)
The household’s optimization problem is to choose the path of c to maximize overall utility given as
U=
Z
∞
u[c(t)]e−ρt dt
0
subject to the flow budget constraint (6) .
The Hamiltonian can be given as
J = u(c)e−ρt + v[a(1 − F )r + w − c]
The first order conditions result in
ċ
θ = r(1 − F ) − ρ
c
7
(7)
Government
Government produces goods using a fraction F of foreign aid and output,
Y . In particular, suppose that government provides public services(facilitate
the accumulation of human capital, provide infrastructure, maintain an effective system of law). We assume government undertakes these activities
by purchasing part of private output and together with foreign aid as a major complement, creates an enabling environment for producers. Proceeding
13
from the above, G can be specified as
G = F βY
(8)
where β is measure of the share of aid in the production of government goods
and services (G).
8
Firms
Firms produce goods and services using labor and capital as inputs. I also
assume that the flow of government services, G ,augments technology. The
production function is specified as
Y = AL1−α
kiα G1−α
i
(9)
Using the production function (9) and government services, (8) I obtain
¢1
¡
G = F β LA α k
(10)
Government services is a function of capital and labor as well as foreign
aid.
In the spirit of the public-goods model of productive government services,
I formulate a production in which each firm exhibits constant returns to scale
in the private inputs, Li and ki . For fixed G, the economy faces diminishing
returns to the accumulation of aggregate capital k. If G rises along with k ,
then diminishing returns will not arise. The form of the production function
implies that public services are complementary with the private inputs in
the sense that an increase in G raises the marginal products of L and k. The
firms profits can be given as
π = AL1−α
kiα G1−α − w − rki
i
Profit maximization results in the following first order conditions
kiα G1−α
r = αAL1−α
i
14
(11)
Substituting (10) into (11), the rental rate can be given as
¢ 1−α
¡
(1−α)
1−α
r = αAL1−α F β LA α = αAL1−α F β α LA α
(12)
Using (12) in (7) the growth rate can be expressed as
(1−α)
(1−α)
1−α
1−α
ċ
θ = αAL1−α F β α LA α − αAL1−α F β α +1 LA α − ρ
(13)
c
From (13) , it can be established that there exist a certain threshold value
of aid, F ∗ such that aid tends to have a positive and nonpositive effect on
growth. This is given as
β (1−α)
∗
α
F =
1 + β (1−α)
α
As discussed above, a proxy for macroeconomic policy is the contribution
of government services to total production. The higher the augmenting effect
of government policy given by 1 − α, the better the macroeconomic policy.
This effect plays a role in determining F ∗ as shown above.
9
Conclusion
In this study, I investigate the impact of foreign aid on economic growth visa-vis macroeconomic policy. The measure of economic policy is a weighted
average of openness, inflation and fiscal balance. Using my preferred method
of estimation(Generalized Method of Moments), I find a remarkable interaction between foreign aid macroeconomic policy. Furthermore, inference from
the results obtained suggest the existence of a threshold value of aid such that
below this value aid tends to have a positive impact on growth but beyond,
aid may have a non positive effect on growth due to diminishing returns to
aid. This diminishing returns could be due to the inability of policy to facilitate an effective absorption and utilization of aid. This threshold value is a
function of macroeconomic policy. Therefore, the better the policy the higher
the likelihood that aid will affect growth positively. For two economies with
different macroeconomic policies, similar aid inflows will have different effects
15
on economic growth. In a ’bad’ policy environment, diminishing returns sets
in relatively more quickly than in a ’good’ policy environment.
16
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19
Table 1
Method of Estimation: Ordinary Least Squares
Independent Variable: Growth rate of GDP per capita
1
-0.870∗
(0.420)
Assasinations
-0.454
(0.324)
Ethnic Fractionalization
-0.005
(0.008)
Assasination x Ethnic Fractionalization
0.007
(0.006)
Institutional Quality
0.678∗∗
(0.191)
M2/GDP(lagged)
-0.007
(0.016)
Sub-Saharan African Dummy
-1.888∗∗
(0.716)
East Asia Dummy
0.944∗∗
(0.387)
Policy
1.005∗∗
(0.175)
Aid/GDP
-0.078∗∗
(0.012)
Aid/GDP x Policy
Initial GDP per capita
(Aid/GDP)2
R2
No. of Observations
Standard Errors in Parenthesis
∗∗
Significant at the 5 percent level20
∗
Significant at the 10 percent level
2
3
-0.882∗
(0.423)
-0.451
(0.325)
-0.005
(0.008)
0.007
(0.006)
0.678∗∗
(0.192)
-0.007
(0.016)
-1.888∗∗
(0.718)
0.987∗∗
(0.318)
0.975∗∗
(0.231)
-0.096∗∗
(0.033)
0.012
(0.061)
-0.852∗∗
(0.425)
-0.452
(0.325)
-0.005
(0.008)
0.007
(0.006)
0.696∗∗
(0.193)
-0.006
(0.016)
-2.000∗∗
(0.738)
1.145∗∗
(0.339)
0.867∗∗
(0.263)
-0.079∗∗
(0.035)
0.121
(0.140)
—0.011
(0.012)
0.286
263
0.283
263
0.283
263
Table 2
Method of Estimation: Generalized Method of Moments (GMM)
Dependent Variable: Growth rate of GDP per capita
Independent Variables: Assumed to be Strictly Exogenous
1
Growth rate of GDP per Capitat−1
2
0.819** 0.750**
(0.138) (0.133)
Assasinations x Ethnic Fractionalization 0.008
0.008
(0.008) (0.008)
M2/GDP
0.001
0.001
(0.002) (0.002)
Policy
0.012
-0.002
(0.012) (0.014)
Aid/GDP
0.019* 0.033**
(0.010) (0.011)
Aid/GDP x Policy
0.007*
(0.003)
2
(Aid/GDP)
-
3
0.770*
(0.135)
0.008
(0.008)
0.001
(0.002)
-0.010
(0.018)
0.030**
(0.011)
0.002
(0.010)
-0.001
(0.0001)
Test of Overidentifying Restrictions
Sargan Test
26.8
28.64
28.73
[0.021]
[0.01]
[0.01]
Test of the Joint Significance of the Independent variables
Wald Test
60.78
66.76
66.54
Test for Second Order Serial Correlation
Z
-1.38
-1.54
-1.68
[0.17]
[0.13]
[0.11]
No. of Observations
209
209
209
Standard Errors are in Parenthesis while p-values are in brackets
∗∗
Significant at the 5 percent level
∗
Significant at the 10 percent level
21
Table 3
Method of Estimation: Generalized Method of Moments (GMM)
Dependent Variable: Growth rate of GDP per capita
1
2
3
Growth rate of GDP per Capitat−1
0.883** 0.742**
(0.124) (0.094)
Assasinations x Ethnic Fractionalization
0.000
0.000
(0.0001) (0.0001)
M2/GDP
0.0003
0.0003
(0.001) (0.001)
Policy
0.029*
0.022*
(0.011) (0.010)
Aid/GDP
0.004
0.028*
(0.019) (0.015)
Aid/GDP x Policy
0.007
(0.005)
(Aid/GDP)2
-
0.750**
(0.090)
0.000
(0.0001)
0.0003
(0.001)
0.030*
(0.030)
0.025*
(0.011)
0.010∗∗
(0.002)
-0.001*
(0.0005)
Test of Overidentifying Restrictions
Sargan Test
42.5
57.29
58.9
[0.430]
[0.420]
[0.820]
Test of the Joint Significance of the Independent variables
Wald Test
101.16
121.9
123.48
Test for Second Order Serial Correlation
Z
-1.61
-1.66
-1.88
[0.10]
[0.12]
[0.11]
No. of Observations
209
209
209
Standard Errors are in Parenthesis while p-values are in brackets
∗∗
Significant at the 5 percent level
∗
Significant at the 10 percent level
22
S im ulation of P referred E s tim ation
0.7
0.6
P olic y Index = 2.5
Growth Rate(%)
0.5
0.4
0.3
P olic y Index = 0.5
0.2
0.1
0
0
5
10
15
A id/G DP (% )
20
25
30
Figure 1:
Simulation of Preferred Estimation
0.6
Policy Index =2
0.4
Growth Rate(%)
0.2
0
-0.2
Policy Index =-1
-0.4
-0.6
-0.8
0
5
10
15
Aid/GDP(%)
Figure 2:
23
20
25
30