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Foreign aid, taxes and public investment: A further comment
Journal of Development Economics Vol. 45 (1994) 155-163
ELSEVIER
JOURNAL OF Development ECONOMICS
Foreign aid, taxes and public investment: A further comment Howard White * Institute
ofSocial Studies, PO Box 29776, 2502 LT Den Haag, The Netherlands Received Scptembcr
1992, final version received May 1993
Abstract The paper in this journal by Gang and Khan (1991) employed Heller’s (1975) fiscal response model to demonstrate that aid to India has all been used to finance government investment. This conclusion is shown to be a misinterpretation of the model’s results which actually suggest that aid has had no impact on government investment at all. However, the reported parameters are determined by the estimation procedure adopted by Gang and Khan and not by the Indian government’s fiscal behaviour. Kqwords:
Foreign aid; Taxes; Public investment
JEL classification:
C51, E6
1. Introduction In their paper in this journal, Gang and Khan (1991) presented empirical estimates of the model, due to Heller (1975), ’ of the relationship between aid inflows and recipient government fiscal behaviour for the case of India. This comment discusses a number of theoretical and methodological short-comings in their analysis.
* The author would like to thank Neal Forster, Mark McGillivray and two anonymous referees for comments on an earlier version of this paper. ’ I have elsewhere (White, 1992), labelled this model the ‘fiscal response model’. Other papers adopting the same approach include Khan and Hoshino (19921, Forster (1992) and McGillivray and Papadopoulos (1992). 0304.3878/94/$07.00 0 1994 Elsevier Science B.V. All rights reserved SSDI 0304-3878(94)00032-8
156
H. White/Journal
ofDevelopment Economics 45 (1994) 155-163
First, as shown in Section 2, the model is an incorrect statement of the fungibility problem: the budget constraints over-restrict recipient budgetary behaviour. Section 3 shows that the procedure used to determine the series of target variables drives the results of the whole analysis. There are also problems in the interpretation of the results - Gang and Khan look only at partial results, ignoring reduced form equations and suppressing the model’s implicit dynamic element. Section 4 concludes that, on account of the problems discussed here, the results reported by Gang and Khan tell us nothing about foreign aid, taxes and public investment and presents a strategy for further research.
2. Model specification The Heller model supposes that recipient governments maximise a loss function comprising five choice variables subject to two budget constraints. The choice variables are: government investment (I,), government expenditure on socio-economic (or developmental) and other civil (or non-developmental) purposes (G, and G, respectively), taxation (T) and borrowing (B). Denoting a target variable by an asterisk (* ), the objective function used by Heller and adopted by Gang and Khan is:
-
Q,(T_
T*)
-
Z(T-
T*)* -
‘Y9(B -B*)
-
+-B*)2. (1)
Binh and McGillivray faulted the specification given in Eq. (1) on the grounds that the model is not optimised when the target values of the choice variables are achieved, so that the targets may not truly be considered targets. To avoid this problem Binh and McGillivray suggested the specification: 2
’ This specification had already been used by Mosley et al. (1987) in their application of the fiscal response model. But these authors did not explain their reascms for preferring this functional form.
H. White/Journal
ofDevelopment
Economics 45 (1994) 155-163
1.57
Table 1 Model simulation Assumptions:
parameters,
Utility function parameters
% a1 a2 a3 a4 as
targets and aid ,tlows Target variables and aid inflows
Budget constraint parameters 0.00 0.20 0.20 0.20 0.20 0.20
Pl P2
P3
4 GS CC T B lJ
1.08 -0.79 - 0.03
G G,* G,* T* B* ‘% Al
100 100 200 2.50 0 100 50
153.6 66.6 166.6 290.4 -53.6 - 962.1
from which it is clear that utility is maximised (to aO> when the targets are satisfied. The loss function given by either Eq. (1) or (2) is then maximised subject to budget constraints: I,=B+(~-p,)T+(l-p,)A,+(l-P,)A,, G, + G, = plT+
p*A, + psA,>
(3) (4)
where A, and A, are grant aid and loans respectively. The rationale for the separate budget constraints is that governments will not finance recurrent expenditure out of borrowing. This rationale notwithstanding, it is odd to write the budget constraint in a way which pre-determines the allocation of the income terms in given proportions. Such allocation is usually the outcome of the utility maximization problem. We may see how writing the budget constraint as Eqs. (3) and (4) over-restricts government budgetary behaviour by considering the following simulation. Table 1 shows the values of the ps obtained by Gang and Khan and a hypothetical set of (YSwhich give equal weight to each target. A hypothetical set of policy targets is then given exogenously. The aid inflows are also exogenous to the model, and have been selected here to ensure that the government’s targets can all be met. Using Eq. (2) as the utility function, utility will be maximised to zero by each endogenous variable being equal to its target level. To solve the model the seven first-order conditions derived from the Lagrangean given by combination of Eqs (2), (3) and (4) (one for each of the five endogenous variables and the two Lagrangean multipliers) were obtained. The
158
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Economics 45 (1994) 155-163
resulting simultaneous system was solved on spreadsheet, giving the solution values shown in Table 1. The level of utility was then calculated from Eq. (2). Even though the maximum utility (of (~a, which is set equal to zero) is attainable given the amount of aid received, the model does not find this solution. It is intuitively obvious that the solution to the problem being set is for the choice variables to be equal to their targets if the value of the exogenous variables allows such an outcome: this is true regardless of the value of the model’s parameters (e.g. the (YSand ps). The failure of the model to find the intuitively obvious result in the case reported here is indicative of a problem in model specification, since it does not find the correct solution to this problem. The problem in the model’s structure is the restriction imposed by the ps. Utility would only equal zero if the ps reflected the values required to allocate spending optimally in the scenario given here - but the ps are model parameters, not variables to be determined in the solution. On account of this problem we may wish to use instead the single budget constraint: Z,+G,+G,=T+B+A,+A,.
(5)
It is shown in White (1993) that the fiscal response model will produce the result of fungibility when the utility function is combined with this budget constraint. That is aid inflows do not fully fund expenditure increases, but are partly used to decrease taxes and borrowing - which is what the model is intended to demonstrate - even when the budget constraint is written as in Eq. (5). However, the budget constraint in Eq. (5) is also problematic since different types of aid are analytically equivalent, which will only be the case where all aid is fully fungible. Aid will not be fully fungible if the target level for a category of expenditure is less than the aid tied to that use since actual expenditure on a category must be at least equal to the aid inflow tied to that purpose - that is the budget constraint should be kinked. ’ Further work, which is beyond the scope of this comment, is therefore required on theoretical modelling of fungibility.
3. Estimation
and interpretation
of results
Gang and Khan solve the model algebraically
to obtain the structural equations:
z,=~,+(~-P~)Z~*+P~{(~-P,)T+(~-P~)A~+(~-P~)AI}~
(6)
G,=p,-(l-Pz)G,*+P,G:‘+-p,(l-p,)T+p,(l-p,)A, - /+(I
- &)A,,
3 For a more formal demonstration
(7)
of this point see White (1992).
H. White/Journal
G,=
of Development
Economics 45 (1994) 155-163
-P1+(1-P2)Gc*-P2G,*+~1P2T+~2P2Ag+P3P2A,~
T= & +
~1
159
(8)
P,(G,*- GJ + PST*
+ P,(l - P,){l, - (1 - P2)Ag- Cl- P3PJ~
(9)
To estimate the parameters of Eqs. (6) to (9) it is first necessary to obtain values for the target variables. To do this the targets are defined as follows:
I;[ = Yl
+
Y*yr- 1 + Y&v
(10)
G:,
+
Y~ENR, + Y,Y + rk
(11)
=
~4
Gc*,i= yx + y&c,,T,* =
710
B,? =O,
+
Y,lY,
12 +
Y12Mt-17
(12) (13)
(14)
where Y is GDP and Y growth of GDP, Zr private investment, ENR primary school enrolments and M imports. The parameters for the target equations (10) to (13) are obtained by OLS using the actual values of the variables Za etc. as the regressand. The fitted values from these regressions are then used as the target values. There are two problems with this approach. First, there is no guarantee that the targets so produced will be consistent with the budget constraints - indeed, they almost certainly shall not. A better approach may be to model targets for expenditure and taxes, and then model target borrowing as that required to fill the gap once expected aid flows are taken into account. 4 The second problem is more serious. Suppose that, for example, Za is very closely related to the variables selected to determine the target level. Suppose in fact that the R2 from this regression is 1. Then I,* is Zg! When we come to estimate Eq. (6), which involves regressing Z, on I,*, we will be regressing Z, on itself - the coefficient on I,* will of course be unity, and all the other coefficients insignificant. In practice the R2 will not be 1, but if it is high then the problem will still be present. If the R2 is low it is difficult to see how the fitted values calculated using the estimated coefficients may be meaningfully interpreted as values of the targets. The fit will be poor either because the wrong variables have been included in the target equation, or because the outturn was far removed from
4 Whilst the approach suggested here is intuitively appealing it may well render the model inestimable. If actual aid flows are close to expected then there will be extreme multicollinearity when attempting to estimate reduced form equations (as is required for the 3SLS approach used in the literature): if expected aid flows equal actual then there will be perfect multicollinearity. It may therefore not be possible to estimate the reduced form since the matrix of regressors may be singular or near singular.
160
ofDevelopment Economics 45 (1994) 155-163
H. White/Journal
Table 2 Gang and Khan’s parameter
estimates
Parameter
Estimate
t-statistic
P1 PZ P3 ;:
1.08 - 0.79 - 0.03 - 125.57 0.72
32.26 - 1.53 -0.07 - 12.52 0.05
P.? P4 Ps ;:
2162.67 - 0.43 0.98 214.53 -2.17
0.35 - 1.80 15.24 - 0.24 0.79
0.00
0.04
Pa Source:
Gang and Khan (1991: Table 1).
the target. In the latter case the coefficients will not be those used in the formation of targets. Gang and Khan’s results are repeated in Table 2. 5 Consider, for example, the parameters for the tax equation. If the argument of the preceding paragraph is correct we would expect & to be unity and &, p4 and & to all be insignificant. This is indeed the case. For the estimate of Eq. (6) we expect & to be zero again this is the case. The other two equations are more complicated. From Eq. (7) we may expect & to have a value of one - but from Eq. (8) we expect a value of zero! Since the coefficient cannot be both zero and one, it falls between the two. ’ It therefore appears that Gang and Khan’s results are derived from the way in which the target series are estimated: as such the results can tell us nothing about the Indian government’s fiscal response to aid inflows. But even if we ignore the above-mentioned problem then we may still argue that Gang and Khan give a misleading interpretation of their results for two reasons: (i) failure to report reduced form coefficients; and (ii) suppression of the model’s implicit dynamics. I discuss each of these in turn. Gang and Khan write that foreign aid does not have any statistically significant effect on government consumption (p. 363). This conclusion is based on the result that the estimates for p2 and p3 are insignificantly different from zero, and so do not enter the budget constraint for government consumption. By the same reasoning, we would suppose that all aid is used to increase government investment. Using Gang and Khan’s point estimates, this interpretation is summarised in the
‘These are their results when aid is divided into grants and loans. The same problem may be observed in their results (not shown here) for the division of aid into bi- and multi-lateral. ’ A problem not pursued in this comment is the failure of the authors (or any other studies in this literature) to test the cross-equation restrictions imposed on the data.
H. White/Journal
of Development Economics
45 (1994) 155-163
161
Table 3 Impact of aid from Gang and Khan’s results Budget constraints Al
A, ‘s Gs GC T B Source;
Structural
179 _ -79 _ _
A,
‘%
103 _ -3 _
Reduced forms
equations
Al
A,
0
0
0
-22 -57 -31 - 148
-1 -2 - 18 -85
-49 - 127 -90 - 186
0 -8 -25 -30 - 104
Derived from Gang and Khan (1991: Table 1).
first two columns of Table 3. An increase in loans of 100 units, for example, causes an increase in government investment of 103 units and a drop in total government consumption of 3 units. But it is rather odd to look at the coefficients of the budget constraint. For these results do not imply that Z, will increase by 103 units if A, increases by 100 units: for the results to mean this would require B and T to be constant in the face of the increased aid. But the whole point of the model is that B and T are not constant indeed, fungibility suggests that some aid will be used to reduce these domestic revenue sources. It is interesting to turn to the structural equations and see what they suggest about aid’s impact. For example, from Eq. (6) we see that an increase in A, leads to an increase of 1, of &(l - p3> - this is zero. Contrary to Gang and Khan’s argument, the structural equations suggest that aid has no impact on government investment. The calculated coefficients for the structural equations are summarised for each variable in the middle column of Table 3. ’ But neither do the structural equations tell the full story since they also contain endogenous variables - for example Eq. (6) contains the endogenous variable T. In order to analyse the total impact of aid on the different categories of government expenditure and revenue we must either derive the reduced forms or otherwise obtain solution values for the system of structural equations. For illustrative purposes I ran spreadsheet-based model simulations using Gang and Khan’s parameter values for the /?s and ps and a hypothetical set of exogenous variables (reported in the appendix) to examine the impact on the various categories of expenditure of an increase in A, and A, of 100 units. The results of these simulations are shown in the final two columns of Table 3. The results of these simulations are rather a stark contrast to the conclusions drawn by Gang and Khan. An increase in grant aid reduces borrowing by nearly twice the value of the increase in aid and taxes by nearly the amount of the aid that is the reduction in the recipient’s own revenue raising efforts sets off the new
‘The change in borrowing constraint, Eq. (3).
is calculated
by taking
total differentials
of the investment
budget
162
H White/Journal
ofDevelopment Economics 45 (1994) 155-163
aid monies more than two and one half fold. The result is that higher aid must lead to a reduction in total expenditures. This reduction falls entirely on government consumption. Neither type of aid has any impact at all on government investment. These reduced form results are still not the whole story since the model contains an implicit dynamic element which has been ignored in the discussion thus far. The target for G, depends on the lagged value of that variable. A one-off increase in aid will cause a drop in G, and therefore a change in the target value, G,*, in the subsequent period. The change in G,* will affect all the endogenous variables in the following period (and, through the new G,, in the period after that etc.). Since the target equations are not reported by Gang and Khan, it is not possible to calculate the magnitude of these dynamic effects. But such effects have been analysed in Forster’s (1992) application of a version of the fiscal response model to Papua New Guinea, and he finds that they can be considerable - about one third of the adverse impact of aid on taxation is, in the long run, removed. Meanwhile, the beneficial impact of aid on government investment is substantially reinforced. Even of the feedback effect through the target variables were incorporated, analysis based on this model would remain a partial one since it contains no economic feedback mechanisms. For example, two of the target equations include income and/or income growth. It is not realistic to suppose that higher aid inflows will leave income unaffected. White (1993) simulates a simple version of the model incorporating feedback through the targets equations from aid-induced increases in income. The results show that such effects can offset the reduction in taxes, even in the period of the inflow. Other economic relationships that might be added are an aid-augmented import function (see Moran (1989)) and a crowding in/out i.e. a relationship between aid (or government investment) and private investment (see Mosley (1987) and White and McGillivray (1992)). 4. Conclusions Gang and Khan claimed that their results showed that the Indian government has channelled all aid into investment. This is a misinterpretation of their own results - these results actually show aid to have no effect on investment at all. But their estimates are shown here to be a statistical artifact consequent upon the method of deriving the target variable series. The discussion has highlighted a number of additional problems that help highlight priorities in further research. These are: (i) development of a theoretical model that accurately captures the relationship between fungibility and tying; (ii) satisfactory procedures for estimating target variables; (iii) recognition of the implicit dynamic effects that will operate through the target equations; and (iv) incorporation of feedback through aid’s impact on income, imports and crowding in/ out.
H. White /Journal
of Development Economics 45 (1994) 155-163
163
Appendix Values used for reduced form model simulations Parameters: results reported by Gang and Khan (shown in Table 2 in text above). Target variables: I,* = 15,000; G,* = 15,000; G,* = 20,000; T* = 25,000 Aid inflows Base case: A, = 1,000; A, = 3,000 Two simulations were run - each increasing A, and A, by 100 (with the other remaining constant). The figures shown in Table 3 are the change in each of the endogenous variables between the cases of higher aid and the base case.
References Binh, T. and M. McGillivray, 1993, Foreign aid, taxes and public investment: A comment, Journal of Development Economics 41, no., 1, 173-76. Forster, N., 1992, A developing country’s fiscal response to foreign aid: The case of Papua New Guinea, 1970-88, Unpublished MA thesis (Institute of Social Studies, The Hague). Gang, 1. and H. Khan, 1991, Foreign aid, taxes and public investment, Journal of Development Economics 34, 355-369. Hellcr, P., 1975, A model of public fiscal behaviour in developing countries: Aid, investment and taxation, American Economic Review 65, 313-327. Khan, H. and E. Hoshino, 1992, Impact of foreign aid on the fiscal behaviour of LDC governments, World Development 20, 1481-1488. McGillivray, M. and T. Papadopoulos, 1991, Foreign capital inflows, taxation and public expenditure: A preliminary analysis of the case of Greece, Working paper no. 9108 (Faculty of Commerce, Deakin University, Geelong). Moran, C., 1989, Imports under a foreign exchange constraint, World Bank Economic Review 3, 279-295. Mosley, P., 1987, Overseas aid: Its defence and reform (Wheatsheaf, Brighton). Mosley, P., J. Hudson and S. Horrell, 1987, Aid, the public sector and the market in less developed countries, Economic Journal 97, 616-641. White, H., 1992, The macroeconomic impact of development aid: A critical survey, Journal of Development Studies 28, 163-240. White, H., 1993, Aid and government: A dynamic model of aid, income and fiscal behaviour, Journal of International Development, forthcoming. White, H. and M. McGillivray, 1992, Aid, the public sector and crowding in, Working paper no. 126 (Institute of Social Studies, The Hague).
ELSEVIER
JOURNAL OF Development ECONOMICS
Foreign aid, taxes and public investment: A further comment Howard White * Institute
ofSocial Studies, PO Box 29776, 2502 LT Den Haag, The Netherlands Received Scptembcr
1992, final version received May 1993
Abstract The paper in this journal by Gang and Khan (1991) employed Heller’s (1975) fiscal response model to demonstrate that aid to India has all been used to finance government investment. This conclusion is shown to be a misinterpretation of the model’s results which actually suggest that aid has had no impact on government investment at all. However, the reported parameters are determined by the estimation procedure adopted by Gang and Khan and not by the Indian government’s fiscal behaviour. Kqwords:
Foreign aid; Taxes; Public investment
JEL classification:
C51, E6
1. Introduction In their paper in this journal, Gang and Khan (1991) presented empirical estimates of the model, due to Heller (1975), ’ of the relationship between aid inflows and recipient government fiscal behaviour for the case of India. This comment discusses a number of theoretical and methodological short-comings in their analysis.
* The author would like to thank Neal Forster, Mark McGillivray and two anonymous referees for comments on an earlier version of this paper. ’ I have elsewhere (White, 1992), labelled this model the ‘fiscal response model’. Other papers adopting the same approach include Khan and Hoshino (19921, Forster (1992) and McGillivray and Papadopoulos (1992). 0304.3878/94/$07.00 0 1994 Elsevier Science B.V. All rights reserved SSDI 0304-3878(94)00032-8
156
H. White/Journal
ofDevelopment Economics 45 (1994) 155-163
First, as shown in Section 2, the model is an incorrect statement of the fungibility problem: the budget constraints over-restrict recipient budgetary behaviour. Section 3 shows that the procedure used to determine the series of target variables drives the results of the whole analysis. There are also problems in the interpretation of the results - Gang and Khan look only at partial results, ignoring reduced form equations and suppressing the model’s implicit dynamic element. Section 4 concludes that, on account of the problems discussed here, the results reported by Gang and Khan tell us nothing about foreign aid, taxes and public investment and presents a strategy for further research.
2. Model specification The Heller model supposes that recipient governments maximise a loss function comprising five choice variables subject to two budget constraints. The choice variables are: government investment (I,), government expenditure on socio-economic (or developmental) and other civil (or non-developmental) purposes (G, and G, respectively), taxation (T) and borrowing (B). Denoting a target variable by an asterisk (* ), the objective function used by Heller and adopted by Gang and Khan is:
-
Q,(T_
T*)
-
Z(T-
T*)* -
‘Y9(B -B*)
-
+-B*)2. (1)
Binh and McGillivray faulted the specification given in Eq. (1) on the grounds that the model is not optimised when the target values of the choice variables are achieved, so that the targets may not truly be considered targets. To avoid this problem Binh and McGillivray suggested the specification: 2
’ This specification had already been used by Mosley et al. (1987) in their application of the fiscal response model. But these authors did not explain their reascms for preferring this functional form.
H. White/Journal
ofDevelopment
Economics 45 (1994) 155-163
1.57
Table 1 Model simulation Assumptions:
parameters,
Utility function parameters
% a1 a2 a3 a4 as
targets and aid ,tlows Target variables and aid inflows
Budget constraint parameters 0.00 0.20 0.20 0.20 0.20 0.20
Pl P2
P3
4 GS CC T B lJ
1.08 -0.79 - 0.03
G G,* G,* T* B* ‘% Al
100 100 200 2.50 0 100 50
153.6 66.6 166.6 290.4 -53.6 - 962.1
from which it is clear that utility is maximised (to aO> when the targets are satisfied. The loss function given by either Eq. (1) or (2) is then maximised subject to budget constraints: I,=B+(~-p,)T+(l-p,)A,+(l-P,)A,, G, + G, = plT+
p*A, + psA,>
(3) (4)
where A, and A, are grant aid and loans respectively. The rationale for the separate budget constraints is that governments will not finance recurrent expenditure out of borrowing. This rationale notwithstanding, it is odd to write the budget constraint in a way which pre-determines the allocation of the income terms in given proportions. Such allocation is usually the outcome of the utility maximization problem. We may see how writing the budget constraint as Eqs. (3) and (4) over-restricts government budgetary behaviour by considering the following simulation. Table 1 shows the values of the ps obtained by Gang and Khan and a hypothetical set of (YSwhich give equal weight to each target. A hypothetical set of policy targets is then given exogenously. The aid inflows are also exogenous to the model, and have been selected here to ensure that the government’s targets can all be met. Using Eq. (2) as the utility function, utility will be maximised to zero by each endogenous variable being equal to its target level. To solve the model the seven first-order conditions derived from the Lagrangean given by combination of Eqs (2), (3) and (4) (one for each of the five endogenous variables and the two Lagrangean multipliers) were obtained. The
158
H. White/Journal
of Development
Economics 45 (1994) 155-163
resulting simultaneous system was solved on spreadsheet, giving the solution values shown in Table 1. The level of utility was then calculated from Eq. (2). Even though the maximum utility (of (~a, which is set equal to zero) is attainable given the amount of aid received, the model does not find this solution. It is intuitively obvious that the solution to the problem being set is for the choice variables to be equal to their targets if the value of the exogenous variables allows such an outcome: this is true regardless of the value of the model’s parameters (e.g. the (YSand ps). The failure of the model to find the intuitively obvious result in the case reported here is indicative of a problem in model specification, since it does not find the correct solution to this problem. The problem in the model’s structure is the restriction imposed by the ps. Utility would only equal zero if the ps reflected the values required to allocate spending optimally in the scenario given here - but the ps are model parameters, not variables to be determined in the solution. On account of this problem we may wish to use instead the single budget constraint: Z,+G,+G,=T+B+A,+A,.
(5)
It is shown in White (1993) that the fiscal response model will produce the result of fungibility when the utility function is combined with this budget constraint. That is aid inflows do not fully fund expenditure increases, but are partly used to decrease taxes and borrowing - which is what the model is intended to demonstrate - even when the budget constraint is written as in Eq. (5). However, the budget constraint in Eq. (5) is also problematic since different types of aid are analytically equivalent, which will only be the case where all aid is fully fungible. Aid will not be fully fungible if the target level for a category of expenditure is less than the aid tied to that use since actual expenditure on a category must be at least equal to the aid inflow tied to that purpose - that is the budget constraint should be kinked. ’ Further work, which is beyond the scope of this comment, is therefore required on theoretical modelling of fungibility.
3. Estimation
and interpretation
of results
Gang and Khan solve the model algebraically
to obtain the structural equations:
z,=~,+(~-P~)Z~*+P~{(~-P,)T+(~-P~)A~+(~-P~)AI}~
(6)
G,=p,-(l-Pz)G,*+P,G:‘+-p,(l-p,)T+p,(l-p,)A, - /+(I
- &)A,,
3 For a more formal demonstration
(7)
of this point see White (1992).
H. White/Journal
G,=
of Development
Economics 45 (1994) 155-163
-P1+(1-P2)Gc*-P2G,*+~1P2T+~2P2Ag+P3P2A,~
T= & +
~1
159
(8)
P,(G,*- GJ + PST*
+ P,(l - P,){l, - (1 - P2)Ag- Cl- P3PJ~
(9)
To estimate the parameters of Eqs. (6) to (9) it is first necessary to obtain values for the target variables. To do this the targets are defined as follows:
I;[ = Yl
+
Y*yr- 1 + Y&v
(10)
G:,
+
Y~ENR, + Y,Y + rk
(11)
=
~4
Gc*,i= yx + y&c,,T,* =
710
B,? =O,
+
Y,lY,
12 +
Y12Mt-17
(12) (13)
(14)
where Y is GDP and Y growth of GDP, Zr private investment, ENR primary school enrolments and M imports. The parameters for the target equations (10) to (13) are obtained by OLS using the actual values of the variables Za etc. as the regressand. The fitted values from these regressions are then used as the target values. There are two problems with this approach. First, there is no guarantee that the targets so produced will be consistent with the budget constraints - indeed, they almost certainly shall not. A better approach may be to model targets for expenditure and taxes, and then model target borrowing as that required to fill the gap once expected aid flows are taken into account. 4 The second problem is more serious. Suppose that, for example, Za is very closely related to the variables selected to determine the target level. Suppose in fact that the R2 from this regression is 1. Then I,* is Zg! When we come to estimate Eq. (6), which involves regressing Z, on I,*, we will be regressing Z, on itself - the coefficient on I,* will of course be unity, and all the other coefficients insignificant. In practice the R2 will not be 1, but if it is high then the problem will still be present. If the R2 is low it is difficult to see how the fitted values calculated using the estimated coefficients may be meaningfully interpreted as values of the targets. The fit will be poor either because the wrong variables have been included in the target equation, or because the outturn was far removed from
4 Whilst the approach suggested here is intuitively appealing it may well render the model inestimable. If actual aid flows are close to expected then there will be extreme multicollinearity when attempting to estimate reduced form equations (as is required for the 3SLS approach used in the literature): if expected aid flows equal actual then there will be perfect multicollinearity. It may therefore not be possible to estimate the reduced form since the matrix of regressors may be singular or near singular.
160
ofDevelopment Economics 45 (1994) 155-163
H. White/Journal
Table 2 Gang and Khan’s parameter
estimates
Parameter
Estimate
t-statistic
P1 PZ P3 ;:
1.08 - 0.79 - 0.03 - 125.57 0.72
32.26 - 1.53 -0.07 - 12.52 0.05
P.? P4 Ps ;:
2162.67 - 0.43 0.98 214.53 -2.17
0.35 - 1.80 15.24 - 0.24 0.79
0.00
0.04
Pa Source:
Gang and Khan (1991: Table 1).
the target. In the latter case the coefficients will not be those used in the formation of targets. Gang and Khan’s results are repeated in Table 2. 5 Consider, for example, the parameters for the tax equation. If the argument of the preceding paragraph is correct we would expect & to be unity and &, p4 and & to all be insignificant. This is indeed the case. For the estimate of Eq. (6) we expect & to be zero again this is the case. The other two equations are more complicated. From Eq. (7) we may expect & to have a value of one - but from Eq. (8) we expect a value of zero! Since the coefficient cannot be both zero and one, it falls between the two. ’ It therefore appears that Gang and Khan’s results are derived from the way in which the target series are estimated: as such the results can tell us nothing about the Indian government’s fiscal response to aid inflows. But even if we ignore the above-mentioned problem then we may still argue that Gang and Khan give a misleading interpretation of their results for two reasons: (i) failure to report reduced form coefficients; and (ii) suppression of the model’s implicit dynamics. I discuss each of these in turn. Gang and Khan write that foreign aid does not have any statistically significant effect on government consumption (p. 363). This conclusion is based on the result that the estimates for p2 and p3 are insignificantly different from zero, and so do not enter the budget constraint for government consumption. By the same reasoning, we would suppose that all aid is used to increase government investment. Using Gang and Khan’s point estimates, this interpretation is summarised in the
‘These are their results when aid is divided into grants and loans. The same problem may be observed in their results (not shown here) for the division of aid into bi- and multi-lateral. ’ A problem not pursued in this comment is the failure of the authors (or any other studies in this literature) to test the cross-equation restrictions imposed on the data.
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Table 3 Impact of aid from Gang and Khan’s results Budget constraints Al
A, ‘s Gs GC T B Source;
Structural
179 _ -79 _ _
A,
‘%
103 _ -3 _
Reduced forms
equations
Al
A,
0
0
0
-22 -57 -31 - 148
-1 -2 - 18 -85
-49 - 127 -90 - 186
0 -8 -25 -30 - 104
Derived from Gang and Khan (1991: Table 1).
first two columns of Table 3. An increase in loans of 100 units, for example, causes an increase in government investment of 103 units and a drop in total government consumption of 3 units. But it is rather odd to look at the coefficients of the budget constraint. For these results do not imply that Z, will increase by 103 units if A, increases by 100 units: for the results to mean this would require B and T to be constant in the face of the increased aid. But the whole point of the model is that B and T are not constant indeed, fungibility suggests that some aid will be used to reduce these domestic revenue sources. It is interesting to turn to the structural equations and see what they suggest about aid’s impact. For example, from Eq. (6) we see that an increase in A, leads to an increase of 1, of &(l - p3> - this is zero. Contrary to Gang and Khan’s argument, the structural equations suggest that aid has no impact on government investment. The calculated coefficients for the structural equations are summarised for each variable in the middle column of Table 3. ’ But neither do the structural equations tell the full story since they also contain endogenous variables - for example Eq. (6) contains the endogenous variable T. In order to analyse the total impact of aid on the different categories of government expenditure and revenue we must either derive the reduced forms or otherwise obtain solution values for the system of structural equations. For illustrative purposes I ran spreadsheet-based model simulations using Gang and Khan’s parameter values for the /?s and ps and a hypothetical set of exogenous variables (reported in the appendix) to examine the impact on the various categories of expenditure of an increase in A, and A, of 100 units. The results of these simulations are shown in the final two columns of Table 3. The results of these simulations are rather a stark contrast to the conclusions drawn by Gang and Khan. An increase in grant aid reduces borrowing by nearly twice the value of the increase in aid and taxes by nearly the amount of the aid that is the reduction in the recipient’s own revenue raising efforts sets off the new
‘The change in borrowing constraint, Eq. (3).
is calculated
by taking
total differentials
of the investment
budget
162
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aid monies more than two and one half fold. The result is that higher aid must lead to a reduction in total expenditures. This reduction falls entirely on government consumption. Neither type of aid has any impact at all on government investment. These reduced form results are still not the whole story since the model contains an implicit dynamic element which has been ignored in the discussion thus far. The target for G, depends on the lagged value of that variable. A one-off increase in aid will cause a drop in G, and therefore a change in the target value, G,*, in the subsequent period. The change in G,* will affect all the endogenous variables in the following period (and, through the new G,, in the period after that etc.). Since the target equations are not reported by Gang and Khan, it is not possible to calculate the magnitude of these dynamic effects. But such effects have been analysed in Forster’s (1992) application of a version of the fiscal response model to Papua New Guinea, and he finds that they can be considerable - about one third of the adverse impact of aid on taxation is, in the long run, removed. Meanwhile, the beneficial impact of aid on government investment is substantially reinforced. Even of the feedback effect through the target variables were incorporated, analysis based on this model would remain a partial one since it contains no economic feedback mechanisms. For example, two of the target equations include income and/or income growth. It is not realistic to suppose that higher aid inflows will leave income unaffected. White (1993) simulates a simple version of the model incorporating feedback through the targets equations from aid-induced increases in income. The results show that such effects can offset the reduction in taxes, even in the period of the inflow. Other economic relationships that might be added are an aid-augmented import function (see Moran (1989)) and a crowding in/out i.e. a relationship between aid (or government investment) and private investment (see Mosley (1987) and White and McGillivray (1992)). 4. Conclusions Gang and Khan claimed that their results showed that the Indian government has channelled all aid into investment. This is a misinterpretation of their own results - these results actually show aid to have no effect on investment at all. But their estimates are shown here to be a statistical artifact consequent upon the method of deriving the target variable series. The discussion has highlighted a number of additional problems that help highlight priorities in further research. These are: (i) development of a theoretical model that accurately captures the relationship between fungibility and tying; (ii) satisfactory procedures for estimating target variables; (iii) recognition of the implicit dynamic effects that will operate through the target equations; and (iv) incorporation of feedback through aid’s impact on income, imports and crowding in/ out.
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Appendix Values used for reduced form model simulations Parameters: results reported by Gang and Khan (shown in Table 2 in text above). Target variables: I,* = 15,000; G,* = 15,000; G,* = 20,000; T* = 25,000 Aid inflows Base case: A, = 1,000; A, = 3,000 Two simulations were run - each increasing A, and A, by 100 (with the other remaining constant). The figures shown in Table 3 are the change in each of the endogenous variables between the cases of higher aid and the base case.
References Binh, T. and M. McGillivray, 1993, Foreign aid, taxes and public investment: A comment, Journal of Development Economics 41, no., 1, 173-76. Forster, N., 1992, A developing country’s fiscal response to foreign aid: The case of Papua New Guinea, 1970-88, Unpublished MA thesis (Institute of Social Studies, The Hague). Gang, 1. and H. Khan, 1991, Foreign aid, taxes and public investment, Journal of Development Economics 34, 355-369. Hellcr, P., 1975, A model of public fiscal behaviour in developing countries: Aid, investment and taxation, American Economic Review 65, 313-327. Khan, H. and E. Hoshino, 1992, Impact of foreign aid on the fiscal behaviour of LDC governments, World Development 20, 1481-1488. McGillivray, M. and T. Papadopoulos, 1991, Foreign capital inflows, taxation and public expenditure: A preliminary analysis of the case of Greece, Working paper no. 9108 (Faculty of Commerce, Deakin University, Geelong). Moran, C., 1989, Imports under a foreign exchange constraint, World Bank Economic Review 3, 279-295. Mosley, P., 1987, Overseas aid: Its defence and reform (Wheatsheaf, Brighton). Mosley, P., J. Hudson and S. Horrell, 1987, Aid, the public sector and the market in less developed countries, Economic Journal 97, 616-641. White, H., 1992, The macroeconomic impact of development aid: A critical survey, Journal of Development Studies 28, 163-240. White, H., 1993, Aid and government: A dynamic model of aid, income and fiscal behaviour, Journal of International Development, forthcoming. White, H. and M. McGillivray, 1992, Aid, the public sector and crowding in, Working paper no. 126 (Institute of Social Studies, The Hague).