Abstract
This paper articulates a positive economic theory of foreign aid and presents a novel analysis of the nexus between institutions, foreign direct investment (FDI), and aid. In the model, aid is motivated by non-altruistic economic considerations, namely the desire of the donor country to protect FDI from expropriation. We first identify the conditions under which aid will be granted and characterize how the quantity of aid varies with the host country’s development stage. We then endogenize the host country’s institutions and identify the conditions under which institutional reform (adoption of a commitment technology) will be carried out, as well as the conditions that give rise to an expropriation trap—a situation where neither will the host country reform its institutions voluntarily nor will the donor country provide incentives for the institutional reform.
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Notes
For a list of countries, see http://www.state.gov/e/eb/ifd/bit/117402.htm.
Bräutigam and Knack (2004) explore the institutional impact of aid.
For discussions on various motives for foreign aid, see Dudley and Montmarquette (1976), Lumsdaine (1993), Alesina and Dollar (2000), Boone (1996), Schraeder et al. (1998), Maizels and Nissanke (1984), among others. See Mavrotas (2010) and Riddell (2007) for recent discussions on a broad range of issues related to foreign aid.
The analysis is broader than bilateral sovereign aid. The foreign country can also be a multilateral agency that is set up to promote international trade and investment.
It is important not to confuse \(\theta \) with the share of capital in a Cobb–Douglas production function. A full description of the production technology would include capital and other factor inputs. Here we have suppressed the problem of hiring the other inputs in order to simplify notation.
The availability of the commitment technology and the choice to adopt it will be considered in Sect. 3.
\(\left( Y_{h}^{N}-Y_{h}^{E}\right) \) attains a positive maximum value when \(\gamma =1-\theta \beta \).
Note that the effect of A on \(k^{M*}\) via \(\hat{\tau }\) vanishes due to the envelope theorem.
Using data from the International Country Risk Guide, Asiedu and Villamil (2000) obtain estimates of country-specific \(\beta \) that ranges from a high of 0.95 to a low of 0.23 for 40 different countries.
Krasa and Villamil (2000) analyze the distinction between the ex ante contract and ex post monitoring in the costly state verification framework.
Svensson (2000) discusses the commitment problem by the donor country in inducing the recipient countries to exert efforts to alleviate poverty.
The assumption that capital depreciates fully each period is not critical for this insight. A natural question to ask is whether allowing for the dynamics of capital will make the host country postpone consumption and accumulate enough capital so that it is completely self-financed, i.e., does not need foreign investment. We conjecture that this is not case. In different settings, it has been shown that impatient agents will never accumulate enough capital to be self-financed and will keep borrowing from patient agents (e.g., Carlstrom and Fuerst 1997 and Iacoviello 2005). Although we do not explicitly model capital accumulation, we note that expropriation frictions are relevant in our theory precisely because the host country is impatient, thus the results from the previous literature will likely carry through.
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Appendix
Appendix
Proof of Proposition 2
As long as the foreign country chooses a positive amount of optimal aid, it must be better off than providing no aid at all. To show that the host country is also better off with aid, differentiate \(H^{N}\) with respect to A :
This indicates that the effect of aid on the host country’s total discounted income comes from two sources. The first is the direct effect, captured by \( h^{\prime }\left( K^{H}+A\right) >0\): foreign aid augments the host country’s domestic capital stock and increases its production. The second is the indirect effect coming from the enhancement of FDI due to a reduction in \(\tau \). Note that only when the host country’s optimal choice of \(\tau \) equals \(\hat{\tau }\) is this second effect present, which is positive since \( \hat{\tau }>1-\theta \) and \(\mathrm{d}\hat{\tau }/\mathrm{d}A<0\). If the optimal choice of \( \tau \) is \(\tau ^{*}\equiv 1-\theta \), which is independent of aid (\( \mathrm{d}\tau ^{*}/\mathrm{d}A=0\)), then the second effect will be zero. Nevertheless, the direct effect is still strictly positive. Therefore, it is always true that \(\mathrm{d}H^{N}/\mathrm{d}A>0\).\(\square \)
Proof of Proposition 3
Totally differentiating the NEC (5) with \(\hat{ \tau }\left( \overline{A}\right) =1-\theta \) with respect to \(K^{H}\) gives
Totally differentiating (9) obtains
If \(\bar{A}\ge A^{*}\) at \(K^{H}=0\), then it is obvious that the optimal aid equals \(A^{*}\), which is positive and monotonically decreasing in \( K^{H}\) until it reaches \(\bar{K}^{H}\). We now consider the case where \(\bar{A }<A^{*}\) at \(K^{H}=0\). In this case, \(K_{1}^{H}>0\) exists and is unique. When \(K^{H}=K_{1}^{H},\) we obtain the maximum amount of aid, denoted by \( A_{\max }.\) Note that \(\hat{\tau }\left( \overline{A}=A^{*}\equiv A_{\max }\right) =1-\theta .\) At \(A_{\max }\), the first-order condition (9) can be simplified as
Since \(\beta <\theta \), we have \(h^{\prime }\left( K_{1}^{H}+A_{\max }\right) >r/\beta =h^{\prime }\left( \bar{K}^{H}\right) \), or \( K_{1}^{H}+A_{\max }<\bar{K}^{H}-A_{\max }<\bar{K}^{H}\). Evaluating the NEC at \(A=A_{\max }\), \(K^{H}=K_{1}^{H}\) and \(k^{M*}\left( \tau =1-\theta \right) =\left( r/\theta ^{2}\right) ^{1/\left( \theta -1\right) }\) yields
The above Eqs. (14) and (15) can be used to pin down \(K_{1}^{H}\):
To complete the proof, we need to show that \(\overline{A}_{\min }<A_{\max }.\) Note that \(\overline{A}_{\min }\) is determined by the non-expropriation constraint evaluated at \(K^{H}=0\) and \(\hat{\tau }\left( \overline{A}\right) =1-\theta ,\) which can be simplified as
Combining (15) and (16) yields \(h\left( K_{1}^{H}\right) +h\left( \bar{A}_{\min }\right) =h\left( K_{1}^{H}+A_{\max }\right) \). The concavity of h, however, implies that \(h\left( K_{1}^{H}\right) +h\left( \bar{A}_{\min }\right) >h\left( K_{1}^{H}+\bar{A} _{\min }\right) .\) Thus, \(A_{\max }>\bar{A}_{\min }\). This also implies that \( K_{1}^{H}>0\).\(\square \)
Proof of Lemma 2
Since \(L\left( \bar{A}\right) >0\) for any positive \(\bar{A},\) the host country will not adopt the commitment technology voluntarily. Consider Fig. 5. We know that (1) \(G\left( A=0\right) =L\left( A=0\right) =0;\) (2) \( G^{\prime }\left( A\right) =r/\left( 1-\beta \right) >0;\) (3) \(L^{\prime }\left( A=0\right) =\left[ h^{\prime }\left( K^{H}\right) -r\right] /\left( 1-\beta \right) >0\) and \(L^{\prime \prime }\left( A\right) =h^{\prime \prime }\left( K^{H}+A\right) /\left( 1-\beta \right) <0.\) So we must have \( L^{\prime }\left( A=\tilde{A}_{f}\right) <G^{\prime }\left( A=\tilde{A} _{f}\right) .\) Recall that \(\mathrm{d}F^{N}/\mathrm{d}A|_{A=\bar{A}}>0\) for \(K^{H}\in (0,K_{1}^{H}].\) This implies that
That is, \(L^{\prime }\left( A=\bar{A}\right) >G^{\prime }\left( A=\bar{A} \right) =G^{\prime }\left( A=\tilde{A}_{f}\right) >L^{\prime }\left( A= \tilde{A}_{f}\right) .\) Therefore, \(\bar{A}<\tilde{A}_{f}.\) \(\square \)
Proof of Lemma 3
\(L\left( A\right) \) is increasing and intersects the horizontal axis at \(A= \tilde{A}_{h}\) because (1) \(L\left( A=0\right) =\left[ \hat{\tau }\left( A=0\right) f\left( k^{M}\left( \hat{\tau }\left( A=0\right) \right) \right) -\tau ^{*}f\left( k^{M*}\right) \right] /\left( 1-\beta \right) <0\) since \(\tau ^{*}\) maximizes the host country’s tax revenue; and (2) \( L^{\prime }\left( A\right) =h^{\prime }\left( K^{H}+A\right) \left( 1-\hat{ \tau }\right) /(1-\hat{\tau }-\beta \theta )>0\). If \(A^{*}\le \tilde{A} _{h},\) that is, \(L\left( A^{*}\right) \le L\left( \tilde{A}_{h}\right) =0,\) then the host country will adopt the commitment technology voluntarily. Otherwise, if \(A^{*}>\tilde{A}_{h},\) or \(L\left( A^{*}\right) >L\left( \tilde{A}_{h}\right) =0\). Note that \(G^{\prime }\left( A\right) =-\mathrm{d}F^{N}\left( \hat{\tau }\left( A\right) ,A\right) /\mathrm{d}A\). Then, \(G\left( A\right) \) is a convex function and obtains the minimum at \(A=A^{*}\ \) (since in the foreign country’s problem, \(F^{N}\left( \hat{\tau }\left( A\right) ,A\right) \) is concave and obtains the maximum at \(A=A^{*}\)). Let \(\pi \left( \tau \right) \equiv \left( 1-\tau \right) f\left( k^{M}\left( \tau \right) \right) -rk^{M}\left( \tau \right) ,\) the profit of the foreign firm. Then, \(G\left( A\right) \) can be written as \(G\left( A\right) =\left[ \pi \left( \tau ^{*}\right) -\pi \left( \hat{\tau } \right) +rA\right] /\left( 1-\beta \right) \). Since \(d\pi /d\tau =-f\left( k^{M}\right) <0\) and \(\tau ^{*}<\hat{\tau }\), we have \(G\left( A\right) >0 \) for all A. This result also implies that \(\tilde{A}_{h}<\tilde{A}_{f}\) as \(G\left( A\right) \) can never be negative. Therefore, there exist three possibilities: \(A^{*}\le \tilde{A}_{h},\) \(\tilde{A}_{h}<A^{*}\le \tilde{A}_{f},\) or \(A^{*}>\tilde{A}_{f}\). And the result follows. \(\square \)
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Jin, Y., Zeng, Z. Expropriation and foreign direct investment in a positive economic theory of foreign aid. Econ Theory 64, 139–160 (2017). https://doi.org/10.1007/s00199-016-0973-4
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DOI: https://doi.org/10.1007/s00199-016-0973-4