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The authors thank Peter Fallon, Aart Kraay, Miguel Messmacher, Genevieve Verdier, and David Weil for their useful comments, as well as the staff of the Western Hemisphere Division of the IMF Institute and the attendees of an IMF Institute seminar. The paper was written, in part, while Dalgaard was a Visiting Scholar at the IMF Institute. The hospitality and support of the IMF Institute are gratefully acknowledged. Carl-Johan Dalgaard is an Associate Professor at the University of Copenhagen. Lennart Erickson is an Economist in the IMF Institute.
“We are united in our desire to achieve the Millennium Development Goals and in our assessment that more aid is needed to achieve them,” statement by Rodrigo de Rato, Managing Director, IMF at the Annual Meetings the Board of Governors of the IMF and World Bank, Washington, October 3, 2004.
The other target contemplated in the MDG#1 was to, in the same period, reduce by half the number of people who suffer from hunger. This will not be addressed in the present paper.
Strictly speaking Easterly attacks the “two-gap” model, rather than endogenous growth models. Since the underlying structure of the two models is the same, however, one could equally well see it as a criticism of “pure” AK models. That is, an endogenous growth model where the marginal product of capital is constant at all points in time.
Mourmouras and Ranzagas also study policies that aim to affect fertility, which is an issue not examined in the present paper.
Technically the poverty line is US$1.08 a day per person, calculated at 1993 prices (Besley and Burgess, 2003).
As pointed out by Bourguignon (2002), the elasticity will in general depend on the characteristics of the underlying income distribution and the level of GDP per capita. Assuming a lognormal distribution of income, Bourguignon shows that the elasticity is increasing in the standard deviation of log income, and in the ratio between the poverty line and GDP per capita. Hence, whether the elasticity rises or declines in the medium run (the focus of our analysis) would depend on the changes in both the mean and variance of the distribution.
In the analysis which follows we invoke the positive representative agent assumption. This assumption, of course, does not imply that the underlying distribution of income needs to be perfectly egalitarian. Instead we implicitly assume that the underlying distribution of income is such that the elasticity rule (1) is a meaningful description of how individuals move above a certain threshold level of income. See Stiglitz (1969) for an analysis of the dynamics of wealth (and income) inequality within a representative agent Solow model, augmented by subsistence consumption. Caselli and Ventura (2000) extend the analysis to the Ramsey-Cass-Koopmans framework.
The data source is the 2005 edition of World Development Indicators. “Aid” refers to ODA. The 30 countries are: Benin, Botswana, Burkina Faso, Burundi, Cameroon, Central African Republic, Chad, Democratic Republic of Congo, Republic of Congo, Cote d’Ivoire, Gabon, The Gambia, Ghana, Kenya, Lesotho, Madagascar, Malawi, Mauritania, Niger, Nigeria, Rwanda, Senegal, Seychelles, Sierra Leone, Sudan, Swaziland, Togo, Uganda, Zambia, and Zimbabwe.
A recent paper by Young (2005), which aims to assess the welfare cost of the AIDS epidemic, also assumes g=0. In a footnote Young presents some evidence in favor of the assumption deriving from growth accounting, while recognizing that the quality of input data for such exercises in Africa is rather doubtful.
The basic approach taken by Caselli and Feyrer consists of using the fact that capital’s share in theory equals (User cost of capital) *(K/Y). With data on K, Y, capital’s share, and the relative price of investment to output, one can calibrate MPK= [(Price of output)/(Price of investment)]*(Y/K)*Capitals share. A key element in their analysis relates to which measure of capitals share to invoke, which is where natural wealth adjustments comes into the picture.
MPKs likely vary across countries and time. Hence Dalgaard and Hansen develop a correlated random coefficient approach to estimating average returns. A range of estimators are employed to take endogeniety into account. The issue of weak instrumentation is addressed also.
Is equation (1.15) still valid if externalities are present? The answer is a qualified “yes” and the details are shown in Section V.
Setting ω=1 is almost certainly an overstatement of the capital accumulation content of aid donations. For example, about 6 percent of aid flows are emergency relief (White, 2002, Table 15). However, as noted, it is comparatively easy to assess the consequences of changing the size of ω for aid requirements, for which reason we will continue to assume that all aid propels capital accumulation.
This range for aid requirements is based on pooled GDP data for 2002. Specifically, the countries included are: Angola, Benin, Burkina Faso, Burundi, Cameroon, Central African Republic, Chad, Democratic Republic of Congo, Republic of Congo, Cote d’Ivoire, Eritrea, Ethiopia, Ghana, Guinea, Kenya, Liberia, Madagascar, Malawi, Mali, Mauritania, Mozambique, Niger, Nigeria, Rwanda, Senegal, Sierra Leone, Sudan, Tanzania, Togo, Uganda, Zambia, and Zimbabwe.
When λ=0.5, the term [1-e−λT] in equation (15) is 0.99; associating this case with an “infinite rate of convergence” (where the term is 1 exactly) is therefore fairly reasonable.
As pointed out by these authors (pp. 121–22): “Our explanation is that tropical Africa, even the well-governed parts, is stuck in a poverty trap, too poor to achieve robust, high levels of economic growth and, in many places, simply too poor to grow at all… We argue that what is needed is a ‘big push’ in public investments to produce a rapid ‘step’ increase in Africa’s underlying productivity… In particular, we argue that well-governed African countries should be offered a substantial increase in official development assistance (ODA) to enable them to achieve the Millennium Development Goals (MDG)… by 2015.”
In practice, of course, there is a major difference: In the former case some actual effort on the part of the government is required in the sense of reforms, in the latter case the investment increase will appear by itself.
As Sachs et al. (2004, p. 185) puts it, “The current level of ODA is surely a limiting factor for achieving the MDGs in the well-governed African countries. It is not only necessary but also possible to remove this constraint. We have found that well-governed African countries need an additional $40 or so per capita per year in development assistance. If we supposed that 620 million Africans were to receive that amount, it would add about $25 billion a year to the $18 billon a year provided in 2002, or more than a doubling of aid flows to the continent.”
Alternatively, one could have invoked potential flows stemming from the over-all pledge by world leaders to raise aid flows to 0.7 percent of GNI, from its 2004 level of about 0.3 percent. In this case, however, we would have to speculate as to what fraction of this additional aid would be allocated to Africa. Yet another approach would be to implement an increase in aid, which was pledged at the 2006 G8 summit at Gleneagles, i.e. a doubling of aid to sub-Saharan Africa. Under the proposal of Sachs et al., used below, aid is assumed to more than double in the years to come.
Alternatively one could view expenditures on health and schooling as accumulation of another capital good, human capital. In Section V we discuss how our calibrations are affected if multiple capital goods are introduced.
The calibrations are unrestricted, as can be seen from row 1 of the table; it goes without saying that an increase in s of anything close to (or in excess of) 100 percent is meaningless for practical purposes.
Rodrik (2000) finds evidence that aid inflows stimulate savings. According to his estimates roughly half the inflows are turned into savings. This could be taken to suggest that
Here, we would only be considering improvements in health or education which would operate through increases in productivity. Alternatively, such improvements could be modeled as improving the stock of health or human capital. These will be discussed in Section V.
It should be noted, however, that there are relatively recent cases of countries achieving even higher productivity growth. Estimates for Total Factor Productivity (TFP) growth in China during 1978–95 range up to 3.7 percent (Yeh, 2005), while high estimates for TFP in India reach to 2.4 percent (Rodrik and Subramanian, 2004).
The decentralized equilibrium in the RCK model is Pareto Optimal, so we can save some space by focusing on the planner’s solution.
Arellano et al. (2005) reach similar conclusions using a general equilibrium two-sector model. They find that permanent aid flows will be directed towards consumption.
A more general treatment is found in Dalgaard et al. (2004), involving a distribution of aid flows among both young and old. The paper also contains a discussion of why the two work horse models (RCK and Diamond) lead to so different conclusions regarding aid effectiveness.