In the text we make a number of assertions which are proved here.
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International Monetary Fund and Princeton University, respectively. The views expressed herein do not necessarily reflect those of the institutions with which the authors are affiliated. We would like to thank William Branson, Willem Buiter, Malcolm Knight, and Masao Ogaki for useful discussions and comments.
Defined as the ratio of gross domestic savings (GDP minus total private and government consumption) to GDP.
The Charts use World Bank data for annual average growth of real per capita income (1965-90) and levels of per capita income in 1990 US$ (World Bank Atlas method); the savings rate is gross domestic savings as a fraction of GDP, and the sample covers 97 developing countries for which data are available. Some countries in the sample went from low savings rates and low growth rates to much higher savings and growth rates during this period, so that the picture of two distinct groups may be clouded by these observations.
There is, indeed, a large body of literature that explores the link between “cultural factors” and economic development, including the works of Max Weber and Gunnar Myrdal; Packard-Winkler (1989) provides a more recent discussion.
The term “aggregate” production function need not refer to the national level. If there is little borrowing and lending across regions then the aggregate production function, as used here, can simply mean the regional production function.
For an excellent recent treatment of the Rosenstein-Rodan model see Murphy, Shleifer and Vishny (1989).
For reasonable specifications of the production function, the low steady state implies a capital/labor ratio of zero; that is, the economy necessarily “implodes” at the bad steady state.
Krugman (1991) and Matsuyama (1991) discuss the role of multiple equilibria in models where the action of moving from one sector to another is costly for labor, but increasing returns prevail in the manufacturing sector. Accordingly, only if each agent believes that many others will move to manufacturing in the future will it be worthwhile for him to move into the manufacturing sector himself.
Schumpeter, in fact, defines economic development as “that kind of change arising from within the system which so displaces its equilibrium point that the new one cannot be reached from the old one by infinitesimal steps” Schumpeter (1959) p. 64.
Between 1960 and 1985, for example, net flows of foreign direct investment into developing countries averaged only 0.5 percent of GDP, and portfolio investment another 0.45 percent, so that the total inflow averaged less than one percent of GDP. (Griffin (1989), p. 83).
Despite the increased role of capital flows in recent years many developing countries, particularly the poorer ones, still have only limited access to international credit markets.
Theoretically, savings can be either an increasing or a decreasing function of the rate of return, depending upon whether income or substitution effects dominate. There is a large body of literature which examines the relation between savings and interest rates in developing countries; Fry (1982) surveys some of these studies and concludes that real interest rates have a positive effect on savings.
There is a substantial body of literature that seeks to link savings behavior in developing countries with either the level or the growth rate of per capita income (Gersovitz (1988) provides a survey). Usually these studies focus exclusively on the effect of income on savings, and their results are somewhat mixed: Leff (1969) and Modigliani (1970) find that the rate of growth of income affects savings, while the level of per capita income is a much less significant determinant. Ram (1982), in contrast, finds fairly strong support for the level of per capita income affecting savings. In the model developed here, of course, savings, and both the level and rate of growth of income, are all endogenous. Nevertheless, the “good” dynamic path will be associated with higher levels of savings and income, as well as a higher growth rate of income, as compared to the “bad” dynamic path. It is not clear that linear regressions that incorporate either the level or growth rate of income will be able to yield very robust results on the link between savings and income if economic development does indeed involve a discrete jump from one dynamic path to another of the type considered here.
The closest model to ours is the human capital model of Becker, Murphy and Tamura (1990). In their model, multiple steady states can occur but not multiple equilibria within a period. Azariadis and Drazen (1990) develop a model in which sufficient human capital must be acquired before the economy can take off.
The sudden spurt in growth is, as in our model, a property of the Gerschenkron model (Gerschenkron (1962)).
This is an analytically convenient way to specify increasing returns to investment. The implied cost of investment is given by:
therefore, Cs > 0 and CK < 0, that is, the cost of undertaking investment is an increasing function of the amount of investment and a decreasing function of the capital stock in place.
Notice that the good equilibrium, Sa, can exist either on the upward or the downward sloping portion of the r(S) curve in the NE quadrant. Corresponding to Figure 1, however, even when the good equilibrium occurs on the downward sloping portion of the r(S) curve it necessarily entails a higher interest rate.
It is the aggregate wage bill which is of relevance here because in the overlapping generations model savings are undertaken by the young and therefore must be financed out of wages.
That is, if S(K) < δK where K is the lowest capital stock.
The condition F < μW/(1+μ) is sufficient, though not necessary, for equilibrium to exist.
That is, the model no longer provides a sensible description of the economy.
Condition (18) is very much a sufficient condition rather than a necessary one. Simulations suggest the existence of a considerably lower bound on the minimum F but an analytic proof is difficult.
For models embodying Markovian conjectures in the industrial organization literature see e.g. Friedman (1977) (chapter 5). In the following section we introduce taxes and government revenues; for simplicity we assume that all such revenues are invested in the aggregate production function so St denotes the sum of private and public savings.
For simplicity, with (correlated) probability across agents.
As Becker, Murphy and Tamura (1990) write, “Many attempts to explain why some countries and continents have had the best economic performance during the past several centuries give too little attention to accidents and good fortune.” p. S14.
For the moment we do not impose the government’s budget constraint.
Along the interest rate function (32), dr/dS ⇒ -∞ as S ⇒ 0 so dS/dr ⇒ 0.
In particular, there is no need for the government to be involved in production, only in coordinating savings by the private sector.
That the culture is altered within half a generation is, of course, a result of our assumption on Markov beliefs. More generally it may take longer to create a high savings culture if beliefs depend upon more distant savings rates as well. Presumably no government would deliberately move the economy from the good equilibrium path to the bad equilibrium path though theoretically it is possible by raising sufficiently high taxes and then spending revenues on government consumption rather than using them for investment.