OCP- 6 BENJAMIN B. KING Public Disclosure Authorized NOTES ON THE MECHAN ICS : OF GROWTH-AND DEBT WORLD BANK STAFF OCCASIONAL PAPERS NUMBER SIX Public Disclosure Authorized Public Disclosure Authorized INTERNATIONAL BANK FOR RECONSTRUCTION AND DEVELOPMENT Public Disclosure Authorized World Bank Staf Occasional Papers, Hugh Latimer, Editor No. 1. Herman G. van der Tak, The Economic Choice between Hydroelectric and Thermal Power De- velopmenits, with a Note on Joint Costs, 11.00 No. 2. Jan de Weille, Quantification of Road User Savings, $1.00 No. 3. Barend 1. de Vries, The Export Experience of Developing Countries, $1.50 No. 4. Hans H. Adler, Sector and Project Plann-ing in Transportation, $1.50 No. 5. A. A. JI'alters, The Economics of Roaid User Charges, $5.00 No. 6. Benjamin B. King, Notes on the Mdechanics of Growth and Debt, $1.50 Editorial Committee Barend A. de Vries, Chairman Bernard R. Bell Samuel Liokowiiz Manfred G. Blobel K. S. Krishnaswamv Vinod Dubev K. N. Raj Hugh Latimer C. H. Thompson This paper may not be quoted as representing the view of the Bank and affiliated organizations. They do nol accept responsibilityfor its accuracy or completeness. WORLD BANK STAFF OCCASIONAL PAPERS NUMBER SIX "Whom have you got on board?" said I. Said he, "Astrologers, fortune-tellers, alchymists, rhymers, poets, painters, projectors, mathematicians, watch- makers, sing-songs, musicianers, and the devil and all of others that are subject to Queen Whims. They have very fair legible patents to show for it, as anybody may see." Panurge had no sooner heard this, but he was upon the high-rope, and began to rail at them like mad. The Heroic Deeds of Gargantua and Pantagruel FRANKOis RABELAIS BENJAMIN B. KING NOTES ON THE MECHANICS OF GROWTH AND DEBT Distributedby The Johns Hopkins Press Baltimore, Maryland Copyright ©)1968 by the Internatonal Bank for Reconstruction and Development All rights reserved Manufactured in the United States of America Library of Congress Catalog Card Number 68-8701 FOREWORD I would like to explain why the World Bank Group does research work, and why it publishes it. We feel an obligation to look beyond the projects we help to finance towards the whole resource allocation of an economy, and the effectiveness of the use of those resources. Our major concern, in dealings with member countries, is that all scarce resources, including capital, skilled labor, enterprise and know-how, should be used to their best advantage. We want to see policies that encourage appropriate increases in the supply of savings, whether domestic or international. Finally, we are required by our Articles, as well as by inclination, to use objective economic criteria in all our judgments. These are our preoccupations, and these, one way or another, are the subjects of most of our research work. Clearly, they are also the proper concerns of anyone who is interested in promoting development, and so we seek to make our research papers widely available. In doing so, we have to take the risk of being misunder- stood. Although these studies are published by the Bank, the views expressed and the methods explored should not necessarily be v considered to represent the Bank's views or policies. Rather they are offered as a modest contribution to the great discussion on how to advance the economic development of the underdeveloped world. ROBERT S. McNAMARA President International Bank for Reconstruction and Development 4ugust 15, 1968 VI TABLE OF CONTENTS Foreword v Preface ix I. Introduction 1 II. The Accumulation Function: A Necessary Tool 6 III. Savings Models: Rules of the Game 13 Table 1: Generalized Model 18 IV. The Model on Different Assumptions about Savings 19 Examples 1, 2, 3, 4 21,23 Chart 24 Table 2: The Effect of a Single Investment 25 Table 3: The Effect of a Single Investment: Numerical Example 26 V. Use and Abuse of the Model 30 Table 4: GNP Growth in 10 years 34 Vil VI. Further Complications 35 Table 5: GDP and GNP with Initial Conditionis 36 ANNEXES 1. Properties of the Accumulation Function 37 2. Target Rate of Growth 41 3. Investment with a Two-year Lag 44 4. Notation, Brevity, and Accuracy 47 ACCUMULATION FUNCTION TABLES 1-S Second Generation (5, 10, 15, 20, and 25 years) 50-54 6-10 Third Generation (5, 10, 15, 20, and 25 years) 55-59 Notation - nil or negligible ... not available viii PREFACE Every bank is interested in the debt servicing capacity of its clients. It is not surprising therefore that international debt and its burden on nations is a traditional subject of study for economists in the Bank. This paper originated as a comment on some conclusions in the longer-term analysis in Economic Growth and External Debt (1964), and thus represents a continuation of that discussion. There is every prospect that the relations between growth and debt, once a peculiar concern of planners and of public lenders, will attract wider attention in the future, as the realities of "the long haul" in development become explicit. That is why we are opening to the public what might otherwise be thought of as a private debate. Cournot in his Souvenirs over a hundred years ago wrote that the function of prediction is not to foretell the future but to cast a sharper light on the present. I suggest that the wise use of the ideas presented in B. B. King's Notes will help us to analyze better the present debt position of many countries. ANDREW M. KAMARCK Director, Economics Department ,x AUTHOR'S NOTE The author is indebted to Bela Balassa for many pertinent comments and for patient encouragement at every stage. Other useful comments came from Hugh Collier at an earlier stage and from Ted Hawkins, Nicholas Carter, and Atle Elsaas in the later ones. Huguette Angel wrote the program for the tables on the accumulation function; the numerical examples were checked by Constantinos Giatrakos and Rogelio David; Germaine Gagnon typed the manu- script indefatigably. The editor, Hugh Latimer, has been more than helpful throughout in a variety of ways. No one but the author is responsible for any mistakes. B. B. K. I INTRODUCTION This paper grew out of an exploration of the way in which inflow of capital from abroad affects the growth of an economy, if there is a return flow of interest payments on the debt thereby created. There are two sides to this coin. The obverse is to suppose that the creditor country or countries supplies a given amount of capital on certain terms; what then happens to the growth of the recipient country? The reverse is to set a target rate of growth for the recipient country; what then is required of the donor countries in the way of aid to the recipient country? Models which answer some of these questions, on certain assumptions, exist already of course.' The answer will be different according to the dominant constraints on the economy, i.e. whether there is a balance of payments or a savings gap. In this paper we shall only be concerned with the savings gap, not out of a conviction that the other gap can be ignored, but only because there is an advantage in taking one thing at a time. Most such models end up with rather long mathematical expres- 1 For example, H. B. Chenery and A. M. Strout, "Foreign Assistance and Economic Development," American Economic Review, LVI, Number 4, Part I (September 1966); Dragoslav Avramovic and Associates, Economic Growth and External Debt, (Johns Hopkins Press, Baltimore 1964). l sions, whether they are in exponential form or in compound interest form. This is of course not very surprising. Growth, if one assumes a constant rate, introduces one element of compound interest. The interest on the debt itself introduces another. If one supposes that the inflow of capital is the generating factor, and that it is increasing at a particular rate, then one has a third rate of growth to contend with. An unexpected by-product of the exploration is a mathematical function which has here been called the accumulation function. It has been giveni this name because the expressions which give rise to it are a result of accumulation in one form or another at compound interest or a kind of compound compound interest. With the aid of it, it is possible to reduce the long mathematical expressions to a simple notation. Furthermore, it is possible to work with this function in a reasonably simple way. The function is in fact only an extension of the sort of expressions that one finds in annuity tables. But instead of one rate of growth there may be two or three. Since this function, which is introduced in Chapter II, is new, it imposes a burden on the reader, even though most of the more esoteric mathematics have been relegated to Annex 1. Those who have no stomach for such things had better stop at this point. But those who feel inclined to try to master it-it is not that difficult-may find that it has wider application than growth or debt models. Now it is one thing to build up these long mathematical expres- sions in a model, insert specific figures in the place of the symbols and then to make statements about the results. It is another thing to understand why, when one changes the values of the parameters, certain things happen. Do they happen because of some inviolable law of nature or do they happen because some implicit assumption has been built into the model? It is not usually easy to give an answer to this question as long as the model is in a rather complicated form.