RESEARCH REPORT
Vi
c16c
16
Intersectoral Factor Mobility
and Agricultural Growth
by Yair Mundlak
The International Food Pollcv Research Institute is an independent nonprofit or ;,irlzalion
which conducts research on policy problems related to the food needs of the c. .'loping
world. IFPRI's research is directed toward policy makers at the national and internal .: rai le, el
and is distributed to those concerned ,ith tood policy issues
INTERSECTORAL FACTOR MOBILITY
AND AGRICULTURAL GROWTH
The research presented in IFPRI's Research Reports is conducted at the Institute; however, the
interpretations and views expressed are those of the authors and are not necessarily endorsed
by the Institute or the organizations that support its research.
INTERSECTORAL FACTOR MOBILITY
AND AGRICULTURAL GROWTH
Yair Mundlak
Research Report 6
International Food Policy Research Institute
February 1979
Copyright 1979 International Food Policy Research Institute
All rights reserved. Sections of this report may be reproduced with
acknowledgement to the International Food Policy Research Institute.
Library of Congress Cataloging in Publication Data
Mundlak, Yair, 1927
Intersectoral factor mobility and agricultural growth.
(Research reportInternational Food Policy Research Institute ; 6)
Includes bibliographical references.
1. AgricultureEconomic aspectsjapanMathematical models.
2. Rural developmentJapanMathematical models. 3. Ruralurban
migrationJapanMathematical models. I. Title. II. Series:
International Food Policy Research Institute. Research
reportInternational Food Policy Research Institute ; 6.
HD2092.M8 338.1'0952 794588
ISBN 0896290077
CONTENTS
Foreword
1. A Framework for Analysis and Some Consequences 11
Yair Mundlak
2. Migration Out of Agriculture: Empirical Analysis 19
Yair Mundlak
3. Occupational Migration Out of Agriculture in Japan
Yair Mundlak and John Strauss 33
4. The Flow of Savings Out of AgricultureThe Case of Japan 43
Yair Mundlak and John Strauss
5. Agricultural Growth in the Context of Economic Growth 56
Yair Mundlak
6. A Quantitative Interpretation of Some Aspects of the Japanese Experience 75
Yair Mundlak and John Strauss
Appendix A The Data for Chapter 2 and Their Sources 103
Appendix B Background of Chapter 3 Analysis 106
Appendix C Estimating Saving Rates 115
Appendix D A Description of the Simulator 120
Appendix E Initial Values of Parameters and Variables Used in Chapter 5 125
Appendix F Data Sources for Chapter 6 127
Bibliography 133
TABLES
1. Estimates of migration equation (M1), 70 countries, 196070 27
2. Estimates of migration equation (Mi), OECD countries, 195070 29
3. Estimates of migration equation (M2) 30
4. Values of 8 (m = 0) for the OECD countries 31
5. Results of applying the CCS equation to postwar Japanese data 34
6. Estimates of the migration equation, postwar Japan 37
7. Alternative forms for the migration equation 39
8. Estimates of the flow equation for the prewar period, 190938 48
9. Postwar estimates of the savings flow equations, 195564 and 195470 49
10. Estimates of the savings flow equation, data pooled 50
11. The response of savings flow to differential returns on capital 53
12. Numerical solutionsselected results for t = 21 68
13. Directional effects of parametric changes along growth path 72
14. Actual and simulated levels of some economic variables for prewar Japan 80
15. Actual and simulated levels of some economic variables for postwar Japan 89
16. Restrictions on resource flow, 1937 96
17. Restrictions of resource flow, 1968 97
18. Prewar economy with postwar technical change and saving rates, simulation
results, 1937 99
19. Postwar economy with prewar technical change and saving rates, simulation
results, 1968 100
20. Summary measures of the data 105
21. Migration and related variables, fiveyear averages, 190670 107
22. Means, coefficients of variation, and correlation coefficients for various vari
ables, prewar and postwar periods 108
23. Estimating sectoral saving rates for the prewar period 117
24. Summary statistics, savings flow variables 119
25. Initial values of variables and parameters for basic runs 129
26. Restrictions imposed for completion of Tables 16 and 17 131
27. Restrictions imposed for completion of Tables 18 and 19 131
ILLUSTRATIONS
1. Actual and Predicted Migration, Post World War II Japan 35
2. Migration Elasticities with Respect to FarmNonfarm Income Differences and
to the Labor Force Ratio, Postwar Period Elasticity 40
3. Flow of Funds and Related Variables 19091938, 19551970 47
4. Momentary Equilibrium Determination 62
5. Actual and Simulated Per Capita Outputs, Prewar Period 83
6. Actual and Simulated Labor Force Levels, Prewar Period 84
7. Actual and Simulated Capital, Prewar Period 85
8. Actual and Simulated Terms of Trade Between Agricultural and Nonagricultural
Sectors, Prewar Period 86
9. Simulated Wages and Capital Returns, Prewar Period 87
10. Actual and Simulated Per Capita Outputs, Postwar Period 90
11. Actual and Simulated Labor Force Levels, Postwar Period 91
12. Actual and Simulated Capital, Postwar Period 92
13. Actual and Simulated Terms of Trade Between Agricultural and Nonagricultural
Sectors, Postwar Period 93
14. Simulated Wages and Capital Returns, Postwar Period 94
15. Annual Migration and Related Variables, 19051972 111
FOREWORD
The appropriateness of an agricultural development strategy, the intensity with
which that strategy is pursued, and the effect it has upon agricultural growth and
fulfillment of nutritional and income needs all depend upon the nature of the
interdependency and linkages between agricultural and other sectors of an economy.
The importance of these links is emphasized by the frequent failure of effective
demand for food to accompany increased agricultural production and by the too
frequently encountered reticence of official growthoriented planning agencies and
finance ministries to accord high priority to the types of rural expenditures requiring
massive resource allocation.
The research program of the International Food Policy Research Institute includes
work on several aspects of this linkage problem, among which are analysis of the
influences on effective demand for food, the sources of agricultural growth, and
descriptions of production and consumption linkages of agriculture to the other
sectors of the economy.
Research conducted by Yair Mundlak at IFPRI has led to the development of a
model for analyzing the relation between particular aspects of agricultural growth and
other sectors of the economy. The model is elegant and illuminating. Applied to Japan
in this Research Report, it gives particular emphasis to the role of capital and labor
flows among sectors and the effect of these flows upon growth. Yair Mundlak is
currently applying the model to Argentine data, and exploratory discussion on using
it with Mexican data is under way. As IFPRI's research on growth linkages increases,
this model, and modified versions of it, will be useful in quantifying relationships and
in diagnosing the potentials for faster, more efficient growth.
John W. Mellor
Washington, D.C.
February 1, 1979
ACKNOWLEDGEMENTS
Much of the discussion on economic growth is inspired by stylized facts. The casual
observer can easily discover that while the style has remained fairly constant over a
long period of time, the facts vary a great deal over time and space. Thus, it is
suggested that more insight can be gained by concentrating on the facts. I was
fortunate and grateful to learn that IFPRI shared a similar view and was willing to
sponsor its implementation in the study of agricultural growth. This research report
brings together the first set of results of this study, some of which have been
previously circulated as individual papers.
This study is largely empirical in nature and could not.have been accomplished
without the assistance of various individuals to whom I am greatly indebted. The
burden of the empirical work was very skillfully carried out by John Strauss. The
computer program for the numerical solution of the growth path was written by Selig
Starr. The final stages of the computations were carried out by Diane Skellie.
Earlier drafts of some chapters were discussed at IFPRI seminars and were also read
by Tuvia Blumenthal, James Gavan, Constantino Lluch, and Virabongsa Ramangkura.
Their valuable comments affected the preparation of the final draft. This final draft
was edited by Charlene Semer. Kate Hathaway and Barbara Barbiero were responsible
for bringing the manuscript through the press.
1
A FRAMEWORK FOR ANALYSIS AND SOME CONSEQUENCES
Most of the world's population still lives in countries that are largely rural, and the
development of such countries is of general interest. The development of a rural
economy is largely related to the development of its agricultural sector.1 The agricul
tural sector is not isolated; however, it is interdependent with the rest of the economy
through the factor and product markets, and changes in such markets affect all major
sectors. This interdependence must be taken into account when important policy
questions and measures are considered and evaluated. Specifically, the effects of
changes in resource endowment and in supply of final or intermediate products (for
instance, due to foreign aid) cannot be limited to one sector, and the feedback
cannot be ignored. That, of course, also holds true with respect to price policies,
changes in technologies, and any other important measures.
The Framework of the Present Analysis
In dealing with the role of agriculture in the process of economic growth, it is
important to have a conceptual as well as an operational framework which takes into
account the relationships between agriculture and the rest of the economy. Such a
formulation can be constructed at various levels of aggregation. The decision on the
level of aggregation should largely depend on the questions asked: the more specific
the question, the less aggregated the models. When disaggregation is carried far
enough, however, the problem may well be studied within a partial rather than
a general framework.
The present framework is general, and the analysis is carried out at the highest level
of aggregation, which facilitates concentration on the process of agricultural growth.
It should be noted that aggregation is not the invention of the analyst but is rather a
result of the need to simplify. We talk about agriculture and agricultural policy or food
and food policy under the assumption that they convey unambiguous meanings.
When we need to deal with a specific product, we refer to that product. Similarly, the
present framework could be disaggregated to any desirable, and yet meaningful,
degree.
In order to be able to assess the consequences of development policies, it is
necessary to understand the process of growth. The distinction between the two
concepts is made here in order to emphasize that the concept of development implies
some intervention in the process of economic growth. Intervention is generally
motivated by the desire to achieve targets, such as higher rates of growth or im
'This is also well recognized by policy makers. Cf. Chapter 2, "Policy and Strategy," National Commis
sion on Agriculture, Government of India, Abridged Report (1976).
provement in the distribution of income or consumption, and it will result in altering
the process of growth. A full understanding of these results requires evaluating them
within a dynamic framework which allows comparing the growth paths that will occur
under different intervention measures in any given economy.
There are various models that deal with sectoral growth in the context of general
equilibrium.2 However, the empirical relevance of such models has not been estab
lished. The main difficulty emerges from a rather fundamental methodological flaw:
the process of resource allocation is detached from real time. To explain this point,
reference is first made to neoclassical general equilibrium models, which assume that
at any point in time factor prices are equal among the various sectors.3 Geometrically,
such equality is achieved by finding a point on the transformation frontier of the
economy which also satisfies the demand conditions. Being on the efficiency frontier
implies equal factor prices across sectors. Once this point is achieved, time is brought
in by assuming a given rate of growth for the primary resources, and the growth path
is evaluated.
There is nothing wrong with the logic of such a model, only with its relevance. This
is particularly so with respect to labor surplus economies, in which reaching the point
of factorprice equality may require several decades. To make the model more
realistic, it is important to take explicit account of the fact that it takes time for
resources to be allocated and that the rate of such allocation is an economically
determined quantity. This is the approach of this work.
Chapter 5 presents the model and illustrates some empirical results. Basically, the
model starts with the assumption that at any given point in time resource allocation is
predetermined and, given the technology, the total product supply is also predeter
mined. Product prices are determined by the demand for final consumption and for
investment. Given the technology and the resource allocation, factor shadow prices
are determined, and they in turn determine the flow of resources from a sector of low
to a sector of high returns. This resource flow, together with population growth and
capital accumulation, determines the availability of resources to the two sectors in the
next period. Adding the effects of changes in technology, product supply in that
period is determined, and the process repeats itself.
This system can be described by difference equations which are solved numeri
cally. The solutions are data specific; unlike analytic results, they are not data robust.
But perhaps this is the strength, rather than the weakness, of the model. Growth
scenarios are generated for given initial conditions, and it is quite likely that given
exogenous changes will produce different effects on the growth paths in different
countries. Some empirical applications are demonstrated.
The key relationships in this model are the intersectoral resource flows. Chapters 2
and 3 deal with labor migration, and Chapter 4 deals with the flow of savings out of (or
2Some of the models evolved from the work of W. A. Lewis on labor surplus economies: "Economic
Development with Unlimited Supplies of Labor," The Manchester School of Economics and Social Studies,
22 (1954): 139191, and "Unlimited Labor: Further Notes," The Manchester School of Economics and Social
Studies, 26 (1958): 132. This model emphasizes some important aspects of the early stages of development
but overlooks other aspects.
3Cf. Y. Mundlak and R. Mosenson, "TwoSector Model with Generalized Demand," Metroeconomica, 22
(1970): 22758.
into, as the case may be) agriculture. The basic premise in dealing with these flow
equations is that the flow of resources is motivated by differential returns. This is
hardly a new notion. Yet, as elementary as it is, it has not been documented suffi
ciently in the empirical literature. This fact may reflect misspecification of the basic
equation. Chapter 2 discusses the specification of labor migration out of agriculture
and applies it to country crosssection data. The advantage of such data is that they
have a wide spread in the explanatory variables. The outcome is an empirical migra
tion equation that relates the rate (per unit of time) of labor migration out of agricul
ture to economic variables.
The empirical migration equation is integrated into the model to produce numeri
cal solutions. In this case, it is desirable to use an equation derived for the country
under investigation. The difficulty with country data is that the spread in the explana
tory variables is by far narrower than with the crosssection data. This problem is
discussed in Chapter 3, which deals with the estimation of the migration equation for
Japan.
Applying a similar approach to the flow of savings out of agriculture requires data
which are not readily available. Chapter 4 deals with this problem, again using the
data for Japan. There are no data based on direct observation of the rate of flow of
savings out of agriculture, but estimates were constructed under alternative assump
tions with respect to sectoral savings behavior. The resulting time series of the rate of
flow is used to estimate the savings flow equation. This equation, like the labor
migration equation, explains the rate of savings flow in terms of differential returns
and other economic variables. Chapter 6 integrates these results and applies the
model to the analysis of some of the issues related to the contribution of agriculture to
economic growth in Japan.4
Summary of Selected Results
An important feature of this analysis is that, in evaluating numerically growth paths of
the economy, it is data specific. However, the way the model postulates the work of
the system depends to a large extent on the process of intersectoral resource alloca
tion. For this reason, the study of the intersectoral factor flow is of as much interest as
the evaluation of the consequences of these flows. Together, these empirical analyses
have general implications, both in terms of formulating the problem and in terms of
the actual results. We therefore start our summary with the flow equations.
Labor Migration
It has been postulated that the rate of migration out of agriculture is determined by
the income differential between the two sectors, the composition of the labor force,
'Japan was selected for the empirical analysis in this volume for a combination of reasons: it has recently
undergone the transformation from a largely rural to an industrial economy; it has good data which are
readily accessible, and its experience has been analyzed by many writers, making it possible to draw on
such analyses and to compare results.
the natural growth rate of the labor force, and some other related variables. A
migration function was formulated that takes the role of each of these variables into
account. The function was first fitted to data for 70 countries for the decade 1960 to
1970 (or thereabout) as well as for 17 Organization for Economic Cooperation and De
velopment (OECD) countries for two decades, 1950 to 1960 and 1960 to 1970. For the
70country sample, the average annual migration rate was 2.1 percent (of the agricul
tural labor force) and the range was from 0.2 to 6.7 percent. The variables used explain
the intercountry differences in the rate of migration very well. Furthermore, for the
subsample of the OECD countries, the results did not reveal a "decade effect," nor
were there any important differences between the results obtained for the OECD
countries and for the whole sample, which includes less developed countries. It
appears, therefore, that the economic variables capture a good part of the systematic
variations in the rate of migration.
There has been a great deal of discussion, which usually lacks any empirical
content, as to how the income differential should be measured. In the present
formulation, there is a builtin mechanism to find whether the particular variable used
to represent income maintains the property that migration stops when the income
differential disappears.
A similar analysis was conducted for Japan, which realized a rapid migration in the
postwar yearsthe average migration rates were 1.1 percent for 191040 and 4.7
percent for 195172. The same formulation that was used for the country crosssection
explained Japan's postwar migration well. In order to explain the prewar migration,
the level of activity of the economy was also introduced into the analysis and new
variables were created in order to reduce the number of parameters. By doing this, it
was possible to pull the two periods together and develop a single equation that
summarizes the Japanese experience.
Flow of Savings
The development of the Japanese economy was accompanied by a flow of savings
from agriculture to the rest of the economy. Measurement of this outflow was
obtained by indirect calculations that depend on the saving rates in the two sectors.
Although these saving rates are not known, they were estimated for the prewar data.
The estimates indicate that saving rates in agriculture remained constant and rela
tively high and that saving rates in the rest of the economy were lower, but increased
with per capital production in that sector. The savings flow series was obtained under
various assumptions with respect to the ratio of saving rates in the two sectors.
The basic premise that was tested and empirically supported by this study is that the
flow of savings can be attributed to differential returns to capital in the two sectors.
The magnitude of the response of the savings flow to changes in differential returns
depends on the data series used to measure the flow and to measure differential
returns. The response of the flow, measured as a percentage of agricultural savings, to
a change in differential returns on capital, measured in terms of average produc
tivities, was .566 when saving rates were assumed to be equal in the two sectors; it was
.214 when the agricultural saving rate was assumed to be twice that of the nonagricul
tural sector.
Complementarity of Factor Flows
Savings flow plays an important role in the process of development. The flow is
initiated by higher capital returns in the nonagricultural sector; that is, when there are
better opportunities out of agriculture. In a static situation, the flow of savings tends
to equalize returns in the two sectors, and eventually the flow will diminish. The
process cannot be isolated from other processes, however. There is a flow of labor
along with the flow of capital, and the two flows affect each other. The migration of
labor out of agriculture increases the capitallabor ratio in agriculture, which reduces
the rate of return on agricultural capital and increases it in the other sector. Thus,
labor migration increases the differential in returns and augments the flow of savings.
By a similar argument, the flow of savings augments the migration of labor. These
complementary relationships between labor and savings flows imply that the low
income sector contributes to increases in both capital and labor in the highincome
sector.
Consequences of Factor Flows
The nature of the Japanese experience and the lessons to be drawn from it have
been discussed by various authors. There is a general agreement among most writers
that savings flows out of agriculture provided an important source of funds for the
growth of the nonagricultural sector. The present framework was used to examine
this issue as well as other related issues. Basically, the method of evaluating the
importance of a particular variable is to compare the growth paths of the economy
under various assumptions with respect to the value of that variable. For instance, in
order to assess the importance of savings flow, a growth path is obtained under the
assumption of no flow, and this path is compared with that obtained under the actual
situation as reflected by the flow equation. This is simply an exercise in comparative
dynamics in which the effect of a particular change is evaluated, not only in the
present, but also in the periods that follow. In order to carry out this comparison, it
was first necessary to fit the model to the Japanese data; that is, the empirical values
that were selected for the parameters in question were those which generated growth
paths reasonably close to the actual data.
This evaluation indicated that the contribution of the outflow of agricultural savings
did not contribute much to the growth of the nonagricultural sector in Japanat least
not since 1907, the beginning year for the analysis. The quantitative effect of savings
outflow has been by far less important than that of labor migration. Labor seems to be
the dominant contribution that Japanese agriculture made to the growth of the
nonagricultural sector.
Regardless of the verdict on the role of intersectoral savings flow, one can still
conclude that social organizations that are conducive to the reallocation of resources
in line with their relative returns contribute to economic growth. Other things being
equal, the larger the intersectoral difference in returns, the larger the potential for
growth from resource reallocation.
Savings, Capital Accumulation and Technical Change
High saving rates in Japan, particularly in the postwar period, resulted in rapid
capital accumulation. Thus, high saving rates are usually considered to be a major
factor contributing to Japanese growth. It turns out, however that the direct quantita
tive effect of this accumulation on growth is not conspicuously large. Those who
believe that the effect of capital accumulation is pronounced may find it difficult to
demonstrate this belief convincingly to a nonbeliever. Such an endeavor would
probably require attributing to capital accumulation an important effect on technical
change, along the lines of the embodiment hypothesis. If this approach proves to be
successful, then it may also lead to modifying the view suggested here with respect to
the quantitative effect of the savings outflow.
In considering such an approach, however, it might be noted that although the
flow of agricultural savings financed only a relatively small fraction of nonagricul
tural investment, throughout most of the period the outflow represented a relatively
large proportion of agricultural savings. Consequently, if technical change depends
significantly on the rate of investment, then the savings flow should have created a
wide gap between the rates of technical change in the two sectors. On the surface,
this is not clearly supported by evidence, but it is a point that requires more attention.
Whatever the causes of technical change, it is clear that it played an important role
in Japanese development. It basically freed agricultural resources to move into the
nonagricultural sector.
Some Reflections
Some of the reasons the present framework was chosen may not be readily appar
ent, and some aspects of the framework may raise questions or suggest directions for
future analysis. These considerations call for some comments.
Scope
Growth is generated by having more resources and by using them more efficiently.
This is well known, and for that reason, there is no need for frameworks of the kind
discussed here. Furthermore, some important issues related to agricultural growth
can be discussed without explicit reference to sectoral interdependence.5 There are
some important issues that may be discussed better within a comprehensive frame
work, but the choice of formulation still is determined by the purpose of the dis
cussion." The present framework emphasizes an explicit sectoral formulation, not for
its own sake, but as a framework tor empirical analysis. The purpose here is to
formulate a model that can be given empirical content and that generates results
which can be confronted with the actual data. Such a model makes it possible to
5Cf. T. W. Schultz, Economic Growth and Agriculture (New York: McGrawHill, 1968).
6Cf. John W. Mellor, The New Economics of Growth: A Strategy for India and the Developing World
(Ithaca and London: Cornell University Press, 1976).
provide a quantitative assessment of the effects of applying various policy instru
ments. Again, there is nothing new in this endeavor in general, although it is less
common in the framework of growth analysis.7
The desirability of having a framework that can be confronted with the data led to
replacing the neoclassical model with what is considered to be a more realistic, and
therefore more productive, formulation in which the role of resource allocation is an
economically endogenous variable. In this formulation, the rates and the directions
of changes of variables in the economy are not determined solely by exogenous
factors.
It appears that the end product may offer a convenient framework for analyzing
substantive issues related generally to sectoral growth and specifically to agricultural
growth. It should also prove useful in organizing and integrating research because it
brings together various subjects such as production, consumption, and sectoral and
functional income distributions. Of course, the present formulation is just an instru
ment in the analysis and can be modified according to needs.
Methodology
Applying the model requires fitting it to the data. The system is a dynamic one, and
the choice of parameter values affects the various variables, not only at a given point
in time, but also along the growth path. Any selection of a single criterion for judging
the choice of the empirical values for the parameters in question is at best arbitrary.
Thus, there can be various sets of parameters that will give reasonable fit. Fur
thermore, there is no need to assume or require that the parameters remain constant
throughout the period of application. In the method used here for computation, it
may be relatively simple to allow the parameters to change with time or with the
values of some of the variables of the model. Thus, though we deal with a variable
coefficients model, we have not pursued the possibilities of varying coefficients very
far, except that we have a different set of values for the prewar and postwar analyses.
Basically, the question raised here is the question of identification, which, in the
present framework, may be more acute than in the standard, constant coefficient
model. However, it should be kept in mind that this problem is not peculiar to this
particular model; it is of a rather general nature and faces every researcher who tries
to infer from data, regardless of whether he uses a formal model to do so.
Substance
The emphasis in this work has been on the nature and consequences of resource
allocation in the process of growth. More profoundly, there is an attempt to view
correctly the process of economic dynamics in which the economy is ever adjusting to
changing conditions at rates that are considered to be economically endogenous
variables. Such aview is applicable to many subjects in economics. Our objective has
7There are some possible exceptions. Cf. A. C. Kelly, J. G. Williamson, and R. Cheetham, Dualistic
Economic Development (Chicago: University of Chicago Press, 1972).
been to apply it to the study of agricultural growth. In so doing, we have formulated
the growth process. Naturally, such a formulation does not cover exhaustively all
phenomena that are, or may be, pertinent to growth. The work can, and should, be
broadened so as to also include the study of those phenomena. Such a study will
require modifications in the formulations of the economy, but it can be conducted
within the framework suggested here and thus lead to confrontation with the data.
Growth models generally view growth as primarily supplydetermined. The ques
tion has been posed whether this view is justified and whether growth should not also
be viewed as demanddetermined.8 Stated differently, the question is whether there
is really a dichotomy between shortrun and longrun macro models. Our formula
tion has gone part way in incorporating demand in the analysis. Yet longrun phe
nomena, such as unemployment in what is called labor surplus economies, require
some further consideration.This question is related to the scope of the analysis and
the extent to which the nonagricultural sector can be made to grow much faster.
Another aspect of the role of demand appears when the economy has access to
foreign markets. The extension of the formulation to include foreign trade may have
an important effect on sectoral development; the nature of the effect, of course,
depends on whether the country is foodexporting or foodimporting. In addition to
the immediate effect on the sectors, there is an effect on domestic investment,
depending on the direction or sign of foreign savings. Because the size and sign of
foreign savings depends on world price variations, the inclusion of foreign trade
brings in possible fluctuations that may have an important effect on the countries in
question.9
The present formulation assumes that decisions are made freely by individuals in
the system. To take a step toward reality, the model should be extended to include
government and the various effects that it may have on the system.10 Such an exten
sion will provide policy instruments intended to affect the development of the system
and at the same time will provide the framework for quantitative evaluation of the
effectiveness of these instruments.
Along with foreign trade, there are many other sources that may introduce fluctua
tions into the economy. One source is particularly worth mentioning: the depend
ence of agriculture on the weather. Granted that there are fluctuations that cannot be
avoided, the question is whether such fluctuations have any effect on growth in
general and sectoral growth in particular or whether growth depends only on average
performance.
81 am indebted to John Mellor for pointing this out to me.
'The experience of the seventies provided plenty of evidence on this subject. Cf. D. G. Johnson, World of
Agriculture in Disarray (London: Macmillan, 1973).
"1This is not the place to list the various effects that government may have on system. Yet it should be
mentioned that some of the agricultural outflow of savings was brought about in Japan, as well as in other
countries, through the tax system.
2
MIGRATION OUT OF AGRICULTURE: EMPIRICAL ANALYSIS
It is well known that economic growth leads to changes in the industrial composi
tion of the economy, and these changes, in turn, affect the growth rate of the
economy.1 The aspect of immediate interest to this study is the declining importance
of agriculture.
A change in industrial composition results from a change in resource allocation,
including that of labor, leading to "occupational migration." Part of this phenomenon
involves actual occupational changes by workers, and part involves different occu
pational choices by new employees. The relative importance of these two situations
depends largely on the rate at which the economy changes its industrial composition
compared with the natural rate of population (labor force) growth. Regardless of
which force is dominant at any point in time, existing employment opportunities
dictate the allocation of workers among different occupations: the more attractive
the new opportunities are, the more people will pursue them. It is this premise,
almost axiomatic to economists, that this study purports to measure.
Occupational mobility is closely related to geographical mobilityat leastwhen the
migration is away from agriculture. The two measures are not identical, however, and
need not be so. The general subject of migration is not new; a recent, partial survey
listed 250 references on the subject.12 More specifically, there is a considerable body
of literature dealing with the empirical aspects of migration away from the farm. This
literature deals largely with the American experience.13
"The seminal work of Simon Kuznets has quantified various aspects of this process; see, for example,
Modern Economic Growth, Rate Structure and Spread (New Haven: Yale University Press, 1966) and
Economic Growth of Nations: Total Output and Production Structure (Cambridge: Harvard University
Press, 1971).
12M. J. Greenwood, "Research on Internal Migration in the United States: A Survey," Journal of
Economic Literature 13 (1975): 397433.
'3See, for example, C. E. Bishop, "Economic Aspects of Changes in Farm Labor Force," in Labor Mobility
and Population in Agriculture (Ames: Iowa University Press, 1961); G. K. Bowles, Farm PopulationNet
Migration from the RuralFarm Population, 19401950, U.S. Department of Agriculture, Agricultural Market
ing Service, Statistical Bulletin no. 176 (Washington, D.C., June 1956); D. E. Hathaway, "Migration from
Agriculture: The Historical Record and its Meaning," American Economic Review 50 (1960): 37991, and
"Improving the Search for Employment" (Paper delivered to the Conference on Creating Opportunities for
Tomorrow, 1968); W. E. Johnston, "Projecting Occupational Supply Response," in Study of U.S. Agricul
turalAdjustments, ed. G. S. Tolley (Raleigh: North Carolina State University, n.d.); W. E. Johnston and G. S.
Tolley, "The Supply of Farm Operators," Econometrica 36 (1968): 36582; and L. A. Sjaastad, "Occupational
Structure and Migration Patterns," in Labor Mobility and Population in Agriculture (Ames: Iowa University
Press, 1961).
In recent years, farm migration has come to a halt in the United States.14 The process
has also ended in some other mature economies, and the lessons to be drawn from
their experiences have become particularly important as interest in economic devel
opment grows. An important role in development has been attributed to migration
out of the traditional sectorusually agricultureinto the modern sector.15 The
emphasis placed on surplus labor in this process immediately raises the question of
how the labor market mechanism operates in the traditional sectorspecifically,
whether labor in that sector is at all productive at the margin. Some interesting
evidence has been produced that the marginal productivity of such labor is, indeed,
positive.16
Sectoral migration is of prime importance and bears important policy implications,
as well as an analytic role. The analysis of sectoral migration is associated with the
attempt to model and quantify the causal relationships that are involved in the
process of growth and development. An interest in these relationships prompted the
present study.
In spite of the importance of the subject, however, there does not seem to be any
empirical sectoral migration equation at the macro level. The reason for this void is
not clear. It is possible that aggregation blurs the data and makes it difficult to obtain
acceptable estimates. Whether or not this is the reason, it is clear that if such an
equation is important, the data should reveal it, and there must be a wayto estimate it.
It has been suspected that the lack of empirical macro equations reflects lack of
success rather than lack of attempts.17 A good reason for the lack of success may be
the use of data with little spread in the interesting variables and considerable spread
in other variables. For this reason, the present study uses data with large spread in the
important variablesthat is, country crosssection data.18
The following section deals with the formulation of the problem; it relies on
existing and known concepts, and it concentrates on bringing these concepts to
gether for the purpose at hand. The next section presents the empirical results. A few
concluding remarks appear in the final section. The data sources are discussed in
Appendix A.
1E. G. Schuh, "The New Macroeconomics of Agriculture," American Journal of Agricultural Economics
58 (1976): 80211.
"See W. A. Lewis, The Theory of Economic Growth (London: Allen and Unwin, 1955); G. Ranis and
J. C. H. Fei, "A Theory of Economic Development," American Economic Review 51 (1961): 53365; and
D. W. Jorgenson, "The Development of a Dual Economy," Economic Journal 71 (1961): 30934.
"See T. W. Schultz, Transforming Traditional Agriculture (New Haven: Yale University Press, 1964),
chapter 4.
"1For partial results, see Sjaastad, "Occupational Structure," and Bishop, "Economic Aspects."
"The use of information based on country cross sections is not new. For instance, a great many of Simon
Kuznets' findings are based on this type of data. There are also known works using regression analysis
based on such data; for example, in consumption functions: H. S. Houthakker, "An International Com
parison of Household Expenditure Patterns: Commemorating the Centenary of Engel's Law," Economet
rica 25 (1957): 53251; in production functions: K. J. Arrow, H. B. Chenery, B. S. Minhas, and R. M. Solow,
"Capital Labor Substitution and Economic Efficiency," Review of Economics and Statistics 43 (1961): 22550;
and in development: H. B. Cheneryand M. Syrquin, Patterns of Development, 19501970 (London: Oxford
University Press, 1975).
Model Formulation
The background for our model is a neoclassical, twosector economy, consisting of
an agricultural sector and a nonagricultural sector.19 Appropriately specified, such an
economy has a competitive shortrun equilibrium in which wage rates of the homo
geneous labor input are equal in the two sectors. Changing the exogenous variables
(which need not be specified here) results in a new shortrun equilibrium. It is thus
possible to obtain a sequence of shortrun equilibrium solutions that yield, among
other things, the labor allocation and wage rates. Two aspects of this process are
worth emphasizing: first, no calendar time enters the formulation; and second, wage
rates are always the same across sectors. In this context, migration simply reflects a
change in the competitive allocation of labor.
These two aspects limit the empirical application of the model. The two points are
not independent. Labor mobility is hindered by friction, and as a result, low rate of
mobility is insufficient to lead to wage equality; consequently, the data show wage
differentials across sectors. Specifically, in terms of our dichotomy, agriculture is the
net supplier of labor, andbecause of the friction on mobilitythe wage rates in
agriculture are lower than in the nonagricultural sector. It is possible to analyze the
behavior of the economy under the constraint of wage differentials.20 In order to
endogenize the wage differentials, however, it is necessary to take explicit account of
the determinants of the rate of migration. To do this, we have formulated a migration
equation.
The basic premise of the equation is that migration is motivated by an income
differential, which we denote by 8. Migration is also affected by exogenous variables
(z) to be specified later. The premise, then, is that
M=f(6,z), f > 0, (2.1)
where
M = migration from the agricultural to the nonagricultural sector per unit of time,
and
f8 = partial derivative with respect to 8.
Equation (2.1) takes no account of the size of the agricultural labor force (L1), which
constitutes the source of labor supply. For any given value of the argument of (2.1)
migration should increase with L,.21 In addition, migration depends on prospects in
the nonagricultural sector, and those can be measured by L2, the nonagricultural
19Cf. Mundlak and Mosenson, "TwoSector Model," pp. 22758.
20Cf. Z. Tropp and Y. Mundlak, Distortion in the Factor Market and the Short Run Equilibrium," Discus
sion Paper 454, Harvard Institute of Economic Research (Cambridge, 1976).
21 P. Zarembka, "Labor Migration and Urban Unemployment: Comment," American Economic Review 60
(1960): 18486; and H. S. Houthakker, "Disproportional Growth and the Intersectoral Distribution of
Income," in Relevance and Precision, from Quantitative Analysis to Economic Policy; Essays in Honor of
Pieterde Wolff, eds. J. S. Cramer, A. Heertje, and P. E. Venekamp (Alphen aan den Rijn: Samsom and New
York: North Holland, 1976).
labor force. A given rate of migration will be absorbed more easily with a larger
absorbing sector.
The introduction of L, and L2 into the migration equation should be done in such a
way as to maintain a "constantreturnstoscale" property with respect to the size of
the country. That is, for any given 8 and z, doubling the size of the country, and
therefore the labor force in the two sectors, should double the migration. When (2.1)
is expanded to include the labor force variables, then
M = f (8, z) L11" Li, 0 < 3 < 1. (2.2)
The equation can also be written in terms of migration as a proportion of the
agricultural labor force.
m = f (8, z) r", (2.3)
where
m = M/LI, and
r = L2/L,.
In addition to the existing composition of the labor force, migration is affected by the
rate of growth of the labor force, n. Adding this factor to equation (2.3), then
m = f(8,z)r12(1 +n)13. (2.4)
The introduction of (2.4) to a twosector model makes it possible to "close" the
model and to trace its equilibrium path, which also determines the values for 8 and r,
as a function of time and the exogenous variables in question.22 However, statistically
8 and r are predetermined at any point in time, and (2.4) basically can be estimated by a
single equation method.
Definition of the income variable depends on the nature of the decision made by
the individual. If the nonfarm opportunities are close to, or in, the rural areas and
there is a continuous twoway shift between the two sectors, wage rates may be
appropriate for measuring income differentials. If, however, the decision involves
changing occupation and possibly residence as well, then the relevant variable
should be the discounted stream of income over the life horizon.23 To allow for
uncertainties about obtaining a job in the new sector, Todaro suggested that earnings
be weighted by their probabilities.24 Because the present analysis is concerned with
22Houthakker, "Disproportional Growth," and J. R. Harris and M. P. Todaro, "Migration, Unemployment
and Development: A TwoSector Analysis," American Economic Review 60 (1970): 37991.
"2L. A. Sjaastad, "The Cost and Returns of Human Migration," Journal of Political Economy, Supplement,
70 (1962): 8093.
24M. P. Todaro, "A Model of Labor Migration and Urban Unemployment in Less Developed Countries,"
American Economic Review 59 (1969): 13848.
longrun structural changes, expected income, rather than wage rates, is the more
appropriate variable.
If V,(t) and V2(t) are the expected lifetime earnings in sectors 1 and 2 respectively,
and C(t) is the cost of migration, then the assumption is that a person will tend to
migrate as long as
V2(t) V,(t) > C(t). (2.5)
Using this formulation, it is possible to justify the monotonicity of migration with
respect to 8. Individuals are not homogeneous in their expected earnings and costs of
migration, but the larger the gap between the two sectors, the more individuals will
find that the difference in earnings justifies the change.
This argument may seem somewhat inconsistent with the assumption of homoge
neous labor, which is made in simple models. However, one attribute, age, enters
here which does not violate the assumption of homogeneous labor. The integrals
which result in V,(t) and V2(t) depend on the planning horizon, 7. It is possible that a
given difference in the rates of earning may meet the condition of (2.5) for a large
value of T but not for small values. Furthermore, the cost of migration by itself is likely
to decrease as r increases.25 For this reason, we may expect the younger age groups to
be more than proportionately represented among migrants.26
The expected income variables are not directly measurable. In aggregate analysis, it
is possible to approximate them by using the average percapita production originat
ing in the respective sectors and allowing for growth. Strictly speaking, the discussion
calls for a measure based on labor income; but there is no need to be so restrictive
because it is not quite clear that people exclude nonwage income from their life
expectations.
A question that has been dealt with in various works is the extent to which
unemployment in the nonagricultural sector affects migration. The essence of To
daro's formulation has been to show that migration is compatible with unemploy
ment in the receiving sector. The result is obtained by weighting the future stream of
income by the probabilities of being employed. The probabilities are approximated
by the proportion of employment to total labor force in the receiving sector. This
approach offers one way to handle the effect of unemployment empirically. Consist
ent treatment, however, calls for a similar allowance for employment contingencies in
agriculture; for that matter, there is a tendency to disregard unemployment in
agriculture, which is questionable in itself. However, in agriculture, there is addi
tional uncertainty with respect to natural factors such as floods and droughts. It would
be desirable to account for some of these nonwage considerations that affect migra
tion.
To formulate (2.4) more explicitly for empirical study, the equation is assumed to be
25Younger persons, whose planning horizons are long, are likely to have a lower cost of migration. Cf.
A. Schwartz, "Migration, Age and Education," Journal of Political Economy 84 (1976): 70119.
26For empirical evidence on this question, see Bowles, Farm Population; Hathaway, "Migration from
Agriculture"; Kuznets, Modern Economic Growth, p. 125; Johnston, "Projecting Occupational Supply,"
p.146.
of the CobbDouglas form. To allow for zero migration, the variable (8 c,) is used
instead of 8, where c, is some constant. Thus,
m = eo(8 ci)"1 rl2( + n)3Z l4, (2.6)
and when 8 = ci, then m = 0. By definition, a natural value for c, is 1; that is, an
ideal measure of the income differential, (8 cl), should lead to no migration if
the income ratio is 1. However, it is not quite clear that a reported income series
fulfills such a requirement. First, there is the uncertainty referred to above. In
addition, favorable arguments have been advanced for the quality of farm life.
The uncertainty argument should lead to a value of c, that is smaller or larger than 1,
depending on whether uncertainty is larger or smaller in the receiving sector as
compared with the sector of origin and on individual attitudes toward risk.27 If the
quality of farm life is more attractive than the "city lights," the value of c, would tend
to be larger than 1; that is, it would require a premium to get people out of agricul
ture.
To some extent, the relative importance of these two considerations depends on
the level of development. The quality of life argument is perhaps more important in
wealthier economies, where it might be possible to have negative migration. To allow
for negative migration, a constant, Co, can be added to the lefthand side of (2.6).
Thus, the basic equation that is actually estimated can be written as
Mn (m+Co) = /o + g3 en (8c,) + 32 enr+13 en (1+n) + 34 enz+u, (2.7)
where u is a disturbance variable, which we assume to possess the standard proper
ties. It should be noted that the value of c, which corresponds to zero migration
obviously must be related to the value of co.
The exogenous variables, represented by z, have not been specified thus far. The
working hypothesis was that education contributes to mobility.28 As a measure of
education, we used the proportion of secondary school enrollment to the second
aryschoolage population. A more appropriate variable would have been the level of
education in the migrating sector, but such data were unavailable. The second
variable represented in z is age. Each of two measures was used: (1) persons aged
1529 as a proportion of total population, and (2) persons aged 3039 as a proportion of
total population.
Empirical Results
Data on 72 countries for the years 1960 and 1970 constitute the basis for the
crosssection analysis. The data and their sources are discussed in Appendix A. The
27The variable c, could be considered to depend on the risk and other variables as well. This formulation
is not explored here because the sample data are not sufficiently rich to allow empirical analysis.
28M. Gisser, "Schooling and the Farm Problem," Econometrica 33 (1965): 58292.
labor force data are the economically active population in the farm and nonfarm
sectors. The simple average annual migration over the decade was obtained from
these data by comparing the actual labor force with that which would have been
realized if there had been no migration. The resulting formula is
M = 1/t (Lt) 1 +n, ot (2.8)
1+n
where
M = simple average annual migration,
n, = decade rate of growth of the agricultural labor force,
n = decade rate of growth of the total labor force,
Lt = total labor force in year t,
10 = proportion of sector 1 in the total labor force in the base year, and
it = proportion of sector 1 in the total labor force in year t.
For some countries, the data are for years other than 1960 and 1970; in these cases,
simple annual average migration is calculated by dividing migration during the rele
vant period by t, the number of years between the two surveys.
There is no series of sectoral labor force growth rates covering all the countries in
question, so we computed two migration series. In series 1 (ml), we assumed growth
rates are equal in the two sectors; series (M2) assumes they are different. The
difference in labor force growth rates between the rural and urban sector may be very
high, as much as 3 to 1.29 However, it is unlikely that this ratio is a constant; it is more
likely that it declines in the process of development. For series 2, then, we assumed
that (1) at one limit, f, = 1 and n2 = 1/4 nj, where n2 is the labor force growth rate for the
nonfarm labor force; (2) at the other limit, ei =0 and n2=nj; and (3) intermediate
values are given by linear interpolation. Using n = en, + e2n2, this assumption leads
to
n = nl (1 % f[12). (2.9)
The M2 series was computed by substituting (2.9) in (2.8). As expected, the two series
are highly correlated and yield basically similar results.
Because the statistics used are for the economically active, rather than the total,
population, we dealt primarily with occupational, rather than geographical, migra
tion. The two are different, though related, concepts, but occupational migration is of
more immediate interest in the present context.
The income variable was measured by the ratio of the average productivity in sector
2 to that in 1, where the average productivity was obtained by dividing the gross
domestic product (GDP) originating in each sector by the economically active popula
tion in that sector. The labor force data include the unemployed, and therefore
29Kuznets, Modern Economic Growth, p. 116.
average productivity was adjusted for the probability of obtaining employment in
Todaro's sense.
Estimates Using Equal Growth Rates
The main results for the first migration series are summarized in Table 1. The
regression was obtained by ordinary least squares (OLS), with some iteration on Co
and c1.30 The first five regressions in the table report some interesting results of this
iteration. All the variables proved to be empirically pertinent and to possess the right
sign; as expected, the coefficient of r is a positive fraction. There was no particular
prior expectation about the order of magnitude of the coefficients.
Considering the fact that the dependent variable is migration as a proportion of the
agricultural labor force, rather than total migration, the fit is rather good. The iteration
on the c's slightly affects the fit and the tratios.31 Somewhat better results were
obtained for co = 0.012 and c, = 0.5.32 When the values of the c's change, the
coefficients change correspondingly.
Several variables that were tried did not prove statistically significant. The model
assumes constant returns to scale, and this was tested empirically by adding the
nonagricultural labor force as another variable. The resulting tratio for the coeffi
cient of this variable was very low, and the assumption remained unchallenged. An
attempt to add age variables did not yield any significant change, perhaps because of
the small spread in the data. Finally, the rate of expansion of the nonagricultural
sector was introduced to measure the expansion in demand for migratory labor; it
also was not significant. Explicit treatment of an unemployment variable was not tried
because of lack of data.
Considering the nature of the data, statistical difficulties are likely, and the extent to
which the usual optimal statistical properties can be attributed to the results is
questionable. Without attempting to minimize this point, a practical check could be
applied. Because the values used for r, 8, and education are for 1960, it was possible to
use the 1970 values as instrumental variables. For the same reasons that the data are
suspect, one may assume that existing errors are unlikely to be highly correlated
during the period of a decade.
The result of the instrumental variable analysis is given in line 8 of Table 1 for the
case of Co = c, = 0. The major change is that the education variable disappears.
Because this variable is positively correlated with r, the coefficient of r increases
slightly. Otherwise, results are surprisingly close to the OLS, reflecting the wide
30This was done to avoid nonlinear estimation at this stage.
31Strictly speaking, the improvement in fit is not a very meaningful criterion here since the dependent
variable is changing as Co changes. Expanding en(m + c) as a Taylor's series around m yields
c 1 c\ 1 c\
en(m+c) en(m) (C) + +....
m 2m 3\ m
The fit serves as a good criterion when the righthand side is negligible.
32A value of c, = 1 was not used in the iteration because there were some observations with 8 between
0.9 and 1.0.
Table 1Estimates of migration equation (M1), 70 countries, 196070
Regression 8 r ed 1 + n R2
Number
1 0 0 4.559 0.522 0.489 0.197 8.623 .580
(15.9) (3.4) (4.5) (1.9) (2.6)
2 0 0.9 4.115 0.244 0.449 0.204 9.627 .565
(18.0) (3.0) (4.2) (2.0) (2.9)
3 0 0.5 4.362 0.427 0.493 0.195 8.943 .581
(17.4) (3.4) (4.5) (1.9) (2.7)
4 0.012 0 3.708 0.267 0.263 0.108 4.622 .596
(24.4) (3.3) (4.6) (2.0) (2.7)
5 0.012 0.5 3.609 0.220 0.266 0.107 4.781 .598
(27.1) (3.3) (4.6) (2.0) (2.8)
6 (i) 0 0 4.761 0.436 0.540 0.142 9.605 .619
(15.5) (2.9) (4.7) (1.2) (3.1)
7 (i) 0 0.9 4.533 0.307 0.571 0.115 9.867 .623
(18.0) (3.1) (4.9) ( .9) (3.2)
8 (ii) 0 0 4.785 0.467 0.620 0.062 9.717 .559
(16.6) (2.1) (3.9) ( .4) (2.9)
Note: Numbers in parentheses indicate the absolute values of the corresponding tratios.
aEstimated by OLS: regressions 15 use beginningoftheperiod values for the explanatory variables; regressions 68 use the following methods:
i = explanatory variables averaged for the beginning and end of period
ii = estimated by instrumental variables
spread in the country crosssection data, which perhaps dominates any other distur
bances in the data. The analogy to crosssection analysis of Engel's curves is im
mediate.
The same factors are also reflected in regressions 6 and 7, which are obtained by
averaging the explanatory variables over the period (except for n +1). Averaging
serves two purposes: first, it reduces observation errors; second, it avoids the possibil
ity that the indicators for the beginning of the decade are less effective toward its end.
Averaging somewhat improved the fit and reduced the significance of the education
variable, but in a qualitative sense it left the result unchanged.
Estimates Using Two Observations per Country
The availability of repeated observations in a crosssection analysis adds valuable
information in examining the sensitivity of the results to systematic variations not
captured by the explanatory variables. Data for another decade, 1950 to 1960, exist for
some OECD countries.33 The analysis was repeated for these countries, resulting in
observations for each country. Because information on the education variable was
not readily available for the first decade, it was excluded from the analysis. Its
omission is not likely to be serious, particularly because the spread of this variable in
the subsample is smaller than that observed in the original sample.
The results of this analysis are reported in Table 2. The regressions are based on the
whole subsample, 34 observations. In each of the regressions, the hypothesis of a
"decade effect" was tested and found to be not significantly different from zero, with
the tratios varying around 1 to 1.3; so we concluded that the explanatory variables
capture the important changes that took place over time. Because there were only
two observations per country, we did not test the existence of a country effect. A
comparison of the results with those of Table 1 shows close similarities, which
suggests that if country effects exist, they may not have a very important influence on
the crosssection estimates.
Results for the M2 Series
The results obtained with the M2 migration series are reported in Table 3. The first
part of the table presents the results for the sample as a whole, and the second part
presents the results of the OECD countries. In both cases, the fit improved somewhat
compared with that for the M, series. The results for the more mature economies,
which are also assumed to have better statistics, are very similar to those obtained for
the sample as a whole. Furthermore, there is no serious "decade effect." The results
tend to confirm those found for the two M1 series.
Effect of Changes in the c's
For the M2 series, the values of c, that seem to work better are 0.8 for the sample as a
33This group of 17 countries is hereafter referred to as the OECD sample.
Table 2Estimates of migration equation (M1), OECD countries, 195070
Regression co b r 1 + n R2
Numbers
1 0 0 4.232 .390 .346 11.704 .397
(14.7) (1.4) (3.2) (1.5)
2 0 .85 3.977 .232 .372 10.883 .431
(33.0) (2.0) (3.8) (1.4)
3 .012 0 3.621 .259 .219 8.910 .429
(20.6) (1.5) 3.3) (1.8)
4 .012 .85 3.453 .156 .238 8.326 .469
(47.1) (2.2) (4.0) (1.8)
5 .5 .85 0.653 .012 .017 .757 .513
(127.9) (2.4) (4.1) (2.4)
aEach of the 17 countries had two observations; beginningofdecade values were used for the explanatory variables; equations were estimated by OLS.
o Table 3Estimates of migration equation (M2)
Regression
RegNbeco c, bo 8 c r ed 1+n R2
Number
70 countries, 196070
1 0 0 4.304 .320 .414 .136 13.191 .630
(19.4) (2.7) (4.9) (1.7) (5.2)
2 0 .8 4.122 .235 .431 .132 13.553 .643
(23.2) (3.2) (5.2) (1.7) (5.5)
3 0 .9 4.064 .188 .416 .136 13.753 .640
(23.7) (3.1) (5.2) (1.8) (5.5)
OECD countries, 19501970
1 0 0 4.229 .394 .324 17.61 .447
(15.5) (1.5) (3.2) (2.3)
2 0 .85 3.967 .226 .346 16.95 .477
(3.45) (2.0) (3.7) (2.3)
3 .012 .85 3.447 .151 .224 12.03 .508
(47.8) (2.2) (3.8) (2.7)
4 .5 .85 0.652 .012 .016 1.045 .549
(126.1) (2.4) (3.9) (3.2)
whole and 0.85 for the OECD sample. There was some improvement in fit by setting
values of co at values other than zero. For the M, series using the OECD sample, the
iteration over c, gave the best fit at c, = 0.85. The iteration on Co showed an
improvement in fit, although at a slow rate, up to about co = 0.5.
What effect does this improvement have on the results? Particularly, what is the
value of 8 for which the migration would be zero? When c, = 0, the answer is cl, but in
general m = 0 implies, in terms of the present framework and assuming u = 0, that
(m = 0) = c, + exp (nco 02 (nr/3n(1 +n)4en ed (2.10)
Substituting estimates for the coefficients in question, the values for 8 in (2.10) were
estimated for the OECD sample for the cases of co0O in both migration series.
For the great majority of countries, the second term on the righthand side of (2.10)
added little to cl. The results for the mean points of the sample are given in Table 4.
It is clear that as Co changes, compensating changes in the regression coefficients
leave the resulting values of 6(m = 0) largely unchanged.
Table 4Values of 8 (m = 0) for the OECD countries
Migration Seriesa Co C, 6 (m = 0)
M, 0.012 0.850 0.8504
M1 0.5 0.850 0.8560
M, 0.012 0.850 0.8503
M, 0.5 0.850 0.8550
aComputed from (2.10) for the given values of Co, c,, and the corresponding regression coefficients.
Because migration for most countries was positive, the value of m = 0 which we
selected to check the sensitivity of the system to changes in Co is on the margin of the
observations. Thus stronger results are expected for evaluations within the domain of
observations. It is interesting that the value of c, obtained in this study is close to 1. In
fact, the changes in the fit in the neighborhood of c, = 0.8 were not drastic; so we
cannot reject the value of 1. This does not, of course, settle the refined points of
which variable should be used for measuring income differentials (or for that matter
utility differentials), but it does indicate that the data used are indeed pertinent and
give instructive results. Future studies may examine whether this property is shared
by other measures of income differentials, such as wages. This finding, together with
the robustness of the result to the instrumental variable estimation, indicates that
strong empirical findings would be necessary to make other results more acceptable.
Summary and Conclusions
It has been postulated that the annual migration rate away from agriculture is
determined by the income differential between the two sectors, the composition of
the labor force, the natural growth rate of the labor force, and some other related
variables. A migration function was formulated that took the role of each of these
variables into account. The function was fitted to data on 70 countries for the decade
1960 to 1970 (or thereabout) as well as on the 17 OECD countries for two decades, 1950
to 1960 and 1960 to 1970.
The selected variables explain the intercountry differences in the rate of migration
very well. Furthermore, for the subsample of the OECD countries, the results did not
reveal a "decade effect," nor were there any important differences between the
results obtained for the OECD countries and for the sample as a whole, which
includes less developed countries. It appears, therefore, that the economic variables
capture a good part of the systematic variations in the rate of migration.
There has been a great deal of discussionwhich usually lacks any empirical
contentas to how the income differential should be measured. In the present
formulation there is a builtin mechanism to find whether the particular variable used
to represent income maintains the property that migration stops when the income
differential disappears. In the present analysis, the use of average labor productivity
to measure income performed well in this respect.
The results indicate that the process of growth or development creates forces that
act in opposite directions on migration. With growth, the ratio of the nonagricultural
to agricultural labor forces increases, and that affects the rate of migration positively.
At the same time, the growth process leads to a decline in the income differential,
which in turn slows down migration.34 If the rate of population growth also declines
with economic growth, migration slows down. When education is statistically signifi
cant at all, it speeds up migration. The effect of age on migration, which has been
significant in microstudies, was not detected here, probably because the data lacked
sufficient variation.
Thus, the qualitative results of this study are in line with economic thinking. It is
more difficult to evaluate the quantitative results because alternative estimates are
lacking. If we had to choose among the various regressions, we would probably
suggest regression 2 or 3 in Table 2.
"". .. the intersectoral difference in product per worker between the agricultural and other sectors
narrows steadily as we move from the low to the high percapita product ratios." (Kuznets, Economic
Growth of Nations, p. 211).
3
OCCUPATIONAL MIGRATION OUT OF AGRICULTURE IN JAPAN
During the twentieth century, Japan has experienced a considerable amount of
migration out of agriculture, but the motivation for such migration is by no means
selfevident. Ohkawa and Rosovsky attributed this migration to "factors other than
income differentials."35 Their view may reflect the difficulty of distilling the effect of
income differentials from timeseries data, in which the spread in the systematic
component of the income differential is small relative to the spread in its transitory
component. This was not much of a problem with country crosssection data, so it
seemed possible that the equation developed in Chapter 2 might be relevant in
explaining the Japanese experience. One could simply apply this equation (herein
after called the CCS equation) to the Japanese timeseries data and compare the
results with the actual experience in migration. This procedure is one step removed
from directly estimating a migration equation for Japan from the given data. In this
chapter we apply both steps.36
The following section applies the country crosssection analysis of Chapter 2 to the
postwar Japanese experience. The results are subject to relatively large sampling
errors, and, therefore, some alternative formulations are discussed in the subsequent
section. The findings are summarized in the final section. A descriptive discussion of
the Japanese experience, including a description of the data, the variables used, and
their sources can be found in Appendix B.
The Country CrossSection Equation and the Japanese Postwar Experience
To test the relevance of the CCS equation to the Japanese experience, we used the
second regression in Table 2 to compute migration in the postwar period (1951 to
1972).
Using the actual data for the farmnonfarm income differential (8), the labor force
ratio (r), and the percentage of the labor force that migrated (m), a value for In m was
35K. Ohkawa and H. Rosovsky, Japanese Economic Growth: Trend Acceleration in the Twentieth Century,
(Stanford, Ca.: Stanford University Press, 1973), p. 127.
31For differing approaches to this subject, see R. Minami, "Population Migration away from Agriculture in
Japan," Economic Development and Cultural Change 15 (1967): 183201, and "The Supply of Farm Labor
and the 'Turning Point' in the Japanese Economy," in Agriculture and Economic Growth: Japan's Experi
ence, eds. K. Ohkawa etal. (Princeton: Princeton University Press, 1970); M. Umemura, "Agriculture and
Labor Supply in the Meiji Era," ibid., pp. 17597; A. R. Tussing, "The Labor Force in Meiji Economic Growth:
A quantitative study of Yamanashi Prefecture," ibid., pp. 198221; Y. Masui, "The Supply Price of Labor:
Farm Family Workers," ibid., pp. 22249; and Ohkawa and Rosovsky, Japanese Economic Growth. A remark
by Minami in "Population Migration" (p.193, n. 17) indicates that most of the prior statistical analyses of this
subject have dealt with interregional migration rather than intersectoral migration.
obtained for each year and compared with actual migration for those years. The
intercepts were determined by the data so as to allow the residuals to average zero.
The resulting residuals were subject to firstorder serial correlation. The autoregres
sive scheme was incorporated to yield a new set of estimates of fn m. The results are
reported in Table 5 and in Figure 1.
Table 5Results of applying the CCS equation to postwar Japanese data
FirstOrder Sum of Squares
Type of Data Serial Estimated Country Total Residual R2b
Correlationa Intercept Effect
Annual 0.058 3.8289 1.16 4.453 3.442 0.227
Moving average 0 3.7558 1.25 0.619 0.284 0.541
Moving average 0.519 3.7616 1.24 0.619 0.185 0.701
(corrected)
aFirstorder serial correlation (FOC) coefficients estimated from the data and used in estimating (n m. A
twostage procedure was used. First, the CCS equation was used to compute In m. Using the computed
values, residuals were obtained from which the FOC was calculated. The FOC was used to recalculate
In m and the residuals. Thus, when FOC = 0, no adjustment was necessary.
S= 1 residuals sum of squares
total sum of squares
Because we apply the equation to data not used in the estimation, the residuals need not be orthogonal
to the regression values, and therefore R2 is not necessarily equal to the "usual" coefficient of deter
mination, R2.
The first line in Table 5 reports the results for the annual data. Because the serial
correlation for the annual series was so low, it did not seem necessary to report
separately results for the annual regression adjusted for serial correlation. The sec
ond column of the table gives the corrected intercept; that is, the intercept given is
the actual one, rather than the one determined by the CCS equation. The percentage
difference between the two intercepts can be considered the "country effect" of
Japan. Column three is the antilog of this difference1.16which indicates that the
rate of migration in postwar Japan was 16 percent larger than the CCS equation would
have predicted based on the values of the explanatory variables. The fourth column
indicates that the sum of squares of the dependent variable was 4.453, and the
following column indicates that the residual sum of squares was 3.442. The implied
"R2like" measure is
3.442
2 = 3.442 = 0.227.
4.452
The remaining rows of the table are interpreted in a similar way.
A good part of the annual variance in migration (or, to be precise, in en m) is
averaged out by using movingaverage data. This explains why various authors have
chosen to work with smoothed data. We have made the same choice because our
main interest is in the relationships between the systematic components of the
variables, not the transitory components. In spite of the smaller variance of the
movingaverage migration0.619, instead of 4.453 for the annual dataa larger
Figure 1. Actual and Predicted Migration, Post World War II Japan
A. Annual Data
............... Predicted
 Actual
B. FiveYear Moving Averages
.............. Predicted
Actual
1951 '52 '53 '54 '55 '56 '57 '58 '59 '60 '61 '62 '63 '64 '65 '66 '67 '68 '69 '70 '71 '72
Year
C. Corrected FiveYear Moving Averages
66.0 ............. Predicted
64.0 Actual
62.0
60.0
3 58.0 .
 56.0
oL 54.0 
 52.0
0 50.0 o
 48.0 ,
" 46.0 ,
S44.0,
42.0 "*. .. ....... ..
E 40.0 
38.0:
34.0 '.*
32.0
1951 '52 '53 '54 '55 '56 '57 '58 '59 '60 '61 '62 '63 '64 '65 '66 '67 '68 '69 '70 '71 '72
Year
proportion of it is explained by the CCS equation. The implied values for R2 are 0.541
and 0.701 for the uncorrected and corrected series, respectively. It is somewhat
remarkable that the CCS equation has this much explanatory power when applied to
timeseries data.
The results of directly estimating the migration equation using data for postwar
Japan are given in Table 6. Line 1 reports unrestricted estimates. The fit is better than
that obtained by applying the CCS equation. Part (and only part) of the improvement
is due to the elimination of the firstorder serial correlation. However, the coefficients
of the variables themselves are subject to relatively large sampling errors. This
suggests that there is not enough variation in the data to allocate precisely the total
effect of each of the variables on migration.
To make sure that farmnonfarm income differences influence migration at all, a
simple regression on the income differential (8) was estimated; the results are re
ported on line2 of Table 6. Line 3 reports the simple regression on the labor force ratio
(r). The fit is good in both cases, so the difficulty in obtaining significant coefficients in
direct estimation must result from the multicollinearity. In this case, it is possible to
impose the results obtained by applying the CCS equation, which fits the data well.
This is done in three steps: in line 4, only the coefficient of (80.85) lagged one year
was imposed;37 in line 5, the country crosssection value of the r coefficient was
added; and in line 6, the coefficient for the labor force growth rate was included along
with the other two.38 In each of these steps, the drop in R2 is very small, indicating that
the restriction imposed by the country crosssection results cannot be rejected by the
data. In fact, testing the most extreme hypothesesthe regression in line 6 against
that of line 1gives a relatively low Fvalue. It is therefore concluded that the country
crosssection results are not rejected by the timeseries data.
In conclusion, the large sampling error (in part due to multicollinearity) results in
large confidence regions (or ellipsoids), so the country crosssection results are not
rejected. At the same time, we do not reject the null hypothesis with respect to the
coefficients of either 8 or r. The results for the prewar period gave even larger
sampling errors and did not yield significant results. In view of this outcome, it was
desirable to explore alternate formulations.
Alternate Formulations
As an alternate to the CCS equation, we tried to account for the migration in the
prewar period in terms of the level of economic activity.39 This was measured by the
37Throughout, we use (8 c,) rather than 8 alone, and only the value 0.85 is used for c,. This was done
in order to allow comparison with the CCS equation.
Lagging (8 0.85) one year gave somewhat better fit than (8 0.85) for the current year. Hereafter, the
empirical results are in terms of the oneyear lagged values of (8 0.85).
"The effect of the natural rate of labor force growth was not significantly different from zero in the
various regressions. This reflects the small variation in the data for this variable. It was included here in
order to maintain consistency with the CCS equation, but henceforth this term will be neglected.
39Other exogenous variables, such as education and age distribution, were not treated in this analysis
because data were not available. Judging from the CCS analysis, however, it is unlikely that introducing
these variables would have changed the results substantially.
Table 6Estimates of the migration equation, postwar Japan
Income Labor Natural
differential Force Labor Force FirstOrder Durbin
Regression (6 0.85), Ratio Growth Rate Serial Watson
Number Intercept Lagged One Year (r) (I+n) Correlationa R2 Statistic
1 3.751 0.591 0.165 4.94 0.438 0.741 1.97
(1.70) (1.32) (0.82)
2 3.720 0.843 0.509 0.705 1.95
(3.400)
3 3.311 2.71 0.522 0.700 1.80
(3.07)
4 3.553 0.232b 0.252 4.818 0.478 0.725 1.90
(2.7) (.8)
5 3.714 0.232b 0.372b 8.73 0.520 0.717 2.0
(1.6)
63 3.755 0.232b 0.372b 10.883b 0.518 0.712 2.0
aEstimated from the data and used for secondstage least squares correction.
bValue imposed from the CCS equation.
'The 8 variable used for Table 5 was not lagged, so there is a slight variation between this line and the last
line of Table 5.
rate of growth of the gross national expenditure in constant prices (gy). A thirddegree
polynomial was fitted to the annual data for the period 1910 to 1940 with the following
result:
ln(m+.025) = 3.449 + 12.967 g, 430.969 g2 + 3689.g,,
(3.11)
(3.90)
(3.1)
(2.75)
R2 = 0.610
Firstorder serial correlation = 0.377
DurbinWatson Statistic = 2.190
where gy = gy + 1, and numbers in parentheses are tratios.
The next step was to combine the rate of growth (gy) with the CCS equation in a
form that preserves the nature of the equation.40 For instance, the 8 coefficient and
intercept were allowed to differ for years where 8 increased or decreased. There was
an improvement in the fit, but it was not sufficient to sustain empirically all the
coefficients.
"4Ohkawa and Rosovsky, Japanese Economic Growth, attribute much of the variation in the sectoral labor
force to the swings of the economy.
It was decided to search for a formulation more efficient in terms of the number of
parameters in order to overcome the difficulty of sustaining all the variables in the
regression. A natural way to reduce the number of parameters was to take a product
of the two variables, (8 0.85) and r. This led to the equation:
Mn m = 3o + p3l,/ + u, (3.2)
where
/, = en (8 0.85) Inr.
According to (3.2), the partial derivative of one variable depends on the level of the
other variable. Specifically, the elasticity of migration with respect to the income
differential depends on the labor force ratio. The effect of the income differential
increases with r, indicating that a given percentage change of (8 0.85) has a larger
effect the larger r is or the smaller is the share of agriculture in the total labor force. It
should be remembered that m is the proportion of migrants in the agricultural labor
force; the response of absolute migration to changes in r will be somewhat weaker
than that of relative migration.
The elasticity of m with respect to the income differential may also depend on the
overall performance of the economy, and this may be treated similarly by introducing
into (3.2) the term 12 = en(8 0.85) In (g, + 1). The resulting equation was also fitted
to the annual data.41
n (m + Co) = po + 111 + /322 + u. (3.3)
U is allowed to have an autoregressive structure, but otherwise it is assumed to
possess the standard properties.
The coefficients estimated by (3.2) and (3.3) appear in Table 7. The table is divided
into three panels: postwar, prewar, and both periods combined. For each period,
results were obtained for the fiveyear moving averages and for the annual data, and
for selected values of co. Also for five of the regressions, no correction was made for
the firstorder serial correlation.
Comparing the postwar period results with those using crosssection data, the
coefficients of 12 are not significantly different from zero. Other attempts to bring in
the level of economic activity did not improve the results in an important way. This
was true both for movingaverage and for annual data. It is, however, important to
note that the coefficient of I1 in regression 5 (annual) is close to that of 4 (the
corresponding movingaverage equation).
It appears that for the postwar period, regression 2 of Table 7 summarizes that data
well. The partial derivatives with respect to 8 and r obtained from this equation are
shown in Figure 2. The coefficient (elasticity) with respect to r varies between 0.13 in
1951 to about 0.31 in 1966; recall that the constant elasticity in the CCS equation was
0.392. Similarly, the elasticity with respect to (8 0.85) varies between zero in 1951 to
0.5 in 1972, as compared with the constant elasticity of 0.232 from the CCS equation.
These represent similar orders of magnitude.
4A constant, Co, is added because in some years migration was negative.
Table 7Alternative forms for the migration equation
Regression FirstOrder Durbin
Number and Type of Prewar Serial Watson
Period Dataa Co Intercept 1 12 en (g, + 1) Dummyb Correlationc R2 Statistic
Postward
1) FMA 0 3.311 0.360 (5.9) 0.632 1.1
2) FMA 0 3.312 0.349 (4.0) 0.429 0.727 1.8
3) FMA 0 3.393 0.425 (5.1) 0.924 (0.8) 0.341 0.858 1.9
4) FMA 0.025 2.838 0.281 (5.0) 0.464 (0.6) 0.361 0.853 1.9
5) Annual 0.025 2.889 0.259 (1.5) 0.889 (1.0) 0.183 2.0
Prewar
6) FMA 0 5.107 0.230 (0.3) 10.747 (1.8) 0.652 0.573 1.9
7) FMA 0.025 3.452 0.061 (0.3) 2.714 (2.0) 0.714 0.667 2.0
8) Annual 0.025 3.711 0.362 (1.0) 6.811 (3.5) 0.437 0.336 2.2
Both
periods
9) FMA 0.025 3.334 0.484 (4.6) 3.888 (2.6) 0.654 0.2
10) FMA 0.025 0.328 0.424 (1.9) 1.968 (2.3) 0.900 0.944 2.0
11) FMA 0.025 0.583 0.310 (2.2) 1.976 (2.3) .25 0.810 0.947 1.9
12) FMA 0.060 0.262 0.278 (2.2) 1.071 (2.3) 0.900 0.951 1.9
13) Annual 0.025 3.407 0.576 (3.0) 3.239 (2.1) 0.299 2.3
14) Annual 0.025 4.066 0.333 (2.2) 4.066 (2.9) .25 0.250 0.411 2.1
15) Annual 0.025 3.368 0.585 (3.0) 2.147 (2.0) 0.292 2.3
aFMA = fiveyear moving average.
blmposed value.
CFOC was obtained from residuals of the OLS regression and was then used to obtain the second stage estimates reported in the table.
dRegressions 1 and 2 are for 195172; all other postwar regressions are for 195170.
eThe war years are omitted, so the two periods included are 191140 and 195170.
Figure 2. Migration Elasticities with respect to Farm Non farm
Income Differences and to the Labor Force Ratio,
Postwar Period Elasticity
Elasticity with respect to
(685), legged one year.
Elasticity with respect to r. "***,,,,... I,,**
Source: Partial derivatives from Regression 2 Table 33
'67 '68 '69 '70 '71 '72
.400
.300
U
C .250
0
o 2
.200
1951 '52 '53 '54 '55 '56 '57 '58 '59 '60 '61 '62 '63 '64 '65 '66
Year
Turning to the prewar year, 11 is not significantly different from zero. On the other
hand, 12 passes the null test with both types of data, but only marginally so for the
moving averages. Regression 8 is the only regression that catches the effect of the
income differential in the prewar years. The elasticity of relative migration with
respect to (8 0.85) derived from this regression is (m + .025)/m 6.811 in(g, + 1). The
extreme movingaverage values of g, in the prewar period and the corresponding
values of m were:
Year gy m elasticity
1919 0.07417 0.0172 1.196
1924 0.00126 0.0099 0.030
It appears that the range of the prewar elasticity with respect to the income differen
tial covers larger values than for the postwar period.
The equations for the prewar period in Table 7 are preferable to the cubic equation
(3.1), which includes only the effects of economic growth. Because of the large
variance of the error term, statistical comparisons of the two were not performed; but
evidence suggests a response to the income differential in the prewar period. This
evidence is amplified when data for the prewar and postwar periods are pooled so as
to add the betweenperiods variations.
Regressions 9 and 10 in Table 7 give the results with and without correction for the
firstorder correlation. There is a close correlation between the prewar effect on the
intercept and 11, which results from the monotonicity of r with time. To allow for this
effect, a dummy for the prewar effect was added in regression 11, and its coefficient
was restricted to a level that still leaves the other coefficients significant; the signifi
cance of I1 is reduced, however. Iterations on co indicated that the fit could be
improved somewhat by setting Co = 0.06 (regression 12).
The movingaverage regressions now are subject to high firstorder correlation. To
see if this is avoided by using annual data, regressions 13 and 14 are compared with
regressions 10 and 11, respectively. The coefficients of 1, conform quite well, but
there are large differences in the coefficients of 12 and in the intercepts. The poor fit of
the annual data compared with the movingaverage data indicates that the equation
predicts the rate of migration better than the exact timing. Thus, there is a great deal
of annual variation fluctuating around the systematic component, which itself varies
with the explanatory variables.
Summary and Conclusions
A migration equation was formulated and estimated using Japanese data for the
period 1910 to 1972, excluding the war years 194150. Migration was explained in terms
of income differences between the agricultural and nonagricultural sectors. The
relative sizes of the two sectors and the labor force rate of growth were taken into
account. The same equation was estimated previously from country crosssection
data for the OECD countries for the postwar period. Here, a measure of the economic
rate of growth was introduced into the equation to represent expectations with
respect to obtaining employment in the nonagricultural sector.
In the initial empirical analysis of the Japanese data the country crosssection data
was applied to the Japanese postwar data, and the fit was found to be "reasonable." In
the postwar period, Japan had a migration rate 16 percent higher than that which
could be accounted for by the explanatory variables. Coefficients for the same
equation are then estimated using the postwar Japanese data; there was a little
improvement in fit. Fitting the same equation to the prewar data did not yield
significant results. The rate of growth of the labor force did not contribute much to
the explanation and it was omitted in further analysis. On the basis of this analysis, it is
concluded that postwar migration in Japan can be attributed to the farmnonfarm
income differential and the composition of the labor force.
The formulation was then changed so as to bring in the effect of economic growth
of migration; this was done to capture any effect that changes in the level of economic
activity might have on the subjective probabilities of obtaining a job within a given
period. The results indicate that this variable was important in the prewar, but not in
the postwar, period. The prewar period was one in which there were substantial
fluctuations in overall activity levels and therefore the prospects of finding employ
ment, and expectations with respect to such prospects, also fluctuated. There was a
statistically important spread in this variable. On the other hand, the postwar period
has been one of continuous growth, with only moderate variations in the rate of
growth. Consequently, employment expectations have not changed much; they have
been favorable throughout. As a result the important determinants of migration have
been income differentials and the labor force composition.
It should be noted that, once the expectation variable was introduced along with
the other two variables, the income differential, which taken alone had little explana
tory power in the prewar period, became important in explaining the relatively low
rate of migration during this period. The threevariable formulation permits pooling
data for the two periods so as to make use of the variations between the periods.
In conclusion, all the economic variables have the expected qualitative effects, and
there is no reason to rule out the importance of income differentials in explaining
migration.
4
THE FLOW OF SAVINGS OUT OF AGRICULTURE
THE CASE OF JAPAN
The process of allocating production factors among sectors over time is not
restricted to labor. In this chapter, we consider the intersectoral flow of savings. There
is a basic difference between the flow of labor and that of capital. The total labor force
of a particular sector, and not just the addition to the labor force, is movable within a
given period. This is not the situation with respect to capital; a good portion of
existing capital is sector specific. Thus, it is better to assume that the allocation
decision is made primarily with respect to new investment and that the most that can
be invested during any given year is the gross savings of the economy for that year.
There is also a practical difference between labor and capital: the data necessary for
analyzing the flow of savings are less available than those for labor force changes.
Even indirect computations of the flow variable and expected rates of returns require
data that do not always exist. Often it may be necessary to exploit whatever data are
available, even if some of the findings offer only a first working hypothesis. This was
the case in estimating the flow of savings equation for Japan.
Japanese agriculture is thought to have played an important role in financing
investment for industrialization. According to Ohkawa and Rosovsky, "agriculture
was a source of savings in the economy and these savings were translated into
investment, i.e., capital formation."42 The study of the Japanese experience is handi
capped by lack of data, but with a relativelyweak assumption it is possible to compute
investment flows by using standard national accounting data. Such data are used in
various other econometric analyses, and there is no reason why they should not also
be used in this one. Nevertheless, Ohkawa and Rosovsky have cautioned that data on
investment flows are inadequate, so analysis based on the Japanese national accounts
must be taken as tentative and should be verified with additional information.
The plan of this chapter is as follows: the savings flow equation is formulated in the
next section, followed by a discussion of the variables; the empirical results are
discussed in some detail in the third section and are summarized in the final section.
Methods of estimating the sectoral saving rates, sources of data, and summary
statistics can be found in Appendix C.
The Model of Intersectoral Savings Flows
The agricultural and nonagricultural sectors each generate savings that can be
"4K. Ohkawa and H. Rosovsky, "The Role of Agriculture in Modern Japanese Economic Development,"
Economic Development and Cultural Change 9 (1960): 60; cf. K. Ohkawa, "Agricultural Policy: The Role of
Agriculture in Early Economic Development," in Economic Development with Special Reference to East
Asia, K. Berrill, ed. New York: St. Martin's Press, 1964, p. 323.
invested in either sector. If F denotes the net flow of savings from sector 1 to sector 2,
then total savings (or investment) in each sector may be defined as
S, = I1 + F, S2 = 12 F. (4.1)
A basic assumption of our analysis is that the flow of savings is determined by
expected returns on investment in the two sectors, that is,
F ~ (8e), > 0 (4.2)
where
8r = r1/r2,
r = return on capital in the designated sector, and
e = expectations.
It is also assumed that for any value of 8r, the size of the flow depends on the
magnitude of the savings in the two sectors; the larger the sector's savings, the larger
is the flow. Also, other things being equal, it is easier to invest a certain amount in a
large capital market than in a small one. If the size of the market is measured by S, and
we assume that F is monotonically increasing in Si and S2, then
F ( S2\,
S r 01) (4.3)
0
This relation should maintain the constant returns to scale hypothesis, so that for any
given 8r, doubling S, and S2 should double F.
To formulate (4.3) more explicitly for empirical study, we assume it to be of the
CobbDouglas form. To allow for a zero flow, we use the variable (8 cl) instead of 8e,
where c, is some constant. Also, to allow for a negative Fthat is, a flow of savings
from sector 2 to sector 1we add a constantCo to the lefthand side. The equation can
then be written as:
In(f + Co) = 3o + 31 ln(8e c,) + 32 In R + u, (4.4)
where R = S,/S,, and u is a disturbance term, which we assume to possess the
standard properties.
Variables and Data
Data for variables in (4.4) are not readily available, particularly for the flow variable
F. F was obtained by using (4.1) to write:
f = 1 I (4.5)
S,/S
where S = S, + S2 = .43
Elaborating on (4.5), the savings in any sector may be defined as a product of its
saving rate and its output. For sector 1, for example, S, = sPY1, where s, is the saving
rate, Y, is agricultural output and P, is its price. The flow of savings from sector 1 to
sector 2, then, can be written as:
f= 1 p, +1 (4.6)
where
Pi = Ii/1,
r = P1Y1/P,1Y + P2Y2, and
X = s/1s2.
In order to compute f by using (4.6), the share of sector 1 in output and in gross
investment must be known; these data are readily available. The ratio of savings rates
in the two sectors must also be known, but we do not have such data.44 Therefore, we
computed and used under various assumptions with respect to the savings ratio; the
different f series are highly correlated.
There are also no measurements of 86, nor are there direct measurements of the
ratio of returns in the two sectors. The rates of returns were obtained indirectly. Using
data on capital shares and on average productivities, the rate of return on capital (r) in
any one sector is equal to (PY/K)Pf in that sector, where P represents the sector's
capital shares and K its capital stock.45 There are limitations on these data, too,
however. Available figures on factor shares in agriculture change every five years,
rather than annually, and they appear to be based on assumptions with respect to the
interest ratewhich is what we were seeking in the first place.
Because of these deficiencies, we decided to approximate marginal returns by
using average returns. This provides two possible measures:
Sr = 2 P/32/ ,, and (4.7)
K K,
ar 2 / ~1 (4.8)
K2 1
"Following Ohkawa in "Agricultural Policy," p. 333, we neglect capital import or export.
"Some attempts to estimate the sectoral savings rates are discussed in Appendix C. However, the
computation of does not depend on the actual values of s, nor on the assumption that these values are
constant; it is only necessary to assume that their ratio is constant.
'Sources of these data are discussed in Appendix C.
Sar ignores the ratio of capital shares in the two sectors. If this ratio is fairly stable, 8ar
may yield an accurate approximation, up to a scalar, of the ratio of returns to capital.46
The data for marginal and average returns are plotted in Figure 3. Both measures
show a considerable difference in returns between the sectors. The reasons for this
difference and the behavior of the rates over time will not be explored here, but the
considerably higher rates of return in the nonagricultural sector may well explain the
flow of savings out of agriculture during most of the period examined.
To obtain some indication of how expectations affect savings flows, we formed the
product, INT = en(8 c) In(1.1 + gy), where gy is the rate of growth of the economy.
The idea is that expectations improve with high rates of growth and increase the flow
of investment for any given value of 8.47
Under this alternative, (4.4) takes the form:
nn(f + Co) = /o + /1 en(8 cl) en(1.1 + gy) + 32enR + u. (4.9)
In a final variation on equation (4.4), instead of using R = S2/S, we use the ratio (7r) of
the sectoral outputs to total output; that is, R = (1 rT)/Tr. When the ratio of the
saving rates in the two sectors remains fairly constant, R provides a good approxima
tion up to a scalar.
Our manipulation of (4.4) yielded a rich variety of combinations with which to
estimate the flow equation. These combinations reflect (1) iterations to find the best
fitting Co and cl, (2) the search for the effect of changing the ratio s1/s2, (3) the choice
between 8, and 8ar as measures of the differential returns, and (4) the attempts to
eliminate some of the possible errors in the 8 variable by using instrumental variables
estimates. In view of the exploratory nature of this work and the lack of similar
studies, estimates were obtained under alternative assumptions so as to gain some
notion of the empirical meanings of such assumptions.
Empirical Results
Figure 3 shows that the prewar savings flow calculated for X = 1 was subject to
fluctuations. Its highest value, 69.4 percent, was reached following World War I, when
in 1919 the economy reached a local peak in activity. The lowest value,18 percent
representing a flow of savings from the nonagricultural to the agricultural sector
occurred in the midst of the depression. The postWorld War II data are characterized
by a downward trend in F and much narrower fluctuations. The savings flow fluc
tuated around 40 percent in the late 1950s and early 1960s and then declined almost
continuously until it finally reached a negative value in 1970.
The analysis was first conducted separately for two periods, 1909 to 1938 and 1955 to
1970; later the data were pooled. The results are summarized in Tables 8 through 10.
46Note that when dealing with logarithmic transformations, the scalar becomes additive, and in linear
forms it is absorbed in the intercepts.
47Because in some years g, is negative, we added a constant to g, so that the variable is always positive.
Furthermore, we wanted the 'n of the variable to preserve its sign, so we selected this constant to be 1.1
rather than 1.
Figure 3. Flow of Funds and Related Variables 19091938, 19551970
 Flow of funds
... Delta r marginal
 Delta r average
............. Ratio of product
1.4
S1.0 / .. ...........
>
.2
.I. I*
.0
.2
1909 '15 '20 '25 '30 '35 '55 '60 '65 '70
Time
1 Table 8Estimates of the flow equation for the prewar period, 190938
Serial Correlation
Durbin
Regression First Second Watson
Number Intercept Ab Co c1 INTc n R Order Order R2 Statistic
1.(i) 0.320 (0.7) 1.0 0.25 0 1.73 (2.3) 0.54 (1.6) 0.613 0.531 1.7
2. 0.673 (1.1) 1.0 0.25 0 8.80 (2.6) 1.34 (2.7) 0.822 0.538 1.8
3. 0.042 (0.1) 1.0 0.25 0.5 2.27 (2.8) 0.88 (2.3) 0.723 0.566 1.6
4. (ii) 0.020 (0.03) 1.0 0.25 0 3.39 (2.6) 1.2 (2.4) 0.822 0.538 1.8
5. (ii) 0.228 (0.05) 1.0 0.25 0.5 2.41 (2.8) 0.74 (1.9) 0.723 0.566 1.6
6. 0.754 (1.3) 0.8 0.05 0 8.80 (2.4) 1.24 (2.5) 0.760 0.519 1.8
7. 0.524 (0.9) 1.2 0.01 0 7.85 (2.6) 1.28 (2.8) 0.866 0.561 1.7
8. 0.114 (0.3) 1.2 0.01 0.5 1.95 (2.8) 0.80 (2.3) 0.758 0.585 1.5
9. 0.129 (0.3) 1.5 0 0 5.02 (2.3) 0.88 (2.6) 0.874 0.581 1.5
10. 0.154 (0.6) 2.0 0 0 2.19 (1.6) 0.40 (2.0) 0.843 0.569 1.4
11.e 0.588 (6.0) v 0 0 2.80 (2.1) 1.9 (1.4) 1.10 0.49 0.669 2.2
12.e 0.680 (7.6) v 0 0.5 1.05 (4.0) 0.18 (1.6) 1.18 0.59 0.746 2.1
13. (i)e 0.703 (7.4) v 0 0 0.762 (3.2) 0.12 (1.0) 1.07 0.49 0.724 2.2
Note: The independent variables are lagged one year. Figures in parentheses are the absolute values of the tratios.
a(i)in this equation 8, is used for the differential returns, otherwise 8 is used. (ii)The equation was estimated by the instrumental variables method, and 8ar, or
INT derived from 86,, serves as the instrumental variable.
bVvariable A as obtained from Appendix C.
'INT = 'n(6 c,)On(1.1 + gy), where 8ar is used for 8 unless otherwise indicated (see note a above) and gy is the rate of growth of per capital gross
national expenditures.
dR2 obtained by 1 Sum of squares residuals/sum of squares total.
eFor variable X, instead of tn R, the variable used is in (R/A).
Table 9Postwar estimates of the savings flow equations, 195564 and 195470
Regression Durbin
Number and Watson
Period Intercept x Co c, In (8 C,) INT en R R2 Statistic
195564
16a 0.250 (2.5) 1 0.25 o 1.85 (3.4) 0.21 (2.8) 0.633 1.9
17 0.025 (0.2) 1 0.25 0.5 2.70 (3.4) 0.33 (3.2) 0.626 1.9
18 0.119 (0.6) 1 0.25 0.5 0.48 (1.6) 0.28 (1.6) 0.279 1.9
195470
19b 0.659 (0.8) 1 0.25 0.5 0.64 (1.7) 0.91 (2.0) 0.859 2.0
Note: Also see Table 8.
aBased on 8, rather than 8ar.
bCorrected for secondorder autoregression.
S Table 10Estimates of the savings flow equation, data pooled
Regression Durbin
Number and Prewar Auto Watson
Perioda Intercept x co c, INT In R Effect regression R2 Statistic
191038 and 195664
20b 0.235 (0.9) 1 0.25 0 1.71 (2.6) 0.65 (2.1) 0.755 (1.9) 0.625 0.551 1.8
21 0.488 (1.9) 1 0.25 0.5 2.25 (3.2) 0.98 (3.0) 1.000 (2.7) 0.625 0.581 1.5
22' 0.297 (1.2) 1 0.25 0 2.36 (3.1) 0.78 (2.5) 0.876 (2.2) 0.625 0.580 1.5
191038 and 195570
23 0.482 (2.3) 1 0.25 0.5 2.29 (3.4) 1.09 (3.9) 0.992 (2.7) 0.650 0.619 1.6
Note: Also see Table 8.
'One year is lost at the beginning of the second period because of the method used for eliminating the firstorder serial correlation.
bBased on 8r rather than 8ar.
'Instrumental variable estimates. Where INT was computed with (Sa, 0.5), the instrument was (INT, 0.650 INTt,.).
Unless otherwise specified, the 8a, series was used for 8. The variables are lagged one
year in order to avoid spurious correlation because of the appearance of 7r on both
sides of the equation. Lagging may also be appropriate because of some lag in the
response of investment to returns on capital.
In general, the fit improves somewhat with lower values of co. Thus, in the search
for estimates of the other parameters, we used low values of Co but not so low that F +
Co would be zero or negative. Different values of A result in different F series, so co had
to be changed accordingly. The fit also improves as values of c, increase. The limit to
the increase in the value of c, is set by the smallest value of 8, because 8 c, should
always be positive. For that reason, c, was only applied to 8ar series; the values of 8r are
so low that introducing the c, coefficient would produce a negative value.
In regression 1 in Table 8 the INT variable was computed with 8r, whereas in
regression 2 the 8a, series was used. There is a little difference in the fit, but in all cases
the difference was only moderate. The main difference between the first two re
gressions is in the size of the coefficients, which occurs because the variables are
different. Changing the value of c, in regression 2 from 0 to 0.5 leads to regression 3;
that change reduced the standard error of the INT coefficient somewhat.
The 8 series and the 6ar series are not identical, and they both can be subject to
independent errors. For this reason, it is possible to use one series as an instrumental
variable in estimating an equation with the other series. The results in line 4 are
instrumental variable estimates of the regression estimated in line 1 in which the
instrument is fn 8ar en(1.1 + gy). Similarly, the results in line 5 are instrumental
variable estimates of the same regression in which the instrument is en(Sar 0.5)
en(1.1 + gy).
The remaining prewar regressions use different values of X (the ratio of the saving
rates). The different f series, which were obtained by changing the ratio of the saving
rates, are highly correlated, but their actual values differ and so do the resulting
regression coefficients. Differences among the various regressions in tratios and in
fit are not large enough to allow a clearcut empirical choice among the values of X.
Independent information would be necessary to select the correct X, but not having
such information, we have tried to extract it from the data with somewhat inconclu
sive results." The results suggest that in the prewar period A varied within the range of
approximately 1.5 through 2, with an average value of 1.78.
An f series was also constructed under the assumption that X varies. Regressions 11
through 13 are derived from this series. Regression 11 incorporates the same assump
tions as regressions 9 and 10, except for X. The value of X varies between 1.5 and 2, and
it is seen that the coefficient of INT falls between the values it had when X was treated
as a constant set at 1.5 or at 2. The value of the INT coefficient increases when
correction is made for second order autoregression.
Regression 12 is like 11 except that c, is set at 0.5 rather than 0, which has the effect
of reducing the value of the coefficient of INT. Regression 13 is obtained by using 8r
rather than 8ar. The result is to decrease the coefficient of INT and bring it closer to
that obtained for c, = 0.5.
"This analysis is summarized in Appendix C.
The pattern established in these estimates is that the results obtained for the prewar
data in which the F series was derived from a varying X are similar to those from a
constant A if this constant ratio is set at values within the range of X's variation. The
evidence on X is not conclusive, so not much is lost by continuing the analysis under
the assumption of equal saving rates.
The results for the postwar period appear in Table 9. The analysis is conducted for a
short period, 195564, and a longer period 195470. The shorter period was chosen
because the 8, series is only available for this period, but it also has another
significanceTable 9 shows that the savings flow variable started a steep downward
trend in 1964. That strong trend has been reflected in a strong secondorder auto
regressive scheme in the regressions calculated for the longer period. For that
reason, the results for the shorter period may be more reliable, despite the fact that
the number of observations is smaller.
Looking at the results for the shorter period, regressions 16 and 17 are, respectively,
the postwar versions of regressions 1 and 3 of Table 8. In the 8r series (16), the
coefficients of the INT variable are quite close to the prewar values, and there is a
somewhat greater difference for the 8ar series (17). This difference is not substantive
when the standard errors are considered, however. The results for the shorter period
are not subject at all to autoregression.
For the series based on 8ar, it is possible to obtain regression 19 for the longer
period. Probably because of the strong autoregressive scheme, the coefficient of the
INT variable is not significant. Better results are obtained by using en(8a, 0.5) as a
variable, rather than INT. Regression 19 is comparable to regression 8 in Table 8,
which is the same regression for the shorter period. The coefficients of ln(8ar 0.5)
and INT are similar for the two regressions. For the shorter period, the fit using
fn(8ar 0.5) is much worse than that for INT. Thus, INT appears to be a superior
variable for that subperiod. The good fit in regression 19 is largely because of the
secondorder correction for autoregression.
One way to avoid some of the difficulties is to pool the data for the two subperiods.
These results are reported in Table 10. Regression 20 is the pooleddata version of
regressions 1 and 16. In all cases, the coefficients of INT are very close. There are
differences in the coefficients of in R, and the prewar intercept is negative. Similarly,
regression 21 is the pooleddata version of regressions 3 and 17. The coefficient of INT
in 21 is very close to that of the prewar period. Using INT with (8ar 0.5) corrected for
serial correlation, as an instrumental variable for 8r, has little effect on the coefficient
of INT, as can be seen from regression 22. Extending the period to 1970 in regression
23 also changes the coefficient of INT very little.
Our ultimate interest in these estimates was to capture the partial effect of differen
tial returns on capital (8) on the savings flow. Apparently this effect differs with the f
series, and thus it depends on X. It also depends on whether the A or the 8ar is used
and which value of c, is used. A comparison of the calculated coefficients for several
of the cases considered appears in Table 11. The elasticity of the savings flow with
respect to differential returns (8) may be written:
af a n(f + co) df d(8 c,)
a8 aen (8 c) den(f + co) d8
Table 11The Response of savings flow to differential returns on capital
afn (f + co)/S8n (8 c,) af/l8
Regression Standard Coefficients Standard Coefficients
Number X co C, Average Deviation of Variation Average Deviation of Variation
1a 1.0 0.25 0 0.218 0.086 0.394 0.561 0.397 0.708
2 1.0 0.25 0 1.108 0.436 0.394 0.797 0.467 0.585
3 1.0 0.25 0.5 0.286 0.113 0.395 0.566 0.415 0.733
6 0.8 0.25 0 1.029 0.405 0.394 0.896 0.524 0.585
7 1.2 0.10 0 0.989 0.389 0.393 0.632 0.366 0.579
8 1.2 0.10 0.5 0.245 0.097 0.396 0.432 0.313 0.725
9 1.5 0 0 0.650 0.251 0.386 0.405 0.220 0.543
10 2.0 0 0 0.295 0.114 0.386 0.214 0.107 0.500
Note: Computed by using (4.10) and the coefficient of INT in Table 8 for the numbered regressions.
aBased on 8,, rather than 8.r
a~n(f + Co) (f + Co) (f + co)
= bfn(1.1 + gy) (4.10)
an(8 c,) (8 c,) (8 cl)
Table 11 reports the prewar results for the elasticity of f + c, with respect to 8 c, in
terms of equation (4.9). Because gy varies from year to year, so does the elasticity
coefficient, and therefore the table reports average values, standard deviations, and
coefficients of variation. The elasticities in these regressions differ with the variables
used but the coefficients of variations are practically the same for all the regressions
shown. Table 11 also gives the values for the coefficients of obtained by using
equation (4.10). The results here depend on the values of ft and 8t.
The first three regressions in Table 11 are for the f series that resulted when X = 1.
There is a great similarity in the response coefficients of the 6r and the 8ar series,
particularly when c, is used to correct 6ar. Thus, the average coefficient for the prewar
8 series is 0.561 (regression 1) and that for regression 3, using (8ar 0.5), is 0.556.
When the value of X is changed, different values for the savings flow variable result,
and therefore coefficients are different.
Summary and Conclusions
The development of the Japanese economy was accompanied by a flow of savings
from agriculture to the rest of the economy. Our measurement of this outflow was
obtained by indirect calculations which depend on saving rates in the two sectors.
Although these saving rates are not known, they are estimated for the prewar data.
The estimates indicate that the saving rates in agriculture remained constant and
relatively high and that the saving rates in the rest of the economy were lower, but
increased with per capital production in that sector. The savings flow series was
obtained under varying assumptions with respect to the ratio of saving rates in the two
sectors.
The basic premise that was tested and empirically supported by this study is that the
flow of savings can be attributed to differential returns to capital in the two sectors.
The magnitude of the response of the savings flow to changes in the differential
returns depends on the data series used to measure the flow and to measure differ
ential returns. Regression 3 in Table 11 indicates that when saving rates are equal in
the two sectors then af/aS = 0.566 and when the ratio of agriculture to nonagricul
ture saving rates is 2, then af/a8 = 0.214, where 8 is the ratio of the rate of returns to
investment in agriculture to that in the rest of the economy. The difference between
the two coefficients largely reflects the difference in the value of the savings flow
variable under the two saving rate ratios. The prewar arithmetic average of ffor X = 1 is
0.335 and that of f for X = 2 is 0.588 (see Appendix C, Table 24).
The results here were obtained from regressions in which the ratio of returns to
capital (8) is measured by the ratio of the average productivities of capital. More
refined data will make it possible to obtain clearer results, but until such data become
available, there is no reason not to accept the present results.
Savings flows play an important role in the process of development. The flow is
initiated by higher capital returns in the nonagricultural sector; that is, there are
better opportunities out of agriculture. In a static situation, the flow of savings tends
to equalize returns in the two sectors, and eventually it will diminish. This process
cannot be isolated from other processes, however. There is a flow of labor along with
the flow of capital, and the two flows affect each other. The migration of labor out of
agriculture increases the capitallabor ratio in agriculture, which reduces the rate of
return on agricultural capital and increases it in the other sector. Thus, the labor
migration increases the differential in returns and augments the flow of savings. By a
similar argument the flow of savings augments the migration of labor. These com
plementary relationships between labor and savings flows imply that the lowincome
sector contributes to increases in both capital and labor in the highincome sector.
When dynamic changes are taken into account, the flow of savings depends on the
productivity of capital, or more technically, on the capital share in the production
function. In turn, the level of productivity or technology may depend on investment.
If this is the case, the flow of savings need not decrease the differential in returns to
capital, and there is no need to assume that static forces will eventually halt the flow of
savings; it can continue for a long time. The flow eventually will exhaust itself,
however, because the agricultural sector may become so small that the effect of the
flow on the other sector will be relatively unimportant.
5
AGRICULTURAL GROWTH IN THE
CONTEXT OF ECONOMIC GROWTH
There is a considerable volume of work on the growth of the agricultural sector and
its relationship to the overall growth of the economy. Some of this work is carried out
on the basis of a dual economy which consists of a traditional, largely rural sector and
a nontraditional, largely urban sector. It is infeasible to survey this work here; instead
we concentrate on introducing the present framework.49
Empirical findings have indicated that various sectors of an economy grow at
different rates.50 These growth differences can result from unequal (and therefore
nonunitary) income elasticities, nonzero demand elasticities, capital accumulation,
and technical change. All these attributes can be accounted for within a neoclassical
framework, which assumes that the economy develops through a sequence of short
run equilibria characterized by market clearing and equal factor prices.5'
Although the qualitative results of these models have been analyzed, their empiri
cal relevance has not been established. The fact that, in general, factor prices in
agriculture are not equal to those in the other sectors of the economy has cast doubt
on the "real world" utility of the models. Thus, attempts have been made to analyze
the growth process under the assumption that distortions exist in factor markets.52
This approach is subject to the same limitation as the neoclassical approach. It
assumes that at any instant in time factors can be reallocated so as to correspond to a
predetermined factor price differential between the two sectors. This assumption
seems open to question.
The existence of a factor price differential indicates that allocation requires time
and that it is not fully accomplished within the period of analysis (a year). An empiri
cally relevant model should take this fact into account. Furthermore, the process of
resource allocation should be viewed as an economic activity in which the rate of
allocation depends on economic variables. This notion is related to the recognition
that dynamic paths are determined by the systems.53
The main point of departure is the assumption that factor allocation among sectors
49For a recent literature survey on dual economies, see C. Lluch, "Theory of Development in Dual
Economies: A Survey," mimeographed (Washington, D.C.: The World Bank, 1977).
5sSimon Kuznets, "Quantitative Aspects of the Economic Growth of Nations, II: Industrial Distribution of
National Product and Labor Force," Economic Development and Cultural Change, 5 (1957): 1111; and Six
Lectures on Economic Growth (Glencoe, III.: Free Press, 1959).
51Cf. Mundlak and Mosenson, "TwoSector Model."
52Tropp and Mundlak, "Distortion in the Factor Market."
53A discussion of this point within a micro framework appears in Y. Mundlak, "On Microeconomic
Theory of Distributed Lags," The Review of Economics and Statistics 48 (1966): 5160.
at any given point in time is predetermined by historical events.54 Factors move
between sectors, but this movement takes time; the rate of factor mobility depends
on economic variables, and so it can be estimated empirically. Thus, in away, calendar
time is introduced explicitly into the analysis. The shortrun properties of this model
are examined in the first five sections of this chapter. The properties of the factor
markets and the flow of migration equations are treated in the sixth section, and the
growth of the system is discussed in the next section.
The system is too complex to yield growth paths analytically, so they are calculated
numerically, using Japanese data for the year 1905 as the starting point. The calcula
tions depend on various parameters. The sensitivity of the growth path to some
changes in these parameters is examined in the final section of this chapter.55 The
framework for the numerical solution and the initial data and parameter values are
described in Appendix D.
Supply Conditions
Assume the economy consists of two sectors and, at any given point in time, the
distribution of resources between the two sectors is largely predetermined by past
developments. Specifically, each of the sectors has K,(t) units of capital and Lj(t) units
of labor. Agriculture, in addition, has A(t) units of land. The production function for
each sector summarizes the technology in that sector, and it is expressed in terms of
available, rather than employed, resources. That is, for agriculture,
Y,(t) = F,{K,(t), L,(t), A(t), t}, (5.1)
and for the rest of the economy,
Y2(t) = F2{K2(t), L2(t), t}. (5.2)
It is assumed that these production functions are firstdegree homogeneous in the
inputs and have positive first partial derivatives and negative second own partial
derivatives. Otherwise, the functions are of general form and can change over time.
The production functions and the resource allocation summarize the supply condi
tions of the model. The supply conditions are distinct in both their inclusions and
omissionsnamely, the conditions that the value marginal productivities equal factor
prices. This point is restated to emphasize an important feature of the formulation: at
any given point in time factor allocation is predetermined. Consequently, for any
given technology, the marginal productivities and, therefore, real factor prices are
uniquely determined and have no role in the factor allocation for the instant period;
they do influence the allocation in future periods. This specification, in general,
1"In some of the important features the model is similar to the disequilibrium model discussed in Kelley,
Williamson, and Cheetham, Dualistic Economic Development.
55The simulator used for solving the system is constructed in such a way as to facilitate tracing the impact
of various policy measures, but these impacts are not examined here.
allows for unequal factor prices in the two sectors, a situation that has been dealt with
under the topic of distortion in the factor market. The two models can be directly
related, however.
Momentary equilibrium is achieved by selecting a relative price p = p,/p2 (the price
of the first product in terms of the second one) that clears the commodity markets.
Production (y) is used for investment and for final consumption. The supply of these
two components in each sector is denoted by Xi and Xs, respectively. Consequently,
in agriculture,
Y1 = X, + Xi, (5.3)
and in the rest of the economy,
Y2 = Xj, + X2. (5.4)
The investment goods for sector 1 are produced partly in that sector and partly in
sector 2. Let 0 < X (p) < 1 be the proportion of I, that is produced in sector 1. The
higher is p, the smaller is X; hence X'(p) < 0.56 Investment for sector 2 is produced
completely within sector 2 so that in agriculture,
Xi = X(p) 1,, (5.5)
and in the rest of the economy,57
X2 = /2 + [1 (p)] p. (5.6)
Because the model assumes a closed economy, domestic savings are the only
source of investment funds. It is assumed:58
S, = spY1, (5.7)
and
S2 = S2Y2. (5.8)
"AX(p) may also depend on variables other than p, but the dependence on p is of interest here. In what
follows, where no ambiguity will result, we write for simplicity X rather than X(p).
s5For symmetry, we could assume that part of 12 is produced in sector 1. For the dichotomy of agriculture
and nonagriculture, this assumption is rather artificial and therefore ignored.
"We can start by assuming that saving rates differ by the source of income; i.e.,
The savings need not be fully invested in their sector of origin. LetpF represent the
value of funds flowing from sector 1 to sector 2; then
S,(t) =p(t)(l,(t)+F(t)),
S2(t) = 12(t) P(t)F(t).
(5.9)
(5.10)
Combining (5.3) through (5.10),
X1 (t) = X,(p) [sY,(t) F(t)],
X2(t) = s2Y2(t) +p(t)T[p(t),t],
(5.11)
(5.12)
where T[p(t),t] = [1 X(p)] [slY(t) F(t)] + F(t)
is the net draw of sector 1 on the supply of Y2. It consists of investment goods for sector 1
and the net investment in sector 2 financed by savings generated in sector 1.
The supply conditions can now be summarized:
Xs(. .) = Yj(t) X~(p) [sY,(t)F(t)],
(5.13)
S, = SLW1L1 + SK(rlKI + RA),
and
S2 = SLW2L2 + SK2K2,
where
S = total savings in each sector,
w, r = wage and rental rates, respectively, in each sector,
R = land rent, and
SL,SK = are the saving rates for wages and profits, respectively.
Dividing through by the value of the sectoral output,
s, = alSL + (1 aI)SK,
PY1
and
S2
S2 2  = 02SL + (1  2)SK,
Y2
where
a, is the labor share in the jth sector.
X(..) = (1s2)Y2(t) p(t) T (..), (5.14)
where (..) = [p(t), t)];
and
axs(. .)
X. (p)I1, (5.15)
dp
and
aX,
(..)= T(. .) + A'(p)/,P, (5.16)
ap
axs axs
where 11 > 0 implies > 0 and < 0.
Op Op
It is to be noted that at any time (t), the supply of X, for final consumption depends
on production in that sector and on the proportion of investment in sector 1 pro
duced in that sector. This proportion is monotonically decliningwith p. Therefore the
supply of X, for final consumption increases with p.59 The supply of X2 for final
consumption is negatively affected by the draw of sector 1, and the magnitude of this
effect depends on p.
Final Demand
The formulation of final demand follows that of Mundlak and Mosenson.60 Let
x/ X4/L be per capital demand in both sectors for final consumption of product j,
and y = py, + Y2, (Yj = Yj/L) be per capital income. We can then write the demand
equations,
xd = D,(p,y), (5.17)
and
xg = D2(p,y), (5.18)
Sg"t is independent of p when X(p) is constant. This includes the extreme case, X = 0, in which all
investment goods used by agriculture are produced by the nonagricultural sector. This was the assumption
used in Mundlak and Mosenson "TwoSector Model." It is also possible to have X = 1; however, this case
is of less interest here.
"oMundlak and Mosenson, "TwoSector Model."
where
Dj(p,O) = O, Dj(p,y) > 0 for all 0 < p 0.
Now, let E1, and Ej represent the price and income elasticities, respectively, of the
jth product. For all admissible values of p and y, E,, < 0, E2p > 0, and Ejy > 0. Under the
last assumption, that income elasticities are positive,61 (5.17) and (5.18) can be com
bined to yield
xA = D(p,x'), (5.19)
alnx El, Inxl
with =  > 0, and oDo= El EE2p < 0.
wtnx2 E2y l Inp
It should be noted that demand is not differentiated by sectors; differences in
consumption patterns between sectors are attributed to differences in income.62
Momentary and Comparative Equilibria
Equilibrium is achieved by selecting a price that equates aggregate sectoral demand
with sectoral production. This is the same as equating supply and demand for final
consumption; that is
xZ (..) = x( .) xj, (5.20)
wherexfr XP/L. Using (5.20) forxd, the demand equation (5.19), subject to its restrictions,
can be written as
xg = D*(p,xl). (5.21)
If the excess demand function is defined as
(. .) = D* [p(t),x l (..)] x .(. ),
then, using the conditions on the demand function and equations (5.15) and (5.16) we
have for I1, 0:
9( )8xl (l/p) Oxj/a(1/p) < 0.
p(1/p) (5.22)
6'Extending the argument to nonnegative elasticities is rather a straightforward matter but somewhat
cumbersome in presentation.
621n a more realistic model, differences in prices between sectors should also be allowed for. Such
differences also contribute to differences in consumption.
The solution is illustrated in the figure below:
Figure 4. Momentary Equilibrium Determination
(1s2)y2
1/p 1/p
The momentary equilibrium determines the pricep(t); point A in the figure repre
sents the initial such equilibrium point. Reference to the figure indicates that vari
ations in the various exogenous variables or parameters affectp(t) by affecting either
the demand or the supply for xi(t). The effect of changes in the demand or the supply
of xj(t) on p(t) are largely signed in the following:
Changes in:
yl(t)
Y2(t)
f(t)
S1
S2
x1(t)
xd(t)
For instance, an increase of per capital production in sector 1 increases the investment
in the sector. Some of the capital goods for sector 1 are purchased from sector 2, and
consequently less of y2 is available for final consumption, and xs declines. At the same
time, xs increases and, by the demand condition, x increases. This is because of the
income effect of an increase in yl. Thus, the excess demand increases and 1/P
increases (recall that p2 is the numeraire), or p declines.
Point B in the figure represents such a change. The initial increase in yl(t) can result
either from an increase in that sector's resources or from a change in technology. In
tracing the effect of a change in y,, f was considered to be fixed. In the discussion of
the flow equation in Chapter 4, and below, it is stated that af/a(s2yl) > 0, afla(s2y2) > 0.
This condition augments the effect just considered.
To this condition we can also add a quantitative assumption, alla(sly1) > 0,
al2/a(s2y2) > 0. Under these assumptions, aTla(s2y2) > 0 aTla(sy,) > 0. With these
conditions, the table can be completed. This simple framework makes it possible to
trace the effects of various factors and variables on prices, p(t). Changes in p (t) have
further repercussions on the system, and those are discussed next.
Factor Markets
The distribution of inputs between sectors determines their marginal produc
tivities. Once the price is determined, we also have the value marginal productivities.
Thus, for agriculture,
w,(t) =p(t)FiL, (5.23)
r,(t) =p(t)FlK,
R =p(t)FlA,
and for the rest of the economy
w2(t) = F2L, (5.24)
r2(t) = F2K,
where
w,r = wage and rental rates, respectively, in each sector,
R = rent on land, and
Fj(i = L,K,A) = the marginal productivities evaluated for the given inputs and
technology at time t.
The factor prices need not be equal. They are now endogenous to the system, and
so are their ratios; that is, 8r = rl/r2 and 8w = w1/w2. It is possible to analyze the
economy under the assumption that such ratios are constant, but other than one.63
The approach in such an analysis is somewhat different than the present one. The
supply conditions consist of defining all the resource allocations that result in a given
level of distortion in the factor markets. The equilibrium solutions consist of those
allocations that result in market clearance. Thus, the distortion analysis can be
considered somewhat a dual analysis to the present one; that is, a solution to the
present model is a solution to a factor price distortion analysis, and vice versa. Clearly,
however, once it is admitted that resource allocation is largely determined by histori
63Tropp and Mundlak, "Distortion in the Factor Market."
cal events, the equilibrium approach to the analysis of distortion in the factor market
loses much of its relevance for empirical analysis.
The essence of the present analysis is that the allocation of factors between sectors
takes time. More specifically, there is a flow of resources between the sectors. There
is a difference between the flow of capital and that of labor. It is assumed that the
value of the capital flow is bounded by the value of savings in the sector of origin.
Only gross investment can be allocated. In contrast, the flow of labor can exceed
growth in the labor force. Let M(t) be the migration of labor from sector 1 to 2 and n,
be the natural rate of population growth in sector 1; then,
M(t) = (1 + n,)L,(t) L,(t + 1). (5.25)
The labor flow variable M(t) and the flow of funds F(t) can be considered as
functions of variables whose values are determined by the state of the economy at
time t and by expectations with respect to the future. Such functions were estimated
empirically in Chapters 2 to 4. The flow variables can also, within bounds, be consid
ered in development models as instrumental or policy variables.
On the basis of Chapter 2,
M(t) L2(t) 1im
m(t) W W L(t) j m* [8*(t), z(t)], (5.26)
Li(t) L (t)J
where
0 < 131m < 1, z = various exogenous variables, including policy instruments, and
8* = expectation at t about the ratio of the wage rates in the two sec
tors.64
A similar approach was followed in Chapter 4 with respect to the flow of funds; that
is,65
p(t)F(t) [2r2(t1) 1a
pS(t) t) r(t^) f*[8* (t), z(t)], (5.27)
Sl(t) L7,(t1) I
where the or(t) are the proportion that each sector's income is of total income, and z(t)
is a set of exogenous variables. Note that both (5.26) and (5.27) are formulated so as to
maintain "constant returns to scale;" that is, doubling the labor force in the economy,
while holding the relative allocation and the other variables unchanged, will leave
m(t) unchanged. A similar interpretation follows for the flow equation.
641n empirical analysis it is preferable to use the ratio of income per capital in each of the two sectors rather
than the ratio of wages (Chapter 2). This, however, is not important for the present discussion.
"6Actually, 7r2/lr1, is used as a proxy for S,/S,. This point is discussed in Chapter 4.
The Growth of the System
The system defining the momentary equilibrium consists of equations (5.1) through
(5.10), (5.19), and (5.20). The system is expected to change constantly because of the
growth of resources, changes in their allocationas given in (5.26) and (5.27)and
changes in technology.
The change in the sectoral capital stock is given by Kj = Ij/Kj A, where A is the
depreciation rate. Drawing upon equations (5.7) through (5.10),
K, = sY,/K, F/K, A, (5.28)
and
K2 = s2Y2/K2 + pF/K2 A. (5.29)
Labor is assumed to grow at exogenously determined rates nj. Taking into account
labor migration, (5.25) and (5.26), we obtain for the growth in the labor force
Li = n, m, (5.30)
and
i2 = n2 + m(f/1 e), (5.31)
where e = L1/L.
Technical change can take various forms. Part of the value of the exercise is to trace
the consequences of various forms of technical change on the growth pattern. The
problem begins with the empirical applications, in which the evidence is generally
not sufficiently rich. We can write for the effect of technical change on output
Y9 = ay,1L + 31K + (1 alj81) y1A= 1, (5.32)
K,L1, A
and Y2 = a22L + 32 Y2K 2, (5.33)
K2, L2
where YjL is the rate of increase in the efficiency of labor in each sector.
Given equations (5.26) and (5.27) and the various parameters in question, equations
(5.28) through (5.33) and the production functions determine the rates of change of
sectoral outputs, Yj. To express such changes on a per capital basis, we need
i = n, e + n2(1 ). (5.34)
Changes in outputs are allocated between, changes in final consumption and
changes in investment. To obtain the change in final uses, it is necessary to differ
entiate equations (5.3) through (5.10) with respect to time. Bringing in the differentials
of (5.19) and (5.20), the rates of change of the various components of the system can
be expressed in terms of the predetermined variables, including migration, flow of
funds, and the rate of change in the flow of funds. If, however, expectations with
respect to differential sectoral income or factor returns are related to current factor
returns, the system is not quite closed.
To solve for the rates of change of the various components, we need the rates of
change of factor returns and some assumptions about how they affect the formulation
of expectations. In the numerical illustration that follows,it is assumed that these
expectations are naive; that is, that current factor prices are expected to continue.
The sensitivity of the growth process to this assumption is of interest, but it is not
discussed here.
Factor prices are determined by (5.23) and (5.24). In addition to the explicit roles they
play in flow equations (5.26) and (5.27), they play an implicit role in the computation of
factor shares. That requires an explanation. The production functions described by
(5.1) and (5.2) are quite general and need not be closely specified. We need to know
the rates of change of the outputs with time, but for this it is sufficient to know the
production elasticities. Thus, the problem of specifying a production function is
reduced to that of specifying the marginal productivities.66 Furthermore, for any set of
initial values, all that is needed is the rates of change in the marginal productivity
conditions. Thus,
wi = FIL, 1 K p F, R p = FlA, (5.35)
and
2 = F2LI, 2 = F2K. (5.36)
It should be recalled, however, that marginal productivities cannot change freely
because, by assuming constant returns to scale, they are subject to the Euler equa
tion. Differentiating the Euler equation and substituting factor prices for value margi
nal productivities,67
y, = aiv + 17 + (1 a1 3P) R 5, (5.37)
and
Y2 = a2V2 + (1 a2) ?2. (5.38)
6"This has important econometric implications which are not fully recognized and which will be dis
cussed elsewhere.
67These are the rates of change in the cost functions and could be obtained from different points of view.
Thus, for practical application, the rates of change of the marginal productivities have
to be specified. In the applications of this model, we chose the constant elasticity
of substitution (CES) form. The results are summarized in a compact form in
Appendix D.
Some Numerical Illustrations
In the present model, analytic solutions of growth paths are infeasible, and one has
to resort to numerical solutions.68 By its very nature, a numerical solution is specific to
the choices of data and parameters. Inductive generalizations for a relevant choice of
data and parameters are possible but are not of immediate importance. Therefore, we
will confine our numerical examination of the performance of the model to situations
of direct interest.
We have selected Japan of 1905 as our initial point in order to illustrate the calcula
tion of growth paths, to point out some relationships among the endogenous
variables along these paths, and to examine the sensitivity of the paths to changes in
the parameters. In so doing, we compare results obtained under alternative assump
tions.
This is not a discussion of the Japanese experience as sucha subject which will be
treated in Chapter 6; it is a methodological analysis. We, therefore, will not explain
and justify the choice of the values used for the parameters. The essence of the
method is described in Appendix D, and the initial data and parameters are described
in Appendix E.
We consider several alternative growth paths, but it would require too much space
to present the entire paths for all variables in question. Instead, we present results for
the initial year, t = 1, and for t = 21. The results are summarized in Table 12.69
The first column of Table 12 reviews the results of the basic run. The basic run is
obtained under the assumption that in the initial year (t = 1) sector 1 experiences
technical change of 1.52 percent, population growth of 1.3 percent, and a migration
rate of 2.8 percent. The migration rate increases to 3.5 percent in t = 21.70 As a
consequence, the sector 1 labor force declines from 16.2 in t = 1 to 11.7 in t = 21, and
per capital production declines from 18.3 to 16.4. The decline in sector 1's per capital
supply and the increase in real income result in an increase in the price ratio to the
level of 1.9. Factor prices in sector 1 increase because of the increase in p, the
technical change, and, in the case of labor, the decline in labor intensity caused by
migration. To eliminate the price effect, factor prices are also reported in terms of
sector 1's product.
The sectoral gap in wages causes labor migration. In order to trace the effect of
"Cf. Kelley, Williamson, and Cheetham, Dualistic Economic Development; and Houthakker, "Dispro
portional Growth."
"In this analysis A is treated as exogenous. Also, savings flow is restricted so as to be independent of the
differential returns. This restriction is removed in the next chapter.
7"These rates are higher than the actual prewar rates, and the reader who is interested in the Japanese
experience should keep it in mind. This is discussed further with the results for lower migration rates.
O Table 12Numerical solutionsselected results for t = 21
t = 21: Basic run and modifications
Variable t = la (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16) (17) (18) (19) (20) (21) (22) (23) (24)
16.4 19.7 21.1
106 89 81
11.1 15.6 17.6
21.3 16.8 14.8
3668 3840 3907
10808 9799 9380
1.9 1.3 1.1
89 53 44
175 189 197
.056 .043 .038
.250 .225 .212
107 84 76
330 246 222
508 585 634
.34 .48 .54
.39 .33 .31
.23 .22 .22
47 42 40
.030 .033 .035
57 66 70
625 313 242
1.23 .54 .38
.035 .016 .010
1.07 .33 .19
(51) (51) (51)
16.9 15.6 18.8 20.2 18.2 16.9 19.2 22.0
103 110 94 86 106 106 106 107
11.8 10.2 14.3 16.3 11.0 11.1 11.0 10.9
20.6 22.2 18.1 16.1 21.4 21.3 21.4 21.5
3701 3608 3789 3864 3764 3697 3821 3960
10614 11153 10112 9653 10804 10807 10795 10791
1.8 2.1 1.4 1.2 1.6 1.8 1.5 1.2
82 100 61 50 82 87 83 75
177 174 184 191 175 175 175 174
.054 .061 .046 .041 .051 .057 .048 .044
.248 .252 .233 .221 .251 .250 .251 .250
103 114 90 81 104 105 95 89
314 355 265 237 342 334 347 365
516 502 559 600 506 507 505 502
.36 .31 .44 .56 .34 .34 .34 .34
.38 .40 .35 .33 .36 .38 .34 .30
.22 .23 .22 .22 .21 .22 .21 .20
46 48 43 41 52 48 57 64
.030 .029 .033 .034 .032 .032 .033 .038
58 55 64 68 65 58 65 76
557 737 378 286 547 599 509 429
1.08 1.47 .68 .48 1.10 1.20 1.01 .85
.034 .033 .019 .014 .036 .036 .036 .038
1.16 .93 .43 .28 .96 1.04 1.00 .88
(51) (51) (51) (51) (51) (51) (51) (51)
16.2 32.3 16.6 14.4 14.7 16.7 16.3 16.6 16.4 16.3 16.9 16.2 17.0
146 122 97 107 99 107 124 112 106 106 105 107 104
10.9 15.3 14.6 11.2 14.7 11.2 10.9 11.0 11.3 11.1 11.7 10.8 11.8
21.5 17.1 22.4 25.8 27.0 21.2 21.4 21.3 21.1 21.2 20.6 21.5 20.5
3663 4435 3805 3667 3804 4343 3664 4289 3663 3666 3685 3660 3688
12545 11242 10993 11623 11810 11031 15493 12289 10803 10807 10878 10788 10894
Y,/L=y, 18.3
Y,2L=y, 40
L, 16.2
L2 8.8
K, 3679
K, 4242
p 1
w, 29
w, 122
r, .025
r, .187
R 54
k, 227
k2 482
/ .65
p .46
if .31
w,/p 29
r,Ip .025
R/p 54
pk, 227
pk,/k, .47
m .028
8,(t)
(t)
1.8 2.3 2.2
75 109 92
172 164 161
.058 .070 .071
.256 .274 .280
113 134 139
260 327 258
492 450 437
.40 .30 .35
.38 .43 .41
.23 .24 .24
43 46 42
.033 .032 .033
64 56 64
459 768 558
.93 1.71 1.28
.034 .033 .033
.74 .99 .98
(51) (31) (41)
1.9 1.9
92 91
177 211
.052 .057
.246 .189
112 109
389 335
520 723
.34 .34
.43 .31
.23 .20
48 47
.026 .030
58 56
756 649
1.45 .90
.035 .038
1.06 .73
(51) (51)
1.9 1.9
96 92
174 174
.053 .055
.253 .250
96 103
328 329
510 509
.35 .34
.39 .39
.23 .23
50 48
.028 .029
50 54
625 625
1.23 1.23
.034 .034
1.04 .95
(41) (41)
2.8 1.6 3.0
129 74 137
179 174 179
.086 .046 .099
.240 .253 .242
164 88 176
314 338 311
527 501 531
.36 .33 .37
.49 .35 .51
.31 .19 .33
46 48 45
.030 .030 .030
58 56 58
888 527 936
1.69 1.05 1.80
.028 .038 .027
1.03 .86 1.07
(31) (51) (31)
aThe units of measurement for the following variables are: y, K,,, k, w,/p, R/p, and r,. They are measured in terms of the sector 1 product; y,2, Kw,, w,, r, and pk,,
are measured in terms of the sector 2 product; r, and rlp are pure numbers.
2.3 7
106 47
244 260
.067 .033
.291 .267
127 72
336 291
584 657
.34 .47
.40 .21
.20 .14
47 71
.030 .049
56 110
759 192
1.30 .29
.037 .019
.88 .11
(51) (51)
bThe columns represent various parameter assumptions. The changes for each column are:
(1) The basic run; data for this run are described in Appendix E.
(2) bom, the intercept of the migration equation is 4.5 instead of 3.755.
(3) bom is 5.
(4) The slope of the wage differential in the migration equation, b,,, is 0.1 instead of 0.232.
(5) b2 = 0.5.
(6) bom = 4.5 b2m = 0.5.
(7) bom= 5, b2m =0.1.
(8) Landaugmenting technical change in sector 1, yA, is 0.03 instead of 0.0152.
(9) Capitalaugmenting technical change in sector 1, y,, is 0.03 instead of 0.0152.
(10) Laboraugmenting technical change in sector 1, yL, is 0.03 instead of 0.0152.
(11) yA = yK =yL = 0.03.
(12) Y72 = 72K = 0.03, instead of 0.0167.
(13) bom = 4.5, 1,, = yK = y,L = 0.04, y,2 = y2 = 0.03.
(14) Natural rate of growth in sector 1, n,, is 0.026 instead of 0.013.
(15) n2 = 0.026 instead of 0.013.
(16) n, = n, = 0.026.
(17) The saving ratio in sector 1,s,, grows at the rate of 3 percent ( = 0.03) instead of zero growth.
(18) S2 = 0.03 instead of 2 = 0.
(19) Depreciation rate, A, is 0.02 instead of 0.03.
(20) The direct elasticities of substitution in the two sectors are reversed in size: rr, = 0.8, o, = 1.2.
(21) ,1 =
(22) The "income elasticity", ), is 0.6 instead of 0.3.
(23) The "demand elasticity" oD = is 0.9 instead of 0.6.
(24) r, = 0.3.
labor migration on factor prices, we present the value of 6, = w1/w, for a specified
year in the distant future. Thus, at t = 51, 8, = 1.07; that is, the agricultural wage rate
slightly exceeds the nonagricultural wage. For the same year, the rental on capital in
agriculture still lags behind that in the nonagricultural sector.
The effect of labor migration on factor intensity is reflected in the capitallabor
ratios, and, in general, there is a faster capital deepening in agriculture. Capital in
sector 1 is reported in terms of that sector's product. To make it comparable with the
capital of the nonagricultural sector, it is multiplied byp to yield pkl, and this product
is compared with k2 by computing, pkl/k2. The ratio increases from 0.47 in t = 1 to 1.23
in t = 21, indicating that sector 1 has become more capital intensive. In the present
run, this is largely an outcome of rapid labor migration and the restricted mobility of
capital, which results in relatively low returns on capital in agriculture.
Finally, the relative importance of sector 1 is reflected in its share in the labor force
(f),the overall capital stock (p), and total output (w). Obviously, the sharpest decline
was in f, from 0.65 to 0.34.
We can now evaluate some of the effects of the parametric changes. First, we
consider two kinds of changes in migration: in the level of the migration equation;
and in the slope, or elasticity, with respect to the wage differential. The actual
equation used was taken from Chapter 3; that is,
m = exp 3.755 + .232 In 2 0.85 +
0.372 In ( + 10.88 In (1 + n) (5.39)
This equation was obtained by finding the intercept (in this case, bom = 3.755) that
will best fit the Japanese data for 195172 if the other coefficients are obtained from
CCS analysis.
The postwar period has been a period of intensive migration, and therefore the
intercept obtained may be relatively large; exp 3.75 = .0235, so even without the
contribution of any other terms we get a migration rate of 2.35 percent, which is
somewhat high for the period under consideration. Columns 2 and 3 in Table 12
report results for lower migration rates: the intercepts are exp 4.5 = 0.011 in
column 2 and exp 5 = 0.0067 in column 3. A comparison of the two columns
indicates that reducing migration rates causes the per capital product in sector 1 to
increase instead of decline as it did in the basic run. This is because with less
migration, more of the labor force remains in agriculture. Also, because part of sector
1's savings are invested in that sector, smaller migration leads to large total savings
accumulation in sector 1, but these "extra" savings are not enough to match the larger
labor force. Therefore, the capitallabor ratio decreases as migration decreases.
The smaller migration is, the smaller is the pressure on prices from the supply side.
Also, smaller migration reduces per capital production in sector 2, and, therefore,
puts less pressure on p from the demand side. The values of p at t = 21 are 1.27
for bom = 4.5 and 1.09forbom = 0.5. The factor prices reflect the changes in factor
intensities. A decrease in migration decreases k, and increases r/p, the real return on
capital. However, since p also decreases, rl, the rate of return evaluated at "current
prices," decreases with a decline in migration. The behavior of real wages is in the
opposite direction. As a consequence, the smaller is the migration, the larger is the
intersectoral wage differential. Obviously, the amount and the rate of closure of the
wage differential depend on the rate of migration.
Table 13 summarizes the effect of these parametric changes by presenting the signs
of the changes along the growth path. Column bom for example, summarizes the
direction effect of changes in the level of the migration equation. Columns 4 and 5 of
Table 12 report results due to changes in the slopes of the wage differential in the
migration equation; instead of 0.232, used in the basic run, there is a decline to 0.1 in
column 4 and an increase to 0.5 in column 5. Basically, increasing the slope increases
migration, and consequently the direction of changes along the growth path are
similar to those obtained by changing the intercept. This can be seen by comparing
columns bor and b2m of Table 13.
Various forms of technical change are considered in columns 8 to 13 of Table 12. In
the basic run, each of the technical change components in sector 1 is 1.52 percent and
in sector 2, 1.67 percent. Increasing each component in sector 1 separately to
3 percent increases output; the total increase in output is weighted by the particular
factor share. Again, an increase in sector 1 output is accompanied by a decline in p as
compared with the basic run and bya decline in factor prices in sector 1. However, the
real values of factor prices (deflated byp) rise because of the technical change. These
changes are relatively small, and therefore they do not affect migration rates.
A more pronounced effect is obtained when all the components of the agricultural
technical change are allowed to change by 3 percent: this leads to larger agricultural
output, lower p (1.18), lower w, (75), and therefore a somewhat larger migration rate,
3.8 percent in t = 21. The wage ratio is still less than 1 in t = 51. The directional effects
of changing all the components appear in column y, of Table 13. Column 12 in Table 12
reports results for a technical change of 3 percent in sector 2. In that case, p goes up,
indicating that the relative price of nonagricultural output declines. The directional
effects of increasing y2 are reported in Table 13.
In most of the various runs, per capital agricultural producteither declines with time
or increases slightly. This is because of strong migration, and only moderate technical
change as compared with population growth. Column 13 in Table 12 is an excep
tionit assumes a 4 percent technical change in sector 1, 3 percent in sector 2, and a
small migration rate; this results in a per capital production of 32.3 in t = 21, compared
with 18.3 in the base year.
The remaining columns can be reviewed in a similar way. Columns 14, 15, and 16
report changes because of the doubling of the natural rates of population growth to
2.6 percent in one or both sectors. Total population increases at faster rates, and any
per capital figures are thus lower. Otherwise, the increase in the differential rates of
population growth affect product prices and factor prices as expected; factor inten
sities are affected similarly (but not independently).
In columns 17 and 18, the saving rates are allowed to increase every year at the rate
of 3 percent; in column 19, the depreciation rate is decreased from 3 to 2 percent.
These changes directly affect the capital stock. It is obvious that because of the
Table 13Directional effects of parametric changes along growth path
Parameters
Variables bom b2m y1 Y2 n1 n2 s, s2 71 O D
y, + + + + 
Y2 + + + + + + + +
S + + + +
+ + + + + + + +
K, + + + + +
K2 + + + + + + + +
p + + + + 0 0 +
w, + + + + + + +
w2 0 + + + + 
ri + + + + + + +
r2 + + 0 + + + +
R + + + + + + + + 
k, + + + + + + + +
k2 + + + + 
S 0 0 + 0 0 + 
p + + + + + +
7T + + 0 + 0 + 
w,/p + + + 0 + 0 +
rlp + 0 + + 0 0 0
Rip + 0 + + +
pk/,k2 + + + + + + 
Note: 0 signifies no effect, while and + signify negative and positive effects respectively.
aThe direction of changes is obtained by comparing changes in different columns of Table 12 as follows:
bom From columns (1), (2) and (3).
b2, From columns (1), (4), and (5).
y, From columns (1), (4), and (5).
Y2 From columns (1) and (12).
n, From columns (1) and (14).
n2 From columns (1) and (15).
s, From columns (1) and (17).
s2 From columns (1) and (18).
i7 From columns (1) and (22).
OD From columns (1), (23) and (24).
restriction on the mobility of capital funds, the sector in which savings increase is
important.
The presentations in columns 20 and 21 of Table 12 indicate that the results are not
very sensitive to the choice of the elasticity of substitution. The effect of the elasticity
of substitution on growth is only of secondorder importance. One result, however,
is that the effect on prices also is not substantial. This may explain why many analysts
have not succeeded in obtaining empirically "proper" values for elasticities of substi
tution.71
71 It should be noted that the values of oi which appear in the table are only the initial values. The model
allows for changes in rj with time. These changes, however, were not large in most cases.
The last three columns report results due to changes in demand parameters.
Increasing the "income elasticity," 1, from 0.3 to 0.6 increases the demand for the
sector 1 product that results from higher real income arising from technical change
and capital accumulation. The increase in demand increases p and factor prices in
sector 1, and consequently the migration rate is reduced somewhat.
Changing the "price elasticity" from 0.6 to 0.9 and to 0.3 has a significant effect
on p, on factor prices, on the migration rate, and on relative capital intensity. When p
increases along the growth path, as in the present case, increasing the (absolutevalue
of the) price elasticity implies a decline in the quantity demanded of sector 1's
product. As a consequence, the directional effect on the system should be the
opposite of the effect of increasing income elasticity. This is indeed the case here, as
can be seen by comparing the last two columns of Table 13.
A different way to interpret Table 13 is to read the rows and examine the causes for a
particular change in the endogenous variables. This is left for the reader with one
exception. As argued elsewhere, the proper measure of the terms of trade of agricul
ture is the return on its specific factors;72 in this case, the return on land as measured
by R. Changes in R originate in changes inp and in real rent. Real rent is measured by
Rip, or the share of land in the average (per unit of land) productivity. Average
productivity increases with factor intensity and with technical change. The effect of p
depends on the values of p. Most of the runs indicate upward pressures on sector 1's
p, and this contributes to an increase in R. However, in a situation where declines,
such as in run 13, the price effect is to suppress considerably the rent measured in
"value" terms. Obviously, with less elastic demand, technical change in sector 1 may
result in actually reducing rent.
The lack of immediate factor mobility implies that a change generated in one
market does not spread immediately to other markets. This can be seen in Table 12.
The degree of rigidity is determined by the rates of factor flow, but these in turn are
considered to be economic variables. Yet, policy measures that can speed up flow
also assist in spreading the effect among the various markets.
Eventually, if factor mobility is greater than a minimal rate, equality of factor prices
is achieved. That may take a long time, even when the annual migration accounts for
3 percent of the labor force. However, once the point of equality is reached, analytic
results obtained from neoclassical models, which assume equality of factor prices,
are pertinent and should not differ from the results obtained from the present model.
Our analysis here raises an important methodological issue. These runs have been
obtained by changing a small number of parametersin many cases only one param
eter. It is clear that there is a great deal of freedom in creating various forms of growth
paths. Furthermore, a particular path can be created by more than one set of parame
ters. How, then, can a reconstruction of a particular history be used as evidence that
the "right" set of parameters has been used?
Obviously, this is a problem of identification in a somewhat different context. If the
system is identified, then in principle it should be possible to estimate the parameters
72Y. Mundlak, "The Terms of Trade of Agriculture in Context of Economic Growth" in Economic
Problems of Agriculture in Industrial Societies, eds. U. Papi and C. Nunn. (New York: St. Martin's Press,
1965), pp. 63456.
in some optimal sense by using nonlinear techniques. Although this subject is outside
the mainstream of our analysis, it is important to emphasize that, in general, there are
no onetoone onto relations between a set of parameters and a growth path. There
fore, reconstructing a historical growth path from a particular set of parameters, or
more generally by using a particular model, does not prove that this model is the true
or correct one. It is legitimate, however, to use the procedure we have demonstrated;
that is, to evaluate the response of the growth path to a particular change in parameters.
6
A QUANTITATIVE INTERPRETATION OF
SOME ASPECTS OF THE JAPANESE EXPERIENCE
During the last century, Japan has been transformed from a largely rural and back
ward economy to a major industrial economy.73 "Perhaps the most outstanding feature
of Japan's development is its rapidity, or what is even more important, the sustained
character of the growth process."74
The Growth Process in Japan
Because of its growth record, the Japanese experience has been broadly investi
gated. Various approaches have been tried. First, there are the simplistic views, the
single concept or criterion framework. For instance, there is some preoccupation with
the concept of the prerequisite for growth. Did Japan grow because it met the prerequi
site, established by the British experience, that an agricultural revolution must precede
the industrial revolution?
Ohkawa states that "so far as agriculture is concerned, this notion seems to be not
applicable to the Japanese case."75 Instead, "the point is that Japanese agriculture
developed ... side by side with the process of speedy industrializationa concurrent
growth of industry and agriculture."76This interpretation is in line with Gerschenkron's
idea that prerequisites have substitutes.77 That, of course, raises the question of the
usefulness of the concept of prerequisites.
Basically, growth originates in using existing resources better as well as in adding to
available resources. Adding resources and improving technology can be a purely
domestic activity or one assisted by the outside world. The growth process can be
accomplished in various ways, through various combinations, and at various rates. It
is more instructive, therefore, to study the process itself rather than to select a
particular aspect of it and try to generalize from it. Indeed, Hayami et al., after
examining various lessons drawn from the Japanese experience, conclude that "the
lessons from the Japanese experience, if any, should be the process by which a
unique pattern of agricultural and economic development was created in exploiting
""We chose 1868, the year of the Meiji Restoration, as the point of departure for modern economic
growth in Japan." K. Ohkawa. Differential Structure and Agriculture: Essays on Dualistic Growth (Tokyo:
Kinokuniya Bookstore Co., 1972) p. 166.
74Ohkawa and Rosovsky "The Role of Agriculture," pp. 4357.
'"Ohkawa, Differential Structure, p. 167.
761bid., p. 170.
77A. Gerschenkron. Economic Backwardness in Historical Perspective (Cambridge: Harvard University
Press, 1962) pp. 3151.
the available opportunities specific to Japan. . ."8
Several writers have studied various aspects of Japan's growth process.79 All contri
butors seem to agree on the main features of the process, such as the role of
agriculture in financing investments for industrialization, in providing food for in
creased demand, and in supplying cheap labor to the other sectors of the economy.80
Different analysts vary in the weights they give to different features of the process.
Most of the discussions, though based on empirical evidence, do not quantify the
process in the way that was outlined in Chapter 5. It is desirable, therefore, to
supplement the literature by fitting our model to the Japanese data to see how the
process can be examined in its entirety within the framework we have proposed. This
analysis can be used to quantify the effects of some of the features of Japan's growth
process.
The next section of this chapter reviews briefly some of the highlights of the
Japanese experience. It is followed by two sections which describe how the model is
fitted to prewar and postwar Japanese data. Next, the role of intersectoral resource
flow is examined quantitatively. The approach is to obtain the development paths of
the economy without labor migration, without a flow of savings from agriculture,
then without either of the two. A similar approach is followed in examining the
importance of technical change and rates of capital accumulation. In so doing, light is
cast on the quantitive importance of these features.
Growth in Agriculture
Various studies indicate an overall growth of Japanese agriculture for a long span of
time. Yamada and Hayami state that the average annual rate of growth in agriculture
for the period 1880 to 1965 was 1.6 percent.81 They divide this period into subperiods
which differ in the growth rates of agricultural output, as well as in some other
economic attributes. The growth rate subperiods are:
118761904 (1.2 percent), a period of steady growth.
11190418 (3.5 percent), a period of accelerated growth.
111191838 (0.9 percent), a period of relative stagnation.
IV193847 (2.8 percent), the war period.
V194757 (4.4 percent), the postwar recovery.
VI195767 (2.8 percent), spurt following the recovery.
The growth in output was accompanied by a slower increase in aggregate input.
78Hayami et al. A Century of Agricultural Growth, p. 215.
7Ohkawa and Rosovsky, "The Role of Agriculture," and Ohkawa, "Agricultural Policy."
8"Gustav Ranis. "The Financing of Japanese Economic Development," in Economic Growth andAgricul
ture.
"8S. Yamada and Y. Hayami, "Growth Rates of Japanese Agriculture, 1880195," mimeographed, (The
Food Institute, EastWest Centre, University of Hawaii, and Economic Development Center, University of
Minnesota, 1972). Similar results are also reported in Hayami etal., A Century of Agricultural Growth.
Yamada and Hayami attribute 40 percent of the overall increase in output (or value
added) to an increase in aggregate input; the remaining 60 percent was attributed to
the residual, technical change; that is, of the 1.6 percent increase in agricultural
output, 0.6 percent can be attributed to aggregate input and about 1 percent to
technical change.
The input trend reflected a decline in agricultural labor from a level of 16 million
workers in 1907 to about 14.5 million in 1937; this decline was subject to some
fluctuations related to overall economic activity. In the 1950s the labor force was again
16 million, reflecting the return to agriculture during the war years, but in the postwar
period this level went down to nearly 10 million workers in the late 1960s, and it has
continued to decline throughout the 1970s.
Other agricultural inputs increased. Land increased by 30 percent during the whole
period; capital increased slowly in the prewar period and rather rapidly in the postwar
period, and inputs of raw materials, such as fertilizers, also increased.82 Hayami, etal.
claim that the technical change was partly due to nonconventional inputs, such as
education and research; to a smaller degree, however, the change reflected a statisti
cal point related to the selection of proper weights.83 It is important to note here that
the interwar period was basically a period of stagnation in technical change.84
Growth in Other Sectors
The nonagricultural sector experienced more rapid growth than the agricultural
sector. This, in part, reflects the growth of resources in the N sector. The growth of
the labor force consisted of the natural rate of increase, as well as the migration of
labor from agriculture. (See Figure 6.) The N labor force increased from a level of 9
million workers in 1907 to 17 million in 1937, a near doubling of the labor force. The
situation in the postwar period was even more remarkable. The labor force increased
from 24 million workers in 1955 to 42 million workers in 1969.
It is generally agreed that the flow of labor from the A sector is a response to
changing economic opportunities. There is less agreement on the nature of the
economic opportunities. The lack of consensus to a large degree reflects difficulties
in measuring the factors related to the migration. In Chapter 3, we show that migra
tion from agriculture into another sector can be explained in terms of income
differentials between the two. These income differentials are themselves endogen
ous to the process of growth.
It is interesting to note that despite the differential rate of growth of output of the
two sectors, agricultural prices did not increase much relative to other prices during
the entire survey period; in fact, throughout a good part of it, they declined. Figure 10
shows that for the prewar period the ratio of agricultural prices to N sector prices went
up from 1 in 1907 to 1.1 in 1922. It declined thereafter, reaching its lowest value of .68
in 1932. In part, the decline reflects the fact that domestic agricultural production was
82The detailed time paths of output, capital, and labor are shown in Figures 4, 6, and 8.
83Hayami et al., A Century of Agricultural Growth, chapter 4.
a41bid., chapter 5.
not the only source of supply; it was supplemented by food imports. Imports became
important following the food riots of 1918.85
In the postwar period, using the 1955 ratio of prices as a base, we see that agricul
tural prices declined up to 1960, and from then on there is a general trend toward
price increases reaching a level of about 1.2 in 1969 (see Figure 13). This perhaps
indicates a relative scarcity of agricultural products. A higher relative price forA sector
products acts to close the gap in per capital income between the two sectors and to
discourage offfarm migration.
Although this may have been the case in recent years and is the prospect for the
future, it was not true of prewar Japan. In that period, the relative price of agricultural
products did not show a significant upward trend, and the income differential was
considerable. That is an indication that the rate of offfarm labor migration was not
high enough to offset the effect of the natural rate of labor force growth on agricul
tural incomes. Only in more recent years has this trend reversed, tending to narrow
the intersectoral income differential.
Some writers have emphasized, in addition to the flow of labor, the importance of
the flow of savings out of agriculture in financing growth of the nonagricultural
sector. The quantitative effect of such a flow has not been discussed explicitly, at least
not in sufficient detail, in the literature. Even though on a priori grounds one can
agree with the qualitative aspect of this argument, it is difficult to nail down the
quantitative effect of the flow of savings. Some of these issues were explored in
Chapter 4, and some measures of the flow itself were developed in order to estimate
the quantitative effect of the variables that determine such a flow. This analysis
suggested a gap in returns and an outflow of up to40 percent of agricultural savings in
the prewar years. The outflow declined in the postwar years, and recently it has been
disappearing.
In brief, the two sectors have grown at different rates, and agriculture has contrib
uted labor and capital to the nonagricultural sector, but has managed to maintain its
overall per capital growth by technical change. The flow of resources has been
motivated by income differentials, which in turn reflect factor scarcity, as well as the
levels and the changes in the levels of technology in the two sectors. Thus income
differentials are endogenous to the process of development.
A theory or framework for analyzing this process requires a system which explains
the behavior of all these variables simultaneously. The approach outlined in Chapter 5
will be used here to explain or simulate the Japanese experience we have just
reviewed.
Fitting the Model: Prewar Data
Obtaining numerical solutions to Japan's growth path requires making assump
tions about the values of the parameters which enter into the model. Appendix F lists
all the variables that enter the analysis and their initial values for the prewar (1907) and
postwar (1955) periods.86 Some of the more important assumptions involved labor
"Ibid., pp. 6164.
"It should be noted that we use fiveyear moving averages to fit the data and for the simulation. We did
and savings flows. For offfarm labor migration we use the empirical results obtained
in Chapter 3. The migration equation was fitted separately to the prewar and postwar
data so as to obtain intercepts for the two subperiods that are consistent with the fact
that migration was much slower in the prewar than in the postwar period. The actual
values used for the intercepts were 3.785 percent and 4.8 for the prewar and
postwar years, respectively." Otherwise, the empirical equation is the same as the
one used in Chapter 5.
The flow of savings equation that is used is:
din (F/S,) = 0.17din (S21/S) 0.091 din8,
Unlike labor migration, the initial values for the savings flow must conform to
national accounting identities for the base years. For all other years, the values were
obtained by deriving the rates of change of the flow variable using the flow equation.
The intercept does not enter into this derivation.
Savings flows cannot be analyzed independently of knowledge of, or assumptions
about, saving behavior in the two sectors. Estimates of the sectoral saving rates and
their effect on the estimates of the rates of flow were taken up in Chapter 4. Prewar
saving rates in agriculture were estimated to be about 20 percent. The saving rate of
the N sector increased steadily as a function of per capital income in that sector,
starting from a level of 9 percent in 1907 and reaching 16 percent in 1937. Using these
values in the simulation yielded accumulation rates which were somewhat below the
actual rates, so the saving rates for the prewar period were adjusted up moderately.
Factor shares for agriculture reported by Yamada and Hayami indicate a low value
about 0.1 for the capital share, a land share of about 0.3, with the labor share
accounting for the remaining 0.6.88 The shares for the N sector were taken from
Ohkawa and Rosovsky. The initial value for the labor share is slightly less than 0.6. The
value changes throughout the period because the shares are endogenous in this
analysis, and they are computed for every year according to the simulated results for
that particular year.
The initial values for technical change in the two sectors were obtained from the
same sources as the factor shares. However, these values were adjusted to improve
the fit of the model.
Initially, the analysis was carried out under the assumption of a residual technical
change in A of 1.1 percent per year and of 0.75 percent per year in N. The results are
reported in Table 14 under the headings of Run 1 for 1920 and for 1937. The actual
values are reported also for purposes of comparison. The values were obtained for all
years and were plotted against the actual values.
In general, the fit of the simulated values to the data was "good." The exception was
not have a comprehensive set of annual data for years prior to 1905. Working with fiveyear averages, the
analysis starts with 1907.
87The reference here is to the intercept in the logarithmic form of the equation. The respective natural
values are: 0.0082 and .0227.
"Yamada and Hayami, "Growth Rates of Japanese Agriculture," Appendix. In some runs we tried some
different values, but those are not reported here.
0 Table 14Actual and simulated levels of some economic variables for prewar Japan
1920 1937
Initial Values:
Variable initial Values: Actual Values Run 1C Run 2d Actual Valuesb Run 1c Run 2d
1907
Yi
Y2
L,
L2
K,
K2
P
W,
W2
r,
r2
R
k,
k,
t
w,7P
r1/P
r, IP
Pk,
Pklk2
M
25.8
45.9
16.1
9.1
3.9
5.0
1.0
42.6
138.2
3.4
18.7
76.6
2.4
5.4
0.638
0.440
0.360
42.6
3.4
2.4
0.447
0.9
27.6
71.0
14.8
12.5
4.5
11.7
1.12
3.1
9.4
0.542
0.277
0.280
1.6
25.8
67.1
15.6
12.2
4.4
9.7
1.03
53.1
185.4
3.7
15.5
86.2
2.8
7.9
0.600
0.321
0.284
51.6
3.6
2.9
0.371
1.1
28.1
67.1
15.6
12.2
4.5
9.7
0.96
53.9
185.5
3.7
15.7
87.5
2.9
7.9
0.560
0.309
0.287
56.2
3.9
2.8
0.351
1.1
25.2
105.6
14.5
17.2
5.7
24.8
0.91
4.0
14.4
0.458
0.188
0.193
1.2
25.7
108.4
14.4
17.1
5.8
24.8
1.07
72.0
283.1
3.8
10.8
99.7
4.0
14.5
0.457
0.199
0.202
67.6
3.6
4.2
0.294
1.3
23.8
101.1
14.5
17.1
5.8
24.1
1.11
69.8
263.9
3.7
10.5
96.7
4.0
14.1
0.458
0.212
0.208
62.7
3.3
4.5
0.317
1.3
Note: Empty cells indicate that data were not available.
aUnits of variables are as follows (monetary values in constant 1907 yen):
Y1, Y2 yen
L,, L2 millions of workers
K, K2 billions of yen
w,, w2 yen
r,, r2 percent
R yen
k,, k, hundred yen
r,/p percent
pk, hundred yen
m percent
bActual values are fiveyear moving averages centered at indicated year. Empty cells indicate no comparable data were available.
CRun 1 is the basic prewar simulation run.
dRun 2 divides the prewar into subperiods 1907 to 1920, 1920 to 1937. For the first subperiod y, is set at 0.0175. For the latter subperiod y, is 0.0015 and y2 is 0.004.
Otherwise, the values of the initial data and parameters are the same as in the basic run.
per capital agricultural production, for which the simulated path did not pick the
turning point in 1918. This may have been because the rate of technical change was
greater during the first part of the period.
Run 2 accounts for this difference by assuming a residual technical change in
agriculture of 1.75 percent per year for 1907 to 1920 and only 0.15 percent per year for
the remaining prewar years. Similarly, to get a better fit for nonagricultural output,
the rate of technical change was reduced from .75 percent to .40 percent for the
second subperiod.
The results of Run 2 are plotted in Figures 5 through 9. The simulated per capital
agricultural output values shown in Figure 5 fit the actual values reasonably well. In
particular, the model simulates the turning point and the interwar retardation.89
Attributing the turning point to technical change does not reveal many factors, but at
this level of aggregation we do not go into a more refined explanation of this term.
Our main interest is to examine how the assumptions with respect to the parameters
of the model help us to explain the overall observed trends in the main economic
variables. The figure shows similar results for the nonagricultural sector. Here, there
is a much stronger trend in the data, and this trend is well depicted by the simulated
results.
In Figure 6, we see that agricultural labor declined constantly, except for some
cyclical fluctuations during the period. This trend is depicted by the simulated results,
but the simulation does not pick up the cyclical variations. An even better fit of the
simulated results to the data is obtained with respect to the N labor force.
Capital accumulation in each sector is shown in Figure 7, and again the simulated
results come close to the actual values. The simulation would come even closer if the
saving rate in agriculture were increased somewhat.
Figure 8 traces the trend, or rather the fluctuations in the ratio of nonagricultural to
agricultural prices. It is apparent that the price ratio fluctuated a great deal during this
period. The simulated path detects some of the trend in the data, reflecting during the
first part of the period a relative scarcity of agricultural compared to nonagricultural
outputs and a later reversal of this situation.90
There are no good data for wages to be compared with the simulated results, but it
is of some interest to compare the simulated wage rates in the two sectors, and this is
done in the top panel of Figure 9. The comparison shows that the gap in wage rates
widens in the prewar period, which indicates that migration out of agriculture was not
fast enough to decrease the relative oversupply of labor in agriculture.
The situation is somewhat different with regard to returns on capital shown in the
lower panel. The return to capital in the N sector declined rather fast, reflecting the
rapid capital accumulation, whereas the rate of return in agriculture increased only
slightly. As a result, the differential returns on capital declined during the prewar
period.91
89The period covered by the prewar simulation covers periods II and III in the classification of Yamada
and Hayami discussed previously.
"The model is basically a closed economy model, but net imports can and were introduced exogenously.
Apparently, this procedure was not sufficiently refined to produce the observed annual price variations.
910n the whole, the rate of returns in agriculture are rather low. These low returns reflect the base data,
figure j. /ciTua ana 3imularea rer iapia vurpurs, rrewar renoa
Agriculture
25.50
2 O. Actual
25.00
24.50 
24.00
Simulated
23.50
110.00 Nonagriculture
105.00
100.00
95.00
90.00 Simulated /
85.00 Actual
80.00 ......"""
75.00
70.00
65.00
60.00
55.00
50.00 ......*...
45.00 1 1
1907 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 1937
Figure 6. Actual and Simulated Labor Force Levels, Prewar Period
16.10 Agriculture
16.00
15.90
15.80
15.70
15.60
15.50
C 15.40
0 15.30
S15.20 1
S15.20 Actual Simulated
. 15.10
15.00
14.90
14.80 /
14.70
14.60
14.50 "*
14.40 ". ..***
14.30
Nonagriculture
17.50
17.00
16.50
16.00
15.50
15.00
14.50
5 14.00
Actual
 13.50 Ac
c 13.00
. Simulated
i 12.50
12.00
11.50
11.00
10.50
10.00
9.50
9.00
1907 8 9 10 11 1213 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 361
Years
figure /. Actual and Simulated Lapital, Prewar Period
Agriculture
Actual
Nonagriculture
Actui
5.
4Q.
( 5
U
m 5.
CO
30
OD 4.
( 4.
U. 4.
2 4
U
4.0 1 i I
1907 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 1937
Years
Figure 8. Actual and Simulated Terms of Trade Between Agricultural and Nonagricultural Sectors, Prewar Period
1.15 
1.10 
1.05 :\ *.. Simulated
S.95
o Actual
C .90 
.80 
.75
.65 I
1907 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 1937
Years
Figure 9. Simulated Wages and Capital Returns, Prewar Period
Capital Returns
*. Nonagriculture
Agriculture
Wages
(Shadow Prices)
culturee
Agriculture
C
Q)
121
0
 11I
10(
0
O 9(
1907 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 1937
Years
Fitting the Model: Postwar Data
One of the reasons given for the high growth rates of the postwar period is the rapid
capital accumulation resulting from high saving rates. To take this source into ac
count, we select initial values of .33 and.25 respectively, for the A and N saving rates.
The rates are increased constantly until in 1969 they reach .43 for the A and .38 for the
N sector. Our empirical analysis of the postwar data detected the dependence of
saving rates on income. Although the simulator can accommodate such dependence,
the relationship was simply ignored, and rates of change in the saving ratios were
imposed exogenously.
The considerably higher migration rate in the postwar than in the prewar years was
introduced into the simulation by selecting a higher value for the intercept of the
postwar migration equation. The rates of technical change for the postwar period
were also considerably different from the values used for the prewar years. For
agriculture, we used a value of 4 percent a year, and for the nonagricultural sector, we
used a value of 5.25 percent a year. Consequently, it is assumed that the growth in
production is attributable to rapid capital accumulation and a rapid increase in the
level of productivity. However, there is another source for increase in production in
the N sectorthe flow of savings from the agricultural sector.
The values of the variables relevant to Japanese growth are summarized for the
initial year 1955 and for years 1962 and 1968 in Table 15. The simulated results and
actual data for the postwar year appear in Figures 10 through 14. By and large, the fit
for the postwar period is even better than that obtained for the prewar period.
Again, the main differences between the simulated data and the actual data are in
variables which fluctuate; in the postwar years, that means fluctuations around trend
lines. For example, the top panel of Figure 10 shows annual or cyclic fluctuations
around the simulated trend line which represents the overall increase in the agricul
tural per capital output. The other variable which shows fluctuations is the price ratio,
shown in Figure 13. The simulation model does not take into account factors which
lead to the decline in the price ratio in the period 196367. Yet, the two price ratio
series, simulated and actual, are subject to an overall upward trend, and they con
verge in 1967.
The analysis demonstrates that this model fits the Japanese data with a good deal of
precision. Further modifying some of the parameters or dividing the period could
improve the fit, but the purposes of this analysis are not particularly advanced by such
refinements. These results have nothing new to offer in terms of the qualitative
phenomenon of Japanese development. However, they do provide quantitative
estimates of the importance of the relative variables and offer a framework for
analyzing the importance of assumptions about parameter values in explaining Ja
pan's development. The model of the Japanese experience may be used to analyze
some of the broader and more important issues of economic development in general.
which are derived from the capital shares. The capital shares are taken from Yamada and Hayami. It seems
that some further experimentation with the value of capital shares, and thereby with the rate of return in
agriculture, might be instructive.
Table 15Actual and simulated levels of some economic variables for postwar
Japan
1962 1968
Variablea Initial Values Actual Valuesh Simulated Values Actual Valuesh Simulated Values
1955
y, 13.5 14.9 15.0 16.3 16.0
Y2 77.3 146.7 146.0 263.3 249.5
L, 16.3 13.5 13.1 10.7 10.3
L2 24.8 32.1 32.5 39.9 39.6
K, 6.2 8.3 8.4 11.6 11.0
K, 18.8 36.8 36.1 72.2 70.5
P 1.0 .95 1.09 1.20 1.20
w, 47.5 74.3 114.1
w2 206.9 332.7 515.3
r, 2.3 2.4 2.4
r2 9.3 9.2 7.6
R 47.5 62.7 79.8
k, 3.8 6.1 6.4 11.1 10.7
k2 7.6 11.5 11.1 18.1 17.8
( .396 .296 .287 .211 .206
p .247 .184 .202 .139 .157
7T .149 .092 .100 .058 .071
w,/P 47.5 68.4 95.4
r,/P 2.3 2.2 ?
Pk, 3.8 7.0 12.8
Pk,/k2 .501 .628 .722
m 4.2 4.7 5.1 5.5 6.0
Note: Empty cells indicate that data were not available.
aUnits of variables are as follows, with monetary values in constant 1955 yen:
y,, Y2 thousand yen
L,, L, millions
K,, K, trillion yen
W1, w2 thousand yen
y y percent
R thousand yen
k1, k2 hundred thousand yen
wi/P thousand yen
r,IP percent
Pk, hundred thousand yen
m percent
bActual values are fiveyear moving averages centered on year shown.
The Role of Resource Flow
In historical perspective, the decline in the relative importance of agriculture in
mature economies is a recent phenomenon. In fact, most countries are still in the
early stages of development, and agriculture is their major economic sector. The
importance of resource flow between the two sectors in the process of development
is qualitatively well known. In the process of growth, agriculture contributes labor
Figure 10. Actual and Simulated Per Capita Uutputs, Postwar Period
16.40] Agriculture
O 11
01,
o 1!
"4
o
rv 1
"n
I"
270.0
260.0
250.0
240.0
230.0
220.0
210.0
200.0
190.0
180.0
170.0
160.0
150.0
140.0
130.0
120.0
110.0
100.0
90.0
80.0
70.0
19;
Actual
Nonagriculture
Actual
Simulated
55 56
57 58 59 60 61 62 63 64 65 66 67 1968
Years
16.00
15.50
15.00
14.50
Simuli
Nonagriculture
Simulated
67 1968
Figure 11. Actual and Simulated Labor Force Levels, Postwar Period
Agriculture
*Actual
^S.'""*.Actual
. 14.00
0 13.50
0
13.00
12.50
12.00
11.50
11.00
10.50
37.0
36.0
35.0
S 34.0
0 33.0
S32.0
.2 31.0
S30.0
29.0
28.0
27.0
26.0
25.0
1955 56 57 58 59 60 61 62 63 64 65 66
Years
Figure 12. Actual and Simulated Capital, Postwar Periods
12.50 Agriculture
12.00
11.50
11.00 Actual
10.50
Simulated
10.00
9.50
9.00
8.50
8.00
7.50
7.00
6.50
Nonagriculture
40.0
35.0
30.0
25.0
20.0
Actui
1955 56 57 58 59 60 61 62 63 64 65 66 67 1968
Years
Figure 13. Actual and Simulated Terms of Trade Between
Agricultural and Nonagricultural Sections, Postwar Period
Actual
1955 56 57
58 59 60 61
62 63 64 65 66
Years
67 1968
Figure 14. Simulated Wages and Capital Returns, Postwar Period
Wages
Nonagriculture
Agriculture
Capital Returns
90.0
85.0
80.0
75.0
 70.0

4 65.0
4 60.0
S55.0
0
50.0
I
45.0
40.0
35.0
30.0
25.0
20.0
1955 56
Nonagriculture
Agriculture
57 58 59 60 61
62 63 64 65 66 67 1968
Years
100.0
95.0
and in some cases also capital to the N sector. This mutual relationship is sometimes
considered the contribution of agriculture to the N sector.92 This is a somewhat
limited point of view, because basically the N sector contributes to economic growth
by accepting and employing the surplus labor of the A sector. The difference is largely
semantic; what really matters is the flow of resources and products.
In order to quantify the importance of resource flows in development, we con
ducted the following experiment: we simulated the growth of the Japanese economy
under the assumption that there were no intersectoral resources flows. We isolated
the individual effects of labor and savings flow growth paths by simulations in which
there was (1) no flow of eitherfactor, (2) no labor migration butflow of savings, and (3)
labor migration but no savings flow. The restriction of no savings flow requires
adjusting initial investment figures in order to maintain the national accounting
identities. With this modification, each sector's savings are invested completely
within that sector.
The prewar analysis was carried under the assumptions of Run 1. The period is
analyzed as a whole rather than subdivided into two separate periods, and the values
of the parameters are those of Run 1 except that the flow of resources is restricted as
specified. Representing the prewar years, Table 16 reports for 1937. For purposes of
comparison, the table also reports the results of Run 1 and actual values for1937 taken
from Table 14. Results for each alternative formulation are also expressed as a per
centage of the actual values. Table 17, which reports for the postwar year 1968, is
similarly constructed.
In terms of the effect on per capital output it is quite clear that labor migration was by
far more important than the flow of savings. For instance, the simulated values for
1937 indicate that if the Japanese economy had experienced only labor migration but
no savings flow, per capital production in A and N would have been 105 and 99 percent
of their respective actual valuesa minor change indeed. On the other hand, savings
flow without labor migration would have resulted in per capital production 123 and 75
percent of the actual values in the A and the N sectors, respectively,
The basic run (Run 1) did not perform well on simulating the actual price ratio; for
1937, the difference is 17 percent. The run with no savings flow is not far from Run 1,
and its price result does not differ much. On the other hand, the nomigration run
brings the price ratio down to 93 percent of the actual, and restricting the flow of both
factors brings the price ratio down to 89 percent of the actual.
Turning to the factor allocation, the nomigration restriction results in a 39 percent
increase in the agricultural labor force and a decline of similar order of magnitude in
the N labor force. This restriction also results in greater capital accumulation in
agriculture; K, is 15 percent more than the actual, and K2 is only 84 percent of the
actual.
The restriction on savings flow is not translated quickly and strongly into the labor
market; labor allocation is unaffected. On the other hand, restricting savings flow
increases the A capital stock by about 20 percent and decreases the N capital stock by
9 percent. The reason that the savings restriction affects output less than the restric
92Cf. Ohkawa, Differential Structure, pp. 16972.
M Table 16Restrictions on resource flow, 1937
No Migration/
Variable Actual Run 1 No Savings Flow No Migration No Savings Flow
S P S P S P S P
y, 25.2 25.7 1.02 32.0 1.27 31.0 1.23 26.5 1.05
Y2 105.6 108.4 1.03 75.7 0.72 78.8 0.75 104.3 0.99
L, 14.5 14.4 0.99 20.1 1.39 20.1 1.39 14.5 1.00
L2 17.2 17.1 0.99 11.4 0.66 11.4 0.66 17.1 0.99
K, 5.7 5.8 1.00 8.0 1.39 6.6 1.15 7.4 1.28
K2 24.8 24.8 1.00 18.7 0.75 20.9 0.84 22.4 0.91
p 0.91 1.07 1.17 0.81 0.89 0.85 0.93 1.02 1.11
w, 72.0 50.3 51.4 70.34
w2 283.1 298.1 313.6 270.5
r, 3.8 2.7 3.4 3.0
r, 10.8 9.9 9.0 11.7
R 99.7 91.6 93.6 97.6
k, 4.0 4.0 1.01 4.0 1.00 3.1 0.77 5.1 1.29
k2 14.4 14.4 1.00 16.3 1.14 18.2 1.27 13.1 0.91
t 0.458 0.457 1.00 0.638 1.39 0.638 1.39 0.459 1.00
p 0.188 0.199 1.06 0.258 1.37 0.201 1.07 0.250 1.33
Tr 0.193 0.202 1.05 0.256 1.33 0.251 1.30 0.205 1.06
wJ/p 67.6 61.8 60.3 69.2
r,/p 3.6 3.3 4.0 3.0
pk, 4.2 3.2 2.6 5.2
pk,/k2 0.294 0.198 0.143 0.394
m 1.2 1.3 0.0 0.0 1.3
Note: S = simulated values; P = simulated/actual; empty cells indicate that data were not available.
aSee Table 14 for units.
Table 17Restrictions on resource flow, 1968
No Migration/
Variable a Actual Base Run No Savings Flow No Migration No Savings Flow
S P S P S P S P
y, 16.3 16.0 0.98 24.3 1.49 24.0 1.47 16.1 0.99
Y2 263.3 249.5 0.95 199.3 0.76 200.0 0.76 248.6 0.94
L, 10.7 10.3 0.96 19.7 1.84 19.7 1.84 10.3 0.96
L, 39.9 39.6 0.99 30.1 0.75 30.1 0.75 39.6 0.96
K, 11.6 11.0 0.95 13.5 1.16 12.3 1.05 12.0 1.03
K2 72.2 70.5 0.98 62.5 0.87 63.6 0.88 69.3 0.96
P 1.20 1.197 1.00 0.683 0.57 0.696 0.58 1.173 0.98
w, 114.1 56.3 56.7 113.0
w2 515.3 538.4 541.0 513.0
r, 2.4 1.7 1.8 2.2
r2 7.6 6.6 6.5 7.8
R 79.8 66.1 66.5 79.0
k, 10.9 10.7 0.99 6.8 0.63 6.2 0.57 11.7 1.07
k2 18.1 17.8 0.98 20.8 1.15 21.1 1.17 17.5 0.97
t 0.211 0.206 0.98 0.396 1.88 0.396 1.88 0.206 0.98
p 0.139 0.157 1.13 0.128 0.92 0.118 0.85 0.168 1.21
T 0.058 0.071 1.22 0.077 1.33 0.077 1.33 0.071 1.22
wl/p 95.4 82.4 81.5 96.3
r, p 2.0 2.4 2.6 1.9
pk, 12.8 4.7 4.3 13.7
pk,/k, 0.722 0.224 0.204 0.781
m 5.5 6.0 0.0 0.0 6.0
Note: S = simulated values; P = simulated/actual; empty cells indicate that data were not available.
aSee Table 15 for units.
tion on migration is in part related to the fact that labor allocation is not greatly
affected by restricting savings flow and in part to the fact that capitalproduction
elasticities are smaller than laborproduction elasticities. This is basically related to
the old question of the direct contribution of investment to growth. The no
migration, noflow alternative combines the two individual effects in an obvious way.
The postwar results are similar in nature, buttheyare basically o ia larger magnitude
than the prewar results. This primarily reflects the importance of labor migration
during the later period. Table 17 shows that the absence of migration up to 1968 would
have resulted in 47 percent larger per capital agricultural production in 1968 than in
1955. The discrepancy was accumulated during a 13year period (195568); during the
30 years (190737) of the prewar period, a 23 percent discrepancy accumulated. The
effect on per capital production in the N sector is to reduce it to 76 percent of the actual
value, or 80 percent of the base run.
Obviously, such drastic changes in production have corresponding effects on
prices. Had there been no labor migration in the postwar period, the price ratio would
have gone down to a level of 64 percent of its actual value and to a level of 58 percent
of that obtained in the base run.93 Thus, it would have been disastrous for Japanese
agriculture if the high rate of technical change realized in the postwar period had not
been associated with high rates of migration. It is the labor migration that made it
possible to reduce the agricultural labor force by almost onehalf during a 13year
period. This change is reflected in the deepening of capitallabor ratio at a rate faster
than that realized in the N sector.
The Role of Technical Change and Accumulation
There was a great deal of difference in the saving rates and in the rates of technical
change between the prewar and the postwar periods. From a historical perspective,
the question really is whether an economy's more crucial parameters must change
gradually in order to achieve high growth rates or whether it is at all possible to make
some shortcuts in moving into the set of highgrowth parameters. The problem, then,
is how to induce high rates of technical change and possibly high rates of accumula
tion. Such inducements are not priceless, so the question is whether the benefits of
such inducements are worth the cost. This problem is approached in the literature
from different points of view, and there is a whole set of studies that evaluate the
consequences of research and development.
Another approach to evaluating the consequences of speeding up technical change
and savings is simply to trace the growth path of the economy. We have performed
this evaluation under the following assumptions. First, we asked what would have
been the course of the prewar development of Japan if the prewar rates of technical
change were replaced by the postwar rates of about percent per year for agriculture
and more than 5 percent for the rest of the economy. We followed a similar procedure
I31n fact, the effect is likely to be somewhat weaker. The production function used in the simulation does
not include raw materials such as fertilizers, seeds, etc. The effect of changes in these inputs over time is
embedded in the residual technical change. As such, it is implicitly assumed that the level of their use is
independent of price. Such an assumption may yield a reasonable approximation for smalltomoderate
price variations. The price deviations realized in the present exercise are larger by far.