Farm Size Land Yields and the Agricultural Production Function An

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					World Developmenr. Vol.      13, No.   4, pp. 513-534.                                                 0305-750x/85 $3.00 + 0.00
Printed in Great Britain.                                                                          0    1985 Pergamon Press Ltd.

               Farm Size, Land Yields and
         the Agricultural Production Function:
      An Analysis for Fifteen Developing Countries

                                       GIOVANNI ANDREA CORNIA’”
                                             UNICEF, New York

         Summary. - The paper analyzes the relationship hetwcen factor inputs, land yiclda and labor
         productivity  for farms of different size on the basis of FAO farm managcmcnt          data for 15
         developing countries. For all but three countries a strong negative correlation is found between
         farm size on the one side, and factor inputs and yields per hectare on the other. The fitting of
         unconstrained production functions to the above data suggests that in only few casts the dcclinc
         in yields for increasing farm size can he attrihutcd to decreasing returns to scale. The higher
         yields observed in small farms are mainly to he ascrihcd to higher factor inputs and to a more
         intensive use of land. Therefore, where conspicuous labor surpluses exist. the superiority of small
         farming provides solid arguments in favor of land redistribution.  Such an agrarian reform would
         determine higher output. higher labor absorption and a more cquitahle income distribution, thus
         contributing in a decisive manner to the alleviation of rural poverty. The paper also provides
         estimates of cross-sectional production     functions for the IS countries analyzed.      Empirical
         relations are found between the output elasticities of land. labor and intcrmcdiatc      inputs and
         physical indicators of their scarcity. The paper concludes by proposing a simple method for
         deriving a long-term production     function for agriculture.

       1. INTRODUCTORY                  REMARKS                        initial conditions      from which low growth has
                                                                       taken place were already quite distressing. Aver-
   The importance          of sustaining       agricultural            age per capita food supply was conspicuously
production    to improve nutritional standards has                     lower than requirement,         while food consumption
been recognized        by all countries        throughout              was      traditionally      very       skewed.       Recent
history. However, in the economic literature of                        investigation’      has shown that such inequality
the 1950s and 1960s the role of agriculture                 in         would appear to have increased even in countrres
development     was considered       ancillary to that of              experiencing     relatively rapid agricultural growth.
the modern industrial sector where most of the                         Thus, the combined effect of low starting points,
accumulation     and growth was expected to take                       slow or negative         growth of food output per
place. Subsequent       theoretical    investigation     and           capita, and the worsening of income distribution
the very disappointing        performance       of agricul-            and food consumption         explain the increase in the
ture in many developing countries have led to the                      number      of people suffering         a deficient    food
belief that the role of agriculture in development                     intake and why the food threat continues to hang
should be re-examined.                                                 over many developing           countries.
   Erratic and inegalitarian growth, persistence of                       Nowadays,       there is a large consensus on the
malnutrition,     periodic     famines     together     with           need for increasing           agricultural     output   and
increased food dependence           from abroad, have
continued to affect a large number of developing
countries. Table 1 shows that, with the exception
                                                                       *The author wishes to thank among others John Dixon,
of West Asian countries             and the Centrally
                                                                       Mike    Hopkins,    Ajit   Chose.     Massimo   Riccottilli,
Planned Economics of Asia, agriculture and food                        Jacques Royer and an anonymous referee for comment-
output    per capita have increased             at low or              ing on an earlier draft of this paper. None of them bears
negative rates.                                                        any responsibility for the errors that may remain. The
   The situation is, however, substantially           worse            views expressed in this paper are those of the author
than highlighted      by these trends.        Indeed.     the          and not necessarily of his organization.

s14                                              WORLD       DEVELOPMENT

                                Table 1. Growth rates of agricultural output per capitu

                                                     Agricultural                    Food output
                                                  output per capita                      per capita
                                                1960-65              1970       196G-65               1970
                                                to 1970            to 1976      to 1970             to 1976

                      Africa                       0.2              -1.5           0.1                -1.4
                      Latin America                0.2                0.1          0.8                  0.5
                      West Asia                    0.4                1.1          0.3                  1.4
                      Far East                     lJ.8               0.1          0.9                  0.2
                      Asian CPE                    1.0                0.7          0.9                  0.6

                      Source: FAO, Fourth World Food Survey (Rome,                       1977).

improving nutritional standards.           However. views            and because of the inherent changes in modes of
and policies differ widely on how to attain such                     production.       The formulation       of a consistent
objectives.     A large number of strategies               have      strategy     of agricultural   development         requires
been proposed          ranging from ‘the technocratic                therefore     an analysis of the evolution          of such
option,’     which stresses        the increased        use of       modes of production        and of the contribution         of
modern machinery,           pesticides and fertilizers.       to     each factor in relation to its changing availability.
others which consider that the existing economic                     This is the second focus of this paper. Indeed in
and power structure in agriculture is the major                      Section 3 the FAO data are used to estimate
obstacle to rural development.           According to the            cross-sectional     country production      functions. By
latter view, the provision of more and improved                      relating    the parameters      of such functions          to
inputs. although necessary,            would not be suffi-           indicators     of factors availability,    an attempt is
cient to ensure a fast and egalitarian                 growth        made to identify the contribution        of each produc-
capable of eliminating            rural poverty.      The in-        tion factor at different levels of development           and
crease in input supply should be accompanied                  by     to tentatively     work out a long-term        production
measures ensuring broadly equal access to land                       function for agriculture.      Conclusions       follow in
and other productive          assets to the rural popula-            Section 4.
tion. This could be achieved                  through      land
redistribution.     One of the arguments            often put
forward in favor of land redistribution                  is the                 2. FARM SIZE AND LAND
assumed superiority of small peasant farming as                                      PRODUCTIVITY
opposed to large estates. This is the first focus of
this paper. Indeed, Section 2 analyzes the validity                    (a) Theoreticalframework                urrd evidence   in the
of the above hypothesis            on the basis of so far                                         literature
unexplored       farm-level      data for IS developing
countries, provided by the United Nations Food                          The current literature on rural development          is
and Agriculture         Organization     (FAO).                      replete with studies about the effect of farm size
   The adoption of one instead of another of the                     on land productivity.     The controversy    is impor-
strategies    mentioned       above would have widely                tant for it provides information     on the existence
differing    implications       in terms of distributive             of economies     of scale in agriculture and on the
equity and removal of malnutrition.                IIowever,         choice of an optimal farm size,’ besides supplying
whatever      approach       to the transformation            of     ammunition     to those who are in favor or against
agriculture     is followed, it will imply substantial               the thorny issue of land reform. The modern
changes over time in production              techniques.      in     version of the controversy        on the size effect
supply and prices of production              factors and in          started with the publication     in the 1950s of the
their relative       contribution      to the production             results of the Indian Farm Management          Studies,
process.                                                             which showed that there was an inverse rela-
    In this regard, the policy-maker           often finds it        tionship between farm size and land productivity.
difficult to plan adequately the agricultural sector                 Subsequent     empirical investigation    leaves little
over the long term precisely               because      of the       doubt about the validity and generality         of this
changing availability         of the production         factors      phenomenon      observed in many developing coun-
        FARM      SIZE. LAND        YIELDS      AND    THE AGRICULTURAL                PRODUCTION           FUNCTION           51s

tries of Asia and Latin America characterized                 by   Financial institutions        providing      credit to small
widely different natural and climatic conditions,                  farmers       are little developed          in rural areas,
types of soil, agrarian structures            and cropping         making farmers dependent              on the local money-
patterns.                                                          lenders, who generally charge high and usurious
    In most developing countries. production con-                  interest rates. The little agricultural credit avail-
ditions in agriculture        differ substantially        from     able on soft terms generally goes to the richer
those encountered        in advanced nations. Broadly              peasants,      because of their higher creditworthi-
speaking, production        takes place under bimodal              ness and also because they generally exert some
conditions,    i.e. with large farms showing a high                control on the institutions             channeling     official
proportion     of unused land, while excess labour.                finance to the rural areas. The cost and access to
with little opportunity        for productive        employ-       credit may be inversely            related to farm size.
ment, is crowded on the small farms or in the                      Consequently,         the different cost of finance for
landless    labor force.        Capitalist     relations      of   large and small farms often encourages                      the
production      are little developed         and in some           substitution      of capital equipment         for labour on
developing countries, virtually non-existent             (as in    the large holdings.
part of Tropical Africa and South Asia). Markets                      Similarly, on the land murket. small farmers
of means of production          (land, labor. fertilizers)         face a higher effective price of land. The purch-
or commodities       are limited and monopolized            to a   ase of a small plot generally entails a higher unit
large extent by rich landowners            who control the         price than that of a large estate. In addition, each
access to available resources.           Under these cir-          purchase often involves some long-term borrow-
cumstances,      the utilization of various resources              ing, the interest rate and maturity of which will
depends on their relative availability and cost for                be more favorable to the large operator because
different farmer groups. The central theme in the                  of his better credit rating. The small peasant
literature on the subject is that small and large                  therefore      faces a real price of land higher than
farms systematically       face different sets of factor           the large cultivator who could thus make less
prices giving them different access to resources                   intensive use of the land. This phenomenon                     is
and different incentives to produce. Very gener-                   often reinforced         by the tendency        among large
ally, it could be said that the effective price of                 owners to hold land for prestige or as a portfolio
land and capital is usually higher for small                       asset rather than as a production input, especially
farmers, whereas the effective price of labour is                  in countries that experience           prolonged inflation-
lower.                                                             ary pressures.
    On the labor murket,            under conditions          of      The resource position (i.e. the access to, and
severe excess labor supply, a complete clearing of                 the cost of the production factors) of the different
the market should bring the wage rate close to                     groups of farmers determines               how the various
zero. In practice, however.           the wage rate will           factors are combined”            and what effect these
probably     be equal to a minimum               purchasing        combinations        have on land yields. As a result of
power corresponding         to the caloric requirements            the mentioned         prices distortions     and of the zero
which allow the wage-earners           to reproduce their          (or low) opportunity         costs of excess labor. small
labor efficiently. Large farmers theretore tend to                 farmers       put into the production              process      a
employ labor till its marginal product equals such                 substantially higher amount of man-days per unit
a wage rate. This leaves a large proportion of the                 of farmland than larger farmers. They do so in
labor force without the possibility of obtaining a                 several ways, including:
job on the large farms. Labor may be more                              (i) a more intensive use of Iubor in each crop
abundant and cheaper for small farmers; indeed,                        activity.    Although     for each single crop and
given the scarcity of available land, poor farmers                     with constant technology,            there may not be
have, in principle,       a large excess of labor. The                 much scope for variation in factor proportion
possibility of utilizing this excess labor in off-farm                 (i.e. factors would be strictly complement-
jobs is limited due to the narrowness of the labor                     ary), yields can be increased by more intens-
market. Thus. the opportunity           cost of employing              ive land preparation,        better seeding, etc. The
members      of the family on one’s own farm is                        marginal increase in yield, due to additional
expected to be very low (equal to the disutility of                    application        of labor,     however.      is rapidly
the effort).      This implies that a much larger                      decreasing,       determining      a sharp decline in
amount of labor, even with a low and rapidly                           average productivity per worker. Large farms
decreasing     marginal productivity         (probably       be-       tend to use more capital; however, the domin-
low the market wage rate), is imputed into small                       ant relation between labor and mechanized
holding farming.                                                       equipment        is one of substitution,       so that an
    The situation is often reversed with regard to                     increase in mechanization             almost invariably
access to cupital markets and intermediate             inputs.         has a labor-displacing          effect, with, as most
516                                                     WORLD          DEVELOPMENT

     available      evidence        shows, no influence               on     when, because of their financial weakness. they
     yields;                                                                 cannot benefit from the introduction                   of new,
     (ii) cdtivntion       of u higher proportkm                 of the      input-intensive       production     technologies,        (as in
     ulwiluhle land 0s the furm. Land use patterns                           the case of the HYV) which are, on the other
     vary remarkably             among farms of different                    side, available and affordable              to medium and
     sizes. with larger farms devoting                         a much        large farmers. Unless credit and extension                    ser-
     higher proportion             of their land to grazing,                 vices are made available to all classes of farmers
     forest, fallow or other uses. as shown by a                             (which is seldom the case), technological               innova-
     substantial amount of empirical evidence’. On                           tion tends to favor, in terms of production
     very large farms, for instance.                 conspicuous             advances,     the medium and large farms.
     expanses of land remain idle:                                              Two types of information            are available in the
     (iii) more intensive 14sc of thelunti              riirring     the     current literature on the hypothesized             effect that
    year.    Double - or at times. triple ~ cropping                         land redistribution          would      have on output,
     IS more     frequent        on small farms;                             employment        and income equity: a-mtc data on
     (iv) a choice of labor-intensive             crops. Such as             agrarian structure (resource use and yield by size
     Vegetables and other crops. where the role of                           of the farm): and ex-post historical                  data for
     mechanization          remains limited.                                 countries which have carried out redistribution.
    Lastly, it should be noted that in traditional                           This section provides           a short account of the
agriculture part of the excess labor in the small                            existing literature on the subject with the intent.
farm sector is. ceteris puritms, used for works of                           although the list of quotations           is far from being
land improvement,                 such as land terracing,                    exhaustive.     to show the generality of the phcno-
canalization.       repairing storage and facilities. so                     menon. As far as the cwurlte appraisal of the
that small holdings generally have a better land                             size/yield relation, data are available for at least
infrastructure          and      higher      investment            ratio     the following countries:         Argentina.      Brazil. Co-
(excluding       purchased           equipment)       than large             ombia.      Chile. Ecuador,         Guatemala.         Mexico.
estates. The same applies to those intermediate                              Bangladesh,         India,     Japan.        South       Korea.
inputs (e.g. manure) which are produced on farm                              Malaysia, Pakistan, the Philippines, Egypt, Kenya
as a by-product           of other activities.                               and Malawi.’         The main conclusion             of these
   All in all. in traditional           labor surplus agricul-               studies is that small farms are almost universally
ture. small farms characterized               by acute land and              characterized      by a more intense land utilization
financial scarcity may have, on the whole. (with                             due to a higher cropping intensity, and/or to the
the exception            of machinery           and purchased                cultivation    of a higher proportion           of operated
intermediate       inputs), a total resource use per unit                    land. Labor use per unit of land is thus negatively
of land substantially             higher than that of large                  correlated with farm size: similarly. this can also
farms: consequently.             output per unit of land is                  be observed for land productivity.
expected      to be higher.            Small farming             would          The historical       er-/~~st empirical       evidence        is
therefore     appear to be the most efficient. The                           more controversial.        The principal problem is that
same conclusions are also likely to be valid when                            of disentangling         temporary       disruptions        from
considering      as an indicator of efficiency the total                     long-term effects. Poor data availability, particu-
factor productivity,          i.e. the ratio of farm output                  larly with regard to total production             as opposed
to the social cost (e.g. the opportunity               cost) of all          to marketed production (as me of the first effects
factors used in production.              As a possible excep-                of land reform is to increase the self-consumptioti
tion. the very smallest farms (where the scale tif                           of small farmers         while compressing           the food
operation      is much too reduced to allow for any                          supply available to urban dwellers) further com-
form of efficiency) probably have a total social                             plicates    the er-post analysis.          Significant       land
factor productivity          lower than the other types of                   reforms have taken place in Latin America.”
farm. These general conclusions are subject to a                             namely in Mexico.            Bolivia, Cuba. Chile and
number of exceptions,               especially in the cast of                Peru. The effcctivencss          of these reforms IS the
land-rich countries and when the phenomenon                             is   subject of a recent World Bank studv which
analyzed      in dynamic perspective.                In land-rich            concludes     that ‘.         the effects of r&m               on
countries. labor and capital, rather than land. are                          agricultural     production     were generally positive,
the limiting factors in production.                   while labor            with the possible exception of Peru. Moreover. in
inputs per unit of land. land-use pattcrna.                         and      all cases, the effect of reform was to make the
farming techniques             do not vary markedly                  for     distribution     of income more equal.’ Similarly, in
farms of different size. In such cases. therefore,                           Asia. land reform proved extremely successful in
there are no CI      priori reasons for small farms to be                    three     East Asian        countries,       namely      Japan,
more efficient than the larger ones. Small farms                             Taiwan and South Korea.’ In these countries.
may also lose their demonstrated                       superiority           characterized       by a high degree             of holding
       FARM      SIZE.   LAND     YIELDS      AND    THE    AGRICULTURAL            PRODUCTION          FUNCTION           s17

fragmentation,        the reform mainly transformed                farms, for each country, come from the same
previous tenant-farmers          into owner-cultivators,           hydro-geological    area, this should not intro-
while the redistribution       of larger holdings played           duce an excessive bias in the analysis;
a less important         role. The success of China’s              (iii) land use intensity,   defined here as the
agriculture in terms of output, employment                and      ratio of cropped to farm area. This definition
equity, is largely to be ascribed to the multi-stage               is useful since it allows to summarize for each
land reform of the late 1940s and IYSOs, as noted                  farm, both the information      on the proportion
by both T. G. Rawski and A. R. Khan.” For the                      of land cultivated (as opposed to owned, or
Middle      East.     Doreen     Warriner     found” that          leased) and that on cropping intensity strictu
extensive     land reform        had successfully       been       serlslc;

implemented         in Iran, despite several adverse                 (iv) capital inputs including machinery, cattle,
short-term      effects on investment         and income             orchards.    excluding    the value of land and
distribution:      Iraq, on the contrary,           suffered         incuding half of the values of the buildings;
worse results because of a long period of uncer-                     this latter assumption,      highly arbitrary.        pre-
tainty. In all these cases, much of the success of                   supposes that 50% of the on-farm buildings
the reform has depended upon the swiftness with                      are used for production          purposes     (storage,
which it has been implemented              and upon the              cattle raising,     etc.) while the other 50%
administrative       capability of those in charge. The              provides lodging services to the farm family;
control by the peasantry of the credit and input                     (v) an estimate of the intermediate           inputs to
supply as well as the necessary commercial                and        production,     e.g. seeds. pesticides,      fertilizers
transport infrastructure        has also played a crucial            and fuel;
role.                                                                (vi) the total value of farm output and an
   In many other developing countries, including                     estimate of the farm value added.
very large nations in Latin America and South                       The data were transformed            into comparable
Asia. land reform has mostly remained a rhetor-                 units, that is. all land values were expressed in
ical exercise,       with a loophole      legislation     and   hectares and all value figures were transformed
minimal implementation             owing to the strong          into 1070 US dollars.           National     figures were
political power of the landed gentry.                           converted into 1970 domestic prices by means of
                                                                the implicit price deflator          of the agricultural
                                                                value added, and transformed            then into dollars
              (b) Illltstrutiorl of the dutu                    using the 1970 exchange rates. The original data
                                                                from 3,167 farms belonging             to I8 developing
   Between      1973 and 1979 (and possibly later),             countries were then debugged from errors exist-
the FAO Farm Management                and Production           ing in the original figures (due to material and
Economics       Service collected    in a standardized          reproduction      errors, or to incomplete reporting).
form and stored on tape a large amount of farm                  In addition, all farms with value added, or with
level information        for at least 18 developing             capital stock inferior to $10 or comprising                 less
countries.     These data were generally collected              than 0.10 hectares, or with a labor input of less
concurrently     with the implementation      of techni-        than 10 man-days per year were deleted from the
cal assistance projects,      each of which involved            file. Tunisia was deleted because of incomplete
several dozen farms. The data concern overall                   reporting,     while Sri Lanka and the Caribbean
farm and crop yield accounting. They refer to a                 were deleted         because    the number        of farms
time period of one year and are expressed in local              sampled was too small.
prices and local land units. For each farm, a few                   A number of comments            can be made upon
hundred data are available on the original file.                examination       of the information        retained      after
Through       the reading     of 47 of the original             debugging the original file. First, the data gener-
variables at the farm level, it was possible to                 ally cover small and medium farms and do not
derive 32 variables for each farm (including 17                 always include the very small and the very large
original indicators,     plus 15 ratios obtained from           holdings. The comparison,         for a few countries, of
them) measuring        in sufficient detail:                    the sample distribution of farm land by size of the
    (i) on-farm labor inputs (in man-days and in                farm with the corresponding          figures provided by
    workers per year) as well as the amount of                  the 1970 World Census of Agriculture                  clearly
    hired labor;                                                shows this phenomenon.            The variability of the
    (ii) land inputs, including the proportion         of       sample is thus smaller than that of the universe;
    irrigated    land per farm; land inputs are                 the conclusions about farm size, resource use and
    expressed in hectares only as it was impossible             land productivity        drawn on the basis of the
    to account for variations       in land quality by          sample are therefore likely to hold true a fortiori
    pricing the various types of farmland. As all               for the universe.
518                                            WORLD DEVELOPMENT

    Second, the quality of the data varies from                   higher than on large estates (i.e. having, with the
country to country and from one variable to                      exception      of most Latin American             countries,      a
another. Judging by the ratio between “deleted                    minimum area of 7-10 hectares).                  This phcno-
over total” number of farms, the countries with                   menon      is much more marked                 for land-rich
the least accurate data seem to be Bangladesh,                   countries (such as Syria, where the ratio of small
India and Mexico. All computed             variable5 con-        vs large farm yields reaches the value of 10 to 1)
tain a certain degree of arbitrariness           reflecting      than in land-scarce countries (in South and South
the conventions     adopted for defining them. In                 East Asia the same ratio is 2 to 1). The
particular,   the evaluation       of the intermediate           phenomenon          tends to disappear in countries such
inputs    (manure,    fertilizers,    seeds,    etc.) and        as Bangladesh and Thailand where differences in
capital stock implies a number of methodological                 size of the farms included in the sample are very
as well as practical problems,        so as to suggest a         small and. perhaps, non-significant.                By examin-
certain amount of care when making inference on                  ing the present data it is impossible to establish
the basis of them.                                               whether the higher outputs per hcctarc on small
   Third, the data, although being expressed in a                farms are due to higher yields for each crop
 common currency (US dollars) and in prices of                   activity (which would entail decreasing returns to
 the same year (l970), are not comparable             cross-     scale), or to a more intensive use of land, or to
country.    As explained       above, the price index            different     cropping patterns.        Land-use       intensity
 used for expressing all value data in 1970 prices is            (measured       here by the ratio of cropped to farm
the national implicit price deflator of agricultural             areas) declines a5 farm 5ize rises. A positive
 value added of each country considered.                This     relation     is observed       only for Mexico.           If one
differs by an unknown extent from the local price                 assumes constant returns to scale of the effectively
index. Furthermore,       the data are not expressed             cropped       area, the phenomenon              of increasing
 by means of the same price basket, and the                      output per hectare as farm size declines could
conversion     in US dollars         through     the IY70        tentatively be attributed to a more intensive use
exchange rates introduces an unknown degree of                   of land, that is, to the mentioned higher cropping
distortion which varies from country to country.                 intensity and to better land use patterns as well as
    Fourth and last, although the information               IS   to higher labor, and other inputs per hectare.
collected and stored in a standardized           form and        The validity of this assumption             will de tested in
according to precise criteria, allowance has to be               Section 3.
made for a certain degree of “human arhitrari-                        Man-day5 per hectare also decline as farm size
ness” introduced       into the data both by the                  increases. confirming the previous hypothesis on
farmers surveyed       (who may unconsciously              bc     labor u5e by farm size; the drop in labor input is
biased in different ways when reporting               about       particularly sharp when moving from the small to
their farm) and by the interviewers.                              the medium holding sector. The wide variations
                                                                  in labor input according            to farm size strongly
                                                                  suggest a declining average. and therefore                  mar-
                                                                  ginal, productivity         of labor. This hypothesis           is
                                                                  confirmed       for all countries       (see variable GO-
   Table 2 presents      the values of several farm               WO).      Although        the different       data arc not
variables concerning      resource inputs, land yields            comparable       because they refer to different crops.
and labor productivity       by farm size. As one can             kt’bor input per unit of land is systematically
see, farm size is defined by intervals. the ampli-                higher in traditional         labor-surplus      Asian coun-
tude of which varies from country to country                      tries (again with the exception of Thailand) than
depending      on the overall variability      of each            in the generally land-abundant            countries of Afri-
sample.                                                          ca. the Middle East and Latin America.                       This
   The diversity     of economic,      geological   and           could possibly be attributed to the higher propor-
climatic conditions as well as of cropping patterns               tion of irrigated land encountered              in the Asian
of the countries under examination       gives the data          countries.      This hypothesis,       however, could not
a good degree of generality.                                      be tested formally. The data al50 show that the
   The examination      of Table 2 indicates that, for            proportion.of       the off-farm wage labor out of total
all countries analyzed, with the exception of Peru                labor inputs (variable OFLI in Table 2) increases
and Bangladesh.       output per unit of farm land                steadily together with farm size, thus confirming
systematically    declines as farm size rises. The               the hypothesis          that, on average,          large farms
drop is particularly     intense when passing from                adopt a capitalistic mode of production               based on
very small (1-2 hectares) to medium- and large-                   wage-labor,       while small farms tend to make a
scale holdings. Land productivity on farms of less                larger use of on-farm family labor. This pheno-
than 1.5-2 hectares can be as much as 3 to 5 times                menon         again      shows       wide       cross-country
Barbados    < 0.1       134.2    1.90    1560.0   2980.0   2850.0     461.7   0.95   2.20     0.00
            0.1-0.2     112.5    3.00     686.0   2115.4   1777.9    7376.9   0.84   0.79     0.10
            0.2-0.3     336.6    6.80    1058.4   7241.5   2818.8    7335.8   0.38   0.72     0.00
            0.3-0.4     127.7    1.80     448.2    821.5    559.4   10411.3   0.68   0.81     0.00
            0.4-0.5      25.7    0.40     510.2    234.0    120.4     870.6   0.51   0.92     0.00
            OS-O.6      159.5    2.70     270.4    745.2    440.0    4051.1   0.59   0.41     0.09
            0.6rl.O     310.7    3.90     505.3   1977.5   1654.5    2565.4   0.83   0.30     0.04
            1.0-2.0     254.0    4.10     238.4    979.2    508.7     442.4   0.51   0.76     0.05
            2.0-3.5     159.4    2.10     146.7    309.7    218.1    1162.0   0.70   0.40     0.00
            3.5+        587.9    7.50     153.9   1166.7    398.8    1474.7   0.34   0.44     0.00

Mexico      < 1.0         16.3    0.76     64.8     49.6     49.3    130.4    0.99   1.00      0.00
             1.O-2.0     138.5    8.19     32.3    265.0    211.6    107.6    0.79   1.00      0.32
             2.S3.0       45.3    1.51     62.6     95.0     95.0     16.3    1.00   1.00      0.00
             3.0-4.0     361.3   16.45     78.5   1292.5    582.5    273.8    0.45   1.00      0.00
             4.0-6.0     258.3   27.08     10.6    288.3    268.4     71.6    0.93   1.00      0.00
             6.0-8.0      92.5    3.54     29.1    103.3     96.1    194.8    0.92   0.98      0.00
             8.0-10.0    132.7    4.60     16.1     74.2     63.5    423.3    0.85   1.02      0.07
            10.0-15.0    135.1    5.46     10.8     59.4     48.9    230.6    0.82   1.08      0.06
           15.0-20.0     478.8    5.08     16.8     85.6     44.7    258.7    0.52   1.27      0.23
           20.0-30.0    1044.9   13.03      8.0    104.6     61.5    286.2    0.58   1.49      0.27
           3o.CL35.0    1164.1   12.53      5.6     70.3     34.6    185.2    0.49   1.17      0.32
           35.0+         858.9   14.19      2.4     34.5     17.4     28.5    0.50   0.92      0.35

Peru        < 1.0        31.2     0.73   265.1     194.7    151.0    240.7    0.77   1.00     0.13
             1.0-2.0     35.9     0.67   209.2     140.3    111.9    165.9    0.79   1.00     0.07
            2.C3.0       71.3     1.21   104.2     126.9     89.0    123.6    0.70   0.92     0.26
            3.0-4.0      58.7     0.96   150.9     145.8     97.3    287.4    0.66   0.81     0.46
            4.0-5.0     193.3     2.20    75.6     166.7    105.0     53.0    0.62   0.89     0.60
            5.0-7.0     718.0    17.99    47.0     846.7    798.5    117.1    0.94   0.80     0.27
            7.0-10.0    253.4     4.23    56.0     237.5    171.5    430.2    0.72   1.00     0.75
           10.0-15.0    379.7     6.82    59.5     406.3    293.1    338.1    0.72   0.86     0.92
           15.0-20.0    347.7     2.37    63.2     150.5     96.2     63.0    0.63   0.59     0.66
           20.0+        680.7     3.74    36.2     135.5    103.2    107.9    0.76   0.54     0.76

              CLS       GO-W0    GO-MD   MD-LN    GO-LN    VA-LN    KA-LN     VA-GO   LUI    OFLI

Bangladesh   < 0.1        19.3    0.9     530.0    480.0    350.0    3798.4    0.72   2.00   0.17
             0.1-0.2       9.3    0.8     343.7    275.0    221.8    1586.2    0.80   1.80   0.26
             0.24.3       25.1    1.1     382.8    440.0    234.9    1254.2    0.45   1.90   0.33
             0.3-0.4      93.5    2.9     426.8   1210.1   1026.9    1370.7    0.80   1.94   0.62
             0.4-0.5      36.5    1.0     556.5    562.5    350.6    1326.2    0.62   1.43   0.29
             OS-O.6       47.5    1.5     387.0    589.7    414.1     685.1    0.70   1.48   0.36
             0.6-0.7      48.7    1.2     337.8    426.8    225.1     746.2    0.52   1.64   0.61
             0.7-0.8      30.0    0.6     534.4    365.8    224.1     706.0    0.61   1.56   0.60
             0.8-0.9      62.8    1.1     391.8    455.7    273.9     643.9    0.60   1.78   0.66

             0.9-l .o     55.9     1.3    530.3    705.8    446.0     739.2    0.63   1.69   0.61
              1.0-1.5     75.2     1.2    402.6    494.2    392.6     574.5    0.79   1.51   0.60
              1.s2.0      83.1     1.6    269.2    454.5    344.1     553.1    0.75   1.10   0.61
              2.0-2.5     81.7     1.0    472.4    504.5    380.7     504.0    0.75   1.61   0.85
             3.0+         71.1     1.1    348.2    408.0    384.3     529.7    0.94   1.20   0.79

Burma         < 0.5      106.1    1.74   1029.7    797.3    136.0     397.7    0.63   1.00   0.09
              O.Sl.0      59.5    1.18    412.2    486.5    167.0     546.3    0.34   2.01   0.17
              1.0-1.5     52.1    0.89    269.6    240.5     96.1     203.1    0.39   1.20   0.21
              1.s2.0      44.6    0.65    276.0    181.7     48.5     219.4    0.26   1.09   0.16
              2.0-3.0     85.3    1.01    185.9    189.3     81.8     231.1    0.43   1.31   0.28
              3.0-4.0     70.1    1.08    140.3    151.8     58.8     173.1    0.38   1.09   0.25
              4.0-5.0     82.3    1.04    159.2    166.5     71.9     192.7    0.43   1.15   0.39
              5.cM.o     158.8    1.69    138.5    234.5    113.3     194.4    0.48   1.07   0.60
              6.0-7.0    121.4    1.77    113.9    202.5     87.0     277.4    0.42   1.00   0.38
              7.~10.0    119.0    1.78    190.6    186.0     99.2     223.9    0.55   0.98   0.43
             10.&13.0    123.1    1.64    114.9    188.7     66.9     210.1    0.35   0.90   0.50
             13.0+       150.4    1.39     78.3    109.5     26.9     208.8    0.24   1.00   0.79

India        < 1.0        47.7    0.86    851.1    736.7    180.0     967.9    0.24   1.78   0.03
              l.Sl.5     112.4    2.23    224.6    501.6    218.0     319.8    0.43   2.00   0.10
              1.s2.0     149.9    1.97    335.4    658.9    277.2     514.9    0.42   1.89   0.10
             2.CL2.5     138.3    1.49    407.1    609.3    209.9     470.7    0.34   2.26   0.17
             2.5-3.0     241.4    3.83    183.1    702.7    333.8     408.7    0.47   1.82   0.05
             3.0-3.5     202.4    2.51    253.1    635.4    233.7     448.9    0.36   2.50   0.31
             3.s4.0      194.8    1.98    276.9    551.0    244.6     510.0    0.44   1.88   0.09
             4.c5.0      265.1    3.22    162.4    524.4    265.1     324.9    0.39   2.00   0.54
             5.M.O       148.5    1.39    264.0    368.5    153.1     194.4    0.41   2.00   0.24
             6.C8.0      300.3    3.99    137.2    548.8    253.8     503.2    0.46   2.00   0.31
             8.0-10.0    109.0    1.55    177.6    277.0    168.4     361.5    0.39   1.92   0.33
Nepal             < 0.2           22.8      0.85        936.0      792.5       677.5      1345.8      0.85     2.57      0.18
                   0.2-0.4        45.9      0.47       1444.1      693.1       492.4       590.5      0.71     2.31      0.39
                   0.4-0.6        51.2      8.75        585.0      441.4       365.9      1279.4      0.82     1.75      0.68
                   0.6-0.8        52.4      0.91        639.8      583.6       433.8       278.5      0.74     1.69      0.22
                  0.8-1.0         86.3      0.63       1064.7      677.1       503.0       468.4      0.74     1.67      0.16
                   1.0-1.5        58.8      0.61        651.4      399.5       303.4       274.1      0.75     1.41      0.12
                   1.5-2.0        82.7      0.61        537.3      332.4       274.0       152.0      0.82     1.42      0.16
                   2.0-2.5        71.2      0.81        456.2      370.0       282.3       341.5      0.76     1.33      0.18
                   2.5-3.0        85.8      0.69        369.4      256.3       191.8        88.6      II.74    1.26      0.15
                   3.0-3.5       127.9      0.79        474.7      377.2       331.1       284.4      0.87     1.59      0.29
                  3.5+            85.0      0.69        462.7      320.5       250.2       419.8      0.78     1.75      0.11

Korea             < 2.0          246.8       4.67       192.0      897. I      642.2      1569.7      0.71      1.00     0.08
                  2.0-3.0        175.1       3.58       143.7      516.0       429.2       437.7      0.83      1.OO     0.14
                  3.0-4.0         81.2       1.21       211.7      258.0       198.8       507.3      0.77      0.87     0.15
                  4.0-5.0        369.1      11.27        51.8      584.9       545.0       533.7      0.93      1.00     0.30
                  5.0-6.0        324.1       8.88        37.0      328.7       279.4       248.6      0.84      1.01     0.30
                  6.0-7.0        188.8       4.43        68.5      303.8       245.0       387.8      0.80      1.00     0.21
                  7.0+           546.4      13.09        22.7      297.4       232.7       143.8      0.78      1.00     0.35

Thailand          < 1.0           41.8       1.85        82.4      152.7       144.5       503.2      0.94     1.33      0.17
                   1 .O-2.0       35.4       1.55        75.1      116.5        99.2        33.0      0.85     1.00      0.23
                  2.0-4.0         59.7       1.54        87.1      135.1       119.0        98.1      0.88     0.99      0.16
                  4.0+            79.5       2.03        42.7       87.2        84.6        18.1      0.97     0.98      0.49

*All values are expressed   in 1970 US dollars; land figures are expressed     in hectares. The meaning of the symbols is:
CLS = farm size (intervals expressed in hectares); GO-W0    = gross output per worker: GO-MD = gross output per man-day; MD-LN
= man-days per hectare; GO-LN = gross output per hectare; VA-LN = value added per hectare: KA-LN = capital stock (land
excluded) per hectare; VA-GO = value added/gross       output rate: LUI = land use intensity; OFLl = percent of off-farm labor.
524                                              WORLD DEVELOPMENT

 variations,     with African countries           being more       (c) Labor productivity log GO/W0 = (I + h log LN (6)
 family labor-based         than others.                                                  log GO/MD = u + h log LN (7)
   Table 2 also shows that, with the exception of                  where MD = man-days,                   KA = capital stock,
Peru, capital per hectare of farm area declines                    (GO-VA)         = intermediate          inputs, LUI = land
surprisingly      as farm size rises. These findings               use intensity,         GO = gross output.                 WO =
seem to contradict the received notion of higher                   workers and LN = farm area. Table 3 contains
capital intensity of large capitalistic            farms. As       the values of the h parameters                for each country
noted earlier. however. capital is defined here as                 and for each variable. The values of the constant
the sum of the following assets: half of the farm                  term and of the other statistics is omitted because
buildings, I” cattle, permanent           crops (orchards),        not relevant in this context. The main conclu-
land improvement           - investment,        and mechan-        sions to be drawn from Table 3, confirming and
ical and transport         equipment.       It has not been        supplementing          the above discussion.               can be
possible      to compute        separately     the value of        summarized        as follows:
purchased       investment       goods. Possibly,       capital        (i) An inverse relation between farm size and
per hectare would be higher for larger farms if                        land productivity            is generally        found.     All
only purchased investment goods were accounted                         parameters       are negative and significant with
for. In addition,         an examination         of the data           the exception of Peru, Bangladesh                  and Thai-
shows that capital intensity               as measured       by        land for which no relation was found. For
capital per worker is highest in larger farms for                      Thailand, this is probably due to the limited
nine of the 15 countries               analyzed.      Land is          number of observations,               while for Peru the
accounted for (in hectares) as a separate produc-                      information       is scanty. The case of Bangladesh
tion factor and is not icluded in the capital stock.                   reflects the general weakening                of the above
The high capital intensity            of small farms can               relation in land-scarce           countries where farm
therefore      be explained        by the higher relative              differentiation       is limited. The negative elasti-
value of those investment                goods which are               cities are much higher                 for the land-rich
produced on farm (buildings, permanent                  invest-        countries of Africa and the Middle East than
ment in land) through the realization of the value                     for the densely populated                 Asian countries.
of surplus labor, and by higher cattle-intensity.                      where land use patterns                   among different
As a complementary           explanation for the negative              classes of farms are less diverse than in other
relation     between       farm size and capital            per        developing       regions.
hectare one may add that large holdings are                            (ii) Land use intensity (which is defined as the
indeed more capital-intensive            for each effective            ratio of cropped            to farm area and which
crop activity, but are - on average - less so                          therefore      reflects      both different         land use
because of the low rate of utilization of the farm                     patterns and cropping intensity) is negatively
area. Similar results are found for the use of                         related to farm size in nine cases out of 15.
intermediate       inputs (see the ratio VA/GO                in       while for three countries               no relation what-
Table 2). Most of the countries in fact show a                         soever was found. In three cases, the relation
significantly     constant     ratio of value added to                 is positive. It follows that the relation between
gross output. A constant ratio of value added to                      farm size and land-yield is less pronounced                    if
gross output implies, however. that the input of                       differences     in land use patterns and cropping
intermediate       goods, per unit of land is more                     intensity are accounted             for.
intense on small than on large holdings.                    For        (iii) With few exceptions,             all resource inputs
traditional backward agriculture, the explanation                     per unit of land bear a significant                   negative
possibly lies in the higher availability of farmyard                   relation to farm size. This relation holds true
manure       on small farms, which have a large                       for inputs of labor. capital and intermediate
number of cattle per unit of land.                                    goods per unit of land. and it is particularly
   Regression       analysis may be used to obtain a                  intense for the first two factors. Furthermore,
rigorous test of the hypotheses           formulated     about        the negative elasticity of labor and capital per
resource     use, land and labor productivity              and         hectare      with       respect      to farm         size.    is
farm size. To this purpose, the followng models                       systematically          higher      than     that     of land
have been estimated for each country, based on                        productivity         ~JCTSII.S   farm size. suggesting
the original cross-sectional          farm data:                      decreasing marginal returns to both labor and
                                                                      capital inputs. The decrease in marginal re-
(a) Resource use            log MD/LN = (I + h log LN       (I)
                            log KA/LN = u + h log LN        (2)       turns to labor and capital inputs seems to be
                            log (GO-VA)/LN = (1 +           h         particularly      acute in several Asian countries
                            log LN                          (3)       analyzed, as well as for Nigeria and Mexico.
                            log LUI = u + h log LN          (3)       The inputs of intermediate              goods on the other
(b) Land yield              log GO/LN = (1+ h log LN        (5)        hand show negative elasticities in 11 cases out
          FARM   SIZE,   LAND      YIELDS        AND   THE     AGRICULTURAL              PRODUCTION          FUNCTION              525

Table 3. Elasticity of output, man-days, intermediate inputs, capital (all per hectare), land use intensity and labor
                                      productivity with respect IO farm size

Country                  GO/LN         MD/LN            GO-VA/LN                KAILN           LUI        GO/W0         GO/MD

Barbados                  -0.36         -0.51                  **                -0.53        -0.22*         0.37            **
Mexico                    -0.20         -0.77                  0.32              -0.38          0.07         1.07          0.58
Peru                         **         -0.43                  **                   **        -0.1s          0.80          0.47
Ethiopia                  -0.55         -0.94                -0.30               -1.00           **          0.26          0.38
Nigeria                   -0.23         -0.57                -0.1x               -0.56           **          0.59          0.29
Tanzania                  -0.47         -0.57                -0.67               -0.95        -0.07          0.27          0.04*
Uganda                    -0.74         -0.83                -0.74               -0.59        -0.41          0.1s*         0.09
Syria                     -0.64         -0.71                -0.60               -0.63        -0.17          0.20          0.08
Sudan                     -0.42         -0.43                -0.27               -0.45           **          0.28            **
Bangladesh                   **         -0.09*               -0.44               -0.37        -0.17          0.58            **
Burma                     -0.58         -0.65                -0.51               -0.44        -0.05*         0.16            **
India                     -0.18         -0.52                -0.25               -0.32          0.08         0.61          0.33
Nepal                     -0.21         -0.23                -0.30               -0.50        -0.17          0.50            **
Korea                     -0.42*        -1.40                -0.73               -1.26           **          0.73’         1.06*
Thailand                     **            **                   **               -1.08        -0.15          0.41*           **

Source: Computations       of the author; all parameters   are significant at over 90% level of probability.     unless
otherwise    stated;
*Significant    at over 80%;
**Significant at less that 80%. In such cases. the value of the estimated parameter. which is generally close to zero,
is omitted.
Legends: GO/LN = gross output per hectare; MD/LN = man-days per hectare; (GO-VA)/LN                    = intermediate
inputs per hectare; KA/LN = capital stock (land excluded) per hectare: LUI = land use intensity; GO/W0         = gross
output per worker;      GO/MD     = gross output per man-day.

    of 15. while in three cases no relation was                       found to hold true for the vast majority of the
    found.                                                            countries analyzed.       It was seen, however, that
    (iv) Increasing       average labor productivity          is      the intensity of this relation varies according to
    found with the growth of farm size. All the                       land scarcity. It may be worthwhile,             then, to try
    elasticities     are found       to be significantly              to understand how factor scarcity affects produc-
    positive with the exception of Burma, Nepal,                      tion techniques.       In a more general sense, to
    Thailand and Sudan when expressing                  labor         formulate    a consistent      strategy of agricultural
    inputs in man-days            (M,D). The relation is              development,        it is necessary       to analyze       the
    more robust and the elasticities              generally           evolution of the modes of production                  and the
    higher       when     expressing    labor    inputs      in       importance     of each production        factor in relation
    number of workers. This possibly indicates a                      to its varying availability. In view of this aim, the
    lower number of man-days worked by each                           FAO farm data can be used for estimating
    worker per year in smaller farms. Note that                       country production         functions.     By relating the
    the elasticicy of GO/MD is exactly equal to the                   parameters      of these functions          to appropriate
    difference      between      the elasticity    of gross           indicators    of factor availability,         it may prove
    output per hectare (GO/LN) and that of man-                       possible to identify the role of each production
    days per hectare              (MDILN).      When       the        factor at various stages of development                and to
    difference      is very small, the value of the                   work out a long-term           production       function for
    GO/MD         elasticity    tends to become          non-         agriculture.    In addition, since the availability of
    significant.                                                      ‘produced      factors,’    such as equipment             and
                                                                      intermediate      inputs (fertilizers,     pesticides,   fuel,
                                                                      etc.),   also depends        on policy decisions,          the
    3. PRODUCTION FUNCTIONS   AND                                     results of the estimations         can be used to make
  RETURNS TO SCALE IN AGRICULTURE                                     policy suggestions about agricultural moderniza-
           (a) Some theoretical considerations                           In traditional     agriculture,     the supply of the
   In the previous section, the negative relation                     ‘produced factors,’ capital and intermediate                in-
between   farm size and land productivity      was                    puts, is modest, the level of technology rudiment-
 526                                                   WORLD DEVELOPMENT

  ary and the volume of agricultural output deter-                        (in hectares),    LUI = land use intensity (i.e. the
  mined mostly by a country’s endowment                            with   ratio of cropped to farm area), KA = capital
   land and labor (if institutional                factors as land        stock, MD = man-days. GO-VA = intermediate
  concentration         and tenancy are considered             invari-    inputs, A is a constant to be estimated and Q. 6,
  ant). Natural conditions and demographic                      forces    y, 6 are the output elasticities of the production
  determine,          under equally traditional             settings,     factors, different modes of production     are likely
  different      modes of production;                 in backward         to be reflected     in changing sets of elasticities.
  countries of West Africa, for instance, where the                       Results of prior empirical investigation     indicate
  land/man ratio is high, shifting cultivations on a                      that. in the case of a country function estimated
  slash-and-burn         basis are in use, while in equally               cross-sectionally   on farm data at time 0 and again
  backward,         land-scarce      countries,      a very labor-        at time I, one would most likely be faced with the
  intensive agriculture           is practiced in highly frag-            following results:
  mented parcels. In both cases, the contribution
 of capital and purchased               intermediate        goods is         CX,, II,, + yc, + b,,=u, + 13, y, + d,= I
                                                                               +                          +                        (8)
 extremely         limited.                                                  % 2 (4; IL 2 Ii; ‘{II;; ;‘,: h, 2 0,                  (9)
      In the process of economic development                       and
                                                                          that is. with a situation where. according to (8).
 depending on natural conditions,                  social structure
                                                                          the sum of the elasticities at time 0 and t would be
 and policy choices. agricultural production                     tends
                                                                          roughly the same and perhaps               close to one,
 to become more input-intensive,                  in the sense that
                                                                          whereas the elasticity of each production            factor
 the contribution          of mechanization         and intermedi-
                                                                          would most likely have changed as described in
 ate input increases in importance.                 The effects on
                                                                          (9). The analysis which follows attempts                  to
 modes of production,                 land productivity            and
                                                                          demonstrate     that the parameters       u. (3, y. h seem
 income        distribution        of a strategy          based     on
                                                                          to follow pre-established      trends as the modes of
 mechanization           or on increased inputs of fertiliz-
                                                                          production    change.
 ers and pesticides,          are, however. very different,                  In this regard.     previous     studies”     on cross-
 First. a fertilizer strategy is. technically speaking,
                                                                          section measurement       of similar production       func-
 neutral with respect to scale because of its high
                                                                          tions have broadly shown. for Asian countries,
 divisibility,      while mechanization            has economies          constant   returns to scale, output elasticitics          of
 of scale. Therefore.          the former can be applied to               land larger than the output elasticities of labor
 farms of any size, while the latter is more
                                                                          and capital (the ratio being about 3 to I). and a
 efficient if applied to large units. Second. while
                                                                          general tendency      of the land elasticity to de-
 fertilizer inputs are complementary                  to labor, the
                                                                          crease over time in favor of the other two during
 relation of mechanization                to labor is, broadly
                                                                          the course of development.            For instance.      for
speaking,        one of substitution.”
                                                                          Japan Ohkawa found the elasticities              shown in
     In addition to relative availability,               the evolu-       Table 4.
 tion of the factors proportion               also depends upon
 the degree of ease with which land, labor, capital
and intermediate               inputs      can technically          be
substituted for each other. Although it is difficult
to fully disentangle               the relations        of comple-
mentarity and substitutability               among factors, the           Year                Labor         LXld    Capital    Sum
following indications             can be retained from the
 literature:”        (a) intermediate        inputs are comple-           1xxx-90             0.215        0.613    0. 154    0.9x2
mentary         vis-&vis other factors; an increase in                    1937                0.237        o.sss    0.205     O.YY7
their use generally entails an increase in one or                         I Y38               0.280        0.510    0.155     O.Y1S
all the other factors: (b) the degree of aubstitut-                       I ‘X32-6I           0.523        0.315    0.407     I.245
ability between land and labor is usually high. To
a certain extent it is possible to raise yields by                        Source: Ohkawa (lY72). Pp. 27’) and 287.
increasing labor inputs per hectare; (c) with few
exceptions,          the dominant        relationship      between
                                                                              (b) Etnpiricd       rrsdts: productior~ fitr~ctim
labor and capital is one of substitution,                       while
there is limited evidence of mechanization                    having
effect on yields.
     In a production            function      approach.       as for         The FAO farm data were used for the cross-
instance       :
                                                                          sectional estimation  (i.e. across farms) at a
                                                                          country level of a production    functions of the
GO =     A * (LN * LUI)” * MD” * KA’( ’ (GO-VA)”                          tYPc
where GO = gross output,               LN = size of the farm              GO =   A * (LN ’ LUI)” ’ MD” ’ KA:’ ’ (GO-VA)“( IO)
       FARM SIZE, LAND YIELDS AND THE AGRICULTURAL                               PRODUCTION        FUNCTION         527

where the symbols are as explained above. The                  elasticities   might be somewhat       affected     by a
function was estimated          by means of the OLS            possible heterogeneity     of the inputs.
procedure after linearization       in double-log form.           Table 5 gives the ordinary least-squares       (OLS)
No constraints have been put on the parameters.                estimates     of the coefficients    of the various
Their sum therfore can be used as an indicator of              factors. Constant returns are assumed to occur
returns to scale. Indeed, if their sum is signifi-             when the sum of the parameters           significant at
cantly higher (lower) than unity, one would                    over 80% falls within the interval 0.9.5-1.05;
obtain increasing     (decreasing)     returns to scale.       below 0.95 or above 1.05, one has decreasing or
These results can be used to check if the negative             increasing returns. Therefore,      Table 5 indicates
relation between output per hectare and farm                   that there is evidence of decreasing         returns to
size observed in Section 2 is likely to be the result          scale in seven of the 15 countries         considered.
more of an inverse relation between size and                   Constant returns appear to prevail in five coun-
other inputs than of scale diseconomies.         It should     tries, while for Peru and Tanzania the evidence is
be stressed here that the test of such an hypoth-              more in favor of increasing returns to scale. The
esis has been made possible by expressing land                 estimates for Korea are completely out of range.
inputs in terms of the area effectively cropped                These results are all the more significative when
i.e. LN * LUI, rather than in terms of total farm              considering      that land inputs (LN * LUI) are
area, i.e. LN. This permits control for different              expressed     in terms of actually cultivated        land
land use intensity.                                            multiplied by its cropping intensity, and not in
    A note of caution is necessary before illustrat-           terms of total farm area. In this way, the effects
ing the results. Indeed, an important assumption               of different       land use patterns    for farms of
about the right-hand        side variables is that all         different    sizes has been eliminated        from the
inputs are sufficiently homogenous          and unambi-        production      function.
guously defined. Labor, for instance, consists of                  Although it is impossible to generalize,        since
family and hired labor; the two types of labor                 the country results refer to different         crops, it
have been added, thus implicitly assuming that                 would appear that decreasing returns to scale are
they have the same effect on output.                  This,    prevalent in land-rich countries of Africa and the
however,     is only a hypothesis.            Analogous        Middle East, while in South and South East Asia
assumptions have been made for the definition of               constant returns are predominant.         The findings
capital and intermediate       inputs. The value of the        on returns to scale confirm previous results only

                                   Table 5. Elasticities   of the production   function

country             Constant         LN*LUI            MD           KA         (GO-VA)        SUM’       SUM”      R’

Barbados                2.32           0.16**         0.33*         0.07**       0.39          0.95      0.72     0.67
Mexico                  3.53           0.16*          0.13*         0.03**       0.36          0.68      0.65     0.48
Peru                    2.49           0.52           0.23          0.03**       0.37          1.15      1.12     0.82
Ethiopia                0.88           0.14s          0.35          0.20         0.30          0.99      0.99     0.65
Nigeria                 4.05           0.51           0.12          0.11         0.17          0.91      0.91     0.80
Uganda                  3.80           0.20           0.01**        0.15         0.30          0.66      0.65     0.68
Tanzania                2.07           0.34           0.34          0.19         0.20          1.07      1.07     0.65
Sudan                   2.02           0.11*          0.25          0.29         0.22          0.87      0.87     0.51
Syria                   2.10           0.10           0.07          0.02*        0.65          0.84      0.84     0.70
Bangladesh              4.79           0.97           0.04**        0.08**       0.04**        1.13      0.97     0.65
Burma                 -0.55          -0.12            0.31          0.38         0.46          1.03      1.03     0.85
India                   2.59           0.33           0.07**        0.01**       0.53          0.94      0.86     0.88
Nepal                   3.69           0.66           0.01**        0.26         0.12          1.05      1.04     0.80
Korea                   7.81           0.44         -0.39           0.08**       0.09          0.22      0.14     0.51
Thailand                4.70           0.74         -0.09**       -0.03**        0.30          0.92      1.04     0.90

Source: Author’s computation.
AI1 parameters are significant at over 90% level of probability unless otherwise stated.
*Significant at over 80%.
**Significant at less than 80%.
528                                               WORLD        DEVELOPMENT

  to a certain extent. It is generally assumed in the                 the test imposed    is not a very severe one),
  literature   on South Asian agriculture,                that re-    considering  the cross-sectional nature  of the
  turns to scale are constant                  on the whole.          observations  and the occasional narrowness   of
  Decreasing      returns were only found in paddy                    the samples.
  areas. ” The interesting            finding of decreasing
  returns for the land-rich countries of Africa and
  the Middle East cannot be compared to previous                       (c)   Empiricul         rm4lt.s:   ol4tp4t    elasticities   vs factor
  results owing to the limited evidence existing for                   availuhility      and    the long-ntn        productiorl     firnctim
 these regions in the literature.
      As for the coefficients       of the different factors              The parameters            of the production              function
 of production,        land elasticity is highly significant           estimated for each country across farms define a
 with very few exceptions.           It is interesting to note         given mode of production               at a given moment in
 that land elasticity is regularly higher in land-                     time. Such functions. however, are of the short-
 scarce than in land-rich countries.                Bangladesh         term type for they have been obtained                           from
 and Syria, countries with respectively                little and      farms      characterized           by      broadly         speaking
 large amounts of available land, are situated at                      homogenous         modes of production.                In the long
 the two extremes of the spectrum.                Labor inputs         run, when factor availability (and, hence. factor
 tend to show sizeable and statistically significant                   proportion)       is likely to change noticeably,                     it
 elasticities for all but South and South East Asian                   would be inappropriate               to make use of such
 countries as well as for Uganda. In these coun-                       production functions. since the output elasticities
 tries, the estimated low and often non-significant                   of the production          factors are likely to change in
 labor elasticities are in conformity with previous                    response to the changes in factor availability.                      It
 empirical     analyses       showing that the marginal               is. therefore,       necessary to see how the former
 product of labor under labor-surplus              conditions is      vary in relation to changes in the latter, if a
 very low. As a second argument,                      the labor       long-term production             function for agriculture             is
elasticities    are found to be non-significant                be-    to be worked out. According                       to mainstream
cause for these countries                there is not much            production      theory. changes in factor proportion
variation in the values over the sample farms.                        occur in response to shifts in their relative prices,
 Labor elasticity is systematically            higher in coun-        which, in turn, are to be considered                   as signals of
tries with a high land/man ratio. This relation -                     the relative scarcity of each factor. Following this
symmetrical to the relation betwen land-elasticity                    approach,      given the initial conditions                 and the
and land-scarcity’-           would appear to confirm the             changes in the wage-rate, rental price of land and
hypothesis      of substitutability        between land and           capital, and in the price of intermediate                     inputs.
labor postulated          above.                                      the farmer combines the factors in such a way as
     The output elasticity of capital is. with the                    to obtain the highest profit. The heuristic limits
exception      of Burma, uniformly low and often,                     of such an approach are well known, especially
non-significant       (in seven countries out of IS). Its             under semi-feudal            modes of production.               when
value oscillates around 0.1(&0.20. confirming the                     commodities          and factor           markets         are little
values found in previous studies. This result is.                     developed,        strongly      monopolized            and highly
perhaps.      partially influenced          by the problems           interlocked,      the access of several cultivators                  to
encountered        in the definition       and measurement            these markets          is severely        restricted,       and the
of the capital stock. The output elasticity                     of    economic       decisions        of small farmers               highly
intermediate        inputs is highly significant           except     conditioned      by existing power structures.                Be this
for Bangladesh and thus turns out to be the most                      as it is, the FAO data do not allow the analysis of
significant parameter of the production function.                     the changes in factor proportion                    in relation to
Together with land elasticity it explains a large                     changes in their relative prices since, for each
part of the variation of output; it seems to have a                   country, all data refer only to a point in time (i.e.
stronger     effect on production             than labor and          a period of one year).
capital inputs.                                                          Therefore,      output elasticities have been analy-
     With the exception          of Korea, which shows               zed empirically           in relation        to some physical
results completely out of range. the estimates can                   indicators     of the scarcity of each production
be considered        satisfactory from a statistical point           factor. If a clear cross-country                 relation can be
of view. The sign and the size of the parameters                     found between            the output         elasticity      of each
appear to be plausible on the whole and not too                      production      factor and a physical indicator of its
removed from previous findings. The estimates                        availability.     then it may be possible to under-
are also satisfactory          in terms of total variance            stand the laws of motion of such output elastici-
explained and of level of significance                (although      ties and a long-term               production         function      for
      FARM      SIZE,   LAND   YIELDS          AND    THE         AGRICULTURAL                  PRODUCTION              FUNCTION         529

agriculture could be derived - if a few assump-                           Although less evident than the previous one,
tions are made on the returns to scale. With this                     an inverse relation would appear to exist betwen
aim in mind the output             elasticities of land               the two variables, confirming         the low marginal
estimated above (see Table 5) have been plotted                       productivity of labor in labor surplus agriculture:
against the corresponding          values of the 1975                 the opposite would hold true in land-rich coun-
average land/man ration of each country consi-                        tries. Also in this case, one may derive the
dered. Land, here, is total national farmable                         long-term output elasticity for a given country by
land, while the denominator          reprsents the 1975               assuming the value of the agricultural labor force
total agricultural     population.     As one can see                 per hectare in the target year.
from Figure 1, a clear inverse functional relation                        Finally, the output elasticity of intermediate
appears to exist between the two variables.                           inputs (seed, fertilizers,     fuel) has been plotted
   When available land per capita declines, the                       against the average        value-added/gross       output
output elasticity of land increases steeply, reflect-                 ratio of each national sample. The lower this
ing most probably a more intensive use of land.                       ratio, the higher is the contribution      of intermedi-
When using this relation over time for a single                       ate inputs to production.        Figure 3 shows again
country, it is legitimate to suppose that when the                    the existence of an inverse relation between the
land/man ration increases (as an effect of rural-                     two variables.
urban migration, for instance) the output elastic-                        The higher the value of the value-added/gross
ity of land might decrease,        as described by the                output ratio, the lower the input of intermediate
above empirical relation, reflecting the shift to a                   goods and the lower, hence, the output elasticity
new technology       (or mode of production).                         of intermediate   inputs. When the ratio decreases,

  of land (u)




                                                     .IND                        .TAN

                                                                                         lETH                                      SUD

                                           I                 I                                                   1            I      +
                          Oh              0.2               0.3            014                0.5               0.6         0.7
            - 0.1                                                 lBUR                                     Land/man ratio

                          Figure   I.   Land/man       ratio      vs output      elasticity    of land (a)

   In a similar way, the output elasticity of labor                   the production       process   becomes    increasingly
(in man-days) estimated above has been plotted                        input intensive and, accordingly, the correspond-
against an indicator of countrywide availability of                   ing output elasticity assumes higher values. In
agricultural   labor force (drawn from the IL0                        this case, therefore,      a positive relation exists
Labour Statistics) per hectare of farmable land,                      between the use of intermediate        inputs and the
both measured in 1975. Figure 2 illustrates the                       corrresponding     output elasticity.
empirical relation between the output elasticity                         For all the three cases analyzed above, a linear
of labor and the agricultural      labor force per                    0, = a + bx + u) and a hyperbolic 0, = a + b/x +
hectare.                                                              u) specification   have been fitted econometrically
530                                                                                 WORLD           DEVELOPMENT

 e$atkity          o,4

 labour (6)                                                            lETl-t
                   0.3-                                               r3& *TAN

                  0.2-                                              .PER

                   O.l-                                 lNGR
                                     lSYR                                                    .IND                                                                             l0GD
                                                                           WGA                                                                                                     .NEP
                                I,         ,        I   I       I     I        I     I I ,I             I I,,            I    I        I     /       I,,             I        IT          I I   b
                             0.1     .2   .3       .4   5       6     .7       .8    .9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8
                 - O.l-                                                                .THAI                                           Agricultural labour force per hectare

             - 0.2-

                       Figure        2. Agricultural                  labor          force    per hectare       vs output             elasticity           of labor       (p)

            .60                                                     .SYR



                                                                                                                                           .ETH            .UGA




                 si    “,A
                                               I            I              I            I           I     I         I             I

                                                                                                                                                 I            I           I           I
                              .40         .45           .50           .55             .60      .65       .70      .75        .80            65               90          .95

                                                                                    Value added /Gross - output ratio

         Figure              3. Value-added/gross-output                                ratios      vs output    elasticity           of intermediate               inputs          (b).
       FARM      SIZE.      LAND     YIELDS       AND     THE       AGRICULTURAL                   PRODUCTION               FUNCTION       531

to the three couples of variables discussed above,                      output elasticity of capital (y) will be equal to 1
i.e. to output elasticity of land (a) vs land/man                       - (a+b+ti).
ratio (l/m), to output           elasticity    of labor in                 The results illustrated above are to be consi-
man-days       ((3) vs agricultural       labor force per               dered    as highly preliminary        from both the
hectare     (If/h),     and to output          elasticity    of         methodological      and empirical     points of view.
intermediate        inputs (6) vs value-added/gross-                    They might be of some use, however,                    in
output ratio (va/go). If our hypotheses                 on the          disentangling    the importance     and role of each
relation    between       factor elasticities     and factor            production     factor   under   different   conditions
availability were to be confirmed,            the values of             concerning its scarcity, and in attempting to work
parameter b should turn out to be negative. This                        out a long-term production      function for agricul-
is precisely what is shown in Table 6 below where                       ture.
in all three cases the estimates of the b paramet-
ers are negative and significantly different from
zero for both the linear and the hyperbolic cases.                         4. CONCLUSIONS                   AND POLICY               OPTIONS
Table 6 also provides evidence of the statistical
superiority     of the latter specification.                                 In the preceding         pages, it has been shown that

               Tahle     6. Purumeters    of the   relurions between factor elasticity and fuctor availability’;

               Relation                         a = f(llm)                   13 = f(lf/h)                 h = f(valg0)

                                          *         b         R’       u          b          R’       a              h        R2

                Linear case              0.54     -0.43      0.27     1.34      -2.74       0.32     0.96      -0.73         0.44
               Hyperbolic     case       0.58     -0.0s      0.56     1.76      -0.41       0.43     1.2x      -0.37         0.94

               Source: Author’s       computation.
               *All parameters       are significant      at over    90%, level of probability              unless       otherwise

     A similar analysis could not be carried out for                    small farms are characteriied        by a more intensive
the output elasticity of capital because of the                         use of land and by resource inputs per hectare
problems encountered        in the construction       of an             higher than large estates. As a result, land yields
indicator of capital availability. The information                      are significantly     higher in sinall farms both for
on this matter included in the sample is excessive-                     total farm area and for cultivated             areas. This
ly biased by measurement,         prices and exchange                   phenomenon       decreases in intensity (and tends to
rate distortions,     to be used for cross-country                      disappear)     in those countries        where holding
analysis, while indications of capital intensity in                     fragmentation      is very high and where land use
agriculture are conspicuously        absent in National                 patterns do not vary significantly across farms of
Accounts.     Most of the output elasticities             of            different size. Similarly, the observed yield-gap
capital, on the other hand, are non-significant.                        between large and small farms tends to level off
   These three empirical relations can be used for                      when sufficient       job opportunities       in the non-
attempting     to derive the parameters             of the              agricultural    sector become available.
agricultural long-term production function for all                         The relations described above have been found
the cases when fundamental         changes in terms of                  to be valid for several Asian and Latin American
relative availability    of production        factors are               countries (confirming       previous findings), as well
expected because of, for instance,           rural-urban                as for countries        of Tropical     Africa and the
migration,     land extension,       increased      use of              Middle East characterized             by high land/man
fertilizers, and other factors. The values of their                     ratios and agrarian         structures    different   from
physical indicators     permit the identification         of            those    prevailing      in South      Asia and Latin
the new elasticities     of land (a), labor (fl) and                    America. The findings of this study are particu-
intermediate     inputs (b), while the assumption                       larly important in the case of Africa as, for this
made on the returns to scale allows us to derive                        part of the world, available evidence is extremely
by difference that of capital (y). For example, if                      limited.
constant returns to scale are hypothesized,             the                A second finding of interest             concerns    the
 5.32                                               WORLD        DEVELOPMENT

  existence of decreasing returns to scale for some                    present levels. In these regions by the year 2000,
  land-rich countries of Africa, the Middle East as                    all potential       arable land will be fully utilized.
  well as for Mexico. There, the negative relation                     Cropping intensity, yields and labor absorption
  between output per hectare and farm size should                      will therefore         have to step up substantially.
  be attributed to scale diseconomies             in addition to          Therefore,        if the joint targets of increasing
  the higher resource-use           per hectare observed in            food output, yields and labor absorption                      are to
 smaller farms. These conclusions,                however,       re-   be achieved, a few policy interventions                  should be
 quire further investigation.          For most of the Asian           recommended.             Such recommendations,                  how-
 countries included in our sample, broadly const-                      ever, implicitly assume that dynamic effects (such
 ant returns to scale were found. In such cases, the                   as the introduction          of new technologies,          changes
 superiority of small farming is due exclusively to                    in the social structure,            rapid urbanization            and
 a more intensive application of inputs per unit of                    others) will not reverse, at least in the short and
 land and to better land use patterns.                                 medium         term. the conclusions             arrived       at in
     As a third finding, the paper provides cross-                     Section 2 and 3. Three among the main policy
 country evidence            of an empirical       relation be-        measures        needed to achieve the above targets
 tween the output elasticities              of the factors of          can be singled out:
 short-term production functions and indicators of                          (1) Lund reform giving the rural poor direct
 their physical         availability.     In particular,        the         access to productive assets (land, water rights,
 results indicate that the output elasticity of land                       current inputs, infrastructure,              etc.) Because
 varies inversely          to the land/man           ratio. The            of the demonstrated                superiority       of small
 opposite      relation       was found for the output                      vis-ri-vis large farming,            land redistribution
 elasticity of labor, while the output elasticity of                       would        have,     if thoroughly          implemented,
 intermediate       inputs was found to vary positively                    immediate        beneficial effects in terms of out-
 with the intensity of their use. These results were                       put growth,          enhanced       income       distribution
 used for tentatively          determining    the parameters               and, as a result, of alleviation of rural poverty.
 of a long-term         agricultural     production      function          It would also bring about a resource use more
 and for solving             the traditional       problem        of       in line with the factor endowment                 of develop-
 changes of the structural              parameters       faced in          ing countries by increasing              labor absorption
 long-term      planning models.                                           (especially self-employment),               while forestall-
    These findings are helpful in formulating                      a       ing premature            labor-displacing        mechaniza-
strategy of agricultural development               aimed at the            tion. The potential advantages of land reform.
alleviation of poverty in rural areas. This is all the                     however,       vary according          to the amount of
more true if one discounts the indications on the                          land available for redistribution                 and would
future supply of labor and land. According to a                            likely be more beneficial in countries where
recent United Nations study.” the rural working                            land concentration           is high.
age population         is expected to increase, between                    (2) Promotion of more labor-intensive                   techni-
 1980 and 2000, by 78 million in Tropical Africa,                         ques.      Labor inputs per hectare                  could be
 167 million in the Indian Subcontinent,              52 million          increased       through a more intense land use.
in South East Asia, 19 million in North Africa                            since in most countries                  double      or triple
and the Middle East and 12 million in Latin                               cropping is still limited. More labor-intensive
America        (where        the present       high rates of              farming practices for each crop activity should
urbanization        are expected to accelerate).             Since        also be promoted,           such as better land prepara-
the prospects          for expanding         employment           in      tion, frequent weeding, line transplanting                    (for
manufacturing          and services in rural areas are                    rice) instead of random transplanting                   as well
generally quite modest, there is a consensus that                         as the application of larger amounts of fertiliz-
a large proportion          of the new job-seekers         should         ers. An increase in cropping intensity and the
find employment           in agriculture.    Land extension,              diffusion of labor-intensive               practices     would
however, is expected to be substantially                  smaller         likely entail the presence of water throughout
than in the past and very unequally distributed.n’                        the year and would require,                  therefore,        the
Tropical      Africa and Latin America                still have          execution of infrastructural             work of irrigation
large reserves         of unused farmland            and could            and water control,             higher labor inputs per
benefit between 1980 and 2000 from an increase                            hectare and substantially              larger amounts of
in arable land of 24 and 64% respectively.                  In the        fertilizers.      Broadly       speaking,       this ‘water-
Middle East as well as in South and South East                            fertilizer-labor-intensive’          technology has been
Asia, the possibilities             of land extension           are       followed in the East Asian agriculture.                         Its
practically      exhausted        (given the present           and        results in terms of land yields and employment
foreseable      state of technology),         and such as to              have been very satisfactory,                  and such to
allow an increase of only 8 and 12% vis-&vis                              explain the wide differences in yields vis-ic-vis
             FARM SIZE, LAND YIELDS AND                          THE      AGRICULTURAL             PRODUCTION                FUNCTION               533

         South    Asian   agriculture.    As Ishikawa notes                        generally   been rather disappointing.       Often
              . the statistical    data on the number of                           improvised    at times of harvest failure, they
         man-days      (and the amount           of fertilizer)                    have failed to make permanent        additions to
         applied to each hectare of cultivated land . .                            the capital stock in the countryside,         while
         indicate that there are signficant differences in                         their random nature had only a modest impact
         per hectare       labor     (and   fertilizer)     input                  in terms of alleviation of poverty. In the case
         among countries        and major regions                 .                of China and Japan, however, the mobiliza-
         (ranging) from around 100 man-days in the                                 tion of seasonally     idle labor for works of
         Northwestern      and Western regions in India                            digging canals, land terracing,     afforestation
         to more than 600 days in Japan for 1956.                                  and the like has been rather successful, in the
         They also indicate          that these differences                        sense that either the communes       in China or
         correlate positively with per hectare output.                             the small farmers in Japan have been in the
         Very broadly, the countries with the smaller                              condition of internalizing   the benefits of such
         per hectare labor (and fertilizers) inputs and                            works.‘” At the same time large amounts of
         per hectare      output     are found to be the                           workers have been mobilized (up to 30% of
         countries where the problems of employment                                the total labor force). Hence, if rural employ-
         and rural poverty are more acute.‘17                                      ment programs are to be successful as anti-
         (3) The creation       of additional      employment                      poverty devices and as stimuli to agricultural
         opportunities     in agriculture,        through     the                  growth, they should focus on the creation of
         establishment     of rural employment          schemes.                   durable assets the benefit of which should
         So far, the results of such programs                have                  accrue to those who have actually built them.


    1.    See, for instance, IL0        (1977).                                9    Doreen     Warriner       (1970).

 2. For          the choice of      the optimal farm size              in   10    This hypothesis,  highly arbitrary,        presupposes
England,         see for instance    Lund and Hill (1979).                  that 50% of the on-farm         buildings      are used for
                                                                            production   purposes  (storage,     cattle-raising,     etc.),
  3. In practice, the shape of the ‘production       function’              while the other 50% provides lodging services to the
depends   not only on the resource          position    of the              farm family.
various farmer groups, but also upon the extent of
technical   substitutability        and/or complementarity                  11. As major exceptions to this rule, Japan and China
among the different        factors.                                         have   experienced      forms of farm    mechanization
                                                                            complementary      to labor.
 4. See: ‘World Census              of Agriculture’,     (1960)     and
(1970), FAO, Rome.                                                          12. See Berry and Cline, (1979). Chapter 2. See also
                                                                            Merrill (197_5), quoted in Berry and Cline (1979), p.
 5. See among others CIDA (1971); Cline (1970);                             225. See also Thirsk (1974).
Berry and Cline (1979); Ohkawa  (1972); Hossain
(1977); Chose (1979).                                                        13.    Lau and     Yotopulos          (1971);   Bardhan      (1973).

 6. As a sample of the vast literature on the subject.                       14.    See Bardhan          (1973),    p. 1,379.
see: Berry and Cline (1979); Nguyen and Martinez
Saldivar (1979); Collins (1979).                                             15.    United     Nations      (1979).

 7. See Lee (1979).            For a dissenting        voice     on the      16.    See FAO       (1979).
subject, see Apthorpe           (1979).
                                                                             17.    Ishikawa     (1978).
 8. Rawksi           (1979);   Rahman       Khan       (1979);     IL0
(1977).                                                                      18.    Rawski     (1979),     p. 79; Akino         (1979).


Akino, M., ‘Land infrastructure improvement   in agri-                        an Asian model land reform re-analyzed,’         World
  cultural development:   The Japanese   case, 196@                           Development   Vol. 7 (1979).
  1965,’ Economic Development and Cultural Change                           Bardhan, P. K., ‘Size, productivity and returns to scale:
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