Redistributive land reform - Myweb.dal.ca

Redistributive Land Reform and Productivity∗
˙ scan†
Talan B. I¸
May 7, 2015
Abstract
In landlord systems with sharecropping arrangements, cultivators are often owners and tenants at
the same time, which leads to inefficient allocation of effort on owned and leased land. Using a
general equilibrium model, I examine the impact of redistributive land reform on farm productivity
and reallocation of labor out of agriculture in such settings. At the individual level, cultivators
respond to land reform by reallocating their effort over owned and formerly-leased land, and, at
the aggregate level, labor responds by reallocating from farm to nonfarm employment due to low
income elasticity of demand for farm goods and complementarity in consumption between farm
and nonfarm goods. The strength of these responses depend on the initial degree of land inequality
and initial income. I provide a quantitative analysis of these responses using Japan, South Korea,
and Taiwan as historical cases.
JEL classification: O41, O11, N1.
Keywords: redistributive land reform; labor reallocation; productivity; structural change; land
inequality; East Asia
∗
I thank Francisco Alvarez-Cuadrado, Ben Dennis, Andrea Giusto, Dozie Okoye, and the participants of the MED
study group for comments, and Universidad Carlos III de Madrid for its hospitality during the early stages of this
research. My understanding of the land reforms in Japan, South Korea, and Taiwan owes a great deal to Qi Chen.
This research was not externally funded. The author declares no competing financial interests.
†
Dalhousie University. E-mail : [email protected]
1
Introduction
Recent research has emphasized the significance of historical differences in wealth inequality, in
particular, land inequality, in understanding contemporary differences in economic outcomes across
countries and regions (Engerman and Sokoloff, 1997; Banerjee and Iyer, 2005; Frankema, 2010). In
many poor, agrarian societies where land constitutes the biggest component of non-human wealth,
many economic decisions surrounding investment, labor supply, occupational choice, and migration
cannot be thought in isolation of distributional issues—especially when inequality deprives some
segments of the society of full utilization of their productive capacity.
One well-studied implication of land inequality is resource allocation, especially in those societies
where landlords have claims on economic surplus generated by tenant, cultivator farmers. When
credit market imperfections are acute, wealth poor but otherwise perfectly capable tenants cannot
purchase the land they cultivate because they cannot borrow against their future earnings. With
landlords as claimant on their effort, tenants provide suboptimal effort on leased land and landlords
respond by suboptimal investment in land (Shaban, 1987; Laffont and Matoussi, 1995). While,
such findings have long been used as an economic argument for land redistribution, the empirical
literature found mixed results concerning the impact of land redistribution on productivity in
agriculture (Binswanger, Deininger, and Feder, 1995). Thus, there appears to be a disconnect
between the evidence emerging from direct estimates of efficiency in sharecropping environments
and land reform episodes that reduce or eliminate sharecropping.
In this paper, I reconcile these seemingly inconsistent findings using a general equilibrium model,
and I identify a number of mechanisms that have hitherto been overlooked in the literature. The
basic economic reasoning builds on the fact that in landlord systems with sharecropping arrangements, cultivators are often owners and tenants at the same time. In the model, this combination
of owned and leased land presents itself to the cultivators as an effort allocation problem, whose
solution delivers exerting inefficiently higher effort on owned land. In other words, the initial
distribution of land and the resulting sharecropping arrangements can be seen as an economic
distortion, whereby allocation of effort across different plots of land is inefficient. Consequently,
following a redistribution of ownership rights from landlords to tenants, the cultivators reallocate
their effort: they reduce effort on owned land and increase it on formerly leased land. Elementary
economic reasoning then suggests that such an improvement in allocative efficiency alone improves
farm productivity. And, higher the degree of initial land inequality, the stronger the effects of this
channel on labor productivity. As such, the model generates intersectoral productivity differences
across plots of land, and points to endogenous gains in farm productivity through the elimination
of inefficiencies arising from sharecropping.
At the same time, this effort reallocation channel has mixed consequences for labor versus
1
land productivity, particularly once one takes into consideration the general equilibrium effects.
First, as a result of more efficient allocation of effort on different plots of land, labor productivity
increases, but, all else equal, less intensive use of owned land reduces its productivity. Moreover,
as long as effort has an opportunity cost, a redistribution not only frees cultivators from claimants
on their effort, which, at the margin, tends to increase effort, but also by reallocating effort
more efficiently, it increases income, which tends to reduce effort. This is particularly the case if
additional productivity does not generate proportionate demand for farm goods and instead simply
reduces their relative price—as would be the case when the income elasticity of demand for food
is less than one or farm and nonfarm goods are complements in consumption. If this reallocation
effect by cultivators is sufficiently strong, total effort may end up declining. This in turn may lead
to a weak association between land redistribution and productivity growth in agriculture at the
aggregate level.
In addition, the general equilibrium ramifications of land redistribution extend beyond the farm
sector. By increasing the share of income going to cultivators, land redistribution stimulates their
demand for domestic nonfarm goods. The combination of rising efficiency in the farm sector, falling
farm prices, and rising demand for nonfarm goods leads to rural to urban migration. Consequently,
a redistribution of land ownership rights accelerates structural transformation, and acts like a labor
saving and land using productivity growth in agriculture.
Finally, the magnitude of land and labor productivity growth in agriculture, as well as the pace
of labor reallocation out of agriculture in the aftermath of a redistributive land reform depend both
on the initial distribution of land between landlords and tenants and initial income. For instance,
relative to countries with low initial inequality and high income, those with high initial inequality
and low income tend to exhibit a faster pace of structural change following a redistributive land
reform. As such, differences in initial conditions can also weaken the association between land
redistribution and productivity growth in agriculture.
In the empirical part of the paper, I use this general equilibrium framework to account for the
possible impact of land reforms on farm productivity and reallocation of labor out of agriculture in
postwar Japan, South Korea, and Taiwan.1 All three countries undertook extensive redistributive
land reforms in the late 1940s and early 1950s, when their economies were still highly reliant on
agriculture and farms employed a large share of their labor force. These reforms had dramatic
impacts on the distribution of land among farm households: after the reforms, land distribution
became highly equal and tenancy almost disappeared in all three countries. What is critical
1
I refer to the Korean peninsula occupied by Japan before World War II as Korea, the territory of the contemporary Republic of Korea as South Korea, and the island of Taiwan, Province of China, as Taiwan. At the end of
the World War II (WWII) in 1945, the Korean peninsula south of the 38th parallel was occupied by the United
States, and the north was occupied by the Soviet Union. In 1948, the south declared independence by founding the
Republic of Korea, and the north founded Democratic People’s Republic of Korea. In 1950 North Korea triggered
a war devastating for both sides and that ended in 1953 with an armistice, which remains fragile even today.
2
about these cases is that their land reforms were largely exogenous, with no explicit or implicit
objective to improve efficiency in the farm sector. Yet, most studies have found that redistributive
land reforms have uniformly improved agricultural productivity in these countries, but there does
not appear to be an explanation in the literature for why their responses to reforms were also
significantly different.2 Their subsequent rates of reallocation of labor from farm to nonfarm
sectors, capital accumulation, and economic growth were also remarkably high (Young, 1995), and
many commentators have alluded to land reforms and low land inequality as factors contributing
to these outcomes as well (e.g., Rodrik, 1995).3 Yet, there has been limited attempts to quantify
the contribution of redistributive land reform to rapid resource reallocation across sectors in these
countries, a gap I also fill with this paper.
Related literature.
This paper contributes to the literature on the impact of initial wealth
distribution on subsequent economic performance. I study the consequences of (exogenous) redistributive land reforms that reset the initial conditions in Japan, South Korea, and Taiwan.
A different methodology employed in the historical literature studies those cases in which initial
wealth inequality is determined by geography. For instance, Engerman and Sokoloff (1997, 2006)
argue that, during colonization, wealth inequality in the Americas was primarily determined by
geographic factors: plantation agriculture in sub-tropical regions and mining resulted in highly concentrated wealth distributions that gave way to a coercive social and economic structure ruled by
elites, whereas family-farming in temperate regions resulted in highly equal land distributions that
gave way to a participatory social and economic structure. According Engerman and Sokoloff, these
exogenous variations across regions in inequality had echoes in educational attainment, health, and
emergence of democracy even centuries later.
However, such geography-based explanations encompass both markets and institutions as intermediating determinants of inequality. The reason is that regions in the Americas with sub-tropical
climates and rich mineral resources specialized in plantation agriculture and mining and were
almost exclusively oriented toward export markets. This blunted the necessity to develop local
markets and to increase domestic income and demand, cementing initial inequality. Northern
regions of the Americas, by contrast, faced a fiercely competitive export market for the crops
and products they produced, and hence responded to these market conditions by encouraging the
development of their local economies. See Binswanger et al. (1995).4
2
See, for instance, Kaneda (1980) on Japan, Jeon and Kim (2000) on South Korea, and Koo (1968) on Taiwan.
This is consistent with the view that land inequality retards economic growth because it creates a political
arms-race between those for and against redistribution (Alesina and Rodrik, 1994; Galor, Moav, and Vollrath, 2009;
Falkinger and Grossmann, 2013).
4
See Easterly (2007) for a cross-country examination of the link between inequality as caused by geographic
factors and economic development. Frankema (2010) emphasizes the influence of pre-colonial land tenure systems
and social conditions in shaping colonial origins of inequality.
3
3
In pre-reform Japan, South Korea, and Taiwan, land equality had different determinants. Before
WWII, land inequality in Japan was primarily the legacy of the Land Tax Revision in 1873, which
granted ownership rights to landowners (who were responsible for the feudal land tax), and not to
the traditional tenants (Kawagoe, 1999). In South Korea and Taiwan, land inequality was largely
due to coercive colonial practices. Moreover, none of these countries had plantation agriculture
based on hired, indentured or slave labor. While as temperate-zone countries Japan and South
Korea are not suitable for growing plantation crops, Taiwan with its tropical climate is suitable for
sugar cane and banana farming. However, plantation agriculture never took foothold in Taiwan.
Monsoon rice farming by family labor was the predominant form of traditional agriculture in all
three cases (Oshima, 1986). Both South Korea and Taiwan became large exporters of rice to Japan
during the colonial period, but this was the result of extractive Japanese colonial policies and high
tariffs in Japan on agricultural imports outside her colonies.5 As a result, the histories of these
three countries contain episodes of both high and low land inequality, and their determinants are
distinct from those observed in the Americas.6
Outside the Americas, there is a growing literature on the nexus between land inequality and
economic performance in India. In particular, Banerjee and Iyer (2005) argue that, while, during
their colonial rule in India, British granted tax collection powers to landlords in some regions, they
directly taxed individual cultivators (independent farmers or village collectives) in others, and
that these regional variations were based on historical accidents rather than economic reasons—
thus creating a landlord class in certain places where it previously had not existed. According to
Banerjee and Iyer (2005), more than a century later non-landlord regions had superior education
and health outcomes than landlord districts.7
There is also an empirical literature which studies the impact of tenancy and redistributive
land reforms on agricultural productivity. Ghatak and Roy (2007) survey this literature on India
and conclude that while many Indian states have legislated land redistribution and tenancy laws
after independence, the timing and implementation of these laws varied considerably across states.
They find that West Bengal, with the best record in implementing a serious land reform, had a
superior productivity growth in agriculture.8 Overall, the literature on India suggests that, after
controlling for the intensity and effectiveness of the land reform legislation, there is a positive
5
Before the Korean peninsula was politically divided, North was the industrial base, and South was largely rural.
Also, as a qualifier, I should add that cotton (a plantation crop) can grow in some islands of Japan, but its production
disappeared under international competition in the early twentieth century (Honma and Hayami, 2009).
6
Of course, all three countries, later in the second half of the twentieth century developed highly export-oriented
manufacturing sectors, but this was largely due to their rapid industrialization rather than the cause of it (Rodrik,
1995).
7
Banerjee and Iyer (2005) argue that, in their data, initial regional variation in land inequality is exogenous and
is correlated with the tax collection system instituted by the British.
8
See Besley and Burgess (2000) for a chronology of land reform legislation by state in India, and (Banerjee, Gertler,
and Ghatak, 2002) for a discussion of the reforms in West Bengal, as well as their consequences for agricultural
productivity.
4
causal link between land reform and subsequent productivity growth in agriculture.
There is also a substantial theoretical literature that links distribution of wealth to economic
performance. Some of the causal channels studied in this literature include those related to demand for and supply of education (Engerman and Sokoloff, 2006; Galor et al., 2009), agricultural
investment (Ghatak and Roy, 2007), occupational choice (Falkinger and Grossmann, 2013; Banerjee and Newman, 1993), and endogenous technological change through scale economies or learning
by doing (Greenwood and Jovanovic, 1990; Matsuyama, 1992). In this paper, I focus on a productivity channel driven by endogenous effort, and link redistributive land reform specifically to
reallocation of labor out of agriculture.
Finally, a recent literature has pointed to misallocation of resources both within and across
sectors as a source of underdevelopment (Hsieh and Klenow, 2009; McMillan and Rodrik, 2011).
Here, equilibrium allocation of effort by cultivators across leased and owned parcels of land constitutes an example of such misallocation. Otherwise, there are no distortions that directly affect
the allocation of labor across sectors.
The organization of the rest of the papers is as follows. Section 2 provides background information on redistributive land reforms on Japan, South Korea, and Taiwan. Section 3 presents a
two-sector macroeconomic model, in which farmers cultivate multiple plots of land, either leased
or owned. Section 4.2 discusses the principal economic mechanisms included in the model and
that are responsible for farm productivity growth and structural change in the aftermath of a redistributive land reform. Section 5 compares the actual outcomes observed in the three countries
with those predicted by the model. Section 6 concludes.
2
Land reforms in Japan, South Korea, and Taiwan
Since the model and the economic analysis below relies on the concrete cases of Japan, South
Korea, and Taiwan, I start with a description of their land tenure systems at the time of their
land reforms. Historically, these have been land-scarce countries with labor-intensive paddy rice
farming: in 1955 arable land per farm household was merely one hectare in Japan, .9 hectare in
South Korea, and 1.19 hectare in Taiwan—some of the lowest in the contemporary world. Until
recently, land was the single most important asset for the majority of their households.9 Land
tenure and agriculture not only shaped their traditional economies, but also shaped the relations
among these three countries.
In early twentieth century Japan, South Korea, and Taiwan, ownership rights over land were
9
Japan’s arable land has been about twice as big as that of South Korea, which in turn has had slightly more than
twice the arable land in Taiwan (Honma and Hayami, 2009). In 1959, land in South Korea was about 75 percent
of total wealth (land, structures, and producer durables), and between 1961–1981 on average land accounted for 87
percent of tangible fixed assets in agriculture, and 16 percent of such assets in non-agriculture (Young, 1995).
5
held by a small landlord class, which leased the land to a large peasant class. In return for
the use rights, landlords typically received about 50 percent of the annual crop yield as rent—an
arrangement that is quite common in many agricultural societies. While in isolated cases landlords
provided inputs and were responsible for substantial investments in land, high rents were essentially
a manifestation of land scarcity and ownership rights bestowed on landlords—through either feudal
or colonial coercion.
By the turn of the twentieth century, Japan already had a land registration system in the service
of a broad-based, advanced land tax, had established agricultural research and extension services,
and invested in major irrigation and drainage infrastructure. Japan also colonized Korea and Taiwan during its imperialist expansion from 1895 lasting until the end of WWII. Taiwan was acquired
at the end of the Sino-Japanese war in 1895, and Korea was first declared as a protectorate in 1905,
and then fully annexed in 1910. In Korea and Taiwan, Japanese colonial governments invested
in irrigation projects and extension services for new seed varieties and fertilizers with the aim of
converting them into suppliers of cheap rice (Ban, Mun, and Perkins, 1980; Honma and Hayami,
2009).10 Even before such major investments in agriculture, the Japanese colonial governments
had conducted extensive land surveys and registered land holdings for better tax administration
and collection; in Taiwan from 1898 to 1905 and in Korea from 1911 to 1918 (Yoo and Steckel,
2010). In a way, by lowering administrative costs and reducing the incidence of contested claims
on land, this pre-existing legal infrastructure facilitated post WWII land redistribution.
At the time of their redistributive land reforms, all three countries had largely rural-based
economies with considerable land and income inequality.11 Even in 1955, the share of agricultural
workers in economically active population was 34 percent in Japan, 54 percent in Taiwan, and
80 percent in South Korea (Honma and Hayami, 2009, Table 2.1).12 Land and rural income
distributions were highly skewed: In Japan (1935), 3.2 percent of the farm households owned 30
percent of the cultivated land (Kawagoe, 1999, Table 4-9); in Taiwan (1930), about 6 percent of
the farm households owned half of the cultivated land (Ryoo, 1978, Table 10); and in Korea (1945),
about 3 percent of the farm households owned two-thirds of the cultivated land, and 4 percent of
the rural population received about a quarter of total farm income (Ban et al., 1980). Although
a small percentage of peasants was landless,13 most scholars point to the lack of wage labour and
10
This colonial policy was supplemented by tax-free rice imports to Japan from its colonies in the aftermath of
1918 Rice Riots. For instance, in pre-war (1938) Korea, rice and barley constituted about 70 percent of agricultural
output (Ban et al., 1980, Table 47). Rice continued to be the single most important crop in all three countries after
the war.
11
Chen (1961), Ban et al. (1980), and Dore (1959) are excellent individual accounts of land reforms in Japan,
South Korea, and Taiwan. See Dorner and Thiesenhusen (1990) for a review.
12
For these countries, the only pre-war estimate of the share of employment in agriculture I came across is for
Japan at 43 percent in 1938/40 (Hayami and Ruttan, 1971, Table C3).
13
For estimates of hired farm labor in pre-reform Taiwan see footnote 23 below, and in pre-reform South Korea
see Table 1.
6
socio-economic differentiation among non-landlord cultivators in Japan, South Korea, and Taiwan
in the pre-reform period (e.g., Honma and Hayami, 2009).
The trigger for redistributive land reforms in all three countries was the historically contingent
events during and following the end of WWII. During the war, price controls and compulsory
deliveries to secure food supplies had already undermined the economic and political powers of
landlords. After the war, the political turmoil in the region contributed greatly to the implementation of land reforms. In Japan, the land reform (1947–1949) was implemented under the directive
of the American Occupation Forces, fitting in with the broader objectives of the allied forces after
the war to keep Germany and Japan pastoral–rural societies in which a non-militarist democracy
would flourish.14 In Taiwan, the land reform (1949–1953) was initiated in order to solidify the local
political support for the breakaway Chinese Nationalist government Kuomingtang on the island.
The Sino-American Joint Commission on Rural Reconstruction, which administered the U.S. foreign aid in Taiwan was highly instrumental and provided technical assistance. In South Korea, the
land reform moved in two phases. The first phase (1945–1946) involved the expropriation of land
from the Japanese landlords by U.S. occupation forces. The second phase (1949–1952) was in part
prompted by Kuomingtang’s failure to implement a thorough land reform in mainland China and
its subsequent failure to hold on to political power. It was also an attempt to counterbalance the
sympathy for the regime in the North, which had earlier completed a wholesale land redistribution
to peasants (Ban et al., 1980; Dorner and Thiesenhusen, 1990; Kawagoe, 1999; Jeon and Kim,
2000).15
In all three cases, land reforms were essentially confiscatory from the viewpoint of former
landlords, involved sales of public land to smallholders, and resulted in a highly equal distribution
of farmland. In all cases, reforms set a ceiling on the farmland size. At the same time, prices paid
to compensate former landlords and for public land bought by farmers were highly advantageous to
farmers, set at below market rates. In Japan, the purchase price was based on 1938 nominal rental
values, which had been eroded in value substantially through wartime inflation, and even that
amount was to be paid over 30 years at a fixed interest rate of 3.6 percent (Dore, 1959; Kawagoe,
1999). In South Korea, the compensation of non-Japanese landlords was 1.5 times the annual yield
paid over five years with no interest (and in many cases, these payments were extended to 8 years).
This effectively amounted to the confiscation of land (Ban et al., 1980). In Taiwan, starting with
the farm rent reduction program in 1949, the government first limited the rents to 37.5 percent of
the total main crop (usually rice) yield, and then instituted a land-to-the-tiller program in 1953.
14
Japan had a smaller scale land-to-the-tiller reform program from 1926 to 1937, which provided tenants with
credit to purchase the land they leased. So, there already was an administrative system in place (Kawagoe, 1999).
15
The U.S. occupation was favorable to and even instrumental in these three land reforms because of political
expediency. In the Philippines, where it had similar political influence and where land inequality was possibly even
higher, the United States exerted no such political pressure.
7
The public lands and land above the set ceiling that were sold to the incumbent cultivators at a
price of 2.5 times the average annual yield paid over 10 years (Chen, 1961).16
The consequences of these land reforms were striking. After the reforms, tenancy almost disappeared and all three countries had relatively low and similar inequality in land, as measured by
their low Gini coefficients for land holdings (Table 1).17 Overall, there is no disagreement about
the equalizing consequences of the land redistributions in Japan, South Korea, and Taiwan.
In all the three cases, the stated objectives of redistributive land reforms were consistently
framed along political dimensions. To my knowledge, there was no attempt to estimate the
expected economic impact of these policy changes. The interest in the topic surged after the
implementation of the reforms and acceleration in agricultural productivity.
3
A two-sector model
To examine the consequences of the types of redistributive land reforms discussed above for productivity and structural change, I develop a general equilibrium model, which captures the broad
features of the pre-reform agrarian structure with characteristics seen in post-war Japan, South
Korea, and Taiwan. Consistent with the empirical findings from the literature on the inefficiency
of sharecropping (e.g., Shaban, 1987), in equilibrium, tenants exert less effort on leased land relative to owned land (Section 3.1). I embed this agrarian structure within a two-sector economy
(Section 3.2), and then describe its general equilibrium connections (Section 3.3).
Preliminaries.
Consider a small open economy with no labor and capital mobility across bor-
ders; only final goods are exchanged and balance on trade is zero in each time period. Time is
discrete t = 0, 1, 2, . . .. There are two distinct goods f (“food”) and n (“non-food”). Food is produced in the farm sector using land and labor effort (as defined below), and non-food is produced
in the nonfarm sector using capital and labor services. There are no land markets.
There are four classes of individuals defined by their “occupations”: capitalists, workers, cultivators, and absentee landlords. Capitalists own the (domestic) physical capital stock. They do
not own land. Workers, indexed by h = 1, 2, . . . , H, work in the non-food sector. They do not
own assets. Cultivators indexed by i = 1, 2, . . . , I work in the farm sector. They own and operate
distinct plots of land. Absentee landlords indexed by j = 1, 2, . . . , J own and lease plots of land
and provide no other input into production. Denote total population by N . Total labor force is
16
In pre-war Korea, land prices were four to five times the normal annual crop yield (Jeon and Kim, 2000). As a
point of international comparison, Besley and Burgess (2000) report that in several Indian states which implemented
land reforms, the purchase price of land from the landlords was 15 to 20 times the normal annual yield.
17
Income inequality in the overall population also decreased. In Japan, income Gini index declined from 46.7
in 1940 to 32.2 in 1956. In South Korea, income Gini index was 34.0 in 1953 and in Taiwan it was 44.5 in 1959
(WIDER, 2008).
8
Table 1: Land tenancy and inequality of land holdings in Japan, South Korea, and Taiwan—
selected pre- and post-reform years
Country/
Year
Tenancy status of
farm households, %
Tenancy status of
cultivated land, %
Ownera
Tenantb
Year
Owner
Tenant
Year
Gini
coefficient
52
56
85
91
48
44
15
9
1941
1947
1949
1955
54
60
87
91
46
40
13
9
1937c
0.50
1960
0.40
44
48
93
56
49
7
1945
1965
36
82
64
18
1970
0.37
61
83
89
40
17
11
1948
1956
56
85
44
15
1960
0.39
Japan
1941
1947
1949
1955
South Korea
1938
1945d
1965
Taiwan
1946
1955
1970
a
Owner farmers include owner-farmers, who own 90% or more of the land they cultivate, and owner-tenants, who
own 50% to 90% of the land they cultivate.
b
Tenant farmers include tenant-owners, who own 10%–50% of the land they cultivate, and tenants, who own less
than 10% of the land they cultivated.
c
Refers to Gini for rural income distribution, and the midpoint of the range 0.45–0.55 given in the original source.
The postwar Gini for rural income distribution is about 0.35.
d
Remaining 2.7% of farm households is classified as “farm laborer and burnt field farmers.”
Sources: Tenancy status for Japan are from Kawagoe (1999, Tables 6-1, 6-2); South Korea from Ban et al. (1980),
and for Taiwan tenancy status of farm households is from Ryoo (1978, Table 66) and that of cultivated land is from
Chen (1961, Table 10). Gini coefficients are from Kawagoe (1999, pp. 1–2) for Japan in 1937, Frankema (2010) for
Japan and Taiwan in 1960, and from (FAO, 2013, Table 2) for South Korea in 1970.
9
L = I + H, with lf = I/L denoting the share of labor in the farm sector (similarly for ln for the
nonfarm sector). The number of capitalists is N − L − J. Below, the relative sizes of cultivators
and workers, will change over time, but I keep the sizes of landlords and capitalists fixed.
3.1
The farm sector
Production.
Landlords own plots and rent them to cultivators, who are both tenants and own-
ers of land. Cultivators use their owned and leased plot for fodder (for livestock) and cereal (for
humans) production. Fodder production could be either a by-product of cereal production or
product of fallow land. Cereal production requires management time, effort, and land t. Each
cultivator has one unit of “management time”. “Quality” of management is identical across cultivators. Each cultivator also has one unit of “work-time” which can be used with varying intensity,
called “effort.”18
Total farmland T in the economy is fixed. Each landlord can have multiple tenants, but each
tenant has at most one landlord. Let tij ≥ 0 represent a plot leased by cultivator i from landlord
j. Similarly, let tii ≥ 0 denote a plot of land owned and operated by farm a operator i. Together,
tii and tij completely characterize the distribution of land.19 Below, in the numerical solution of
the model, I ensure that, in equilibrium, it is optimal for a cultivator to lease land.
In general, I write xij for a generic input x used by tenant i on a plot leased from landlord j,
and xii for the same input on a plot owned by the farmer. I also refer to those cultivators who
do not rent from landlords as tenants with the understanding that xij = 0. Finally, I denote the
vector of input choices by cultivator i by xi = {xii , xij }.
Farm output by tenant i renting from landlord j a plot of land size tij is
(
f
yij
=
βtij ,
if eij = 0,
β ∗ tij + zf g(f f (eij , tij )), if eij > 0,
(1)
where the parameters β > 0 and β ∗ > 0 determine land productivity relevant for fodder in units
of cereal and corresponding to zero and non-zero effort levels, eij , respectively; zf > 0 is farm
total factor productivity (TPF); f f (e, t) is a constant returns to scale production function, which
combines the two inputs effort and land; and g(f f ) is a diminishing returns to scale production
18
In principle, landlords may own more land than they lease. Here, the analysis takes the amount of land to
be leased as given. Thus, throughout I work under the assumption that the participation constraint for absentee
landlords is always satisfied: they have no alternative use for the leased land and surplus extraction. Resident
landlords would have alternative uses to leasing, including farming with hired labor. However, hired work-time
requires costly monitoring to extract effort. I leave those complications surrounding monitoring of hired labor in the
background, and simply assume that monitoring hired work-time in the farm sector is prohibitively costly.
19
In non-coercive environments with proper land markets, the distribution of land leased by cultivators from
landlords has elements of choice driven by a surplus optimization problem solved by each landlord combined with an
optimization problem solved by each tenant. Yet, in the cases I study, this distribution is historically determined,
with landlords seizing (often with force) property rights from resident farmers (see also Binswanger et al., 1995).
10
function, which combines the managerial input with combined effort and land—managerial input
is non-rival across plots.20 Only tenants can transform fodder into cereal equivalents.
There is a similar expression for output from the cultivator-owned plot (with eii > 0):
yiif = β ∗ tii + zf g(f f (eii , tii )).
(2)
Notice that each cultivator faces an effort allocation problem, so the effort level on owned plot and
thus yiif depends on whether the cultivator as a tenant shirks or not.
Contracts and enforcement. Rent contracts specify a 0 < λ < 1 fraction of cereal that is kept
by the tenant, and the remaining 1 − λ fraction of cereal is handed to the landlord (sharecropping).
Effort is unobservable and thus cannot be specified in a contract. For the landlord, zero effort e = 0
amounts to “shirking”: fodder has no use value for the landlord.21 Thus landlords monitor tenants
to prevent from shirking. Monitoring has a probabilistic rate of success in catching those who
shirk, but otherwise is not costly; this structure simplifies the landlord’s problem. If a tenant
shirks and is caught, which occurs with probability 0 < π < 1, the landlord evicts the tenant,
confiscates the fodder as punishment and collects a fixed rent τ ≥ 0. If a tenant shirks but is not
caught, the tenant blames the weather or other exogenous factors for crop failure and gets away
with fodder equivalent to βtij units of cereal. The landlord receives nothing.
Farm output yi received by tenant i renting from landlord j depends on contract share λij ,
effort, land input, and the outcome of monitoring by the landlord. There are three cases: farm
income when the tenant shirks (eij = 0) and is caught; income when the tenant shirks and is not
caught; and income when the tenant does not shirk (eij > 0). These income levels depend on
output:22

f


 yii − τ
yif =
yiif + βtij


 yf + λ yf
ii
ij ij
if eij = 0, and caught (prob. π),
if eij = 0, and not caught (prob. 1 − π),
(3)
if eij > 0.
It follows that the farm output yij received by landlord j leasing to tenant i also depends on
20
This formulation is in the spirit of “span of control” approach to production (Lucas, 1978).
Koo (1968, p. 31) notes that in pre-reform Taiwan farm by-products were also subject to rent, and Johnston and
Kilby (1975, p.253) stress the significance of livestock feed in Taiwanese agriculture. Shaban (1987, p. 898) reports
that under sharecropping contracts, crop by-products, mostly fodder, were left to tenants in at least one semi-arid
village (Dokar) in India.
22
I express the share contract over the entire output when eij > 0, despite the fact that fodder has no use value
for the landlord. Doing so is reasonable because landlords anticipate the value of fodder to their tenants, and set the
contract share based on composite output. If, for some reason, this were not possible, it would be straightforward
to adjust the β ∗ by the share parameter. So, the precise formulation pursued here is not restrictive for the analysis
that follows.
21
11
whether the landlord detects a shirking tenant


if eij = 0, and detect (prob. π),

 τ
`
yij
=
0


 (1 − λ )y f
ij ij
if eij = 0, and not detect (prob. 1 − π),
(4)
if eij > 0.
Finally, total output received by landlord j is yj` =
`
i yij .
P
Preferences. Cultivators have identical preferences, which are represented by an additively separable lifetime utility function. Their instantaneous utility depends on consumption of food cf
and non-food cn , and effort e ∈ [0, emax ]:
u(cf , cn ) − v(e),
(5)
where u and v are both strictly concave functions defined over positive values of cf , cn , and positive
and feasible values of e. (I specify the functional forms used in the quantitative analysis below in
n
o
Section 4.1.) Let ci = cif , cin denote the consumption vector of tenant i with the two elements
representing food and non-food consumption, respectively.
Landlords, on the other hand, have preferences for a luxury good c∗ only produced abroad,
represented by a utility function U increasing in c∗ : U (cj∗ ) is the utility by landlord j consuming
c∗ ≥ 0. This formulation is consistent with the view that absentee landlords’ income typically
represented a “leakage” for the local economy, and were not recycled back into the local market.
The relative price of this good q in terms of the nonfarm good is exogenous.
Resource constraints.
Two features of the model, identical managerial quality across cultiva-
tors and costly monitoring of hired labor on the farm ensure that only own time and effort is used
in production by each cultivator.23 Thus, the following budget constraint of a cultivator describes
their feasible consumption allocations:
p cif + cin ≤ p yif ≡ wi (λij ),
(6)
where p is the relative price of the farm good in terms of the nonfarm good. Cultivators and
landlords take this price as given, though in a general equilibrium setting (described below), it is
endogenous.
Solving for contract share and effort. To characterize the fraction of output that remains
with the tenant λ (“share”), focus on those contractual arrangements that, conditional on leasing
23
Hired hands were a small share of agricultural population. In Taiwan, before the land reform, hired farm labor
was only about 6 percent of total agricultural population, and after the reform, it declined to below 5 percent of the
total (Chen, 1961, Table 11; Ryoo, 1978, pp. 427–428). For South Korea, see table 1.
12
a plot, induce positive effort on owned land eii and on leased land eij . While contracts cannot
stipulate effort, landlords can still extract surplus and effort from their tenants by taking the
tenant’s incentive compatibility constraint (ICC) into account. This ICC is:
j=0
j=0
j=0
π u(cf (p yiif (eii ), p), cn (p yiif (eii ), p) − v(eii )
j=0
j=0
j=0
+ (1 − π) u(cf (p(yiif (eii ) + βtij ), p), cn (p(yiif (eii ) + βtij ), p) − v(eii )
j>0
j>0
j>0
f
f
≤ u(cf (p(yiif (eii ) + λij yij
(eij )), p), cn (p(yiif (eii ) + λij yij
(eij )), p)) − v(eii + eij ),
(7)
where cf (wi , p) is the consumption function for cf (similarly for cn (wi , p)), which is feasible—as
j=0
defined in equation (6), eii
j>0
is the effort level on owned land when eij = 0, and eii
is the effort
level when eij > 0. The terms on the left-hand side of the inequality constitute the expected utility
when the tenant shirks, and the term on the right-hand side is the utility when not-shirking. The
above ICC, when satisfied with equality, describes a share–effort “surface” above which the tenant’s
participation constraint is automatically satisfied.
For a given λij ∈ (0, 1), the allocation of tenant i’s effort between the leased and owned land
obtains from the solution to the following utility maximization problem:
max
cif ,cin ,eii ,eij
u(cif , cin ) − v(eii + eij )
(8)
s.t. p cif + cin ≤ wi (λij ),
cif ≥ 0, cin ≥ 0, eii ≥ 0, eij ≥ 0, and eii + eij ≤ emax .
Denote (ˆ
eii (λij ), eˆij (λij )) as the optimal effort on owned and leased land, respectively, given
the output share offered by the landlord. In extracting the maximum surplus from the tenant, the
landlord incorporates the share delineated by the ICC (7) and the corresponding effort on owned
and leased land consistent with the tenant’s utility maximization problem (8). This maximum
surplus corresponds to the optimal effort on leased land induced by the contract share, and is
found as a solution to the following problem:
h
i
ˆ ij = arg max (1 − λij )y ` (ˆ
λ
e
(λ
))
ij ij ij
(9)
s.t. eˆij (λij ) > 0 satisfies the ICC (7).
bij = λ of about 50%, which I take as an
Notice that, historically tenants faced a uniform λ
equilibrium outcome in the rest of the paper.
Redistributive land reform. Consider a stylized (confiscatory) land reform, whereby the tenant becomes the owner of the land it leases, and the landlord looses all coercive powers and legal
claims (π = 0 and λ = 0). In this case, the consumption bundle and effort level on each parcel of
13
land is determined through the following utility maximization problem by the owner-operator:
max
cif ,cin ,eii ,eij
u(cif , cin ) − v(eii + eij )
(10)
s.t. p cif + cin ≤ wi (λ),
cif ≥ 0, cin ≥ 0, eii ≥ 0, eij ≥ 0, and eii + eij ≤ emax ,
with wi redefined accordingly.
Allocation of effort across plots. One of the decisions made by the cultivators is the allocation of effort between owned and leased land. Then, conditional on leasing, an interior solution
(ˆ
eii , eˆij ) > 0 to problem (8) is characterized by the equality of marginal value product of effort
between leased and own land, which is the familiar condition for production efficiency:
∂g(ˆ
eij , tˆij )
∂g(ˆ
eii , tˆii )
=λ
.
∂eii
∂eij
(11)
This condition shows that λ effectively distorts the effort allocation between owned and leased
land: it not only reduces the effort on leased land, but also leads to an (inefficient) over-supply of
effort on owned land.
With an eye toward the quantitative analysis, let
f f (e, t) = zf eαf t1−αf ,
g(f (e, t)) = f µ ,
(12)
where 0 < αf < 1 determines the elasticity of composite input with respect to effort in farm
production; and 0 < µ ≤ 1 determines the elasticity of output with respect to the composite effort
and land input on plot t.
Consequently, the production efficiency condition (11) can be stated analytically as
1
eii
= λ µαf −1
eij
tii
tij
µ(1−αf )
1−µαf
.
(13)
The ratio of effort on owned to effort on leased land is thus a function of both contract share λ and
the ratio of owned land to leased land tii /tij . Even in the absence of sharecropping, a cultivator
with multiple plots would allocate different levels of effort on plots tii and tij , as long as they are of
difference size. Sharecropping distorts this allocation, and, for a given tii /tij , biases effort toward
owned land, with smaller values of λ corresponding to higher degrees of distortion. Finally, for
a given value of λ, higher values of tii /tij would correspond to higher effort levels on the owned
land, but at a decreasing rate as long as µ < 1.
Thus, the model incorporates two features of sharecropping when there are owner-tenant cultivators: (1) sharecropping distorts effort allocation by cultivators, and (2) owned land gives ownertenants considerable bargaining power over the share contract through their ability to withdraw
14
effort on leased land. (I present a discussion of the “optimal contract” in such settings below.) This
implicit bargaining power becomes most visible in a comparison of pure and mixed tenancy. I thus
pose briefly and demonstrate, using a self-contained numerical example, the partial-equilibrium
implications of sharecropping for agricultural output and productivity under both pure and mixed
tenancy.
3.1.1
Pure tenancy
I envision pure tenancy as a case in which the tenant owns land (a “garden plot”) that is too small
for commercial agriculture (tii = 0) and leases land from the landlord tij > 0.24 The garden plot
yields γ > 0 units of cereals, and requires no costly effort (eii = 0). Thus, the effort allocation
problem involving owned and leased land (problem (8) above) simplifies to a surplus extraction
problem faced by the landlord involving only optimal share λ and effort on leased land eij . This
situation can be thought of as the limiting case of mixed tenancy in which tenant’s bargaining
power through withholding effort is severely curtailed due to a lack of outside alternatives.
In particular, the tenant’s incentive compatibility constraint delivers a frontier in the (λ, eij )
space. Any λ outside the frontier would lead to shirking by the pure tenant, and would yield zero
surplus to the landlord. Any λ inside the frontier would induce effort by the tenant. Given any
effort-inducing λ, the pure tenant picks an optimal effort by solving a utility maximization problem.
The landlord takes this optimal effort (in response to a given λ) into account in optimizing its
surplus. The tangency of the landlord’s isoprofit curves to the pure tenant’s utility maximizing
share and effort frontier determines the optimal surplus extracted by the landlord from the pure
tenant.
Such an outcome is demonstrated in Figure 1 using a numerical example. The upper envelope
of the curve labelled as “ICC frontier” in Figure 1A satisfies the incentive compatibility constraint (7).25 The share–effort frontier that maximizes pure tenant’s utility within that frontier is
shown by the dashed line. The tangency of the landlord’s isoprofit curves to this utility maximizing
frontier corresponds to the share-effort pair that optimizes the surplus extracted by the landlord.
The same figure shows how this surplus compares to the limiting case in which the landlord can
also contract effort (denoted by “max. effort” and “max. share”). If the tenant were to become
the owner, it would exert more effort on the plot formerly owned by the landlord. This efficiency
loss due to tenancy is shown in figure 1B.
24
Such subsistence-sized garden plots are common in many land-tenure regimes, and are actively encouraged by
large landlords (Barraclough, 1970).
25
The frontier and the participation constraint are consistent with the following two λ and eij combinations:
(i) low effort and high share of output by the tenant, and when the tenant is close to subsistence and participates for
survival; and (ii) high effort and high share of output when any additional effort at the margin is extremely costly
in utility terms.
15
Figure 1: Effort and contract share in sharecropping: A numerical example
µ
Note: The numerical examples are based on the following functional forms and parameter values: g(f f ) = eα t1−α ;
u = ln(cf − γf ); v = − ln(emax − e); = .5; probability of being caught shirking, π = .5; garden-plot productivity
γ = .1; subsistence food requirement, γf = γ/5; share of labor in agricultural production, α = .7; elasticity of farm
output with respect to combined effort and labor input, µ = .9; plot size owned land of owner-tenant, i tii = .5;
plot size of land leased from landlord j by tenant i, tij = 1; productivity of leased plot when eij = 0, β = .10;
productivity of leased plot when eij > 0, β ∗ = .01; fixed rent when tenant shirks and caught, τ = 0; maximum
allowable effort level by the tenant, emax = 1.
3.1.2
Owner tenancy
In the case of owner-tenancy, plots owned and leased by the tenant compete for the scarce
resource—cultivator’s effort. Owner-tenants allocate their effort according to the relative return on
each plot. If the size of owned land is sufficiently large, the tenant would have a better bargaining
power in settling the terms of the share contract. Of course, depending on the size of owned plots,
mixed tenancy covers a broad spectrum of land tenure systems ranging from owner-operators to
pure tenants.
Figure 1C demonstrates a tenancy contract for an owner-tenant and effort that is comparable
to the pure tenancy example considered above. In this example, the owner-tenant spends about
14% of maximum available effort on leased land, and the remaining 41% on own land, for a total
16
of 55%. If, as a result of redistribute land reform, the ownership of the land leased by the ownertenant were transferred from the landlord to the tenant, the effort would increase to about 68% of
maximum allowable effort. So, in this numerical example, land redistribution increases agricultural
output and efficiency of land use.
The numerical examples provide some intuition about the consequences of land redistribution
to tenants. However, this analysis leaves many imported mechanisms out: land redistribution and
the subsequent increase in supply of farm goods would in general lead to a change in relative prices,
the number of cultivators, and nonfarm employment. In the next two sections, I introduce the
remaining pieces of the general equilibrium model.
3.2
The nonfarm sector
The nonfarm sector of this economy has workers, capitalists, and a representative firm, which is
solely owned by the capitalists.
Preferences. Capitalists save a constant fraction 0 < θ < 1 of their gross income. They spend
their remaining income on luxury goods from abroad: U (c∗ ).26 Workers in the nonfarm sector
supply one unit of indivisible labor. Nonfarm labor is equivalent to effort intensity eh on farms at
a utility cost of v(eh ) with 0 ≤ eh . The component of the workers’ instantaneous utility function
defined over cf and cn , u(chf , chn ) is identical to that of farmers.
Specifically,
h
iν/(ν−1)
(ν−1)/ν
1/ν
u(cf , cn ) = η 1/ν c(ν−1)/ν
+
(1
−
η)
(c
−
γ
)
,
f
f
n
(14)
v(e) = − ln(emax − e).
(15)
In equation (14), γf ≥ 0 represents the “subsistence” level of food consumption, η is the weight
on nonfarm goods, and ν > 0 is the elasticity of substitution between consumption farm goods
(net of subsistence) and nonfarm goods. Non-homotheticity allows differential demand elasticity
of income between farm and nonfarm goods. When γf > 0, the income elasticity of demand for
food is less than one. When ν < 1, food and non-food are gross complements, and when ν > 1,
they are gross substitutes. In equation (15), emax > 0 is the maximum feasible effort level per
agent.
Production.
The nonfarm sector permits a representative firm, whose output is determined by
a constant returns to scale production function
zn F n (Kn , Ln ) = zn Kn1−αn Lαnn ,
26
(16)
The latter simplification is done to maintain symmetry between absentee landlords and capitalists, but is not
essential. It is easy to maintain tractability as long as capitalists’ commodity demands exhibit linear Engel curves.
17
where 0 < αn < 1 is the elasticity of output with respect to labor in nonfarm production; zn is
nonfarm TFP; Kn is the capital stock, and Ln is labor services.
Factor payments. Workers earn a wage rate which is the value of marginal product of their
labour w = w(k) = αn zn k 1−αn , where k = Kn /Ln (recall that nonfarm sector produces the
numeraire good). Similarly, capitalists earn the rental rate of capital which is the value of marginal
product of capital r = r(k) = (1 − αn )zn k −αn .
Aggregate capital stock.
Initial capital stock is given and denoted by K0 > 0. Changes in
the capital stock between two consecutive time periods depends on gross investment θrK minus
depreciation; K 0 = (1 − δ)K + θrK, where 0 < δ < 1 is the depreciation rate.
Consumption allocations by workers.
Given effort eh , workers maximize utility to determine
their optimal allocations of expenditures across food and non-food consumption goods. That is,
in each period, each worker h solves
max u(chf , chn ) − v(eh )
h
ch
f ,cn
(17)
s.t. p chf + chn ≤ w,
chf ≥ 0, chn ≥ 0.
3.3
General equilibrium
To integrate the farm and nonfarm sectors of this economy, I use two additional conditions that
describe the allocation of resources: (1) a no arbitrage condition for labor allocation across sectors
so that at the margin there is no economic incentive for labor to switch between sectors; and (2) a
condition that describes changes in land holdings.
Allocation of labor across sectors. Tenants and workers are perfectly mobile across sectors.
This implies that each member of the labor force is indifferent (in utility terms) between working
on a farm or in a factory:
u cf (wi , p), cn (wi , p) − v(eii + eij ) = u cf (w, p), cn (w, p) − v(eh ).
(18)
Here effort equivalents of labor supply could vary between the farm and nonfarm sectors, so
that eh is not necessarily equal to eii + eij in equilibrium. This is a flexible formulation to capture
an economically significant farm–nonfarm wage gap, when one exits.27 In such cases, I specify
v(eh ) = v(eii + eij + κ), where κ is the effort-equivalent urban penalty (κ > 0) or bonus (κ < 0).
27
Any farm–nonfarm income gap, either positive or negative, would thus be due to compensating utility differences
in working on a farm versus in a factory. Many factors like psychic costs, including moving away from a familiar
18
Allocation of land across tenants.
I specialize the analysis so that T i and T j are uniform
across tenants and landlords:
tii and tij are identical for i = 1, 2, . . . , I.
(19)
Assumption (19) redistributes the plot of land vacated by a former cultivator equally among
those who remain in the farm sector. Land formerly leased by a tenant from a landlord is also
equally leased among the remaining cultivators. I think of this as capturing the tendency for outmigrants from the farm sector to transfer their claims on land to non-migrating family members
in return for the option value of return migration.
Overall, then, each occupational class consists of identical agents.28 Representativeness of agents
focuses the analysis on the implications of distribution of land between cultivator farmers and
absentee landlords.
Sequential equilibrium. A consumption plan of a cultivator i = 1, 2, . . . , It is a sequence of
consumption vectors cit for time subscript t = 0, 1, 2, . . . , ∞. A consumption plan of a worker is
defined similarly.
A sequential equilibrium in this economy is an initial capital stock K0 , a sequence of consumption
n
o
i h
h
ˆ
ˆ
and effort vectors for cultivators and workers cˆt , cˆt , eˆii,t , eˆij,t , eˆ , sectoral employment It , Ht ,
n o
n
o
ˆ t , capital stocks K
ˆ t+1 ,
owned and leased land distributions tˆii,t , tˆij,t , contract shares λ
factor payments {w
ˆt , rˆt }, and prices {ˆ
pt }, such that, in each period t = 0, 1, 2, . . .,
ˆt;
1. for each cultivator i = 1, 2, . . . , Iˆt , (ˆ
cit , eˆit ) solves (8) given tˆiit , tˆijt , pˆt , and λ
ˆ t solves (9);
2. for each landlord j = 1, 2, . . . , J, λ
ˆ t , cˆh solves (17) given pˆt and w
3. for each worker h = 1, 2, . . . , H
ˆt ;
t
4. investment in physical capital is equal to saving by capitalists:
ˆ t+1 − K
ˆ t (1 − δ) = θ rˆt K
ˆ t,
K
(20)
5. factors of production in nonfarm production are paid their value marginal products, so that
!1−αn
ˆt
K
w
ˆt = αn znt
,
(21)
ˆt
H
!−αn
ˆt
K
rˆt = (1 − α)znt
;
(22)
ˆt
H
rural setting to a city with impersonal relations, urban congestion and pollution, a lack of social diversity in rural
areas (“bright city lights”), and lack of control over one’s own effort in a factory, are often suggested as potential
sources of these income gaps, but are kept in the background.
28
This is equivalent to four occupational classes each permitting a representative member. This is routinely
assumed in the literature, even when wealth is unequally distributed within an occupation (e.g., Banerjee and
Newman, 1993).
19
6. effort by workers eˆh satisfies (18);
7. the distribution of cultivated plots across cultivators satisfies (19);
ˆ t ≤ Lt ,
8. the sum of employment in each sector cannot exceed the aggregate labor supply, Iˆt + H
P
P P
and the demand for land cannot exceed the supply of land, i tˆii + i j tˆij = T ;
9. market clearing conditions for food and non-food goods hold:
Iˆt
X
cˆif t
i=1
Iˆt
X
cˆint +
i=1
ˆt
H
X
+
ˆt
H
X
h=1
cˆhft
≤
Iˆt
X
yi,t ,
(23)
i=1
ˆ t, K
ˆ t ) − rˆt K
ˆ t;
cˆhnt ≤ znt F n (H
(24)
h=1
10. domestic savings equal domestic investment:
ˆ t+1 − (1 − δ)K
ˆ t ≤ θˆ
ˆ t;
K
rt K
(25)
11. landlords and capitalists spend their income on the foreign good (balance on international
trade):
J
X
j=1
`
pˆt yij,t
= qt
J
X
ˆ t = qt (Nt − Lt − J)ˆ
cˆj∗
rt K
c∗t .
t , and (1 − θ)ˆ
(26)
j=1
Finally, I represent a confiscatory redistributive land reform by simply setting λ = 1 in the
model economy, giving a post-reform economy consisting of land-owning cultivators with multiple
plots.
3.4
Discussion of the assumptions
I modelled rents as sharecropping contracts. This was the predominant form of contract on paddy
land in South Korea (Ban et al., 1980, p. 292). In Japan and Taiwan, while formal sharecropping contracts were a small fraction of all tenancy rental contracts, realized rents amounted to
sharecropping. Ryoo (1978, pp. 108–110) discusses the pre-reform rent contracts and notes that
even rent-in-kind and rent-in-cash contracts led to final payments that were adjusted based on
realized yields. Koo (1968, p. 31) mentions “ironclad” clauses (fixed rents) in rent contracts in
pre-reform Taiwan, but these simply set a minimum rent payments, with the rest determined by
sharecropping, which here are captured by the fixed rent parameter τ .29
29
As noted by, among others, Banerjee et al. (2002, pp. 247–248), a combination of fixed rent and share contract
would balance the trade-off landlords typically face: either to provide incentives for effort or to extract surplus from
the tenant. However, simple share contracts have been widespread. In a fixed-rent contract, the landlord would
not receive additional payment in bumper crop years, so it would not yield the optimal surplus for the landlord.
Besides, a fixed-rent requires wealth that can be transferred to the landlord when output falls short of the rent.
When tenants are wealth poor and crop failure is highly possible, fixed-rent contracts would not be observed.
20
The land tenure systems in pre-land reform Japan, S. Korea, and Taiwan were characterized by
absentee landlords. Thus, in the model, landlords are detached from farming, have no particular
farming skills, and face an effort monitoring problem. Eswaran and Kotwal (1985), by contrast,
model a land tenure system with resident landlords, who are the sole suppliers of farm management
skills, and peasants, who are the sole suppliers of farm labor.
In the model, land leased by tenant i from landlord j is given. Although not explicitly modelled
as landlord decision, this can be rationalized as an equilibrium outcome when own-land is (roughly)
equally distributed across tenant cultivators, and there are decreasing returns to scale (due to fixed
managerial input). The reason is that there is no direct cost to each landlord in leasing land to
multiple tenants, and small cultivators have a cost advantage over their larger counterparts, because
of decreasing returns to scale. Moreover, as long as there are monitoring costs, there would be no
hired hands, even if one allowed for a market for hired work-time. Given that each cultivator has
roughly similar returns to own effort, each would find hired work-time prohibitively costly. In fact,
as mentioned above, in none of the three cases, rural proletariat represented a significant social
class, both before and after the reform.
Condition (19) is motivated by the observations made by many scholars on the pre-war agriculture of these countries (e.g., Honma and Hayami, 2009), as well as their relatively low post-war
Gini coefficients for land holdings. It also simplifies the analysis on two fronts. First, there is no
need to keep track of a changing land distribution among cultivators each time migration takes
place from farm to nonfarm.30 Second, it keeps the issues surrounding the markets for farmland in
the background. Complex zoning regulations make it difficult to model the market for farmland,
and doing so in a satisfactory fashion would take this paper too far afield.
The pre-reform land tenure system modelled here is effectively a one-tenant and one-landlord
setup. This is standard in the literature (e.g., Eswaran and Kotwal, 1985). However, if absentee
landlords have an information set that includes the output of their other tenants, and the tenants
of other landlords, they may use such information to infer whether their individual tenants are
shirking, and if so, to evict them. And, eviction may have dynamic costs to tenants. In the current
set-up, all such calculus would be subsumed in the probability of being caught.
The model abstains from investment in land quality. For instance, if irrigation, drainage, and
mulching can improve the quality of land but costs effort by the tenant, then there would be underinvestment on leased land when the landlord is a claimant on effort. Naturally, in such cases, the
impact of land reform on agricultural productivity would be even higher, and the magnitudes I
report below would be conservative.31
30
Only at the later stages of development, rural family size tends to shrink or migration of an entire family
becomes an option. Boyer and Ahn (1991) present some evidence suggesting that, in South Korea, within-family
land transfers were common until the 1980s.
31
Ban et al. (1980, pp. 291–292) mention that, in the 1930s Korea, landlords were responsible for investment that
21
Finally, although part of the domestic output is used to pay for the imported luxury good consumed by capitalists and land owners, the relative price of farm and nonfarm goods is endogenously
determined. This framework is suitable for the pre- and post-land reform Japan, S. Korea, and
Taiwan, as this period predates their export booms. An attempt to model the external demand
for their nonfarm goods would take the analysis (and the period under study) too far afield.
4
Quantitative analysis
In this section, I first calibrate and solve for equilibrium allocations that are broadly consistent with
the pre-reform characteristics of Japan, South Korea, and Taiwan. I rely on available estimates on
a number of variables (called “calibration targets”) that, in my judgement, best summarize their
basic economic structure in the pre-reform era. The targets include the share of employment in
the nonfarm sector, tenant share of farm output λ; the ratio of leased to owned land by cultivators,
tij /tii ; the rate of return to capital, r; the share of consumption expenditures on food; and the
gross saving rate.
While there were many similarities in their land tenure systems, these economies also had
considerable differences in terms of their level of economic development. Table 2 shows the range
of estimates across countries available for these targeted variables (see Appendix A for sources).
For instance, the estimates of pre-reform share of employment in the nonfarm sector ranges from
a high of 65 percent in Japan to 20 percent in South Korea—a reflection of their differences in the
level of economic development. At the same time, there are different estimates of these parameters
for individual countries: the share of employment in the nonfarm sector in pre-reform Taiwan
ranges from 37 percent to 45 percent, depending on the source, in part because of slight differences
in the time periods that these estimates refer to.
Given these differences in the pre-reform conditions across countries, together with the uncertainties surrounding the exact value of some of the parameters, I start with a set of baseline
parameter values and then present an extensive sensitivity analysis. In all cases, I numerically solve
for the equilibrium of the model, both before and after a redistributive land reform. With the preand post-reform solution in hand, I measure the impact of such a reform on effort allocation by
cultivators, sectoral allocation of labor, and capital accumulation in the model. I postpone a more
detailed examination of individual country data to Section 5, and here focus on the main economic
mechanisms that are responsible for the impact of redistributive land reform on farm productivity
and labor reallocation from farm to nonfarm.
required credit or more than 5 days of labor, and, in many cases, provided seed, commercial fertilizer and farm
implements.
22
Table 2: Pre-reform characteristics by country
Description
Mnemonic
Japan
South Korea
Taiwan
Share of employment in nonfarm
Tenant share of farm output
Leased-to-owned land ratio
Farm–nonfarm income ratio
Gross rate of return to capital, %
Share of expenditures on food, %
Gross saving rate, %
ln
λ
tij /tii
wi /w
r
.65 [.51]
.50
1.13
0.70 [.40]
13
60
14
.20 [.23]
.40 [.50]
1.77
1.00
13
...
10.0 [3.2]
.45 [.37]
.40 [.50]
0.64
...
13
...
10.5 [5.1]
Notes: This table shows the range of estimates available from the literature. Alternative estimates for individual
countries, if available, are shown in brackets. See Appendix A for sources.
. . . indicates estimates are not available.
4.1
Baseline calibration and solution
Numerical solution of the equilibrium allocations uses a number of exogenously set preference
and production function parameters. Table 3 panel A presents the parameter values used in the
baseline specification, panel B shows the pre-reform calibration targets, which help pin down the
remaining parameters in the model (panel C). (The sources for baseline parameters are contained
in Appendix A.) I then numerically solve for the pre-reform equilibrium of the model, and report
the equilibrium values of effort on owned and leased land, the relative price, nonfarm TFP, capital
stock, farm and nonfarm output, income earned by cultivators, wage income, and capital income.
(The details of the numerical solution algorithm are contained in Appendix S.1.)
Table 3 panel D reports the numerical solution of the baseline model. In the pre-reform equilibrium, cultivators spend roughly five times more effort on their owned plot relative to the leased plot
despite leased plot size being slightly larger than the owned plot size (by a factor of 1.13). In other
dimensions, the model matches the gross saving rate of 10 percent by attributing a large saving
rate (θ = 0.84) to capitalists, and implies a nonfarm TFP that exceeds farm TFP by a factor of
2.11. In addition, the results indicate that physical capital to income ratio in the nonfarm sector
is about 2.3.
Table 3 panel D also shows the post-reform equilibrium outcomes using a simple decomposition.
The column labelled as “K variable” presents the equilibrium outcome, in the aftermath of reallocation of effort across plots, reallocation of labor across sectors, and the endogenous change in
total savings by capitalists induced by the reform. The column labelled as “K fixed” by contrast
keeps the capital stock at its pre-reform level.
A comparison of pre- and post-reform equilibrium outcomes in this model economy shows that
the land reform leads to a substantial change in the sectoral composition of employment: the
share of nonfarm employment increases from 35 percent in the pre-reform equilibrium to about 46
23
Table 3: Baseline parameter values and equilibrium of the calibrated model
Description
Mnemonic
Value
A. Exogenously set parameters
Elasticity of substitution in consumption
Weight of non-food consumption
Subsistence food requirement
Weight of effort in farm production
Weight of labor in nonfarm production
Returns to scale in farm production
Farm TFP (excluding effort)
Plot size, leased (normalized)
Maximum effort level
ν
η
γf
αf
αn
µ
zf
tij
emax
0.1
0.80
0.30
0.654
0.70
0.90
1.00
1.00
1
ln
λ
tij /tii
wi /w
r
.35
.50
1.13
1.0
13
60
10
zn
θ
eh
2.11
0.84
0.63
B. Calibration targets
Share of employment in nonfarm
Tenant share of farm output
Leased-to-owned land ratio
Farm–nonfarm income ratio
Gross rate of return to capital, %
Share of expenditures on food, %
Gross saving rate, %
C. Calibrated parameters
Nonfarm TFP
Saving rate by capitalists
Total effort, workers
D. Equilibrium outcomes
Pre-reform
Post-reform
K fixed
Share of employment in nonfarm
Effort on owned land (% total)
Effort on leased land (% total)
Relative price farm/nonfarm
Share of expenditures on food, %
Gross saving rate, %
Gross rate of return to capital, %
Nonfarm capital-output ratio
ln
eii
eij
p
K variable
0.350
0.460
0.459
0.523 (83%) 0.301 (48%) 0.301 (48%)
0.107 (17%) 0.330 (52%) 0.330 (52%)
3.607
2.486
2.506
57.2
52.3
52.5
10.0
13.9
13.8
13.0
15.7
15.5
2.31
1.91
1.94
r
Notes: A. This panel reports the baseline parameter values used in the numerical solution of the model. See
Appendix A for details and sources. B. This panel reports the pre-reform calibration targets used in the numerical
solution of the model to pin down the remaining (calibrated) parameters of the model. See Appendix A for details
and sources, as well as those parameter values needed to verify the incentive compatibility constraints. C. This panel
reports the parameters implied by the baseline calibration of the model and that match the calibration targets. D.
This panel reports the equilibrium solution of the baseline model before and after a land redistribution. In the
post-reform calibration λ is set equal to one. The column “K fixed” shows the equilibrium outcomes when the
capital stock remains at its pre-reform level. The column “K variable” shows the equilibrium outcomes after taking
into consideration additional savings by capitalists induced by the reform.
24
percent after redistribution. It is interesting to note that much of this is driven by a “push” factor
out of agriculture: the reallocation of effort across owned and formerly leased plots, the subsequent
increase in the farm goods that become available for market sale, and the declining relative price
of farm goods all lead to a reallocation of labor from farm to nonfarm. The reason is that farm
goods have a low income elasticity of demand (γf > 0). So, farm prices fall disproportionately
more than the increase in farm output, which tends to reduce the cultivators’ income. Cultivators
respond to this tendency by switching to factory work, in the absence of which the relative price
of farm goods would have fallen even further.
The model also has a “pull” factor: as incomes rise, for a given saving rate, total savings and
hence aggregate capital increase. This increases the marginal value product of workers, and some
cultivators. Yet, a comparison of the results with fixed and variable capital stock shows that, at
the margin, the contribution of this channel to farm outmigration is economically small. Hence,
in the model, the results are overwhelmingly driven by the reallocation of effort across plots and
reallocation of labor across sectors: whereas pre-reform cultivators spend 83 percent of their total
effort on their owned plots, post-reform cultivators spend only 48 percent of it. Redistribution
of ownership rights thus can have an economically significant effect on the efficient allocation of
resources.
The consequences of a land reform for several other aggregate variables are also striking. Reforms lead to a reduction in the share of expenditures on food (about 5 percentage points): while
the relative price of farm goods declines, the share of expenditures on food decreases because farm
goods have a low income elasticity of demand. The rate of return to capital rises, because of
a relatively small endogenous accumulation of capital (at the margin) and large farm outmigration, which keeps the wage rate in check. These channels also account for the decline in nonfarm
capital-to-output ratio. This is due to the fact that while the gross saving rate rises, the increase
in capital income is proportionately less than the increase in aggregate income.
Despite these relatively large resource reallocations across plots and between sectors, according
to the model, the aggregate implications of land redistribution are not necessarily large (Table 4).
Relative to the pre-reform outcomes, aggregate income increases by 5.5 percent, and land productivity declines by about 5 percent. The biggest response is in labor productivity in the farm
sector, which increases by 14 percent. The change in land productivity is due to two opposing
effects. First, there is a decrease in farm employment following farm outmigration, which reduces
yield per land. There is also an increase in the efficiency of effort allocation across plots, which
increases yield per land. In the baseline calibration, the first effect dominates the second effect
and, as a result, land productivity in the post-reform equilibrium is lower than that of pre-reform
equilibrium.
A similar reasoning explains the rising labor productivity in the farm sector following land
25
Table 4: Impact of land redistribution on aggregate variables, change relative to pre-reform
Model
Baseline
Tenant share of output, λ = 0.4
Leased-to-owned land ratio
tij /tii = 1.77 (high)
tij /tii = 0.64 (low)
Share of employment in nonfarm
pre-reform ln = 0.20 (low)
pre-reform ln = 0.65 (high)
Elasticity of substitution, ν = 0.5
Returns to scale, µ = 0.8
Pre-reform farm–nonfarm wage
ratio = .7 (variable effort)
Compensation of landlords
Income
per capita
Labor
productivity
(yield/employment)
Land
productivity
(yield/land)
Share of
employment
in nonfarm
5.4
7.8
13.9
19.6
− 5.2
− 3.6
11
13
5.6
4.7
17.4
10.3
− 9.0
− 3.3
15
12
6.5
3.0
5.2
4.2
10.9
19.6
11.2
11.6
0.2
−14.2
− 0.3
− 6.9
8
10
7
11
18.0
5.3
42.5
11.8
− 0.7
− 1.3
19
8
Notes: This table shows the implications of the numerical solution of the model for aggregate income and farm
productivity. It compares the model-based change in an aggregate variable after a redistributive land reform relative
to its pre-reform value. All variables are in percent, expect the share of employment in nonfarm, which is in
percentage points. See Table 3 for the baseline parameters and the text for a description of the models. Labels
“low” or “high” indicate magnitudes relative to the baseline values. Returns to scale is the elasticity of farm output
with respect to the composite effort and land inputs.
26
redistribution. As different from the sources of land productivity, in this case, a decrease in
farm employment following land redistribution increases average yield per cultivator, bolstering
the efficiency gains due to reallocation of effort across plots. The combined effect of these two
channels increases labor productivity in the farm sector, and, in the baseline model, this effect is
substantial.
4.2
Mechanisms
In this section, I consider the influence of several mechanisms inherent in the model on agricultural
productivity and labor reallocation across sectors. These include pre-reform land inequality and
income, income elasticity of demand for farm products, compensation of landlords in the aftermath
of the reform, and variable effort by cultivators.
Pre-reform land tenure. The ultimate impact of land redistribution depends on a number of
initial conditions prevailing before the reforms. The extent of sharecropping arrangements, as well
as their specifics, while exhibiting many common elements, have not been uniform across countries.
The main differences can be characterized by two concrete dimensions of the land tenure system:
the tenant share of output λ and share of land leased from landlords tij /tii . For instance, the
extent of sharecropping depends on the distribution of land across cultivators and landlords, and
the pre-reform tij /tii ratio, which is an indicator of land distribution, was significantly higher in
South Korea than in Taiwan (Table 2).
To see the sensitivity of the results to changes in these two parameters that characterize the
pre-reform land tenure conditions, I consider parameter ranges that were actually observed in the
pre-reform Japan, S. Korea, and Taiwan. Consider, first, the stand-alone influence of share of
output received by a tenant prior to the land redistribution on post-reform outcomes. In Table 4,
I consider a lower share (λ = 0.4) relative to the baseline (λ = 0.5). Not surprisingly, relative to
the baseline, a confiscatory land redistribution increases income per capita, and labor productivity
even more: with lower λ, misallocation of effort across owned and leased land is higher in the
model, and as a result, the land reform has a considerably larger impact on income and labor
productivity in agriculture (about 40 percent increase in the case of labor productivity relative to
the baseline). The productivity of land still declines after the reform, but this decline is smaller
in magnitude compared to the baseline.
In terms of the ratio of the leased-to-owned land, I consider two alternative parameter values:
a “high” (tji /tii = 1.77) and a “low” (tji /tii = 0.64) ratio, with the baseline value (tji /tii = 1.13)
straddling the two. As one moves from the low toward the high leased-to-owned land ratios, there
is a monotonic increase in the change in income capita and labor productivity in agriculture, and
a monotonic decrease in the change in land productivity. Overall, according to the model, the
27
worse the initial distribution of land, the higher the impact of a land reform on income per capita.
However, the responses are not linear—post-reform income per capita increases at a decreasing
rate as the initial land distribution worsens.32
Finally, for the range of parameter values considered, the results suggest that, when the initial
land tenure conditions are less favourable to tenants, the economy tends to exhibit a faster reallocation of labor out of agriculture. In particular, compared to the baseline results, in the cases
of both low λ and high tji /tii , the increase in the share of employment in nonfarm is relatively
higher. Note, however, that in the case of low tji /tii the pace of post-reform labor reallocation is
also slightly higher than that of the baseline, suggesting that the pace of structural change is only
a partial indicator of the impact of land reform on income.
Pre-reform income. Historically, there has been a close association between income per capita
and the share of employment in nonfarm, ln . In the baseline calibration, this share is 35 percent;
a low but commonly observed value in historical data from currently industrialized countries and
contemporary developing countries. Here, I check the sensitivity of the results to a lower level of
initial nonfarm share of employment ln = .20, as well as a higher level ln = .65.
There are several striking results that emerge from the solution of the model with different
initial income levels (Table 4). First, while the response of aggregate income per capita to a land
reform is considerably larger in the case of low initial ln relative to both the baseline and high
ln cases, the response of labor productivity is considerably smaller. Note that in all the cases
considered, the level of agricultural TFP that is not accounted for by effort is fixed. Thus, in
an economy with relatively lower nonfarm productivity, nonfarm employs relatively more workers
yielding high ln . This results in a relatively more severe misallocation of labor within agriculture.
The reason is that in order to afford the relatively more expensive nonfarm goods, at the margin,
tenant farmers exert (inefficiently) more effort on owned land. Thus, for a given farm productivity,
as productivity in the nonfarm sector increases, ln declines, the relative price of nonfarm goods
falls, and the severity of inefficient allocation of labor diminishes. Consequently, in those cases
where the nonfarm sector is initially less productive, a land reform has a proportionately larger
impact on labor productivity in agriculture.
This allocation of effort under alternative nonfarm productivity scenarios has ramifications for
land productivity as well. In the case of initially low ln , land reform increases land productivity
(although marginally), whereas in the case of high ln , it reduces land productivity. Note that the
interaction between the relative productivity of the nonfarm sector and the land reform is strongly
32
In the case of low tij /tii (a 65 percent increase in the pre-reform tij /tii ratio relative to the baseline), post-reform
land productivity increases by about 35 percent relative to the baseline case. By contrast, in the case of high tij /tii
(a 56 percent increase in the pre-reform tij /tii ratio), post-reform land productivity increases by 25 percent relative
to the baseline case.
28
intermediated through the gross complementarity between farm and nonfarm goods. If, for some
reason, the two goods were substitutes, the relative price effect described above would have led to
opposite resource flows, and would reverse the direction of the results. In other words, much of the
reasoning behind this result emanates from the fact that a relatively faster productivity growth in
the nonfarm sector reduces nonfarm employment, and here this is uniquely a function of the gross
complementarity between the two goods.
Demand elasticity and technology.
As the above discussion suggests, gross complementarity
and effort allocation between the leased and owned land are critical for the quantitative and
qualitative results. Therefore, I examine the sensitivity of the results to alternative parameters
that have immediate bearings on these two issues. In the model, ν determines the degree of
complementarity and µ returns to the combined inputs of land and effort, and both have an
influence on the allocation of effort across different plots (equation 11).
In the baseline, consistent with the empirical estimates and economic intuition, I considered a
relatively low elasticity of substitution between food and nonfood consumption categories (ν = 0.1).
Increasing this elasticity to ν = 0.5 makes no substantial difference to the main findings, and
economically most significant impact of this parameter appears to be on the reallocation of labor
across sectors (Table 4). With a lower degree of complementarity, the land reform releases less
labor from agriculture. The reason is that, as farm output increases, the relative price of the farm
good declines. When ν is relatively high, this leads to a relatively smaller increase in the demand
for nonfarm goods, and thus a relatively smaller degree of structural change.
As for the elasticity parameter µ, in the baseline I set it at 0.90, and reducing it to µ =
0.80 appears to make little qualitative difference for the results. The main quantitative point to
emphasize is the response of income per capita. In this case, as the elasticity of farm output with
respect to effort decreases, the aggregate benefits of a land reform, in terms of income per capita,
also decrease in relative terms.
Variable effort by cultivators. One feature of the above analysis is that redistributive land
reform does not affect the total effort exerted by each cultivator. As a result, practically all the
productivity and income benefits associated with a land reform arise from efficiency enhancing
reallocation of resources. The model, however, has considerable flexibility in accounting for situations in which total effort by each cultivator also changes after a redistributive land reform. This
can be captured in the model when the pre-reform equilibrium exhibits farm–nonfarm wage gaps,
say due to an internal passport system which restricts labor mobility or psychic relocation costs,
and a redistributive land reform may also eliminate such barriers to mobility.
To see this, suppose that the wage rate in the nonfarm sector was initially higher relative to
29
that of in the farm sector, because of restrictions on intersectoral labor mobility. I model this as an
equivalent non-pecuniary “penalty” of moving from farm to nonfarm. In the pre-reform solution
this can be treated, from the cultivators’ perspective, as corresponding to an additional effort
associated with nonfarm work. After the reform, once the mobility costs are removed, cultivators
re-optimize, exert additional effort up to the point that this shadow price (or the marginal value)
of effort is equalized across sectors, so that farm and nonfarm wages equalize.
Table 4 shows the impact of such variable effort when initial farm–nonfarm wage ratio is 0.70.
In this case effort by cultivators increases by 33 percent, and not surprisingly, this further stimulates farm outmigration—the share of nonfarm employment rises by 19 percentage points; from an
initial 35 percent of employment to about 55 percent. The aggregate impact of the combination of
variable effort and within and across sector reallocation of labor on productivity in the farm sector
is dramatic, corresponding to a 42 percent increase in labor productivity following a land redistribution. Nevertheless, variable effort and reallocation of this additional effort have a negligible
impact (a small decline) on land productivity.
Compensation of landlords. The results so far are based on a confiscatory land redistribution
in which absentee landlords receive no compensation in return. While land reform was highly
advantageous for the cultivators, former landlords were nevertheless compensated to some degree
(see Section 2). To explore the impact of such compensation on economic outcomes, I use a fixed
(annual) transfer from cultivators to former landlords equivalent to 25 percent of pre-reform yield
on formerly leased plot—a number that is consistent with the actual compensation schedules.
Table 4, last column, shows the results for this case. The compensation scheme considered
here is effectively a transfer to former landlords, and does not distort incentives faced by farmers.
Relative to the baseline in which land reform is confiscatory, compensation of landlords reduces the
agricultural output (surplus) available for workers in the nonfarm sector. This increases the relative
price of farm goods, and translates into slower reallocation of labor out of agriculture, a smaller
increase in labor productivity in the farm sector, and a more moderate decline in land productivity.
Since the levies on farmers do not distort allocation of effort across plots, compensation of landlords
has a relatively small quantitative effect on income per capita.
5
Some comparative evidence
I now turn to a more detailed examination of individual country data, and ask whether the mechanisms identified by the model could also account for the observed responses of Japan, S. Korea,
and Taiwan to their redistributive land reforms. Table 5 reports the numerical solution results
that match the individual country characteristics in the pre-reform period as reported in Table 2.
30
Consistent with the discussion above, according to the model, land redistribution increases labor
productivity significantly in each of the three countries. By contrast, according to the model, land
redistribution has a mixed effect on land productivity: it decreases substantially in Japan, only
mildly in Taiwan, and it increases in South Korea. In all the cases, land reform triggers substantial
structural change, with about 10 percent of the labor force reallocating from farm to the nonfarm
sectors.
I map the model’s quantitative predictions into qualitative statements in Table 6, which also
indicates the two initial conditions that vary considerably across the three countries: leased-toowned land ratio (tij /tii ) as an indicator of land inequality, and share of employment in nonfarm
(ln ) as an indicator of income per person. According to these indicators, pre-reform S. Korea
exhibits relatively high inequality and low income, and Taiwan exhibits low inequality and low
income, whereas pre-reform Japan is characterized by medium inequality and high income.33 The
model predictions are ranked according to the expected magnitude of the response of a particular
outcome variable to a land reform. I consider three outcome variables: yield per farm worker, yield
per hectare of land, and the share of employment in the nonfarm sector. In each of these cases, I
report the ranking of each country in terms of their model-based responses to a confiscatory land
reform. I use qualitative rankings because the model abstracts from any land-saving technological
progress that is known to have increased land productivity in these countries considerably over
this period (Hayami and Ruttan, 1971; Johnston and Kilby, 1975).
Unfortunately, there are limited empirical estimates of the impact of land redistribution on
farm productivity in these countries that can be directly compared with the model-based estimates presented in Table 5. There is scant data on pre-reform agricultural output and inputs
(Appendix A.3). Ryoo (1978, p. 431) cites the Taiwanese Provincial Food Bureau for an estimate
of about a 40 percent increase in paddy rice per hectare after the combined implementation of
land-rent reduction and land-transfer programs, with about 88 percent of this increase occurring
after the land-rent reduction program.34 In the case of S. Korea, Jeon and Kim (2000) find that
tenancy rate had a negative impact on agricultural output—although they do not quantify the
impact of agricultural land reform on land or labor productivity. However, using their published
data, it is possible to infer that there was about a 40 percent increase in land productivity from
the 1955/59 period relative to the 1940/44 period. In Japan, the growth of rice yield over the
same period was about 13%.
S. Korea has data on labor input in rice production, which points to about 2% increase in
33
In the available data, the mapping from the share of employment in nonfarm to income per capita is not perfect:
while Taiwan had a higher share of employment in nonfarm, in 1955 its per capita income was slightly lower than
that of S. Korea (Honma and Hayami, 2009, Table 2.1). Given the margins of error involved in these calculations,
it might be best to view S. Korea and Taiwan as similar in terms of their market-based income per capita.
34
Unfortunately, there is no information about the methodology underlying these estimates.
31
Table 5: Solution of the model for Japan, S. Korea and Taiwan, change relative to pre-reform
Model
Income
per capita
Labor
productivity
(yield/employment)
Land
productivity
(yield/land)
Share of
employment
in nonfarm
4.9
10.4
5.6
20.4
19.6
15.9
−14.4
1.1
− 3.5
10
12
9
Japan
S. Korea
Taiwan
Notes: This table shows the implications of the numerical solution of the model for income and productivity using
the target parameters shown in Table 2 for individual countries. For S. Korea and Taiwan there are no pre-reform
estimates of share of expenditures on food, and the solution uses 0.6 (based on available estimates for Japan). For
Taiwan, there is no estimate of farm–nonfarm income ratio, and the solution uses 1. For the remaining parameters,
each model uses the baseline parameters in Table 3. The table reports the model-based change in an aggregate
variable after a redistributive land reform relative to its pre-reform value. All variables are in percent, expect the
share of employment in nonfarm, which is in percentage points.
Table 6: Relative impact of land redistribution on the farm sector productivity
Model predictions for
Country
Initial conditions
Relative outcomes
Yield per
Yield
Structural
Yield per
Yield
Structural
farm worker per hectare change
farm worker per hectare change
Japan
Medium inequality;
high income
high
low
medium
...
low
medium
S. Korea
High inequality;
low income
high
high
high
“low”
high
high
Taiwan
Low inequality;
low income
low
medium
low
...
high
low
Notes: Initial conditions are based on the comparison of the following variables in Table 3: leased-to-owned land
ratio as an indicator of land inequality, and share of employment in nonfarm as an indicator of income. Yield is
based on rice output. Structural change is measured by the increase in the share of employment in nonfarm. Model
predictions are based on the quantitative results reported in Table 4. See Appendix A.3 for the data underlying
“relative outcomes.”
. . . indicates estimates surrounding the reform period are not available.
32
output per employment from 1940s to 1950s.35 Since there are no comparable estimates for Japan
and Taiwan, it is impossible to judge how “low” these estimates actually are.
Several sources report data on the share of employment in agriculture. According to this
indicator, in the immediate aftermath of their respective land reforms, S. Korea had the highest
rate of structural change, followed by Japan, and then Taiwan. Overall, then, although the available
data are sketchy and incomplete, the evidence points to heterogeneous responses to land reform
by the three countries. These actual responses are also ranked and summarized in Table 6.
A comparison of the model predictions and the actual outcomes reveals that the observed
heterogeneity in responses are broadly consistent with the predictions of the model. This suggests
that the mechanisms identified by the model could account for the diverse responses observed in
these countries.
6
Conclusion
I developed a two-sector model in which landlords use share contracts to extract a surplus from their
tenants, but this blunts effort on leased land, and results in a misallocation of effort on owned
and leased plots of land. A redistributive land reform realigns incentives, and increases labor
productivity in the farm sector, leading to an accelerated reallocation of labor out of agriculture.
However, land reform has a relatively minor impact on land productivity. I find that qualitative
implications of the model are broadly consistent with the economic performance of Japan, S. Korea,
and Taiwan in the aftermath of their redistributive land reforms.
While these cases provide concrete historical episodes in which the link between initial conditions (here land distribution) and future economic growth can be examined, there are several
reasons to think that the same topic might deserve a different treatment in other contexts, with
implications for empirical cross-country studies. It is thus appropriate to conclude the paper by
briefly discussing some of these reasons.
My analysis relies on economic and political histories of Japan, S. Korea, and Taiwan to identify
as exogenous the redistributive land reforms that gave way to an egalitarian initial distribution of
land. In these cases, there was no noticeable political backlash in response to redistributive land
reforms by former landlords whose political and economic powers were severely curtailed after
World War II. Historically, however, redistributive land reforms have not always been peaceful
and have always faced severe political opposition. In particular, in those countries where plantation agriculture dominates the agrarian structure, and land distribution is extremely skewed and
correlated with political power, both the modelling of pre-reform agriculture and the responses of
agents to a land reform require an approach that is significantly different from the one presented
35
Labor employed in S. Korean rice farming is reported by Jeon and Kim (2000) in units of “men equivalents.”
33
here (Binswanger et al., 1995). Along similar lines, in countries where ethnic/racial and class
boundaries overlap significantly, the possible implications of land reform for agrarian development
is possibly more complex to study (Barraclough, 1970). It is also worth mentioning that the analysis has made no attempt to formally link initial land distribution to economic policies toward
agriculture—a topic that has also received surprisingly little attention.
Appendix
A
Data sources and parameter choices
In this appendix, I discuss the choice of the baseline and alternative parameter values, as well
as the calibration targets in the pre-reform equilibrium. Unless there is strong evidence to the
contrary, I set identical utility and production function parameters for each country.
A.1
Exogenously set parameters
˙ scan,
Elasticity of substitution in consumption, ν: Most of the earlier work (e.g., Dennis and I¸
2009; Herrendorf, Rogerson, and Valentinyi, 2013) finds gross complementarity between food
and non-food consumption goods. I set ν = 0.1 as the benchmark, and use ν = 0.5 to
evaluate the sensitivity of the results to changes in this parameter.
Weight of non-food in composite consumption, η: This parameter is the share of consumption expenditures on non-food in the asymptotic steady-state of the model. Consistent with
a value of γf > 0, this share has increased over time in industrialized countries. For instance,
in the United States, at the turn turn of the twentieth century it was 42.5 percent and increased to 87.9 percent at the turn of the twenty-first century (U.S. Department of Labor,
2006, p 3, and Table 29). I use 80 percent as the baseline parameter.
Subsistence food requirement, γf : I set this parameter equal to .3 (30 percent of initial farm
TFP). For this parameter I do not use a calibration target, such as share of expenditures
on food, because, in this class of models, it is difficult to independently match the share of
expenditures on different consumption goods and the share of employment by sector. For
the purposes of completeness, I report in the text the share of expenditures on food by the
cultivators and workers. For the purposes of comparison, I note that Honma and Hayami
(2009) report that in Japan this share (“Engel coefficient”) was “higher than 60 percent”
in the early twentieth century and was 52 percent in 1955. Cha and Kim (2012) report
that in Korea food consumption-to-income (GDP) ratio was about 65 percent in 1938/40,
and suggest a lower ratio for Taiwan; consistent with this estimate, for Taiwan, Oshima
34
(1986, p. 795) recommends a five percentage point adjustment to the Engel coefficient in
South Korea.
Weight of effort in farm production, αf : There are no direct estimates of this elasticity parameter for the early periods. Given the Cobb-Douglas specification of farm production, and
competitive factor markets (except land), this parameter is closely related to share of labor
in farm output (which includes return to effort and managerial time). For the pre-reform
Japan (1936), Ryoo (1978, Table 27) reports the following factor shares: labor income 61
percent, capital income 6 percent and rents 33 percent. In their study of growth accounting
for Korea in the first half of the twentieth century, Cha and Kim (2012) use the following
factor shares: labor 0.51, capital 0.26, and land 0.23. Given that about 80 percent of the
labor force at that time was in agriculture, and land was primarily used in agriculture, I
imputed the share of labor in agriculture as αf = (.8 × .51)/(.8 × .51 + .23) = .64. This is
the baseline parameter in all three cases.
Weight of effective labor in nonfarm production, αn : Following the methodology for αf , I
compute the share of labor in nonfarm by (.2 × .51)/(.2 × .51 + .23) = .69. I use this as
the baseline parameter. For the non-agricultural sector (1966–1990), Young (1995) reports
αn = 0.70 for South Korea and 0.74 for Taiwan.
Elasticity of farm output with respect to effort and land, µ: I set µ = .9 as the benchmark, and use ν = .8 to evaluate the sensitivity of the results to a change in this elasticity
parameter.
Farm total factor productivity, zf : Normalized to 1. Note that this productivity factor excludes changes in effort.
Initial capital stock, K0 : Since estimates of capital stock are notoriously noisy, I normalize the
initial capital stock in the model, by setting the initial period capital-labor ratio equal to
land-labor ratio:
˜0
K
= tii,0 + tij,0 .
H0
(A.1)
I report the capital–output ratio implied by the solution of the model in table 3.
Parameters related to incentive compatibility constraints: The following parameters are
only needed to check and verify that (1) leasing a plot is optimal for a cultivator in the prereform period; and (2) the incentive compatibility condition (7) is satisfied in equilibrium:
fixed land rent when the tenant shirks and is caught by the landlord, τ = 0.3, set equivalent
to subsistence consumption requirement; land productivity for fodder when the tenant exerts
no effort on leased land (eij = 0), β = 0.10; land productivity for fodder when the tenant
35
exerts effort on leased land (eij > 0), β ∗ = 0.01; fixed rent when tenant shirks and is caught,
τ ; and probability of being caught after shirking, π = 0.5. Since livestock agriculture has
been relatively unimportant in Japan, South Korea, and Taiwan, I have set the productivity
terms β and β ∗ “low” relative to the farm TFP.
A.2
Calibration targets
Share of employment in nonfarm, ln : The closest empirical counterpart of this variable is one
minus the share of employment in agriculture (including fishing and forestry). However,
several sources report significantly different shares, especially for Japan and Taiwan. In
Table 2, I report the share of employment in nonfarm for 1955 from Honma and Hayami
(2009): 65 percent in Japan, 20 percent in South Korea, and 45 percent in Taiwan (data
are rounded slightly). The alternative estimates are for 1950 from Larson and Mundlak
(1997, Table B2): 51 percent in Japan, 33 percent in South Korea, and 37 percent in Taiwan.
Tenant share of farm output, λ: I set the pre-reform contract share (of tenants) based on
historical accounts of share contracts. For Japan, Kawagoe (1999) suggests a rental rate
of 50 percent of annual crop yield, λ = 0.50. For South Korea, Dorner and Thiesenhusen
(1990) suggest a rental rate of 60 percent, whereas Ban et al. (1980) suggest 50 percent. In
Taiwan, according to Chen (1961), the rental rate was 50 percent to 70 percent of the total
annual main crop yield. In the baseline model, I use λ = 0.40 (and also for South Korea and
Taiwan), and λ = .50 for sensitivity analysis.
Ratio of leased-to-owned land by tenants, tij /tii : In pre-reform (1941) Japan, 53 percent of
the cultivated land was under tenancy. This gives the ratio between own and leased land
before the land reform as tii /tij = 47/53 = .89, or tij /tii = 1.13. In pre-reform (1945) South
Korea, 64 percent of the cultivated land was under tenancy. This gives the ratio between
owned and leased land before the land reform as tii /tij = 36/64 = .56, or tij /tii = 1.778. In
pre-reform (1949) Taiwan, 39 percent of the cultivated land was under tenancy. This gives
the ratio between own and leased land before the land reform as tii /tij = 61/39 = 1.56, or
tij /tii = 0.64. (See table 1.)
In the case of South Korea, it is possible to confirm the plausibility of these values using data
on redistributed land, which took three forms: (1) redistributed land through the reform act
by the Korean government (302,000 jungbo)36 ; (2) land owned by the Japanese and sold to
tenants by the U.S. occupation (273,000 jungbo); and (3) land sold by landlords in the market
before the reform act was implemented (714,000 jungbo, which was about 37 percent of the
36
One jungbo is equivalent to about .992 hectare (ha).
36
arable land). This direct and indirect redistribution thus amounted to about 67 percent of
the arable land in South Korea (Jeon and Kim, 2000, Table 1, p. 258).
Although what matters for the analysis here is the ratio of leased to owned land, it is important to mention that not all leased land was owned by “landlords” as the term is commonly
used. For instance, according to a 1924 survey in Japan, absentee and village landlords,
who were nonfarming and owned more than 5 hectares of land, owned about 13 percent
(810 ha/5, 983 ha) × 100 of the cultivated land—though apparently the landlord class grew
and became more “parasitic” over time until the war (Kawagoe, 1999, Tables 4.1 4.8, p. 19).
Farm–nonfarm wage gap, wi /w: I use the pre-reform value of this ratio to calibrate the nonfarm urban premium or penalty κ. Unfortunately, the data counterparts of model variables
for farm–nonfarm wage ratio are difficult to come by. The closest empirical variable available
is the ratio of per capita income in a farm household divided by per capita income in a nonfarm household, which does not account for off-farm income by farm households, does not use
an equivalence scale, and does not adjust for differences in human capital. Whereas off-farm
income by farm households tend to overstate farm income per capita in a farm household,
relatively larger farm-household sizes overstate differences in farm–nonfarm incomes.
Unfortunately, there is limited data on off-farm income to gauge the precise direction of a
possible bias in this empirical variable. In the pre-reform Japan, off-farm income was usually
less than 25 percent of total farm household income, and as low as 10 percent (Kaneda, 1980).
In the post-reform Japan and Taiwan, nonfarm employment was a significant component of
rural development strategy. As a result, off-farm income as a percent of total income of a
farm family with average farm size, which was 25 percent in 1957 Japan, and 24 percent in
1958 Taiwan, increased gradually over time. However, in South Korea, even by 1968 off-farm
income was only 19 percent of total farm income (Oshima, 1986). To my knowledge, there is
virtually no pre-reform data on household sizes. For the post-reform era, Honma and Hayami
(2009) report that in 1955 the number of persons per farm household was 6 in Japan and
South Korea and 6.3 in Taiwan, and United Nations (1997, Table 27) reports for Japan that
in 1985 the household size was 3.6 in rural areas and 3.0 in urban areas. Overall then, there
is evidence for opposing effects, but it is impossible to state with any certainty whether these
effects have offset each other during the period under study.
Turning to available data, for Japan, Honma and Hayami (2009, Table 2.7) report farm–
nonfarm income ratio of .38 in 1935 and .77 in 1955. Thus, I use .40 in the baseline model
and .70 in the sensitivity analysis. For South Korea, many accounts point to significantly
higher pre-reform rural poverty, but not necessarily to significantly higher urban incomes.
Boyer and Ahn (1991, Chapter 2) report a rural–urban household mean income ratio of 1.03
37
in the early 1960s, which I use as the baseline. For sensitivity analysis, I use .70 as in Japan.
Unfortunately, there is no comparable estimate for Taiwan, so I use the same value as in
South Korea.
Gross saving rate: This calibration target is used to pin down θ, the saving rate for capitalists.
There are two distinct and possible measures in this context; (1) the investment-to-GDP
ratio, and (2) household saving-to-GDP ratio (since the model does not have a government
and external sector). For the earliest (non-war) year available, Heston, Summers, and Aten
(2012) report the following investment-to-GDP ratios at current prices (ci): 14 percent for
Japan in 1950, 10 percent for South Korea in 1955, and 10.5 percent for Taiwan in 1951. For
the household saving rate, Oshima (1986, Table A1) report personal and corporate savings
as a percent of GDP, the sums of these savings rates for the 1950s are 3.2 percent for South
Korea and 5.1 percent for Taiwan.
Gross rate of return to capital: I use 5 per cent as the net annualized rate of return to capital. For Korea in the first half of the twentieth century, Cha and Kim (2012) compute a
depreciation rate δ of 7.9 percent. Combining these two figures gives a target of about 13
percent.
A.3
Data sources for Table 6
Table 6 reports qualitative indicators of realized “relative outcomes” for Japan, S. Korea and
Taiwan. These are based on the following observations:
Output per farm worker: The data are for rice production and labor used in rice production
(measured in units of “1,000 men equivalent”), and are reported in Jeon and Kim (2000).
The production data are in units of suk converted into metric units (1 suk = 0.101269 metric
tons). According to these data, over the period 1940–1944, average rice output per farm
worker was 1,100 kg, and over the period 1955–1959, it was 1,122 kg, representing a “low”
labor productivity growth of 2%.
Yield: Yield is measured as kilos per hectare. For Japan, data are from Statistics Japan (2014, Table 07-14), with an average yield of 2,966 kg/ha in the 1940s, and 3,345 kg/ha in the 1950s
(a 12.78% increase). For S. Korea, data are from Jeon and Kim (2000), with an average
yield of 1,351 kg/ha from 1940 to 1944, and 1,122 kg/ha from 1955 to 1959 (a 40% increase).
For Taiwan, Ryoo (1978, p. 431) notes, somewhat confusingly, that “According to statistics
compiled by Provincial Food Bureau, an increase of farm returns as a result of land reform
was about 487kg. (= 1,947 kg. - 1,460 kg.) of paddy rice per hectare after land-rent reduction
program and additional 63 kg (=1,460 kg. - 229 kg - 1,168 kg.) of paddy rice per hectare
38
after implementation of land-transfer program.” I take these numbers as suggesting that the
total estimated change in yield during the Taiwanese of land reform was 550kg., with the
initial yield being 1,397kg/ha. This gives a 40% increase in rice yield during the Taiwanese
land reform. Note that, the relative rankings of farm labor and land productivity growth
in post-reform Japan and Taiwan in table 6 are consistent those reported by Johnston and
Kilby (1975, Table 4.1).
Share of employment in nonfarm (structural change): For Japan, according to Statistics
Japan (2014, Table 19-07), in 1952, this share was 56.1%, and by 1960 it increased to 71.3%
(a rate of change of 27%). For S. Korea, (Honma and Hayami, 2009, Table 2.1) report a
share of 20% in 1955, rising to 40% in 1960 (a rate of change of 100%). For Taiwan, (Taiwan,
Republic of China, 2006, Table 2-9b) reports the share of employment in primary industry
as 56.1% in 1952, and 50.2% in 1960. Based on these data, the rate of change in the share
of employment in the rest of the industries is 13%.
39
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42
S
Online Supplementary Material
S.1
Numerical solution algorithm
I solve the equilibrium of the model numerically for two cases: before and after the implementation
of land reforms and for each country separately. Consistent with the model and its focus on the
stand-alone effect of a redistributive land reform on economic outcomes, I interpret these as the
steady-state solutions. To parametrize the model, I use data on pre-reform outcomes.
Exogenously set parameters: The exogenously set parameters are:
1. The elasticity of substitution between food and non-food items in consumption, ν;
2. Weight of non-food consumption in composite consumption, η;
3. The subsistence food requirement, γf ;
4. Weight of effort in farm production, αf ;
5. Weight of effective labor in nonfarm production, αn ;
6. The return to span of control by farmers, µ;
7. The depreciation rate, δ;
8. Farm total factor productivity, zf ;
9. Plot size of leased land, tij ;
Pre-reform targets. The remaining parameters are pinned down by matching the following
calibration target values from the pre-reform period:
1. Share of employment in nonfarm, H/L ≡ ln ;
2. Tenant share of farm output as stipulated by norms and sharecropping contracts, λ;
3. Ratio of leased to owned land by tenants, tij /tii ;
4. Wage (or income) gap between farm and nonfarm households, wi /w; and
5. Gross rate of return to capital, r;
6. Share of consumption expenditures on food;
7. Gross saving rate.
S.1
Pre-reform equilibrium solution: The numerical solution of the model uses the exogenously
set parameters, calibration targets, equations for factor payments in the nonfarm sector (21) and
(22), the market clearing conditions for the goods produced by the farm and nonfarm sectors (23)
and (24), the allocative efficiency condition for tenant effort (13). The solution to the pre-reform
equilibrium proceeds as follows:
Step 1 : Set the parameters γf and the weight on the utility of leisure .
Step 2 : Given the farm–nonfarm relative wage, share of employment in nonfarm ln , ratio of leased
to owned land by tenants tij /tii , and tenant share of farm output λ, solve for the triplet,
the relative price of farm–nonfarm goods p, tenant effort levels on owned and leased land eii
and eij , which (i) clears the market for food [equation (23)] and (ii) maximizes tenant utility
(assuming eij > 0).
Step 3 : Solve for, using the labor mobility condition (18), eh and the implied urban penalty (or
bonus) κ measured in units of effort.
Step 4 : Solve for the nonfarm TFP zn and initial capital stock K0 by targeting the gross rate of
return to capital r, and nonfarm income.
Step 5 : Solve for the share of consumption expenditures on food. If this is substantially different
from the calibration target, revise γf and , and repeat.
Step 6 : Solve for the average propensity to save by capitalists θ by targeting the gross saving rate.
Step 7 : Check and verify that renting a plot from a landlord is optimal for a cultivator.
Step 8 : Check to verify that incentive compatibility condition (7) is satisfied.
Notice that the economy features both market and non-market allocation mechanisms; while
labor and goods are entirely allocated through markets, capital markets exhibit limited participation (by capitalists only) and there is no market for land. The model also features Walrasian
(competitive) and non-Walrasian markets: whereas labor and goods markets are Walrasian, landlords set the terms of share contracts. The dynamics of the economy are highly stylized as well:
while there is savings and capital accumulation, economic decisions underlying such considerations
are independent of the state of the economy.
S.2
S.2
Characterization of equilibrium allocations
In sequential equilibrium, sectoral employment shares are endogenous. Given our monotonicity
assumption on the utility functions, in equilibrium, the market clearing conditions stated in per
employment L terms must be satisfied:
(1 − ˆlnt )ˆ
cf (ˆ
yi,t , pˆt ) + ˆlnt cˆf (w
ˆt , pˆt ) = (1 − ˆlnt )ˆ
yi,t ,
(1 − ˆlnt )ˆ
cn (ˆ
yi,t , pˆt ) + ˆlnt cˆn (w
ˆt , pˆt ) + rˆt kˆt ˆlnt = ˆlnt zn f n (kˆt ),
(S.1)
(S.2)
where lnt is the share of employment in nonfarm sector at time t. Solutions to (8) and (17) involve
equating marginal rate of substitution in consumption between food and non-food:
csf t , cˆsnt )
ucf (ˆ
ucn (ˆ
csf t , cˆsnt )
= pˆt ,
(S.3)
where s = {i, h}.
Also, in the case of cultivators, at the margin, disutility from additional effort either on leased
or owned land equals the utility gain from additional income due to additional effort:
!
f (w i , p)
n (w i , p)
∂c
∂g(eii , tii )
∂c
p zf ucf (cif , cin )
= ve (eii + eij ),
(S.4)
+ ucn (cif , cin )
f
f
∂eii
∂yi
∂yi
!
f (w i , p)
n (w i , p)
∂g(eij , tij )
∂c
∂c
λij p zf ucf (cif , cin )
+ ucn (cif , cin )
= ve (eii + eij ).
(S.5)
f
f
∂eij
∂yi
∂yi
For an interior solution (ˆ
eii , eˆij ) > 0, taking the ratio of the above expressions gives the production
efficiency condition given in equation (11).
Note that the tenant has an option to shirk. To ensure that the set of allocations computed by
the algorithm are optimal (i.e., incentive compatible) we need to compare the utility of the tenant
when effort on leased land is positive with that of zero effort eij = 0. Of course, when the tenant
has an option to exert no effort on the leased land, the optimal effort on the owned land would
also be different. So, we calculate the expected utility when the tenant shirks.
h
i
max π u(cf (wi (eij = 0, 1), p), cn (wi (eij = 0, 1), p))
eii
h
i
+ (1 − π) u(cf (wi (eij = 0, 0), p), cn (wi (eij = 0, 0), p)) − v(eii ),
(S.6)
wi (eij = 0, 1) is tenant’s income when the effort on leased land is zero, and the tenant is caught,
and wi (eij = 0, 0) is income when effort on leased land is zero but the tenant is not caught.
In this case, the optimal effort level is characterized by the following first-order condition
!
∂wi (eij = 0, 1)
∂u ∂cf (wi , p)
∂u ∂cn (wi , p)
π
+
∂eii
∂cif ∂wi (eij = 0, 1) ∂cin ∂wi (eij = 0, 1)
!
∂wi (eij = 0, 0)
∂u ∂cf (wi , p)
∂u ∂cn (wi , p)
∂v
+(1 − π)
+
−
= 0.
(S.7)
i
i
i
i
∂eii
∂eii
∂cf ∂w (eij = 0, 0) ∂cn ∂w (eij = 0, 0)
Note that, conditional on shirking on leased land, the marginal product of effort on owned land
does not depend on whether the tenant is caught or not.
S.3
Therefore, for s = {i, h}, the equality of the marginal rates of substitution in consumption
between food and non-food (S.3) is
csn
η
ν
=p
.
(S.8)
csf − γf
1−η
We can use the above condition and the budget constraints to solve for individual demand functions:
cf (w,
˜ p) =
w
˜ + γf pν η/(1 − η)
,
p + pν η/(1 − η)
cn (w,
˜ p) =
pν η/(1 − η) (w
˜ − γf p)
,
ν
p + p η/(1 − η)
(S.9)
where w
˜ = p yi ≡ wi for cultivators and w
˜ = w for workers. Income of a cultivator depends on
effort, which is a choice variable.
S.4
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