Annex of the Paper: Land and the Transition from a
Dual to a Modern Economy
August 26, 2005
1
A Model with Hired Labor
In this section we extend the model in the main body of paper to allow for the possibility of
monitoring the labor e¤ort, e; with an intensity m per worker. As a result, if n is the number of
plots an individual farms directly by using monitored labor, the cost of his monitoring e¤ort is
C(n) =
(mn)2
2a .
Moreover, let us assume that outcomes on all plots of land are perfectly correlated,1
and depend on the intensity of the workers’labor in the following way:
8
n
P
>
>
ei
>
>
>
i=1
< n
;
with probability
nn
qA (n) =
P
>
>
ei
>
>
>
: 0 with probability 1 i=1 :
n
As before, an agent can produce in the M-sector by using his unit of time, with a cost C(e) =
(1)
e2
2a :
In order to simplify the analysis, we suppose that every landlord owns the same number, N; of
plots.2 Each landlord has two organization options for each plot owned: either she hires a worker
at the …xed market wage w and monitors him, or lets him farm the plot with a tenurial contract
(r; s) without any monitoring (as in the main model). Following Binswanger et al. (1995) we
de…ne the production unit consisting of n 6 N plots operated with hired workers as a home-farm,
while we refer to plots operated with the contract as single-owner tenancies. If N > n and the
other N
1
n plots are operated as tenancies, we say that the farm is organized as a hacienda. If the
This seems to be reasonable, but we would have qualitatively the same results if we assumed, as before, output
in di¤erent plots to be totally uncorrelated.
2
It is possible to show that the land market generates this equilibrium, if landlords are not wealth constrained.
1
landlord rents all her land so that n = 0 (as in the main model) we de…ne this last arrangement
as a Landlord Estate. Finally, we de…ne the organization N = n as a Junker Estate.
In the case of excess land demand, L < 1
N
!
l, the landlord has to select n.3 The remaining
n plots owned are allocated to a single farmer each. If e1 is the monitored e¤ort in the home
farm and e2 is the e¤ort of the tenants, the landlord’s problem is
(mn)2
nw + (N
max e1 n
e1 ;e2 ;n;s
2a
8
>
w C(e1 );
>
<
s:t:
e2 (s) 2 arg max e2 (1 s)
>
>
:
N n:
n) (e2 s)
(2)
(IR)
e22
2a ;
(IC)
Constraint (IR) is the usual individual rationality constraint, while (IC) is the incentive compatibility constraint for the tenants.
With excess demand for land, a landlord can extract all the surplus from his workers, and so
(IR) will always hold strictly. Therefore, we can replace w = C(e1 ) in (2) to …nd e1 = a; i.e. the
landlord chooses a …rst best level of e¤ort for her workers as she completely internalizes the cost
of the workers’e¤ort. On the other hand, the level of the tenant’s e¤ort is suboptimal, e2 = a=2;
given that s = 1=2.
We can notice that the worker‘s utility is zero, so he is strictly worse o¤ than a tenant, and
the quantity of wealth that poor dynasties can accumulate is strictly lower if landlords use hired
a
labor, since 1=2 > a=2. In particular, if we suppose that (1
) < h, a worker o¤spring cannot
2
migrate to the M-sector. Therefore the higher is the number of hired workers, the lower the level
of migration.
Substituting e1; e2 ; w and s in (2), we can maximize expression (2) for the organization
a2
a2
variable n: We …nd that n =
is
the
optimal
size
for
the
home
farm.
When
N
then
4m2
4m2
2
2
a
a
n = N and the farm is a Junker Estate. When N >
then n =
and the farm as a
2
4m
4m2
hacienda.
3
In order to avoid problems related to the discrete nature of
n we suppose that a landlord can split a plot of
land and give it to the same worker with two di¤erent contractual arrangements. The worker will split his unit
of time and will work partly as a tenant and partly as a hired worker. The worker farms a portion
worker and the other
1
as an hired
as a tenant. The outcome is linear in the quantity of land. This implies that the
: Since e is the intensity of e¤ort per unit of time, an individual can split his
e2
e2
time accordingly and use a level of e¤ort 2a
and (1
) 2a
for the two di¤erent plots. In that way, n can be
share of plot
yields a revenue
considered a continuous number.
2
a) No Hired Labor
Utility
landlord
b) Hired Labor
Utility
Absentee
Utility
Absentee
Utility
landlord
N
N
N
a2/4m2
Figure 1: Two possible organizations
Accordingly, we have the following indirect utility function for a landlord:
8
N (a2 m2 N )
a2
>
>
<
for N
;
2a
4m2
V A (N ) =
3
2
a
a
a
>
>
:
+ N for N >
.
2
32 m
4
4m2
(3)
a
a
h+N
:
2
4
and we determine two possible cases. In Figure 5a,
A
(N ) =
While the landlord’s total utility in the landlord estate is: Vabsen
A
In Figure 5 we compare V A and Vabsen
A
> V A ; and the landlord estate is the only form of organization.
Vabsen
More precisely, we can state that a necessary condition for hired labor is
h>
a
2
1
16a2
m2
:
(4)
When this condition is not ful…lled, a landlord will always prefer to rent out all his land and invest
in human capital. This is true when the opportunity cost of farming is high (h low) and when
the monitoring costs m are high.4 This case corresponds to the model already analyzed in the
previous sections.
We will now focus on the case h >
a
2
16a2
m2
. From Figure 5b we can see that a N exists
¯
such that landlords with N N prefer to stay in the agrarian sector and to organize the farm in
¯
a junker estate or in an hacienda style.
4
1
These …ndings are perfectly consistent with the well known model of Eswaran and Kotwal (1985), where the
landlord organizes the farm on the basis of his outside option and of monitoring costs.
3
N 5 , from problem (2) we can conclude that when the initial number
¯
L
of landlords is large, i.e. l
, there will be a number of Junker estates with n = N and
a2
If we assume that N
4m2
no tenants. When instead land ownership is very concentrated, l <
L
a2
4m2
; the agrarian sector will
be characterized by large haciendas with a number of smaller tenancies attached to the landlord
home farm.6
When there is no excess demand for land, L > 1
!
l; there will never be hired labor: some
of the land will be supplied to some of the ! rich landless for a price p = h, and therefore the
landlord cannot extract the entire surplus from the worker; since there is perfect competition,
landlords cannot discriminate between rich and poor and the equilibrium wage would be w = h:
With this wage, landlords can only obtain a pro…t nh, which is the same surplus obtained by
(nm)2
; so landlords will choose
renting out the land without spending the cost of monitoring
2ab
n = 0:
We will now characterize the dynamics of ! t in order to determine the initial conditions leading
to the two di¤erent long-run equilibria. We assumed that hired workers with wage w = C(e ) are
not able to accumulate enough wealth to invest in human capital, like the workers employed in
the informal sector. In order to simplify, we suppose that hired workers leave zero bequest.7
Given that the dynamics in the modern equilibrium are the same as in the model without
a2
L
there are only Junker
hired labor, we consider only the case L < 1 ! l. When
l
4m2
estates in the agrarian sector. Considering that the hired workers cannot accumulate enough to
migrate, there is no supply of skilled workers from the A-sector. Accordingly in this case ! 1 = 0
and the M-sector will collapse in the long run.
Let us consider now the other case, l <
5
L
a2
4m2
(sector organized in large haciendas). The
N . If there is a market
N > N and some others will sell all their land. In equilibrium
¯
all landlords own the same number of plots N > N.
¯
6
Using …gure 6a we can argue that since the marginal value of each plot change with
for land, some landlords will buy some plots until
This relationship between organization of the agrarian sector, and the initial landownership, seems to be
consistent with evidence from some Latin American countries. Otsuka et Al. (1992) show that the agrarian
sector in the Latin American countries, which are notoriously characterized by higher land concentration, is mainly
organized in large haciendas (in average 45 hectares) and only 60% of the land farm is operated directly by the
owner.
7
This is a simplifying assumption, to rule out the possibility that in the next period there could be two kinds
)w: In this case the second type will be able to
obtain a job as a tenant because they can accept a contract r > 0, which, if the price does not change, is more
e¢ cient than r = 0: However the …nal result will not be qualitatively di¤erent, since accumulation for workers will
of poor, those with zero wealth and the those with wealth
always be lower than accumulation of the tenants.
4
(1
dynamics for the number of rich landless are
! t = a! t
1
a2 a
) ;
4m2 2
+ l(N
(5)
a2
) represents all tenancies.
4m2
Solving recursively we have
Where the term l(N
2
a
a(L l 4m
2)
!T =
+ at
2(1 a)
2
!0
a
a(L l 4m
2)
2(1 a)
!
:
The rest of the analysis is similar to that in the main body of the paper. If 1
l
! 1 > L;
the economy is in a dual equilibrium, and it is in a modern equilibrium otherwise.
In the next section we perform a very simple calibration exercise, to determine whether the
model produces realistic predictions for the number of poor individuals in the two equilibria, given
the mass of plots, L; the mass of tenants, (L
1.1
l
a2
);
4m2
and the mass of owners, l.
A Simple Calibration Exercise
It is interesting to explore whether the model can generate realistic levels of poverty for the
di¤erent economies, and whether it can account for observed di¤erences in the levels of poverty
for countries in the di¤erent equilibria. We recall that the predicted number of poor individuals
is given by
1
with d
p
a(a
4 h):
l
!1 =
8
<
:
2
1
l
1
l
a(L l a 2 )
4m
2(1 a)
(a+d) (1 l)
2 a+d
if L < 1
l
!1;
if L > 1
l
!1;
The model is very simple and does not take into account capital accumulation or the technological progress. This omission certainly has an impact on agrarian productivity and hence on
the probability that a dynasty of successful landless farmers migrates to the M-sector. Moreover,
high-income countries tend to put in place, especially in the M-sector, mechanisms of insurance
to prevent dynasties of unsuccessful workers falling below a given poverty line (i.e. a tends to be
higher in high income countries). For this reasons we concentrate on Asian low and lower/middleincome economies, where the agrarian sectors are rather similar. This is true, since in Asia the
di¤erences between countries in amount of invested capital in the agrarian sector are generally
not too di¤erent (Binswanger and Deininger (1997)).8
8
The land per worker ratio ranges between 0.3 and 3. By contrast, the land-to-worker ratio in Latin American
countries ranges between 10% and 30% (ILO Key indicators of the labor market 2003).
5
We normalize the total population between ages 15-64 to unity (From World Bank Dataset:
World Development Indicators, 2004).9 The FAO World census of Agriculture provides data on
the number of holdings, the number of owner cultivated farms and the number of rented farms,
a2
from which we derive l; the number of owners and l(N
); the number of tenants.10
4m2
We take the poverty levels from the World Bank, World Development Indicators (2003).11
We consider a poverty line of $2 income per day, assuming that poverty is distributed uniformly
across the di¤erent generations. Consistent with the World Bank de…nition of the $2 per day line,
individuals below this line of poverty are assumed to be shut o¤ from access to human capital
investment.12
To calculate the mass of plots, L, we note that
L=
Then, land per worker =
Land / Land per worker
# plots
=
:
# Individuals
# Individuals
Land
Employees in agriculture :
L=
(6)
Substituting in (6), we have
Employees in agriculture
;
# Individuals
which is available from the dataset ILO Key Labor Market Indicators (2003).
We then proceed as follows. If the mass of poor is larger (smaller) than L, we conjecture that
the economy is in the dual (modern) equilibrium, and obtain from the model a corresponding
prediction for the poor. Finally, we compare predicted numbers with the actual numbers. Results
are presented in table 4.
9
We preferred this measure rather than the one de…ned as “labor force”, so as to take into account the employed
in the informal sector, who are not accounted in the ”labor force” data.
10
Land is normally rented under di¤erent agreements, and often the same holding under a di¤erent contracts.
Consistently with our model, we do not make any distinction between di¤erent contracts.
11
The …rst issue allowing for comparisons across countries on poverty data.
12
A possible problem is that the …rst WDI survey in the 2003 edition refers to data in the 2000 or thereabouts;
whereas, the agrarian census refers to data of the beginning of 90s. However, the bias should not be too large since
the ownership structure in the agrarian sector tends to change very slowly.
6
Table 4: Calibration,
Country13
= 0:9; a = 0:93; h = 0:25;
Land /
Owners
Worker
l
Tenants
= 0:9:
Land
less 2$
L
a day
Est. Poor
Simulation
1
1
l
!
L
!
Dual Equilibrium
India14
0.80
0.21
0.01
0.40
0.80
0.75
0.55
Bangladesh15
0.26
0.23
0.08
0.42
0.83
0.25
0.07
Pakistan16
1.26
0.09
0.02
0.21
0.65
0.77
0.65
Philippines17
0.96
0.10
0.06
0.23
0.46
0.51
0.38
Modern Equilibrium
Thailand18
1.14
0.14
0.04
0.38
0.32
0.10
Turkey19
3.30
0.09
0.004
0.16
0.10
0.10
We can observe that the model correctly predicts the type of equilibrium in four out of …ve of
the countries we considered. It fails for Bangladesh. This is perhaps due to the very low land-toworker ratio in this country. Indeed, we can observe that the number of landless, 1
l; is smaller
than the number of poor, implying that some of the land owners must be wealth constrained. We
are probably in the situation we discussed in section Low Accumulation from the Agrarian Sector
of the main paper, where land ownership is too fragmented. We can also note that in three cases
the model provides a good estimate of the number of poor individuals; while this number is rather
underestimated in the case of Thailand. A possible reason is that this country in 2000 was still
recovering, in terms of poverty levels, from the e¤ects of the …nancial crisis of 1997.20
Finally, in the last column we simulated an agrarian reform that would redistribute each plot
to each individual, so that l = L; in order to check if an agrarian reform would be enough to push
the country in the dual equilibrium to the modern one. In India, Pakistan and in the Philippines
an agrarian reform could not reduce poverty to an extent su¢ cient to push the economy to the
13
All data, if not speci…ed, are from year 2000.
14
Data on poverty are related to 1999, land per worker and total population are 2001. L ; l, and l(N
a2
)
4m2
are
derived from the census 1995 (FAO).
a2
)
4m2
15
L ; l, and l(N
16
Data on land per worker and total population and poverty are related to year 1998 (World Bank and ILO).
17
L ; l, and l(N
18
L ; l, and l(N
19
L ; l, and l(N
20
Indeed in 1992 the share of population below $2 a day was 23% (World Development Indicators 1998).
a2
)
4m2
a2
)
4m2
a2
)
4m2
are derived from the census 1996 (FAO).
are derived from the census 1991 (FAO).
are derived from the census 2003 (FAO).
are derived from the census 1991 (FAO).
7
modern equilibrium. Therefore we can argue that a policy of education would be in any case
needed in these countries.
8