Misallocation, Selection and Productivity: A Quantitative
Analysis with Panel Data from China†
Tasso Adamopoulos
York University
Loren Brandt
University of Toronto
Jessica Leight
Williams College
Diego Restuccia
University of Toronto
September 2015 (Preliminary and Incomplete)
Abstract
We use micro panel data from China and a quantitative framework to document the extent of
resource misallocation in agriculture within villages, across villages, and over time; and to assess
the total factor productivity (TFP) gains from an efficient reallocation of resources. We then
develop and estimate a tractable heterogeneous-ability two-sector framework of agriculture and
non-agriculture to assess the TFP implications of distortions with ability selection across sectors.
An efficient reallocation of capital and land to existing farmers in China would increase output and
productivity by 84 percent. Resource misallocation in agriculture implies substantial distortions in
occupational choices. Eliminating misallocation across farms in agriculture generates substantial
reallocation across sectors, increasing average ability in both sectors but especially in agriculture,
and generating a large impact in aggregate outcomes.
JEL classification: O11, O14, O4.
Keywords: agriculture, misallocation, selection, productivity, China.
†
Chaoran Chen provided excellent research assistance. Restuccia gratefully acknowledges the support from the
Social Sciences and Humanities Research Council of Canada. Contact: Tasso Adamopoulos, tasso@econ.yorku.ca;
Loren Brandt, brandt@chass.utoronto.ca; Jessica Leight, jessica.leight@williams.edu; Diego Restuccia,
diego.restuccia@utoronto.ca
1
1
Introduction
A central theme in the study of economic growth and development is the understanding of the large
productivity differences in the agricultural sector across countries. Understanding these differences
is essential because poor countries allocate most of their labor to agriculture and, as a consequence,
account for most of the aggregate income differences between rich and poor countries.1 A prominent explanation of productivity differences across countries is differences in resource misallocation
across heterogeneous production units.2 Institutions and policies creating misallocation are highly
pervasive in agriculture in poor countries and can account for a large portion of the productivity
differences across countries as emphasized and quantified in Adamopoulos and Restuccia (2014).
The nature of these policies and institutions is that they diminish the efficiency of land and other
complementary markets in allocating resources to the most productive uses.3
We use micro farm-level panel data from China and a quantitative framework to document the
extent of factor misallocation within villages, across villages, and over time. We find that there
are substantial frictions in the land and capital markets that disproportionally affect the more productive farmers. Our story in this paper is that these distortions reduce aggregate agricultural
productivity by affecting two key margins: the allocation of resources across farmers (misallocation) and the selection of workers across sectors, in particular the type of farmers who operate in
agriculture (selection). The key insight in our paper is that selection can substantially amplify the
misallocation effect via systematic distortions to occupational choices and that these distortions in
occupational choices alter the distribution of productive units in agriculture, affecting our measures
of misallocation.
1
See, for instance, Gollin et al. (2002), Restuccia et al. (2008), among many others.
See Restuccia and Rogerson (2008) and Hsieh and Klenow (2009). Restuccia and Rogerson (2013) review the
expanding literature on misallocation and productivity.
3
See for instance recent studies linking resource misallocation to land market institutions, such as land reforms in Adamopoulos and Restuccia (2015), the extent of marketed land across farm households in Restuccia
and Santaeulalia-Llopis (2015), and the role of land titles in Chen (2015). de Janvry et al. (2014) study a land
certification reform in Mexico delinking land rights from land use allowing for more efficient migration.
2
2
We focus on China for several reasons. First, China is a growing economy with substantial reallocation within and across sectors over time. Yet, productivity growth in agriculture has been
lacklustre at best, especially in the cropping sector which we focus on. Second, the operational
scale in the agricultural sector in China is small, only 0.7 hectares on average compared to 178
hectares in the United States. Third, the institutional framework is such that there is a lack of
well-defined property rights over land which can lead to both factor misallocation within agriculture
and sectoral/occupational choice distortions. Fourth, we have a unique panel dataset of households
with detailed information on inputs and output in agriculture to measure farm productivity and
wages of non-agricultural workers.
We use a panel household survey from China collected by the Research Center for the Rural Economy
under the Ministry of Agriculture. The survey is nationally representative and covers all provinces.
We have access to data for ten provinces that span all the major regions of China. The data is
an unbalanced panel for 9 years with a total sample size given the information required of about
8000 households per year. We use the detailed information on agricultural activities to construct
a real measure of value added for each household farm. We also have information on the total
capital stock used in agriculture, total days and the amount of land operated. Using a standard
production function for agriculture, we measure farm TFP using the information from the panel.
Armed with these constructed measures of farm TFP, we use a standard framework of agriculture
to both measure distortions of capital and land across farmers within a village as well as capital
distortions across villages. We also use the framework to characterize the efficient allocation of
resources given farm-level TFPs and aggregate resources. Under a reasonable parameterization,
we find that the output (productivity) gains from reallocation are large. Nationally, reallocating
capital and land across all existing farmers to their efficient use would increase aggregate agricultural
output and TFP by a factor of 1.84-fold. We find that reallocation within villages is a substantial
contributor to these gains, around 60 percent of the overall gains, with capital misallocation across
provinces accounting for a further 20 percent. We do not find substantial changes in the extent of
3
misallocation over time which is consistent with a fairly constant institutional setting in the land
market. We find that the reallocation gains are large for all provinces in our data and that they
vary from 40 to 120 percent across provinces. We also exploit the panel structure of our data to
construct from the time profiles of TFP of individual farms, an average TFP which we think is a
better measure of permanent ability of farmers. We find that the nation-wide efficient reallocation
gain associated with these measures of average farm TFP is 67% compared to 84% in the baseline.
As a result, transitory variations in our measures of farm TFP are not driving the misallocation
gains emphasized in our paper.
We then embed the agricultural framework into a two-sector model of agriculture and non-agriculture.
We study the impact of misallocation in agriculture on the selection of individuals across sectors.
We use the equilibrium properties of the model to calibrate the parameters to observed moments
and targets from the data for China. We then conduct a series of counterfactual experiments to
assess the quantitative importance of misallocation and the overall impact on aggregate agricultural
productivity. The micro data allow us to estimate key population parameters in the model, in particular, the substantial reallocation of individuals from agriculture to non-agriculture allows us to
pin down the covariance of individual abilities across sectors. We provide a quantitative assessment
of the extent to which factor misallocation in the agricultural sector and the associated distortions
in the sector/occupational choices of heterogeneous workers generate agricultural and aggregate
productivity differences. We find that distortions in agriculture substantially affect occupational
choices and aggregate outcomes.
To document these findings we pursue two sets of counterfactuals. First, we set the correlation of
distortions to ability to zero, that is, we eliminate misallocation across farmers with different levels
of productivity, which is about 50% of the total misallocation losses. We find that eliminating
these distortions increases aggregate agricultural productivity by 74% and consequently reduces
the share of employment in agriculture to 25% (from 42% in the benchmark economy). We argue
4
that this is a substantial increase in agricultural productivity considering that the static gain in
agricultural productivity from eliminating correlated distortions is 24%, so selection in agriculture
amplifies this difference by a factor of 3.08-fold. Second, we compare the productivity gains from
reduced misallocation in the previous counterfactual with an equivalent increase in economy-wide
productivity of 24%. We find that selection in this case only increases agricultural productivity by
26%, an amplification effect of only 1.08-fold. Correlated idiosyncratic distortions generate much
larger selection effects than changes in common sector-specific or economy-wide TFP.
Our paper relates to the broad literature on misallocation and productivity with particular emphasis
in the agricultural sector as discussed earlier. It also relates to role of selection in amplifying
productivity differences across sectors such as that in Lagakos and Waugh (2013). A key difference
in our work is that we provide actual data on distortions in the agricultural sector as the key driver of
low agricultural productivity and show that correlated idiosyncratic distortions in the agricultural
sector generate much larger effects on selection than equivalent changes in economy-wide TFP.
Moreover, the panel dimension of the data allows us to identify a key parameter in these selection
models that deals with the correlation of abilities across sectors. Our paper also relates to many
studies of the Chinese economy who emphasize the importance of agriculture such as Benjamin and
Brandt (2002), Benjamin et al. (2005), Benjamin et al. (2011), Zhu (2012), among many others.
Brandt et al. (2013) emphasize the importance of misallocation across provinces and across state
and non-state sectors for aggregate productivity in the Chinese economy.
The paper proceeds as follows. In the next section, we describe our basic framework for identifying
distortions and measuring the gains from reallocation. Section 3, describes the data from China and
the variables we use for our analysis. In Section 4, we construct our measures of household-farm
productivity and present the main results on misallocation and the reallocation gains to an efficient
allocation. In Section 5, we embed the framework of agriculture into a heterogeneous-ability twosector model with non-agriculture and present the results from our main experiments. We conclude
5
in Section 6.
2
Basic Framework
We describe the industry framework we use to assess the extent of misallocation in agriculture in
China. We derive the equilibrium equations used to identify from data idiosyncratic (farm-village
and village specific) distortions and our summary measure of distortions faced by farmers in China.
We then derive the efficient allocations and measures of the output (productivity) losses associated
with the different types of distortions—within village, across villages and over time.
2.1
Description
We consider a rural economy consisting of V villages, indexed by v. Following Adamopoulos and
Restuccia (2014), the production unit in the rural economy is a family farm. A farm is a technology
that requires the inputs of a farm operator (household), as well as the land and capital under the
farmer’s control. Each village is endowed with Lv amount of farm land and a finite number of
Mv farm operators indexed by i, who are immobile across villages. Farm operators within villages
are heterogeneous with respect to their farming ability svi . The total amount of capital in the
rural economy is K, which is potentially mobile across individuals within villages as well as across
villages.
As in Lucas Jr (1978), the production technology available to farmer i with productivity svi in
village v exhibits decreasing returns to scale and is given by the Cobb-Douglas function,
α 1−α γ
1−γ
yvi = svi
`vi kvi
,
6
(1)
where γ < 1 is the span-of-control parameter which governs the extent of returns to scale at the
farm-level, y, `, and k denote real farm output, land and capital.
We are interested in estimating the extent of resource misallocation (i) across farms within-villages
and (ii) across-villages. Given that we have two factors of production we can separately identify
farm-specific distortions to land and capital within villages. We model farm-specific distortions as
input taxes. Denote by τvi` and τvik the land and capital taxes faced by farm i, in village v. We also
introduce village-specific (but not farm-specific within villages) output wedges to capture villagelevel distortions and thus cross-village misallocation. We denote the village-level output distortion
by τvy . Tax revenues are equally distributed lump-sum across all households.
Given distortions, the profit maximization problem facing farm i in village v is,
max πiv = (1 − τvy ) yvi − 1 + τvik rkvi − 1 + τvi` qv `vi .
`vi ,kvi
(2)
Let the rental prices of land and capital in village v be (qv , r). Given that land is immobile across
villages the rental price of land qv will be village-specific. Given that capital is mobile across villages
in equilibrium the rental price will be equal to r in all villages. The idiosyncratic distortions will
show up as “wedges” in firm-specific marginal products of factors of production.
In equilibrium, the land market must clear in each village and the capital market must clear for the
whole economy. The market clearing condition for land in village v is,
Mv
X
`vi = Lv ,
(3)
i=1
while the rural economy-wide capital market clearing condition is,
V X
Mv
X
kvi = K.
v=1 i=1
7
(4)
2.2
Equilibrium and Identification of Wedges
We use this framework to identify the wedges recursively. In particular, we first identify the within
Mv
village farm-specific wedges τvik , τvi` i=1 from the determination of land and capital allocations
within villages. Second, given the within-village wedges, we identify the across-village wedges
{τvy }Vv=1 from the determination of capital allocation across villages.
Identifying within-village distortions We begin with the identification of the within-village
wedges. Farm-specific land and capital wedges can be identified up to a scalar from the average
product of each factor. The first order conditions with respect to land and capital for farm i in
village v imply,
qv 1 + τvi`
yvi
=
,
M RP Lvi ≡ αγ
`vi
(1 − τvy )
(5)
r 1 + τvik
yvi
=
,
M RP Kvi ≡ (1 − α)γ
kvi
(1 − τvy )
(6)
where M RP L and M RP K are the marginal revenue products of land and capital in turn. Given
that in our model the price of agricultural goods is normalized to one, M RP L and M RP K are also
the marginal products of the respective factors. Equations (5) and (6) show that in the presence of
firm-specific within-village distortions marginal products of factors are not equalized across farms
in the same village.
We can re-write the first-order conditions (5)-(6) as,
qv 1 + τvi`
M RP Lvi
yvi
`
=
=
y ∝ 1 + τvi ,
αγ
`vi
αγ (1 − τv )
(7)
r 1 + τvik
M RP Kvi
yvi
k
=
=
y ∝ 1 + τvi .
(1 − α)γ
kvi
(1 − α)γ (1 − τv )
(8)
Equations (7) and (8) indicate that in the presence of firm-specific within-village distortions the
8
average products (revenue productivity) of land and capital will vary across farms in the same
village by the size of the idiosyncratic distortion faced for each factor. Then (7)-(8) also imply that
land and capital distortions can be identified up to a scalar from the average product of each factor
within a village. Note that because the output tax is common to all farms in the same village, it is
part of that scalar.4
The summary measure of the two within-village distortions for farm i in village v is captured by,
yvi
T F P Rvi = α α =
`vi kvi
M RP Lvi
αγ
α M RP Kvi
(1 − α)γ
1−α
=
1−α α α
1−α
α
1−α
1 + τvik
1 + τvi`
qv
r
=
∝ 1 + τvi`
1 + τvik
.
y
(1 − τv )
αγ
(1 − α)γ
(9)
T F P R corresponds to the concept of what Hsieh and Klenow (2009) call “revenue productivity”
in their framework. As shown, T F P Rvi is proportional to a geometric average of the farm specific
distortions in land and capital.5 We underline that T F P R is different from “physical productivity”
or TFP, which in our model is,
yvi
T F P Qvi ≡ s1−γ
= α 1−α γ ,
vi
`vi kvi
(10)
for farm i in village v. In a world without distortions, within villages farms with higher T F P Qvi
would command more resources, land `vi , and capital kvi , such that marginal products of each factor
equalize across farms. However, with idiosyncratic distortions this need not be the case as indicated
by (7)-(8).
Re-arranging the farm i first order conditions (5)-(6) and summing across all farms in the same
qv
The scalar for the land input common to all farms in the same village is αγ(1−τ
y , while the scalar for the capital
v)
r
input is (1−α)γ(1−τvy ) .
5
Note the village-level output distortion is constant across farms and thus part of the common proportionality
factor in (9).
4
9
village, we derive the average village-level marginal revenue product of each factor,
(1 −
qv
y PMv yvi 1
τv ) i=1 Yv 1+τ `
vi
w
(1 −
P v yvi 1
τvy ) M
k
i=1 Yv 1+τvi
= αγ
Yv
≡ M RP Lv ,
Lv
= (1 − α)γ
(11)
Yv
≡ M RP K v .
Kv
(12)
Combining the farm-level first order conditions (5)-(6) with the village-level marginal revenue product equations (11)-(12) we can solve for the farm-level land and capital allocations,
"
(1 − τvy ) yYviv 1+τ1 `
#
vi
`vi = M RP Lv
Lv ,
qv
"
kvi = M RP K v
(1 − τvy ) yYviv 1+τ1 k
#
vi
Kv ,
r
which we plug into the farm-level production function (1) to get farm i output,
"
yvi =
αγ
(1−α)γ
M RP Lv M RP K v
qvαγ r(1−α)γ
(1
− τvy )γ αγ (1−α)γ
L v Kv
Yvγ
1
# 1−γ
svi
αγ
` 1−γ
1 + τvi
Combining (13) with the definition of total village output, Yv =
PMv
i=1
1 + τvik
.
(1−α)γ
1−γ
(13)
yvi we can derive the village-
level production function,
(1−α)γ
,
Yv = T F Pv Lαγ
v Kv
(14)
where (Lv , Kv ) are total village land and capital, and T F Pv is village-level TFP, which aggregates
up within-village distortions,
T F Pv =
"M
v
X
i=1
svi
T F P Rv
T F P Rvi
10
γ #1−γ
1−γ
,
(15)
with average village revenue productivity given by
T F P Rv =
M RP Lv
αγ
α M RP N v
(1 − α)γ
1−α
.
(16)
Identifying across-village distortions We showed that farm-level behavior in the presence
of distortions aggregates up to a village-level production function with aggregate village land Lv
(exogenous), capital Kv (endogenous), and aggregate village TFP T F Pv , which summarizes the
within village distortions. Note that T F Pv is independent of the village-level output tax τvy .6 What
remains is the determination of the capital allocation across villages {Kv }Vv=1 , given village output
taxes, village TFPs and land endowments. The village capital allocation can be determined as
the solution to a village-level problem of a stand-in farm that operates the village-level production
P
function (15) and the rural economy-wide market clearing condition for capital Vv=1 Kv = K. In
turn, given village-level land Lv and TFP T F Pv , the observed allocation of capital across villages
can be used to back out the village-level output wedges (1 − τvy ).
Given village farm land Lv village-level TFP for the distorted economy T F Pv , the village-level
problem of the stand-in farm is,
(1−α)γ
max (1 − τvy ) T F Pv Lαγ
− rKv .
v Kv
Kv
Since Lv is a fixed factor at the village-level the only choice variable is Kv . The first order condition
to this problem is,
(1−α)γ−1
(1 − α)γ (1 − τvy ) T F Pv Lαγ
= r,
v Kv
or
r
1
Yv
=
.
y ∝
Kv
(1 − α)γ (1 − τv )
(1 − τvy )
6
This is because in (15) both T F P Rvi and T F P Rv are functions of (1 − τvy ) which cancels out in the ratio
T F P Rv
T F P Rvi .
11
Then, the village-level output distortion can be identified up to a scalar from the average product
of capital at the village-level in the data. Note that in the absence of output distortions the average
product of capital should be equalized across villages. The reason is that villages with higher TFP
and larger land endowment would command more capital such that the average product of capital
is the same.
Combining the stand-in farm first order condition and the the aggregate market clearing condition
for capital we solve for the allocation of capital across villages,
Kv
K
1
1−γ(1−α)
[(1 − τvy ) T F Pv Lαγ
v ]
= PV
1
y
αγ 1−γ(1−α)
h=1 [(1 − τk ) T F Ph Lh ]
.
(17)
Aggregate output in the distorted rural economy,
Y =
V
X
Yv =
v=1
V
X
γ(1−α)
T F Pv Lαγ
,
v (Kv )
v=1
and using the solution for Kv from (17) we have,
Y =N
γ(1−α)
γ(1−α)
PV
1
y 1−γ(1−α)
1−γ(1−α)
[T F Pv Lαγ
v ]
v=1 (1 − τv )
nP
oγ(1−α) .
1
V
y
αγ 1−γ(1−α)
v=1 [(1 − τv ) T F Pv Lv ]
(18)
Note that given the described identification of distortions from the data, aggregate distorted output
Y in our model coincides with actual aggregate agricultural output in the data for China.
2.3
Efficient Allocation
To determine the output (productivity) loss associated with misallocation, we compare the equilibrium of the distorted economy to the efficient allocation, obtained from the solution to a planner’s
12
problem. The planner chooses how to allocate capital across villages and land and capital across
farmers within villages. In particular, the planner chooses the allocation of inputs across villages
and farmers to maximize aggregate agricultural output. The problem of the planner is:
max
V X
Mv
X
yvi ,
v=1 i=1
subject to
1−α
`αvi kvi
yvi = s1−γ
vi
Mv
X
γ
,
v = 1, 2, ..., V ;
`vi = Lv ,
i = 1, 2, ...Mv ;
v = 1, 2, ..., V ;
i=1
V X
Mv
X
kvi = K.
v=1 i=1
We can break this problem down into two sub-problems: (a) the determination of the efficient
allocation of capital across villages (determination of Kv ’s) and (b) the determination of the efficient
allocation across technologies within villages, for a given amount of village labor Kv (endogenous)
and land Lv (exogenous). We solve this problem backwards, starting from (b). The details of the
derivations are provided in Appendix A.
Efficient within-village allocations In this sub-problem, Kv ’s are given. The problem of the
planner at this stage is to maximize total village output Yvef f subject to the village-level resource
constraints. In particular, for each village v the optimization problem is:
max
v
{`vi ,kvi }M
i=1
Yvef f
=
Mv
X
yvi ,
i=1
subject to
1−α
yvi = s1−γ
`αvi kvi
vi
γ
,
13
i = 1, 2, ...Mv ;
Lv =
Mv
X
`vi ,
i=1
Kv =
Mv
X
kvi .
i=1
Using the first order conditions to this problem along with the village-level resource constraints, the
efficient allocations within a village involves allocating total village land and capital across farmers
according to relative productivity,
svi
`evi = PMv
svj
svi
e
kvi
= PMv
svj
j=1
j=1
Lv ,
(19)
Kv ,
(20)
where the superscript e denotes the efficient allocation. Equations (19) and (20) indicate that the
more productive a technology (production unit) is relative to the average of the village the relatively
more land and capital it will command in the efficient allocation.
Efficient across-village allocation This sub-problem determines the efficient allocation of aggregate capital K across villages, i.e., the Kv ’s that were taken as given in the previous problem.
It is convenient to determine this allocation using village-level production functions. Using that
P v
aggregate village output is Yvef f = M
i=1 yvi along with individual technologies and the allocation of
capital and land within villages as derived above we can obtain a village-level production function
for each village v,
γ(1−α)
,
Yvef f = Av Lαγ
v Kv
where
Av =
Mv
X
i=1
14
!1−γ
svi
.
The across-village allocation problem is given by,
max
{Kv }V
v=1
Ykef f
=
V
X
γ(1−α)
Yv = Ev Lαγ
, v = 1, 2, ..., V ;
v Kv
v=1
subject to
V
X
Kv = K.
v=1
Note that Ykef f is the aggregate agricultural output under the efficient within-village allocation of
capital and land and across village allocation of capital. Using the first order condition to this
problem and the agricultural economy-wide resource constraint for capital we solve for the share of
capital allocated to village v under the efficient allocation,
Kv
K
1
e
1−γ(1−α)
(Av Lαγ
v )
= PV
1
αγ 1−γ(1−α)
h=1 (Ah Lh )
,
(21)
where e denotes the efficient allocation. This says that in an undistorted world more capital should
be allocated to villages that are relatively more productive (higher Av ) and have a relatively larger
endowment of farm land (higher Lv ), compared to other villages. The implied aggregate output
under efficient allocation of capital:
Ykef f = K γ(1−α)
( V
X
[Ev Lαγ
v ]
1
1−γ(1−α)
)1−γ(1−α)
.
v=1
Nationwide efficient allocation We can also calculate the output (productivity) gains of a
nation-wide reallocation of capital and farmers across space in China, that is, we can calculate
the efficiency gains in reallocating total agricultural capital and land in China across all farmers
in China, eliminating the village-level restriction in our previous calculations. The problem of the
planner is to maximize total nationwide output Y ef f given nationwide farm TFPs subject to the
15
nationwide resource constraints (K, L):
max Y
{`i ,ki }M
i=1
ef f
=
M
X
`αi ki1−α
s1−γ
i
γ
,
i=1
subject to
L=
M
X
`i ,
i=1
K=
M
X
ki .
i=1
Similar to the within-village allocation problem, the efficient allocations in this case are given by,
si
`i = PM
sj
si
ki = PM
sj
j=1
j=1
L,
K.
We measure aggregate agricultural output reallocation gains by comparing efficient output to actual
output in the Chinese economy and we decompose these gains in terms of within-village reallocation,
across village reallocation of capital, and nation-wide reallocation. Since aggregate factors are kept
the same across these comparisons, the output gains are TFP gains. In the next section, we discuss
the data we use to perform our analysis and then present our main misallocation results.
3
Data
We use the household survey data collected by the Research Center for the Rural Economy under the
Ministry of Agriculture.7 This is a nationally representative survey that covers all provinces. The
7
For a detailed description and analysis of the data see Benjamin et al. (2005).
16
survey has been carried out annually since 1986 with the exception of 1992 and 1994 when funding
was an issue. The sampling is as follows: an equal number of rich, medium and poor counties
was selected in each province, and within each county a similar rule was applied in the selection of
villages. Within villages, households were drawn in order to be “representative. Important changes
in survey design in 1993 that expanded information collected on agriculture, and enable more
accurate estimates of revenue and expenditures in agriculture. Surveys before 1993 are problematic
in their estimates of farm revenue and expenses.
We have obtained access to data for a subset of the survey. We have data for ten provinces that
span all the major regions of China, and use the data for the period between 1993 and 2002. The
data are in the form of an unbalanced panel. In each year, we have information on approximately
8000 households drawn from 110 villages. For 104 villages, we have information for all 9 years.
The average number of household observations per village-year is 80, or a quarter to a third of all
households in a village. We have data for all 9 years for approximately 6000 households. Attrition
from the sample is not a concern and is examined in detail in Benjamin et al. (2005). Much of
the attrition is related to exit of entire villages from the survey. Household exit and entry into the
sample is not systematically correlated with key variables of interest.
The survey provides disaggregated information on household income and labor supply by activity.
For agriculture, we have data on total household landholdings, cultivated area, sown area and
output by crop, and major farm inputs (labor, fertilizer, farm machinery). For nonagricultural
activity such as family businesses, we have information on revenues and expenditures that enable us
to estimate net incomes from each type of household non-family business. We also have information
on household wage earnings.
Value Added Agricultural Output We utilize the detailed information on farm output by
crop in physical terms to construct estimates of “real” farm output. Output of each crop is valued
17
using a sample-wide average price (unit values) constructed over the period between 1993 and 2002.
Hence, aggregate output at the farm level is a common-price real measure. Unit values are computed
using information on market sales, and are exclusive of any “quota sales at planned (below market)
prices. In these calculations, households own consumption is implicitly valued at market prices.
Intermediate inputs such as fertilizers are treated in an analogous way. We subtract expenditures
on intermediate inputs from gross output providing our estimate of net income or value added from
the cropping sector. In what follows, we use this measure of real value added at the farm level when
we refer to farm output.
Land Ownership rights of farmland reside with the collective or village. Households are allocated
use rights to the land. The allocation of use rights is based on an individuals registration or
hukou, with all individuals with registration in the village entitled to land. Earlier work suggests
that allocation of land within a village was generally fairly egalitarian. With the introduction of
rural reform in the late 1970s, households were supposed to enjoy use rights for a period of 15
years, but there is enormous heterogeneity across villages in terms of the “security of the claims
that households enjoy. Village-wide reallocation in which villages took the land back and then
reallocated land amongst households was common. In the late 1990s, use rights on cultivated land
were extended for an additional 30 years. In addition to use rights, households in principle have
other rights, most importantly, the right to rent or transfer their use rights to other households.
(Land cannot be used as collateral for purposes of borrowing however.) These rights have been
abridged in a variety of ways and over the period we examine, the rental market has been relatively
thin. In fact, a frequent claim is that use it or lose it rules existed in these villages over the
period we analyze. Households that did not use their land and rented it to others (or possibly let
it lie fallow) risked losing the land during the next reallocation. These kinds of rules may have
prompted households to only allow immediate relatives (father, brothers, etc) to use their land, and
discouraged land from going to those households that valued it most. It may have also impacted
18
decisions to migrate. The measure of land that we use in our analysis is cultivated land by the
household.
Capital The survey provides household-level information beginning in 1986 on the value at original purchase prices of farm machinery and equipment, larger hand tools, and draft animals used
in agriculture. Assuming that accumulation began in 1978, the year the reforms of the agricultural
system began, we utilize the perpetual inventory method to calculate the value of farm machinery
in constant RMB. The survey does not capture smaller farm tools and implements, and so for in
upwards of a third of household-years, the value of their capital stock is zero. To deal with these
cases, we impute to all farm households a value equal to the amount of land operated by the household times ten percent of the median capital to land ratio by village and by year. We have verified
that our results are not crucially sensitive to the amount of adjustment assigned to households.
4
Measuring Farm TFP and Misallocation in Agriculture
Recall from our basic framework that a farmer has access to the following production function for
agricultural output:
γ
yi = si1−γ `αi ki1−α ,
where ` is operated land by household i, k is the household capital stock, and s1−γ is farm-level
TFP. Using data for output, capital, and land, we use this production function to measure farm
TFP.8 In our analysis, we use γ = 0.54 which reflects the total income share of labor and α = 2/3
8
We note that households also differ in the amount of hours worked in the farm. However, the total variation in
hours is relatively small and uncorrelated with TFP. For this reason, in all our analysis we abstract from farm hours
by dividing output, land, and capital by total hours in the farm. We emphasize that our results are nearly identical
if instead we explicitly consider the variation in hours.
19
Figure 1: Farm-Level Total Factor Productivity in China 2000
to match a land income share of 0.36 and hence a capital income share of 0.18.9
Figure 1 documents the distribution of log farm-level TFP in China. The dispersion in farm TFP
is substantial, the 90 to 10 percentile ratio in farm TFP is 6-fold whereas the 75 to 25 percentile
ratio is 2.4-fold. To put it in perspective, this dispersion in farm-level TFP is substantially smaller
than the dispersion of farm TFP in Malawi reported in Restuccia and Santaeulalia-Llopis (2015)
and in plant-level TFP documented in Hsieh and Klenow (2009) for Indian, Chinese and U.S.
manufacturing. For instance, the 90/10 ratio of plant-level TFP is 12.7-fold whereas the 75/25
ratio is 3.8-fold. In U.S. manufacturing these ratios are 7.8-fold and 3-fold respectively.
Figure 2 documents the pattern of farm allocations in land and capital by farm-level TFP. As
suspected from our description of the institutional arrangement in China where use rights of land
are fairly uniformly distributed among members of the village, the land use allocations are roughly
9
We note that data for the United States would attribute a similar income share of labor (same γ) but a larger
role for capital. Our results documented in the next section are stronger using a larger capital share.
20
Figure 2: Factor Allocations by Farm TFP in 2000
Land
Capital
Land Productivity (Yield)
Capital Productivity
constant across the productivity of farm households. Recall that an efficient allocation of land
involves a tight positive relationship between the land input and farm productivity. Similarly,
for the capital allocation we find that capital is not allocated to the most productive farmers;
if anything, the opposite occurs and on average less productive farmers have more capital than
more productive farmers. Again, an efficient allocation involves a tight relationship between capital
allocation and productivity. The consequence of these patterns of land and capital allocation is
that individual factor productivity is not equalized across farmers, in particular, land productivity
(output per unit of land) and capital productivity are strongly increasing in farm TFP.
We measure the output (productivity) gains of eliminating misallocation in different layers as follows: (1) Eliminating within-village misallocation by reallocating capital and land within each
21
Figure 3: Efficiency Gains over Time
Eliminating within−village misallocation
Plus eliminating across−village capital misallocation
Eliminating nationwide misallocation
2.2
Efficiency Gain
2
1.8
1.6
1.4
1.2
1
1995
1996
1997
1998
1999
2000
2001
2002
Year
village to their efficient allocation given (Kv , Lv ) and siv , given by Yvef f /Y . (2) Eliminating withinvillage and across village misallocation: by also eliminating the capital misallocation across villages,
given by Ykef f /Y . (3) Eliminating nationwide misallocation: reallocation gain from efficient allocation of K and L across all farmers in China, given by Y ef f /Y .
Figure 3 reports the output gains of efficient reallocation over time from 1995 to 2002. We note
that there is not substantial change in the reallocation gains over time in China. Eliminating
within-village misallocation of capital and land across farmers is a substantial source of reallocation
gains, an increase in output (and hence TFP) of around 40 percent. Eliminating across-village
misallocation of capital increases the reallocation gains to around 60 percent. When capital and
land are efficiently allocated across all farmers in China, the increase in output is close to 80 percent
in the 90’s and almost 90 percent in 2002.
Figure 4 reports the reallocation gains across provinces. The province-wide reallocation gains are as
low as 40 percent in Jilin and as high as 120 percent in Shanxi. Potential gains are also especially
22
Figure 4: Efficiency Gains across Provinces
2.8
Eliminating within−village misallocation
Plus eliminating across−village capital misallocation
Eliminating nationwide misallocation
2.6
Efficiency Gain
2.4
2.2
2
1.8
1.6
1.4
1.2
xi
l
Ji in
an
gs
Zh u
ej
ia
ng
An
hu
H i
en
an
H
un
G
ua
a
ng n
do
Si ng
ch
ua
n
G
an
su
Ji
an
Sh
C
ou
nt
ry
1
Province
high in Guangdong and Zhejiang, the two most developed provinces in our sample. In all cases, the
within-village misallocation is a substantial component of the overall reallocation gains.
5
Misallocation and Selection across Sectors
We now integrate our framework of agriculture into a standard two-sector general-equilibrium Roy
(1951) model of selection across sectors to assess how farm-specific distortions in agriculture alter the
occupational choice of individuals between agriculture and non-agriculture and at the same time how
selection alters measured misallocation in the agricultural sector. Distorted occupational choices
affect both measured static misallocation in the agricultural sector and the overall productivity
gains from reallocation.
We augment our model along the following dimensions. First, we extend the agricultural model to a
23
two-sector model by introducing a non-agricultural sector. Second, we introduce preferences for individuals over consumption goods for agriculture and non-agriculture, with a subsistence constraint
for the agricultural good. Third, individuals are now endowed with a pair of productivities, one for
each of the two sectors. Fourth, individuals now face an occupational choice, whereby they choose
whether to become farm operators in agriculture or workers in the non-agricultural sector. We
show that a key determinant of the occupational choice is the farm-specific distortions individuals
would face if they become farm operators. For analytical tractability, we now allow for a continuum of individuals. The fraction of individuals that choose agriculture, and thus the number and
productivity distribution of farms is now endogenous. In what follows, we describe the economic
environment in detail, defining equilibrium and describing some key properties of the model.
5.1
Environment
At each date there are two goods produced, agriculture (a) and non-agriculture (n). The nonagricultural good is the numeraire and we denote the relative price of the agricultural good by
pa . The economy is populated by a measure N of individuals indexed by i. For simplicity in this
section we abstract from the village layer in our misallocation framework. However, the effective
farm-specific tax that individuals face in agriculture includes the village-level output tax.
Preferences Each individual i has preferences over the consumption of the two goods given by,
Ui = ω log (cai − a) + (1 − ω) log(cni ),
where ca and cn denote the consumption of the agricultural and non-agricultural good respectively,
a is the subsistence requirement for the agricultural good, and ω is the preference weight on agricultural goods. The subsistence constraint implies that when income is low a disproportionate amount
24
will be allocated to the consumption of the agricultural good. Individual i faces the following budget
constraint,
pa cai + cni = Ii + T,
where Ii is the individual’s income, and T the transfer to be specified below.
Sector-specific abilities Individuals are heterogeneous with respect to their abilities in agriculture and non-agriculture. In particular, each individual i is endowed with a pair of abilities,
one for each sector, (sai , sni ) drawn from a known population joint distribution of skills with cdf
F (sai , sni ). We allow for the possibility that skills are correlated across sectors. In particular, we
assume a bivariate log-normal distribution for (sai , sni ) with mean (µa , µn ) and variance,



Σ=
σa2
σna
σan 
.
σn2
We denote the correlation coefficient for abilities by ρan =
σan
.
σn σa
Individuals face two choices: (a) a consumption choice, whereby they determine how to allocate their
total income between agricultural and non-agricultural goods; (b) an occupational choice, whereby
they choose whether to work in the non-agricultural sector or the agricultural sector. Working in
the agricultural sector involves operating a farm and is subject to idiosyncratic distortions ϕi as
will become clear once we specify the technologies. We denote the income individual i would earn
in agriculture as Iai and that in non-agriculture as Ini . The individual chooses the sector with the
highest net return. We abstract from barriers to labor mobility across sectors. We denote by Hn and
Ha , the sets of (ϕi , sai , sni ) values for which agents choose each sector Hn = {(ϕi , sai , sni ) : Iai < Ini },
and Ha = {(ϕi , sai , sni ) : Iai > Ini }.
25
Consumption Allocation To determine the allocation of income between agricultural and nonagricultural goods individuals maximize utility subject to their budget constraint, given their income
Ii + T , and the relative price of the agricultural good pa .The first order conditions to individual i’s
utility maximization problem imply the following consumption choices,
cai = a +
ω
(Ii − pa a) ,
pa
cni = (1 − ω) (Ii − pa a) .
Production – Non-agriculture The non-agricultural good is produced by a stand-in firm with
access to a constant returns to scale technology that requires only effective labor as an input,
Yn = An Zn ,
where Yn is the total amount of non-agricultural output produced, An is non-agricultural productivity (TFP), Zn is the total amount of labor input measured in efficiency units, i.e., accounting for
the ability of workers,
Z
sni di.
Zn =
i∈Hn
The total number of workers employed in non-agriculture is,
Z
Nn =
di.
i∈Hn
The representative firm in the non-agricultural sector chooses how many efficiency units of labor to
hire in order to maximize profits. The first order condition from the representative firm’s problem
in non-agriculture implies,
wn = An .
26
Production – Agriculture A described previously, the production unit in the agricultural sector
is a farm. A farm is a technology that requires the inputs of a farm operator with ability sai as well
as land (which also defines the size of the farm) and capital under the farmer’s control. The farm
technology exhibits decreasing returns to scale and takes the form used previously,
α 1−α γ
1−γ
yai = sai
`i ki
,
(22)
where ya is real farm output, ` is the land input, and k is the capital input.
An individual that chooses to operate a farm faces farm-specific taxes on output τiy , land input
τi` and capital input τik . In the data this set of taxes is identified by wedges recovered using the
framework in Section 1. Tax revenues are redistributed equally to the N workers regardless of
occupation, with T being the transfer per individual. The profit maximization problem for farm i
is given by,
max πi = pa (1 − τiy ) yai − 1 + τik rki − 1 + τi` q`i ,
(23)
`i ,ki
where (q, r) are the rental prices of land and capital.10 The first order conditions to farm operator
i’s problem imply that farm size, demand for capital input, output supply, and profits depend not
only on productivity but also on the farm-specific distortions,
`i = [γpa (1 − τiy )]
1
1−γ
"
1−α
r 1 + τik
ki = [γpa (1 − τiy )]
1
1−γ
yai = [γpa (1 − τiy )]
γ
1−γ
"
"
"
# γ(1−α)
1−γ
1−α
r 1 + τik
1−α
r 1 + τik
10
α
q 1 + τi`
# 1−αγ
"
1−γ
# 1−γ(1−α)
1−γ
α
q 1 + τi`
# γ(1−α)
"
1−γ
sai ,
(24)
αγ
# 1−γ
α
q 1 + τi`
sai ,
(25)
αγ
# 1−γ
sai ,
(26)
Note that here there is one rental price of land for the whole economy, as there is one market clearing for land,
as we abstract from the village layer.
27
πi = (1 − γ) γ
γ
1−γ
[pa (1 − τiy )]
"
1
1−γ
1−α
r 1 + τik
# γ(1−α)
"
1−γ
α
q 1 + τi`
αγ
# 1−γ
sai .
(27)
The income of a farmer is his real output. As a result farmer income includes not only the return
to the farmer’s labor input π but also the land and capital incomes.
We can re-write real farm output as,
yai = wa ϕi sai ,
where ϕi captures the overall farm-specific distortion faced by farmer i,
"
ϕi ≡
(1 −
1+
γ
# 1−γ
τiy )
1−α
τik
1 + τi`
α
,
and wa is the component of the farmer’s return that is common to all farmers,
wa ≡ (γpa )
γ
1−γ
1−α
r
αγ
γ(1−α)
1−γ
1−γ
α
.
q
Note that wa is a function of the endogenous relative price of agriculture pa , the rental price of land
q, and the rental price of capital r.
Idiosyncratic Distortions and Agricultural Abilities We allow for the possibility that idiosyncratic distortions and agricultural abilities are correlated. In particular, we assume a bivariate
log-normal distribution for (ϕi , sai ) with mean (µϕ , µa ) and variance,


Σa = 

σϕ2
σaϕ
28
σϕa 
.
σa2
We denote the correlation coefficient between agricultural ability and farm-specific distortions as
ρϕa =
σϕa
.
σϕ σa
Occupational choice Individuals can become farm operators in the agricultural sector or they
can become workers in the non agricultural sector. If individual i chooses to become a nonagricultural worker then their income is,
Ini = wn sni .
If individual i chooses to become a farm operator then his income is,
Iai = wa ϕi sai .
We note that these incomes are net of the transfer T , which is common to all individuals regardless
of occupation, and as a result does not affect the occupational choice. Individual i will choose
the sector that provides the highest possible income, given the individual’s triplet (ϕi , sai , sni ).
Individual i will choose agriculture, i.e. i ∈ Ha , if Iai > Ini and non-agriculture otherwise. As a
result individual i’s income is given by,
Ii = max {Iai , Ini } .
Market clearing conditions All markets clear.
Labor:
Na + Nn = N,
29
where Na =
R
i∈Ha
di. Land:
Z
L = Na
`i di.
i∈Ha
Capital:
Z
K = Na
ki di.
i∈Ha
Agricultural goods:
Z
Ya ≡ Na
Z
yai di = N
i∈Ha
5.2
Z
cai di + N
i∈Ha
cai di.
i∈Hn
Analysis
Next we derive the shares of individuals that choose each sector as well as the average log-ability
and average log-income of those that choose each sector. We establish some notation to show these
results.
We define deviations of log draws from means,
uai = log sai − µa ,
uni = log sni − µn ,
uϕi = log ϕi − µϕ .
Define the deviation of log effective agricultural ability from mean,
u
bai = log ϕi + log sai − µϕ − µa = uϕi + uai .
Note that uni is normally distributed with mean E (uni ) = 0 and variance V AR (uni ) = E (u2ni ) = σn2 .
30
In turn, u
bai is also normally distributed with mean E (b
uai ) = E (uϕi ) + E (uai ) = 0 + 0 = 0 and
variance,
V AR (b
uai ) = E u
b2ai = E (uϕi + uai )2 =
ba2 .
= E u2ϕi + u2ai + 2uϕi uai = σϕ2 + σa2 + 2ρϕa σϕ σa ≡ σ
The covariance of u
bai and uni is given by,
COV (b
uai , uni ) = E [(b
uai − E (b
uai )) (uni − E (uni ))] = E (b
uai uni ) =
= E [(uai + uϕi ) uni ] = E [uai uni ] + E [uϕi uni ] = σan = ρan σa σn .
Finally we note that (un − u
ba ) has mean and variance given by,
E (uni − u
bai ) = E (uni ) − E (b
uai ) = 0 − 0 = 0.
V AR (uni − u
bai ) = E (uni − u
bai )2 =
=E u
b2ai + u2ni − 2b
uai uni = σ
ba2 + σn2 − 2ρan σa σn ≡ σ 2 .
The log-income of individual i from agriculture and non-agriculture respectively is,
log (Iai ) = log (wa ) + log (ϕi ) + log (sai ) ,
log (Ini ) = log (wn ) + log (sni ) .
We can re-write agricultural and non-agricultural incomes as the sums of constants and log mean
deviations,
log (Iai ) = ba + uϕi + uai = ba + u
bai ,
log (Ini ) = bn + uni ,
31
where
ba ≡ log (wa ) + µϕ + µa ,
bn ≡ log (wn ) + µn .
Sectoral Employment The probability an individual chooses to become a farm operator in
agriculture,
na = P r {log (Iai } > log (Ini )) = P r (ba + u
bai > bn + uni ) =
uni − u
bai
ba − bn
>
.
= P r (ba − bn > uni − u
bai ) = P r
σ
σ
Let b ≡
ba −bn
σ
and note that ξi ≡
uni −b
uai
σ
is a standard normal random variable. Then,
na = Φ (b) ,
where Φ(.) is the standard normal cdf. Given that we have a continuum of individuals of mass
one, na is also the fraction of individuals that choose agriculture. Similarly, we can show that the
probability an individual chooses to become a worker in non-agriculture (and therefore the fraction
of individuals that choose non-agriculture) is,
nn = 1 − Φ (b) .
Note that Na = na · N and Nn = nn · N .
Sectoral Average Log-Ability Conditional on Sectoral Choice Mean log-ability in agriculture conditional on choosing agriculture,
E {log (sai ) |i ∈ Ha } = E {log (sai ) | log (Iai } > log (Ini )} =
32
= E {µa + [log (sai ) − µa ] | log (Iai } > log (Ini )} =
ba − bn
uni − u
bai
>
=
= µa + E uai |
σ
σ
COV (uai , ξi )
E (ξi |ξi < b) =
V AR (ξi )
uni − u
bai
= µa + E (uai ξi ) E (ξi |ξi < b) = µa + E uai
E (ξi |ξi < b) =
σ
= µa + E {uai |b > ξi } = µa +
= µa +
σan − σa2 − σϕa
E [uai (uni − u
bai )]
E (ξi |ξi < b) = µa +
E (ξi |ξi < b)
σ
σ
E {log (sai ) | log (Iai } > log (Ini )} = µa +
σan − σa2 − σϕa
E (ξi |ξi < b) ,
σ
or
E {log (sai ) |i ∈ Ha } = µa +
σa [ρan σn − σa − ρϕa σϕ ]
E (ξi |ξi < b) .
σ
(28)
Following the same steps as above we can show that mean log- effective ability conditional on
choosing agriculture is,
E {log (ϕi ) + log (sai ) |i ∈ Ha } = µϕ + µa +
σan − σ
ba2
E (ξi |ξi < b)
σ
(29)
Similarly average log-ability for those choosing non-agriculture is,
E {log (sni ) |i ∈ Hn } = E {log (sni ) | log (Iai } < log (Ini )} = µn +
σn2 − σan
E (ξi |ξi > b)
σ
or
E {log (sni ) |i ∈ Hn } = µn +
σn [σn − ρan σa ]
E (ξi |ξi > b)
σ
33
(30)
Note that (28) and (30) each contain a truncated standard normal variable, which implies that the
mean will be different from 0 (the unconditional mean). With lower tail truncation E [ξ|ξ ≤ b] < 0
and with upper tail truncation E [ξ|ξ > b] > 0. In particular, using the first moment of a truncated
standard normal distribution,
b2
e− 2
φ (b)
= −p
<0
E [ξ|ξ ≤ b] = λ (b) = −
Φ (b)
(2π)Φ (b)
b2
φ (b)
e− 2
E [ξ|ξ > b] = λ (b) =
=p
>0
1 − Φ (b)
(2π) [1 − Φ (b)]
Sectoral Average Log-Income Conditional on Sectoral Choice
5.3
E {log (Iai ) |i ∈ Ha } = ba +
σan − σ
ba2
E (ξi |ξi < b) .
σ
(31)
E [log (Ini ) |i ∈ Hn ] = bn +
σn2 − σan
E (ξi |ξi > b) .
σ
(32)
Calibration
Our strategy is to calibrate distortions, abilities, and sectoral selection in a Benchmark Economy
(BE) to the panel household-level data from China. We proceed in two steps. First, we infer
population parameters on abilities and distortions from observed moments on sectoral incomes.
Second, given the calibrated population moments in the first step, we calibrate the remaining
parameters from the general equilibrium equations of the sectoral model to match relevant data
targets. We now describe these steps in detail.
34
First Step There are 8 population parameters/moments to calibrate:
• 3 means — µa , µn , µϕ ,
• 3 variances — σa2 , σn2 , σϕ2 ,
• 2 covariances — σaϕ , σan .
These moments govern the occupational choices of individuals in the economy. We construct in the
model 8 moments on incomes, conditional on sectoral choices. We then solve an 8 by 8 system to
match the 8 empirical moments. We target the mean of the log of agricultural income, log nonagricultural income, and log distortions; the standard deviation of the log of agricultural income,
log non-agricultural income, and log distortions; the covariance of log agricultural income and
log distortions; and the covariance of log agricultural income and log non-agricultural income for
switches from agriculture to non-agriculture. The means in this step can be identified from the
data up to a constant. At this stage we restrict this constant to be such that at the aggregate
level, the occupational choices of individuals are consistent with the observed share of employment
in agriculture of 42% in China.
The following are the specific procedures we follow to recover the 8 population moments.
1. Recalling that in the model the share of employment in agriculture is given by na = Φ(b)
where Φ is the standard normal and b ≡
ba −bn
,
σ
we invert the standard normal to recover the
b that produces a share of labor in agriculture of na = 0.42. This gives a b = −0.20.
2. Recognizing that the 5 equations (put numbers...) on the variances and covariances are independent of the means, we solve this as a 5 × 5 system targeting 5 moments from the
data: variance of log agricultural income/output (d
v ara ); variance of log nonagricultural income (d
v arn ); variance of log distortions (d
v arϕ ); covariance of agricultural income/output and
35
distortions (cov
c aϕ ); covariance of agricultural income/output and non-agricultural income for
switchers, i.e., for those that were initially employed in agriculture and subsequently switched
to non-agriculture (cov
c an ). The 5 × 5 we solve is the following:
3. Variance of log-agricultural income conditional on choosing agriculture,
(
vd
ara = σ
ba2
1−
(
vd
arϕ = σϕ2
1−
(
vd
arn = σn2
1−
2
σϕ2 + σaϕ
σσϕ
2
σn2 − σan
σσn
2
)
λ (b) [λ (b) − b]
)
λ (b) [λ (b) − b]
)
λ (b) [λ (b) − b]
σϕ2 + σaϕ
σ
σan − σ
ba2
σ
σn2 − σan
σ
σan − σ
ba2
σ
cov
c aϕ = σaϕ −
cov
c an = σan +
σan − σ
ba2
σb
σa
1 + λ (b) b − λ (b)2
1 + λ (b) b − λ (b)2
4. Given the variances/covariances, we use the three equations on the conditional means to get
the population means.
E {log (Iai ) |i ∈ Ha } = ba +
E {log (ϕi ) |i ∈ Ha } = µϕ −
E [log (Ini ) |i ∈ Hn ] = bn +
σan − σ
ba2
λ (b)
σ
σϕ2 + σaϕ
σ
λ (b)
σn2 − σan
λ (b)
σ
Note that ba = log(wa ) + µa + µϕ and bn = log(wn ) + µn . However, there is no guarantee that
the implied ba and bn from the above equations will reproduce b =
ba −bn
σ
required to ensure
na = 0.42. But notice that the conditional mean log equations for incomes above are exactly
36
the same as conditional mean log equations for effective abilities save for a constant in each
case,
E {log (ϕi sai ) |i ∈ Ha } = µa + µϕ +
E [log (sni ) |i ∈ Hn ] = µn +
σan − σ
ba2
λ (b) ,
σ
σn2 − σan
λ (b) .
σ
This implies that the gap in mean log income between agriculture and non-agriculture is
equal to the mean log effective ability gap save for a constant x = log(wa ) − log(wn ). We
use this insight to recover the population means for agricultural ability, distortions, and nonagricultural ability from the observed means (m
b a, m
b n, m
b ϕ ):
σan − σ
ba2
λ (b)
m
b a = µa + µϕ +
σ
m
b ϕ = µϕ −
m
b n = µn +
σϕ2 + σaϕ
σ
λ (b)
σn2 − σan
λ (b)
σ
5. We pick the constant x to reproduce the b implied by na = 0.42. This implies x = 4.1.
The results of this procedure are summarized in Table 1. Note that the correlation of abilities
across sectors is positive and equal to 0.35 as implied by the estimates of the covariance of abilities
and the variances of income in each of the sectors. Because of the positive correlation of abilities
in agriculture and non-agriculture, and a higher dispersion of ability in the non-agricultural sector
than of effective abilities in the agricultural sector, the selection pattern across sectors results in
more-abled individuals choosing to work in the non-agricultural sector. This pattern suggests that
removing misallocation in the agricultural sector would dampen the selection in occupational choice
whereby more productive individuals would find it optimal to work in agriculture. We pursue this
quantitative experiment in the next section.
37
Table 1: Calibrated Population Moments
Population Moments
(calibrated)
Observed Moments
(targets)
Parameter
Description
Value
µa
µn
µϕ
mean ag. ability
mean nonag. ability
mean distortion
10.3
6.9
-7.9
mean ag. income
mean nonag. income
mean farm wedges
2.7
7.9
-7.2
σa
σn
σϕ
STD ag. ability
STD nonag. ability
STD distortion
0.43
1.78
1.41
STD ag. income
STD nonag. income
STD farm wedges
0.88
1.32
1.28
σaϕ
σan
COV ag. ability-distortions
COV ag.-nonag. ability
-0.66
0.26
STD farm wedges
COV ag.-nonag. income
of switchers
-0.59
0.11
Note: All variables refer to logs.
38
Description
Value
Table 2: Benchmark Economy (BE)
Statistic
Value in BE
Real Agr. Labor Productivity
Share of Employment in Agr.
Non-Agr. to Agr. Productivity Gap
Average Effective Ability in Agr.
Average Ability in Non-Agr.
Ratio of Non-Agr. to Agr. Ability
1,311.7
0.42
2.5
39.0
317.3
8.1
Second Step We calibrate the remaining parameters given the recovered population moments in
the first step. The parameters to calibrate in this step are: An productivity in non-agriculture which
is normalized to 1; (α,γ) the elasticity parameters in the technology to produce the agricultural
good, which are set to α = .66 and γ = .54, following our analysis of measuring farm TFP and
misallocation in agriculture in Section 4; φ, the weight of the agricultural good in preferences, is
set to 0.01 to match a long run share of employment in agriculture of 1%; the endowments in
agriculture of capital and land Ka , L, are set to match a capital output ratio in agriculture of 0.3
and an average farm size of 0.45 hectares, both observed in our micro data. We then solve the
equilibrium of the model to obtain ā and Aa , the subsistence consumption of agricultural goods in
preferences and the productivity in agriculture to match a share of employment in agriculture of 42%
and the ratio of average non-agriculture to agricultural labor productivity of 2.5. The benchmark
economy reproduces exactly the data targets and we report additional statistics on this economy in
Table 2.
5.4
Results
We perform the following counterfactual experiment. We eliminate the correlation of ability and
distortions (i.e., set σaϕ = 0). In the data, more able farmers face larger distortions as they are
39
unable to operate larger farms (i.e., obtain more land and capital for their operation). This suggests
that eliminating distortions will have an important effect in the occupational choice of more-abled
farmers, which in turn will substantially increase agricultural productivity.
Note that in this experiment there is still misallocation related to the dispersion of distortions. As
we discussed previously, in the data there are two types of misallocation: misallocation of factors
across farmers with different productivity, as well as misallocation of factors among farmers with
the same productivity, each of which accounts for roughly 50% of the efficient reallocation gains.
In this experiment, we only eliminate the distortions across farmers with different productivity and
only eliminate misallocation due to within village distortions and across village capital distortions.
As a reference for comparison, consider that the “static” gains of the efficient reallocation from
eliminating these distortions increases aggregate agricultural TFP by 24%.
The results of this quantitative experiment are summarized in Table 3. We find that agricultural
labor productivity rises by 74% (a threefold factor increase compared with the static gains of
reduced misallocation). As a consequence of this increase in productivity, the share of employment
in agriculture drops 17 p.p. (from 42% to 25%). Aggregate agricultural productivity increases
for two reasons. First, given a fixed set of farmers in agriculture, reduced misallocation improves
productivity. Second, reduced misallocation via eliminating systematic distortions to high ability
farmers improves occupational choice based more closely on comparative advantage. This raises the
average ability of farmers remaining in the agricultural sector. This result shows that correlated
distortions substantially affect occupational choices.
In the context of our model, improvements in resource allocation in agriculture produce an increase
in aggregate agricultural productivity and labor reallocation away from agriculture. The same
effects can be reproduced through an appropriate increase in agricultural TFP or economy-wide
TFP. To put our results from reduced misallocation in context, we ask: What increase in agriculturespecific TFP or economy-wide TFP is needed to generate the same effect on labor reallocation as
40
Table 3: Results of Counterfactual Experiment σaϕ = 0
Statistic
BE
Real Agricultural Productivity (Ya /Na )
1.00
Share of Employment in Agriculture (Na ) (%)
0.42
Real Non-Agricultural Productivity (Yn /Nn )
1.00
Average Effective Ability in Agriculture (Ẑa /Na ) 1.00
Average Ability in Non-Agriculture (Zn /Nn )
1.00
Ratio of Non-Agr. to Agr. Ability
1.00
σaϕ = 0
1.74
0.25
0.79
3.47
0.79
0.23
All variables, except the share of employment in agriculture, are relative to the same statistic in the Benchmark
Economy (BE). The counterfactual σaϕ = 0 eliminates the covariance between farm-level distortions and productivity
in agriculture.
observed in the counterfactual of reduced misallocation? In order to reproduce the same impact on
labor reallocation (and roughly the same effect on real aggregate agricultural productivity) a 75%
increase in TFP would be needed in each case. This is a very large increase in TFP that is required
to generate the same impact as reduced misallocation.
We emphasize that changes in occupational choices and selection are markedly different if they are
driven by changes in patterns of misallocation rather than changes in sector-specific or economywide TFP which are common to all individuals. To appreciate this point note that changes in
economy-wide TFP only have an effect on occupational choices and selection through general equilibrium effects whereas reduced misallocation via changes in idiosyncratic distortions can alter the
pattern of occupational choices and selection even holding constant aggregate prices. To illustrate
quantitatively the importance of this distinction, we pursue the following counterfactual. In the
first experiment we increase agriculture TFP (Aa ) by 24% and in the second experiment we increase
economy-wide TFP (Aa , An ) by 24%. Recall that 24% is the increase in aggregate agricultural TFP
from eliminating correlated distortions while holding fixed the set of farmers in agriculture. Table
4 summarizes the results from these counterfactuals compared with our baseline counterfactual of
no correlation of ability and distortions σaϕ = 0.
41
Table 4: Results of Other Counterfactual Experiments
Statistic
σaϕ = 0
Real Agricultural Productivity (Ya /Na )
Share of Employment in Agriculture (Na ) (%)
Real Non-Agricultural Productivity (Yn /Nn )
Average Effective Ability in Agriculture (Ẑa /Na )
Average Ability in Non-Agriculture (Zn /Nn )
Ratio of Non-Agr. to Agr. Ability
1.74
0.25
0.79
3.47
0.79
0.23
↑ Aa ↑ (Aa , An )
(24%)
(24%)
1.26
0.35
0.90
1.05
0.90
0.89
1.26
0.35
1.11
1.05
0.90
0.89
All variables, except the share of employment in agriculture, are relative to the same statistic in the Benchmark
Economy (BE). We choose the increase in agricultural and economy-wide TFP of 24% which is the TFP gain from
eliminating correlated distortions for a constant set of farmers.
Our results are striking. A 24% increase in TFP produces an increase in agricultural labor productivity of 26%. This is an amplification of only 1.08-fold generated by selection and the reallocation
of labor from agriculture to non-agriculture as the share of employment in agriculture falls from
42% to 35%). Alternatively, eliminating correlated distortions which we showed particularly affect
productive farmers, results in a much larger effect on agricultural productivity of 74%, representing
an amplification effect of 3.08-fold. This is due to both a stronger effect on selection in agriculture
and, as a consequence, a stronger effect on labor reallocation, with the share of employment in
agriculture falling to 25%.
This result is important as the literature has struggled to find measurable drivers of sectoral reallocation and increased productivity in agriculture relative to non-agriculture. Lagakos and Waugh
(2013) for example have proposed selection as an important amplification mechanism, emphasizing
differences in economy-wide productivity as an important driver. However, restricting economywide productivity differences to observed labor productivity differences in non-agriculture between
rich and poor countries, selection generates an amplification effect (an increase in agricultural productivity over and above non-agricultural productivity) which is only a factor of 1.4-fold versus the
42
10.7-fold observed in the data (see Table 5 in Lagakos and Waugh (2013)). In this paper, we provide
a measure of idiosyncratic distortions in agriculture and a quantitative assessment of the importance of this specific driver of low agricultural productivity in the context of an otherwise standard
model of farm size and occupational selection. Our results show that agricultural distortions in
the Chinese economy have a strong effect on occupational choices and selection, generating both
a direct effect on agricultural productivity and an amplification effect that is orders of magnitude
larger than the effect from aggregate distortions or economy-wide productivity differences.
6
Conclusions
Our estimates from a simple quantitative framework and micro panel data for China suggest that
capital and land are severely misallocated across productive farmers. Given the institutional characteristics in China, we associate factor misallocation to restrictions in the land market, which also
dampen access to credit to farmers. The allocation of land-use rights is such that individuals have
fairly equal amounts of land input, suggesting that the more productive farmers face larger wedges.
We find that the resulting pattern of misallocation shows no systematic tendency to improve over
time which is consistent with the constant institutional restrictions in the Chinese economy. We
find that the reallocation gains to an efficient allocation of factors would increase aggregate output
(and TFP) by 84%, with 60% of these gains attributed to within-village reallocation of capital and
land.
Using our summary measure of idiosyncratic distortions (wedges) across farmers in China, we develop and estimate a two-sector general-equilibrium model of occupational selection. The panel data
provide us with information on income in agriculture and wages in non-agriculture for individuals
that switch occupations, which we use to restrict the correlation of abilities across sectors in the
population. We find that measured distortions substantially affect the observed distribution of farm
43
TFP in the Chinese data and that eliminating the correlation of these distortions with farmer’s ability improves aggregate agricultural productivity via reduced misallocation and improved selection
of better able farmers into agriculture. This effect substantially contributes to structural change
and growth.
44
References
Adamopoulos, T. and Restuccia, D. (2014). The Size Distribution of Farms and International
Productivity Differences. American Economic Review, 104(6):1667–97.
Adamopoulos, T. and Restuccia, D. (2015). Land Reform and Productivity: A Quantitative Analysis with Micro Data.
Benjamin, D. and Brandt, L. (2002). Property rights, labour markets, and efficiency in a transition
economy: the case of rural china. Canadian Journal of Economics, pages 689–716.
Benjamin, D., Brandt, L., and Giles, J. (2005). The evolution of income inequality in rural china.
Economic Development and Cultural Change, 53(4):769–824.
Benjamin, D., Brandt, L., and Giles, J. (2011). Did higher inequality impede growth in rural
china?*. The Economic Journal, 121(557):1281–1309.
Brandt, L., Tombe, T., and Zhu, X. (2013). Factor market distortions across time, space and sectors
in china. Review of Economic Dynamics, 16(1):39–58.
Chen, C. (2015). Land Tenure, Occupational Choice and Agricultural Productivity,. Unpublished
manuscript, University of Toronto.
de Janvry, A., Emerick, K., Gonzalez-Navarro, M., and Sadoulet, E. (2014). Delinking land rights
from land use: Certification and migration in mexico.
Gollin, D., Parente, S., and Rogerson, R. (2002). The Role of Agriculture in Development. American
Economic Review, 92(2):160–164.
Hsieh, C.-T. and Klenow, P. J. (2009). Misallocation and Manufacturing TFP in China and India.
The Quarterly Journal of Economics, 124(4):1403–1448.
Lagakos, D. and Waugh, M. E. (2013). Selection, agriculture, and cross-country productivity
differences. The American Economic Review, 103(2):948–980.
Lucas Jr, R. E. (1978). On the size distribution of business firms. The Bell Journal of Economics,
pages 508–523.
Restuccia, D. and Rogerson, R. (2008). Policy Distortions and Aggregate Productivity with Heterogeneous Plants. Review of Economic Dynamics, 11(4):707–720.
Restuccia, D. and Rogerson, R. (2013). Misallocation and Productivity. Review of Economic
Dynamics, 16(1):1–10.
Restuccia, D. and Santaeulalia-Llopis, R. (2015). Land misallocation and productivity. Unpublished
manuscript, University of Toronto.
Restuccia, D., Yang, D. T., and Zhu, X. (2008). Agriculture and aggregate productivity: A quantitative cross-country analysis. Journal of Monetary Economics, 55(2):234–250.
45
Roy, A. D. (1951). Some thoughts on the distribution of earnings. Oxford economic papers, 3(2):135–
146.
Zhu, X. (2012). Understanding chinas growth: Past, present, and future (digest summary). Journal
of Economic Perspectives, 26(4):103–124.
46
A
Planner’s Problem
Within-village allocation Let the village-level Lagrange multipliers on the land and capital
resource constraints be respectively λLv and λKv . Taking the first order conditions with respect to
(`vi , kvi ) implies that the capital-land ratio will be the same across technologies within villages and
equal to,
1 − α λLv
kvi
=
`vi
α λKv
The allocation of land and labor to technology i as a function of the village-level shadow prices is:
`vi =
α
λLv
kvi =
1−γ(1−α)
1−γ
α
λLv
γα 1−γ
1−α
λKv
1−α
λKv
γ(1−α)
1−γ
1
γ 1−γ svi
1−γα
1−γ
1
γ 1−γ svi
Plugging these into the village-level resource constraints for land and capital we can solve for the
shadow prices of land and capital in village v:
λLv =
γ(1−α)
Kv
αγ 1−αγ
Lv
λKv = (1 − α)
Mv
X
!1−γ
svj
j=1
Mv
X
Lγα
v
1−γ(1−α)
Kv
!1−γ
svj
j=1
Across-village allocation Let λ be the Lagrange multiplier on the aggregate labor resource
constraint. Taking the first order condition with respect to Kv implies a labor allocation as a
function of the multiplier,
1
1−γ(1−α)
(1 − α)γ
αγ
Kv =
Av Lv
λ
Plugging this into the resource constraint solves for the multiplier,
(1 − α)γ
λ = 1−γ(1−α)
K
( V
X
(Av Lαγ
v )
1
1−γ(1−α)
)1−γ(1−α)
v=1
Plugging this back into the first order condition we can solve for the share of labor allocated to
village v,
1
1−γ(1−α)
Kv
(Av Lαγ
v )
= PV
1
N
(Ah Lαγ ) 1−γ(1−α)
h
h=1
47