Journal of Agricultural Economics, Vol. 66, No. 2, 2015, 442–469
doi: 10.1111/1477-9552.12086
Considering Technical and Allocative
Efficiency in the Inverse Farm
Size–Productivity Relationship
Heath Henderson1
(Original submitted October 2013, revision received May 2014, accepted August
2014.)
Abstract
In the leading explanations for the oft-observed inverse relationship (IR) between
farm size and productivity in developing country agriculture, labour market imperfections have commonly occupied a central role. However, an emerging literature
suggests that disparities in technical or allocative efficiency may be driving productivity differentials. Using nationally-representative panel data from Nicaragua,
we develop and employ a four-stage empirical framework to simultaneously test
the competing explanations for the IR. While efficiency differences exert a significant impact on all productivity indicators, their explanatory power is insufficient
to rule out labour market imperfections as the driving force behind the
relationship.
Keywords: Inverse relationship; farm size–productivity; technical and allocative
efficiency; smallholder agriculture; Latin America; Nicaragua; labour market.
JEL classifications: D24, O13, Q15.
1. Introduction
While the existence of an inverse relationship (IR) between farm size and productivity is a relatively well-established empirical regularity in developing country agriculture,2 the explanation for the relationship remains unclear. Moreover, it is the
1
Heath Henderson is with the Department of Economics, Iowa State University, 166D Heady
Hall, Ames, Iowa, USA. E-mail: [email protected]. The author would like to thank Paul
Winters, Amos Golan, and Alan Isaac for the numerous comments and discussions they so graciously provided throughout the duration of the project. Thanks are also due to anonymous referees for their helpful comments on earlier drafts.
2
The earliest empirical accounts of this finding are associated with India’s Studies in the Economics of Farm Management. See Sen (1962), Bardhan (1973), Yotopoulos and Lau (1973), and
Carter (1984) for examples. For influential cross-country studies illustrating the universality of
the IR, see Barraclough and Collarte (1973), Berry and Cline (1979) and Cornia (1985). Finally,
for more recent assertions of the existence of an IR in developing country agriculture, see van
Zyl et al. (1995), Heltberg (1998) or Deininger et al. (2003).
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explanation that is of genuine policy relevance. To the extent that the IR provides
justification for land access policies that reallocate land toward the lesser endowed
(World Bank 2008, 90–91), ascertaining the potential net gains from such policies
depends on the long-term stability of the relationship, which in turn depends on the
underlying forces driving productivity differentials. In considering the rather large
body of theoretical and empirical literature exploring the topic, five competing
hypotheses can be distinguished: (i) decreasing returns to scale; (ii) land quality heterogeneity; (iii) differential responses to uncertainty; (iv) labour market imperfections; and (v) differences in technical and/or allocative efficiency. Though the
returns to scale, land quality heterogeneity, and uncertainty explanations have been
found in the empirical literature to lack explanatory power, the labour market
imperfections and efficiency differences hypotheses have both received ample
support.
Regarding returns to scale, Heady and Dillon (1961), Cline (1970), as well as
Hayami and Ruttan (1970) provided the earliest illustrations of the existence of
constant returns to scale in developing country agriculture. Other influential assertions of this finding include Yotopoulos and Lau (1973), Bardhan (1973), Berry
and Cline (1979), Carter (1984) and Cornia (1985). The IR is thus infrequently
attributed to decreasing returns to scale. Similarly, land quality heterogeneity and
differential responses to uncertainty are both explanations that appear to have faltered under empirical scrutiny. While Bhagwati and Chakravarty (1969), Bhalla
and Roy (1988), and Benjamin (1995) all contended that land quality differences
potentially hold considerable explanatory power, the analyses of Barraclough and
Collarte (1973), Carter (1984), and Barrett et al. (2010) suggest that controlling
for land quality differences at best weakens the observed IR in most contexts.
With respect to differential responses to uncertainty, Srinivasan (1972) illustrated
theoretically that, in the face of uncertainty due to the vagaries of weather, it may
indeed be optimal for smaller farmers to use more labour per hectare than larger
producers, thus generating an IR. However, in the empirical realm, Rosenzweig
and Binswanger (1993) found that while profit rates of small farmers always
exceeded those of wealthier farmers, increasing rainfall variability tended to equalise profit rates across wealth classes. The authors suggested that in riskier environments farmers select asset portfolios less sensitive to rainfall variability and
efficiency losses associated with risk mitigation are higher among lesser-endowed
farmers.
In contrast to considerations of returns to scale, land quality, and uncertainty, the
labour market imperfections hypothesis has received considerable theoretical and
empirical support. While Sen’s (1966) ‘dual labour market’ theory was among the
first appeals to the centrality of labour market imperfections, Eswaran and Kotwal
(1986) is perhaps the more celebrated exposition of the phenomenon. Eswaran and
Kotwal (1986) modeled an agrarian economy where agents face two primary constraints in their optimization problem: (i) a working capital or credit constraint
where access to credit largely depends on the amount of land an agent owns, and
(ii) a time or supervision constraint where hired labour is only an imperfect substitute for one’s own labour time due to moral hazard. Given such factor market
imperfections and examining the equilibrium allocation of resources, the authors
found land-to-labour ratios to be increasing in land endowments, which implied an
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Heath Henderson
IR between land productivity and land endowments.3 Regarding empirical investigation of the hypothesis, the productivity differentials observed by Barraclough and
Collarte (1973), Berry and Cline (1979), Carter (1984) and Cornia (1985) were all
said to follow from a more intensive use of land and higher per hectare resource
inputs on small farms. Further, more recent investigation employing the ‘market
imperfections framework’ (further discussed below) has suggested that supervision
and transaction costs associated with hired labour on large farms are the likely cause
of the IR (Binswanger et al., 1995; van Zyl et al., 1995; Heltberg 1998; Deininger
et al., 2003).
While the labour market imperfections hypothesis has become a leading explanation for the IR, a seemingly parallel line of inquiry has emerged suggesting that disparities in technical and/or allocative efficiency across the farm size spectrum may
be driving productivity differentials. Yotopoulos and Lau (1973) developed and
applied an empirical model to test for the relative technical and allocative efficiency
of Indian agricultural producers and found that small farms displayed approximately 20% greater technical efficiency, which was said to have induced greater
profitability on those farms. Bravo-Ureta and Pinheiro (1997), examining peasant
farmers in the Dominican Republic, exploited the self-dual nature of the CobbDouglas production function to decompose profit efficiency into its constituent elements (i.e. technical, allocative and economic efficiency),4 and found that mediumsized farmers (those operating between 3.25 to 6.5 hectares) were the most technically, allocatively, and economically efficient. In a final noteworthy study, Helfand
and Levine (2004) used data envelopment analysis to explore the relationship
between farm size and technical efficiency in the Centre-West of Brazil, and found a
U-shaped relationship between farm size and technical efficiency.5 Therefore, technical and/or allocative efficiency differences may exert considerable influence on productivity outcomes, and represent a potentially important source of omitted variable
bias, primarily in those analyses espousing the labour market imperfections
hypothesis.
This discussion suggests that labour market imperfections and considerations of
technical and/or allocative efficiency both appear to be reasonable explanations for
the IR. As such, we put forth the following research question: Do asymmetric market
imperfections continue to hold explanatory power when controlling for efficiency differences between large and small agricultural producers? In an attempt to address this
question, we develop a four-stage empirical framework to simultaneously test the
competing accounts for the IR. To date, there does not appear to exist an empirical
inquiry that jointly considers these explanations and our primary contribution is an
attempt to remedy this shortcoming in the literature. In applying the empirical framework, we look at the case of Nicaragua where evidence of a labour market imperfections-induced IR (Deininger et al., 2003) coincides with the finding of efficiency
3
That is, where credit market imperfections preclude the equalising of factor ratios across producers, the relatively low shadow price of labour witnessed by lesser endowed producers – as
occasioned by labour market imperfections – may induce an IR.
4
A producer is fully profit efficient if, and only if, that producer is technically, allocatively and
scale efficient (Forsund et al., 1980). However, under constant returns to scale, scale efficiency is
irrelevant. Further, note that economic efficiency is simply a composite (i.e. the product) of
technical and allocative efficiency.
5
Technical inefficiency increased for farms up to 1,000–2,000 hectares and fell thereafter.
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differences between small and large producers (Abdulai and Eberlin 2001).6 Further,
in addition to the presence of an IR, the data suggest the existence of constant returns
to scale and the persistence of productivity differentials after controlling for land quality heterogeneity, all of which imply that the Nicaraguan case appears representative
and, as such, of general interest.
After discussing Nicaragua’s nationally-representative LSMS-type panel data
(for the years 1998, 2001 and 2005) (section 2), we elaborate upon the four-stage
empirical framework through which we investigate the existence and explanation
of an IR between farm size and productivity in Nicaragua’s agricultural and livestock sector (section 3). In turning to the results of the analysis (section 4), it
appears that, while technical and allocative efficiency differences frequently exert a
statistically significant impact on alternative productivity indicators across different
samples, the explanatory power of these variables is evidently insufficient to rule
out labour market imperfections as the driving force behind the observed IR. We
conclude with an elaboration of the policy implications of these findings (section
5).
2. Data
Nicaragua’s Encuesta Nacional de Hogares Sobre Medici
on de Nivel de Vida
(EMNV) is a nationally-representative living standards measurement survey that
contains detailed information regarding household characteristics, individual-level
demographic traits, health and education levels, household expenditure and income
information, and considerable data on agricultural and livestock production. The
EMNV is panel in nature and consists of 4,209, 4,191, and 6,879 observations in the
years 1998, 2001, and 2005, respectively. Of the households surveyed, not all were
involved in agricultural or livestock production. As such, the sample is restricted
according to the dual criteria that included households reported operating land for
agricultural and/or livestock purposes as well as reported non-zero revenue from
those activities,7 which leaves 1,385, 1,491, and 2,867 observations across the
3 years.
The EMNV is then an unbalanced panel. Of the 5,743 observations, there were
3,813 distinct households surveyed, where 640 households were surveyed in all
3 years, 650 were surveyed in 2 of the 3 years, and the remainder were only
6
While Abdulai and Eberlin (2001) did not specifically examine the relationship between farm
size and efficiency, the authors did find that family size and access to credit displayed a positive
and significant impact on technical efficiency. Accordingly, producers heavily reliant on family
labour (i.e. small farms) are likely to witness greater technical efficiency. However, such efficiency gains may be partially offset by a lack of access to credit as small-scale producers are less
likely to possess the necessary collateral.
7
There are a few households in the sample that reported land operated but no revenue. The
decision was made to drop these households for the simple reason that revenue is a crucial variable in the analysis and requires logarithmic transformation for the production frontier. This is
not possible with zero values. With uncertainty regarding the reason for the zero values, dropping the households is preferable to some arbitrary scaling of the revenue variable. Only 21, 11
and 9 households in 1998, 2001, and 2005, respectively, were dropped as a result of the revenue
criteria.
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surveyed once.8 Based on the population census of 1995, the 1998 survey sampled
the population by (i) random selection of census segments (50–60 households per
segment) with probabilities of selection proportionate to population size and (ii)
random selection of a fixed number of households in each segment (12 in urban
segments and 10 in rural segments). The 2001 sample included all households surveyed in 1998 that remained within their respective segment, any households that
did not respond to the 1998 survey, and a number of new households. The 2005
survey took a similar approach, but selection of new households were based on the
2005 population census. All data, unless otherwise noted, was compiled and disseminated by the FAO’s Rural Income Generating Activities (RIGA) project (RIGA,
2011).
Of specific interest are the agriculture/livestock modules of the respective surveys.
Each year of administration collected comprehensive information regarding the value
of output, size of landholdings (both owned and operated), quantity of household
and hired labour used, value of agricultural/livestock assets, and expenditure on seeds,
fertilisers, pesticides, etc., among other information. Table 1 defines all variables relevant to the analysis and Table 2 reports descriptive statistics by year. Unless noted
otherwise, all variables reported in value terms are normalised by a producer’s (output) price index9 (base year 1998) derived from data available through the FAO’s
FAOSTAT (FAO, 2011). To get an understanding of the sample and the Nicaraguan
agricultural/livestock sector in general, it is beneficial to highlight some of the
statistics.
While per capita consumption is not used in the analysis, it provides a useful starting point. The EMNV defined the nominal national poverty line at 4,259 (2,246),
5,157 (2,691), and 7,155 (3,928) c
ordoba for the years 1998, 2001, and 2005, respectively (extreme poverty line in parentheses).10 With mean nominal per capita consumption at 4,513, 5,492 and 7,207 c
ordoba, it is clear that the average household
hovers just slightly above the national poverty line. However, sample means do not
8
As pointed out by an anonymous referee, attrition is a potential issue. Of the 1,385 households
observed in 1998, 640 were also observed in 2001 and 2005. Further, 290 of the 1,385 households were observed in 1998 and one additional year. The remaining households were only
observed in the first year. Accordingly, following the widely used diagnostics outlined in Becketti et al. (1988) and Fitzgerald et al. (1998), a battery of attrition tests was conducted to
address concerns of attrition bias. A subset of these results – the Fitzgerald et al. (1998) attrition probits – are presented in Table S1 in the online Appendix (full results available upon
request). The outcomes of the attrition tests decidedly suggest that the below-discussed regression estimates are not subject to any appreciable attrition bias. Thus, to avoid undue complication of the econometric analysis, we refrain from using any potential correction procedures.
9
The commodities included in the index are those with price and quantity data available in each
year in question. The list of goods is as follows: bananas, beans, cabbages, cassava, cattle meat,
chicken meat, cocoa beans, coffee, cow milk, fresh fruit, goat meat, groundnuts, hen eggs, horse
meat, maize, pig meat, pineapples, plantains, potatoes, rice, seed cotton, sesame seed, sheep
meat, sorghum, soybeans, tobacco and tomatoes. The index is a Fisher index, which is calculated as the geometric mean of the Laspeyres and Paasche indexes (see Coelli et al. (2005) for
the specific calculation). An anonymous reviewer suggested that deflation can be problematic if
relative prices changed considerably throughout the period in question. Inspection of the available price series reveals that changes in relative prices from 1998 to 2005 were, however, minimal. Price data and depictions of relative price movements are available upon request.
10
In April of 2005, 1 USD = 16.30 c
ordoba.
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Table 1
Variable definitions
Variable
Definition
Age
Assets
Age of the household head
Value of agricultural and forestry assets (ploughs, tractors,
trucks, and seeding, harvesting, fumigation and irrigation
equipment) as well as the value of livestock (cattle, pigs, horses,
poultry, etc.) (c
ordoba)
Distance to nearest health centre (kilometres)
Years of education of the household head
The total value of output less all cash expenditures where cash
expenditures includes agricultural and forestry (i.e. land rental,
hired labour, seeds, fertiliser, pesticides, etc.) as well as livestock
outlays (i.e. feed, medical, enclosure, etc.) (c
ordoba)
Gender of the household head (Female = 1)
Number of female household members between the ages of 14
and 60 years
Number of federal or local government programmes from which
the household benefits
Days of hired labour employed for agricultural or livestock
production
Days of household labour employed for agricultural or livestock
production
Indigenous household as determined by the native language of
the household head (Indigenous = 1)
Number of male household members between the ages of 14 and
60 years
Marriage status of the household head (Married = 1)
Median reported daily wage by municipality (c
ordoba)
Land owned plus land rented, borrowed, or sharecropped from
others less land rented, borrowed, or sharecropped to others
(manzanas)
Value of agricultural (seeds, fertiliser, pesticides, etc.) and
livestock inputs (feed, medical, enclosure, etc.) (c
ordoba)
Quantity of cultivable land, pastureland, or forestland owned
(manzanas)
Yearly household consumption divided by the reported number
of household members (c
ordoba)
Share of income from wage labour, off-farm self-employment,
and non-labour sources (remittances, pensions, interest, etc.)
The value of output is the sum of revenue from agricultural and
livestock production. Agricultural revenue includes the sale of
crops and crop by-products, the value of own crop consumption
as well as sales and the value of own consumption from forestry
production. Livestock revenue includes the sale of livestock and
livestock by-products as well as the value of own livestock
consumption (c
ordoba).
Distance to health centre
Education
Farm value added
Female
Female labour
Government programmes
Hired labour
Household labour
Indigenous
Male labour
Married
Municipality wage
Operated
Other variable inputs
Owned
Per capita consumption
Share
Value of output
tell the entire story as 65 (27)%, 63 (24)%, and 66 (26)% of the sample fall below the
poverty line in the respective years (percent below extreme poverty line in parentheses). Even though it can be shown that the real poverty line increased moderately
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Heath Henderson
Table 2
Descriptive statistics by year
1998
Variable
Age
Assets
Distance to health centre
Education
Farm value added
Female
Female labour
Government programmes
Hired labour
Household labour
Indigenous
Male labour
Married
Municipality wage
Operated
Other variable inputs
Owned
Per capita consumption*
Share
Value of output
N
Mean
2001
SD
46.31
15.73
5,510.57 8,663.81
5.04
5.98
2.20
3.00
4,708.00 5,160.44
0.11
0.32
1.42
0.96
0.93
1.00
39.85
110.65
352.23
241.19
0.03
0.17
1.58
1.04
0.46
0.50
28.44
8.73
14.17
26.02
563.88
838.92
18.05
39.65
4,513.04 5,576.06
43.66
45.09
6,726.41 6,457.24
1,385
Mean
2005
SD
47.43
15.70
9,422.76 15,041.39
6.20
9.58
2.27
3.09
7,177.56
7,302.92
0.13
0.33
1.51
0.99
1.26
1.46
40.16
128.15
357.71
235.65
0.04
0.20
1.64
1.12
0.47
0.50
36.07
9.18
12.57
21.71
509.12
697.08
15.63
33.45
5,492.36
5,242.95
49.48
39.90
10,170.59
9,858.94
1,491
Mean
SD
47.03
15.82
11,272.08 20,279.45
5.54
7.42
3.33
4.01
10,165.07 11,896.11
0.23
0.42
1.44
0.99
1.40
1.32
45.59
124.78
579.78
314.16
0.06
0.25
1.43
1.06
0.41
0.49
36.53
7.77
14.49
24.23
631.10
840.41
18.29
38.71
7,206.57
6,509.62
49.27
38.72
11,198.62 12,468.50
2,867
Note: *Per capita consumption is in nominal terms.
throughout the survey period, it appears poverty remained quite prevalent despite the
value of output and farm value-added trending definitively upwards from 1998 to
2005.
Looking to the share of income from off-farm activities (i.e. Share), it can be seen
that the incomes of the sampled households, on average, were not solely derived from
agricultural and livestock production. However, those activities did provide a large
share of total income, being 56%, 51% and 51% in each year.11 Given the central role
of agriculture and livestock production (and, of course, the objective of the analysis),
it is of most importance to touch upon the land endowments of the sampled households. With mean land owned at 18.05, 15.63, and 18.29 manzanas and mean land
operated at 14.17, 12.57, and 14.49 manzanas12 for 1998, 2001 and 2005, respectively,
it would appear that the average household possesses a non-negligible quantity of
land. Again, however, the sample means can be misleading here as 60 (56)%, 57
(55)% and 56 (54)% of households owned (operated) less than five manzanas in each
year, respectively. Therefore, a relatively small number of large farms push mean land
owned and mean land operated definitively upward. Similar trends are observed when
examining the value of agricultural/livestock assets possessed (i.e. Assets).
11
The share of income from agriculture and livestock activities is simply one minus the share of
income from off-farm activities.
12
1 manzana = 0.70 hectares.
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As a final data consideration, household demographic characteristics deserve a brief
mention. The typical household head is male, age 40–50 years, and non-indigenous. It
is also apparent from the descriptive statistics that the observed education levels are
quite low, with averages of 2.20, 2.27 and 3.33 years for each survey year. Moreover,
51%, 49% and 41% of household heads reported no education whatsoever. Therefore, overall, a few defining characteristics of the sample emerge: the typical Nicaraguan agricultural/livestock producer (i) falls below the national poverty line and
sometimes far below; (ii) possesses only a relatively small plot of land (frequently
below five manzanas); (iii) has few productive assets with which to work; and (iv) has
had minimal education.
3. Methodology
As the goal of the analysis is to determine whether asymmetric market imperfections
continue to hold explanatory power when controlling for (technical and allocative)
efficiency differences between large and small farmers, a methodological framework is
required that permits robust conclusions to be drawn while staying within the confines
of the available data. Barrett et al. (2008) developed a four-stage method for estimating structural labour supply models in the presence of unobservable wages and deviations of on-farm marginal revenue product of labour from shadow wages (i.e.
allocative inefficiency). While the estimation of structural labour supply models is not
of primary interest, the methodology employed by the authors does provide an adequate framework through which to explore the present research question. Our modified framework is also composed of four different stages and what follows is an
elaboration of those stages (see Henderson, 2012 for an expanded methodological
discussion).
3.1. Market imperfections framework
In order to motivate the analysis and maintain comparability with earlier studies, we
begin with a simple examination of the farm size–productivity relationship using the
so-called market imperfections framework. Originally developed by Binswanger and
Rosenzweig (1986), the market imperfections framework consists of estimating the
following simple model:
y ¼ fðOW; OP; H; ZÞ
ð1Þ
where y represents, alternatively, productivity, profitability, or input variables (further
discussed below), OW is the amount of owned land, OP denotes the size of the operated holding, H represents labour endowments, and Z is a vector of other exogenous
variables influencing the chosen dependent variable. In line with the previous theoretical and empirical work, the expected signs on the parameters of primary importance
0
are as follows: (i) fOW
[ 0 as a greater quantity of owned land relaxes the credit con0
straint; (ii) fOP \ 0 as more operated land exacerbates the supervision constraint; and
(iii) fH0 [ 0 as additional family workers relaxes the supervision constraint. Importantly, the above model is a multiple correlation as land rental decisions, embodied in
the difference between ownership and operational landholdings, cannot be considered
exogenous. Therefore, the parameter estimates represent partial correlation coefficients that illustrate the impact of the regressors for a given level of the other righthand side variables (Heltberg, 1998).
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It is necessary to elaborate upon three primary specification issues. First, omitted
variable bias is potentially problematic as variables such as land quality, the household’s farming skills, preferential access to markets, etc. are unobserved. As such
variables are reasonably time-invariant, these omitted variables can be modeled as
household-specific constant terms.13 Second, while much of the literature on the IR
has employed land productivity as the dependent variable of interest, this is not
entirely satisfactory given that land productivity is only a partial measure of productivity. Farm value-added (or return to household labour) is thus used as an alternative dependent variable. While farm profitability may be preferable, the definition of
profitability in traditional agriculture is inherently problematic as it requires imputing the value of family labour. Given that the valuation of family labour at market
wage rates results in estimated losses for approximately 64% of observations in our
sample, it appears that such imputations overestimate the opportunity cost of
labour. Finally, it is necessary to mitigate the raw correlation between land owned
and operated so as to avoid multicollinearity issues. As in van Zyl et al. (1995),
then, land owned is operationalised by the percentage of land operated that is
owned.
In light of the above, the empirical model is as follows:
yit ¼ ai þ X0it b þ eit ;
ð2Þ
which is estimated for three alternative dependent variables: (i) land productivity (i.e.
the total value of output per unit of land operated); (ii) farm value-added per unit of
land operated; and (iii) labour usage per unit of land operated (where total labour
usage is the sum of the days of household and hired labour employed). The first two
dependent variables follow immediately from the above discussion, but the third merits brief elaboration. As labour market imperfections are manifest empirically in relatively greater labour usage per unit of land operated on small farms – due to a
relatively low shadow price of labour – a robust IR between this dependent variable
and operational landholdings would theoretically substantiate the labour market
imperfections hypothesis. Thus, in general, the examination of the relationship
between operational landholdings and the three dependent variables is a means of
assessing the sensitivity of the results to alternative specifications.
Regarding the right-hand side of equation (2), ai is a household-specific constant
and Xit includes time dummies, land owned divided by land operated, land operated
(fit with a third-order polynomial to capture non-linearities), male and female labour
endowments, and the share of income from off-farm activities (to control for involvement in agriculture). A number of alternative regressors were initially included in the
model (e.g. number of plots, area under irrigation, receipt of technical assistance,
etc.), but their insignificance gave way to the more parsimonious specification
employed here. Furthermore, while it could be argued that the relationship between
our dependent variables and the household labour covariates is probably non-linear,
the relevant hypothesis tests suggest that the linear specification is most appropriate.
Finally, in an attempt to mitigate output composition effects, the analysis throughout
is conducted not only with all producers in the sample, but also with subsamples of
13
It should be noted that fixed effect specifications are not immune to omitted variable bias that
arises from the exclusion of time-variant regressors.
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beans and maize as well as diversified producers.14 Observations were designated to
the beans and maize subsample if more than 50% of the value of their output was
derived from those activities. The remaining producers were grouped into the ‘diversified’ category (i.e. the subsamples are mutually exclusive).15 While a more disaggregated approach is perhaps desirable, data limitations render this unfeasible.
3.2. Technical efficiency: Stochastic frontier analysis
The objective of the second stage is to retrieve estimates of technical efficiency, which
can be accomplished via the fitting of a production frontier. To start, consider the following model proposed by Caudill et al. (1995):
ln yi ¼ X0i b þ vi ui :
ð3Þ
The deterministic portion of the above equation represents a production function
where Xi is a K 9 1 vector of inputs for the ith producer that is mapped to the (logarithmic) output measure yi. The error component vi represents a symmetric disturbance, which is assumed to be independently and identically distributed. The error
component ui (the inefficiency component) is assumed to be distributed independently
of vi and satisfy ui ≥ 0. Estimating via maximum likelihood, Caudill et al. (1995)
assumed vi Nð0; r2v Þ; ui Nþ ð0; r2ui Þ, and rui ¼ expðZ0i cÞ where Zi is a J 9 1 vector
of exogenous determinants of technical inefficiency and c is a parameter vector to be
estimated.16 Finally, on the basis of the above model it is possible to predict ui as
Eðui jei Þ and then calculate technical efficiency as TEi = exp(ui) (Jondrow et al.,
1982). The resulting measure of technical efficiency falls between zero and one, where
one represents full efficiency.
In the development of a ‘true’ random effects frontier, Greene (2005) offered a salient extension to the above model. The ‘true’ random effects model is crucial here for
three primary reasons: (i) panel models previously in common use confounded unobserved heterogeneity with that of technical efficiency; (ii) a ‘true’ fixed effect estimator,
in addition to being inconsistent as a result of the incidental parameters problem,
would eliminate any time-invariant component of household-specific technical efficiency; and (iii) the ‘true’ random effects model, as a practical consideration, reduces
14
The choice of subsamples draws inspiration from the typology of rural Nicaraguan producers
laid out in Deininger et al. (2003). Based on primary income sources, the authors developed a
fourfold categorisation of rural Nicaraguan producers: (i) livestock ranchers; (ii) coffee growers;
(iii) bean and maize cultivators; and (iv) diversified/other farmers. Given the aggregative nature
of the diversified/other category and a relatively small number of observations on coffee and
livestock growers, the decision was made to confine the subsample analysis to the aforementioned categories.
15
See Berry and Cline (1979) for a similar approach. Also, note that once a producer is classified
into a given category their total output value is included in the dependent variable.
16
It is worth noting that a leading alternative to the model proposed here is that which assumes
u to be distributed Nþ ðl; r2u Þ (i.e. truncated normal) and models l as a function of some exogenous determinants. Given (i) the perceived heteroskedasticity in u as the observations in the
sample differ substantially with respect to land operated, and (ii) the extreme volatility of the
‘mean’ model, which is due to the weak identification of the parameter l, the proposed model
appears appropriate at present.
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computational burden as the ‘true’ fixed effect model requires ‘brute force’ estimation
(Greene, 2005; Barrett et al., 2008). Consequently, consider the following:
ln yit ¼ a þ X0it b þ wi þ vit uit
ð4Þ
where wi is a random firm-specific effect. At first glance, identification appears an issue
given the three-part disturbance. However, Greene argued that this is not the case, as
the model actually has a two-part composed error and can be written as follows:
ln yit ¼ ða þ wi Þ þ X0it b þ eit ¼ ai þ X0it b þ eit :
ð5Þ
The above is an ordinary random effects model where the time-varying component
has an asymmetric (non-normal) disturbance (wi may, however, be normally distributed). The model may be estimated via maximum likelihood and readily incorporates
exogenous determinants of technical inefficiency.17
Moving to the empirical model, it is conventional to specify the production function
as either Cobb-Douglas or translog. While the Cobb-Douglas is a simpler functional
form, it does impose unitary elasticity of substitution. Moreover, with the translog
being a more flexible functional form and merely a generalisation of the Cobb-Douglas, it is less restrictive to begin with the translog specification and then conduct the
relevant joint hypothesis test for the nested Cobb-Douglas. Accordingly, the empirical
model is as follows:
ln yit ¼ai þ h1 d2001 þ h2 d2005 þ
K
X
bk ln xkit
k¼1
K X
L
K
X
1X
þ
bkl ln xkit ln xlit þ
sk dkit þ vit uit
2 k¼1 l¼1
k¼2
ð6Þ
where vit Nð0; r2v Þ; uit Nþ ð0; r2uit Þ; and r2uit ¼ expðZ0it cÞ. In the above, yit represents
the total value of output for the ith producer at time t, d2001 and d2005 are dummy variables for the years 2001 and 2005, xkit corresponds to the kth production input (land
operated, household labour days, hired labour days, and other variable inputs), and
dkit is a dummy variable that equals one when the kth input takes a value of zero.18 In
the variance model, Zit corresponds to a J 9 1 vector of technical inefficiency determinants: time dummies, land owned divided by land operated, land operated, male
and female labour endowment, gender of the household head, age of the household
head, the education of the household head, and the share of income from off-farm
activities. When necessary, higher order polynomials are included to capture non-linearities in land operated. As a final point, then, once a satisfactory model is specified
and estimated, Eðuit jeit Þ and TEit can be readily calculated.
It should be mentioned at this point that the presence of simultaneous equation bias
in our single-equation production model depends crucially on how producer behaviour is conceptualised. Importantly, the behavioural model justifying the estimation
17
In order to estimate the model via maximum likelihood, it is necessary to integrate the common term out of the likelihood function. As there is no closed form for the density of the compound disturbance, integration is done by quadrature or simulation.
18
The inclusion of the dummy variable dkit is a simple approach to obtaining consistent parameter estimates when scaling is necessary to facilitate logarithmic transformations of zero-valued
explanatory variables (Battese, 1997). Note that a dummy variable for land operated is not necessary, as this input never takes on a value of zero. All other inputs have zero values.
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of many single-equation production models is that of Zellner et al. (1966). The
authors put forth a theoretical model based on two primary assumptions: (i) the production process is neither instantaneous nor deterministic, and (ii) producers are
aware of the stochastic nature of production. With agents then maximising profit with
respect to anticipated output rather than realised output, the authors demonstrated
that inputs do not depend on the disturbance in the production function. Accordingly,
to the extent that we believe the above behavioural assumptions are more appropriate
than standard deterministic behavioral postulates,19 there does not appear to be a
strong theoretical justification for concern about simultaneous equation bias.
3.3. Allocative efficiency: Heckman two-step
The objective of the third stage is to retrieve estimates of allocative efficiency for all
producers in the sample. We begin by first calculating allocative inefficiency for those
households that participated in wage labour (which is 493, 561 and 1,081 households
in 1998, 2001, and 2005, respectively) where AIit = ln (wit/MRPLit), which is simply
the natural logarithm of the ratio of the observed median daily household wage and
the marginal revenue product of a day of on-farm household labour, where
MRPL = oy/oL is calculated from the production frontier. Note that the measure of
AI is zero when w = MRPL, negative when w < MRPL (signaling an under-application of labour), and positive when w > MRPL (signaling an over-application).
With the AI estimates in hand, we then regress AI on a series of exogenous inefficiency determinants. Here it is necessary to account for sample-selection bias so as to
obtain consistent parameter estimates and, as such, the model is estimated with the
Heckman two-step procedure as developed in Heckman (1979). Given the pervasive
use of the two-step procedure, we offer only a brief summary. The first step is to estimate a probit-type selection equation that describes the selection mechanism (e.g.
participation in wage employment) and then for each observation calculate the
inverse Mills ratio using the probit coefficients. The second step entails linearly
regressing the primary dependent variable of interest (e.g. AI) on the chosen regressors and the estimated inverse Mills ratio. When including the inverse Mills ratio in
the second stage, the primary equation can be estimated consistently with OLS.20 It is
important to note here, however, that it is necessary to adjust the standard errors,
which are inconsistent (see Heckman, 1979; or Greene, 1981 for the specific
calculations).
Once a satisfactory model has been specified, the parameters can then be used to
cit for those households that did not participate in
impute allocative inefficiency AI
wage labour. Given estimates of allocative inefficiency for all households, it is beneficial to transform those estimates in order to facilitate interpretation. Analogous to the
case of technical efficiency, we require a transformation that yields the value of one
19
For example, see Hoch (1958).
A large body of literature has developed regarding specification issues in the Heckman twostep procedure. As, theoretically, it is frequently desirable to include the same variables in the
probit and primary models, the researcher runs the risk of introducing excessive multicollinearity in the primary model via the inverse Mills ratio, as the inverse Mills ratio is an approximately
linear function over a wide range of its argument. As such, the present analysis uses two methods in an attempt to avoid or mitigate these issues: (i) exclusion restrictions, and (ii) condition
numbers. See Henderson (2012) for further discussion.
20
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Heath Henderson
when AI = 0, and approaches zero as AI deviates from zero. The kernel of the normal
density function readily provides such properties. Consider the following expression
for allocative efficiency:
AI2
AEit ¼ exp 2it
2rAI
ð7Þ
where l has been set to zero (as this represents perfect allocative efficiency), and r2AI is
the observed variance of AI as calculated around a mean of zero. It is clear, then, that
when AI = 0 the resulting value of AE is one.
A few further comments should be made regarding this step in the analysis. First, in
the probit model, a dummy variable for participation in wage labour (participation
equals one) is regressed on a series of managerial and household characteristics,
including: year dummies, prevailing wage in the household’s municipality, distance to
the nearest health centre (as a proxy for proximity to employment opportunities),
quantity of land owned, value of agricultural/livestock assets, ethnicity (i.e. Indigenous), gender of the household head, marriage status of the household head, age of
the household head, education of the household head, number of male and female
labourers, and number of government programmes from which the household benefits. It should be noted that the wage, distance to health centre, and asset variables
serve as valid exclusion restrictions as they naturally influence wage labour participation (both theoretically and statistically), but not allocative inefficiency.21 The variables in the primary model are precisely those in the variance equation of the
production frontier plus the inverse Mills ratio. Second, the Heckman two-step is estimated in a pooled manner as the quantity of unobserved wage data renders a panel
specification unfeasible. Given our inability to control for time-invariant unobservables, we might then expect a certain degree of omitted variable bias in this stage.
While our focus here is on prediction, we nevertheless seek to minimise the bias
through the inclusion of appropriate time-invariant characteristics (e.g. gender, education, etc.). Finally, following Barrett et al. (2008), as a result of the estimated nature
of AI, standard errors of the primary equation are bootstrapped with 1,000
replications.
3.4. Market imperfections framework revisited
Regarding the final stage, we revisit the market imperfections framework, a revisitation motivated by way of omitted variable bias. Following Greene (2008), consider
the following correctly specified regression:
y ¼ X1 b1 þ X2 b2 þ e
ð8Þ
where y is a NT 9 1 vector for observations i = 1, 2, . . ., N at times t = 1, 2, . . ., T,
Xj is a NT 9 Kj matrix for j = 1, 2, bj is a Kj 9 1 vector of parameters, and e is a
NT 9 1 vector of disturbances. Further, let y and X1 embody the specification elaborated upon in section 3.1 and let X2 contain the time-varying technical and allocative
21
That is, a priori it is unclear how the aforementioned variables might influence allocative inefficiency. In addition, we find that each of the variables is statistically insignificant in the primary
model. Below we highlight the statistical significance of the variables in the probit model.
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efficiency estimates discussed in sections 3.2 and 3.3. Regressing y on X1 without the
inclusion of X2 yields the following estimator:
1
1
1
ð9Þ
b1 ¼ X01 X1 X01 y ¼ b1 þ X01 X1 X01 X2 b2 þ X01 X1 X01 e:
Taking the expectation then, we have:
1
E½b1 jX ¼ b1 þ X01 X1 X01 X2 b2
ð10Þ
where unless X01 X2 ¼ 0 or b2 = 0 it is evident that b1 is biased. It follows immediately
from the above discussion that a priori we cannot assume X01 X2 ¼ 0 or b2 = 0. Thus,
in this final stage we include the estimates of technical and allocative efficiency in the
market imperfections framework so as to examine the direction and magnitude of the
omitted variable bias. Lastly, due to the estimated nature of technical and allocative
efficiency, the standard errors are bootstrapped with 1,000 replications.
4. Results
4.1. Market imperfections framework
Tables S2–S4 display the results from the initial estimation of the market imperfections models for the samples of all, beans and maize, and diversified producers,
respectively.22 Note that each table presents the results for each of the three aforementioned dependent variables. Given that this stage of the analysis is largely motivational, here we confine our attention to the coefficient estimates associated with
operational landholdings. For each regression in each table, the robust statistical significance of the higher-order terms suggests that a cubic specification is most appropriate.23 Further, the coefficients on all first-, second- and third-order terms are
negative, positive and negative, respectively, thereby suggesting similar non-linear
relationships across specifications.
The two inflection points implied by the parameter estimates are quite similar
across regressions within each sample of producers. For the samples of all, beans and
maize, and diversified producers, the first (second) inflection point occurs at approximately 53 (137), 45 (128), and 57 (141) manzanas, respectively.24 In each of these samples, 94%, 95% and 92% of producers, respectively, operate landholdings below that
of the first inflection point, which suggests that an IR applies for the vast majority of
producers in each sample. The magnitude of the estimated performance differentials is
also economically meaningful. For example, for the sample of all producers, we predict that a producer operating one manzana will witness land productivity values
approximately 4,000 (9,000) units greater than a producer operating 50 (200)
22
Only core results are displayed in the text. Ancillary tables and figures are prefixed by the letter ‘S’ and located in an Appendix. The Appendix is available online.
23
Note the division of the second- and third-order terms by 100 and 1,000, respectively. The
transformation, by shifting the decimal place in the parameter estimates, merely facilitates the
presentation of the results. Any subsequent calculations, however, necessarily take into account
the transformed data. Such transformations are used throughout the analysis, but in no way
affect the final results.
24
Inflection points for the market imperfections models are calculated from the parameter estimates of a least squares regression of the predicted values from the relevant regression on a
third-order polynomial of land operated.
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Heath Henderson
manzanas. Given less statistical uncertainty and outlier sensitivity associated with the
downward-sloping portion of the relationship, not only does it appear that smallerscale producers display higher levels of output and farm value added per manzana,
but the most likely explanation for these findings is the greater application of labour
per manzana. With relatively high R2 values for each regression in each table, it is evident that the market imperfections framework conforms with the data reasonably
well, but the question remains as to whether the specification suffers from omitted
variable bias.
4.2. Technical efficiency: Stochastic frontier analysis
Tables 3–5 present the core results of the technical efficiency analysis. To start, consider jointly Tables 3 and 4. Table 3 displays the results of the random effect production frontier for all (All), beans and maize (BM), and diversified (D) producers. To
understand the coefficient estimates, however, it is beneficial to focus on Table 4,
which provides a series of relevant Wald tests. First, Wald test (1) examines the joint
significance of the translog terms (i.e. all quadratic and interaction terms). For each
sample, we reject the null hypothesis of a nested Cobb-Douglas production technology at any conventional level of significance. Second, hypothesis tests (2)–(5) present
Table 3
Random effect production frontier with logarithmic value of output as dependent variable
All
Variable
d2001
d2005
ln OP
ln HH
ln HL
ln VI
2
1
2 ln (OP)
ln OP 9 ln
ln OP 9 ln
ln OP 9 ln
2
1
2 ln (HH)
ln HH 9 ln
ln HH 9 ln
2
1
2 ln (HL)
ln HL 9 ln
2
1
2 ln (VI)
dHH
dHL
dVI
N
Coeff.
HH
HL
VI
HL
VI
VI
BM
SE
0.39***
0.04
0.27***
0.03
0.35***
0.05
0.13
0.09
0.33***
0.07
0.62***
0.09
0.01**
0.01
0.02**
0.01
0.02***
0.004
0.02**
0.01
0.02
0.02
0.01
0.01
0.06***
0.01
0.03**
0.02
0.03***
0.01
0.05*
0.03
0.35
0.38
0.34***
0.12
0.06
0.04
5,743
Coeff.
0.36***
0.21***
0.32***
0.11
0.27***
0.56***
0.06***
0.004
0.02***
0.02
0.05**
0.01
0.07***
0.06***
0.01*
0.04
0.56
0.51***
0.15***
2,596
D
SE
0.05
0.04
0.06
0.12
0.09
0.12
0.01
0.01
0.01
0.01
0.02
0.01
0.02
0.02
0.01
0.03
0.50
0.15
0.05
Coeff.
0.33***
0.44***
0.29***
0.12
0.32***
0.60***
0.01
0.02
0.02***
0.01
0.02
0.01
0.04**
0.02
0.03***
0.07*
0.25
0.18
0.01
3,147
SE
0.05
0.05
0.07
0.11
0.10
0.12
0.01
0.01
0.01
0.01
0.02
0.01
0.02
0.02
0.01
0.04
0.53
0.17
0.06
Notes: aP-values <0.01, 0.05 and 0.10 correspond to ***, ** and *, respectively.
OP, HH, HL and VI refer to land operated, household labour, hired labour, and other variable
inputs, respectively.
b
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Table 4
Wald tests
All
BM
D
Hypothesis
Est.
Test stat.
Est.
Test stat.
Est.
Test stat.
(1) Nested Cobb-Douglas
(2) ɛOP = 0
(3) ɛHH = 0
(4) ɛHL = 0
(5) ɛVI = 0
(6) ∑ɛk = 1
–
0.28
0.26
0.15
0.15
0.84
123.98***
320.10***
6.40**
29.39***
45.06***
2.09
–
0.15
0.47
0.18
0.07
0.87
146.63***
63.11***
11.45***
19.63***
9.36***
0.79
–
0.21
0.24
0.12
0.14
0.71
82.55***
97.98***
3.45*
11.48***
13.14***
4.16**
Notes: aP-values <0.01, 0.05 and 0.10 correspond to ***, ** and *, respectively.
b
OP, HH, HL and VI refer to land operated, household labour, hired labour, and other variable
inputs, respectively.
an estimate, for each sample, of the mean output elasticity for each input in addition
to the test of statistical significance.25 It is evident that all output elasticities for each
sample are positive and statistically significant, frequently at the 1% level. Finally,
Wald test (6) displays the estimated elasticity of scale for each sample,26 which is not
significantly different from unity for the sample of all producers and the sample of
beans and maize producers. However, for the diversified producers, we reject the null
hypothesis of constant returns to scale at the 5% level.27
Of primary interest is the technical inefficiency model in Table 5, especially those
results that pertain to operational landholdings. Regarding the sample of all producers, the statistical significance of the higher-order terms of operational landholdings
suggests that a cubic specification is fitting. Accordingly, there are two inflection
points, which occur at approximately 71 and 100 manzanas. That is, technical inefficiency is estimated to increase in operational landholdings up to 71 manzanas,
decrease from 71 to 100 manzanas, and then increase again thereafter. Importantly,
96% of the sample operates landholdings less than 71 manzanas, which suggests that
an IR between operational landholdings and technical efficiency is effective for the
majority of producers. With respect to beans and maize producers, as a linear specification appears most appropriate, it is clear from the positive and statistically
P
The output elasticity of the kth input ek ¼ @ ln y=@ ln xk ¼ bk þ K
j¼1 bkj ln xj . Also, note the
distinction between the elasticities evaluated at the mean and the mean elasticities. Given the
skewed distribution of some inputs (e.g. operational landholdings), calculating each elasticity at
the input level for each producer and then taking the mean of these elasticities is preferable as
the resulting distributions of the elasticities are approximately normal.
26
The scale elasticity is simply equal to the sum of the output elasticities for each input. The production function exhibits locally decreasing, constant, or increasing returns to scale when the
elasticity of scale is less than, equal to, or greater than unity.
27
The finding of decreasing returns to scale for diversified producers is by no means surprising
as one rationale for diversification is decreasing returns to scale in a given crop. Further, recalling that the diversified category includes coffee producers, decreasing returns to scale is consistent with existing empirical evidence on coffee growers in Latin America (e.g. Wollni and
Br€
ummer, 2012).
25
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Heath Henderson
Table 5
Technical inefficiency model
All
Variable
Intercept
d2001
d2005
Owned/operated
Operated
Operated2/100
Operated3/1000
Male labour
Female labour
Female
Age
Education
Share
N
Coeff.
0.21***
0.18***
0.21***
0.02***
0.01***
0.01***
1e-3***
0.05***
0.01
0.03
4e-3***
0.01**
0.01***
5,743
BM
SE
0.08
0.04
0.03
0.01
2e-3
4e-3
2e-4
0.01
0.01
0.03
1e-3
3e-3
3e-4
Coeff.
0.63***
0.02
0.20***
0.02*
3e-3**
–
0.05***
3e-3
0.02
1e-3
1e-3
0.01***
2,596
D
SE
0.11
0.07
0.05
0.01
1e-3
–
–
0.01
0.02
0.04
1e-3
0.01
1e-3
Coeff.
0.49***
0.29***
0.17***
0.02***
3e-3**
3e-3***
–
0.05***
0.01
0.04
0.01***
0.01***
0.01***
3,147
SE
0.10
0.04
0.04
0.01
1e-3
1e-4
–
0.01
0.02
0.03
1e-4
4e-3
4e-4
Note: aP-values <0.01, 0.05, and 0.10 correspond to ***, ** and *, respectively.
significant coefficient on land operated that the finding of an IR persists with this subsample of producers. Conversely, turning to the diversified producers, where we
employ a quadratic specification, the parameter estimates suggest a statistically significant, negative, and convex relationship in technical inefficiency. With a minimum
being reached at approximately 57 manzanas and 92% of producers in this subsample
operating landholding less than this minimum, it is evident that a direct relationship
between operational landholdings and technical efficiency exists for the vast majority
of this sample. Thus, the estimated IR for the entire sample appears to be driven by
the sample of beans and maize producers.
Some other interesting conclusions also emerge from Table 5. First, the ratio of
owned to operated landholdings is negative and statistically significant for all samples, which suggests that increasing ownership landholdings may indeed improve
technical efficiency via credit constraint relaxation (Binswanger et al., 1995). Second,
technical inefficiency is significantly decreasing in household male labour endowments for all samples, which is in accordance with accepted theory on moral hazard
associated with hired labour in developing country agriculture (as, all else equal, lesser endowments of household labour require greater quantities of hired labour to
meet production targets). There appears, however, a certain asymmetry between
male and female labour, as the coefficient on female labour is not statistically significant in any sample. Finally, technical inefficiency is significantly increasing in the age
and education of the household head (for the samples of all and diversified producers) as well as the household share of income from off-farm activities (for all
samples).
As a final consideration, descriptive statistics and kernel density estimates of the
technical efficiency scores are provided in Table S5 and Figures S1–S3 in the online
Appendix. Regarding Table S5, for all samples and all years, mean technical efficiency
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459
hovers around 60%, which is largely in accordance with other empirical studies of
Latin American agricultural and livestock production.28 Further, while bean and
maize producers tend to witness higher average technical efficiency scores, there do
not appear to be any definitive trends in the scores across time. Lastly, Figures S1–S3
illustrate that in all cases the distributions of the TE scores are slightly skewed with
modes at approximately 70%. Thus, even though the depictions of the entire distributions illustrate that the majority of the producers witness TE scores above that of the
sample means, there still appears to be considerable room for improvement in technical efficiency.
4.3. Allocative efficiency: Heckman two-step
As discussed, before estimation of the Heckman two-step, it is necessary to calculate
AIit = ln (wit/MRPLit) for the subsample of households that participated in wage
labour. While the daily wage is observed, the marginal revenue product of labour
must be calculated using the parameters from the production frontier, where
MRPL = oy/oL, which is evaluated at the observed input levels of each producer. It
is common in these calculations, as is the case here, to find negative values for
MRPL (for examples see Jacoby, 1993 or Skoufias 1994). While there are numerous
possible ways to treat the issue, in an effort to limit introducing undue bias into
subsequent estimation, these observations are simply omitted from the analysis.29
The negative values, however, are only witnessed for approximately 7%, 3% and
6% of the samples of all, beans and maize, and diversified producers, respectively,
so the loss of observations, while unwelcome, is minimal. For the remaining observations, Table S6 presents descriptive statistics for the resulting AI estimates by year
and sample. In examining the descriptive statistics, it is evident that, for all years
and all samples, mean AI lies above zero (i.e. perfect allocative efficiency), which
suggests that, on average, Nicaraguan households over-applied labour to agricultural and livestock production.30 Moreover, across time, there does not appear to
be any discernible trend toward improved allocative efficiency for any of the
samples.
Moving forward, Tables 6 and 7 display the results from the probit and primary
models for the Heckman two-step procedure where the dependent variable of the
probit model is participation in wage labour and the dependent variable of the sample selection model is allocative inefficiency. With respect to the probit model, it is
first important to note that the primary exclusion restrictions (i.e. the wage, distance
28
See Bravo-Ureta and Pinheiro (1993) for a review of technical efficiency estimates in developing country agriculture. Further, see Bravo-Ureta and Evenson (1994) for an example of an
empirical study of Latin American agriculture that observes technical efficiency estimates in the
vicinity of 60%.
29
A battery of t-tests reveals that the omitted households are not statistically different from the
included households on the basis of observable characteristics. Further, regression-based tests
reveal that the coefficient estimates associated with our Heckman two-step procedure are not
statistically different when excluding these households.
30
Recall that AI is only calculated for those households that participated in wage labour. While
the market wage is, by definition, to some extent available to all these households, quantity
rationing may potentially pose a threat to the validity of the calculations. We are, however,
unable to gauge the extent to which quantity rationing occurs with the available data.
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Heath Henderson
Table 6
Probit model with participation in wage labour as dependent variable
All
BM
D
Variable
Coeff.
SE
Coeff.
SE
Coeff.
SE
Intercept
d2001
d2005
Municipality wage
Distance to
health center
Owned
Owned2/100
Assets
Indigenous
Female
Married
Age
Education
Male labour
Female labour
Government
programmes
Pseudo R2
N
0.79***
0.04
0.07
0.01***
0.01***
0.10
0.05
0.05
2e-3
3e-3
0.86***
0.04
0.10
0.01***
0.01***
0.14
0.09
0.07
3e-3
0.01
0.68***
0.01
0.02
3e-3
0.01***
0.14
0.07
0.07
3e-3
3e-3
0.01***
0.01***
0.01***
0.45***
0.08
0.13***
3e-3**
0.02***
0.10***
0.10***
0.06***
2e-3
1e-3
1e-3
0.09
0.05
0.04
1e-3
0.01
0.02
0.02
0.01
0.02***
0.01***
0.01***
0.10
0.09
0.12**
3e-3*
0.01
0.07***
0.07***
0.06***
3e-3
2e-3
3e-3
0.16
0.07
0.06
2e-3
0.01
0.03
0.03
0.02
0.01***
3e-3***
0.01***
0.58***
0.05
0.15***
2e-3
0.02***
0.13***
0.12***
0.07***
2e-3
1e-3
2e-3
0.10
0.07
0.05
2e-3
0.01
0.02
0.03
0.02
0.05
5,331
0.05
2,521
0.06
2,943
Note: aP-values <0.01, 0.05, and 0.10 correspond to ***, ** and *, respectively.
Table 7
Primary model with allocative inefficiency as dependent variable
All
BM
D
Variable
Coeff.
SE
Coeff.
SE
Coeff.
SE
Intercept
d2001
d2005
Owned/operated
Operated
Male labour
Female labour
Female
Age
Education
Share
k
R2
N
8.08***
0.09
0.43***
0.01
2e-3
0.07***
4e-3
0.01
3e-3**
0.02***
3e-3***
0.15
0.08
2,008
0.28
0.06
0.06
0.01
2e-3
0.02
0.03
0.06
1e-3
0.01
1e-3
0.19
9.43***
0.08
0.36***
0.01
2e-3
0.01
0.04
0.13*
1e-3
4e-3
3e-3***
0.32
0.09
984
0.37
0.09
0.08
0.02
4e-3
0.03
0.03
0.07
2e-3
0.01
1e-3
0.26
0.47
0.04
0.26***
1e-3
4e-3*
0.10***
0.02
0.08
4e-3*
0.04***
4e-3***
0.23
0.07
1,055
0.32
0.08
0.08
0.02
2e-3
0.03
0.03
0.09
2e-3
0.01
1e-3
0.22
Notes: aP-values <0.01, 0.05, and 0.10 correspond to ***, ** and *, respectively.
b
Standard errors are bootstrapped with 1,000 replications.
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to health center, and assets variables) are highly statistically significant in each
model.31 Perhaps more interestingly, it is evident that the signs on all coefficients are
in accordance with theory. For the majority, if not all, of samples, the prevailing
municipality wage and proximity to employment opportunities (as proxied by distance to nearest health center) are both factors that appear to exert a statistically significant ‘pulling’ influence on household labour, whereas a lack of land owned and/
or productive assets can be viewed as ‘push’ factors that induce wage labour participation. Further, regarding demographic characteristics, indigenous households and
households with married heads display a significantly negative relationship with
wage labour participation whereas older and more educated households as well as
households with greater (male and female) labour endowments are significantly more
likely to participate in wage labour. Finally, benefitting from government programmes significantly enhances the likelihood of wage labour participation in all
samples.
Moving to the primary model, it can be seen from Table 7 that land operated is
only statistically significant for the sample of diversified producers, albeit at the
10% level. The positive coefficient here implies that larger producers are more allocatively inefficient than their smaller counterparts, a finding which contrasts with
that of the aforementioned direct relationship between operational landholdings
and technical efficiency for this sample of producers. With respect to other findings, regarding demographic characteristics, it is evident that, at least for the samples of all and diversified producers, households with more male labourers, older
household heads, and/or household heads with greater education levels tend to be
significantly more allocatively inefficient. The only truly unexpected result here is
the parameter estimates on education, but the exploration of the explanation is
beyond the scope of the present analysis. Further, the share of income from offfarm activities is positive and statistically significant for each sample, which
implies that those households less dependent on agricultural and livestock production witness greater allocative inefficiency. Lastly, while the insignificance of the
inverse Mills ratio (k) for each sample suggests that selection bias is not of immediate concern, for the sake of theoretical integrity, we maintain the two-step
specification.
With the estimates from the Heckman two-step, it is then possible to impute AI for
all observations and apply the above-discussed allocative efficiency transformation.
Descriptive statistics and kernel density estimates are presented in Table S7 and Figures S4–S6, respectively. The descriptive statistics show that mean allocative efficiency
consistently hovers around 60%, with the only exception being those estimates for
diversified producers for the years 1998 and 2001, which are approximately 70%.
Importantly, the data suggests that allocative efficiency declined for all samples of
producers from 1998 to 2005, a deterioration that reaches approximately 10% for the
sample of diversified producers. Moreover, regarding Figures S4–S6, there appears
substantial variation in the estimates as, across samples, they cover a wide range of
values, with minimum values nearing zero and maximum values approaching one.
Consequently, these estimates point toward non-negligible resource allocation issues
in Nicaraguan agricultural/livestock production.
31
The only exception to this statement is the municipality wage variable in the regression for the
diversified producers.
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Table 8
Fixed effects model revisited (all)
Land productivity
Variable
d2001
d2005
Owned/operated
Operated
Operated2/100
Operated3/1000
Male labour
Female labour
Share
TE
AE
R2
N
Coeff.
SE
971.57***
130.36
324.12*
175.44
8.10
15.26
162.56***
16.76
226.27***
34.90
8.27***
1.68
86.68
66.17
16.52
46.24
2.33
1.67
9,507.13*** 1,206.14
4,497.65*
2,678.48
0.62
5,743
Value added
Coeff.
Labour usage
SE
774.84***
116.97
760.39***
90.53
4.84
13.88
137.98***
10.60
181.81***
21.00
6.40***
1.03
37.87
37.03
29.81
53.99
9.23***
1.75
5,372.22***
390.21
3,988.60**
1,856.24
0.73
5,743
Coeff.
SE
18.35**
9.32
63.79***
6.35
0.11
0.64
12.53***
0.75
16.94***
1.61
0.60***
0.08
0.93
2.64
4.18
4.96
0.22
0.14
18.23
26.48
817.09*** 155.54
0.80
5,743
Notes: aP-values <0.01, 0.05 and 0.10 correspond to ***, ** and *, respectively.
b
Standard errors are bootstrapped with 1,000 replications.
4.4. Market imperfections framework revisited
Tables 8–10 and Figures 1–3 present the revisited market imperfections models, which
now include as regressors the estimates of technical and allocative efficiency. With
respect to Table 8 and the sample of all producers, it is evident that the coefficients on
technical efficiency are positive and highly statistically significant for the land productivity and farm value-added models. Theoretically, such parameter estimates are to be
expected given that, all else equal, enhanced technical efficiency increases output/revenue, which in turn exerts a positive influence on the dependent variables. Conversely,
for all models, the coefficients on allocative efficiency are negative and statistically significant. Given the observed widespread over-application of labour and barring pervasive quantity rationing in local labour markets, improved allocative efficiency
entails allocating on-farm labour to off-farm activities, which consequently diminishes
output/revenue and thereby each dependent variable.
In light of the results in Tables 5 and 7, then, it appears as if the omission of technical efficiency may bias the parameter estimates on land operated, at least for the land
productivity and value-added regressions. As such, it is necessary to reconsider those
coefficient estimates. The estimates on the first-, second-, and third-order terms here
maintain their signs as well as their statistical significance. As depicted graphically in
Figure 1, which was created by fitting a third-degree polynomial least squares line to
the predicted values of each regression (denoted LP, VA, and LU, respectively),32 the
first (second) inflection point occurs at 55 (138), 55 (138) and 51 (137) manzanas for
each model, respectively. Once again, the overwhelming majority of producers in this
sample – 94% in each case – operate landholdings below that of the first inflection
32
The predicted values for the labour usage regression are multiplied by ten so as to facilitate
presentation.
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Technical and Allocative Efficiency in the IR
Table 9
Fixed effects model revisited (beans and maize)
Land productivity
Variable
d2001
d2005
Owned/operated
Operated
Operated2/100
Operated3/1000
Male labour
Female labour
Share
TE
AE
R2
N
Coeff.
Value added
SE
Coeff.
773.00***
139.10
841.21***
132.61
36.61*
20.35
275.49***
86.42
590.82*
351.67
31.97
34.67
2.07
47.29
69.17
59.14
5.41***
1.47
6,998.62***
457.87
2,695.24**
1,362.32
0.94
2,596
Labour usage
SE
888.69***
138.52
1,033.89***
133.86
9.60
24.95
234.00***
73.64
505.95*
286.34
27.47
27.60
66.74
52.66
74.76
54.03
6.58***
1.50
5,766.08***
392.52
1,378.79
1,271.30
0.95
2,596
Coeff.
SE
1.98
9.80
88.54***
12.32
0.29
2.13
22.35***
6.02
46.02*
25.60
2.41
2.59
4.55
6.39
0.58
5.85
0.13
0.17
15.37
42.47
663.11*** 180.17
0.96
2,596
Notes: aP-values <0.01, 0.05 and 0.10 correspond to ***, ** and *, respectively.
b
Standard errors are bootstrapped with 1,000 replications.
Table 10
Fixed effects model revisited (diversified)
Land productivity
Variable
d2001
d2005
Owned/operated
Operated
Operated2/100
Operated3/1000
Male labour
Female labour
Share
TE
AE
R2
N
Coeff.
SE
647.36***
142.18
181.74
303.03
15.70
24.91
149.28***
13.70
186.86***
27.89
6.47***
1.37
251.75
182.60
19.47
102.13
1.36
2.28
8,703.27***
1,419.48
1,902.19
1,289.23
0.84
3,147
Value added
Coeff.
Labour usage
SE
403.91***
86.79
635.03***
156.45
20.14
26.54
136.23***
11.88
167.82***
21.02
5.64***
0.98
147.79
91.14
52.14
68.60
4.92***
1.64
4,911.80***
509.79
778.44
580.02
0.88
3,147
Coeff.
SE
6.96
50.08***
0.26
9.80***
12.16***
0.41***
13.39***
3.27
0.23**
22.03
141.16***
0.86
3,147
7.27
8.77
0.94
0.64
1.22
0.06
4.23
5.05
0.11
39.05
20.78
Notes: aP-values <0.01, 0.05 and 0.10 correspond to ***, ** and *, respectively.
b
Standard errors are bootstrapped with 1,000 replications.
point, which implies that a robust IR between operational landholdings and the three
dependent variables continues to hold after controlling for technical and allocative
efficiency.
Turning to Table 9 and Figure 2, for the sample of beans and maize producers, it is
again evident that the coefficient on technical efficiency is positive and highly
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Heath Henderson
Figure 1. Operational landholdings and predicted outcomes (all producers)
Figure 2. Operational landholdings and predicted outcomes (beans and maize producers)
statistically significant for the land productivity and value added models. Further,
regarding allocative efficiency, while insignificant in the value added regression, the
coefficients remain negative and statistically significant for the land productivity and
labour usage models. Accordingly, coupled with the results in Tables 5 and 7, it is evident that the parameter estimates on operational landholdings, for the land productivity and value-added models, may again be subject to bias from the omission of
technical efficiency. Returning to the coefficients on operational landholdings, it is
apparent that, for each model, the parameter estimates maintain their signs and,
though not for the third-order terms, statistical significance. As illustrated in Figure 2,
the estimates imply that the first (second) inflection point occurs at 47 (130), 46 (129),
and 44 (129) manzanas for each model, respectively, and we find that approximately
95% of producers operate landholdings below each of these values, which affirms that
a robust IR between operational landholdings and each dependent variable remains
for the majority of producers in this sample.
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Figure 3. Operational landholdings and predicted outcomes (diversified producers)
Regarding Table 10 and Figure 3, for the diversified producers, we see that the
coefficients on technical efficiency remain positive and statistically significant for
the land productivity and value-added models whereas the parameter estimates on
allocative efficiency, while negative for all models, are only statistically significant
for the labour usage regression. Thus, again in light of the results in Tables 5
and 7, there is evidence that the omission of technical (in the land productivity
and value added models) and allocative (in the labour usage regression) efficiency
may bias the parameter estimates on operational landholdings. With respect to
those estimates, then, for each model, we see that each term in the third-order
specification remains highly statistically significant and of the same sign as the initial models. Referencing Figure 3, the coefficients imply that the first (second)
inflection point occurs at 58 (140), 59 (141) and 54 (140) manzanas for the three
models, respectively, which once again suggests a persistent robust IR between
operational landholdings and our dependent variables, as approximately 92% of
producers in this sample operate landholdings below the first inflection point of
all models.
Overall, as evidenced by the R2 values, the final models possess non-negligible
explanatory power. Thus far, however, we have confined our attention to the regressors of primary interest and have not examined the contribution of the other righthand side variables. It can be seen from Tables 8–10 that the coefficients on the ratio
of owned to operated landholdings as well as male and female labour are, for the most
part, statistically insignificant for each model in each sample. Conversely, the parameter estimates on the share of income from off-farm activities frequently factor in negative and statistically significant, a finding that points to the importance of controlling
for involvement in off-farm activities. Given the relatively small change in R2 between
the initial and revisited models, it therefore appears as if the explanatory power of the
model is primarily driven by operational landholdings, the household-specific constants, and the share of income from off-farm activities. Finally, for all samples, given
the persistent inverse farm size–labour usage relationship, it appears that the most
likely explanation for the observed relationship between operational landholdings and
land productivity as well as value-added per unit of land operated is indeed found in
labour market imperfections.
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Heath Henderson
5. Conclusions
In considering the alternative explanations for the oft-observed IR between farm size
and productivity in developing country agriculture, five competing hypotheses can be
distinguished: (i) decreasing returns to scale; (ii) land quality heterogeneity; (iii) differential responses to uncertainty; (iv) labour market imperfections; and (v) differences
in technical and/or allocative efficiency. In the presence of (i) constant returns to scale;
(ii) the persistence of productivity disparities after controlling for land quality heterogeneity; and (iii) evidence that differential responses to uncertainty tend to equalise
profit rates, we focused our attention on whether asymmetric market imperfections
continue to hold explanatory power when controlling for efficiency differences
between large and small agricultural producers.33 Using nationally-representative
panel data from Nicaragua, we developed a four-stage empirical framework to simultaneously test these competing explanations for the IR, an empirical exercise that, to
date, appears yet to be undertaken.
The results suggest that labour market imperfections are the probable driving force
behind the IR, as technical and allocative efficiency differences – though commonly
exerting a statistically significant impact on alternative productivity indicators across
different samples – were found to be insufficiently potent sources of omitted variable
bias. We further find that the relationship between farm size and land productivity is
highly non-linear. For the sample of all producers, for example, land productivity is
decreasing in farm size up to 55 manzanas, increasing from 55 to 138 manzanas, and
then steeply decreasing thereafter.34 Given that approximately 35% of private agricultural landholdings in Nicaragua are controlled by producers holding greater than 200
manzanas (Henderson, 2012, Table 2.1),35 our results therefore suggest that scope
exists for achieving productivity gains through appropriately targeted redistributive
measures.
Supporting Information
Additional Supporting Information may be found in the online version of this article:
Table S1. Attrition probits with attrition indicator as dependent variable.
Table S2. Fixed effects model (all).
Table S3. Fixed effects model (beans and maize).
Table S4. Fixed effects model (diversified).
Table S5. Technical efficiency estimates by year.
Table S6. Allocative inefficiency estimates by year.
Table S7. Allocative efficiency estimates by year.
Figure S1. Kernel density estimates of TE scores (all producers).
Figure S2. Kernel density estimates of TE scores (beans and maize producers).
Figure S3. Kernel density estimates of TE scores (diversified producers).
Figure S4. Kernel density estimates of AE scores (all producers).
33
It is important to note here that we were able to substantiate points (i) and (ii) with the Nicaraguan data.
34
It is important to note here that the majority of producers in our sample fall below the first
inflection point and, as such, there is greater uncertainty associated with the point estimates for
larger producers.
35
The data cited are based on Nicaragua’s 2001 agricultural census.
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Figure S5. Kernel density estimates of AE scores (beans and maize producers).
Figure S6. Kernel density estimates of AE scores (diversified producers).
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