Economics of barani (rainfed) farming and farm household production behaviour in Pakistan.
Mahmood, Amir
INTRODUCTION
Agriculture research and development efforts in Pakistan have
traditionally been focused on raising the farm productivity of irrigated
areas. Among other factors, the underlying causes for this irrigated
bias could be attributed to: the importance given to the irrigated areas
in the overall planning framework; the dominance of the irrigated farm
lobby at all levels of research, politics, and government; the relative
progressiveness of irrigated farmers in terms of adoption of new
technologies; and the presence of risk-reducing natural conditions
prevailing on irrigated farms, e.g., certainty of subsidised water
supply when it is most needed. Further, like other parts of Asia, the
Green Revolution has helped the irrigated farmers in Pakistan to raise
the productivity of their major crops, such as wheat, cotton, and rice.
On the other hand, the rainfed (1) areas of Pakistan have drawn little
benefit from the Green Revolution. The average yields achieved on the
rainfed areas remain significantly lower than the yields derived by the
traditional irrigated farmers. The rainfed farmers are also subject to
subsistence farming conditions with per capita incomes well below the
national average. (2) Given the size of the area under rainfed
conditions and the problems faced by the rainfed farmers, there have
been attempts by the government, international donor agencies, and
non-government organisations to come up with strategies to raise the
productivity as well as income of the rainfed farmers. Such efforts,
however, must take into account the production behaviour of the
farm-households under rainfed conditions.
The objective of this paper is to analyse the production behaviour
of barani farm-household while using the profit-function approach
developed and advanced by Lau and Yotopoulos (1971, 1972, 1973, 1979).
(3) Since its conception, the profit function technique has been used
extensively as an alternative approach to analyse farm household
production behaviour. (4) Specifically, the study will test the profit
maximisation hypothesis in the context of the utilisation level of
variable inputs in wheat production, (5) as the central question in the
theory of production is whether farm-households strive for profit
maximisation. Second, the paper will attempt to determine whether wheat
farming in the rainfed areas of Pakistan exhibits constant returns to
scale. Third, the profit-function approach will be used to test the
hypothesis of equal relative economic efficiency of the farmers
belonging to different rainfall zones.
The paper is organised as follows. The model employed in this study
is discussed in Section 2. Section 3 provides an empirical specification
of the model and outlines the estimating procedures. This section also
presents a brief discussion on the data and variable construction. The
empirical results, along with policy implications, are presented and
analysed in Section 4. Section 5 summarises the conclusions drawn from
the study.
THE MODEL
To describe the nature of farm production in the barani areas of
Pakistan, it is assumed that farm households' production decisions
can be analysed separately from their consumption decisions (6) and the
production function is of Cobb-Douglas form:
Y = A [L.sup.[alpha]1] [K.sup.[alpha]2] [F.sup.[alpha]3]
[S.sup.[alpha]4] [N.sup.[alpha]5] [Z.sup.[beta]] ... ... ... ... ... (1)
where Y is wheat output plus its by-product (wheat straw) in wheat
equivalents; L is labour services in man-days; K is capital services in
hours; (7) F is fertiliser in kilograms; S is seed rate in kilograms; N
is animal input in animal-days; and Z is land input in acres. The study
assumes that, while the use of L, K, F, S and N can be varied, Z is
fixed in a single production period. As demonstrated by Lau and
Yotopoulos (1971, 1972, 1979), if the underlying production function is
of Cobb-Douglas form, then the corresponding estimating equation for the
normalised restricted profit function, [[PI].sup.*] ([P.sub.j], Z),
would be:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)
where [P.sub.L], [P.sub.K.sup.8], [P.sub.F], [P.sub.S], [P.sub.N]
are respectively farm-specific prices of labour, capital, fertiliser,
seed, and animal inputs, all normalised by the price of output (wheat).
DL is the dummy variable taking the value of 1 for high rainfall zone and 0 for the low rainfall areas.
An interesting property of (2) is that, under the profit
maximisation assumption, its differentiation with respect to factor
prices provides the corresponding factor demand functions. (9) The
demand for each variable factor of production, therefore, is given by:
[V.sub.j] = - [partial derivative][PI]/[partial derivative]
[P.sub.j], j = L, K, F, S, N ... ... ... ... (3)
(3) implies that the five variable factor share estimating
equations are:
--[P.sub.L] [V.sub.L]/[[PI].sup.*] = [[alpha].sub.1.sup.**] +
[[epsilon].sub.2] ... ... ... ... ... (4)
--[P.sub.K] [V.sub.K]/[[PI].sup.*] = [[alpha].sub.2.sup.**] +
[[epsilon].sub.3] ... ... ... ... ... (5)
--[P.sub.F] [V.sub.F]/[[PI].sup.*] = [[alpha].sub.3.sup.**] +
[[epsilon].sub.4] ... ... ... ... ... (6)
--[P.sub.S] [V.sub.S]/[[PI].sup.*] = [[alpha].sub.4.sup.**] +
[[epsilon].sub.5] ... ... ... ... ... (7)
--[P.sub.N] [V.sub.N]/[[PI].sup.*] = [[alpha].sub.5.sup.**] +
[[epsilon].sub.6] ... ... ... ... ... (8)
Where [V.sub.L] is total labour days; [V.sub.K] is total capital
services in hours; [V.sub.F] is the total quantity of fertiliser in
kilograms; [V.sub.S] is the total quantity of seed in kilograms.
[V.sub.N] is the total animal days.
Equations (2) and (4-8) form a set of equations that can be used to
test the hypothesis regarding profit-maximising behaviour of the rainfed
farmers by estimating the parameters of the above set of equations.
If the rainfed farmers are price-takers, then their
profit-maximisating behaviour can be tested by comparing the estimated
coefficients, [[alpha].sub.i.sup.**]'s, in the factor demand
equations to the corresponding coefficient [[alpha].sub.i.sub.*]'s,
in the normalised profit function. For a given sample of
farm-households, the two estimates do not have to be equal. However, if
the farmers do maximise profit, then the test for profit-maximisation
requires that [[alpha].sub.i.sup.*] = [[alpha].sub.i.sup.**] (10)
The hypothesis that rainfed farming in Pakistan is characterised by
constant returns to scale can be tested by finding out whether the sum
of the elasticities of the normalised profit function with respect to
fixed inputs is equal to one. (11) In the present case, with land as the
only fixed factor, rainfed farming would exhibit constant returns to
scale if [[beta].sup.*] = 1.
THE DATA AND THE STATISTICAL METHODOLOGY
The study uses the data collected from a comprehensive
cross-sectional survey of 156 farm-households from 30 barani villages of
the Punjab and the North West Frontier Province (NWFP) in 1989. (12) The
survey followed a two-stage sampling technique. First, by selecting the
villages and then from sampled villages selecting the farm-households.
The farms with negative profits, zero variable input cost, and zero
cultivated land area were eliminated from the sample. Out of 156
farm-households, 23 were eliminated from the sample, leading to the
final sample size of 123.
Following the usual assumptions regarding the stochastic disturbance terms, (13) the study applies the Zellner's (1962)
method of imposing known constraints on the coefficients in the
estimating equations. (14) As argued by Lau, Lin and Yotopoulos (1979),
p. 27, this is an asymptotically efficient method under the given
conditions.
EMPIRICAL RESULTS
The results of estimation of the model are presented in Table 1.
The first column provides the coefficients of the model estimated
through equation by equation application of the ordinary least-squares
(OLS) method. (15) The OLS technique provides consistent but inefficient
estimators under the stochastic specification. The results of the
Zellner's (1962) unrestricted efficient parametric estimates are
given in Column 2. The efficiency of these estimates is enhanced further
once we impose the linear restrictions implied by the profit
maximisation hypothesis. The results of the restricted coefficients are
consistent with the profit function assumption, i.e., profit is an
increasing function of the fixed inputs and a decreasing function of the
variable inputs. Moreover, the sign of the coefficient attached with the
dummy variable suggests that farmers in the high rainfall-zone are
economically more efficient.
The hypothesis of profit maximisation, constant returns to scale,
and equal relative economic efficiency of high and low rainfall zone farms are tested by using statistical tests based on F-ratios. The
hypothesis testing is based on the unrestricted estimation of the model.
The results are provided in Table 2.
First, the hypothesis of profit maximisation is examined. The
tested hypothesis implies that [[alpha].sup.**]'s, in the factor
demand equations and [[alpha].sub.i.sup.*]'s, in the normalised
profit function are equal.
Ho: [[alpha].sub.i.sup.*] = [[alpha].sub.i.sup.**] i = 1, 2....5
The result, as shown in Table 2, rejects the hypothesis of profit
maximisation at the 1 percent level of significance (99 percent level of
confidence). This result implies that during the survey year the rainfed
farmers were in a state of disequilibrium, i.e., the farmers were not
equating the value of marginal products of variable inputs to their
factor prices. A reasonable explanation of the rejection of this
hypothesis is that the rainfed farmers are subject to subsistence
farming conditions in a risky environment where the priority is to meet
the food security requirement rather than to pursue an economic
efficiency (profit maximisation) objective which may undermine their
food security considerations. This implies that production decisions do
depend on households' consumption choices. In other words,
separability may not be a reasonable assumption to model the production
behaviour of the rainfed farmers facing both production as well as
consumption risk. (16)
Given the significance of the profit maximisation hypothesis, the
rejection of this hypothesis prompted separate tests for each equality
restriction to identify the inputs for which the farmers do equate the
marginal revenue product of a factor to its marginal factor cost. Except
for fertiliser, the hypotheses regarding the profit maximising factor
hiring rule were rejected for all other inputs at the l percent level of
significance. These results point to a possible explanation. Except for
fertiliser, the markets for other inputs, such as hired animal, seed,
tractor, and labour, are imperfect in the sense that the farmers do not
consider the prices for these inputs as true reflections of their
contribution in the production process, as, unlike irrigated farming,
the contribution of these factors is difficult to determine at planting
time under rainfed conditions. Therefore, the factor hiring rule as
characterised by the profit maximisation hypothesis breaks down for
these variable factors of production. In the case of chemical
fertiliser, however, the barani farmers prefer to apply chemical
fertiliser after rain when they are assured of crop establishment. (17)
Consequently, the fertiliser application validates the factor hiring
rule as characterised by the profit maximisation hypothesis. This
indicates that the rejection of the profit maximisation hypothesis is by
no means a manifestation of "irrational behaviour" by the
rainfed farmers; rather it is an outcome of a risk-averse strategy
applied by the farmers under erratic rainfall conditions.
Second, the hypothesis of constant returns to scale is tested from
the unrestricted estimation of the model. The tested hypothesis is:
Ho: [[beta].sup.*] = 1
This hypothesis cannot be rejected at 1 percent level of
significance. This implies that if the fixed input (land) is doubled,
without changing the normalised prices for all inputs, the normalised
profits will be doubled. Following Lau and Yotopoulos (1973), as
constant returns to scale exists, an argument for a consolidation of
small farms-on the basis of economies of scale is not valid for the
rainfed areas. Therefore, under rainfed conditions, a policy debate on
the issue of optimum farm size becomes irrelevant.
Finally, the hypothesis of equal relative economic efficiency of
the farmers from low and high rainfall zones is tested using
unrestricted estimation of the model. The null hypothesis for this test
is:
Ho: [[delta].sub.L] = 0
The above hypothesis is rejected at I percent level of
significance. The rejection of this hypothesis implies that the level of
economic efficiency, as measured by normalised profits, differs between
the high and low rainfall-zone farmers. This test confirms that farmers
in the high rainfall-zone are economically more efficient.
SUMMARY AND CONCLUSIONS
The results of this study provide an interesting insight into the
production behaviour of barani farm-households and the nature of the
production process under rainfed conditions. Given output and variable
input prices and given the quantity of fixed factor, the results do not
validate the profit maximisation hypothesis under rain fed farming
conditions. The rejection of this hypothesis, however, should not be
interpreted as a "rationality test" for the barani farmers. It
is the contention of this paper that rainfed farming is subject to risky
farming conditions where the objective function is to meet food security
requirements rather to pursue an economic efficiency objective, which
may undermine their food security considerations. Second, the study
confirms that rainfed farming is characterised by constant returns to
scale. Therefore, any policy reform that calls for consolidation of
small farms based on economies of scale is invalid under rainfed
conditions. Third, the paper confirms a common belief that the level of
economic efficiency, as measured by normalised profits, increases as one
moves from low to high rainfall zone. This study concludes that a
stratification by rainfall zones is an essential step in the formulation
of appropriate research design on the basis of various ecological zones.
The empirical results of this study, especially the rejection of
the profit-maximisation hypothesis, should be treated with some caution
as these findings warrant qualifications due to the partial nature of
the model. First, because of the importance of wheat in rainfed farming,
the study has ignored other crops and production activities, such as
livestock, in the formulation of the profit function. It is the
contention of this study that one may arrive at different conclusions if
the model is based upon the "farm profit function" rather than
the crop-specific profit function. Second, following the traditional
farm-household econometric models, the study assumes that the production
decisions can be analysed separately from the consumption decisions. A
major weakness of the separability assumption is that the conditions
essential for a farm-household model to be separable are quite
stringent. (18) In spite of this drawback, this study has made this
assumption owing to data limitations. Finally, the findings of this
study suggest that future research regarding farm-household production
behaviour in the barani areas should tackle the issue of separability in
order to bring the model closer to reality.
Comments
Amir Mahmood's paper presents a systematic explanation of some
of the important aspects of nature-dependent risky economy of the barani
lands in Pakistan. He focuses his production behaviour analysis to test
three hypotheses, viz., profit maximisation in the context of wheat
production; constant returns to scales in wheat farming; and equal
relative economic efficiency of the farmers. Using the Lau Yotopoulos
profit function approach to data collected from 123 households of 30
villages in the area of Haripur (NWFP) and Gujar Khan (Punjab), he
confirms that (i) rainfed farming is subject to risky farming conditions
where the objective function is to meet food security requirements
rather than to pursue an economic efficiency objective; (ii) that
rainfed farming is characterised by constant returns to scale; and (iii)
that economic efficiency increases while moving from low to high
rainfall.
I welcome this exploratory novel effort that helps to rationalise a
few aspects of the indigenous knowledge prevailing in rainfed
agriculture. My major concerns, however, pertain to the complex nature
of pluvial characters. Agriculture is not the mainstay of economic life
in the tract under consideration and, hence, it is not appropriate to
assign exclusive weightage to the crops sub-sector, especially the
wheat, for analysing the imperatives of profit maximisation. Immense
variation in the iso-hyetal distribution and the geo-physical resources
defines the huge diversity in the barani agro-ecologies, and it demands
a bit broader vision besides wheat, i.e., the farming systems approach.
For example, in the Punjab, the Murree-Kahuta, Siwalik Piedmont, Potohar
Plateau, the Salt Range, D. G. Khan, and the Tribal Areas, the Thal and
Riverine belts; and in the NWFP, the Sulaiman Piedmont, Bannu Basin,
Peshawar Valley, and the Swat-Chitral pockets carry area-specific
distinct features. So the sampling plan has to be well-stratified.
Secondly, the population and composition of stall-feds and ruminants in
the rangelands, which fluctuate from high to low rainfall, cannot be
under-scored as a final refuge for barani farmers during the lean
year(s) of drought spell(s). Barani livestock with newly emerging
silvi-pastoral and agro-pastoral models have comparatively shown a more
dynamic role in the rainfed economy. Further, the debate on the use of
"Costly Water" entailing from water conservation practices in
the barani lands vis-a-vis irrigated plains has promoted the wisdom to
shift from wheat to cash crops like orchards, vegetables, groundnuts,
chickpeas, and sorghum etc. Nevertheless, the food security perspective
does persist, although barani subsistence farming alone cannot pull on
with the farm family needs without the off/non-farm support. Moreover,
the institutional and policy framework in rainfed agricultural
development also requires due reference because of its irrational
approach and strategic inefficiency in comprehending the popular
discourses on community-based initiatives.
Ch. Hasnat Ahmad
Agency for Barani (Rainfed) Areas Development, Planning and
Development Department, Punjab, Lahore.
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(1) The terms 'rainfed' and 'barani' are used
interchangeably.
(2) BARD (1989); Government of Pakistan (1988).
(3) For benefits of using profit function approach as a preferred
alternative to other techniques, see Jones and Moussa (1991), pp. 21-22.
(4) The profit function approach has been applied in a wide range
of situations to analyse issues related to agricultural production. See,
for example, Lau and Yotopoulos (1971, 1972, 1973); Sidhu (1974); Somel
(1979); Tamin (1979); Lau, Myers and Chou (1979); Adulavidhaya, et al.
(1979); Kuroda (1979); Khan and Maki (1979, 1980); Lau and Yotopoulos
(1979) and Jones and Moussa (1991).
(5) Wheat is a major Rabi crop in the barani region.
(6) The model, therefore, is based on the restrictive separability
assumption.
(7) K is a sum of mechanical services (e.g., tractor, cultivator,
planter, sheller, thresher, etc.) required at different stages of wheat
production.
(8) [P.sub.K] is a sum of hourly prices of mechanical services,
required at all stages of wheat production. This includes the use of
tractor, cultivator, planter, sheller, and thresher.
(9) This result is known as Hotelling-Shephard Lemma.
(10) For the derivation of this result, see Lau and Yotopoulos
(1979), pp. 11-22.
(11) A property of the normalised profit function is that if the
underlying production function exhibits constant return to scale in
variable as well as fixed inputs, then the normalised restricted profit
function is characterised by constant return to scale in fixed inputs
[Lau and Yotopoulos (1979), p. 109].
(12) The survey areas include, Haripur (high rainfall zone, with an
average annual of 750 mm) in the North West Frontier Province, and
Doultala and Mangial (low rainfall zone, with an annual average rainfall
of 500 mm) in the Punjab.
(13) The additive rotor term is assumed to have zero mean and
non-zero finite variance for each of the estimating equations of the
model, i.e., Equation (2) and Equations (4-8). The additive term in
(4-8) can arise from unequal abilities to maximise profit or difference
between expected and actual or realised prices. The co-variances of the
errors between different equations (Equation 2 coupled with one of the
Equations 4-8) for any given farm are assumed to be non-zero, whereas,
the co-variances of the errors of each equation corresponding to
different farms are assumed to be zero [Kuroda (1979), p. 70].
(14) Given that the variables on the left-hand side of Equations
(2) and (4-8) are the jointly dependent variables and the variables on
the right-hand am the pre-determined variables (i.e., there am no
endogenous variables on the right-hand side of the equations), ordinary
least squares applied to each of the above equations will be consistent.
These estimates, however, will be inefficient as they do not take into
account the fact that the errors of different equations may be
correlated with one another and in the case of profit maximisation the
same [[alpha].sub.i] appears in (2) and in one of the Equations (4-8).
An efficient approach, therefore, is to estimate Equations (2) and (4-8)
jointly, imposing the restriction that [[alpha].sub.i.sup.**] =
[[alpha].sub.i.sup.*]. Under these conditions, Zellner's seemingly
unrelated regression technique becomes the natural choice. For more on
the rationale of using Zellner's method, see Lau and Yotopoulos
(1972), p. 15. For a comprehensive discussion of seemingly unrelated
regression equations models, see, for example, Srivastava and Giles
(1987).
(15) The profit function and factor share equations were tested for
heteroscedastic errors using the Goldfeld-Quandt test. The test resulted
in acceptance of the null hypothesis of homosecdastic disturbance terms.
(16) Acceptance of risk in the production process, however, implies
that separability can no longer be assumed.
(17) The level of fertiliser applied also depends upon rainfall at
planting time. For more on this, see Supple, et al. (1985), p. 51.
(18) For more on the necessary conditions for a farm-house model to
be truly separable, see Hardaker and Fleming (1993), p. 217.
Amir Mahmood is Lecturer in the Department of Economics, University
of Newcastle, Newcastle, Australia.
Table 1
Joint Estimation of the Normalised Profit Function
and Factor Share Equations
Single
Equation
Variable Parameter (OLS)
Profit
Function
10.809
Constant In A * (10.32)
1.445 *
Labour [[alpha].sub.1] * (0.6005)
5.211
Fertiliser [[alpha].sub.2] * (3.311)
Capital
(Tractor -0.130
Services) [[alpha].sub.3] * (0.0981)
0.369
Seed [[alpha].sub.4] * (0.2595)
1.342
Animal [[alpha].sub.5] * (3.419)
0.958 *
Land [[beta].sub.L] (0.1042)
0.615 *
Dummy [[delta].sub.L] (0.1975)
Factor Share
Equations
-0.3998 *
Labour [[alpha].sub.1] ** (0.0602)
-0.5749 *
Fertiliser [[alpha].sub.2] ** (0.1985)
Capital -0.5150 *
Services [[alpha].sub.3] ** (0.0944)
-0.1917 *
Seed [[alpha].sub.4] ** (0.0312)
-0.0077 *
Animal [[alpha].sub.5] ** (0.0023)
Profit
No Maximisation
Variable Restriction Restrictions
Profit
Function
8.6297 2.0924 *
Constant (6.929) (0.1973)
0.9134 * -0.2540 *
Labour (0.4032) (0.0431)
-3.3786 -0.1943
Fertiliser (2.223) (0.1539)
Capital
(Tractor -0.0880 -0.2392 *
Services) (.0659) (0.0556)
0.3200 -0.1110 *
Seed (0.1742) (0.0218)
1.0881 -0.00469 *
Animal (2.296) (0.0023)
1.045 * 1.0114 *
Land (0.0699) (0.0771)
0.2769 * 0.0072
Dummy (0.1326) (0.1181)
Factor Share
Equations
-0.3998 * -0.2540 *
Labour (0.0602) (0.0431)
-0.5749 * -0.1943
Fertiliser (0.1985) (0.1539)
Capital -0.5150 * -0.2392 *
Services (0.0944) (0.0556)
-0.1917 * -0.1110 *
Seed (0.0312) (0.0218)
-0.0077 * -0.00469 *
Animal (0.0023) (0.0023)
Notes: Coefficients with * are statistically significant at
the 5 percent level; the numbers in parentheses are
asymptotic standard errors.
Table 2 Test of Hypotheses
Critical Critical
[F.sub.0.05, [F.sub.0.01,
Tested Hypothesis Computed F [infinity]] [infinity]]
Profit Maximisation F(5,725) = F(5,725) = F(5,725) =
6.1859 2.21 3.02
Constant Returns to Scale F(1,725) = F(1,725) = F(1,725) =
0.4064 3.84 6.63
Equal Relative Economic
Efficiency of High and
Low Rainfall-zone
Farmers F(1,725) = F(1,725) = F(1,725) =
8.2844 3.84 6.63
