The primary methodological challenges of empirical work on why livestock production is scaling-up are to define a quantitative measure of relative farm competitiveness in production, and then to look in a structured way at all the factors that differ across farms that might explain higher relative competitiveness across farms. The latter include: technical and allocative efficiency, asymmetries in access to assets (credit, liquidity, fixed capital, etc.) and information (education, experience, etc.), externalities (some farmers get away with uncompensated pollution while others do not), and policies (some get a better deal from the State than others).
The omission of relevant factors, such as considering differential efficiency across farms in explaining competitiveness while neglecting transaction cost differences, or vice versa, leads to biased estimates. Furthermore, inclusion of explanatory factors of relative competitiveness that are themselves functions of relative competitiveness leads to simultaneity bias. For example, relative competitiveness might be enhanced through being recognized as a sales-leader, but being recognized as a sales-leader may depend on being more competitive than others. The two-way causality among the variables leads to bias in the empirical estimation of the effect of all variables unless appropriate procedures are used.
Relative competitiveness might be thought of as having the ability to produce at a lower unit cost of production than one's competitors. In fact, if large farms can produce livestock at a lower unit cost than small ones, they will clearly drive small farms out of the market over time. The market price that applies to both large and small, by this reasoning, will fall as large-scale producers expand production, and the small guys will get squeezed out. The only future for smallholders then will be to stay in a few higher-priced niche markets that are not economic for larger farms to serve, if any, and to cut costs by remunerating their own (family) labor less that a large farmer pays to hired labor. Even so, it is unlikely that smaller producers will be able to stay in business long under this situation.
However, the reverse is not necessarily true: if small farms can produce at lower unit costs than large farms, they may still be squeezed out. This is because large-scale farms can remain profitable with very thin profit margins; they make up in volume what they lose in per unit profit. Very low per unit profits coupled with a small sales volume may not provide enough income for a smallholder to stay in business. Thus if large farms have lower per unit costs of production when all labor is costed at market wages, the next question is whether this finding still holds if smallholders do not cost their family labor. If it does, then it is not necessary to proceed further; there is little hope for smallholders in this activity.
If on the other hand small farms can produce at lower per unit cost in the same markets as large farms, perhaps by not costing their own labor at full market wage rates or for some other reason, there is at least hope for them. Thus having higher unit profit, with or without the cost of family labor, is a necessary condition for competitiveness of smallholders, but is not a sufficient one.
To get a more satisfactory measure of relative competitiveness that gets around the issue of larger farms being able to expand production while small ones cannot, it is necessary to appeal to the notion of efficiency. Small farmers are most likely to be able to stay in business-and perhaps to gain market share-if they are more efficient users of farm resources, both in a technical sense (being on the production possibility frontier given existing technology) and the allocative sense (being on the right place on the production frontier, given prevailing prices). If small farms are more efficient users of farm resources, perhaps because they put more care per unit of input into what they do, then they have a market advantage over large-scale producers that will be difficult to dislodge them from. This then yields a measurable index of relative competitiveness: relative farm efficiency in securing profit per unit of output. Ceteris paribus, farmers that are more efficient users of farm resources to secure profits per unit of output are more likely to be able to maintain market share than larger producers who are less efficient in the same sense. Over time, the more efficient are in a position to invest more into the farm enterprise and to grow, whatever their starting size.
A standard way of assessing farm-specific relative profit efficiency is to estimate a "profit frontier" across a sample of farms, and then to measure how far each farm in the sample lies below the frontier. Conceptually, such a frontier can be thought of a function mapping profit per unit to relative input and output prices and quantities of non-traded factors of production, where each point is the maximum profit per unit that a farm can achieve given those relative prices and access to resources. Given a set of prices, the average farm with that level of resources will fall below the frontier. Thus an ordinary least squares regression on data from a sample of farms of different sizes of profits per unit of output against input and output prices and fixed factor of production (land, labor, etc.) will always lie below the theoretical frontier. The frontier itself has to be estimated in some fashion looking at data for farms that perform best at each level of resources. A variety of approaches to this are described by Fried, Lovell and Schmidt (1993).
The measurement of "most efficient" can be improved by estimating a stochastic profit frontier, which allows for measurement error in the econometric estimation of the frontier itself, and thus for the fact that observations for some farms will lie above the estimated "best" frontier (see Battese 1992 for a survey of this literature). In our case, the dependent variable is profit per unit of output, and the explanatory variables are farm-specific fixed resources (land, family labor, sunk capital), farm-specific input prices (feed, medicines, stock, etc.), and farm-specific output prices. In the Philippines situation studied, farm resources such as land may be non-tradable inputs and must be accounted for in the frontier in terms of the amount available, and not their price. The unit prices received for output and prices paid for inputs can also be expected to vary greatly, and reflect (and control for) quality differences and differential transactions costs such as bargaining power and riskiness.
The actual performance of each farm in terms of unit profit can then be compared to an ideal unit profit for that farm, given its resources and prevailing input prices. The difference between the ideal and the actual profit per unit for that farm is the farm's relative profit inefficiency. Following Ali and Flynn (1989), Figure 1 traces a profit frontier for a sample of farms; each dot corresponds to the actual outcome in terms of profit per unit for a specific farm; points on the stochastic frontier curve (estimated my maximum likelihood methods and labeled MLE) are fully efficient farms (on the frontier) and all points below are inefficient farms in terms of their specific resources at prevailing input prices.
Figure 4. 1 Frontier (MLE) stochastic profit function for a sample of farms
Farm-specific profit efficiency (deviations below the frontier) are measured as the ratio of actual profit per unit (Y_{i} in figure 1 for a farm i) and ideal profit (Y*). Note that the curve denoting average profit for any given level of resources (shown as the locus of points Y in Figure 1)-estimated by Ordinary Least Squares Regression (OLS)--is less than ideal profit. The measure of farm efficiency embodied in Y_{i}/Y* is bounded by 1 (best-on the frontier) and worst 0, no profit. Farm-specific inefficiency is the distance below the frontier, (Y* - Yi).
If small farms have on average significantly higher profit efficiency per unit of output when family labor is not costed, then there is hope. This is even truer if it holds when family labor is costed at market wage rate. However this methodology allows going beyond simply making this determination; it also permits the investigation of which elements contribute most to explaining relative unit profit efficiency for large and small farms. Individual farms, large or small, may lie well below the profit frontier for reasons other than technical or allocative inefficiency: farm-specific transactions cost barriers or policy distortions may also impact on their position relative to the frontier.
This leads us to the principle methodological approach, which is to estimate a stochastic profit frontier in the usual way, and thus derive a farm-specific measure of relative inefficiency in securing profit per unit of output. Then, following the lead of Jondrow et al (1982), Ali and Flynn (1989), and Battese and Coelli (1995), the relative profit inefficiency of each farm is explained in terms of the transaction cost barriers and farm-specific policy distortions faced by that farm. The approach thus explains each farm's unit profit performance in terms of technical and allocative efficiency, in a first stage, and then in a second stage explains differences in efficiency in terms of farm-specific differences in transactions costs and policy distortions.
First stage: The stochastic profit frontier
The stochastic profit frontier (SPF) used in this study to estimate profit efficiency is defined as
Y_{i} = f(X_{i}, W_{i}, P_{i}, b)exp(vi - u_{i}) (1)
where Y_{i} = profit per farm normalized by quantity of output Q_{i} (i.e. unit profit) defined as:
Y_{i} = ((P_{i}Q_{i} - C_{i}Q_{i})/Qi) (2)
where:
P_{i}Q_{i} is total revenue from poultry (broiler and layer), swine, or dairy per farm i in question (manure sales included);
C_{i}Q_{i} is total variable costs such as costs on feeds, day old chicks (DOC) or piglets,, hired labor, electricity, medicines, vaccines, water, depreciation, etc., of securing revenue, excluding family labor per farm i; and
Q_{i} is the quantity of output per farm i;
X_{i}= vector of fixed factors used to obtain (e.g., stock of family labor, land, buildings and equipment, fixed capital stock, etc., to control for differences in farm resources) normalized by quantity of output;
W_{i}= vector of farm-specific input prices;
P_{i}= weighted-average output price (weights are the farm-specific transaction quantities);
b= vector of unknown parameters to be estimated; and
v_{i}, u_{i} are random error terms.
The error term (v) is distributed independently and identically as a two-sided normal random variable around the frontier, to account for measurement error on both sides of the frontier, and inefficiency (u), is distributed independently as a one-sided (downwards) random variable relative to the frontier, to allow for the fact that farms in fact fall below the ideal efficiency. Average efficiency can easily be estimated by OLS regression of unit profit per farm against farm-specific input and output prices and farm-specific fixed factors of production. However, the frontier, showing ideal unit profits for any given level of farm resources and prevailing price level, can only be estimated if specific assumptions are made about the distributions of u and v across farms, and then only using a non-linear estimation technique, such as Maximum Likelihood Estimation (MLE). The critical assumption is the distribution of the u (inefficiency) term. We adopt the approach of Battese and Coelli (1995), which allows for systematic differences across farms in the distribution of u, such that we do not assume away what we wish to investigate: viz. that transaction cost factors and policy distortions that are different for different farms help determine their relative profit inefficiency.
Second stage: Technical inefficiency determinant model
Battese and Coelli (1995) base their approach on the assumption that the expected value of the farm-specific inefficiency effect for farm i can be modeled as a function of farm-specific characteristics (which of course vary across farms) and fixed coefficients, which do not. In other words, , where m_{i} = z_{ik}d_{k} is the mean of a truncated-normal distribution of u_{i}. The z_{ik} are k explanatory variables observed for farm i, associated with technical inefficiency effects (u_{i}) and d is a vector of unknown coefficients to be estimated simultaneously with equation (1). Thus, the technical inefficiency effect, u_{i} in equation (1), can then be specified as u_{i} = z_{ik}d_{k} + e_{i}, where e_{i} is the inefficiency error term, defined by the truncation of the normal distribution with mean equal to zero and variance s^{2}. The truncation of e_{i} occurs at e_{i} ³ -z_{ik}d_{k} (Battese and Coelli, 1995).^{[128]}
Specification of an Estimation Model
A translog profit frontier is used because of the flexibility it allows in estimating parameters where it is not desirable to build in through model specification rigid assumptions about substitution relationships among inputs and factors. The full form of the model is:
where Y_{i} is the normalized profit of the i-th farm defined in equation (2); W_{ij} is the price of input j (j= hired labor, capital, feeds, and DOC, used by the i-th farm); X_{ik} is the fixed factor k used by the i-th farm (k =is the normalized value of buildings and equipment, normalized total farm labor in hours, etc.); and D_{i} is a vector of scale dummy variables for farm i. The v_{i}, u_{i} are as previously defined. The a_{kj}, b_{jk} are coefficients to be estimated by MLE using Frontier 4.1 software (Coelli, 1992).
Normalizing by output quantity builds in an assumption of constant returns to scale, so to allow for the fact that larger producers may in fact be using higher grade technology than others, we need to control for non-Hicks neutral technical change on the RHS of the first stage of our stochastic profit functions. To deal with this problem, we allow for the parameterization of Hicks non-neutral technological change by including the feed conversion ratio (FCR), which is probably closely correlated with both technology and managerial ability. We calculate the weighted average FCR per farm as: total feed used in kg divided by total output in kg of live-weight in the case of broiler (in number of eggs in the case of layer, kg of live-weight in case of swine, and liters of milk in the case of dairy).
Translog profit frontiers share the use of logarithms in the dependent variables, and thus do not handle cases of negative or zero unit profits. Yet it is not unreasonable to suppose that for some farms in some years, they lose money. There is in fact no perfect fix for this problem, and we employ a lesser-of-the-evils approach that is adequate for present purposes. A constant scalar is added to the unit profit data in each sample such that unit profit of every farm is positive. As long as the cases of negative average farm profits are few (less than 5%, say), and they are proportionately not very negative relative to average farm unit profit (so that the scalar is small relative to the mean), the resulting bias from a non-linear transformation of the data is judged to be of minor importance compared to the bias that would arise form using a less appropriate functional form or arbitrarily dropping the least efficient sample members.
The technical inefficiency effects (s) generated in equation (3) are estimated within the MLE model specified above as:
u_{i} = d_{0} + d_{1}Z_{1} + d_{2}Z_{2} ... + e_{i} (4)
where Z_{i} is the i-th farm characteristic determining relative inefficiency and e_{i} is distributed as above.
The RHS variables of equation (4), that is the Z, cover all the farm characteristics that proxy different levels of transaction costs faced by each farm, such as access to credit for capital, experience in the specific livestock production, age and education of household head, formal/informal trainings attended, subsidies represented by regional and contract dummies (for differences in policy distortions), access to markets for output, access to information, and the "instrumented" environmental cost (discussed in the next section).
Two remaining methodological problems concern the measurement of the farm-specific data. First, some of the explanatory variables that we may wish to include in the second stage may not be observable at all, or in any event very hard to observe. This is especially true of transaction cost and externality variables. Second, some of the explanatory variables that we may wish to include in the second stage may be endogenous in the sense discussed above: the causality goes both ways, introducing simultaneity bias in estimation. This is particularly a problem for environmental externalities, since farm-specific difference here will help to determine relative unit profit efficiency as we define it, but themselves may be a function of the latter in some cases.
Two problems arise in trying to account for the fact that some farms pollute more per unit of output than others in assessing why some farms have higher profits than others. The environmental externalities of livestock production are both hard to measure and in many cases determined simultaneously with the level of actual profit per unit. An externality is defined here as a return to an economic agent where part of the cost (or benefit) of undertaking an activity accrues to another entity that is not compensated (or charged) in the market. Negative externalities may be created in the production process for animal agriculture through odor, flies, and the nutrient-loading effects on soil of manure that is either mishandled or supplied in excess. Producers capture the benefit of negative externalities by receiving payment for livestock output, while not bearing the full costs to all of their enterprise, in terms of the impact on surrounding communities of odor, flies, poor water quality, etc. Producers who do not pay the full cost of production per unit may show up as "more efficient" (in financial terms) than producers who are otherwise similar but internalize some of the externality by cleaning up after the enterprise, or making compensatory payments to surrounding communities.
The first problem is how to measure the value of not paying for pollution created, particularly if this differs by scale of farm, since it will lead to erroneous comparisons of unit profits across scale categories. Externalities of the sort involved are exceedingly difficult to measure. There is the "non-point source" issue-basically concerning how to decide which farm the pollution in the river came from. There is the issue that farmers themselves suffer some of their own pollution, and this needs to be netted out of the externality. There is the issue that the negative effects of pollution carry over into future time periods. Physical measurements of costs in terms of decreased sustainability are also very difficult. Furthermore, the true consequences for sustainability of a given amount of manure will differ by soil type, temperature, and rainfall, and so forth.
In view of these many difficulties, it is not practical in the present study to attempt to measure actual negative externalities. Instead, we focus on differences across farms in the amount of externality "internalized" when a farmer invests in pollution abatement, through handling manure and dead stock in an ecologically sound manner. Higher expenditure per unit of output on a given farm for abatement of environmental externalities, other things equal, should be inversely correlated with the incursion of net negative environmental externalities per unit of output, under the assumptions above. Thus a farm that spends more per unit of output on environmental abatement is postulated to incur less negative environmental externalities than a farm that spends less on environmental services per unit of output.
The heroic assumption that allows us to proxy environmental mitigation with the money value of manure management is that a given amount of manure of a given sort is equally polluting whatever farm it comes off, if it is not spread on fields (one's own or someone else's). This assumes that spreading manure on crops is uniformly good (despite run-off into watercourses in some cases), and ignores the fact that farms close to population centers and watercourses probably produce more ecological harm per ton of manure than those far from people and watercourses, other things equal. By the same logic, if we are willing to assume that the relationship is cardinal as well as ordinal --$1 per 100 kg of output in abatement on farm A is twice as environmentally friendly as $0.50 per 100 kg of output on a different farm-we have a workable index that differentiates (inversely) across farms in the amount of negative environmental externalities incurred. The assumptions are not perfect, but the only feasible alternative of ignoring negative externalities altogether in econometric production work seems worse.
The components that go into a measure of environmental mitigation include all costs of disposing manure, such as: transport and other costs associated with manure disposal, costs of disposing dead birds, cost of controlling flies, and cost of pollution payment. In addition, the spreading of manure on crops is considered to transform a potential externality (pollution) into a positive contribution to soil structure and fertility. Costing this benefit is hard to do with accuracy. The simple approach adopted is to value all manure sold for spreading on the fields of others (the reason it is purchased) at its sale value at the producing farm gate. Manure spread on one's own fields is valued at what it could have been sold for, at the farm gate. Thus, if manure is spread in the field and has any market value (i.e. people are not just dumping), the latter is included in the internalization of the externality. The worst that any farm can do under this approach is to have no abatement expenditure at all per unit of output, and this is in fact the case for many farms.
Having a working index of environmental mitigation creates a new problem and a new opportunity. The new problem is that this index measured in Reals per kg of broiler (or per egg in the case of layer or per kg of swine meat per pig or liter of milk per cow), is in many cases simultaneously determined with profits per unit. Thus profit per unit depends on environmental mitigation expenditures, but environmental mitigation expenditures are also influenced by profit. The new opportunity is the solution to the econometric problem; this is to create an instrumental variable for environmental mitigation by regressing it on a series of exogenous determinants of environmental mitigation. Opportunity lies in the insights that this also gives into why some farms are more prone to spend more on environmental mitigation than others.
Among the factors accounted for in this study that might influence the difference in the amount of environmental mitigation expenditure across farms are differences across farms in access to assets and information (transactions costs), other farm characteristics such as location, and policy subsidies. Examples of such variables are: education, experience, gender, and age of household head, access to information and technical assistance, mortality rate, family labor, scale dummy, and other locational variables. The predicted value of the dependent variable from these regressions-environmental mitigation-can then be used as an explanatory variable in the second stage regression that explains why some farms are closer to the profit frontier than others.
The measurement of environmental mitigation by the procedure above is only one approach to measuring the important environmental impact of livestock. It was motivated by the need to incorporate environmental factors in the in the analysis of efficiency. However, more direct measures of environmental impact are possible outside this framework. The next section explores a methodology for directly assessing the interaction of animal density and environment.
Studies by Mulla et al (1999) and others indicate that a proper application rate is the only manure management practice affecting the potential contamination of water resources by manure nutrients, and in fact has very little to do with manure management technology per se. Using the above approach to look at the effect on profitability of different efforts to mitigate environmental problems. However, this in fact says little about the effectiveness of these measures or whether they are necessary. To know the latter, one would have to actually follow the nutrient chain from each household to the final uptake of the nutrient by some source. Furthermore, to ensure that the actual uptake was occurring, one would have to do specific measurements of the disposal of the nutrients and the uptake. As noted above, this is beyond the ability of the project to address.
However, it is possible to estimate the potential of the externality in terms of the ability of a farm to utilize all nutrients on farm that it produces from the household survey conducted. If the manure produced exceeds the potential for on-farm use, then one needs to either (1) sell the manure, (2) transport the manure to an area where there is enough land for application, or (3) utilize a processing technology to transform the manure to a product amenable to profitable long distance or produces a product that eliminates the need for transportation. This may also help us understand why some farms may be spending more money on investing on manure mitigation technology than others and it may also help to understand differences across size of operations, particularly if large farms have limited land to dispose of manure.
To see whether a farmer has the ability to utilize all manure on their own farm, the farm balance of manure nutrients relative to the farm's potential to utilize the nutrients through crop production is calculated based on the farm level data collected in the household survey. From these numbers, the amount of nutrients in the manure is estimated in terms of organic nitrogen (N) and phosphate (P_{2}O_{5}). These two nutrients were chosen because they are the nutrients for which regulations are primarily written, assuming that there is any regulation at all. The amount of chemical fertilizer applied per land unit was also included, when available, to compute the mass balance of nutrients applied to the land. Crop assimilation capacity was estimated to determine whether a crop could assimilate all the nutrients produced on farm. Next, the amount of manure sold off-farm, if any was subtracted.
Animal Unit Calculations
Nutrient values from animals were calculated based on animal units, the most commonly used metric to calculate nutrient levels. Animal unit conversions are used because it is recognized that the amount of manure produced from a broiler is not equivalent to the amount produced by one swine. This method is used to equate excretion across species. One animal unit is equal 250 broilers or layers, which is based on averages used by the US Extension Service. Given the level of nutrients may also differ by species based on what is eaten, the amount of nutrients for each species also differs. For instance while 250 chickens produce 298 pounds (135.1 kg) of nitrogen per year and 209 pounds (94.8 kg) of P2O5 per year. Table ___ shows the exact conversions for the other animals.
Table 4.1 Animal Unit Conversions
Animal |
Animal Unit |
# of N |
# of P_{2}O_{5} |
Layer |
250 |
298 (135.1 kg) |
209 (94.8 kg) |
Broiler |
250 |
298 (135.1 kg) |
209 (94.8 kg) |
Swine |
5 |
150 (68 kg) |
118 (53.5 kg) |
Cattle |
1 |
109 (49.4 kg) |
69.5 (31.g kg) |
Different countries have different conversions/limits. For instance, according to the European Community Directive, the number of manure-producing animals per hectare of land is limited to 2 dairy cows, 4 ground stock/beef cattle; 16 fattening pigs; 5 sows with piglets; 100 turkeys, or ducks; 133 laying hens; or 285 ground hens, for 0 to 16 weeks. This is equivalent to a limit of 170 kg/ha/yr of total nitrogen (including that deposited while grazing) in zones deemed vulnerable in regard to nitrate leaching (Williams 1992). It is expected that the above conversion factors will be lower for many of the developing countries, since the amount of nitrogen and phosphate excreted in animal manure depends on diets, species and age of animal (Faassen and van Dijk, 1987).
Total Nutrient Production
From animal unit estimations, the total nutrient deposition from poultry for each household is estimated where the total nutrient deposited by household h was the sum of the nutrient produced by animal units of poultry type l in household h. If data on commercial fertilizer use was available it was added to this calculations to come up with total nutrient use on farm, which would include both organic and inorganic nutrients using the following formula:
where:
l = Livestock category (broilers, layers, swine, and dairy)
n = Nutrient type
h = Household
= Total nutrient n deposited by household
AU_{lh}_{ }= Animal units of poultry type l in household h
= Form of nutrient n applied as commercial fertilizer by household h
= Amount of nutrient n produced per animal unit of animal type l
Estimation of crop up-take
The capacity of these nutrients to be utilized at the household level is estimated assuming that all the available land was planted with crop that would uptake the nutrients. This is done to determine whether a household would have the potential to utilize all the nutrients produced given their current number of animals.^{[129]}
The capacity for each household to use the nutrients produced by livestock operations is computed as the area of cropland available to the household multiplied the nutrient uptake by the crops planted on the land. To determine this, we calculated the potential for corn to take up these nutrients under the assumption that all the available cropland was planted with corn. For the purpose of the calculation we assumed that the nitrogen uptake for corn production is 144 kg per hectare and phosphorus uptake is 57.6 kg per hectare. It is recognized that again the actual figure depends on the type of soil and the ability of the soil to utilize nutrients and that tropical soils require far more nutrients than other types.
Mass balance
In order to determine the nutrient balance on the farm the difference of manure nutrient production and nutrient consumption is calculated. The mass balance (MB) for each nutrient of interest (nitrogen or phosphorus) is expressed by the following equation:
where:
A_{h }= area of cropland on household h
= Total nutrient up take by rice
= Nutrient production by poultry farm
The result is indicative of a household's potential assimilative capacity of nutrients based on the current number of animals on their property. A positive mass balance would imply that there is sufficient land to assimilate the nutrients produced, while a negative mass balance suggests that there is not enough land to absorb them.
Manure Sold off Farm
Although manure is a potentially valuable fertilizer, and soil conditioner, areas with concentrated poultry production may not have adequate cropland for nutrient utilization stemming from by-products on livestock. Therefore, exporting nutrients from concentrated areas to surrounding areas may be both environmentally and economically beneficial. Markets for manure exist in Brazil. Though there may be a market for manure, the market for unprocessed manure may be seasonal, as crops only need fertilizer at certain periods of their growing cycle during sometimes of the year.
To see if the households in this study who do not have the ability to absorb all the nutrients on their own farms are getting rid of excess nutrients through the market we subtract that which is sold or given away from that which is produced. We then compare the results across different size operations to see how different size producers are handling the potential problem.
A complication arises from the inclusion of contract farmers in the empirical analysis. Contract farmers do not pay for feed or other inputs, so their input prices are zero, and their output prices are typically fees negotiated in advance. Thus there is a conceptual and data problem in comparing independent and contract farmers in the same regression.
The solution adopted for the price problem posed by contracting is to use actual prices paid for inputs (zero) and received for outputs (fees) for contract farmers. These balance each other in the computation of profit for the dependent variable. On the RHS of the first stage regression, the zero input prices for contract farmers are handled using slope dummy variables for coefficients of the prices of inputs provided free to contract farmers, where the slope dummy applies if and only if the farmer in question is a contract farmer. This allows for the estimation within the same regression of different response coefficients to input prices for contract and independent farmers. Finally, particular attention has to be devoted to the farm fixed resources (land, family labor, sunk capital) provided by both contract and independent farmers. It is these variables that are central in explaining production levels of contract farmers, who are not constrained by price in expanding production.
^{[128]} The log-likelihood
function of this model is presented in the appendix of Battese and Coelli
(1993). Estimation of the likelihood function also requires the specification of
a relationship among the variance parameters such that g = var(m_{it})/[var(v_{i})
+var(m_{it})], where the parameter
g has value between 0 and 1. ^{[129]} It is recognized that in this analysis the ability for the household to absorb on all land overestimates what can be absorbed. Unfortunately it is necessary to use this estimate as most of the surveys are not detailed enough to delineate crop acreage from building area. |