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III. Approach

3.1 The Methodological Challenges

The primary methodological challenges of empirical work on why livestock production is scaling-up are two: to define a quantitative measure of relative farm competitiveness in production and to look in a structured way at all the factors that differ across farms that might explain higher relative competitiveness. Factors explaining competitiveness 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 farmers get a better deal from the state than others).

The omission of relevant factors, such as 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, the relative competitiveness of certain producers might be enhanced if they are recognized as sales -leaders; but being recognized as sales- leaders may be the result of their being more competitive than others. Unless appropriate procedures are used, the two-way causality among the variables leads to bias in the empirical estimation of the effect of all variables.

3.2 Defining a Farm-Specific Measure of Relative Competitiveness

Relative competitiveness might be thought of as 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 these markets exist, and to cut costs by remunerating their own (family) labor less than a large farmer pays 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: even 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 large farms still have lower per unit production costs if smallholders do not cost their family labor. If so, 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 it 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 in an allocative sense (being at 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 from them. This then yields a measurable index of relative competitiveness: relative farm efficiency in securing profit per unit of output. Ceteris paribus, producers who 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 in 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 as 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 factors 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 situation studied in the Philippines, farm resources such as land may be non-tradable inputs and must be accounted for in the frontier in terms of the amount available, 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 transaction 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 3.1 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 by 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 3.1. Frontier (MLE) stochastic profit function for a sample of farms

Farm-specific profit efficiency (deviations below the frontier) is measured as the ratio of actual profit per unit (Yi 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 Yi/Y* is bounded by 1 (best = on the frontier) and 0 (worst- = 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 the 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 transaction cost barriers or policy distortions may also impact on their position relative to the frontier.

3.3 A Methodology to Decompose the Determinants of Relative Profitability

3.3.1 Building on the Stochastic Profit Frontier Literature

This leads us to the principal 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 transaction 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:

Yi = f(Xi,Wi,Pi;b)exp(ni-ui)


where Yi = profit per farm i normalized by quantity of output Qi (i.e., unit profit) defined as:

Yi = ((PiQi-CiQi)/Qi



PiQi = Total revenue from livestock category (broiler and hogs) per farm i in, depreciation, etc., of securing revenue, excluding family labor per farm i

Qi = Quantity of output per farm i

Xi = Vector of fixed factors used to obtain Yi (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 Qi;

Wi = Vector of farm-specific input prices

Pi = Weighted-average output price (weights are the farm-specific transaction quantities)

b = Vector of unknown parameters to be estimated

ni,ui = 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. Inefficiency (u), is distributed independently as a one-sided (downwards) random variable relative to the frontier. These terms 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 levels, can only be estimated if specific assumptions are made about the distributions of u and v across farms, and then only by 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, ui ~ N(mi,su2), where mi = zikdk is the mean of a truncated-normal distribution of ui. The zik are k explanatory variables observed for farm i, associated with technical inefficiency effects (ui), and d is a vector of unknown coefficients to be estimated simultaneously with equation (1). Thus, the technical inefficiency effect, ui in equation (1), can then be specified as, ui = zikdk + ei where ei is the inefficiency error term, defined by the truncation of the normal distribution with mean equal to zero and variance s2. The truncation of ei, occurs at ei ³ - zikdk (Battese and Coelli, 1995)[41].

3.3.2 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:


(dummies) (input prices) (fixed factors)

(price - factor interactions)

(factor interactions)

+ ni - ui

(random error) (random technical inefficiency effect)

where Yi is the normalized profit of farm i defined in equation (2); Wij is the price of input j (j= hired labor, capital, feeds, and day-old chicks/weanlings, used by the i-th farm); Xik is the fixed factor k used by the i-th farm (k =is the normalized value of land in hectares, normalized value of buildings and equipment, normalized total farm labor in hours, etc.); and Dil is a vector of dummy variables for farm i (l = is dummy for contract, type of production pattern, and scale).

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 right hand side (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.

For hog production, we need to further control for the fact that some farmers do full-cycle operations (farrow-to-finish), while others do farrow-to-wean or wean-to-finish, and still others do combinations of these. The total revenue and total cost figures used to compute total revenue before normalization allow for mixing different kinds of sales and costs, as do the average farm-specific output and input prices used on the RHS of the SPF. In order to pool full-cycle and wean-to-finish producers, we use a binary dummy variable for type of producer on the RHS of the SPF, to allow for fixed differences in mean unit profits among activities on the same farm. The ni, ui are as previously defined. The akj, jkk, bjk are coefficients to be estimated by MLE using Frontier 4.1 software (Coelli, 1992).

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 some farms lose money in some years. There is in fact no perfect fix for this problem. We employ a lesser-of-the-evils approach that proves 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 from using a less appropriate functional form or arbitrarily dropping the least efficient sample members.

The technical inefficiency effects (ui) generated in equation (3) are estimated within the MLE model specified above as:

ui = do + d1Z1 + d2Z2 ... + ei


where Zi is the i-th farm characteristic determining relative inefficiency and ei 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/feeds, existence of policy distortions, experience in livestock business, age and education of household head, formal/informal training 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).

Three 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 they may be 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 differences here will help to determine relative unit profit efficiency as we define it, but the differences themselves may be a function of the latter (profit efficiency)) in some cases. Third, contract farming may be quite prevalent in some cases, and this raises the issue of which output prices and which input prices to use, as these are accounting concepts rather than actual prices for contract farmers.

3.4 Measuring Farm-Specific Internalization of Environmental Externalities

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 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 externalities 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 externalities. 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, 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 externalities "internalized", for example, when a farmer invests in pollution abatement by 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 water courses in some cases), and ignores the fact that farms close to population centers and water courses probably produce more ecological harm per ton of manure than those far from people and water courses, other things being equal. By the same logic, if we are willing to assume that the relationship is cardinal as well as ordinal - $1.0 per 100 kg of output in abatement on farm A is twice as environmentally friendly as $0.5 per 100 kg of output on a different farm - we have a workable index that differentiates (inversely) across farms the amount of negative environmental externalities incurred. The assumptions are not perfect, but the only feasible alternative - that 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 of manure, such as water treatment costs, transport cost associated with manure disposal, costs of disposing of dead animals, taxes, licenses, permits, and other costs of compliance in dealing with environmental problems. 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 pesos (Php) per kg of output, 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 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 in access to assets and information (transaction costs), other farm characteristics such as location, and policy subsidies. Examples of such variables are education, experience, and age of household head; access to credit and technical assistance; mortality rate; size of inventory; feed conversion ratio; proximity to waterways; distance to nearest market; 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.

A final complication with this approach arises from the fact that some farms will have no environmental mitigation expenditures, leading to dependent variable observations that are zero in the environmental regressions. This results in censoring of the error term if such farms are numerous. The solution in this case is to use Tobit analysis and MLE for the environmental regression, with an otherwise similar instrumental variable approach.

The measurement of environmental mitigation by the procedure above is only one approach to measuring the environmental impact of livestock. It was motivated by the need to incorporate environmental factors 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.

3.5 A More Direct Approach: Mass Balance Calculations

3.5.1 Theory of The Mass Balance Calculation Approach

A proper application rate is the principal manure management practice affecting the potential contamination of water resources by manure nutrients. In fact, this factor 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 is limited to the assumption that investment in manure management strategies and dead animal disposal is equated with eliminating a negative externality. However, this says little about the effectiveness of manure management measures or whether they are necessary. To know this, 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 uptake was actually occurring, one would have to do specific measurements of the disposal of the nutrients and the uptake. As noted above, this is beyond the scope of this project.

However, from the household survey conducted 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. 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 sale or a product that eliminates the need for transportation. Estimating the potential externality may help us to understand why some farms may be spending more money on manure mitigation technologies than others and also help us 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 (P2O5). 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.

3.5.2 Animal Unit Calculations

Nutrient values from livestock were calculated based on animal units, the most commonly used metric to calculate nutrient levels. Animal unit conversions were used because it is recognized that the amount of manure produced from a broiler is not equivalent to the amount produced by a swine. This method equates excretion across species. One animal unit is equal to 5 pigs or 250 broilers based on averages used by the US Extension Service. Given that 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 of nitrogen and 209 pounds of P2O5; it only takes 5 pigs to produce a near equivalent.

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 per hectare per year of total nitrogen (including that deposited while grazing) in zones deemed vulnerable with 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 diet, species, and age of animal (Faassen and van Dijk, 1987).

3.5.3 Total Nutrient Production

From animal unit estimations the total nutrient deposition from livestock for each household is estimated where the total nutrient deposited by household h was the sum of the nutrient produced by animal units of livestock type l in household h. If data on commercial fertilizer use was available it was added to this calculation to come up with total nutrient use on farm, which would include both organic and inorganic nutrients using the following formula:


l = Livestock category (broiler and hogs)

n = Nutrient type

h = Household

= Total nutrient n deposited by household

AUlh = Animal units of livestock 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 livestock type l

3.5.4 Estimation of Crop Up-take

The capacity of these nutrients at the household level is estimated assuming that all the available land was planted with crop that would take up 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[42].

The capacity of each household to use the nutrients produced by livestock operations is computed as the area of cropland available to the household multiplied by the nutrient uptake by the crops planted on the land. To determine this, we calculated the potential for rice to take up these nutrients under the assumption that all the available croplands were planted to rice. For the purpose of the calculation, we assum that the nitrogen uptake for rice production is 100 kg per hectare and the phosphorous uptake is 32 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.

3.5.5 Mass Balance

In order to determine the nutrient balance on the farm, the difference of manure nutrient production and consumption is calculated. The mass balance (MB) for each nutrient of interest (nitrogen and phosphorous) is expressed by the following equation:

MBn = bn Ah - Tn


Ah = Area of cropland on household h

bn = Absorptive capacity for nutrient n per unit of land

Tn = Total nutrient uptake by rice

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.

3.5.6 Manure Sold Off-Farm

Although manure is a potentially valuable fertilizer and soil conditioner, areas with concentrated livestock production may not have adequate croplands for utilization of nutrients stemming from -livestock by-products. Therefore, exporting nutrients from concentrated areas to surrounding areas may be both environmentally and economically beneficial. Markets for manure exist for poultry but are limited (or none) for dry swine manure. Occasionally the poultry manure is used directly as a fish feed. 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 some times 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.

3.6 Handling Contract Farming

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 those 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. These variables that central in explaining production levels of contract farmers, who are not constrained by price in expanding production.

[41] 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(µit)/[var(vi) + var(µit)], where the parameter g has value between 0 and 1.
[42] 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.

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