VIII. Stochastic Profit Frontier Estimation for Swine

This study attempts to apply the stochastic frontier function to the profit equation. One can use an analogy of the "ideal" production function to argue that in a world with no transaction cost, there would be an ideal profit function. However, there are two main problems. Firstly, there is no strong theoretical support for such an analogy. Profits are not only determined by the revenue and costs of production, which in turn depends partly upon the production function, but are also significantly influenced by the random factors (or "pure luck"). Most, if not all, entrepreneurs are successful not only because of their ability but also because of luck. Moreover, if we assume zero transaction cost, the economists' definition of profit would have to change. Profits are not simply the residual after all the factors of production are paid for their services. They are the return to risk - taking activity of the entrepreneur. In a world with perfect knowledge and zero transaction cost, there would be no economic profit. Therefore, our profit frontier would be zero.

However, we can argue that the ideal profit is the maximum profit received by "the best entrepreneur" with the highest ability in management and best luck in risk-taking. As a result, the frontier function can be readily applied to estimate the frontier profit.

The second problem is an empirical issue. Our main interests in explaining the differentials in farms' profit cover three major issues, namely, the scaling up of production by structural factors (particularly technology and transaction costs), the externalities and the policy distortions. Our hypothesis is that technological change, the public concern about the negative impact of externalities generated by the pig farms, and some government policies are biased against the small-scale farms. In the estimated profit frontier function, therefore, it is postulated that profit depends upon environmental cost, prices of inputs, prices of output, fixed factors, and other exogenous variables such as farm characteristics, government policies and factors affecting farmers' transaction costs (see the list of independent variables in Table 8.5).

8.1 Estimation Problems

In estimating of the profit frontier, there are some problems with some independent variables and the dependent variable. The independent variables have the following problems: the cost of environmental abatement suffers the endogeneity problem; the problems arising from the fact that the contract farmers do not buy their inputs, e.g. feeds and piglets; and the problems of imputing the wage for the farms that employ only family workers.

8.1.1 The Net Revenue Per Unit of Output

The dependent variable is defined as the net profit per kilogram of output sold. Net profit is the revenue from the swine-growing activities - both direct and by-product income - minus the variable costs. But there are two problems.

The first problem is that our sample consists of 3 groups of farm holders, i.e., the independent growers, the price-guarantee contractees and the wage contract farmers. The letter does not make profit. Instead, they receive fixed wage per kilogram of live pigs (or fixed wage per live piglets) they successfully grow. There are 30 wage contract farms out of 174 sample pig farms. Their net revenue is not the same as the net profit received by the other two groups of farmers, but is defined as the wage income minus the costs of variable inputs, excluding the costs of feeds, piglets and drugs which are paid by their contractor. The variable costs of the wage contractees include labor, utilities, tax, and interest payment.

Since the net revenue received by the wage contractees is not the same as the net profit, the dependent variable has to be re-defined as the net revenue per kilogram of output. Then all the sample farms are pooled in the estimation of the frontier net revenue function. Yet, since the behavior of the wage contract farmers are different from the others, this study also separate the sample into two groups in the estimation of the profit frontier.

The second problem is caused by the fact that a small number of independent farms reported negative profit. To be able to run the profit frontier function, the revenue per unit has to be adjusted upward by a fixed proportion K. It is defined as the highest number that will make the net profit of the farms reporting loss become one or higher.

For the wage contract farms, the adjustment is different. The gross fee is adjusted upward by the difference in the independent farms per unit profit before and after the adjustment by K.

8.1.2 The Cost of Environmental Abatement

One main interest of this study concerns the impact of the environmental abatement on farms' profit. But the cost of environmental abatement is subject to endogeneity problem. The environmental cost does not only affect profit but may also be affected by the farm's profit. This study will use an instrumental variable approach to tackle the problem of the correlation between the disturbances and environmental cost (see the estimated results and discussion below).

8.1.3 Missing Information on Key Input Prices in the Profit Function

The second problem is a possibility of upward bias of the estimated coefficients of the feed prices. Some high caliber farmers may choose to use the high quality feed as they expect the extra revenue from high quality feed is higher than the extra cost. Ideally, some independent measure of feed quality should be included in the first stage of the profit frontier function (SPF), but that is not possible due to lack of data. The only independent measure of feed quality is the dummy variables representing the type of contractual arrangements.

However, there is another issue relating the quality of feed to the type of farms. The survey finds that all of the contract farms have to pay higher prices for their feeds, while the price-guarantee contract farms also receive higher-than-market prices for their pigs sold to the contractor. Moreover, the wage contract farmers do not have to buy any variable input, because the contractor provides them. Therefore, there are no input prices for those wage contract farms, particularly the prices of feeds and the prices of piglets. This study uses two approaches to tackle the problems. The first approach is to assign the value of zero for the prices of feeds and piglets for the contract farms. But then a dummy variable representing "contract farm" should be added in the first stage of the profit frontier (SPF) to control for the fact that contract farms have different relationship between input prices and output prices from the independent farms.

The second approach is to obtain the prices of inputs directly from the contractors. Although the input prices may not directly affect the production costs of the contractee, they may indirectly affect his/her income from the contract. In the wage contract, the contractor has to bear most of the production and price risks. So he will have to charge his contractee higher input prices in his contract account to compensate for the higher risk. But the higher the input prices, the lower the contract wage will be. Since different contractors charge different input prices, the wage income of the contractees will be different. Therefore, the input prices faced by the wage contractors are defined to include the 'accounting prices' charged by the contractor on his contractees' account. The input price data are obtained from the contractors. The net revenue for these wage contract farms is still the actual revenue reported by the farmers. To control for the differences in the relationship between net revenue and input prices of the contractees and the independent farms, the profit function will have to include the interaction terms between the contract dummy and the input prices. Moreover, since the price-guarantee contract farmers also have to buy inputs from the contractor at higher-than-market price and receive the fixed guarantee price for their output, two more interaction terms are included in the profit function, i.e., the interaction between the price guarantee dummy and the feed price, and the interaction between the price guarantee dummy and the pig (output) price.

8.1.4 Imputing Wage in the Profit Function

While most pig farms employ hired labor - both on the daily and monthly basis - many of them, particularly the small farms also use family labor. For those who do not have hired labor, there will be no reported wage rate. This study will use the average provincial wage rate as a proxy for the wages of the family workers. The average wage is the average wage of the hired workers in the pig farms in each province^[113]. We do not use zero wages as in the case of prices of piglets and prices of feeds. In the latter case, the wage contract farms do not buy the inputs. In the case of family labor, the farms owner has to pay their family workers some living allowances-either in-kind or in-cash. But the wages paid may not relate to the productivity of those family workers.

Another problem is the multicollinearity problem caused by the high correlation between the family workers and the market wages. Although the problem will reduce the estimated significance of the coefficients of family labor and wage rate, it is not the main concern of this study. Our focus is to obtain the unbiased residuals of the first stage of the profit function.

8.1.5 Non-Neutral Technical Change

Another main issue of this study is to explore the impact of technological change on the growth of the livestock sector. In the modern swine industry, technological changes do not occur as one major change, but instead they consist of a series of improvements. In the last two decades, one has seen the improvement of imported breeders from Europe, an introduction of the evaporative housing to control the temperature in the pig housing, the improvement in feeds (see Poapongsakorn et.al., 2002). Moreover, the widespread of pig-growing training has allowed farmers to develop deeper tacit knowledge of how to properly grow pigs. As a result, the farmers who have adopted those technological changes have experienced a decline in feed conversion ratio which significantly boost their profit. This study, therefore, will use the feed conversion ratio as the proxy of non-neutral technological change.

8.2 Instrumental Variables for Pollution Abatement Cost

Among farms in the livestock sector, the swine farms are probably the largest source of pollution in term of air, water and soil. Recently the rapid expansion of the swine industry, fuelled by rising income, growing urbanization, and technological change, has resulted in more serious negative impacts on the environment. Since most farms locate in the peri-urban areas and many farms are near the rivers, they are subject to complaints from the nearby community. The complaints include the bad smelt, flies and polluted canals and rivers. As a result, increasing number of farms begin in invest in pollution abatement activities. Fore example our swine farm survey shows that about 30 percent of the sample farms have invested in the water treatment ponds. The annual cost of pollution abatement per ton of pig sold is 1,458 baht per farms per year, and it varies negatively with farm size (measured in terms of stock of pigs, see Table 8.1). But the abatement cost per farm varies positively with farm size. There are as many as 64 farms that do not have any abatement cost. The question is whether or not farm size matters after other independent variables are controlled for.

Pollution abatement is defined as the marginal cost of abatement effort and the fixed costs of equipment and capital used for pollution control. The variable cost includes labor hire to get rid of manure and cost of chemicals and organism. The fixed costs are calculated as the annual depreciation. The value of the manure sold is also included as part of the abatement cost because the farmers have to incur extra cost of getting rid of manure. Finally, the abatement cost is divided by the quantity of pig sold to control for the size of farm. The independent variables are also standardized. The definitions of all the variables are given in Table 8.2.

Since the dependent variable series contains either zero or positive value, the Tobit technique is used to estimate the pollution abatement cost function.

The result is shown in Table 8.3. The coefficient of herd size is negative, but not statistically significant. Though the result is consistent with the cross-tab in Table 8.1, it is contrary to our expectation that the larger farm should invest more in pollution abatement. One possible reason is that pigs are not exported and hence the large companies are not subject to pressure from the foreign buyers. The Thai customers have not yet using their buying power to pressure the swine farms to invest in pollution abatement activities. Those who complain about the pollution problems are people who live near the farm. The complaints are mostly against the small farmers who tend to locate their farms near the village or the town. Yet the distance from the community (DISTVIL) is not significant. While the number of complaints by the nearby villagers is not significant, farmers who have engaged in activities to reduce the number of flies (FLIES) are found to invest more in pollution control. One surprising result is that farms that are farther away from river or canal (DISTVIL) tend to incur higher abatement costs. This may imply that if there is no nearby waterway, then the farmers will have to invest in pollution abatement to avoid having conflicts with the villagers.

The access to long-term credit (LTCREDIT), measure as the ratio of long-term credit to total borrowing, is significantly positive. Moreover, the farms that receive government subsidy (SUBS) to build water treatment ponds or biogas digester tend to invest more in pollution abatement. The results imply that the market failure is the significant factor contributing to negative externalities. Government subsidy and intervention in the credit market can significantly alleviate the negative effects. Farms that have income from crops (CROP) tend to invest more in pollution abatement because manure can be used on their farms. Those with non-farm income (NONFARM) may have enough capital to invest in the pollution abatement activities.

Finally, it should be noted that most of the variables measuring personal characteristics, e.g. age, education, and experience, are not statistically significant. Nor are the provincial dummy variables.

8.3 The Estimation of Stochastic Frontier Function

Each type of swine farm has different cost and revenue structure. For the independent farm, the piglet farms seem to make more profit per kilogram of pig sold than the fattening farms (Table 8.4). Among the independent piglet farms, the medium-scale farms tend to make the highest profit. The lower-medium-scale piglet farms under the price guarantee contract also make more profit than other farms. The observation that the lower-medium-scale farms make the highest profit is consistent with the fact that weaning piglets is a highly care-intensive but the farms have to be large enough to exploit the scale economies in the production process and input purchasing. For the independent fattening farms, the larger farms make more profit than the smaller ones. The large-scale fattening farms under the wage contract also make more net revenue than the smaller farms. Therefore, fattening activities are subject to economies of scale.

Given the above information on profit, it seems logical to estimate the separate profit frontier function for the fattening farms and the piglet farms since they have different production functions. However, since twenty-eight farms grow both piglets and fattened pigs, both activities can be considered as parts of the same production process. Therefore, we will estimate both fattening and the piglet farms.

The dependent variable is the natural logarithm of net revenue per kilogram of pig sole, where the net revenues for the independent farmers and the contract farmers are defined above.

The independent variables can be classified into two groups, i.e., those determining the profit frontier (or the first stage profit frontier, SPF) and the transactions cost that affect the efficiency of each farm. The former consists of the following variables: prices of pig sold per kilogram (output), prices of major variable inputs (wage rate, feeds and piglet), fixed inputs per kilogram of output (capital and family labor), a proxy for technological change (LFEEDC) and the dummy variables representing different production relation among farms (see list of variables in Table 8.5).

The proxies for transaction costs are as follows: personal characteristics of the farmers which are proxies of ability and know-how, e.g., education, age and experience of the farm owner; credit constraint; transportation costs (such as distance from the community); density of pig farms; government services; and regional dummies.

All of the above independent variables, except the dummies, are in natural logarithm (see Table 8.5 for definitions).

The results in Table 8.6 show that the stochastic frontier estimation is statistically significant as shown by the value of Wald Chi-Square. The estimated value of is also significantly different from zero, suggesting that the technical efficiency equation can explain the difference between each farm's profit and the profit on the frontier function. Gamma is 0.83 and significant, suggesting that some variations in farms' profits are caused by the transaction costs.

The estimates show that the output price (LPRICEPIG) has positive and significant impact on farm profit. The feed price (LFEEDP) coefficient is weakly significant and has the expected negative sign. The price of piglet (LPIGLET) also has the negative and significant coefficient. Wages (LWAGE2) are not significant because it is highly correlated with family labor. The capital (LCAPITAL) and family labor (LFMILY) coefficients are positive but not significant. Other dummy variables controlling for the contractual arrangement (CONTRAC1, GUARANTEE) and nature of farm integration (full cycle farm or FCYCLE) are not significant, except the dummy variable representing the piglet farm (BABY). But the most robust parameter is the feed conversion ratio (LFEEDC) that has the expected sign. The higher the feed used to produce one kilogram of pig meat, the lower the profit. This means that the farmers who adopt the best technology in pig production will make more profit. Another interpretation is that farmer with better management capability (or know- how) can make higher profit.

The technical efficiency equation also yields satisfactory result. It should be noted that the positive coefficient represents inefficiency (value of m) because the value of u would be higher when the farm is farther away below the profit frontier. The higher the cost of environmental abatement (PRE-ENVM2), the lower the profit is. Older farmers (LAGEHH) and farms in the East and the Central regions are less efficient. Although formal education (LYEAREDU) is not significant, farmers who receive training (TRAINING) in pig production are more efficient.

The more efficient farms are those that are far from the town (LVILLKM), far from the slaughterhouse (LSLAVGHKM) and farmers who seek advice from the consultant, pig manual or the contractor (MANAGA). Perhaps, the farms that are far from the community and the old slaughterhouse may be the new farms with modern equipment.

Farms that invest more in environmental abatement seem to make less profit since preenvm2 is positive and significant. Farms that buy feeds on credit term (CREDIT) are also more efficient.

Other independent variables are not statistically significant. They include gender of the farm owner (FEMALE), owner's farm experience (LEXPERHH), farm density within 1 square km. (LDENFARM), credit constraint (CRECONST), farms that sell pigs directly to the slaughterhouse or food processors (TRANPRO), and these receiving government services (SERVICE) or having good ventilation system for their pig house (VENTIL), or those changing feed formula last year (CHANGFED).

Table 8.7 also gives another set of frontier estimation with separate prices of two kinds of feeds, i.e., mixed feeds and ready-to-use feeds produced by the feed manufacturers. But the results are not better than the estimation with one feed price.

Table 8.8 presents another set of profit frontier estimation which uses different definitions of input prices, i.e., the input prices of contract farms are not zero but are assigned the value of the average price for each province. In the estimation, several interaction terms between the type of farm and the input and output prices are also included. But the results are not much different from those in Table 8.6. The only interesting result is that the interaction of price-guarantee contract and the pig price (GUAPRIC) is positive and significant, while the price of pig (LPRICPIG) is still significant, but with slightly higher coefficient. This means that the guarantee contract farms that have higher guarantee price will have higher profit than other farms. After the control, the price of pig has larger positive effect on farms' profit.

Although the farm size is not included in the profit frontier function because there is already a proxy of non-constant technological change in the estimation (i.e., logarithm of feed conversion ratio), one can calculate the technical efficiency by farm size. The TE 2 produced by STATA has the value between 1 and 0, with one as the most efficient. The estimates in Table 8.9 show that the large-scale farms have higher efficiency than other farms, while the efficiency of the small- and the medium-scale farms are not different. The results are different from the simple cross tabulation of profit and farm size in Table 8.4. Therefore, after controlling for the independent variables affecting profit, the large-scale farms are relatively more efficient. The findings are consistent with casual observation that in the recent years the average swine farm size has become larger.

8.4 The Profit Frontier of Two Different Types of Farms

As mentioned above, the piglet farms and the fattening farm have different production functions. While the piglet farms are relatively care-intensive activity, the fattening farms are more labor-intensive requiring the employment of unskilled or semi-skilled workers to feed the pigs and to clean the pens on the fixed schedule basis. Thus, the fattening farms can exploit the economies of scale by investing in laborsaving technology. The tasks that are subject to economies of scale include bulk purchasing of inputs, feed mixing process, automatic feeding process and large quantity of pig sold each time. However, the full-circle pig farms still have to grow breeders and wean piglets. Currently more and more large farms tend to separate their piglet farms from the fattening farms by separating the farmhouses or even locating their farms in different location so that the disease problems in one farm do not spread to the others. Unfortunately, our farm survey cannot obtain separate set of financial data for those two types of farms.

Given such constraint, we estimate two profit functions; one for the piglet farm and the other for the fattening farms that sell only fattened pigs. The latter includes both the full-cycle farms (from farrows to finish) and the wean-to-finish farms. The estimated results for piglet farms are shown in Table 8.10. The results are similar to the pooled profit frontier estimation, but the estimates, which contain one variable of feed prices, are slightly better than the one that has two-price variable because the Wald Chi Square is higher.

There are a few interesting results. First, the piglet farms that incur pollution abatement costs are not less efficient than those that do not invest. This is opposite to the pooled estimation. Secondly, family labor (LFAMILY) and capital (CAPITAL) have positive and significant coefficients despite the fact that the wage rate is not significant. Using more family workers can increase profit because the breeder farms are too care-intensive to depend on hired labor. Moreover, the modern breeder farms tend to invest more in the breeder housing and pens so that they can maintain the high degree of hygiene. The price-guarantee farms also receive higher profit. Thirdly, only a few independent variables, which are the proxies for transaction costs, are significant. Though age, education, and experience are not significant, training enables the farmers to make more profit. Farmers who changed the feed formula in the survey year are also more efficient. Farms in the central region (CENTRAL) are also more efficient. But it is very strange that the credit constraint variable (CRECONSI) is negative and significant. Finally, the estimates of the technical efficiency by farm size show that the farms with 101-500 pigs are the most efficient (see Table 8.9). The estimation is consistent with the actual profit shown in Table 8.4.

Most of the profit frontier estimates for the fattening farms are not satisfactory as gamma is almost one, implying that the transaction costs play no role in explaining variation in profits across farms. Fortunately, one specification yields some satisfactory results (in term of LR test and value of gamma), though most of the variables in the first stage of the profit frontier estimation are not significant. In this specification, the feed price has non-zero value and several interactions between the type of contract farm and the prices of inputs or the price of output are included. The results are given in Table 8.11. All of the input and pig prices are not significant. Even the feed conversion ratio (LFEEDC) is not significant. There are only two significant variables in the first stage, i.e., the price guarantee contract dummy and the interaction between the price guarantee contract and the pig price.

Farms that invest more in the environmental abatement are less efficient which are proxies of transaction costs are significant, suggesting that the price variables and technological change play almost no role in explaining variation in farm profits.

The technical efficiency (Table 8.9) also shows that the large farms are more efficient than the small farms.

Table 8.1 Average Cost of Pollution Abatement for Swine

Source: TDRI, Livestock Farm Survey, December 2002.

Table 8.2 Variable List in the Environmental Cost Regressions

Note: Costs of environmental abatement include variable cost (labor and others) and fixed cost (amortized value). Fixed inputs are water tanks, water treatment ponds, bio-gas ponds, water pipes.

Table 8.3 Estimation of Cost of Environmental Abatement

Dependent = enco_vm

Obs. Summary: 29 left-censored observations at encovm<=0
144 uncensored observations
1 right-censored observation at encovm>=18505.05

Table 8.4 Net Revenue Per Kilogram of Pig by Farm Type

Source: Calculate from the Household Farm Survey, 2002.

Table 8.5 Variable List in the Profit Model

Note (1) Annual depreciation with following assumptions

- Cost for open housing at 20 years
- Cost for evap housing at 20 years
- Cost for office and home office at 30 years
- Cost for feed mixing building at 20 years
- Cost for manure, fences, water tanks at 10 years
- Cost for water treatment, bio-gas at 15 years

(2) Since there is no direct questions on the definitions of full-cycle and wean-to-finish farms, the definition has to be determined from 2 questions in the questionnaire, i.e., (1) what type of pigs do you sell? And (2) the stock of pigs classified by type of pigs.

Table 8.6 Results of Profit Frontier Estimation: Pooled Sample

Model 1 (output from the program STATA)

Table 8.7 Profit Frontier Estimates With Two Feed Prices

Model 3

Table 8.8 Profit Frontier Estimates With Positive Feed Price and Interaction Terms

Model 5

Table 8.9 Technical Efficiency by Farm Size: Pooled Sample

Table 8.10 Profit Frontier Estimation of Piglet Farms

Model 1

technical efficiency

Table 8.11 Profit Frontier Estimation of the Fattening Farms

Output from the program FRONTIER (Version 4.1c)

log likelihood function = -0.14700435E+03

LR test of the one-sided error = 0.22189091E+03

with number of restrictions = *

[note that this statistic has a mixed chi-square distribution]

number of iterations = 33

(maximum number of iterations set at: 100)

number of cross-sections = 90

number of time periods = 1

total number of observations = 90

technical efficiency