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XI. Stochastic Profit Frontier Estimation for Dairy Cow

11.1 Estimation of Environmental Equation

The estimation of the environmental equation has two objectives. The first one is to estimate effects of various factors that affect the farm spending on pollution abatement activities. The second objective is to provide an instrumental variable (IV) for the stochastic frontier estimation in section 11.3.

In this estimation, the dependent variable is the extra (marginal) costs that each farm spent specifically for pollution abatement activities per cow. These costs include equipments and materials bought/used for this purpose (e.g., water treatment and drainage system, biogas, manure storage facility, and microbes). It should be noted that these costs do not include the labor cost due to lumpiness nature of labor. Therefore, the pollution abatement cost reported in this study would be lower than the actual costs incurred by these farms.

11.2 Explanatory Variables

The explanatory variables include three group of variables, the operator's characteristics, location of farms, and farm characteristics. The operator's characteristics include the operator's gender, age, whether the farm had been run by the operator's parent(s) before s/he has undertaken it, the operator's (or spouse's) years of education (the greater number of the two). Farm location variables include distance to community, distance to waterway, and whether the farm is in older (long established) zone. Other farm characteristics include farm size (defined by total number of cows in the farm), farm density (farm land per cow), and whether the farm has grazing land for the cow.

Based on the cost measurement-which recorded marginal cost instead of full cost, about 80 percent of farmers reportedly having no pollution abatement cost. Since these cases are likely to be censoring data, we use Tobit estimation instead of ordinary least square regression in estimating the pollution abatement equation.

Out of 92 cases, 77 had complete information on the variables employed in the estimation. For the cases with missing values (most of which was distance to waterway and, to lesser extent, distance to nearest community), the missing values were substituted by provincial means for respective variables. The estimation result is presented in Table 11.1.

The estimation result, shown in Table 11.1, indicates that large farms tend to incur more pollution abatement cost per cow than smaller farms. As for other farmer's and farm characteristics, dairy farms with male operators tend to invest more in abatement schemes. The same is applied for farmers with higher education.

In reality, environmental problem has not been a major issue in dairy, except for small farms without grazing land for cow. Since, however, most of the costs in this category are investment costs (i.e., water treatment and drainage system, biogas and manure storage facility) and not include labor, it turns out that large farms with more educated farmers are more incline to invest in such facilities.

11.3 Estimation of Stochastic Profit Frontier Function

11.3.1 Specification

Dependent variable: Natural logarithm of profit per kilogram of milk Explanatory variables: in three groups

The last variable is included to capture effects of farm's pollution abatement cost on her profit. Since, however, the variable is most likely to be an endogenous one, we needed an instrumental variable for that task. In this case, the variable was obtained from the predicted value of the tobit regression from Table 11.1 above.

It should be noted that an important variable that is hypothesized to affect farm's profit per-kilogram were left out from the equation, namely, farm size, since they are conceivably endogenous variables that are often determined jointly with other choice variables or likely to correlate with the error terms of the profit frontier equation.

11.3.2 Assumptions Employed in Estimating Stochastic Profit Frontier Function

11.3.3 Estimation Result

The estimation was done by employing STATA8 (Frontier with truncated-normal model[117]). The result is shown in Table 11.2, along with the OLS estimation.

The Wald test suggests that the stochastic frontier equation could explain variation on profit across farms. The high value of gamma (which is significantly different from zero) indicates that the technical inefficiency equation plays an important role in the estimation, even though none of the coefficients in that auxilliary equation was statistically significant.

The result of the first stage of the stochastic frontier is similar to that of OLS. The result indicates that farm profit would increase with the output price. On the other hand, an increase in price of concentrate feed would decrease profit per bird significantly. The per kilogram profit also increases with the amount of land per milk-which roughly represents the land:cow ratio. This could be because the farm with abundant grazing land would be less dependent on relatively expensive concentrate feed. Also naturally, farms with higher yield (defined by kilogram of milk per milking and pregnant cows) tend to make more profit per kilogram.

None of the variables in the technical inefficiency equation was statistically significant, however

11.3.4 Farm Size and Technical Efficiency

Table 11.3 shows mean technical efficiency and profit across farm sizes. From Table 11.3, average technical efficiency appears to be similar between small and medium sized farms. However, the large farms (with more than 50 cows) have lower mean of TE. In terms of average net profit per kilogram of milk, the medium size farms made slightly higher profit per kilogram of milk than farms of other sizes. However, the large farms have much higher average yield. Therefore, when one considers profit per cow (that would account for both per kilogram profit and yield)--and especially profit per farm, the large farms tend to make more profit than the medium and small farms.

It should be noted that, as the profit frontier function has already included yield per cow in the first part, the profit frontier function in the first part has become a firm-specific one that also accounts for technological differences among the farms-e.g., on average, large farms clearly had higher yields compare to smaller farms. In effect, the so-called "TE" is simply the remaining residues from the first part, which reflect only non-technological elements. Moreover, with the imprecise estimates-as indicated by low values of t-statistics, one should be cautious not to over-interpret the estimated value of TEs.

11.4 Conclusion

The estimation of the pollution abatement equation (section 11.1) suggests that larger farm is more likely to invest in pollution abatement activity per cow. Male and farm operators with higher education tend to invest more in pollution abatement activities. Farms in newer zones tend to invest more on these activities. It is possible that farms in traditional dairy area may face less pressure from their neighbors and the local authority. In general, however, environmental problem has not been a major issue for dairy farms.

For the stochastic profit frontier function, the output and the major input price-concentrate feed--have the expected sign. Naturally, farms with higher yield per cow tend to make more per-kilogram profit. Also farms with higher land: cow ratio tend to make more profit, as the farm would be less dependent on concentrate feed.

As for the TE estimation, it is rather difficult to interpret the result, as none of the variables was statistically significant. One explanation is that, aside of price and technological differences that were accounted for in the first stage, there have been no significant factors that would affect the farm profit, since most farms use the same method of operation and had very similar contractual arrangement.

Table 11.1 Tobit Estimation of Environmental Equation: Dairy

Dependent variable: expenditure on environment cost per cow (x.01 Baht/cow)

Farm Size (all cows)



Grazing Dummy



Grazing*land per cow



Land per cow



Distance to village



Distance to river



Old zone Dummy



Male Dummy



Ln Age



Maximum Yr of Education (operator or spouse)






Number of observations LR Test chi2 (d.f.=10) Prob > chi2

91 28.89* 0.0013

Number of zero obs


Table 11.2 Stochastic Profit Frontier Estimation: Dairy

a) OLS Estimation






Ln Output Price



Ln Price of Concentrate Feed



Ln Price of Roughage



Ln Capital Cost per kg milk



Ln Farm Land per kg milk



Yield (monthly output of milk per number of milking and pregnant cows)







Adjusted R-squared


b) MLE

Profit Frontier Function




Ln Output Price



Ln Price of Concentrate Feed



Ln Price of Roughage



Ln Capital Cost per kg milk



Ln Farm Land per kg milk



Yield (monthly output of milk per number of milking and pregnant cows)



Technical Inefficiency (U)

Delta (Constant)



Male operator (dummy variable)



Ln Age



Ln Years of Education (maximum year of operator's or spouse's education)



Ln Distance to Community (km.)



Ln Distance to Waterway (km.)



Env cost incurred (Baht per cow) (predicted value)



Sigma squared


s.e. = 6.6551

Gamma (g)


s.e. = 0.0782



Log likelihood function


Wald Chi2 Test


Number of restrictions


*statistically significant at level 0.05 (one tail) or less.

Table 11.3 Average Technical Efficiency and Net Profit by Farm Size

Farm Size

Average TE (N)


Average Net Profit (Baht/Kg)

Average Net Profit (Baht/year)

Average Profit per cow* (Baht/year)

Average Yield per cow* (kg/year)

Average Yield per milking cow (kg/year)


.7411 (34)








.7582 (36)








.6327 (19)








.7283 (89)







Note: *including pregnant cows that are off-milking a few months before calf delivery.

[115] Family Labor was dropped because of possible serious measurement error and also because the possible bias because the wage variable was not available.
[116] E(y*), y* = max(0,XB+u) (using command Predict Varname, Ystar(0,.) in STATA)
[117] This is comparable to Model 2 of FRONTIER4.1 (as described in Coelli 1996).

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