In this section several hypotheses regarding the means of the variables considered in the econometric model are tested. These tests are quite simple and intended to characterize the population studied. Some examples of the tested hypotheses are: do larger farmers earn larger profits? Do larger farmers receive higher output prices? and so on. Questions related to efficiency will more properly de dealt with within the context of the frontier profit function; nonetheless a better characterization of the population on matters related to efficiency may be helpful and recommended. The tests of the population means were carried out by adjusting linear regression of each variable of interest on a set of dummy variables standing for farm size, farmer's education and other characteristics of the farm.
Next the test results are spelled, a figure with the variable means is presented and the statistical estimates reported for each hypothesis. When necessary some explanation is added.
8.1.1 Broiler
1) Unit profit is higher for largescale producers.
Source: CEPEA/ESALQ/USP
Variable 
Coeff 
TStat 
Signif 
Constant 
0.049 
10.013 
0.000 
R 
0.014 
2.663 
0.008 
R = 1 if largescale producers, R = 0 if smallscale producers
Smallscale producers have lower profits per unit of output than do largescale producers. This direct relationship between scale and profit may be related to technology and other possible market advantages possessed by larger producers.
2) Feed conversion ratios are higher for smallscale producers.
Source: CEPEA/ESALQ/USP
Variable 
Coeff 
TStat 
Signif 
Constant 
1.941 
81.562 
0.000 
R 
0.058 
2.249 
0.026 
R = 1 if largescale producers, R = 0 if smallscale producers
This is an expected result, since larger farms would use more intensive technology and have better conditions to reduce input losses in the production process.
3) Large producers receive higher prices for output than small producers.
Source: CEPEA/ESALQ/USP
Variable 
Coeff 
TStat 
Signif 
Constant 
0.070 
21.849 
0.000 
R 
0.011 
3.161 
0.002 
R = 1 if large producers, R = 0 if small producers
Larger farmers receive higher prices; possible reasons are lower transportation costs and more homogeneous product in the case of larger producers.
4) Large producers pay higher prices of input.
Source: CEPEA/ESALQ/USP
Variable 
Coeff 
TStat 
Signif 
Constant 
0.156 
37.003 
0.000 
R 
0.010 
2.129 
0.034 
R = 1 if large producers, R = 0 if small producers
Collecting and truck loading
Source: CEPEA/ESALQ/USP
Variable 
Coeff 
TStat 
Signif 
Constant 
0.014 
18.649 
0.000 
R 
0.002 
2.849 
0.005 
R = 1 if large producers, R = 0 if small producers
Price of Litter
Source: CEPEA/ESALQ/USP
Variable 
Coeff 
TStat 
Signif 
Constant 
10.225 
2.528 
0.013 
R 
14.580 
3.326 
0.001 
R = 1 if large producers, R = 0 if small producers
This is an unexpected result. One possible explanation would be the fact that smallscale farmers are mainly located in Santa Catarina where labor and electricity would be cheaper. In the Center West, where larger farmers are, electricity is either imported from other regions or produced through pore expensive thermoelectric process.
5) Large producers are better educated than the small ones.
Source: CEPEA/ESALQ/USP
Variable 
Coeff 
TStat 
Signif 
Constant 
2.353 
7.750 
0.000 
R 
0.909 
2.762 
0.006 
R = 1 if large producers, R = 0 if small producers
6) Higher education does not lead to higher profits.
Source: CEPEA/ESALQ/USP
Variable 
Coeff 
TStat 
Signif 
Constant 
0.062 
27.595 
0.000 
E1 
0.002 
0.437 
0.663 
E2 
0.013 
1.715 
0.088 
E1 = 0 if E<=complete primary; E1 = 1 if otherwise
E2 = 0 if < complete college; E2 = 1 if otherwise
In general education was not related to profit. However, it was observed that college education is negatively related to profit. A possible reason for this latter result would be a lower dedication of better educated farmers to the farm activity.
7) Small producers have higher expenditures per unit of output on environmental mitigation costs.
Source: CEPEA/ESALQ/USP
Variable 
Coeff 
TStat 
Signif 
Constant 
0.008 
6.494 
0.000 
R 
0.002 
1.658 
0.099 
R = 1 if large producers, R = 0 if small producers
The result shows that small producers have higher expenditures per unit of output on environmental mitigation costs possibly due to higher manure spreading costs.
7) Producers with higher density of animals have lower expenditures per unit of output on environmental mitigation costs.
Source: CEPEA/ESALQ/USP
Variable 
Coeff 
TStat 
Signif 
Constant 
0.008 
10.792 
0.000 
D1 
0.002 
2.337 
0.020 
D2 
0.003 
2.080 
0.039 
D1 = 0 if D<=500 broilers/ha; D1 = 1 if otherwise
D2 = 0 if <=3000broilers; D2 = 1 if otherwise
The result shows that the producers with higher density of animals have lower expenditure per unit of output on environmental mitigation costs. One possible explanation may be the fact that farms with higher animal density sell a larger proportion of the manure while the others face the costs of storing and spreading it over the farm.
8) Producers located near to residential centers or to centers of economic activity do not have higher expenditures per unit of output on environmental mitigation costs.
Source: CEPEA/ESALQ/USP
Variable 
Coeff 
TStat 
Signif 
Constant 
0.006 
11.252 
0.000 
L1 
0.000 
0.039 
0.969 
L2 
0.002 
0.791 
0.430 
L1 = 0 if L<=20 km; L1 = 1 otherwise
L2 = 0 if <=40 km; L2 = 1 if otherwise
9) Producers located in the central west region have lower expenditures per unit of output on environmental mitigation costs.
Source: CEPEA/ESALQ/USP
Variable 
Coeff 
TStat 
Signif 
Constant 
0.007 
10.419 
0.000 
C 
0.002 
1.708 
0.089 
C = 0 if South Region; C = 1 if West Central
This was an expected result because farmers in the Center West tend to sell the manure with the exception of those who willingly produce manure for fertilizing reasons.
10) The importance of the sales of manure and other non meat products is not higher for the small producers' profit.
Source: CEPEA/ESALQ/USP
Variable 
Coeff 
TStat 
Signif 
Constant 
0.109 
4.988 
0.000 
R 
0.037 
1.583 
0.115 
R = 1 if large producers; R = 0 if small producers
11) Swine farmers are better educated than the poultry and milk ones
Source: CEPEA/ESALQ/USP

tratio 
Dairy X Broiler 
2.678 *** 
Dairy X Swine 
 4.309 *** 
Broiler X Swine 
6.368 *** 
*** Significant 1%.
8.1.2 Layer
1) Unit profit is not higher for largescale producers.
Source: CEPEA/ESALQ/USP
Variable 
Coeff. 
TStat 
Signif. 
Constant 
1.317 
0.687 
0.494 
R 
0.988 
0.498 
0.620 
R = 0 if smallscale producers; R = 1 if largescale producers
2) Feed conversion ratios are not higher for largescale farmers.
Source: CEPEA/ESALQ/USP
Variable 
Coeff 
TStat 
Signif 
Constant 
50.162 
17.821 
0.000 
R 
2.052 
0.704 
0.483 
R = 1 if largescale producers, R = 0 if smallscale producers
3) Large producers do not pay lower prices of input.
Source: CEPEA/ESALQ/USP
Variable 
Coeff 
TStat 
Signif 
Constant 
0.474 
18.173 
0.000 
R 
0.019 
0.697 
0.487 
R = 1 if large producers, R = 0 if small producers
Price electricity
Source: CEPEA/ESALQ/USP
Variable 
Coeff 
TStat 
Signif 
Constant 
0.155 
20.347 
0.000 
R 
0.014 
1.764 
0.081 
R = 1 if large producers, R = 0 if small producers
In the case of feed, no difference was observed, but for electricity, larger farmers pay higher prices.
4) Large producers are not better educated than the small ones.
Source: CEPEA/ESALQ/USP
Variable 
Coeff 
TStat 
Signif 
Constant 
4.000 
7.197 
0.000 
R 
0.904 
1.570 
0.120 
R = 1 if large producers, R = 0 if small producers
5) Higher education leads to higher profits.
Source: CEPEA/ESALQ/USP
Variable 
Coeff 
TStat 
Signif 
Constant 
0.434 
0.431 
0.667 
E1 
0.275 
0.201 
0.841 
E2 
0.534 
0.452 
0.653 
E1 = 0 if E <= complete primary; E1 = 1 if otherwise
E2 = 0 if < high school (secondary) complete; E2 = 1 if otherwise
The education level was not related to the level of profit.
6) Small producers, other things equal, have higher expenditures per unit of output on environmental mitigation costs.
Source: CEPEA/ESALQ/USP
Variable 
Coeff 
TStat 
Signif 
Constant 
0.104 
4.098 
0.000 
R 
0.061 
2.306 
0.023 
R = 1 if large producers, R = 0 if small producers
The result showing that small producers have higher expenditures per unit of output on environmental mitigation costs, possibly due to higher manure spreading costs.
6) Producers with higher density of animals have lower expenditures per unit of output on environmental mitigation costs.
Source: CEPEA/ESALQ/USP
Variable 
Coeff 
TStat 
Signif 
Constant 
0.069 
5.783 
0.000 
D1 
0.035 
2.142 
0.035 
D2 
0.006 
0.398 
0.691 
D1 = 0 if D<=0,1 chicken/m^{2}; D1 = 1 if otherwise
D2 = 0 if <= 0,4 chicken/m^{2}; D2 = 1 if otherwise
The result shows that the producers with more than 0.1 chicken/ m^{2} have lower expenditure per unit of output on environmental mitigation costs..
7) Producers located near to residential centers or to centers of economic activity have high expenditures per unit of output on environmental mitigation costs.
Source: CEPEA/ESALQ/USP
Variable 
Coeff 
TStat 
Signif 
Constant 
0.033 
3.938 
0.002 
L1 
0.047 
2.845 
0.006 
L2 
0.021 
0.985 
0.327 
L1 = 0 if <=5 km; L1 = 1 if otherwise
L2 = 0 if <=10 km; L2 = 1 if otherwise
The result shows that the producers located near (less than 5 km) to residential centers or to centers of economic activity have lower expenditures per unit of output on environmental mitigation costs.
8) There is no difference in terms of the importance of the sales of manure and other non meat/dairy products between small and large producers' profit.
Source: CEPEA/ESALQ/USP
Variable 
Coeff 
TStat 
Signif 
Constant 
0.047 
3.301 
0.001 
R 
0.002 
0.120 
0.904 
R = 1 if large producers; R = 0 if small producers
8.1.3 Swine
1) Unit profit is not higher for largescale producers.
Source: CEPEA/ESALQ/USP
Variable 
Coeff 
Testet 
Signif 
Constant 
0.251 
2.969 
0.004 
D 
0.103 
1.126 
0.262 
D = 0 if smallscale producers; D =1 if largescale producers
Both small and large producers faced losses instead of profits. Statistically no difference was detected between theses losses.
2) Feed conversion ratios are not higher for largescale producers.
Source: CEPEA/ESALQ/USP
Variable 
Coeff 
Testet 
Signif 
Constant 
2.221 
27.727 
0.000 
D 
0.110 
1.261 
0.209 
D = 0 if smallscale producers, D = 1 if largescale producers
3) Unit profits are higher for integrated/cooperative producers than for independent producers.
Source: CEPEA/ESALQ/USP
Variable 
Coeff 
Testet 
Signif 
Constant 
0.395 
7.381 
0.000 
D1 
0.373 
5.682 
0.000 
D2 
0.039 
0.612 
0.542 
D_{1} = 0 if independent, D_{1 }= 1 if otherwise
D_{2} = 1 for integrate; D_{2 }= 0 if otherwise
Independent farmers had lower profits than integrated farmers or cooperatives. The profit of the latter two are not different however.
3) The conversion ratios are not higher for integrated producers.
Source: CEPEA/ESALQ/USP
Variable 
Coeff 
Testet 
Signif 
Constant 
2.498 
46.910 
0.000 
D1 
0.246 
3.759 
0.000 
D2 
0.059 
0.924 
0.357 
D_{1} = 0 if independent; D_{1 }= 1 if otherwise
D_{2} = 1 if integrate; D_{2 }= 0 if otherwise
The conversion rate is higher for independent farmers, but not different between integrated and cooperative farmers. A possible explanation may be the rigidity of the integrated system in terms the feed supply to animals.
4) Large producers do not receive higher prices for output than small producers.
Source: CEPEA/ESALQ/USP
variable 
Coeff 
Testet 
Signif 
Constant 
130.055 
11.840 
0.000 
D 
7.313 
0.612 
0.542 
D = 0 if small producers, D = 1 if large producers
6) Large producers do not pay lower prices of input.
Source: CEPEA/ESALQ/USP
Variable 
Coeff 
Testet 
Signif 
Constant 
0.447 
22.030 
0.000 
D 
0.020 
0.906 
0.366 
D = 0 if for small producers, D = 1if large producers
There is no statistically significant difference in terms of input prices between larger and small farmers.
7) Larger producers do not receive higher output prices in integrated system.
Source: CEPEA/ESALQ/USP
Variable 
Coeff 
Testet 
Signif 
Constant 
135.432 
44.207 
0.000 
D 
2.228 
0.607 
0.547 
D_{ }= 0 if small producers; D_{ }= 1 if large producers
Within the integrated system there is no significant difference in terms of output prices between large and small farmers.
8) xLarger producers do not pay lower input prices within the integrated systems.
Source: CEPEA/ESALQ/USP
Variable 
Coeff 
Testet 
Signif 
Constant 
0.445 
17.535 
0.000 
D 
0.019 
0.611 
0.545 
D_{ }= 0 if small producers; D_{ }= 1 if large producers
Within the integrated system large and small farmers pay statistically input prices equal.
9) Large are producers better educated than the small ones.
Source: CEPEA/ESALQ/USP
Variable 
Coeff 
Testet 
Signif 
Constant 
2.500 
6.603 
0.000 
D 
2.273 
5.515 
0.000 
D_{ }= 0 if small producers; D_{ }= 1 if large producers
10) Higher education does not lead to higher profits.
Source: CEPEA/ESALQ/USP
Variable 
Coeff 
Testet 
Signif 
Constant 
0.094 
1.440 
0.152 
D1 
0.055 
0.507 
0.614 
D2 
0.049 
0.507 
0.613 
D_{1} = 0 if < 5 years of education; and D_{1 }= 1 if otherwise
D_{2} = 0 if < 10 years of education and D_{2} = 1 if otherwise
Unit profit is not affected by the level of education of the farmer.
11) Independent farmers are better educated than the integrated ones.
Source: CEPEA/ESALQ/USP
Variable 
Coeff 
Testet 
Signif 
Constant 
8.603 
15.554 
0.000 
D 
2.689 
3.196 
0.002 
D_{ }= 0 if integrate; D_{ }= 1 if independent
Independent farmers presented higher level of education.
11) Small producers, other things equal, does not have higher expenditures per unit of output on environmental mitigation costs.
Source: CEPEA/ESALQ/USP
Variable 
Coeff 
Testet 
Signif 
Constant 
0.034 
6.722 
0.000 
D 
0.006 
1.064 
0.289 
D_{ }= 0 if small producers; D_{ }= 1 if large producers
12) Producers with higher density of animals have higher expenditures per unit of output on environmental mitigation costs.
Source: CEPEA/ESALQ/USP
Variable 
Coeff 
Testet 
Signif 
Constant 
0.000 
0.094 
0.925 
D1 
0.002 
0.278 
0.781 
D2 
0.023 
3.564 
0.001 
D_{1} = 0 if <= 0,00094 animal/m^{2}; D_{1 }= 1 if otherwise
D_{2} = 1 if > 0,00366 animal/m^{2}; D_{2} = 0 if otherwise
Producers with than 0,00366 animal/m^{2 }have higher expenditures per unit of output on environmental mitigation costs. This may due to higher spreading costs associated to longer distances or larger areas to be covered.
13) Farms located near residential centers or to centers of economic activity does not have higher expenditures per unit of output on environmental mitigation costs.
Source: CEPEA/ESALQ/USP
Variable 
Coeff 
Testet 
Signif 
Constant 
0.031 
11.210 
0.000 
D 
0.005 
1.243 
0.216 
D = 0 if <= 9 km; D = 1 if > 9 km
14) Farms located in the central west region do not have lower expenditures per unit of output on environmental mitigation costs.
Source: CEPEA/ESALQ/USP
Variable 
Coeff 
Testet 
Signif 
Constant 
0.027 
11.046 
0.000 
D 
0.005 
1.214 
0.227 
D = 1 if Central West; D = 0 if otherwise
No significant difference was observed in terms of expenditures per unit of output on environmental mitigation costs between farmers from the Center West and from other regions.
15) Quality and sanity regulations are not costlier to small producers.
Source: CEPEA/ESALQ/USP
Variable 
Coeff 
Testet 
Signif 
Constant 
0.096 
2.987 
0.003 
D 
0.047 
1.347 
0.180 
D_{ }= 0 if small producers; D_{ }= 1 if large producers
8.1.4 Dairy
1) Unit profit is not higher for largescale producers
Source: CEPEA/ESALQ/USP
Variable 
Coeff. 
Testt 
Signific 
Constant 
0.037 
2.160 
0.032 
R1 
0.008 
0.299 
0.766 
R2 
0.022 
0.986 
0.325 
R1= 0 if <50 heads; R1 = 1 if otherwise
R2 = 1 if >70 heads; R2 = 0 if otherwise
2) Milk production per cow is not higher for large scale producers.
Source: CEPEA/ESALQ/USP
Variable 
Coeff. 
Testt 
Signific 
Constant 
19.545 
15.257 
0,000 
R1 
0.797 
0.391 
0.697 
R2 
0.828 
0.496 
0.621 
R1= 0 if <50 heads; R1 = 1 if otherwise
R2 = 1 if >70 heads; R2 = 0 if otherwise
3) Large producers receive higher output price than small producers.
Source: CEPEA/ESALQ/USP
Variable 
Coeff. 
Testt 
Signific 
Constant 
0.331 
23.488 
0.000 
R1 
0.007 
0.321 
0.749 
R2 
0.039 
2.107 
0.037 
R1= 0 if <50 heads; R1 = 1 if otherwise
R2 = 1 if >70 heads; R2 = 0 if otherwise
Dairy farmers with more than 70 cows do receive higher milk prices than smaller farmers. Possible reasons are lower transportation cost due to larger volumes and production of better quality milk.
4) Large producers do not pay higher prices of input
Source: CEPEA/ESALQ/USP
Variable 
Coeff. 
Testt 
Signific 
Constant 
712.58 
9.982 
0.000 
R1 
102.16 
0.898 
0.370 
R2 
65.68 
0.707 
0.481 
R1= 0 if <50 heads; R1 = 1 if otherwise
R2 = 1 if >70 heads; R2 = 0 if otherwise
5) Large producers better educated than the small ones
Source: CEPEA/ESALQ/USP
Variable 
Coeff. 
Testt 
Signific 
Constant 
7.400 
7.784 
0.000 
R1 
2.908 
1.920 
0.057 
R2 
1.048 
0.846 
0.398 
R1= 0 if <50 heads; R1 = 1 if otherwise
R2 = 1 if >70 heads; R2 = 0 if otherwise
Larger farmers (50 heads or more) are better educated than smaller farmers.
6) There is no significant relationship between education and unit profit of milk farmers.
Source: CEPEA/ESALQ/USP
Variable 
Coeff. 
Testt 
Signific 
Constant 
0.055 
5.443 
0.000 
E1 
0,016 
1.018 
0.310 
E2 
0,004 
0.282 
0.778 
E1 = 0 if <5 years; E1 = 1 if otherwise
E2 = 1 if > 10 years; E2 = 0 if otherwise
7) Small farmers do not have higher expenditures per unit of on environmental mitigation cost.
Source: CEPEA/ESALQ/USP
Variable 
Coeff. 
Testt 
Signific 
Constant 
0.005 
1.866 
0.0639 
R1 
0.004 
0.991 
0.3231 
R2 
0.001 
0.321 
0.7485 
R1= 0 if <50 heads; R1 = 1 if otherwise
R2 = 1 if >70 heads; R2 = 0 if otherwise
8) Producers with higher density of animals have lower expenditures per unit of output on environmental mitigation cost.
Source: CEPEA/ESALQ/USP
Variable 
Coeff. 
Testt 
Signific 
Constant 
0.017 
13.900 
0.000 
D1 
0.013 
7.039 
0.000 
D2 
0.004 
1.820 
0.071 
D1= 0 if <0.5 heads/ha; D1 = 1 if otherwise
D2 = 1 if >1.0 heads/ha; D2 = 0 if otherwise
9) Farms located near residential centers or to centers of economic activity does not have higher expenditures per unit of output on environmental mitigation costs.
Source: CEPEA/ESALQ/USP
Variable 
Coeff. 
Testt 
Signific 
Constant 
0.0074 
5.258 
0.000 
L1 
0.0011 
0.533 
0.595 
L2 
0.0013 
0.446 
0.656 
L1= 0 if <20 km; L1 = 1 if otherwise
L2 = 1 if >50 km; D2 = 0 if otherwise
10) Producers located in the center west region have higher expenditures per unit of output on environmental mitigation cost
Source: CEPEA/ESALQ/USP
Variable 
Coeff. 
Testt 
Signific 
Constant 
0.005 
3.328 
0.001 
C 
0.006 
3.287 
0.001 
C = 1 if (SP+GO+MG); C = 0 if otherwise
11) Farmers spending more on mitigation costs have lower unit profits.
Source: CEPEA/ESALQ/USP
Variable 
Coeff. 
Testt 
Signific 
Contant 
0.058 
7.594 
0.000 
M1 
0.014 
1.032 
0.304 
M2 
0.053 
3.021 
0.003 
M1 = 1 if < 0.006 R$/litre; M1 = 0 if otherwise
M2 = 1 if < 0.016 R$/litre; M2 = 0 if otherwise
8.2.1. Econometric procedures
The stochastic frontier model, which is considered in this study, is defined by:
(1)
where:
Y_{i} denotes the output for the ith firm;
x_{i} represents a (1 X K) vector whose values are functions of input and output prices and other explanatory variables for the ith firm (fixed factors and prices);
b is a (K X 1) vector of unknown parameters to be estimated;
the v_{i} are assumed to be independent and identically distributed random errors which have normal distribution with zero mean and unknown variance, , and
the u_{i} are nonnegative unobservable random variables associated which the inefficiency of production.
In the model, the technical inefficiency effects are defined by
(2)
where:
z_{i} is a (1 X M) vector of explanatory variables associated which the technical inefficiency effects;
d is an (M X 1) vector of unknown parameters to be estimated; and
the w_{i} are unobservable random variables, which are assumed to be independent and identically distributed nonnegative truncations of normal distributions with mean zero and variance constant (s^{2}).
The method of maximum likelihood is proposed for simultaneous estimation of the parameters of the stochastic frontier and the model for the technical inefficiency effects. The program FRONTIER 4.1 written by Tim Coelli (as described in Coelli 1996  model 2 or "technical efficiency effects model") is used to obtain estimates for parameters.
There is particular interest in testing the null hypothesis that the technical inefficiency effects are not present in the model. The null hypothesis that the technical inefficiency effects are not random is expressed by where:
If g is too close to one, inefficiency effects are important explainers of profit across farms and random noise is not important. Further, the null hypothesis that the inefficiency effects are not influenced by the level of the explanatory variables is expressed by where d' denotes the vector, d, with a constant term omitted, given that it is to included in the expression, z_{it}d.
A CobbDouglas production frontier using crosssectional data was estimated. In all cases, broiler, dairy; swine and layer, the dependent variable is expressed in natural logarithm. Explanatory variables of the stochastic frontier models (variable costs and fixed factors) and explanatory variables of the technical inefficiency models are also in natural logarithm form.
8.2.2. Results for broiler
The maximumlikelihood estimates of the parameters in the stochastic frontier profit function, given the specifications for the technical inefficiency effects, defined by equations (1) and (2) are given in Table 8.1.
Table 8.1 Results for the stochastic frontier profit function  Broiler.

Variable 
Coefficients 
Standarderror 
tratio 
b_{0} 
Constant 
1.259 
0.416 
3.026*** 
b_{1} 
Feed Conversion 
0.640 
0.202 
3.171*** 
b_{2} 
Price Hired Labor 
0.032 
0.010 
3.083*** 
b_{3} 
Price of Electricity 
n.s. 
 
 
b_{4} 
Price of Litter 
n.s. 
 
 
b_{5} 
Collecting and Truck Loading Price 
n.s. 
 
 
b_{6} 
Heating Price 
n.s. 
 
 
b_{7} 
Output Broiler Price 
0.752 
0.063 
11.951*** 
b_{8} 
Agricultural Land 
n.s. 
 
 
b_{9} 
Family Labor 
0.215 
0.092 
2.346** 
b_{10} 
Capital 
n.s. 
 
 
d_{0} 
Constant 
2.626 
1.285 
2.043** 
d_{1} 
Length of Time Decision Maker in Activity 
0.145 
0.079 
1.832* 
d_{2} 
E1 Dummy (0 for < 2,1 for others) 
n.s. 
 
 
d_{3} 
E2 Dummy (0 for < = 6,1 for others) 
0.588 
0.303 
1.939* 
d_{4} 
Length of Time Decision Maker in this Farm 
n.s. 
 
 
d_{5} 
Animal Concentration in Regions 
0.372 
0.219 
1.694* 
d_{6} 
Animal Concentration on Farm 
n.s. 
 
 
d_{7} 
Environmental Cost 
1.777 
0.713 
2.491** 
d_{8} 
Distance of the City 
n.s. 
 
 
d_{9} 
Taxes 
2.551 
0.990 
2.577*** 
d_{10} 
Information Index 
2.118 
0.163 
13.018*** 
d_{11} 
DummyPR 
0.792 
0.330 
2.400** 
d_{12} 
DummyRS 
2.376 
0.963 
2.466** 
d_{13} 
DummyMG 
1.427 
0.436 
3.274*** 
d_{14} 
DummyMS 
1.330 
0.602 
2.210** 
d_{15} 
DummyMT 
1.910 
0.721 
2.650*** 
d_{16} 
DummyGO 
3.322 
0.850 
3.907*** 
s^{2} 
Sigmasquared 
0.473 
0.051 
9.202*** 
g 
Gamma 
0.965 
0.008 
123.806*** 
Source: CEPEA/ESALQ/USP
* Significant 10%
** Significant 5%
*** Significant 1%
Note: All state dummy variables are zero for Santa Catarina.
Mean Efficiency by Stratum
Source: CEPEA/ESALQ/USP
Mean Efficiency by Region
Source: CEPEA/ESALQ/USP
Mean Efficiency by Scale
Source: CEPEA/ESALQ/USP
Mean Efficiency by State
Source: CEPEA/ESALQ/USP
Based on the LR test, the stochastic frontier estimation is statistically different from the OLS estimation in which the technical effects are assumed to be absent (i. e., U_{i }= 0 for all farmers). The generalized likelihoodratio statistic for testing for the absence of the technical inefficiency effects from the frontier is calculated to be 512.447. Hence the null hypotheses of no technical inefficiency effects are rejected (critical values in Kodde and Palm (1986)). The estimated of gamma of 0.965 is also clearly different from zero (standarderror = 0,008), suggesting that the auxiliary equation (the technical efficiency equation) play an important role in the estimation of the frontier function. The gammaestimate is not significantly different from one, which indicates that the stochastic frontier model may not be significantly different from the deterministic frontier, in which there are no random errors in the profit function.
The numbers of observations used in the fitting of the broiler model was 229. Mean efficiency for broiler is 0,860.
8.2.3. Results for layer
Table 8.2 shows the maximumlikelihood estimates of the parameters in the stochastic frontier profit function, given the specifications for the technical inefficiency effects.
Table 8.2 Results for the stochastic frontier profit function  layer

Variable 
Coefficients 
Standarderror 
tratio 
b_{0} 
Constant 
101.202 
1.773 
57.091*** 
b_{1} 
Feed Conversion 
1.443 
0.216 
6.680*** 
b_{2} 
Feed Price 
1.257 
0.201 
6.259*** 
b_{3} 
Price of Hired Labor 
0.169 
0.085 
1.997** 
b_{4} 
Price of Electricity 
n.s. 
 
 
b_{5} 
Price Freight 
n.s. 
 
 
b_{6} 
Agricultural Land 
39.232 
0.695 
56.415*** 
b_{7} 
Family Labor 
n.s. 
 
 
b_{8} 
Capital 
0.060 
0.034 
1.772* 
d_{0} 
Constant 
16.126 
2.202 
7.323*** 
d_{1} 
Length of Time Decision Maker in this Farm 
n.s. 
 
 
d_{2} 
Level of Education for Decision Maker 
3.253 
0.511 
6.371*** 
d_{3} 
Age of the Decision Maker 
n.s. 
 
 
d_{4} 
Length of Time Decision Maker in Activity 
n.s. 
 
 
d_{5} 
Animal Concentration in Regions 
1.843 
0.309 
5.962*** 
d_{6} 
Animal Concentration on the Farm 
n.s. 
 
 
d_{7} 
Environmental Cost 
1.345 
0.237 
5.679*** 
d_{8} 
Distance of the City 
1.136 
0.090 
12.555*** 
d_{9} 
Information Index 
n.s. 
 
 
d_{10} 
DummySP 
10.336 
0.642 
16.088*** 
d_{11} 
DummyPR 
4.527 
0.568 
7.972*** 
s^{2} 
Sigmasquared 
2.743 
0.158 
17.392*** 
g 
Gamma 
0.998 
0.001 
1312.501*** 
Source: CEPEA/ESALQ/USP
* Significant 10%
** Significant 5%
*** Significant 1%
Note: All state dummy variables are zero for Minas Gerais.
The means efficiency by stratum, by State, by scale and by region is presented in the pictures below.
Mean Efficiency by Stratum
Source: CEPEA/ESALQ/USP
Mean Efficiency by Scale
Source: CEPEA/ESALQ/USP
Mean Efficiency by State
Source: CEPEA/ESALQ/USP
The gammaestimate for layer is not significantly different from one, which indicates that the stochastic frontier model may not be significantly different from the deterministic frontier. The estimate for Gamma is 0.998 (too close to 1) and the estimate for standard error is low (0.001). The LR test is also significant (268.602) showing that the null hypothesis of no technical inefficiency effects is rejected.
The numbers of observations used in the layer model was 89. The mean efficiency is 0.817.
8.2.4. Results for swine
The maximumlikelihood estimates of the parameters in the stochastic frontier profit function, given the specifications for the technical inefficiency effects are given in Table 8.3.
Table 8.3 Results for the stochastic frontier profit function  swine.

Variable 
Coefficients 
Standarderror 
tratio 
b_{0} 
Constant 
n.s. 
 
 
b_{1} 
Feed Conversion 
0.816 
0.150 
5.451*** 
b_{2} 
Price of Feed 
0.677 
0.103 
6.588*** 
b_{3} 
Price of Hired Labor 
n.s 
 
 
b_{4} 
Price of Electricity 
n.s 
 
 
b_{5} 
Price of Environmental 
n.s 
 
 
b_{6} 
Price of Output 
0.534 
0.178 
2.991*** 
b_{7} 
Dummy Complete Cycle (1=yes or 0=no) 
0.218 
0.054 
4.074*** 
b_{8} 
Dummy Independent (1=yes or 0=no) 
n.s 
 
 
b_{9} 
Dummy Integrate (1=yes or 0=no) 
0.102 
0.057 
1.774* 
b_{10} 
Agriculture Land 
43.883 
1.666 
26.333*** 
b_{11} 
Family Labor 
n.s 
 
 
b_{12} 
Capital 
n.s 
 
 
d_{0} 
Constant 
n.s 
 
 
d_{1} 
Length of Time Decision Maker in this Farm 
0.203 
0.121 
1.676* 
d_{2} 
Level of Education for Decision Maker 
0.567 
0.242 
2.348** 
d_{3} 
Age of the Decision Maker 



d_{4} 
Length of Time Decision Maker in Activity 
0.256 
0.148 
1.726* 
d_{5} 
Animal Concentration in Region 
0.388 
0.153 
2.540** 
d_{6} 
Animal Concentration on the Farm 
6.649 
3.743 
1.776* 
d_{7} 
Environmental Cost 
8.098 
4.650 
1.742* 
d_{8} 
Distance of the City 
0.325 
0.109 
2.982*** 
d_{9} 
Farm Distance to Nearest Neighbor 
0.206 
0.095 
2.182** 
d_{10} 
Information Index 
0.643 
0.361 
1.782* 
d_{11} 
Dummy SC 
1.205 
0.356 
3.383*** 
d_{12} 
Dummy PR 
n.s 
 
 
d_{13} 
Dummy MS 
2.816 
0.707 
3.983*** 
d_{14} 
Dummy MT 
4.911 
1.509 
3.254*** 
d_{15} 
Dummy GO 
2.601 
0.923 
2.817*** 
d_{16} 
Dummy RS 
n.s 
 
 
d_{17} 
Percent Share of Swine Production Total Income 
n.s 
 
 
s^{2} 
Sigmasquared 
0.478 
0.123 
3.892*** 
g 
Gamma 
0.986 
0.007 
148.389*** 
Source: CEPEA/ESALQ/USP
* Significant 10%
** Significant 5%
*** Significant 1%
Note: All state dummy variables are zero for Minas Gerais.
The means efficiency by stratum, by State, by scale and by region is presented in the pictures below.
Mean Efficiency by Stratum
Source: CEPEA/
Mean Efficiency by Scale
Source: CEPEA/ESALQ/USP
Mean Efficiency by State
Source: CEPEA/ESALQ/USP
Mean Efficiency by Regions
Source: CEPEA/ESALQ/USP
The estimated of gamma of 0,986 (standard errors = 0,007) is significant showing that technical efficiency equation is important in the estimation of the frontier function. The LR test is significant (100.270) suggesting that the null hypothesis related with no technical inefficiency effects is rejected.
The numbers of observations used in the fitting of the swine model was 141. Mean efficiency for swine is 0,767.
8.2.4. Results for dairy
Table 8.4 showing the maximumlikelihood estimates of the parameters in the stochastic frontier profit function, given the specifications for the technical inefficiency effects, defined by equations (1) and (2).
Table 8.4 Results for the stochastic frontier profit function  dairy.

Variable 
Coefficients 
Standarderror 
tratio 
b_{0} 
Constant 
1.682 
0.367 
4.588*** 
b_{1} 
Milk Prod. by Cow in Lactation per Day 
0.268 
0.071 
3.777*** 
b_{2} 
Humid Feed Price 
0.071 
0.017 
4.238*** 
b_{3} 
Dry Feed Price 
0.194 
0.036 
5.345*** 
b_{4} 
Medicine Price 
0.063 
0.024 
2.658*** 
b_{5} 
Genetic Price 
0.025 
0.011 
2.372** 
b_{6} 
Electricity Price 
n.s 
 
 
b_{7} 
Hired Labor Price 
0.048 
0.019 
2.547** 
b_{8} 
Output Price 
0.846 
0.093 
9.121*** 
b_{9} 
Membership of a Cooperative 
n.s 
 
 
b_{10} 
Agricultural Land 
n.s 
 
 
b_{11} 
Family Labor 
0.122 
0.041 
2.973*** 
b_{12} 
Capital 
n.s 
 
 
b_{13} 
Value of Herd 
3.541 
1.110 
3.190*** 
d_{0} 
Constant 
3.691 
1.504 
2.454** 
d_{1} 
Duration of Lactation in the Farm 
4.120 
0.581 
7.092*** 
d_{2} 
Experience in the Activity 
1.311 
0.221 
5.929*** 
d_{3} 
Dummy Propri 
1.925 
0.821 
2.345** 
d_{4} 
Dummy Family 
3.397 
0.924 
3.676*** 
d_{5} 
Manager Experience in the Activity 
n.s 
 
 
d_{6} 
DummyMan 
1.703 
0.603 
2.824*** 
d_{7} 
Age of Manager 
4.614 
0.833 
5.541*** 
d_{8} 
Manager Schooling 
2.005 
0.244 
8.218*** 
d_{9} 
DummyTrain 
1.369 
0.484 
2.828*** 
d_{10} 
Distance between the Farm and the City 
n.s 
 
 
d_{11} 
Information Index 
0.502 
0.161 
3.123*** 
d_{12} 
Environmental Cost 
n.s 
 
 
d_{13} 
DummyRS 
n.s 
 
 
d_{14} 
DummySC 
1.904 
0.790 
2.410** 
d_{15} 
DummyPR 
n.s 
 
 
d_{16} 
DummySP 
2.748 
0.641 
4.288*** 
d_{17} 
DummyMG 
n.s 
 
 
s^{2} 
Sigmasquared 
1.558 
0.213 
7.310*** 
g 
Gamma 
0.998 
0.001 
716.032*** 
Source: CEPEA/ESALQ/USP
* Significant 10%
** Significant 5%
*** Significant 1%
Note: All state dummy variables are zero for Goias.
The mean efficiency by stratum, by State, by scale and by region is presented in the pictures below.
Mean Efficiency by Stratum
Source: CEPEA/ESALQ/USP
Mean Efficiency by Scale
Source: CEPEA/ESALQ/USP
Mean Efficiency by State
Source: CEPEA/ESALQ/USP
Mean Efficiency by Regions
Source: CEPEA/ESALQ/USP
The numbers of observations used in the fitting of the dairy model was 160. Mean efficiency for dairy is 0,756.
The gamma estimated is 0,998 (standard errors = 0,001) clearly significant, showing that the model is no equivalent to the average response function, which can be efficiently estimated by ordinary leastsquare (OLS). The LR test = 291.304 is also significant showing that the null hypotheses of no technical inefficiency effects is rejected.
Using the same methodology for the profit, the equation with dummies variables were adjusted to verify if the efficiency is affected by scale and region where the farm is located. The results are showing below:
Broiler
Variable 
Coeff 
TStat 
Signif 
Constant 
0.880 
73.470 
0.000 
C1 
0.040 
2.365 
0.019 
C1 = 0 if South Region; C1 = 1 if otherwise
Variable 
Coeff 
TStat 
Signif 
Constant 
0.849 
37.780 
0.000 
R1 
0.013 
0.531 
0.596 
R1 = 1 if largescale producers, R1 = 0 if smallscale producers
Layer
Variable 
Coeff 
TStat 
Signif 
Constant 
0.747 
12.130 
0.000 
R1 
0.075 
1.171 
0.245 
R1 = 1 if largescale producers, R1 = 0 if smallscale producers
Swine
Variable 
Coeff 
TStat 
Signif 
Constant 
0.722 
29.587 
0.000 
C1 
0.084 
2.531 
0.012 
C1 = 0 if South Region; C1 = 1 if otherwise
Variable 
Coeff 
TStat 
Signif 
Constant 
0.714 
16.378 
0.000 
R1 
0.062 
1.306 
0.194 
R1 = 1 if largescale producers, R1 = 0 if smallscale producers
Dairy
Variable 
Coeff 
TStat 
Signif 
Constant 
0.761 
32.609 
0.000 
C1 
0.008 
0.263 
0.793 
C1 = 0 if South Region; C1 = 1 if otherwise
Variable 
Coeff. 
Testt 
Signific 
Constant 
0.774 
19.754 
0.000 
R1 
0.039 
0.665 
0.507 
R2 
0.022 
0.450 
0.653 
R1= 0 if <50 heads; R1 = 1 if otherwise
R2 = 1 if >70 heads; R2 = 0 if otherwise
In the broiler case, the results show that the efficiency does not depend on scale, but is higher in the South region if compared to the other. Also, statistics differences between small and large producers were not observed for layer.
For the swine, the efficiency does not depend on scale, but depends on the region where the farm is located. The producers whose farms are localized in other regions (except the South) have higher efficiency.
In the dairy case, the efficiency does not show statistics differences, neither relatively to scale or region where farms are located.