VIII. Econometric Results

8.1 Mean Hypotheses Testing

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 large-scale producers.

Source: CEPEA/ESALQ/USP

R = 1 if large-scale producers, R = 0 if small-scale producers

Small-scale producers have lower profits per unit of output than do large-scale 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 small-scale producers.

Source: CEPEA/ESALQ/USP

R = 1 if large-scale producers, R = 0 if small-scale 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

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

R = 1 if large producers, R = 0 if small producers

Collecting and truck loading

Source: CEPEA/ESALQ/USP

R = 1 if large producers, R = 0 if small producers

Price of Litter

Source: CEPEA/ESALQ/USP

R = 1 if large producers, R = 0 if small producers

This is an unexpected result. One possible explanation would be the fact that small-scale 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

R = 1 if large producers, R = 0 if small producers

6) Higher education does not lead to higher profits.

Source: CEPEA/ESALQ/USP

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

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

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

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

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

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

*** Significant 1%.

8.1.2 Layer

1) Unit profit is not higher for large-scale producers.

Source: CEPEA/ESALQ/USP

R = 0 if small-scale producers; R = 1 if large-scale producers

2) Feed conversion ratios are not higher for large-scale farmers.

Source: CEPEA/ESALQ/USP

R = 1 if large-scale producers, R = 0 if small-scale producers

3) Large producers do not pay lower prices of input.

Source: CEPEA/ESALQ/USP

R = 1 if large producers, R = 0 if small producers

Price electricity

Source: CEPEA/ESALQ/USP

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

R = 1 if large producers, R = 0 if small producers

5) Higher education leads to higher profits.

Source: CEPEA/ESALQ/USP

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

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

D1 = 0 if D<=0,1 chicken/m²; D1 = 1 if otherwise
D2 = 0 if <= 0,4 chicken/m²; D2 = 1 if otherwise

The result shows that the producers with more than 0.1 chicken/ m² 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

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

R = 1 if large producers; R = 0 if small producers

8.1.3 Swine

1) Unit profit is not higher for large-scale producers.

Source: CEPEA/ESALQ/USP

D = 0 if small-scale producers; D =1 if large-scale 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 large-scale producers.

Source: CEPEA/ESALQ/USP

D = 0 if small-scale producers, D = 1 if large-scale producers

3) Unit profits are higher for integrated/cooperative producers than for independent producers.

Source: CEPEA/ESALQ/USP

D₁ = 0 if independent, D₁ = 1 if otherwise
D₂ = 1 for integrate; D₂ = 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

D₁ = 0 if independent; D₁ = 1 if otherwise
D₂ = 1 if integrate; D₂ = 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

D = 0 if small producers, D = 1 if large producers

6) Large producers do not pay lower prices of input.

Source: CEPEA/ESALQ/USP

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

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

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

D = 0 if small producers; D = 1 if large producers

10) Higher education does not lead to higher profits.

Source: CEPEA/ESALQ/USP

D₁ = 0 if < 5 years of education; and D₁ = 1 if otherwise
D₂ = 0 if < 10 years of education and D₂ = 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

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

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

D₁ = 0 if <= 0,00094 animal/m²; D₁ = 1 if otherwise
D₂ = 1 if > 0,00366 animal/m²; D₂ = 0 if otherwise

Producers with than 0,00366 animal/m² 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

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

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

D = 0 if small producers; D = 1 if large producers

8.1.4 Dairy

1) Unit profit is not higher for large-scale producers

Source: CEPEA/ESALQ/USP

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

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

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

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

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

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

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

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

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

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

M1 = 1 if < 0.006 R$/litre; M1 = 0 if otherwise
M2 = 1 if < 0.016 R$/litre; M2 = 0 if otherwise

8.2 Results of stochastic profit frontier

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 i-th firm;

x_i represents a (1 X K) vector whose values are functions of input and output prices and other explanatory variables for the i-th 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 non-negative 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 non-negative truncations of normal distributions with mean zero and variance constant (s²).

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_itd.

A Cobb-Douglas production frontier using cross-sectional 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 maximum-likelihood 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.

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 likelihood-ratio 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 (standard-error = 0,008), suggesting that the auxiliary equation (the technical efficiency equation) play an important role in the estimation of the frontier function. The gamma-estimate 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 maximum-likelihood 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

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 gamma-estimate 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 maximum-likelihood 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.

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 maximum-likelihood 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.

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 least-square (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

C1 = 0 if South Region; C1 = 1 if otherwise

R1 = 1 if large-scale producers, R1 = 0 if small-scale producers

Layer

R1 = 1 if large-scale producers, R1 = 0 if small-scale producers

Swine

C1 = 0 if South Region; C1 = 1 if otherwise

R1 = 1 if large-scale producers, R1 = 0 if small-scale producers

Dairy

C1 = 0 if South Region; C1 = 1 if otherwise

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.