CHAPTER 6: EMPIRICAL RESULTS OF TECHNICAL AND SCALE EFFICIENCY
6.3 Maximum likelihood results and discussion
6.3.1 Elasticity and parameter estimates
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Visual inspection of the plots reveals that CD, STL, and TL specifications appear to display acceptable levels of fit, with all three production technologies representing the actual data reasonably well. GL and NQ specifications displayed very poor levels of fit. Both production technologies failed to model the actual data with any reasonable degree of accuracy.
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elasticities, totalled 1.09 indicating slightly increasing returns to scale. This result is comparable to Tauer & Belbase (1987) and Hadley (2006), but contradictory to the findings of Kompas & Che (2006) and Cabrera et al. (2010) who reported constant returns to scale for Australian and US dairy farms.
Concerning the elasticities of production, Hadley (2006) reported similar findings for a sample of dairy farms from England and Wales, with elasticities for feed cost (0.199), capital (0.123) and herd size (0.293) constituting the largest portion of total output elasticity. In this instance, herd size was found to have the greatest effect on productivity, rather than total feed cost, as indicated by the results of this study.
Table 6.3: Maximum likelihood estimates of the specified production functions, East Griqualand and Alexandria Dairy Farms, 2007 - 2014
Para meter
Cobb-Douglas Simplified Translog
Time invariant Time variant Time invariant Time variant
HN TN HN TN HN TN HN TN
β0 2.279 *** 2.423 *** 2.504 *** 2.589 *** 0.150 ** 0.198 *** 0.144 ** 0.161 ***
βV -0.006 -0.006 0.001 -0.003 0.084 . 0.084 . 0.077 . 0.081 .
βL 0.196 *** 0.193 *** 0.179 *** 0.184 *** 0.084 0.086 0.061 0.053
βF 0.477 *** 0.496 *** 0.465 *** 0.483 *** 0.412 *** 0.450 *** 0.462 *** 0.455 ***
βH 0.276 *** 0.270 *** 0.345 *** 0.323 *** 0.358 *** 0.329 *** 0.371 *** 0.360 ***
βK 0.169 *** 0.147 *** 0.145 *** 0.128 *** 0.190 ** 0.152 * 0.156 * 0.162 **
ζ -0.010 ** -0.009 ** 0.000 0.004 0.001 -0.002 0.005 0.005
λ -0.002 -0.001 -0.001 -0.001
βHT -0.023 -0.020 -0.019 -0.020
βLT 0.023 * 0.024 . 0.031 ** 0.031 **
βVT -0.011 . -0.012 . -0.011 . -0.011 .
βFT 0.010 0.006 -0.002 0.003
βKT -0.003 0.000 0.000 -0.004
α 0.049 0.062 . 0.016 0.033 0.047 0.054 0.001 0.030
σ2 0.025 ** 0.012 *** 0.042 * 0.016 *** 0.025 ** 0.012 ** 0.048 * 0.016 ***
γ 0.731 *** 0.480 *** 0.847 *** 0.614 *** 0.757 *** 0.535 *** 0.878 *** 0.645 ***
μ 0.153 *** * 0.201 *** 0.162 *** 0.204 ***
time -0.098 * -0.087 . -0.095 * -0.075 *
TE 0.893 0.853 0.893 0.854 0.890 0.844 0.883 0.847
Significance codes: ***=<0.001, **=0.001, *=0.05, "."=0.1 ζ = time trend, λ = time trend2, α = regional dummy
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Para Translog Generalized Leontief
meter Time invariant Time variant Time invariant Time variant
HN TN HN TN HN TN HN TN
β0 0.169 *** 0.204 *** 0.164 *** 0.192 *** -0.253 . -0.068 -0.276 * -0.116
βV 0.07 0.083 . 0.065 0.079 0.215 0.209 0.191 0.170
βL -0.017 -0.030 -0.028 -0.045 0.431 0.344 0.391 0.333
βF 0.454 *** 0.478 *** 0.483 *** 0.500 *** -0.297 -0.364 -0.341 -0.413
βH 0.328 *** 0.333 *** 0.332 *** 0.342 *** -0.124 -0.193 0.124 0.097
βK 0.225 *** 0.209 ** 0.215 ** 0.214 ** 0.389 0.356 0.271 0.182
βLL -0.336 * -0.383 ** -0.359 * -0.426 ** -0.716 * -0.723 -0.767 * -0.787 .
βVV -0.021 -0.018 -0.03 -0.028 0.033 0.031 0.024 0.018
βFF -0.57 *** -0.569 *** -0.558 *** -0.589 *** -1.367 *** -1.317 ** -1.367 *** -1.345 ***
βHH -0.488 -0.446 -0.678 . -0.609 -0.911 -0.585 -1.264 . -1.088
βKK -0.088 -0.087 -0.145 -0.122 -0.85 . -0.659 -0.955 * -0.801
βHL -0.075 -0.128 -0.085 -0.166 -0.67 -0.778 -0.645 -0.715
βHV -0.15 * -0.148 * -0.15 * -0.146 * -0.215 -0.216 -0.185 -0.172
βHF 0.551 ** 0.544 ** 0.596 *** 0.612 *** 2.709 *** 2.593 ** 2.881 *** 2.84 ***
βHK 0.023 0.044 0.117 0.129 0.87 0.462 1.122 0.864
βLV 0.021 0.027 0.03 0.038 -0.19 -0.174 -0.184 -0.147
βLF 0.149 0.186 . 0.156 0.22 * 0.966 * 1.083 * 0.933 * 0.973 .
βLK 0.067 0.107 0.085 0.129 0.892 0.956 1.001 . 1.092
βVF 0.07 0.081 0.067 0.077 0.335 0.354 0.334 0.407
βVK 0.075 0.055 0.081 0.06 -0.094 -0.125 -0.099 -0.186
βFK -0.075 -0.096 -0.109 -0.145 0.06 0.055 0.013 0.019
ζ 0.008 0.003 0.008 0.006 0.014 0.015 0.015 0.025
λ -0.005 -0.004 -0.003 -0.002 -0.005 -0.004 -0.004 -0.002
βHT -0.004 -0.003 -0.003 -0.001 -0.014 -0.003 -0.013 -0.007
βLT 0.036 ** 0.038 ** 0.04 ** 0.043 *** 0.059 . 0.059 . 0.07 * 0.07 *
βVT -0.007 -0.008 -0.006 -0.007 -0.01 -0.008 -0.008 -0.006
βFT -0.007 -0.008 -0.013 -0.013 -0.02 -0.029 -0.031 -0.039
βKT -0.013 -0.017 -0.013 -0.02 -0.024 -0.029 -0.024 -0.033
α 0.047 0.052 . 0.024 0.032 0.061 0.061 0.036 0.038
σ2 0.018 *** 0.009 *** 0.027 * 0.012 *** 0.024 *** 0.012 ** 0.032 * 0.016 ***
γ 0.717 *** 0.435 *** 0.809 *** 0.575 *** 0.713 *** 0.455 *** 0.793 *** 0.593 ***
μ 0.125 *** 0.166 *** 0.148 ** 0.195 **
time -0.071 -0.077 . -0.059 -0.069 .
TE 0.91 0.878 0.909 0.873 0.879 0.826 0.876 0.819
Significance codes: ***=<0.001, **=0.001, *=0.05, "."=0.1 ζ = time trend, λ = time trend2, α = regional dummy
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Normalized Quadratic
Time invariant Time variant
HN TN HN TN
β0 -0.054 0.050 -0.073 0.007
βV 0.083 0.084 0.065 0.065
βL 0.262 * 0.221 . 0.234 * 0.192 .
βF 0.545 *** 0.529 *** 0.549 *** 0.536 ***
βH 0.207 0.197 0.315 . 0.287
βK 0.217 . 0.172 0.168 0.137
βLL -0.439 *** -0.432 ** -0.470 *** -0.460 ***
βVV 0.017 0.014 0.015 0.009
βFF -0.724 *** -0.710 *** -0.742 *** -0.735 ***
βHH -0.637 . -0.536 -0.851 * -0.717 .
βKK -0.431 * -0.387 . -0.481 * -0.429 *
βHL -0.060 -0.095 -0.064 -0.103
βHV -0.042 -0.039 -0.039 -0.032
βHF 0.571 *** 0.557 *** 0.620 *** 0.600 ***
βHK 0.280 0.215 0.359 . 0.291
βLV -0.032 -0.034 -0.032 -0.032
βLF 0.141 0.159 . 0.144 0.165 .
βLK 0.164 0.211 . 0.189 0.234 *
βVF 0.067 0.075 0.078 0.090
βVK -0.034 -0.037 -0.040 -0.045
βFK 0.019 0.017 0.008 0.007
ζ 0.008 0.010 0.010 0.017
λ -0.003 -0.003 -0.002 -0.001
βHT -0.009 -0.002 -0.008 -0.004
βLT 0.036 * 0.034 * 0.044 ** 0.042 **
βVT -0.007 -0.006 -0.005 -0.004
βFT -0.018 -0.021 . -0.025 * -0.027 *
βKT -0.011 -0.014 -0.012 -0.018
α 0.044 0.046 0.009 0.020
σ2 0.025 *** 0.012 *** 0.037 * 0.016 ***
γ 0.746 *** 0.502 *** 0.831 *** 0.631 ***
μ 0.156 *** 0.204 ***
time -0.072 . -0.073 .
TE 0.874 0.820 0.871 0.816
Significance codes: ***=<0.001, **=0.001, *=0.05, "."=0.1 ζ = time trend, λ = time trend2, α = regional dummy
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In an application of stochastic frontier analysis to estimate the TE of German dairy farms, Abdulai
& Tietje (2007) reported total expenditure on dairy feeds to have the largest output elasticity followed by herd size. These findings are supportive of elasticities reported in Table 6.3. Mbaga et al. (2003), in a cross-sectional study of TE on Quebec dairy farms, reported an output elasticity for capital of 0.185 for a Generalized Leontief production function with truncated normal distribution. This is broadly comparable to the value of 0.214 estimated in this study.
It is important to note that the variables included in the production functions of Hadley (2006) and Abdulai & Tietje (2007) were expressed in aggregate value terms, as were the production function variables in this study. Expressing these variables in value terms introduces several potential limitations, which will be discussed later in the chapter. This distinction becomes important when attempting to compare the results of different studies. Intuitively, similar studies with a reasonable degree of homogeneity represent acceptable benchmarks against which comparisons may be made.
On the other hand, if two studies adopt different methodologies, use different variables or modelling techniques, the results should not be considered comparable. As such, results presented in Hadley (2006) and Abdulai & Tietje (2007) are considered acceptable benchmarks against which to compare the results of this study.
The relatively large partial elasticity estimate associated with the feed expense variable is not evident in some of the previous literature such as Tauer & Belbase (1987) and Cabrera et al.
(2010), who reported partial elasticities for feed of 0.288 and 0.059, respectively. The large partial feed elasticity observed in this study is most likely due to the nature of its construction. For the purposes of this study, feed expense is expressed as total rand value expenditure on both purchased and home-grown feeds. Home grown feeds are a function of several costs, including but not limited to, fertilizer, seed, planting, harvesting and herbicide and pesticide costs. Purchased feed is expressed as total rand value expenditure on all dairy, heifer and calf meal, and dairy concentrates.
Intuitively, the inclusion of both purchased and home-grown feed components is likely to account for a large portion of the variability in dairy output. Studies considering only one of these aspects are likely to report smaller elasticities. The elasticities of Tauer & Belbase (1987) and Cabrera et al. (2010) are evidence of this as feed expense in these studies is defined in terms of purchased feed alone. Abdulai & Tietje (2007), on the other hand, express feed expense as the sum of costs
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originating from both purchased and homegrown aspects, hence the relatively large reported elasticity for feed of 0.381.
The statistical insignificance of the veterinary expense variable (βV) may be explained, in part, by the nature in which it is calculated. Veterinary expense was included in an attempt to capture farm- level variations in animal health and breeding practices, such as artificial insemination (AI).
However, due to lack of a comprehensive cost break-down of veterinary services, all veterinary expenses were pooled together into total veterinary expense.
The downside to expressing variables as aggregate values is a possible loss of information. For example, the effects of increased expenditure on AI, representing improved breeding practices, cannot be disentangled from expenditure on unhealthy or non-productive animals. To illustrate, consider two farmers who spend the same amount on veterinary services over the same period.
One farmer may have dedicated most of his resources to improving breeding performance, in an effort to positively affect milk output. The other farmer, however, may have dedicated most of his resources to maintaining health among poor producers and sickly animals, which is unlikely to stimulate milk output in the same manner. The resulting effect on milk production for these two scenarios is expected be very different, although, due to lack of information, they cannot be disentangled from one another.
It is proposed that the insignificance of the labour variable may be attributable, in part, to the capital-intensive nature of dairy farming. Commercial dairy farms typically require large investments in capital infrastructure such as milking parlours and machinery and farm implements for the production of home grown feeds. Investment in advanced production management systems is another investment which many commercial dairy farmers make. Investment in equipment of this nature generally has a labour augmenting effect and typically requires fewer, more skilled labourers to operate the equipment. It is possible that the aggregate wage bill does not have a significant effect on milk output due to the large costs associated with other factors of production, such as capital and feed. Another possible explanation for the insignificance of the labour variable may be a lack of variation in the wage data.
Of the remaining parameter estimates, two squared terms and four cross-products are statistically significant at the 95% level. Negative signs on the squared terms indicate decreasing returns to labour and feed. These results are contradictory to a priori expectations and the findings reported
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in the previous literature. According to Wadud & White (2000) and Alvarez & Arias (2003), the squared labour and feed terms are expected to be of positive sign, indicating increasing returns to labour and feed. The coefficient of the regional dummy variable (α) was positive but statistically insignificant, indicating limited variability in the data between the two production regions. This indicates that farms in East Griqualand and Alexandria are reasonably homogeneous.
Broadly, similar temperature and rainfall conditions mean both regions can facilitate the growth of good nutritional pastures. It is possible that farmers in these two regions have adopted similar milk production and feeding structures, centred primarily around grazing, with purchased feeds and concentrates fed to supplement nutritional shortfalls. Given that sampled farms in both regions are considered specialized dairy producers, it is not unreasonable to postulate that diffusion of technology may have occurred at similar rates within these areas. As a result, the levels of technology in these two regions may be relatively similar, resulting in similar production potential for a given set of inputs. Another important consideration is that sampled dairy farms all benefit from the services of a professional agricultural consultant. It is, therefore, possible that despite geographical differences, farms may share a number of similarities in operations, feeding regimes, technology and labour productivity.
The parameter σ2 represents the sum of the variances u and v (𝜎𝑢2+ 𝜎𝑣2) and γ represents the ratio of the variance of u to σ2 (𝜎𝑢2/𝜎2) (Jaforullah & Premachandra, 2003). Each of the coefficient estimates is statistically significant at the 1% level. The significance of σ2 is consistent with a priori expectations and suggests that a conventional average production function is not an adequate representation of the data (Theodoridis & Psychoudakis, 2008).
The statistical significance of γ indicates that technical inefficiency is important in explaining part of the variation in observed dairy output. The estimated value of 0.545 implies that 54.5% of total variation in dairy output may be attributed to technical inefficiency. This is marginally lower than the 61.6% reported by Theodoridis & Psychoudakis (2008) and the 64.4% and 65.4% reported for variable and constant returns to scale models reported by Jaforullah & Premachandra (2003).
Finally, concerning technological change, the estimated parameters ζ and λ incorporated into the production function to account for smooth technological change were statistically insignificant at the 10% level. Although this time trend was expected to capture at least some portion of variability in dairy output attributable to technological change, the results suggest that technological change
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was not a significant determinant of dairy production output. This result should, however, be interpreted with caution as the inclusion of a simple time trend variable to capture technological progress is a crude and somewhat rudimentary approach that may be unable to effectively capture true technological progress. Another possible explanation is that technological progress, or adoption of new technology, in these areas may have been very slow over the study period. Perhaps most farmers have already adopted relatively new technologies, and continue to benefit from them, which is why no significant technological advancement can be identified in the data.