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Abstract
When different technologies are present in an industry, we assume that a homogeneous technology will lead to misleading implications about technical change and inefficient policy recommendations. In this article a latent class modelling approach and flexible estimation of the production structure is used to distinguish different technologies for a representative sample of EU dairy producers, as an industry exhibiting significant structural changes and differences in production systems in the past decades. The model uses a transformation function to recognize multiple outputs; separate technological classes based on multiple characteristics, a flexible generalized linear functional form, a variety of inputs and random effects to capture firm heterogeneity; and measures of first- and second-order elasticities to represent technical change and biases. We find that if multiple production frontiers are embodied in the data, different firms exhibit different output or input intensities and changes associated with different production systems that are veiled by overall (average) measures. In particular, we find that farms that are larger and more capital intensive experience greater productivity, technical progress and labour savings, and enjoy scale economies that have increased over time.
Acknowledgements
This research commenced when J. Sauer was a visiting scholar in the ARE Department at UC Davis. Funding for this research was provided by the British Academy (SG-48134). The authors are grateful to Landscentret, Skejby, Denmark, for making the data available. We thank numerous colleagues for comments on an earlier version of this study, including A. Alvarez, E. Diewert, K. Frohberg and L. Orea.
Notes
Catherine Morrison Paul sadly passed away in July 2010. Professor Morrison Paul is missed as an outstanding economist, senior colleague and friend.
1 It also involves productive response to specific factors such as learning by doing and knowledge spillovers that may be technology-specific, which are beyond the scope of this study but will be addressed in subsequent work.
2 This is sometimes erroneously called a generalized Leontief for a primal function. For example, See Nicholson and Snyder (Citation2008, pp. 310–11).
3 Tauer and Belbase (Citation1987) deleted dairy farms from their data sample that participated in a particular (dairy diversion) program that purchased most of their feed or replacement livestock, or that had a large proportion of nonmilk sales.
4 Variables in levels such as the numbers of cows or hectares could also be included. However, as they are essentially ‘size’ variables that are already included as production structure arguments, and thus are also taken into account in the LCM model, we only included the ratio measures. In preliminary investigation when we did try including such variables, however, their estimated coefficients tended to be quite significant.
5 We initially used an organic subsidies/total subsidies variable but it had many missing values as there is only limited information for these categories of farms before 1990, and is also quite highly correlated with the chemicals ratios.
6 A measure of labour per total output rather than labour per cow was also tried in preliminary estimations.
7 The adaptation of this treatment for the transformation function was outlined by W. Erwin Diewert in private correspondence. Essentially, given the transformation function defined in Equation Equation1, if all inputs are increased by a scale factor S, and one looks for another scalar factor (US) such that U times the initial vector of outputs Y is still on the transformation function, U(S) is implicitly defined by: U(S)Y 1=F(U(S)Y 2,S X,T). The implicit function rule can then be used to calculate the derivative U′(S) evaluated at S = 1: U′(1) = (Σ k d ln F(Y 2, X)/d ln Xk )/(1 − d ln F(Y 2, X)/d ln Y 2). If this measure exceeds one, it implies increasing returns to scale.
8 The ‘delta method’ computes SEs using a generalization of the Central Limit Theorem, derived using Taylor series approximations, which is useful when one is interested in some function of a random variable rather than the random variable itself (Gallant and Holly, Citation1980; Oehlert, Citation1992). For our application, this method uses the parameter estimates from our model and the corresponding variance covariance matrix to evaluate the elasticities at average values of the arguments of the function.
9 Such computations for a particular ‘Class’ are based on using the highest posterior probability to assign farms to a particular group. If some farms have a reasonable probability of being in another class, it may be misleading to choose one reference technology. One way to deal with this is instead to compute a posterior-probability-weighted sum of the measures (Greene, Citation2002; Orea and Kumbhakar, Citation2004). However, if these probabilities are very high this is not likely to be a problem. As our average posterior probabilities range from 0.97 to 0.99 for the different classes, it does not make a substantive difference.
10 We did not provide all the estimates for all the classes as the elasticities rather than the parameter estimates are our primary results to analyse. However, the full set of estimates is available from the authors upon request.
11 The p-value for likelihood ratio tests for the different sets of constraints are all zero to at least six decimal places.
12 Note that this might underestimate the efficiency of class 2 farms as they are more diversified and this only represents the milk production rather than total production.
13 If these fitted values are based on less aggregated data the results are roughly the same, although for class 3 the fitted values for either the class 1 or class 3 technology is virtually equivalent, potentially because the smaller farms’ characteristics are not commensurate with taking advantage of the scale economies of the larger farms in class 1. This is true both when the fitted values are computed by observation and then averaged (this also results in a virtually identical fitted value for each own-class compared to the descriptive statistics) and when the results are fitted for the average values for each farm and then averaged.
14 These estimates are again comparable to those for the constrained model for each class; those estimates are available from the authors upon request.
15 Results for this model are available from the authors upon request.