Conversión alimenticia de las coas

To test the general hypotheses that inefficiency effects are either absent or present, or have a simpler distribution than we have assumed, we use one – sided generalized likelihood – ratio tests. Results from these tests provide evidence to reject/accept the

89 An insignificant estimate of LR - test means that no inefficiency prevails and all of the error is due to random noise and specification of a stochastic frontier model is inappropriate.

hypotheses: that inefficiency effects are absent, that observed inefficiencies have no random component and that the efficiency explanatory (socioeconomic) characteristics of industries are not jointly significant in explaining observed patterns of inefficiency. If we reject, it means that inefficiencies are present, that these inefficiencies have a stochastic component, and that the non – stochastic component of these inefficiencies is systematically related to certain characteristics of the observed industries. We also estimate the information criteria for each estimated model, namely, the Akaike information criterion, the Bayesian Schwarz information criterion and the Hannan – Quinn criterion (model selection criteria). These criteria attempt to answer the question regrading the overall model fit. The criteria differ in how each of these aspects is measured and weighted.

The Akaike information criterion (AIC) is estimated as:

The Bayesian Schwarz information criterion (BIC) is estimated as:

n are often used as a guide in model selection (Aznar Grasa 1989). Information criteria are often used as a guide in model selection. The notion of an information criterion is to provide a metric that strikes a balance between goodness of fit and a small number of parameters. The most accurate models in stochastic frontier estimation present the lowest value of each of these criteria (i.e. minimize the criteria).

As far as the inefficiency effects presence, in this estimation, we use the λ -

se is the estimator for its standard error.

The statistical significance of λ obtained from the ML estimates indicates the existence of a stochastic frontier function (Schmidt and Lin, 1984). If λ is statistically different from zero, it implies that the difference between the observed and the frontier production is dominated by technical inefficiency. If λ is not statistically significant from zero, this implies that any difference in the production is attributed

90 In general, the more variables included in the regression, the smaller will be the RSS. But if a variable only contributes marginally to the reduction of the RSS, it should not be included.

solely to symmetric random errors. In other words, industries are operating on the frontier, are technically efficient and except fro random disturbances, are receiving maximum output response for the combinations of the bundle of inputs used.

The ratio of industry specific variability to total variability, γ, shows the degree in which industry specific technical efficiency is important in explaining the total variability of output produced. The value of γ estimates the percentage of the discrepancies between the observed and the maximum frontier values of output is due to the shortfall of realized output from the frontier is primarily due to factors that are within the control of the industry. In other words, γ measures total variations in output from the frontier attributable to technical efficiency⁹¹.

One can also test whether any form of stochastic frontier production function is required at all by testing the significance of the γ parameter.⁹² If the null hypothesis, that γ equals zero, is accepted, this would indicate that σ_u² is zero and hence that the Uit term should be removed from the model, leaving a specification with parameters that can be consistently estimated using ordinary least squares.

3.5. Concluding Remarks

The objective of this chapter is to estimate the Transcendental Logarithmic Production Function of manufacturing industries in selected E.U. economies, considering a panel data model for inefficiency effects in stochastic production frontiers based on the Battese and Coelli (1992, 1995) models, providing translog effects, as well as industry effects.

91 One can also test whether any form of stochastic frontier production function is required at all by testing the significance of the γ parameter.⁹¹ If the null hypothesis, that γ equals zero, is accepted, this would indicate that σ_u² is zero and hence that the U_it term should be removed from the model, leaving a specification with parameters that can be consistently estimated using ordinary least squares.

92It should be noted that any likelihood ratio test statistic involving a null hypothesis which includes the restriction that γ is zero does not have a chi-square distribution because the restriction defines a point on the boundary of the parameter space. In this case the likelihood ratio statistic has been shown to have a mixed chi-square distribution. For more on this point see Lee (1993).

More specifically, this chapter estimates stochastic parametric frontiers for which the producer effects are first an exponential function of time, followed by the estimation of producer effects as an exponential function of time and related exogenous variables (efficiency explanatory factors). The model decomposes technical efficiency into two components: technological growth (essentially, a shift of production possibility frontier, set by best-practice industries) and inefficiency changes (i.e., deviations of actual output level from the production possibility frontier). The estimated model accommodates not only heteroscedasticity but also allows the possibility that an industry may not always produce the maximum possible output, given the inputs available.

Our analysis presents different alternative models for technical efficiency estimations, as well as their empirical results. The alternative models are being compared according to their results regarding the evolution of technical change during 1980 - 2005, the estimation of technical efficiency, as well as the distribution of technical efficiency. The chapter begins with a description of the model specifications, the data set, and the definition of the variables, along with their descriptive statistics. Then the empirical model is formed with estimation results for different alternative model specifications, providing the industry -level estimates of technical efficiency using the time-varying inefficiency model within a composite error framework. Further, factors that determine variations of technical efficiency are established and a comparison of technical efficiency is made, both before and after accounting for different explanatory variables in the inefficiency term. This includes reporting the estimated technical efficiency of an industry, the discussion of causes of variations in efficiency explanatory efficiency and discussion of the conditional efficiency.

More specifically the model is extended in order to include industry specific effects (by employing industry composite dummies), so as to examine differences in efficiency level among different industries. For this reason, our model is estimated including the industry – specific composite dummies. The results include reporting the estimated technical efficiency and the related explanatory variables.

Chapter 4