The technical inefficiency effects model, originally proposed by Kumbhakar, Ghosh and McGuckin (1991) and Reifschneider and Stevenson (1991), is perhaps the most widely used model in the stochastic frontier analysis. Its main advantage is that it can simultaneously (i) provide firm-specific estimates of technical efficiency and (ii) associate variation in firm performance with variation in exogenous or conditioning variables (e.g., managerial ability, socioeconomic characteristics, ownership form, etc.) characterizing the environment in which production occurs. Another useful aspect of the technical inefficiency effects model, available though only in a panel data setting, is that it permits the identification of the effects of technical change and of time-varying technical efficiency, even if both are modeled via a simple time trend (Battese and Coelli, 1995). This is so as long as the inefficiency effects are stochastic and follow a truncated distribution. Without such a distributional assumption none of the parameters associated with the time trend in the production function and in the one-sided error term capturing technical inefficiency can be identified (Kumbhakar, Heshmati and Hjalmarsson, 1997). And as a result, it is impossible to separate the effects of technical change and of time-varying technical efficiency on productivity changes.
On the other hand, a shortcoming of the technical inefficiency effects model seems to be the rather restrictive specification of the temporal pattern of technical inefficiency, at least as initially modeled by Battese and Coelli (1995). In their set up, the effect of the passage of time on technical inefficiency is necessarily monotonic and whenever is time-varying, it may be either efficiency-enhancing or efficiency- impending, but not both (Wang, 2002). This monotonicity assumption implies further that it would be the same for all observations in the sample. While the assumption that the temporal pattern of technical inefficiency is the same for all firms is quite restrictive, it is not unreasonable for a putty-clay industry (Kumbhakar, Heshmati and Hjalmarsson, 1997). In contrast, in samples with strong firm heterogeneity, it is likely that some firms will tend to improve their technical efficiency scores over time, others will tend to deteriorate them, and some will leave them unaffected. Even though all these outcomes are equally possible at the outset, it is impossible to take them into account appropriately with the specification of the temporal pattern of technical inefficiency used by Battese and Coelli (1995).
Nevertheless, the relative contribution of technical efficiency changes into productivity growth is non-monotonic because of its dependency on an adjustment function (defined as the ratio of the conditional to unconditional variance of the one- sided error term), which differs across observations. That is, the relative importance of technical efficiency changes as a source of growth differs across firms. But since the adjustment function is always positive for the technical inefficiency effects model (Wang, 2002), the effect of technical efficiency changes would be positive or negative according to the sign of the (estimated) time coefficient in the technical inefficiency effect function. And this sign is the same for all observation in the sample. Thus, with the Battese and Coelli (1995) specification of the temporal pattern of technical inefficiency, the effect of technical efficiency changes into productivity growth is qualitatively similar for all firms in the sample but it is quantitatively different.
The objective of this paper is to incorporate a flexible specification of time- varying technical efficiency into the technical inefficiency effect model. For this purpose, the Cornwell, Schmidt and Sickles (1990) specification is used.2 Its main advantages are that allow for firm-specific patterns of temporal variation in technical efficiency and more importantly, for testing for the existence of a common temporal pattern across firms. Consequently, the Battese and Coelli (1995) specification can be obtained as a special case. Moreover, it allows technical efficiency to vary through time employing a quadratic specification. Thus the proposed formulation attempts to combine the advantages of the Cornwell, Schmidt and Sickles (1990) specification (i.e., analyzing flexible temporal patterns of technical efficiency changes) with those of the technical inefficiency effects model (i.e., explaining efficiency differentials).
The proposed formulation is used to analyze the temporal pattern of technical efficiency for USA and 9 European countries (i.e., Germany, France, Italy, Belgium, Netherlands, UK, Ireland, Denmark and Greece). The empirical results indicate that the evolution of technical efficiency in these countries has been different during the period 1973-1993, and for only two countries (i.e., Denmark and Greece) technical efficiency had been time invariant. This in turn means that technical efficiency cannot be considered as a source of growth for these two countries during the period under consideration. On the other hand, it is found that technical efficiency changes have contributed positively to productivity growth in France, Italy, Ireland and USA and negatively in Germany, Netherlands, Belgium and UK. These quite different temporal patterns of technical efficiency changes could not be captured by the Battese and Coelli (1995) specification