Slacks that arise when nonparametrically constructing technologies are relevant because they can be an important source of technical inefficiency. This paper extends the measurement of dynamic inefficiency in the full input-output space in the adjustment-cost theory framework to account for slacks. In particular, the paper develops the dynamic weighted additive model in Data Envelopment Analysis (DEA) and shows its main properties. Additionally, the approach is illustrated by a real application. The empirical application concerns data on large firms in the dairymanufacturing industry in the main dairy-producing countries in the European Union (France, Germany, Italy, Spain, Poland, and the Czech Republic) from 2005 to 2012. The results show the differences in average dynamic inefficiency between the analyzed countries. The findings also indicate that, not surprisingly, firms are, on average, closer to their own-country frontier than the common frontier comprising all firms, regardless of country. Greater inefficiency was also found, on average, in the new approach when related to the dynamic framework that does not account for slacks.

Introduction

The measurement of production (in)efficiency attracts considerable attention in the scientific literature, as it is a relevant topic for managers and policy-makers. 1 Since Farrell’s (1957) work showing how to empirically estimate production functions enveloping all observations in the sample, research on inefficiency measurement focuses on developing and applying static inefficiency models through the nonparametric method of data-envelopment analysis (DEA) (Charnes et al., 1978; Banker et al., 1984) or parametric approaches of deterministic and stochastic frontier models (Aigner and Chu, 1968; Aigner et al., 1977). Static models of inefficiency ignore the dynamic interdependence of firms’ production decisions over time and treat firms’ capital and other quasi-fixed inputs as fixed. If there is dynamic interdependence, assuming a static theory of production results in biased measurements of inefficiency. More recent inefficiency literature, both in DEA and parametric contexts, recognizes the importance of modelling the dynamics of firms’ production decisions (Serra et al., 2011; Silva et al., 2015; Kapelko et al., 2014; Fallah-Fini et al., 2014; Tone and Tsutsui, 2010, 2014). Despite different approaches developed to measure dynamic inefficiency of production, one can broadly classify them into two main groups. The first group of studies, initiated by Shephard and Färe (1975), Sengupta (1995), and Färe and Grosskopf (1996) rely on the idea of multi-stage production systems, in which some activities are carried over from one period to the next. For example, an output in one period is used as an input for the next, or a quasi-fixed input at the end of the period is treated as an additional output in that period. As such, this group of studies is closely related with network inefficiency models (see Avkiran, 2009; Tone and Tsutsui, 2009). Chronologically speaking, Nemoto and Goto (1999, 2003), Sueyoshi and Sekitani (2005), Chen (2009), Chen and Van Dalen (2010), Tone and Tsutsui (2010, 2014), and Skevas et al. (2012) are all examples of this research line of dynamic inefficiency studies. The second group of studies employs the adjustment-cost technology framework, in which the dynamic interdependence of firms’ production decisions is in the form of adjustment costs. These costs that represent transaction or reorganization costs, such as for learning, arise in this framework from the changes in quasi-fixed factors of production associated with investments in these factors.