The adjustment-cost model of the firm: Duality and productive efficiencyby Elvira Silva, Alfons Oude Lansink, Spiro E. Stefanou

International Journal of Production Economics


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Author's Accepted Manuscript

The Adjustment-cost Model of the Firm:

Duality and Productive Efficiency

Elvira Silva, Alfons Oude Lansink, Spiro E.


PII: S0925-5273(15)00244-3


Reference: PROECO6132

To appear in: Int. J. Production Economics

Cite this article as: Elvira Silva, Alfons Oude Lansink, Spiro E. Stefanou, The

Adjustment-cost Model of the Firm: Duality and Productive Efficiency, Int. J.

Production Economics,

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The Adjustment-cost Model of the Firm: Duality and Productive Efficiency

Elvira Silvaa, Alfons Oude Lansinkb, Spiro E. Stefanoub,c

Revised July 2014


We present the theoretical foundation for an adjustment cost technology that supports the intertemporal production decision making behavior using the directional distance function.

Dynamic input efficiency measures are developed that can separate out the impact of variable and dynamic factors inefficiency levels. An approach to implement this theory in a nonparametric fashion is developed and applied to an unbalanced panel of Dutch glasshouse firms. The application finds overuse of all variable inputs and overcapitalization of installations, the overall dynamic efficiency gain of 16% remains possible, with allocative inefficiencies indicating underinvestment in structures and installations. A comparison of static and dynamic efficiency measures finds that the static overall cost inefficiency is overestimated with technical inefficiency being overstated and allocative inefficiency being understated.

Keywords: adjustment-cost technology, directional distance function, dynamic duality, dynamic cost efficiency.

JEL Classification Numbers: D21, D24, D61, D92. a Faculdade de Economia do Porto, Center for Economics and Finance at UP, University of

Porto, Portugal b

Department of Social Sciences, Wageningen University, Netherlands c

Department of Agricultural Economics, Sociology, and Education, Pennsylvania State

University (USA)

Contact Author:

Spiro E. Stefanou 208B Armsby Building

Pennsylvania State University

University Park, PA 16802 USA

Email: 1. Introduction

The adjustment-cost model of the firm is an intertemporal (dynamic) approach to the theory of the firm where adjustment costs associated with changes in the level of the quasi-fixed factors are the source of the time interdependence of the firm’s production decisions (e.g., Lucas 1967;

Treadway 1969, 1970; Rothschild 1971; Mortensen 1973). Harmemesh and Pfann (1996) present an interesting survey of the literature on adjustment costs. The adjustment-cost model of the firm has been widely used in empirical work (e.g., Luh and Stefanou 1993, 1996; Nielsen and

Schiantarelli 2003; Letterie and Pfann 2007; Letterie, Pfann and Verick 2010). However, primal and dual analytical foundations of the production theory with adjustment costs have not yet been explored as in the static theory of production.

Several primal representations of the production technology are defined and characterized axiomatically in the static theory of production, namely the production sets and the Shephard’s distance functions (e.g., Shephard 1970; Debreu 1959; McFadden 1978; Färe and Primont 1995).

Several generalizations of Shephard’s distance functions have emerged in the production literature allowing extensions of the Farrell efficiency measures in the static context (e.g., Färe,

Grosskopf and Lovell 1985, Chapters 5-7; Färe, Grosskopf and Lovell 1994, Chapter 8; Briec 1997; Bogetoft and Hougaard 1998; Chambers, Chung and Färe 1996, 1998; Färe and Grosskopf 2000a, 2000b; Chavas and Cox 1999; Halme et al. 1999). Specifically, the directional distance functions approach has guided recently much of the development in efficiency and productivity analysis (e.g., Chambers 2002, 2008; Ball et al. 2002a, 2002b; Färe et al. 2005).

In contrast, primal representations of the production technology in the context of the adjustment-cost theory of the firm have not yet been explored. The production function has been used, in general, as the primal representation of the adjustment-cost production technology (e.g.,

Epstein 1981; Lasserre and Ouellette 1999; Ouellette and Vigeant 2001). Recently, other primal representations of the adjustment-cost production technology have emerged in the literature allowing for the possibility of multiple outputs. Sengupta (1999) addresses adjustment costs in an optimal control framework with a specification leading to a closed form solution of controls.

Silva and Stefanou (2003) show that an adjustment-cost production technology can be represented by a family of input requirement sets satisfying some regularity conditions. A hyperbolic input distance function is defined in Silva and Stefanou (2007) to represent a production technology with adjustment costs and develop dynamic measures of production efficiency.

In this paper, a directional input distance function is defined and characterized to represent an adjustment-cost production technology. The adjustment-cost (dynamic) directional input distance function generalizes the directional input distance function developed by Chambers, Chung and

Färe (1996) in the static context. We further develop the theoretical foundations of dynamic production decision making behavior via duality relationships and an approach to implement this theory in a nonparametric fashion. Using this foundation for the adjustment-cost technology, measurement of dynamic efficiency using the directional input distance function and intertemporal duality are developed. The dynamic directional input distance function provides difference measures of relative efficiency as opposed to radial measures (e.g., Lin, Chiang and