The hidden cost of investment: the impact of adjustment costs on firm performance measurement and regulation

Abstract

In this study, we address a major problem in the measurement of firm performance and the regulation of natural monopolies, namely the intertemporal character of long-term investment decisions. Specifically, we focus on the impact of adjustment costs of investments on estimates of firms’ technical and cost inefficiency. We make use of a nonparametric dynamic data envelopment analysis to investigate the dynamic inefficiency of electricity distribution and transmission companies in the US during the years 2004–2011. These results are compared to their static counterparts. Our empirical findings reveal that ignoring long-term investments and their corresponding adjustment costs significantly distorts both firm-specific and industrial inefficiency estimates and may thus create misleading incentives for the regulated firms to cut investments.

Appendices

Appendix 1: Parametric approximation of firm-specific shadow values of capital

The dynamic cost function in a quadratic functional form is given by

$$\begin{aligned} W_{it}= & {} \alpha _0 + \alpha _{QE}\,QE_{it} + \alpha _{QC}\,QC_{it} + \alpha _{K}\,K_{it} + \alpha _{w}\,w_{it} + \alpha _{c}\,c_{it}\nonumber \\&+\, \frac{1}{2} \alpha _{QE,QE}\,QE_{it}\,QE_{it} + \frac{1}{2} \alpha _{QC,QC}\,QC_{it}\,QC_{it}+ \frac{1}{2} \alpha _{K,K}\,K_{it}\,K_{it}\nonumber \\&+\, \frac{1}{2} \alpha _{w,w}\,w_{it}\,w_{it} + \frac{1}{2} \alpha _{c,c}\,c_{it} \,c_{it} + \alpha _{QE,QC}\,QE_{it}\,QC_{it} + \alpha _{QE,K}\,QE_{it}\,K_{it} \nonumber \\&+\, \alpha _{QE,w}\,QE_{it}\,w_{it} + \alpha _{QE,c}\,QE_{it}\,c_{it} + \alpha _{QC,K}\,QC_{it}\,K_{it} + \alpha _{QC,w}\,QC_{it}\,w_{it} \nonumber \\&+ \,\alpha _{QC,c}\,QC_{it}\,c_{it} + \alpha _{K,w}\,K_{it}\,w_{it}\nonumber \\&+\, \alpha _{K,c}\,K_{it}\,c_{it} + \alpha _{w,c}\,w_{it}\,c_{it} + \alpha _{t}\,t_{t} + \frac{1}{2} \alpha _{t,t}\,t^2_{t}, \end{aligned}$$

(12)

where the subscripts i and t denote the firm and year, respectively; W represents long-run costs; QE is the flow of electricity; QC is the number of customers; K is the capital stock; t is a time trend; and c and w are the price of capital and the price of the variable input, respectively.

Representing the dynamic cost function by $g(\cdot )$, we estimate the parameters of Eq. 12 by solving the following minimization problem:

$$\begin{aligned} \begin{aligned}&min \sum _{t=1}^T \sum _{i=1}^N \epsilon _{it}^2 \\ s.t. \;&W_{it}= g(\cdot ) + \epsilon _{it}&\quad \forall i,t,&(i) \\&\partial \, g(\cdot ) / \partial \, QE_{it}&\ge 0&\quad \forall i,t,&(ii) \\&\partial \, g(\cdot ) / \partial \, QC_{it}&\ge 0&\quad \forall i,t,&(iii) \\&\partial \, g(\cdot ) / \partial \, w_{it}&\ge 0&\quad \forall i,t,&(iv) \\&\partial \, g(\cdot ) / \partial \, c_{it}&\ge 0&\quad \forall i,t,&(v) \\&\partial \, g(\cdot ) / \partial \, K_{it}&\le 0&\quad \forall i,t,&(vi) \\ \end{aligned} \end{aligned}$$

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The problem minimizes the sum of squared residuals of the quadratic dynamic cost function subject to a set of inequality constraints that impose monotonicity required by economic theory. The shadow value of capital is then approximated by the first derivative of the cost function with respect to the capital stock:

$$\begin{aligned} \begin{aligned} \frac{\partial \, g(\cdot ) }{\partial \, K_{it}}&= \alpha _{K} + \alpha _{K,K}\,K_{it} + \alpha _{QE,K}\,QE_{it} + \alpha _{QC,K}\,QC_{it} + \alpha _{K,w}\,w_{it} + \alpha _{K,c}\,c_{it}. \end{aligned} \end{aligned}$$

(14)

Appendix 2

See Table 4.

Table 4 Data sources