Benchmarking for routines and organizational knowledge: a managerial accounting approach with performance feedback

Abstract

This study proposes a managerial accounting research design that bridges a gap between firm productivity based on frontier techniques and strategic management. In doing so, it operationalizes the theoretical frameworks based on the endogenous components of across-firms heterogeneous resources and routines, which are fundamental for firm performance. The design focuses on industry-level benchmarking to analyze changes in performance and organizational knowledge investments, and proposes some indicators for firm-level strategic benchmarking. An analysis of a 12-year panel of the U.S. technology hardware and equipment industry illustrates the usefulness of the proposals. Findings reveal wider gaps between better and worse performers following economic distress. Increasing intangibles stocks is positively associated with changes in frontier benchmarking, while enhancing R&D spending is linked to frontier shifts. The discussion develops managerial interpretations suitable for control and reward systems.

Appendix: Sensitivity checks

1.1 Accounting for variable and fixed inputs

Separate the vector of inputs ${\mathbf{x}} = (x_{1} , \ldots x_{N} ) \in R_{ + }^{N}$ into a vector of variable inputs ${\mathbf{x}}_{{\mathbf{v}}} = (x_{v1} , \ldots x_{vP} ) \in R_{ + }^{P}$ and a vector of fixed inputs $\left( {{\text{x}}_{{\mathbf{f}}} = (x_{f1} , \ldots ,x_{fJ} ) \in R_{ + }^{J} } \right)$. The output vector maintains its initial specification $\left( {{\mathbf{y}} = (y_{1} , \ldots ,y_{M} ) \in R_{ + }^{M} } \right)$. Technology is now defined by the set $T^{t} \left( {{\mathbf{x}}_{{\mathbf{f}}}^{{\mathbf{t}}} ,{\mathbf{x}}_{{\mathbf{v}}}^{{\mathbf{t}}} ,{\mathbf{y}}^{{\mathbf{t}}} } \right)$, which represents the set of all feasible output vectors (y ^t) that can be produced using the variable $\left( {\mathbf{x}}_{{\mathbf{v}}}^{{\mathbf{t}}}) {\text{ and fixed }} ({{\mathbf{x}}_{{\mathbf{f}}}^{{\mathbf{t}}} } \right)$ input vectors in period t (Fig. 8):

$$T_{{}}^{t} ({\mathbf{x}}_{{\mathbf{f}}}^{{\mathbf{t}}} ,{\mathbf{x}}_{{\mathbf{v}}}^{{\mathbf{t}}} ,{\mathbf{y}}^{{\mathbf{t}}} ) = \,\left\{ {\left. {({\mathbf{x}}_{{\mathbf{f}}}^{{\mathbf{t}}} ,{\mathbf{x}}_{{\mathbf{v}}}^{{\mathbf{t}}} ,{\mathbf{y}}^{{\mathbf{t}}} )\,:{\mathbf{x}}_{{\mathbf{f}}}^{{\mathbf{t}}} {\text{ and }}{\mathbf{x}}_{{\mathbf{v}}}^{{\mathbf{t}}} {\text{ can produce }}{\mathbf{y}}^{{\mathbf{t}}} } \right\}} \right..$$

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Fig. 8

Sensitivity checks of the Luenberger decomposition. Indicators are computed following Eqs. (4) and (5), and the distance function in Eq. (10). All values represent changes at median level between the periods indicated on the horizontal axis. Results of zero show no change; positive/negative results show improvement/deterioration. For the alternative model 1 (top left), variable inputs are cost of goods sold (COGS) and selling, general and administrative expenses, the fixed input is fixed assets, while the output is revenues. For the alternative model 2 (bottom), the variable input is operating expenses, the fixed inputs are fixed assets and the number of employees, while the output is revenues

To estimate the inefficiency of firm k’, the linear programming problem that expands outputs, contracts variable inputs, and accounts for fixed inputs—without contracting them—is now:

$$\begin{aligned} & D^{t} (x_{v}^{t} ,x_{f}^{t} ,y^{t} ) = \hbox{max} \\ & \quad \left\{ {\delta :\sum\limits_{k = 1}^{K} {\lambda_{k}^{t} y_{km}^{t} \ge y_{{k^{{\prime }} m}}^{t} { + }\delta y_{{k^{{\prime }} m}}^{t} ,\quad m = 1,2, \ldots ,M,} } \right. \\ & \quad\quad \sum\limits_{k = 1}^{K} {\lambda_{k}^{t} x_{vkp}^{t} \le x_{{vk^{{\prime }} p}}^{t} - \delta x_{{vk^{{\prime }} p}}^{t} ,\quad {\text{p}} = 1,2, \ldots ,P,} \\ & \quad\quad \sum\limits_{k = 1}^{K} {\lambda_{k}^{t} x_{fkj}^{t} \le x_{{fk^{{\prime }} j}}^{t} ,\quad {\text{j}} = 1,2, \ldots ,J,} \\ & \quad\quad \left. {\sum\limits_{k = 1}^{K} {\lambda_{k} = 1,} \, \lambda_{k} \ge 0,\quad (k = 1,2, \ldots ,K)} \right\}. \\ \end{aligned}$$

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