Quantifying the allocative efficiency of capital: The role of capital utilization
What this paper finds — and why it matters
Standard measures of capital allocative efficiency—based on the dispersion of the average revenue product of capital (ARPK)—are severely biased when capital utilization is endogenous. When utilization is flexible, firms can bypass physical adjustment constraints by varying intensity, so that the correct efficiency measure requires the dispersion of average revenue product of capital services (ARPKS), defined as the log difference between revenue and utilized capital, not of ARPK. Contrary to the standard view that higher ARPK dispersion signals lower allocative efficiency, the paper demonstrates that when efficiency improvements arise from greater utilization flexibility, ARPK dispersion can increase alongside efficiency gains. An application to India’s capital market liberalization reform shows that the standard approach (ignoring utilization) predicts allocative efficiency gains of 5.25% (statistically significant), while the corrected approach accounting for utilization finds gains of only 0.04% (not statistically significant).
Summary based on a working paper version, AI-assisted and human-reviewed. See the linked published article for the authoritative version.
Q1. What is wrong with ARPK dispersion as a measure of allocative efficiency?
ARPK dispersion conflates two conceptually distinct quantities—the dispersion of physical factor allocation and the dispersion of utilization intensity—so it is not a monotone proxy for allocative efficiency when utilization is endogenous. In the Hsieh-Klenow (2009) framework, higher ARPK dispersion is interpreted as higher misallocation. But ARPK is simply revenue over capital inputs, so when firms with too little (too much) capital relative to their productivity simply utilize their capital more (less) intensely, the variance of ARPK rises even as the efficiency of factor services allocation improves. The standard interpretation therefore has the causality backwards in economies with flexible utilization.
Q2. What is ARPKS and why does it correctly measure capital allocative efficiency?
ARPKS—the average revenue product of capital services, defined as the log difference between revenue and utilized capital—is the theoretically correct sufficient statistic for capital allocative efficiency when utilization is endogenous, because it measures the dispersion in the productivity of factor services rather than the dispersion of physical factor inputs. The paper embeds endogenous utilization into a neoclassical investment model and shows formally that the variance of log ARPKS is zero in the efficient equilibrium, while the variance of log ARPK is not. ARPK dispersion is a combination of ARPKS dispersion and utilization variation, and the latter is not a sign of misallocation.
Q3. Can higher ARPK dispersion accompany higher allocative efficiency?
Yes: when allocative efficiency improvements arise from greater flexibility in capital utilization, ARPK dispersion increases even though allocative efficiency improves. Greater utilization flexibility generates more variation in how intensively different firms use their capital, raising the ratio of revenue to physical capital input for high-utilization firms. A researcher using ARPK dispersion would therefore mistakenly conclude that allocative efficiency fell when it actually rose. The paper provides counterfactual simulations illustrating this phenomenon.
Q4. What is the empirical application and what do the results show?
An application to Bau and Matray (2023)’s Indian capital market liberalization reform finds that: the standard approach (ignoring utilization) predicts allocative efficiency gains of 5.25% (statistically significant); accounting for utilization, the corrected estimate is only 0.04% (not statistically significant). The analysis uses firm-level panel data for India including capacity utilization rates and capital maintenance expenses. Maintenance expenses serve as a proxy for capital utilization rates in the model, bridging the gap between observed capacity and the theoretically relevant utilization measure.
Key concepts
average revenue product of capital (ARPK) : the ratio of revenue to physical capital input; commonly used as a proxy for firm-level distortions in the Hsieh-Klenow (2009) framework, but shown to be a biased measure of allocative efficiency when capital utilization is endogenous. average revenue product of capital services (ARPKS) : the ratio of revenue to utilized capital; the theoretically correct measure of capital allocative efficiency when utilization is endogenous; its dispersion is zero in the efficient equilibrium. capital utilization : the intensity with which a firm deploys its physical capital stock; endogenous in the model, allowing firms to partially bypass adjustment constraints; the omission of utilization is the source of the bias in standard ARPK-based efficiency estimates.