Estimating production functions using costs when outputs are restricted

Conventional proxy-variable approaches to production-function identification assume that output quantities are flexibly adjustable, with firms endogenously choosing them in pursuit of profits. But in not so few industries outputs are exogenously restricted, constraining input allocations by producers. Model assumptions of most proxy estimators become untenable in such settings. We provide a new structural methodology based on a dual formulation of firm production, indirectly identifying technology and productivity from cost data while appropriately accommodating exogenous output restrictions. We showcase our methodology on a panel of U.S. natural gas-fired power-generation plants in 2005–2017 facing price-inelastic demand that restricts their outputs in the short run. We find that power plants were scale-efficient, with (short-run) marginal costs of net electricity generation declining over time. With little evidence of productivity growth in the industry during our sample period, we conclude that the reduction in marginal costs was fueled mainly by diminishing input prices and, potentially, convergence to the optimal long-run input allocation.