Statistical inference in efficient production with bad inputs and outputs using latent prices and optimal directions

Researchers employ the directional distance function (DDF) to estimate multiple-input and multiple-output production, firm inefficiency, and productivity growth. We relax restrictive assumptions by computing optimal directions subject to profit maximization and cost minimization, correct for the potential endogeneity of inputs and outputs, estimate latent prices for bad outputs, measure firms' responses to shadow prices rather than actual prices, and introduce an unobserved productivity term into the DDF. For an unbalanced panel of U.S. electric utilities, a model assuming profit-maximization outperforms one assuming cost-minimization, while lagged productivity and energy price have the greatest effect on productivity.