qGMM Estimation of Sunk Costs

This paper estimates a structural model of firm growth and partially sunk investment. In the model, the firm's optimal adjustment keeps the gap between the actual capital stock and its frictionless counterpart between two boundaries. We show that any two quantiles of output growth conditional on the firm's history are sufficient to identify the sunk cost of investment, the firm's span of control, and the distribution of technology shocks; and we estimate these structural parameters using moment conditions based on these conditional quantiles. Because the optimal weighting matrix is known, our one-step GMM estimates are efficient. Furthermore, they require no parametric assumptions on the firm's idiosyncratic shocks. We apply this procedure to estimate the adjustment rule of COMINCO's electrolytic zinc refining facility in Trail, B.C