Estimating Radial Measures of Productivity Growth: Frontier vs Non-Frontier Approaches

In this paper, we propose an alternative econometric framework for estimating and decomposing productivity change that does not require a distribution for inefficiency or the uncorrelatedness between inefficiency and the regressors. We develop our methodology for the input-oriented radial measure of productivity change and establish that this equals the negative of the time change in the log cost function. Our econometric framework is based on a fixed-effects, multiple-output cost frontier, where we decompose productivity change into discrete shifts in the frontier and changes in firm efficiency levels relative to the frontier. We also show that the standard non-frontier specification is nested within our frontier model and thus can produce different estimates of productivity change. Using a panel of twelve US railroads from 1951 to 1975, our estimated cost frontier suggests average annual productivity growth of roughly 0.3 percent, with efficiency change rising then falling over the period. Specification tests reject the non-frontier model, which yields smaller gains in productivity.