Robustness of Productivity Estimates

Abstract

Researchers interested in estimating productivity can choose from an array of methodologies, each with its strengths and weaknesses. Many methodologies are not very robust to measurement error in inputs. This is particularly troublesome, because fundamentally the objective of productivity measurement is to identify output differences that cannot be explained by input differences. Two other sources of error are misspecifications in the deterministic portion of the production technology and erroneous assumptions on the evolution of unobserved productivity. Techniques to control for the endogeneity of productivity in the firm's input choice decision risk exacerbating these problems. MotivationAccurate measurement is at the heart of productivity comparisons. Fundamentally, the objective is to identify output differences that cannot be explained by input differences.To perform this exercise, one needs to observe inputs and outputs accurately and control for the input substitution that the production technology allows. Problems can arise from misspecifications in the deterministic or stochastic portion of the production technology and from measurement errors in the data.Firms use different input combinations to produce one unit of output because their technology differs, which I label productivity differences, or because they face different factor price, which leads firms to pick different points on the production frontier.1 The extent to which one input can be substituted for another is determined by the shape and position of the production function-or any other representation of technology-and is naturally not observable. Methodologies to estimate productivity differ by the mix of statistical techniques and economic assumptions they employ to control for input substitution. Misspecifications in the deterministic part of the production function or in the statistical model underlying the evolution of unobserved productivity will have repercussions on the productivity estimates.Mismeasurement can result, among other things, from unobserved quality or price differences, aggregation problems, recall errors in surveys, or incompatibilities in reference period for output and inputs. The effect on productivity estimates obviously depend on the estimation method. For example, Griliches and Hausman (1986) argue that while firstdifferencing is useful to control for unobserved firm-specific effects, identification based on thinner slices of the data are more vulnerable to measurement errors. Solutions exist for dealing with well-defined forms of measurement error, but they are rarely used in practice.One of the goals in this paper is to verify how sensitive different methods for productivity measurement are to different forms of measurement error.I evaluate the robustness to misspecification and measurement errors for five popular 1 Some authors have argued that some of the output shortfall relative to the best practice frontier is the result of inefficiency. I still classify such shortfall as productivity differences,...

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