Advances in Measuring Productivity

Economists have recognized the importance of productivity since the 1950s, when Nobel laureate Robert Solow showed that increases in productivity appeared to cause the lion’s share of macroeconomic growth. While studies sometimes focus on labor productivity, economists generally prefer to measure total factor productivity (TFP), the relationship of output to all the inputs used by a firm. The concept of TFP has been used to analyze performance and competitiveness in a wide range of firms and industries. Recent improvements in the tools economists use to measure productivity will allow them to address many different issues with greater rigor.

Studies of productivity have been used in considering a wide variety of questions, such as the effects of trade liberalization, the extent of scale economies in electric power generation, the effects of deregulation on the telecommunications equipment industry, and the benefits of investing in information technology. Firm-level TFP analysis also has potentially wide-ranging applications in antitrust. Economists have begun to use these tools to analyze the productivity effects of horizontal mergers. For example, one recent study by Robert Kulick examined horizontal mergers in the ready-mix concrete industry, particularly acquisitions occurring after the promulgation of the 1982 Merger Guidelines, and found the mergers were associated with large productivity gains. Another study, by Orley Ashenfelter, Daniel Hosken, and Matthew Weinberg, found substantial gains in efficiency through reductions in shipping costs in the wake of consolidation in the U.S. brewing industry. That consolidation ultimately led to no appreciable net price increase. TFP analysis also could provide an objective basis for evaluating efficiency defenses that are raised to counter allegations of anticompetitive conduct.

A reliable TFP analysis hinges on accurately characterizing the production function, which describes the mathematical relationship between inputs and output. The particular form of the production function will vary depending on the specific technology and production processes used by a given firm or in a given industry. Important properties of production functions include the elasticity of substitution and returns to scale. The former measures how readily the firm can shift its mix of inputs (e.g., substitute capital for labor) without sacrificing too much output. The latter quantifies the extent to which larger firms are more efficient than smaller firms: With increasing returns to scale, larger firms can produce more output per unit of input; with constant returns to scale, there is no efficiency advantage to being large.

Obtaining a reliable characterization of the production function can be a challenging technical problem. The problem is inherent in the need to distinguish whether a rise in output is due to an increase in inputs or due to technical progress. To the extent that firms choose their inputs based on their own view of their TFP (which is likely more accurate than anybody else’s), it can be easy to mistake one for the other. This difficulty is due to the fact that profit-maximizing firms respond to increases in productivity by expanding output, which increases the use of inputs. Moreover, reductions in productivity may lead firms to pare back output, which decreases the use of inputs. In principle, well-known statistical techniques (dubbed “instrumental variables”) could solve this problem in a relatively straightforward manner. Unfortunately, a lack of adequate data often prevents the use of those techniques to estimate production functions.

Economists have developed a variety of creative approaches to work around this problem. Steven Olley and Ariel Pakes used a rich plant-level data set constructed from U.S. Census files to study the dramatic restructuring of the telecommunications equipment industry that unfolded in the wake of extensive deregulation and technical change. They developed an algorithm for measuring TFP based on the observation that, in response to a change in productivity, firms typically have more flexibility in adjusting some inputs (e.g., labor and materials), than others (e.g., capital). Their algorithm produced markedly different and more plausible TFP estimates than other, more traditional approaches. Olley and Pakes (OP) found that the rate of aggregate productivity growth accelerated substantially after deregulation. Because their methods gave them reliable TFP estimates at the plant level, they were also able to conclude that the observed productivity gains were primarily the result of a reallocation of capital towards more productive establishments.

Jim Levinsohn and Amil Petrin later developed a new method that extended the ideas of OP. Levinsohn and Petrin (LP) pointed to evidence from firm-level datasets suggesting that investment is very lumpy, which implies that firms face substantial adjustment costs. Therefore, it may take a long time before firms change investment levels in response to changes in productivity. These delays are significant because the OP method relies on observed investment decisions as a proxy for the unobserved productivity shock. LP showed that firms’ demand for intermediate inputs can be used as a potentially more reliable proxy for changes in productivity The LP method is readily implemented given data on firms’ raw material usage (which is typically reported along with data on other inputs). This method is now so widely implemented that STATA (a popular statistical software package), offers a pre-programmed LP routine.

An article recently published in Econometrica, a leading economics journal, showed serious shortcomings in both the OP and the LP techniques. The OP and LP methods produce reasonably accurate TFP estimates only under certain key assumptions about firm behavior, and those assumptions may be unrealistic in many industries. The article proposed an alternative estimation procedure that uses techniques similar to those used by OP and LP but yields reliable TFP estimates under much more general conditions. A numerical analysis (a “Monte Carlo study”) yields results consistent with the article’s formal proofs.

Recent advances have made TFP analysis substantially more accurate. The likely result is that such analysis will play an increasingly prominent role in regulation, antitrust, and public policy.

Kevin W. Caves is a Senior Economist at Economists Incorporated. He is a co-author of “Identification Properties of Recent Production Function Estimators,” in the November 2015 Econometrica, which is discussed in this article.