Macro and Micro Dynamics of Productivity: From Devilish Details to Insights

Abstract

Researchers use a variety of methods to estimate total factor productivity (TFP) at the firm level and, while these may seem broadly equivalent, how the resulting measures relate to the TFP concept in theoretical models depends on the assumptions about the environment in which firms operate. Interpreting these measures and drawing insights based upon their characteristics thus must take into account these conceptual differences. Absent data on prices and quantities, most methods yield ``revenue productivity" measures. We focus on two broad classes of revenue productivity measures in our examination of the relationship between measured and conceptual TFP (TFPQ). The first measure has been increasingly used as a measure of idiosyncratic distortions and to assess the degree of misallocation. The second measure is, under standard assumptions, a function of fundamentals (e.g., TFPQ). Using plant-level U.S. manufacturing data, we find these alternative measures are (i) highly correlated; (ii) exhibit similar dispersion; and (iii) have similar relationships with growth and survival. These findings raise questions about interpreting the first measure as a measure of idiosyncratic distortions. We also explore the sensitivity of estimates of the contribution of reallocation to aggregate productivity growth to these alternative approaches. We use recently developed structural decompositions of aggregate productivity growth that depend critically on estimates of output versus revenue elasticities. We find alternative approaches all yield a significant contribution of reallocation to productivity growth (although the quantitative contribution varies across approaches).

Measuring Productivity Dispersion

“…This also implies the dispersion of revenue-productivity is smaller than that of physical productivity or efficiency. Foster et al (2008), and Foster et al (2015) offer empirical evidence supporting this finding. They also highlight that demand shocks exhibit high dispersion relative to physical productivity dispersion.…”

“…This may be an important feature of the approach in cases where the data is subject to non-randomness. The findings in Foster et al (2015) suggest that controlling for the effect of selection may have an effect on dispersion estimates. is especially relevant in the presence of non-convexities in capital adjustment.…”

“…However, in practice, the estimated or computed residual ω it , will vary across methods with different reference productivity when the estimated or computed aggregator F (x;β) differs. Foster et al (2015) demonstrate that empirical differences across the estimated input aggregators often imply numerical differences in both ω it and its dispersion. Foster et al (2015) report average dispersion from productivity distributions for 50 industries where dispersion varies between 0.…”

“…Foster et al (2015) demonstrate that empirical differences across the estimated input aggregators often imply numerical differences in both ω it and its dispersion. Foster et al (2015) report average dispersion from productivity distributions for 50 industries where dispersion varies between 0. 24-0.40.…”

“…The role of dispersion for business dynamism and growth has been explored extensively in the context of the relationship between productivity, growth and reallocation dynamics. A number of papers found that more productive plants are more likely to grow and less likely to exit (recent examples include Foster et al (2016a), and Foster et al (2015)). Another area of application is the frontier literature, which postulates that the technology and practices of the most productive plants, or frontier plants, are adapted by other establishments (e.g.…”