The Productivity J-Curve: How Intangibles Complement General Purpose Technologies

TL;DR

The paper develops a Productivity J-Curve model in which unmeasured intangible investments complementary to general purpose technologies cause productivity growth to be underestimated early and overestimated later. Empirically, it finds substantial ongoing J-curve effects for software and, to a lesser extent, computer hardware, with adjusted TFP 11.3% higher than official measures at end-2004 and 15.9% higher at end-2017.

Key findings

• The model predicts measured TFP growth initially understates true productivity growth when resources are used to build unmeasured intangible capital, then overstates it as intangible capital services generate measured output; in steady state, mismeasurement falls to zero.
• R&D-related intangibles have negligible net measurement effects: the net adjusted productivity level is 1.6% lower than the measured series as of end-2017.
• Software and computer hardware show substantial J-curve effects; assuming an intangible multiplier of 10, the software-adjusted TFP level is over 12.4% higher than measured TFP at the beginning of 2017, and overall adjusted TFP is 11.3% higher than official measures at end-2004 and 15.9% higher at end-2017.
• Intangibles do not explain the post-2004 productivity slowdown under a constant multiplier: measured annual TFP growth slowed by about 1.23% per year from 1995–2004 to 2005–2017, while the adjusted slowdown is larger at 1.49% per year; AI-related effects are small but growing, and explaining the entire 2010–2017 GDP slowdown would require about $107 billion per year of unmeasured intangible investment, implying an AI intangible multiplier of roughly 2.7 to 4.1 times observable investment.

Methods

• The paper augments standard growth accounting with unmeasured intangible capital, deriving expressions for the difference between the standard Solow Residual and true productivity growth; adjusted TFP growth is expressed as a convex combination of standard productivity growth and the difference between unmeasured investment growth and capital stock growth.
• It uses q-theory market value regressions to infer intangible correlates: firm market value is regressed on total assets, R&D stock, and capitalized SG&A stock, using a Compustat panel from 1961–2017 merged with Fernald TFP data extended through 2017 and Peters and Taylor R&D/SG&A stock measures.
• For software and computer hardware, lacking comparable firm-level IT capital data, it applies a range of intangible multipliers λ/z of 10, 5, 3, and 2, guided by Brynjolfsson, Hitt, and Yang (2002), who estimate roughly $12 of market value per unit of observable software and hardware; the AI assessment is described as more speculative.

Limitations

• The paper states that its method requires intangibles to have a nonzero correlation with measured capital, so completely uncorrelated intangible investments cannot be measured; using firm-level data to infer aggregate intangible-to-tangible ratios requires an aggregation assumption that may be problematic, and it therefore reports multiple multiplier values.
• The slowdown analysis assumes the intangible multiplier is constant throughout the period; if it were higher in recent periods, mismeasurement would be greater recently, and the AI analysis is early and speculative. The paper also leaves investment-timing effects, such as lower interest rates prolonging the J-curve, to future research.
• Evident from the text: this version is an NBER working paper and states it has not been peer-reviewed; the empirical estimates also rely on efficient market pricing and external/assumed intangible multipliers.