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The Productivity J-Curve: How Intangibles Complement General Purpose Technologies
1) Technological progress has been accompanied by slow productivity growth over the past decade. This paper explores how intangible capital investments related to new technologies can lead to mismeasurement of productivity over time. 2) As new technologies are adopted, accompanying intangible investments are undercounted as output, causing productivity to be understated. Later, as intangible capital stocks accumulate, they are undercounted as inputs, leading productivity to be overstated. 3) For past technologies like IT hardware, this "productivity J-curve" effect from intangibles appears to have largely run its course. For software, mismeasurement may still be occurring. AI-related intangibles could now be significant enough to
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The Productivity J-Curve: How Intangibles Complement General Purpose Technologies
- 1. The Productivity J-Curve: HowIntangibles Complement General Purpose Technologies Erik Brynjolfsson, MIT Sloan and NBER Daniel Rock, Wharton Chad Syverson, Chicago Booth and NBER
- 2. Technological Progress: MLand Image Recognition
- 3. Technological Progress: MLand Protein Folding
- 4. The Disappointing RecentReality Juxtaposed with technological progress is slow productivity growth, everywhere • We are more than one decade into a slowdown in the U.S. and OECD countries – United States: • 1995-2004: 2.9% per year • 2005-2018: 1.3% per year – OECD: 29 of 30 countries saw similar-sized slowdowns after 2004 • Major emerging markets slowdown later, around 2010
- 5. A Potential Explanationfor the Paradox Our earlier work: Implementation and restructuring lags • Technology is real, but benefits take time to emerge – Must accumulate enough new general purpose technology (GPT) capital to observe effects in aggregates – Full benefits require complementary investments to be invented and installed If this is correct, the paradox is not a contradiction • A period with simultaneous recognition of technology’s potential and poor productivity performance is natural
- 6. What Is aGPT? Bresnahan and Trajtenberg’s Criteria: 1. Pervasive 2. Able to be improved upon over time 3. Able to spawn complementary innovations
- 7. Slowdowns and GPTsin History Prior general purpose technologies (GPTs) associated with implementation lags • “Engels’ pause” during early industrial revolution – Wage growth stagnant even as output rose quickly • Over half of U.S. manufacturing establishments unelectrified in 1919 – 30 years after AC systems standardized • Computer capital in U.S. topped off at about 5% of total nonresidential equipment capital by late 1980s – 25+ years after invention of integrated circuit – Only half that level 10 years earlier
- 8. History’s Lens onToday’s Paradox Labor Productivity in the Portable Power and IT Eras 8 1970 1975 1980 1985 1990 1995 2000 2005 2010 2015 2020 40 60 80 100 120 140 160 180 1890 1895 1900 1905 1910 1915 1920 1925 1930 1935 1940 Portable Power IT
- 9. History’s Lens onToday’s Paradox Labor Productivity in the Portable Power and IT Eras 9 1970 1975 1980 1985 1990 1995 2000 2005 2010 2015 2020 40 60 80 100 120 140 160 180 1890 1895 1900 1905 1910 1915 1920 1925 1930 1935 1940 Portable Power IT
- 10. History’s Lens onToday’s Paradox Labor Productivity in the Portable Power and IT Eras 10 1970 1975 1980 1985 1990 1995 2000 2005 2010 2015 2020 40 60 80 100 120 140 160 180 1890 1895 1900 1905 1910 1915 1920 1925 1930 1935 1940 Portable Power Portable Power (cont.) IT
- 11. Additional Potential Explanationfor the Paradox This paper explores another potential reason why productivity slowdowns accompany new technologies: mismeasurement from GPT-related intangible capital We theoretically characterize this potential using standard growth accounting Empirically estimate effects from past GPTs (computer software and hardware) and, more speculatively, AI
- 12. Intangibles and ProductivityMeasurement How do intangibles affect productivity measurement? 𝑃𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑣𝑖𝑡𝑦 = 𝑂𝑢𝑡𝑝𝑢𝑡 𝐼𝑛𝑝𝑢𝑡 • Intangible capital would be an unmeasured input – As such, this will tend to cause productivity to be overstated • However, intangible capital is also an output (measured as investment flow) – This will cause productivity to be understated • Net effect on productivity measurement depends on relative timing of input vs. output mismeasurement
- 13. Model: Firms Firm’s dynamicprofit maximization with capital adjustment costs (Lucas, 1967) Firm’s PF: 𝑌 = 𝐹 𝑲, 𝑵, 𝑰, 𝐴 K is vector of capital inputs N is vector of flexible inputs I is vector of capital investments 𝐹𝐼 ∙ < 0 as a reduced form way of capturing K adjustment costs (investing takes resources that cost output)
- 14. Model: Firms Firm’s value: 𝑉0 = max 𝑰,𝑵 න 0 ∞ 𝜋 𝑡 𝑢 𝑡 𝑑𝑡 𝜋 𝑡 = 𝑝𝐹 𝑲, 𝑵, 𝑰, 𝐴 − 𝑤′ 𝑵 − 𝑧′ 𝑰 𝑑𝐾𝑗 𝑑𝑡 = 𝐼𝑗 − 𝛿𝑗 𝐾𝑗
- 15. Model: Firms Dynamic FOCs: 𝜕𝐻 𝜕𝐾𝑗 =− ሶ𝜆𝑗 = 𝑝𝐹 𝐾 𝑗 𝑢 − 𝜆𝑗 𝛿𝑗 𝜕𝐻 𝜕𝐼𝑗 = 0 = 𝑝𝐹𝐼 𝑗 − 𝑧𝑗 𝑢 + 𝜆𝑗 This, plus transversality condition, implies value of the firm: 𝑉 0 = 𝑗=1 𝐽 𝜆𝑗 0 𝐾𝑗 0 Intuition: 𝑉 0 is shadow-value weighted sum of capital types
- 16. Model: Firms Suppose twotypes of K, tangible (j = 1) and intangible (j = 2) Firm makes intangible investments that accompany tangible investments, so that 𝐾2 𝑡 = 𝜇𝐾1 𝑡 Firm value is then 𝑉 = 𝜆1 𝐾1 + 𝜆2 𝐾2 = 𝜆1 𝐾1 + 𝜆2 𝜇𝐾1 = 𝜆1 + 𝜆2 𝜇 𝐾1 Regression of firm market value on tangible capital gives insight into stock and shadow value of intangible capital • Every PDV dollar of tangible K implies a PDV of intangible K
- 17. Model: Growth Accounting Growthrate of output: ሶ𝑌 𝑌 = 𝐹 𝐾 𝐾 𝑌 ሶ𝐾 𝐾 + 𝐹 𝑁 𝑁 𝑌 ሶ𝑁 𝑁 + 𝐹𝐼 𝐼 𝑌 ሶ𝐼 𝐼 + 𝐹𝐴 𝐴 𝐴 ሶ𝐴 𝐴 From FOC above, 𝐹𝐼 𝑗 = 𝑧𝑗 − 𝜆𝑗 Rewriting as TFP growth, 𝑔 𝑇𝐹𝑃: 𝑔 𝑇𝐹𝑃 = 𝑔 𝑌 − 𝐹 𝐾 𝐾 𝑌 𝑔 𝐾 + 𝐹 𝑁 𝑁 𝑌 𝑔 𝑁 + 1 − 𝜆 𝑧 𝑧𝐼 𝑌 𝑔𝐼 Note: Τ𝜆 𝑧 is the ratio of a type of capital’s shadow value to its observed purchase price
- 18. Model: Growth Accounting 𝑔𝑇𝐹𝑃 = 𝑔 𝑌 − 𝐹 𝐾 𝐾 𝑌 𝑔 𝐾 + 𝐹 𝑁 𝑁 𝑌 𝑔 𝑁 + 1 − 𝜆 𝑧 𝑧𝐼 𝑌 𝑔𝐼 Two differences from standard growth accounting 1. Intangible capital types may be in K and I 2. The shadow values of investment Call standard Solow residual ෧𝑔 𝑇𝐹𝑃
- 19. Model: Growth Accounting AssumingCRTS, σ 𝐹 𝐾 𝐾 𝑌 = 1 − 𝐹 𝑁 𝑁 𝑌 − σ 𝐹 𝐼 𝐼 𝑌 ሶ𝐼 𝐼 Then difference between actual and standard TFP growth is: 𝑔 𝑇𝐹𝑃 − ෧𝑔 𝑇𝐹𝑃 = 𝜆 𝑧 − 1 𝑧𝐼 𝑌 𝑔𝐼 − 𝑔 𝐾 Intuition: • No mismeasurement if 𝜆 = 𝑧 for all K • If 𝜆 ≠ 𝑧, direction of mismeasurement depends on 𝑔𝐼 − 𝑔 𝐾 – 𝑔𝐼 is about output growth (measured TFP too low) – 𝑔 𝐾 is about input growth (measured TFP too high) – Weight is income paid for investment
- 20. The J-Curve 𝑔 𝑇𝐹𝑃− ෧𝑔 𝑇𝐹𝑃 = 𝜆 𝑧 − 1 𝑧𝐼 𝑌 𝑔𝐼 − 𝑔 𝐾 How might we expect mismeasurement to evolve? • Early in a GPT diffusion process, intangible investment growth (for which 𝜆 > 𝑧 ) likely larger than the growth of the intangible stock, so true productivity growth higher than measured • Later, investment growth rate falls while stock growth continues; true productivity growth lower than measured • Eventually, in steady state, 𝑔𝐼 = 𝑔 𝐾; no mismeasurement (even as intangible investment continues)
- 21. Empirical Strategy • MeasureΤ𝜆 𝑧 using firm value regressions • For different types of capital with 𝜆 > 𝑧, use estimates to construct measure of 𝑔 𝑇𝐹𝑃 − ෧𝑔 𝑇𝐹𝑃 • Integrate to find implied difference in TFP levels
- 22.
- 23. Firm Value Regressions:R&D • Tangible “standard” capital in Total Assets appear to be valued dollar-for-dollar, both across companies and within companies over time • OTOH, $1 of R&D appears to be associated with $2 of shadow value, so perhaps $1 dollar of intangibles • SG&A proxy for intangibles captures some of this, but also seems to be correlated with shadow value above $1
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- 26. Measured and AdjustedTFP Growth: R&D
- 27. Adjusted TFP: R&D Whyis mismeasurement so small if for every dollar of R&D there is an implied additional $1 of intangible capital? It’s because R&D investment rates have been stable for many decades Thus 𝑔𝐼 ≈ 𝑔 𝐾 This can be seen in TFP level breakdown into missing output (investment) and input (stock) components
- 28. Measured and AdjustedTFP Levels: R&D
- 29. Firm Values: Hardwareand Software • We don’t have firm-level IT capital data as we did for R&D • We instead proceed by computing implied mismeasurement for different values of Τ𝜆 𝑧 based on the literature – Brynjolfsson, Hitt, and Yang (2002) estimate $1 of computer hardware and software associated with about $12 (s.e. = $4) of market value – We use Τ𝜆 𝑧 of $10, though also compute for $5, $3, and $2
- 30. Adjusted TFP Growth:IT Hardware
- 31. Adjusted TFP Levels:IT Hardware
- 32. Adjusted TFP Levels:IT Hardware
- 33. Adjusted TFP: ITHardware Adjusted TFP level is 4.4% higher in 2016 than measured • Note this is the total growth measurement error accumulated over almost 50 years • First half of growth J-curve has played out; hardware-related intangible accumulation has lately caused productivity growth overstatement (and brought levels back toward measured level)
- 34. TFP Growth Mismeasurementby Year: IT Hardware
- 35. TFP Accumulated LevelMismeasurement: IT Hardware
- 36. Adjusted TFP Growth:IT Software
- 37. Adjusted TFP Levels:IT Software
- 38. Adjusted TFP Levels:IT Hardware
- 39. Adjusted TFP: ITSoftware Implied mismeasurement due to software-related intangibles is much larger than for intangibles related to R&D or hardware Adjusted TFP level is 17% higher in 2016 than measured First half of growth J-curve might be played out, but less clear than for hardware
- 40. TFP Growth Mismeasurementby Year: IT Software
- 41. TFP Accumulated LevelMismeasurement: IT Software
- 42. Does This Explainthe Post-2004 Productivity Slowdown? No; implied slowdown actually larger A mismeasurement explanation for the slowdown doesn’t require just mismeasurement; it requires a change in mismeasurement (in a particular direction and around 2004) Period Measured Annual TFP Growth (%) Implied Annual TFP Growth (%) Implied – Measured 1995-2004 1.63 2.53 0.90 2005-2017 0.40 0.85 0.45 Slowdown 1.23 1.68 0.45
- 43. Are AI-Related IntangiblesCausing Mismeasurement? • Still very early in AI adoption, but fast investment growth • Estimated U.S. AI investments of $25-40B in 2016 (300% growth since 2013, 60% AGR) – Extrapolated to 2018, that’s $65-100B in 2018 • If Τ𝜆 𝑧 is $10 that’s $650B to $1T in missing output in the form of intangible investments (about 3-5% of GDP) • Likely an upper bound, plus doesn’t account for (still likely small) countervailing input effect of AI-related intangibles – And note pre-2016 AI investments were probably too small to have had aggregate effects
- 44. Conclusion • New technologiesoften require complementary intangible investments • These intangibles can lead to productivity mismeasurement – First as missing output (productivity understatement) – Later as missing input (productivity overstatement) • Recently, this dynamic appears to have largely played out for R&D- and hardware-related intangibles • Still in play for software-related intangibles • AI-related intangibles might just now be creating enough mismeasurement to matter for aggregates