Erik Brynjolfsson - Global Forum on Productivity - 20-21 June 2019, Sydney

1. The Productivity J-Curve:
How Intangibles Complement
General Purpose Technologies
Erik Brynjolfsson, MIT Sloan and NBER
Daniel Rock, Wharton
Chad Syverson, Chicago Booth and NBER

2. Technological Progress: ML and Image Recognition

3. Technological Progress: ML and Protein Folding

4. The Disappointing Recent Reality
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 Explanation for 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 a GPT?
Bresnahan and Trajtenberg’s Criteria:
1. Pervasive
2. Able to be improved upon over time
3. Able to spawn complementary innovations

7. Slowdowns and GPTs in 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 on Today’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 on Today’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 on Today’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 Explanation for 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 Productivity Measurement
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 dynamic profit 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:
𝑉 0 = 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 two types 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
Growth rate 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
𝑔 𝑇𝐹𝑃 = 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
Assuming CRTS, 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
• Measure Τ𝜆 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. Firm Value Regressions: R&D

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

24. Firm Value Regressions: R&D

25. Firm Value Regressions: R&D

26. Measured and Adjusted TFP Growth: R&D

27. Adjusted TFP: R&D
Why is 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 Adjusted TFP Levels: R&D

29. Firm Values: Hardware and 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: IT Hardware
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 Mismeasurement by Year: IT
Hardware

35. TFP Accumulated Level Mismeasurement: IT
Hardware

36. Adjusted TFP Growth: IT Software

37. Adjusted TFP Levels: IT Software

38. Adjusted TFP Levels: IT Hardware

39. Adjusted TFP: IT Software
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 Mismeasurement by Year: IT
Software

41. TFP Accumulated Level Mismeasurement: IT
Software

42. Does This Explain the 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 Intangibles Causing
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 technologies often 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