Growth and Ideas

Chad Jones

Stanford GSB

October 14, 2015

Growth and Ideas – p. 1

U.S. GDP per Person

Growth and Ideas – p. 2

Why?

• The average American is 15 times richer today than in 1870.

• How do we understand this fact?

• What does the future hold?

Growth and Ideas – p. 3

Growth Theory

• Conclusion of any growth theory:

yt

yt= g and a story about g

• Key to this result is (essentially) a linear differential equationsomewhere in the model:

Xt = Xt

• Growth models differ according to what they call the Xt

variable and how they fill in the blank.

Growth and Ideas – p. 4

Catalog of Growth Models: What is Xt?

Solow kt = skαt

Solow At = gAt

AK model Kt = sAKt

Lucas ht = uht

Romer/AH At = RAt

Extension of Romer Lt = nLt

Growth and Ideas – p. 5

The Linearity Critique

Xt = sXφt

• To explain the U.S. 20th century, φ ≈ 1 is required

◦ φ < 1: Growth slows to zero

◦ φ > 1: Growth will explode

• Solow (1994 JEP) criticizes new growth theory for this: “Youwould have to believe in the tooth fairy to expect that kind ofluck.”

◦ But the same criticism applies to At = gAt

◦ Facts ⇒we need linearity somewhere. Where??

Growth and Ideas – p. 6

Solow and Romer

• Robert Solow (1950s)

◦ Capital versus Labor

◦ Cannot sustain long-run growth

• Paul Romer (1990s)

◦ Objects versus Ideas

◦ Sustains long-run growth

◦ Wide-ranging implications for intellectual property,antitrust policy, international trade, the limits to growth,sources of “catch-up” growth

Romer’s insight: Economic growth is sustained bydiscovering better and better ways to use the finiteresources available to us

Growth and Ideas – p. 7

Objects vs Ideas (Paul Romer, 1990)

• Objects: Almost all goods in the world

◦ Examples: iphones, airplane seats, and accountants

◦ Rivalrous: If I’m using it, you cannot at the same time

◦ The fundamental scarcity at the heart of most economics

• Ideas: They are different — nonrival

◦ The Pythagorean Theorem or oral rehydration therapy

◦ My use ; less of the idea is available to you

Growth and Ideas – p. 8

The Nonrivalry of Ideas ⇒ Increasing Returns

• Familiar notation, but now let At denote the “stock ofknowledge” or ideas:

Yt = F (Kt, Lt, At) = AtKαt L

1−αt

• Constant returns to scale in K and L holding knowledgefixed. Why?

F (λK, λL,A) = λ× F (K,L,A)

• But therefore increasing returns in K, L, and A together!

F (λK, λL, λA) > F (λK, λL,A)

• Economics is quite straightforward:

◦ Replication argument implies CRS to objects

◦ Therefore there must be IRS to objects and ideas

Growth and Ideas – p. 9

Nonrivarly ⇒ IRS ⇒Growth follows easily!

Production of final good Yt = Aσt Lt

Production of ideas At = βtRt = βRtAφt

Resource constraint Lt +Rt = Nt = N0ent

Allocation of people Rt = sNt, 0 < s < 1

φ = 0: Useful benchmark!

φ > 0: Standing on shoulders

φ < 0: “Fishing out”

Growth and Ideas – p. 10

gy =σn

1− φ

Growth and Ideas – p. 11

From IRS to Growth

• Objects: Add one computer ⇒make one worker moreproductive.

Output per worker ∼ # of computers per worker

• Ideas: Add one new idea ⇒make everyone better off.

– E.g. the first spreadsheet or email software

Income per person ∼ the aggregate stock of knowledge,not on the number of ideas per person.

But it is easy to make aggregates grow: population growth!

IRS ⇒bigger is better.

Growth and Ideas – p. 12

The Ultimate Resource

• Why are we richer today than in the past?

More people ⇒more new ideas ⇒higher income / person

• Population growth is a historical fact.

◦ If we take it as given, then growth in per capita income isnot surprising

◦ No other ad hoc linearity is needed

• Two applications:

◦ Growth over the last 100,000 years

◦ The future of U.S. economic growth

Growth and Ideas – p. 13

What is graphed here?

0 200 400 600 800 1000 1200 1400 1600 1800 2000

5

10

15

20

25

30

35

40

45

YEAR

INDEX (1.0 IN INITIAL YEAR)

Growth and Ideas – p. 14

Population and Per Capita GDP: the Very Long Run

0 200 400 600 800 1000 1200 1400 1600 1800 2000

5

10

15

20

25

30

35

40

45

Population

Per capita GDP

YEAR

INDEX (1.0 IN INITIAL YEAR)

Growth and Ideas – p. 15

Growth over the Very Long Run

• Malthus: c = y = ALα, α < 1

◦ Fixed supply of land: ↑L ⇒ ↓c holding A fixed

• Story:

◦ 100,000 BC: small population ⇒ ideas come very slowly

◦ New ideas ⇒ temporary blip in consumption, butpermanently higher population

◦ This means ideas come more frequently

◦ Eventually, ideas arrive faster than Malthus can reduceconsumption!

• People produce ideas and Ideas produce people

◦ If nonrivarly > Malthus, this leads to the hockey stick

Growth and Ideas – p. 16

Accounting for U.S. Growth, 1950–2007

• Educational attainment rises ≈ 1 year per decade. Withψ = .06 ⇒about 0.6 percentage points of growth per year.

• Transition dynamics are 80 percent of growth.

• “Steady state” growth is only 20 percent of recent growth!

– Possibly slower as population growth declines...

Growth and Ideas – p. 17

U.S. Educational Attainment

1880 1900 1920 1940 1960 1980 20007

8

9

10

11

12

13

14

15

Adult labor force

By birth cohort

YEAR

YEARS OF SCHOOLING

Growth and Ideas – p. 18

U.S. R&D Spending Share

Private R&D

Government R&D

Software and

Entertainment

YEAR

1930 1940 1950 1960 1970 1980 1990 2000 2010

SHARE OF GDP

0%

1%

2%

3%

4%

5%

6%

Growth and Ideas – p. 19

Research Share of Total Employment

1950 1960 1970 1980 1990 2000 20100%

0.1%

0.2%

0.3%

0.4%

United StatesOECD

OECD plus China

and Russia

YEAR

SHARE OF THE POPULATION

Growth and Ideas – p. 20

Other considerations?

• The development of China and India

◦ 2.5 billion people starting to create ideas!

◦ Ratio of Chinese PhDs in Sci/Eng to U.S.:1978 < 5%, 2010 = 130%!

◦ How many future “Thomas Edisons” are there?

• Can robots create new ideas?

• Is the “idea production function” stable?

Growth and Ideas – p. 21

Why growth?

• Proportional ideas are getting harder and harder to find

• The idea production function essentially looks like:

At

At

= TFPtfalling

· Strising

◦ Falling TFP ⇒ constant growth requires exponentialgrowth in scientists/entreprenuers

Growing human resources devoted to R&D offsetsrising difficulty of discovering new ideas

Growth and Ideas – p. 22

Alternative Futures?

The stock of ideas, A

The shape of the idea production function, f(A)

The past

Today

Increasing returns

GPT"Waves"

Run outof ideas

Growth and Ideas – p. 23