Time Substitution and Network Effects with an Application to Science Policy

for US Universities

Hirofumi FukuyamaFukuoka University

William L. WeberSoutheast Missouri State University

Yin XiaColumbia, Missouri

March 16, 2013

Knowledge spillovers-from university to university and from period to period

“If I have seen further it is by standing on the shoulders of giants.”

Paul Samuelson quoting Isaac Newton at the 1971 Nobel Prize Ceremony

Is US Economic Growth Over? Faltering Innovation Confronts the Six HeadwindsBy Robert J. Gordon, NBER August 2012

Science and Productivity Growth

J. Adams (1990) JPE- 15 to 20 year time lag. Approximately 15% of slowdown in productivity growth in the 1970s is explained by decline in scientists and engineers during WWII. Knowledge stocks add 0.5% to annual productivity growth. Jones and Williams (1998)-QJE-private return to R&D is 7%. Social return is 30%.

Mansfield (1995)-RESTAT-Academic research resulted in new commercialized products accounting for 8.9% of sales and cost savings of 3.5% of sales during 1991-94. Lag between academic research and commercialization is falling.

Federal spending on science and private R&D=1.25% of GDP in 1976, =1% in 2009 (2012 Economic Report of the President)

• Bayh-Dole Act of 1980-Allowed universities and private companies to obtain patents and license inventions that were the result of federal spending.

• Concern-Basic research is a public good.• Boldrin and Levine (2009)-AER, Just and Huffman (2009)-Res.

Policy-When universities are granted monopoly power via patents fewer resources are allocated to production of new knowledge relative to industrial applications.

• Basic research and applied research (patenting) are complementary-Thursby and Thursby (2002)-Manag.Sci., Azoulay, Ding, and Waverly (2009)-J. Indus. Ec., Fabrizio and DiMinin (2008)-Res. Policy.

• Weber and Xia (2011)-Am. J. Ag. Ec.-Morishima elasticities of transformation-As patents increase, shadow revenue share of patents increases relative to shadow revenue share of publications.

“Nanotechnology is the understanding and control of matter at dimensions of roughly 1 to 100 nanometers, where unique phenomena enable novel applications.”

“At the nanoscale, the physical, chemical, and biological properties of materials differ in fundamental and valuable ways from the properties of individual atoms and molecules or bulk matter.”

— National Nanotechnology Initiative (NNI)

What is Nanotechnology?

Size of Nanometers

Companies Spawned by National Science Foundation (NSF) GrantsTo Universities

Acoustic Magic, ALEKS Corp. , Allylix Inc., Amati Communications Corp.Arbor Networks, Audyssey Laboratories, Chromatin Inc., Cognex Corp.,Directed Vapor Technologies International, Eden Park Illumination,Genentech, Google, Integrated Genomics, J.A. Woollam Co., Konix, Lehigh Nanotech, Mersive Technologies, MicroMRI, Molecular Imaging,NanoMas Technologies, Nanopharma Technologies, Pacific Biosciences,PolyMedix, RainDance Technologies, Reactive Nanotechnologies, Seaside Therapeutics, Semiprius, SenSound, Sinmat, Solarmer Energy, Spin Transfer Technologies, Vorbeck Material Corp., Webscalers

Biotechnology/pharmaceuticals-5Nanotechnology-7

International Government R&D Spending on Nanotechnology

Source: Roco, M. Journal of Nano Research (2005), 707.

0 50 100 150 200 250 300 350 400 450

Kansas State UniversityThe University of New Mexico

The University of KansasUniversity of Missouri - Columbia

Tufts UniversityUniversity of Cincinnati

Case Western Reserve UniversityLouisiana Tech University

North Carolina State UniversityThe University of Utah

Columbia UniversityUniversity of Virginia

Rice UniversityThe University of Texas at Austin

Georgia Institute of TechnologyWashington University

The Ohio State UniversityUniversity of Pennsylvania

University of California, Los AngelesThe Johns Hopkins University

The University of Wisconsin - MadisonThe Pennsylvania State University

Stanford UniversityCornell University

University of MarylandUniversity of Washington

University of Illinois at Urbana-ChampaignUniversity of Michigan

Northwestern UniversityHarvard University

Number of Journal Articles

Number of Nanobiotechnology journal articles by Sample Universities, 1990-2006

0 20 40 60 80 100 120 140 160 180 200

Pennsylvania State UniversityLouisiana Tech University

Tufts UniversityUniversity of Kansas

Kansas State UniversityUniversity of New Mexico

University of Missouri-ColumbiaUniversity of Cincinnati

Case Western Reserve UniversityGeorgia Institute of Technology

Ohio State UniversityUniversity of Virginia

Northwestern UniversityWashington UniversityUniversity of Maryland

University of Illinois at-UrbanaRice University

University of California-LosColumbia University

North Carolina State UniversityUniversity of Utah

University of WashingtonStanford UniversityHarvard University

University of Wisconsin-MadisonCornell University

University of PennsylvaniaUniversity of Texas-AustinJohns Hopkins University

University of Michigan

Number of Patents

Number of Nanobiotechnology Patents, 1990-2006

0 10 20 30 40 50 60

University of New MexicoKansas State University

Tufts UniversityUniversity of Missouri-Columbia

Case Western Reserve UniversityUniversity of Utah

University of KansasLouisiana Tech University

University of MarylandWashington University

Georgia Institute of TechnologyUniversity of Cincinnati

Columbia UniversityNorth Carolina State University

Rice UniversityUniversity of Texas-Austin

Ohio State UniversityUniversity of Virginia

University of PennsylvaniaUniversity of Wisconsin-Madison

Johns Hopkins UniversityUniversity of California-Los Angeles

Harvard UniversityUniversity of Washington

Stanford UniversityNorthwestern University

Pennsylvania State UniversityUniversity of Michigan

University of Illinois at-Urbana ChampaignCornell University

Number of Ph.D. Degrees Awarded

Number of Nanobiotechnology Ph.D. graduates, 1990-2006

1

1

1,..., universities (DMUs)1,..., periods

Inputs ( ,..., )

Outputs ( ,..., ) (publications, patents, Ph.D. students)

Knowledge produced last period becomes part of the

t t tk k kN

t t tk k kM

k Kt T

x x x

y y y

11

1

stock of knowledge this period.

a. University 's own production of knowledge

b. Stock of knowledge that spills over from other universities,

t tk k

Kt t

k jj k

z y k

Y y

Some Notation

Output Possibility Set

1

1 1 1

( , , ) { : , 1,...,3,

, 1,..., , , ,

0, 1,..., , 1,..., }

Kt t t t t t

k k k m j jmj

K K Kt t t t t t t t tkn j jn k j j k j j

j j k

tj

P x z Y y y y m

x x n N z z Y Y

j K t T

( , , , ; ) max{ : ( , , )}t t t t t t t t t tok k k k k k k k kD x z Y y g y g P x z Y

Directional Distance Function

1( ,..., ) a scaling vector for outputsMg g g

Outputs= tky

Inputs ( , , )t t tk k kx z Y

( , , )t t t tk k kP x z Y

Knowledge inputs in period t+1 1

1

,

t tk k

Kt t tj k s

s j k

y z

Y y y

From period t-1

1

Aggregate Inefficiency:

( , , , ; ) ( , , , ; )K

t t t t t t t t t to ok k k k k

k

D x z Y y g D x z Y y g

1

Inputs that can be reallocated between universities

and across time ( ,..., )t t tk kF kNx x x

Partition the input vector into fixed and variable inputs

1

Inputs that are fixed

( ,..., )t t tk k kFx x x

1

Reallocation between universities, but not across time.K

t tk

k

x x

1 1

Reallocation among universities and across time.T K

tk

t k

x x

Dynamic Models

Shephard and Färe (1980) Färe and Grosskopf (1996, 2000) Bogetoft, Färe, Grosskopf, Hayes, and Taylor (2009)-JORS-Japan Tone and Tsutsui (2009)Fukuyama and Weber (2012)-

Network Models

Färe, R. and Grosskopf, S. (1996- Ec. Letters, 2000-SEPS)Kao and Hwang (2008)- EJORTone and Tsutsui (2009)-EJORChen, Cook and Zhu (2010)-EJORFukuyama and Weber (2010-Omega, 2011-IJORIS) Akther, Fukuyama, and Weber (2012)-Omega

, 1

1

max subject to

( , , , ) 1,..., ,

, 1,..., .

k k

K

kx k

t t t t t tk k k k k k

Kt tkn n

k

y g P x x z Y k K

x x n F N

( , , , ) 1,..., ,t t t t tk k k kP x x z Y k K

Output Possibility Sets

Government agency (NSF) wants to allocate the variable input so as to maximize the aggregate size of the production possibility sets in a givenperiod

, , 1

1 1 11 1

11 1 1

1

max subject to

, 1,..., , , 1,...,1

, 1,..., , , ,

, 1,..., ,

k k k

Ktkx k

K Kt t t t t tm m j jm n j jn

j j

K K Kt t t t t t t t tn j kn k j j k j j

j j j

Kt t thm h m j jm

j

y g y m M x x n Fk

x x n F N z z Y Y

y g y m M

1

1 1 1

1 1

1

, 1,..., ,

, 1,..., , , ,

, 1,..., , , 1,..., ,

, 1,..., ,

Kt t thn j jn

j

K K Kt t t t t t t t thn j jn h j j h j j

j j j

K Kt t t t t tKm K m j jm Kn j jn

j j

Kt t t tKn j jn K

j

x x n Fk h

x x n F N z z Y Y

y g y m M x x n F

x x n F N z

1

1 1

1

, ,

, 1,..., ,

0, 1,..., .

K Kt t t t tj j K j j

j j

Kt tkn n

k

tj

k Kz Y Y

x x n F N

k K

*

1 No ReallocationWith ReallocationBetween Universities

( , , , ; )K

t t t t t tk o

k

D x z Y y g

Aggregate Inefficiency

Time Substitution-When to begin use of an input and for how long .

t T

Shephard and Färe (1980) Färe and Grosskopf (1996) Färe, Grosskopf, and Margaritis (2010) Färe, Grosskopf, Margaritis, and Weber (2011)

, ,max ( , , , , ; ) subject to

( , , , , ; ) 0, [ , ]

, 1,..., .

t t t t t to k k k k k

x t

t t t t t to k k k k k

tkn kn

t

D x x z Y y g

D x x z Y y g t

x x n F N

For University k

Technological Progress-Delay the starting period, Technological Regress-Begin production early.

Increasing returns to scale-Use input intensively, small Decreasing returns to scale-Use equal amounts of input in each period

, , , , 1

1

1

1

1

max subject to

, 1,..., , 1,...,

, 1,...,

, 1,...,

, 1,..., , 1,...,

, 0, 1,...

Ktk

x k t

Kt t t tkm k j jm

j

Jt t tk j j

j

Jt t t

k j jj

Kt t tkn j jn

j

t t t tkn j jn kn

y y m M k K

z z k K

Y Y k K

x x n F k K

x x x n F

1

, , 1,...,

0, 1,...,

K

j

tj

t

N k K

j K

1 1 1 1

1

1 1 11

1

1 1 1

1

1 1 1

1

1 1 1 1

, 1,..., , 1,...,

, 1,...,

, 1,...,

, 1,..., , 1,...,

, 0,

Kt t t tkm k j jm

j

Jt t t tk k j j

j

K Jt t t t

k j j jj k j

Kt t tkn j jn

j

t t t tkn j jn k

y y m M k K

z z k K

Y Y k K

x x n F k K

x x x n

1

1

1 1

1,..., , 1,...,

0, 1,...,

K

j

tj

t

F N k K

j K

1

1

1

11

1

1

, 1,..., , 1,...,

, 1,...,

, 1,...,

, 1,..., , 1,...,

,

Kt t t tkm k j jm

j

Jt t t tk k j j

j

K Jt t

k j j jj k j

Kt t tkn j jn

j

t t tkn j jn k

y y m M k K

z z k K

Y Y k K

x x n F k K

x x x

1

1

0, 1,..., , 1,...,

0, 1,...,

, 1,..., .

Ktn

j

tj

K

kn nk t

t

n F N k K

j K

x x n N

* *

1 1 1 1 1 No ReallocationReallocation among Reallocation amongUniversities and Universitiesacross time

( ) ( , , , ; )T K T K T

t t t t t t tk k o

t k t k t

D x z Y y g

Aggregate Inefficiency

Three outputs-publications, patents, Ph.D. studentsFixed inputs-University R&D spending in the life sciences,engineering, and physical sciencesVariable input-NSF grants for nanotechnologyOwn knowledge input-university’s past publicationsSpillover knowledge input-past publications from other universities

Data-1990-2005Three year moving average of all outputs and inputs.Lose one observation since lagged knowledge outputsenter the current period technology. Model is estimated for 1993-2005 for 25 universities

Directional vector=g=(1,1,1)

Knowledge Outputs at 25 US universities

Publications in nanobiotechnologyPatents in nanobiotechnologyPh.D. students in nanobiotechnology

Variable Mean Std Minimum MaximumPublications=y1 6.63 6.63 0.3 45.3Patents=y2 3.38 3.26 0 17Ph.Ds=y3 1.49 1.65 0 11University research dollars=x1 (millions of $, base=2005) 251.6 133.5 19.5 662.7NSF funds= (millions of $, base=2005) 3.13 4.65 0 32.5Lagged other publications= 419.2 267.0 124 1112Lagged Own publications=z = 16.08 133.5 1 100

x

11

Kt t

jj k

Y y

11ty

Estimates of Inefficiency

YearNo reallocation of

NSF funds

Reallocation between

universities but not time

Reallocation across time and

reallocation between universities

1993 16 15 151994 16 11 81995 15 13 71996 13 9 41997 19 14 71998 14 10 61999 15 12 52000 15 13 52001 16 12 72002 17 14 82003 15 12 52004 14 15 52005 17 12 4

Number of Frontier Universities

Year Actual NSF Optimal NSF Optimal NSF1993 0.725 (1.724) 0.725 (1.764) 0.7026 (1.740)1994 1.342 (2.829) 1.342 (2.805) 1.8330 (2.886)1995 1.112 (1.871) 1.112 (1.882) 1.0258 (1.819)1996 1.636 (2.631) 1.636 (1.678) 1.1452 (1.581)1997 1.123 (1.734) 1.123 (1.098) 0.7510 (0.469)1998 1.380 (1.648) 1.380 (1.039) 1.1810 (0.748)1999 1.455 (1.782) 1.455 (1.531) 1.1290 (0.762)2000 3.439 (5.288) 3.439 (3.867) 2.2946 (1.309)2001 4.985 (6.660) 4.985 (6.049) 3.7161 (2.221)2002 6.180 (6.183) 6.180 (5.539) 6.0066 (3.618)2003 5.780 (5.162) 5.780 (3.712) 6.1435 (3.575)2004 5.970 (6.080) 5.970 (5.992) 8.9642 (6.298)2005 5.603 (5.107) 5.603 (4.845) 5.8389 (4.796)

Mean Actual and Optimal Values ofStd. Dev. In parentheses

x

Summary and Conclusions

• Slowdown in productivity growth in US and other countries• Social return to R&D high relative to private return• Academic Research has spawned new firms.• Nanobiotechnology knowledge outputs/inputs integrated

into a dynamic network model• Estimates indicate between 91 and 184 extra publications,

patents, and Ph.D. students from realizing greater efficiency and through reallocation of NSF funds.

• University winners and losers-political process limits the extent of reallocation resulting in smaller potential gains.