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Economics of Innovation

General Purpose Technologies

I. The conceptual frameworkII. The Bresnahan-Trajtenberg Model

Manuel Trajtenberg2005

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General Purpose Technologies

Whole eras of technical progress and economic growth seem to be driven by a few key technologies, e.g. the steam engine, electricity, microelectronics.

Is there such a thing as “GPTs”? If so, what are their characteristics, how do they operate?

How about other prominent technologies such as the factory system, the railroad, the automobile, lasers, computers?

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Characteristics of GPTs• General purposeness => pervasiveness, i.e. used as inputs by a wide range of downstream sectors

• Potential for continuous technical advance => ex post sustained improvements in performance.

• “Innovational complementarities”: the productivity of innovative activities in user sectors increases as a consequence of improvements in the GPT

As a GPT advances it spreads throughout the economy, fostering innovation in an ever-expanding array of application sectors, and bringing about generalized productivity gains.

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General Purposeness

The GPT performs some generic function that is vital to the functioning of many products and production systems. E.g. “continuous rotary motion,” by the steam engine and later on by electrical motors; “binary logic” for electronics.

“Not obvious that rotary motion would become a universal functionality: many manual jobs (e.g. sewing, polishing, cutting) could hardly be seen ex-ante as candidates for replacement by mechanical actions originating in continuous rotary motion. Often the substitution did not make economic sense until the steam engine, and then the electric motor, could deliver such functionality at favorably price/ performance ratios.”

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General purposeness of microelectronics

The workings of virtually any system (in particular of any electro-mechanical system) can be broken down into a series of steps that transform a given input into a desired outcome. E.g. a traditional watch transforms the power of the spring into an analog signal, depicting time.

Despite their variety, many of these intervening steps can in principle be done (or be replicated) by the application of binary logic, that is, by activating a circuit consisting of a series of binary elements (e.g. gates, flip-flops, etc.).

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General purposeness of microelectronics – cont.

The general purposeness of binary logic is a striking technological fact that has far reaching economic implications:

• the enormous variety of seemingly disparate products, methods of production, etc. conceal the uniformity of a few underlying technological principles;

• these principles, in turn, give rise to powerful economic forces that shape the process of technical change and growth.

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GPT and application sectors

GPT: microelectronics

Hearing aids Radios,

TVs Computers …. CT Scanners

Cars

Etc.

Application sectors

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Innovational Complementarities

Key feature - examples:

• Electricity: not just reduction in energy costs (substitution), but fractionalization of power within factories, hence design according to workflow, not power requirements.

• Users of micro electronics: most innovative

industries, they wrap their own tech advances around the surging power of silicon.

• In computers: hardware and software…

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Example of Steam Engine in the late 19th century US

Context: competition between waterpower and steam power.

Steam: slow adoption in manufacturing in the US, waterpower dominant till mid 19th century.

Leading hypothesis:

* The advantages of the (Corliss) steam engine helped tip the balance from waterpower to steam power.

* Released the locational constraint of waterpower.

* Enabled intertwined processes of urbanization and industrialization, reap benefits from agglomeration.

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The Impact of GPTs: a more general view

Look up-close how GPTs impact the economy: often through massive “relocation” /reorganization of economic activity, concomitant gains in efficiency.

• The steam engine allowing for urbanization of industry, agglomeration effects.

• Electricity: (i) separate production of energy from use; (ii) fractionalization of power within factories, hence design according to workflow, not power requirements.

• Computers/Internet: greatly facilitate informational exchanges, allow for outsourcing /downsizing, reorganize around B2B; telecommuting, etc.

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Contrast the GPT Approach to Previous Attempts to Assess the Impact of Major Innovations

• Fogel (1964) on railroads: computed cost savings of railroads vs. water canals in the 1860s, “just” a few % of GDP, concluded that “small” impact.

•  Von Tunzelman (1978): cost savings of steam power in Britain versus all other prime movers as of 1800, again very small.

• Robert Gordon (2000) on the impact of Computers/IT...

Focus on cost comparisons or other static measures miss the point: the main impact of a GPT is through the changes they bring about in user sectors, and the positive loop these generate.

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The BT model – notation“General Purpose Technologies: engines of growth?” Journal of

Econometrics, 1995

GPT (indexed “g”) General Purpose Technology

AS (indexed “a”) Application sector

z: Quality of the GPT

w: Market price of the GPT

c: Marginal cost of the GPT

Ta : Technology level of a

Ci : R&D costs of the i-th sector.Recall: partial equilibrium model (in HT: g.e.)

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The Application Sectors

)(),,( aa

aa

TTCTzwΠmax

a

The objective function that the single AS acts as if it maximizes is,

a : The payoff (gross private returns) to technical advance in AS.

Many possible market structures underlying it, by which manufacturers in the AS purchase the GPT, combine it with their own technology, and sell the output to final consumers.

Example: PC producers (Compaq, IBM, etc) buy microprocessors from Intel, sell the PCs to consumers.

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Example of a

),,(]),([ ),,( aaa

aaP

aa TzPXwTzPmaxTzwΠ

a

If the AS consists of a monopoly,

Assuming that the AS requires one unit of the GPT per unit of the AS product; (.): unit cost of production

(in the paper -CSP instead of Xa)

Thus a captures some of the total surplus generated; for welfare analysis enough that a highly correlated with total surplus.

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Properties of the AS functions

0 ,0 ,0 ,0 ,0 aTT

aT

aaa

aaawaTz CCΠΠΠ

0

:2

a

aa

Tz

ΠΠ

(IC)entaritiesal complemInnovation

azT

0 ),,(

)(),,(

z

RzwRT

TCTzwΠmax

aa

a

aa

aa

Ta

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The GPT sector

Aa

aa

w

g TzwXcwmaxcTzΠ ),,()( ),,(

A(w,z): set of sectors that adopt the GPT

The setting of z (the innovative behavior of the GPT):

0 ),,(

)(),,(

a

gg

gg

z

T

RcTRz

zCcTzΠmax

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Equilibrium and Social OptimumA Nash equilibrium is characterized as (multiple equilibria possible):

)(

,)( :},{ogo

oaoa

oo

TRz

azRTzT

*}*,*,{ :

);(maxarg*

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

ATzoptimumsocial

cASA

cASzCTCTzcΠmaxAa

ga

a

Aaa

a

Tz a

The social optimum:

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Market (Nash) equilibrium

z

Ta

),( zwRa

),( ag TcR

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Comparing the market eq. and the Social optimum

Proposition:

The social optimum entails higher tech levels than the (best) decentralized equilibrium, i.e.,

* , , ,* * AAaTTzz ooaa

o

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Two positive externalities1. Vertical (due to IC): higher z would result in

higher T, and vice versa; but parties typically do not fully internalize it.*

2. Horizontal (due to GP): The higher the Ts, the more AS => the higher the demand for the GPT => higher z, which benefits all. But each AS acts myopically.

Hence too low T’s and z.

* Could think of GPT as Stackelberg leader, hence:

Aa

aa

wzwRzwXcwmax ),(,,)(

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How to overcome the disparity between social and private optimum?

Role of large (initial) demanders such as the Government, the military, key users.

Contracting and coordination between key players to break away from limitations of arms-length market transactions.

Informational exchanges as means of moving up the equilibrium z, T (see later).

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Dynamics

Use dynamic oligopoly framework of Maskin and Tirole (1987): Markov Perfect Equilibrium

Assumptions:

• bilateral monopoly

• the GPT and the AS move in alternate periods of fixed length (i.e. the length of time it takes to develop the next generation tech of each)

• fixed w

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Dynamics 2

Each firm maximizes at time t,

rst

sst

is egaiTz

,, ),,(

0

)( ),( 11 tg

tta

t TRzzRT

Markov Perfect Equilibrium (MPE) characterized by the existence of a pair of dynamic reaction functions,

that fulfill certain conditions.

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Dynamics 3

For any discount factor ,

(i) There exists a unique MPE that is dynamically stable.

(ii) The steady state values of z and T equal the static Nash equilibrium when =0, and grow with .

10 , : thatrecall re

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MPE for different

z

T

=0.1

=0.9

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Interpreting the result about

The discount factor can be interpreted as a measure of the difficulty in forecasting the tech development of the other side: the smaller is the more difficult it is for the AS to anticipate the future quality of the GPT and vice versa.

Thus, the more “cooperative” the GPT and the AS’s are in terms of informational exchanges, the higher the eq. levels of z and T.

Larger levels of z and T may translate into faster growth.

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Information and coordination between the GPT and ASs

Intel vis a vis manufacturers of PCs: when do they know the tech details of new micro-processors?

Microsoft vis a vis software developers: when do they know the tech details of new OS (Windows)?

How do the institutional arrangements affect growth?