ECO5532013L_9.pdf

Master Economics and Public Policy

ECO 553. Economic Growth1

Lecture 9Schumpeterian Growth

Pierre Cahuc

Winter 2013-2014

1http://sites.google.com/site/eco553x/1 / 34

Introduction

I Growth is generated to a large extent by innovationsI Previous lecture: innovations = new products with horizontaldi¤erentiation

I increased specialization generates growthI new products do not replace old products

I Actually, growth is also generated by quality improvinginnovations (vertical di¤erentiation) ! new products replaceold products

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Introduction

I Creative destruction: Joseph Schumpeter: Capitalism,Socialism and Democracy, 1942

I innovative entry by entrepreneurs is the force that sustainslong-term economic growth, even as it destroys the value ofestablished companies that enjoy some degree of monopolypower

I the threat of market entry would keep �rms disciplined andcompetitive, ensuring they invest their pro�ts in new productsand ideas.

I Schumpeter believed that it was this innovative quality thatmade capitalism the best economic system

I Renewal of ideas of SchumpeterI globalization and development of service industry: importanceof innovations and scale e¤ects

I empirical evidence shows that the process of creativedestruction is very large: high turnover of �rms, jobs, workers

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Introduction

Outline

1. Creative destruction: some facts

2. A Schumpeterian model of growth2

3. The ine¢ ciency of market equilibrium

2Philippe Aghion and Peter Howitt, 1992, A Model of Growth throughCreative Destruction, Econometrica, vol. 60(2), pp. 323-51. Philippe Aghionand Peter Howitt, 1998, Endogenous Growth Theory, The MIT Press.

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1. Creative destruction: some factsDe�nitions

I Large process of reallocations of workers and jobs

Net Employment Change = Hires - Separations| {z }Workers �ows

Net Employment Change = Creation - Destruction| {z }Job �ows

I Workers �ows are di¤erent from job �ows because di¤erentworkers can occupy the same job consecutively

I Job �ows correspond to reallocation of jobsI across perennial �rmsI due to entry and exit of �rms

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1. Creative destruction: some factsJob �ows

CountryJob

creationJob

destructionNet employment

growthJob

reallocationFrance (84-91) 12.7 11.8 0.9 24.5Germany (83-90) 9.0 7.5 1.5 16.5Netherlands(84-91) 8.2 7.2 1.0 15.4United Kingdom (85-91) 8.7 6.6 2.1 15.3United States (84-91) 13.0 10.4 2.6 23.4

Source: OECD

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1. Creative destruction: some factsJob �ows 1997-2005

CountryJob

reallocationExcess jobreallocation

Brazil 31.9 26.0Finland 23.1 17.3Germany 15.5 14.5Mexico 28.7 26.4United Kingdom 30.0 27.3United states 28.3 25.0

Source: Bassanini and Marianna3

3Andrea Bassanini and Pascal Marianna Looking inside the perpetualmotion machine: Job and worker �ows in OECD countries, OECD socialemployment and migration working paper n�95, September 2009.

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1. Creative destruction: some factsIntra-sector and between-sector job �ows

I If S designates the number of sectors, we look at the netemployment growth in a given sector s (V sn ) and the netemployment growth in the economy as a whole (Vn).

I An initial indicator assesses the extent of job reallocations dueto between-sector movements. It is de�ned by:

RE =S

∑s=1jV sn j � jVn j

I Let Ts be the job reallocation in sector s; the second indicatorcorresponds to the sum of excess job reallocations within eachsector:

RI =S

∑s=1(Ts � jV sn j)

I The fraction of job reallocations due to between-sector shiftsis then measured by the ratio RE/(RI + RE ).

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1. Creative destruction: some factsIntra-sector and between-sector job �ows

Country Period Number of sectors RE/(R I+RE )Germany 83-90 24 0.03United States 72-88 980 0.14France 84-88 15 0.06France 84-91 600 0.17Italy 86-91 28 0.02Sweden 85-91 28 0.03

Source: OECD

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1. Creative destruction: some factsJob �ows in the long run in the US 1947-2005: the great moderation

US Quarterly job �ows trends Manufacturing and NonfarmBusiness

Source: Davis, Faberman and Haltiwanger (2006)4

4The Flow Approach to Labor Markets, Micro-Macro Links, and the RecentDownturn, Journal of Economic Perspectives, vol 20(3), pp. 3�26.

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1. Creative destruction: some factsJob �ows: Reallocation due to entry and exit of �rms 1997-2005

CountryTotal job

reallocation

Job creation

by entry

Brazil 31.9 6.0

Finland 23.1 3.9

Germany 15.5 3.2

Mexico 28.7 5.5

United Kingdom 30.0 5.1

United states 28.3 4.6

Job destruction

by exit

5.0

3.1

2.2

4.2

7.2

4.8

Job reallocation

due to entry and exit

11.0

8.4

5.4

9.7

12.3

9.4

Source: Bassanini and Marianna

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1. Creative destruction: some factsJob �ows and workers �ows

0

10

20

30

40Hi

ring

rate

20 15 10 5 0 5 10 15 20Employment growth rate

Hires and Establishment Growth in France 2007 to 2010. Quarterly data.Source: DMMO

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0

10

20

30

40Se

para

tion

rate


Separations and Establishment Growth in France 2007 to 2010. Quarterlydata Source: DMMO

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0

10

20

30

40Hi

ring

rate


United States

Hires and Establishment Growth in the US, 2001 to 2010. Quarterlydata. Source: Davis, Faberman and Haltiwanger (2012)5

5Labor market �ows in the cross section and over time, Journal of MonetaryEconomic,59 (1), pp. 1�18 14 / 34


0

10

20

30

40Se

para

tion

rate


Separations and Establishment Growth in the US, 2001 to 2010.Quarterly data Source: Davis et al. (2012)

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2. A Schumpeterian model of growth

I Aghion and Howitt (1992, 1998)I Growth is generated by innovations that improve the qualityof products and destroy the result of previous innovations bymaking them obsolete

I Innovations are the result of random discoveries produced byresearch activity driven by pro�ts

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2. A Schumpeterian model of growthBasic framework

I L identical individuals, L constant over timeI Preferences are represented by the welfare function

U =Z ∞

0c(t)e�ρtdt,

ρ > 0 is the discount rate and c(t) consumptionI Risk neutrality ! the interest rate r = ρ

I Every individual o¤ers one unit of labor per unit of time, atzero cost

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I Output, which is consumed, is produced in quantity y(t) withone intermediate product with the technology

y(t) =A(τ)

αx(τ, t)α, 0 < α < 1,A(τ) > 0. (1)

where x(τ, t) stands for the quantity of intermediate productof variety τ used at time t

I Henceforth, for the sake of simplicity, we shall assume thatthe quantity of intermediate product τ is constant over timeand denote

x(τ, t) = x(τ)

I Innovations improve the quality of intermediate products: aninnovation creates a new variety of intermediate productwhose productivity is larger by a multiplicative factor γ > 1than the previous intermediate product

A(τ + 1) = γA(τ)18 / 34


I Individuals can workI either in the intermediate product sectorI or in the research sector

I One unit of labor in the intermediate product sector producesone unit of intermediate product

I Let us denote by n(τ) the quantity of labor in the researchsector when the intermediate produt τ is used:

L = x(τ) + n(τ)

I Innovations are produced at rate λn(τ), (there are λn(τ)dtinnovations over the small interval of time [t, t+dt]) whereλ > 0 is a parameter that measures the productivity ofresearch

I Firms which innovate can monopolize the production of thenew intermediate product

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I Innovations create 3 externalities

1. The monopoly rent obtained by the innovator is generallysmaller than the surplus induced by the innovation

2. Every innovation increases A and then the productivity offuture research (knowledge is a non rival good)

3. Destruction of previous intermediate products

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2. A Schumpeterian model of growthThe value of an innovation

I Let us denote by π(τ) the �ow of pro�t of the �rm thatproduces the intermediate product τ

I The value of innovation τ made at time t, denoted by V (τ, t)is de�ned by

V (τ, t) =1

1+ rdt[π(τ, t)dt + [1� λn(t)dt]V (τ, t + dt)]

orrV (τ, t) = π(τ)� λn(τ)V (τ, t) + V (τ, t)

with V (τ, t) = 0 because π(τ) and n(τ) do not depend ontime, so that, we can write V (τ, t) = V (τ) which satis�es:

V (τ) =π(τ)

r + λn(τ)(2)

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2. A Schumpeterian model of growthWages

I Labor market is perfectly competitive: wages are equal tomarginal productivity

I Marginal productivity in researchI one unit of labor produces an innovation with probability λ perunit of time

I value of an innovation when the intermediate product τ is usedis equal to V (τ + 1)

I therefore, the wage in research when the intermediate productτ is in use is

w(τ) = λV (τ + 1) (3)

I Perfect competition ! unique wage: wage in research sectoris equal to the wage in intermediate product sector.

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2. A Schumpeterian model of growthIntermediate product sector

I Intermediate products are produced by monopoliesI The monopoly which produces the intermediate product τ geta pro�t �ow

π(τ) = maxxp(τ)x � w(τ)x , (4)

where p(τ) denotes the price of the intermediate product τI The relation between the price and the quantity of theintermediate product is deduced from the maximization ofpro�ts of the representative �rm which produces the �nal good

I Final output sector is perfectly competitive ! marginalproductivity of intermediate product in this sector,

A(τ)x(τ)α�1

is equal equal to the price

p(τ) = A(τ)x(τ)α�1. (5)

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2. A Schumpeterian model of growthIntermediate product sector

I Substituting the expression for p(τ) de�ned equation (5) intoequation (4), we see that the �rm which produces theintermediate product τ

maxxA(τ)xα � w(τ)x

I The solution is

x(τ) =

�α

ω(τ)

�1/(1�α)

,ω(τ) � w(τ)/A(τ) (6)

π(τ) = A(τ) (1� α)

�ω(τ)

α

�α/(α�1). (7)

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2. A Schumpeterian model of growthEquilibrium

I The equilibrium value of pro�ts (7), the value of aninnovation (2) and the value of the wage (3), allow us to writethe artitrage equation that equalizes the wage in research andin the intermediate product output:

ω(τ) =λγ(1� α)

r + λn(τ + 1)

�ω(τ + 1)

α

�α/(α�1). (A)

I The equilibrium values of n and ω are de�ned byI (A)I labor market equilibrium, L = x(τ) + n(τ), which can bewritten, using (6):

L =�

α

ω(τ)

�1/(1�α)

+ n(τ) (L)

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2. A Schumpeterian model of growthStationary growth

I Stationary solution, denoted by (ω, n), satis�es equations (A)and (L): �

ω

α

�1/(1�α)

=λγ(1� α)

α(r + λn)(AS)

L =� α

ω

�1/(1�α)+ n (LS)

I (AS) de�nes a decreasing relation between the wage and thequantity of labor used in research

I Interpretation: higher future wages decrease future pro�ts andthen the returns to research

I (LS) de�nes an increasing relation between the wage and thequantity of labor used in research

I Interpretation: wage increases reduce employment in the

intermediate product sector (the term�

αω

�1/(1�α)) and thenincrease employment in research

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I The stationary equilibrium (n, ω) is de�ned by the intercept ofan increasing curve and a decreasing curve in the (n,ω) plane.Thus it is unique when it exists (which is assumed henceforth)

I The stationary value of labor in research is

n =(1� α) γL� (r/λ)

(1� α) γ+ α� 0. (8)

I The quantity of output produced with the intermediateproduct τ is

y(τ) =A(τ)

α(L� n)α,

I This yields, together with A(τ + 1) = γA(τ),

y(τ + 1) = γy(τ),

where τ stands for the sequence of innovations τ = 1, 2...∞27 / 34


I Let us compute the average growth rate of outputI there are λndt innovations over every small interval of timedt ! 0

I every innovation increases the logarithm of output by ln(γ)

I Change in production at between dates t and t+dt can bewritten

ln [y(t + dt)] = ln [y(t)] + λndt ln(γ)

I Using the approximation6

limdt!0 ln[y(t+dt)/y(t)] = limdt!0[y(t+dt)/y(t)]� 1, weget the average stationary growth rate

g = limdt!0

y(t + dt)� y(t)dt

1y(t)

=y(t)y(t)

= λn ln(γ) (9)

6We know that limx!1 ln x = limx!1 x � 128 / 34


I Equations (8) and (9) allow us to de�ne the averagestationary growth rate as function of the exogenous variables:

g = ln(γ)�

λ (1� α) γL� r(1� α) γ+ α

�� 0 (10)

I The logarithm of output increases discontinuously, after everyinnovation, by an amount ln(γ)

I The average spell between 2 innovations is equal to 1/λn.

I In this model, more intensive research, induced by more laborin research, entails more frequent innovations and a highergrowth rate

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2. A Schumpeterian model of growthStatic comparative properties

I The average growth rate

g = ln(γ)�

λ (1� α) γL� r(1� α) γ+ α

�� 0

increases withI L the size of population

I λ the productivity of researchI γ the size of the increase in production induced by innovation

I decreases with

I r the interest rateI α which measures the level of competition in the intermediateproduct sector7

7The absolute value of the elasticity of demand for intermediate products,de�ned equation (5), equal to 1/(1� α), increases with α so that themonopoly power decreases with α.

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I It is possible to compute the optimal growth rate, whichmaximizes

U =Z ∞

0q(t)e�rtdt

I The optimal solution yields the stationary optimal growthrate8

g � = λn� ln(γ)

where n� satis�es

1 =λ(γ� 1)

� 1α

�(L� n�)

r � λn�(γ� 1) (11)

8Details are given in Aghion and Howitt (1998), Chapter 2 pp. 61-63.31 / 34


I The comparison of n (de�ned equation (8)), the stationaryquantity of labor used in research at market equilibrium,which can be written as the solution to

1 = λγ

�1� α

α

�(L� n)r + λn

. (12)

and n�, the socially optimal stationary quantity of labor usedin research, which solves

1 =λ(γ� 1)

� 1α

�(L� n�)

r � λn�(γ� 1) (13)

shows 3 di¤erences between the socially optimal rate ofgrowth and the market equilibrium rate of growth

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3. The ine¢ ciency of market equilibrium1. Di¤erence between the social discount rate, r � λn�(γ� 1),at the denominator of (13) and the private discount rate atthe denominator of (12)

I Social discount rate < private discount rateI Intertemporal externality (present research increasesproductivity of future research)

I Research too low at market equilibrium

2. (1� α) shows up in (12) but not in (13)I The monopolies obtain only a share (1� α) of the surplusinduced by innovations, as shown by the expression of pro�ts(7)

I Appropriability e¤ectI Research too low at market equilibrium

3. (γ� 1) in (13) instead of γ in (12)I Innovators no not take into account the cost associated withdestruction of old products

I Destruction e¤ectI Too much research at market equilibrium

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I The Schumpeterian model shows that the level of researchcan be either too high or too low at market equilbrium, withrespect to the socially e¢ cient level

I The 2 �rst e¤ects dominate when the size of innovations, γ, islarge. In this case n < n�.

I When the monopoly power is strong (α small), and the size ofinnovations su¢ ciently small, the destruction e¤ect dominates.In this case, there is too much growth at market equilibrium

I There are other costs associated with the destruction e¤ect:unemployment9

9Pierre Cahuc and André Zylberberg, 2009, The Natural Survival of Work,Job creation and job destruction in a growing economy, MIT Press

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ECO5532013L_9.pdf