Neoclassical Models of Endogenous Schumpeterian Growth: The Aghion

1
Neoclassical Models of EndogenousSchumpeterian
GrowthThe Aghion Howitt Model
Econometrica, Vol. 60, No. 2 (Mar., 1992) , pp.
323-351Endogenous Growth Theory, 1998, The MIT
Press, pp. 53-80
michael.stastny_at_wu-wien.ac.at http//www.economist
.at SE Evolutionary Growth Theory gerald.silverbe
rg_at_merit.unimaas.nl
2
The Aghion Howitt Model

• Schumpeterian approach to endogenous growth in
  acontext of uncertainty.
• Growth is generated by a random sequence of
  quality-improving innovation that result from
  uncertain research activities. This is a model of
  vertical innovations (quality ladders).
• A model of vertical innovations has the natural
  property that new inventions make the previous
  technology obsolete. Thus, Aghion Howitts
  model is one of creative destruction, hence its
  Schumpeterian nature.
• Research is conducted by firms, because, if
  successful, it will enable firms to acquire a
  patent that will grant them monopoly over the
  innovation. Licensing is an option.

3
Process of Creative Destruction
The fundamental impulse that sets andkeeps the
capitalist engine in motion comesfrom the new
consumers goods, the newmethods of production
or transportation, the new markets,.
This process incessantly revolutionizes
the economic structure from within, incessantly
destroying the old one, incessantly creating a
new one. This process of Creative Destruction is
the essential fact about capitalism. Joseph
Alois Schumpeter (1942) Capitalism, Socialism
and Democracy. New York Harper and Brothers. p.
83
4
The Creative Destruction Feature

• This creative destruction feature has both
  positive and normative consequences.
• On the positive side, it implies a negative
  relationship between current and future
  research which results in the existence of
  a unique steady-state (or balanced growth)
  equilibrium and also in the possibility of
  cyclical growth patterns.
• On the normative side, although current
  innovations have positive externalities for
  future research and development, they also
  exert a negative externality on incumbent
  producers (business-stealing effect).

5
The Three Economic Sectors
Incentive for Innovation The innovator of one
period becomes the exclusive user of the new
technology in the intermediate sector in the next
period. Problem for Economy Allocation of the
given skilled labor pool between RD and
intermediate good production.
6
Assumptions Labor
There are L individuals with the same
intertemporal preferences given by
where y denotes output of the final (consumption)
good and r denotes the time preference (
interest rate).
Societys fixed stock of labor has two competing
uses. It can produce intermediate goods and it
can be used in research
where x (n) is the amount of labor used in
manufacturing (research). The amount of labor in
the final-good sector is assumed constant and
therefore can be neglected. t is the number of
innovations that have occurred so far
7
Competitive Final-Good Sector
The final-good sector produces goods using an
inter-mediate input purchased from a monopolistic
supplier according to the following production
function
i.e. one unit of the intermediate good is
produced by using only one unit of labor.
A is a technology parameter that measures the
stock of technological progress. An innovation
raises A by a constant factor
8
Intermediate Monopolists Decision Problem
Monopolist knows that final good producers
production function is
Profits for the final-good producer (consumer
good is numéraire) are given by
i.e. final-good producers will employ x until its
marginal product equals its price
9
Intermediate Monopolists Decision Problem
Monopolist chooses the level of output, xt, that
maximizes his profits
Defining ?t wt/At as the productivity-adjusted
wage, we can express xt as a decreasing function
of ?t
10
Intermediate Monopolists Decision Problem contd
Substituting for xt in the profits function, we
get
This finding introduces an additional reason,
besides creative destruction, for the negative
dependency of current research on the amount of
expected future research Specifically, a higher
demand for future research labor will push future
wage ?t1 up, thereby decreasing the flow of
profits pt1 to be appropriated by the next
innovator. This, in turn, will tend to discourage
current research, that is, to drive nt down.
11
Innovations

• Innovations occur to a researcher randomly with
  a Poisson arrival rate of ?, i.e. the average
  waiting time is 1/ ?.
• Since Poisson processes are additive, the
  expected arrival rate of n researchers is ?n.
• The arrival of an innovation boosts the
  productivity A in the final sector in the next
  (innovation-)period by a constant factor

12
The Poisson Counting Process
13
Characterization of the Model

• The firm that succeeds in innovating monopolizes
  the intermediate good sector until being
  replaced by the next innovator.
• Since the new technology is freely accessed by
  all researchers (public good), the inventor makes
  it possible for all researchers to begin working
  on the next innovation.
• The fact that a technology can be made
  excludable means that somebody can benefit from
  using it, i.e. can sell it (licensing) or use to
  produce a new good and extract rents from the
  monopoly from that activity.

14
The Research Sector
The objective of a firm is to maximize the flow
of expected profits from research
where Vt1 is the discounted expected payoff to
the (t1)th innovation. wt is the value of an
hour in manufacturing, whereas ?Vt1 is expected
value of an hour in research.
Arrow/Replacement effect The reason why the
monopolist chooses to do no research is that the
value to the monopolist of making the next
innovation would be Vt1 - Vt
15
Defining Vt1
The value Vt1 is the expected present value of
the flow of monopoly profits generated by the
(t1)th innovation over an interval whose length
is exponentially distributed with parameter ?nt1
(1/ ?nt1 waiting time).
The denominator is the obsolescence-adjusted
interest rate and shows the effect of creative
destruction. The more research is expected to
occur, the shorter the likely duration of the
monopoly profits, and hence the smaller the
payoff to innovating.
16
Vt1 in slightly different terms
Says that the expected income generated by a
license on the (t1)th innovation during a unit
time interval, namely rVt1, is equal to the
profit flow minus the expected capital loss
that will occur when the (t1)th innovator is
replaced by a new innovator and therefore loses
Vt1. The flow probability of this loss is the
arrival rate ?nt1.
17
The Two Main Equations

• The model is fully characterized by both
• the arbitrage equation
• the labor market clearing equation

18
The Arbitrage Equation
reflects the fact that labor can be freely
allocated between manufacturing and research
19
Labor Market Clearing Equation
reflects the frictionless nature of the labor
market and determines the growth-adjusted wage
rate
If then it pays to increase nt. Given the labor
market clearing equation from above, this means
that xt decreases, which implies that wt must
increase.
20
Steady-State Level of Research
The steady-state (or balanced growth) equilibrium
is a stationary solution with
Therefore
21
Comparative Statics
22
Comparative Statics

• A decrease in r increases the marginal benefit
  to research, by raising the present value of
  monopoly profits.
• An increase in ? also increases the marginal
  benefit to research, by raising the size of the
  next intervals monopoly profits relative to this
  intervals productivity.
• An increase in ? decreases both the marginal
  cost and the marginal benefit of research,
  because on one hand it results in more
  effective units of research for any given level
  of employment, but on the other hand it also
  increases the rate of creative destruction during
  the next interval. The former effect turns out to
  dominate.
• An increase in L both increases the marginal
  benefit and reduces the marginal cost of
  research, by reducing the wage of skilled labor.

23
Market Power
Arbitrage Equation
The steady-state productivity-adjusted profit
flow is
Therefore, the arbitrage equation can be written
as
24
Market Power contd
The steady-state level of research is a
decreasing function of a that is, a decreasing
function of the elasticity of the demand curve
faced by the intermediate monopolist. In other
words, product market competition is
unambiguously bad for growth the more
competition, the lower the size of monopoly rents
that will be appropriated by successful
innovators, and therefore the smaller the
incentives to innovate.
25
Steady-State Rate of Growth
Moving from t (innovations) to t (time) yields
Now the expected laissez-faire growth rate is
26
Steady-State Growth contd
27
Welfare Analysis
What growth rate would be chosen by a social
planner?
28
Welfare Analysis contd
For comparison between the two levels of
RD-employment we use the following equations
Social Discount Rate Appropriability effect
Business Stealing
29
Welfare Analysis contd

• Intertemporal Spillover Effect The social
  discount rate isless than the private discount
  rate. The social planner takesinto account that
  the benefit to the next innovation will continue
  forever, whereas the private research firm
  attaches no weight tothe benefits that accrue
  beyond the succeeding innovation.gt too little
  research under laissez-faire
• Appropriability effect Reflects the private
  monopolists inability to appropriate the whole
  output flow.gt too little research under
  laissez-faire.
• Business stealing effect The private research
  firm does not internalize the loss to the
  previous monopolist caused by an innovation. In
  contrast, the social planner takes into account
  that an innovation destroys the social return
  from the previous innovation. gt too little
  research under a social planner

30
Uneven Growth
A higher level of research nt1 tomorrow will
both imply more creative destruction and less
profit after the next innovation (t1) occurs.
The two basic equations (A) and (L) boil down to
a single negative relationship between n and nt1
A perfect foresight equilibrium (PFE) is defined
as a sequence nt t 0,,oo satisfying the above
relationship.
31
Uneven Growth contd
The sequence n0,n1, constructed from the
clockwise spiral starting at n0 constitutes a
perfect foresight equilibrium.
32
Growth Patterns

• The steady-state analyzed in the previous
  sections is defined as the fixed point of the
  mapping ?.
• Other equilibria may also exist A two-cycle
  is a pair (n0,n1) such that n0 ?(n1) and
  n1 ?(n0). It defines a PFE of period two.
  If either n0 or n1 is zero, it is a no-growth
  trap the innovation process has stopped.

33
Discussion