ITFD Growth and Development

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ITFD Growth and Development

• LECTURE SLIDES SET 6
• Professor Antonio Ciccone

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Ideas and Economic Growth
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Producing output versus ideas

• Ideas non-rival, accumulable input
• Ideas may be excludable (patents, secrecy) or
  not
• Ideas producing them lowers current, but
  increases future output

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Producing output versus ideas

• Question 1 what is the growth process for a
  given allocation of inputs between producing
  output and producing ideas?
• ? Characterize the join evolution of ideas and
  output in the spirit of Solow

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Producing output versus ideas

• Question 2 how much of inputs is allocated to
  producing ideas in decentralized equilibrium?

• Difficulties
• In these models there are at least 3 inputs
  capital, labor, and ideas
• Holding ideas constant, our reproduction
  argument implies that there are at least
  constant returns to capital (K) and labor (L)
• HENCE, there are increasing returns to K,L, and
  ideas!
• ? It took quite a while to develop a set of
  models (toolbox) where the decentralized
  dynamic general equilibrium could be characterized

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1. A FRAMEWORK FOR ANALYZING GROWTH WITH RESEARCH
AND DEVELOPMENT

• Quantity of output produced
• fraction of total capital stock used in
  production
• fraction of total labor force used in
  production

taken to be exogenous in the spirit of Solow
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• level of technology
• stock of ideas
• ideas non-rival inputs
• new ideas, which are created by using
  capital, labor, and old ideas in the RESEARCH AND
  DEVELOPMENT (RD) process

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• Production of new ideas
• Research and Development (RD) technology
• fraction of total capital stock used in RD
• fraction of total labor force used in RD

taken to be exogenous this is in the spirit of
Solow
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• Returns to scale to K and L in production of
  IDEAS could be increasing or decreasing
• DECREASING replicating inputs could lead to same
  discoveries being made twice
• INCREASING doubling inputs could lead to more
  than twice the discoveries because of
  interactions among researchers (the whole is
  more than sum of its parts)

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• Also, what is the link between stock of ideas and
  new ideas?
• presumably OLD ideas are useful for developing
  new ideas
• doubling stock, doubles discoveries holding
  inputs L and K constant
• effect of stock of ideas on creation less
  than proportional
• effect of stock of ideas on creation more
  than proportional

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• q1 ideas keep growing at same rate even if
  resources allocated to RD constant
• qgt1 growth of ideas accelerates when resources
  allocated to RD constant
• qlt1 to keep growth of ideas constant, more and
  more resources must be allocated to RD

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2. GROWTH WITH RESEARCH AND DEVELOPMENT THE CASE
WITHOUT CAPITAL

• Quantity of output produced
• Production of new ideas
• Population growth (exogenous)

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Growth of ideas ( )
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CASE 1 Balanced (constant) growth path
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• Is the BGP stable?
• Graph on the vertical axis against on the
  horizontal axis
• Check that is increasing when below and
  decreasing when above

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STABILITY OF BGP
0
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• Note that implies that a faster population
  growth n translates into faster growth of ideas
  in the balanced growth path.
• Is there empirical support for the positive
  relationship between n and the long run growth
  rate?
• ? Hard to test as we need long time series for
  that but Michael Kremer 1993, QJE used
  population growth data going back to 1 Million
  B.C.

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• Why does an increase in not raise the long
  run growth rate?
• Reason analogous to why increase in savings rate
  s in the Solow model does not increase long run
  growth Decreasing returns
• Note that yielded
• Increase in al increase the short-run growth rate
  of ideas
• But when qlt1 we get that maintaining the same
  growth rate of ideas becomes harder and harder as
  the stock of idea increases (fishing out the
  pond effect)
• In the long-run we get a level effect only
• ? The fraction of resources allocated to RD is
  IRRELEVANT for long-run growth rate !!

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• IMPORTANT TO NOTE
• Balanced growth path growth rate
• there can only be long run growth of ideas and
  output if
• ngt0
• if n0, there is NO long run growth

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RD and endognous growth

• Hence, there can be long run growth even without
  exogenous technological progress
• BUT the growth rate is linked to population
  growth, which we dont usually think of as a
  policy parameter

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• CASE 2
• Hence implies ever accelerating growth

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• In this case, a small increase in ends up
  having a very large effect on the stock of ideas
  in the long run
• An increase in implies
• short term increase in growth of ideas (as
  before)
• these additional ideas further increase the
  growth of ideas when
• ? for any future time t, the growth rate will be
  higher after the increase in

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CASE 3

• NOW, there is long run growth even if n0!!!

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3. GROWTH WITH RESEARCH AND DEVELOPMENT THE CASE
WITH CAPITAL

• Quantity of output produced
• Production of new ideas

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• standard assumptions of Solow model
• constant savings rate s
• constant population growth rate n
• no depreciation of capital

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The idea and capital growth equations
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CASE 1 (i.e. or )
-ISOCLINE ( )

• Above this line falls
• Below this line increases

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-ISOCLINE ( )

• Above this line falls
• Below this line increases

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ISOCLINES in GROWTH RATES space
0
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EVOLUTION OF GROWTH RATES
0
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DYNAMICS
0
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DYNAMICS plus INITIAL CONDITION
STARTING POINT
0
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Starting point of dynamical system is GIVEN by
INITIAL capital, technology, and labor force
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• IMPORTANT TO NOTE
• there can only be long run growth of ideas,
  capital, and output if
• ngt0
• if n0, there is NO long run growth

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• CASE 2
• we are interested in whether IN THIS CASE there
  will be long run growth even if n0
• hence ALSO assume n0

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-ISOCLINE
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-ISOCLINE

• HENCE
• The two isoclines lie on top of each other
• NOW, there is long run growth even if n0!!!

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betatheta1 CASE WITHOUT POPULATION GROWTH
0
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Michael Kremer's model
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Michael Kremer's model

• "Population Growth and Technological Change One
  Million B.C. to 1990", Q.J.E. 1993
• Michael Kremer's intuition was that in a
  Malthusian world, i.e. a world in which
  population is just big enough to survive, there
  is a link between the state and technology and
  the amount of population If everyone consumes
  just a "subsistence" amount, societies with more
  advanced technology (say, better agriculture)
  will be able to support larger populations
• Hence, we could infer from the level of

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The framework

• Assume the following production function
• where
• indicates the level of technological
  progress
• is population
• is land
• At least for a pre-industrial society, it may
  make sense to have only labour and land as
  production inputs. Note that the production
  function has constant returns to scale the
  replication argument is valid! (ie, double the
  amounts of input, and you double output)

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Malthusian case

• Now express the production function in
  per-capita terms
• and assume that population increases when is
  above some subsistence level .
• This will reduce output per capita, so that it
  is reasonable to assume - if population growth
  reacts fast enough - that population will
  constantly adjust such that always holds.

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Malthusian case

• We can solve for the population level that
  corresponds to
• What does it mean?
• In the absence of changes in , population will
  be constant
• Ceteris paribus, population will be proportional
  to land area
• If separate regions have different levels of
  technology , population or population
  density will be increasing in

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Technological progress

• Now enter technological progress. Assume that
  What does this imply for population
  growth?
• Take logs and derivatives of
• and obtain
• population will grow at a constant rate. True?

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More than exponential growth

• So population growth appears to be increasing in
  population. This implies faster than exponential
  growth, which is what you would achieve with
• Why?
• Key insight Each person has a constant
  probability of inventing a new technology. But
  because "ideas" (insights, designs. . . ) are
  nonrival, the whole society should profit from it.

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Ideas as public goods

• "As for the Arts of Delight and Ornament, they
  are best promoted by the greatest number of
  emulators. And it is more likely that one
  ingenious curious man may rather be found among 4
  million than among 400 persons."
• William Petty
• "If I could redo the history of the world,
  halving population size each year from the
  beginning of time on some random basis, I would
  not do it for fear of losing Mozart in the
  process."
• Edmund Phelps

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Modelling growth and ideas

• So, because every individual has the same
  probability of inventing something new,
  should be proportional to population size
• Insert this into
• Result
• population growth is itself proportional to
  population.
• Aside Results don't change substantially if we
  assume ,
• i.e.

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A natural experiment

• Could we somehow test the model?
• Kremer suggests to consider a "natural
  experiment" the end of the last ice age around
  10'000 B.C., when previously connected land
  masses (EurasiaAfrica, the Americas, Australia,
  Tasmania) were separated and technological
  diffusion wasn't possible any more.
• Assumptions
• These 4 regions had shared the same basic
  technology up to that point (same ).
• Hence, their populations must have been
  proportional to the land areas

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4 (or 5) separated regions
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A natural experiment

• Prediction
• 11500 years of separation (until 1500) should
  have lead technology levels to diverge
• Growth rates of technology will be proportional
  to initial
• population
• Higher growth rates of translate into larger
  populations
• or, given constant area of land masses, into
  higher densities

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The natural experiment results