Chapter 6: Economic Growth

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• Chapter 6 Economic Growth
• Empirical facts of economic growth
• Growth Accounting Identifying the sources of
  economic growth
• Malthusian Growth model
• The Solow exogenous growth model

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• Main Question What affects the level (standard
  of living) and rate of growth (rate of change in
  the standard of living) of per capita consumption
  or output?
• We study both aggregate variables (e.g. Y) and
  per capita variables
• We associate the term standard of living with
  per capita variables
• We will study changes in the economic environment
  that lead to level effects, growth effects, or
  both.

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• Some Facts to be Explained
• Since the industrial revolution there has been
  sustained growth in world per capita income (PCI)
• Growth experiences are different across countries
  at any point in time
• Levels of PCI tend to converge over time among
  regions within a country and among developed
  countries, but there are persistent differences
  in PCI levels across countries

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Figure 6.1 Natural Log of Real per Capita Income
in the United States, 18692002
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Figure 6.2 Output per Worker vs. Investment Rate
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Figure 6.3 Output per Worker vs. the Population
Growth Rate
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Figure 6.4 No Convergence Among All Countries
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Figure 6.5 Convergence Among the Richest
Countries
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Figure 6.6 No Convergence Among the Poorest
Countries
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• Malthusian Growth Model
• A formal model of the writings of Thomas Malthus
  (1798)
• Main message any increases in technology will be
  countered by increases in population and hence
  the standard of living cannot keep increasing
• Production Yt Zt F(Lt,Nt)
• Lt Land
• Population Growth
• Nt1/Nt g(Ct/Nt)
• g(.) is an increasing function of per capita
  consumption
• low consumption poor nutrition
• g(.) is concave because there are limits to
  population growth

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• In this model Ct Yt
• We can then show that
• Nt1 g(ZtF(Lt/Nt,1)Nt
• This equation allows us to solve for steady
  state population and steady state consumption
• The steady state is the long run equilibrium of
  the model. Absent any shocks or changes in the
  economy we will remain at this point
• What happens when we change technology?
• Does the model match the data?
• Policy Implication need population control
• Why was Malthus wrong?

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• The Solow Growth Model Exogenous Growth
• Consumers
• Infinite lifetime, population grows at a constant
  rate
• Nt population, Nt1 (1b)Nt
• Pop grows at rate b, b can be negative, Each
  consumer has 1 unit of time- no leisure (entire
  population works)
• Consumers receive all output Yt (either wage or
  firm profits)
• Saving sYt s is savings rate
• Constant saving is an assumption
• Consumption Ct (1-s)Yt

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• Production (Firm)
• Yt Kt?(ZtNt)1-?
• Zt labor productivity
• Zt1 (1u) Zt u is the rate of technology
  growth and is constant
• note the textbook does not allow for this type
  of growth in technology!
• Kt1 (1-d)Kt It d depreciation rate
• Competitive Equilibrium
• Inelastic labor supply curve determines labor
  market equilibrium (Nt)
• We need to determine the optimal amount of
  capital
• Start by substituting in for investment in the
  capital accumulation equation
• Kt1 sYt (1-d)Kt

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• Divide both side by ZtNt
• Dividing a variable by ZtNt is transforming that
  variable to per capita efficiency units of that
  variable. For example
• The will be used to refer to per capita
  efficiency units of a variable
• This transformation removes growth due to
  technology, and puts the variable in per-capita
  terms
• Variables that are written in per capita
  efficiency units have the property that they do
  not grow once the economy reaches its steady
  state

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• Definition of a Steady State Output, capital,
  consumption and investment in per capita
  efficiency units is constant
• In the steady state the economy has reached the
  optimal capital/labor ratio (adjusted for
  technology growth)
• When an economy reaches its steady state
  aggregate variables still grow, but only at the
  rate given by the exogenous population and
  technology growth rates.
• When an economy reaches its steady state
  per-capita variables still grow, but only at the
  rate given by the exogenous technology growth
  rate.

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• (continuing by dividing both side by ZtNt)
• Which can be written
• Do the same for the production function
• Or Yt (Kt)?
• We call this the concentrated production
  function

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• Our goal is to find the optimal amount of capital
  in per capita efficiency units (K), a variable
  that does not grow in the steady state, and then
  we can add growth back in.
• Given K we can find K1, and then K2, etc.
• K is steady state level of capital in per capita
  efficiency units of labor
• 45 degree line is where Kt1 Kt
• Kt is still growing due to population and
  technology growth!
• Convergence to steady state

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• Analysis of the Steady State
• In steady state
• Capital Stock growth rate
• Since u and b are small, ub is close to 0, so
  capital growth is approximately equal to
  technology growth plus population growth
• In per capita terms, capital stock growth is
• Output growth

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• Output grows at the same rate as capital
• Ct (1-s)Yt and It sYt, so C and I grow at the
  same rate also
• balanced growth path all aggregates grow at
  the same rate
• All growth in per-capita terms is due to
  technological progress
• Effects of Changes in the Economic Environment
• Steady State Capital Kt1 Kt K
• Increase technology growth

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• All aggregates grow faster but capital per
  efficiency unit of labor is smaller because with
  higher technology growth we need more investment
  (which is forgone consumption) to keep K
  constant at the optimal K
• Increases in population growth have the same
  effect on K but no effect on per capita growth
  rates. There is a 1 time level decrease
• What happens after an increase in the savings
  rate? (to K, consumption, output, investment)
• Convergence to new level (after some change in b)
  takes time

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• Convergence across countries 2 countries that
  are identical other than initial capital stock
  will converge to the same level
• Are countries in the world converging?
• Empirical Evidence on Exogenous Growth Models
• Solow model helps understand how 3 sources of
  economic growth (capital growth, TFP growth and
  Population growth) interact to produce growth in
  output and consumption
• Model Predictions
• 1) In the long run, Aggregate Capital, Output,
  Consumption and Investment grow at the same rate

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• 2) The common growth rate of Per Capita K,C, I, Y
  is equal to the rate of growth in technology
• 3)An increase in saving has no effect on long run
  growth of aggregate variables (or per capita
  variables)
• 4) Countries with identical technology and
  population growth rates will converge to the
  same growth rate in aggregate variables. If they
  also have the same savings rate they will
  converge to the same level of aggregate variables
  

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• Do these predictions match the data?
• 1) 1950-1998 Growth Rates output (3.27),
  capital (3.14), very similar
• 2) Model Growth of Y Growth N Growth A
• Data The sum of labor growth (1.63) and
  TFP growth (1.69) is close to the 3.215 output
  growth rate
• 3) High growth countries have had higher savings
  rates
• 4) Some evidence of convergence in developed
  countries but not among poor and rich countries.
  Rich are getting richer, Poor are getting Poorer

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• Conditional convergence countries with similar
  characteristics will converge (some evidence)
• Unconditional convergence all countries (rich
  and poor) will converge

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• Growth accounting Decompose Output growth into
  the amount due to changes in capital, labor, and
  productivity. We can then identify which is the
  most important source of growth across countries
  and time periods.
• Cobb-Douglass production function
• Yt ZtKt?Nt1-? ? 0.36
• Zt is Solow Residual or TFP
• We use the following equation to decompose output
  growth
• This equation follows from taking the ln of the
  production function in periods t and t-1, then
  subtracting the time t-1 equation from the time t
  equation

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• Determinants of Output Growth 1990-1998
• 1990 Y 6136.3, K 12616.6, N118795
• 1998 Y 7551.9, K14944.0, N 131458
• ? in Y due to ? in K
• ? in Y due to ? in N
• ? in Y due to ? in Z
• Post-War Determinants of Output Growth
• 1950 Y 1611.4, K 3388.2, N 58892
• Sources of growth vary by time period and country

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• The Asian Miracle
• miracle was high output growth rates-
  originally thought to be large increases in TFP
• Growth Accounting showed the importance of labor
  growth (population growth and participation
  rates) and capital growth (high savings rate)
• Is this sustainable?
• Growth Accounting and the Productivity Slowdown
  in the U.S.
• TFP growth in 50s and 60s was high
• TFP growth slowed about 1973 and continued to the
  present

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• Some Explanations
• Measurement Error US shifted from manufacturing
  towards services greater bias in measuring
  quality changes in services- downward bias in GDP
  growth
• Oil Prices After oil shocks (73-74 and 79-80)
  old capital became obsolete because it was not
  energy-efficient, but that capital remained on
  the books
• Cost of adopting new technology (computers)
  instead of producing workers are learning the new
  technology, productivity has picked up in the
  90s, one view is that the US should resume its
  expansion
• Environmental Regulation