Prof. Dr. Thomas Steger
Economic Growth | Lecture | WS 13/14
1. Motivation and Basic Concepts
 Why thinking about “economic growth”?
 Kaldor facts – old and new
 Basic tools and concepts
Institut für Theoretische Volkswirtschaftslehre
Makroökonomik
Motivation and Basic Concepts
Institut für Theoretische Volkswirtschaftslehre
Makroökonomik
Why thinking about “economic growth”? (1)
 Questions related to economic growth pop up from time to time in public discussions,
which are indeed of primary importance for well-being of the society and have first-order
policy implications:
What are the major growth engines that drive economic growth?
How can we explain persistent income per capita differences across countries?
Is economic growth sustainable given that there are non-renewable resources (crude oil) which
appear to be essential for production?
How does technical change affect the distribution of income?
How does migration affect well-being of domestic residents?
 What are the dynamic consequences of bursting asset price bubbles?
 To think about questions like these, we need analytical devices (concepts, models,
theories), which help to structure our thinking about the questions enumerated above.
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Why thinking about “economic growth”? (2)
 Why are there poor and rich countries?
 The richest countries are about 30 times richer than the poorest countries (in 1988). (Parente and Prescott, 2000)
 Why do some economies experience rapid growth, while some other stagnate at the same time?
 Niger (NER) versus South Korea (KOR); see PWT!
 Manipulating an economy’s (long run) growth rate seems to have massive welfare consequences.
 If per capita income grows at a growth rate of 1 % it takes about 70 years until per capita income is doubled.
 If per capita income grows at a growth rate of 2 % it takes about 35 years until per capita income is doubled.
 Lucas (1987, 2003) has argued that the complete removal of consumption volatility (→ business cycle
phenomenon) would imply a welfare gain which is equivalent to a permanent increase in consumption of about 0.1% to 1%.
 One should distinguish between the intertemporal elasticity of substitution and the relative risk aversion and employ
recursive utility functions.
 Taking heterogeneity into account should further increase the welfare gain.
 Follow up studies found substantially larger welfare gains of about 10% to 30% (see Lucas, 2003, p. 7).
 The potential welfare gain resulting from the implementation of optimal growth policies appears to be
substantially higher compared to results mentioned above.
 An appropriate policy reform could achieve a welfare gain which is equivalent to a permanent doubling of per capita
consumption (Grossmann, Steger, Trimborn, 2010).
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Why thinking about “economic growth”? (3)
"The consequences for human welfare involved in
questions like these are simply staggering: Once one
starts thinking about them, it's hard to think about
anything else.“ Robert Lucas (1988)
25000
Real GDP per capita (Constant Prices: Chain series)
South Korea
Niger
20000
15000
10000
5000
0
1950 1953 1956 1959 1962 1965 1968 1971 1974 1977 1980 1983 1986 1989 1992 1995 1998 2001 2004
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Why thinking about “economic growth”? (4)
g=0.1
g=0.02
g=0.01
 How long does it take until x(t) is twice its initial value?
 Solve x0egt=2x0 for t to get t=ln(2)/g.
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The (old) Kaldor Facts: a reminder
 In 1961 Nicolas Kaldor listed 6 stylized facts that describe economic growth
in advanced economies
1. Y/L (output per worker) exhibits continual growth.
2. K/L (capital per worker) exhibits continual growth.
3. r (real interest rate) is roughly constant.
4. K/Y (capital-output ratio) is roughly constant.
 Fact #4 is implied by #1&#2.
 Fact #5 is implied by #3&#4.
5. rK/Y, wL/Y (factor shares) are roughly constant.
6. There are wide differences in the rate of growth of productivity across countries.
N. Kaldor (1961), “Capital Accumulation and Economic Growth,” in F. A. Lutz and D. C. Hague, editors, The Theory of Capital. New York: St. Martin's Press.
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The New Kaldor Facts (1)
 In 2010 Charles Jones and Paul Romer have suggested 6 further stylized facts that
should be at the center of growth theory
1. Increases in the extent of the market. Increased flows of goods, ideas, finance, and people —
via globalization as well as urbanization — have increased the extent of the market for all
workers and consumers.
2. Accelerating growth. For thousands of years, growth in both population and per capita GDP
has accelerated, rising from virtually zero to the relatively rapid rates observed in the last
century.
3. Variation in modern growth rates. The variation in the rate of growth of per capita GDP
increases with the distance from the technology frontier.
4. Large income and TFP differences. Differences in measured inputs explain less than half of
the enormous cross country differences in per capita GDP.
5. Increases in human capital per worker. Human capital per worker is rising dramatically
throughout the world.
6. Long‐run stability of relative wages. The rising quantity of human capital relative to unskilled
labor has not been matched by a sustained decline in its relative price.
Jones, Charles I., and Paul M. Romer. 2010. "The New Kaldor Facts: Ideas, Institutions, Population, and Human Capital."
American Economic Journal: Macroeconomics, 2(1): 224–45.
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The New Kaldor Facts (2)
 While trade and FDI are key facets of the
rising extent of the market, the fact itself is
even broader and includes the flow of ideas
and people, within as well as across
borders.
 International flows of ideas are indicated by
cross-country patent statistics. In 1960, 83%
of patents granted by the U.S. Patent and
Trademark Office were to domestic entities.
In recent years, that fraction has fallen to
about 50%.
 Within countries, urbanization rates have
risen sharply. The fraction of the world’s
population living in cities increased from
29.1% in 1950 to 49.4% in 2007 and is
projected to rise even further to 69.6% by
2050 (United Nations, 2008).
 With the rise of the WWW, information flows
both across and within countries have
exploded.
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The New Kaldor Facts (3)
 The rates of growth have
themselves been rising over time.
Kremer (1993) documents this fact
for world population, going back 1
million years in history.
 Fact 2 is about dynamics. More
people lead to more ideas. For most
of human history, more ideas made
it possible for the world to support
more people. This simple feedback
loop generates growth rates that
increase over time.
 Virtually all demographic projections
call for the number of humans on
earth to reach a maximum in this
century. This may lead to a slowing
of growth in technology.
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The New Kaldor Facts (4)
 At the frontier, the United States is one of the
richest countries in the world and exhibits
steady growth at a rate of about 2% per year.
 The variation of growth rates is much smaller
for the richest countries than for the poorest.
Both, rapid catch-up growth and tremendous
lost opportunities can be seen in the growth
experiences among the poor.
 Catch-up growth can occur now faster than it
has ever been. Between 1950 and 1980,
growth in Japan averaged 6.5% per year.
China’s catch-up growth has been even
faster, averaging 8.2% between 1980 and
2004. By comparison, the most rapid growth
in the world between 1870 and 1913
occurred in Argentina, at a rate that averaged
less than 2.5% per year.
 Growth in Ethiopia has been slow and
unsteady. In 1950, Ethiopia was 34 times
poorer than the United States. By 2003,
however, this ratio had risen to 50. For
Nicaragua, the situation is even worse, as
per capita GDP has actually declined over
the last half century.
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The New Kaldor Facts (5)
 Per capita GDP in the poorest countries of
the world is about 1/50th of that in the US.
 Differences in income and TFP across
countries are large and highly correlated:
poor countries are poor not only because
they have less physical and human capital
per worker than rich countries, but also
because they use their inputs much less
efficiently.
 Facts 3 and 4 are closely related: there are
enormous income differences across
countries, but these gaps can occasionally
be closed with remarkable speed. And while
ideas are a generally accepted explanation
for economic growth in the frontier
countries, the role of ideas in explaining
economic development is less widely
appreciated.
 Differences in institutions must be the
fundamental source of the wide differences
in TFP levels. Bad institutions distort the
usage of rival inputs like labor and capital
(cf. Parente and Prescott, 2000).
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The New Kaldor Facts (6)
 Figure 5 documents the
sustained increase in
educational attainment over
time in the US. The cohort born
in 1920 obtained about 10
years of education, while the
cohort born in 1980 went to
school for 14 years.
 Educational attainment for the
entire labor force in a given
year has, until recently,
increased by about one year
per decade.
 Assuming a Mincerian return to
education of 6% per year, this
increase contributes about 0.6
percentage points per year to
U.S. growth, a significant
fraction of the 2% per capita
growth.
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The New Kaldor Facts (7)
 Despite the large increases in educational
attainment in the US, the wage premiums
associated with college and with high
school show no tendency to decline.
 Skill-biased technical change has shifted
out the relative demand for highlyeducated workers, more than offsetting
the downward pressure on the wage
premium that is associated with the
increase in their relative supply (Katz and
Murphy, 1992).
 Why should technical change be skillbiased? Acemoglu (1998) argues that a
key determinant of the direction of
technical change is the number of people
for whom the new technology will be
useful. The rising supply of highlyeducated labor tilts technical change in its
own direction.
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Basic concepts and tools: Differential equations (1)
 First-order, linear, differential equations
 t∈ denotes the independent variable (often the time index) and y:=dy/dt.
 first-order DE: only the first derivative of y w.r.t. time occurs
 linear DE: both y and y appear only in first degree and there is no such term y y
 The homogenous case (u(t)=a, i.e. constant coefficient and w(t)=0 ∀ t, i.e. homogenous DE)
 A solution is easily found as follows
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Basic concepts and tools: Differential equations (2)
 The non-homogenous case (u(t)=a, i.e. constant coefficient, and w(t)=b ∀ t)
 Solution comprises two terms: complementary function yc and the particular integral yp
 Complementary function yc: general solution of the homogenous DE
 Particular integral yp: any particular solution of the non-homogenous equation
 Complementary function yc (→ discussion of the homogenous DE)
 Particular integral yp: try the simplest possible type of solution, i.e. y=k
 y=k implies y=0 and hence y+ay=b yields yp=b/a (assuming a≠0)
 The general solution of the non-homogenous DE is
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Basic concepts and tools: growth accounting (1)
 Growth accounting is due to Solow (1957). This procedure decomposes the growth rate of
GDP (over longer period of time) into several supply side components. As a by-product,
growth accounting allows an assessment of the technological change component.
 The point of departure is a usual CD output technology
 Expressed in terms of growth rates we have
 Y, K, L and α are observable or can be determined empirically.
 Growth accounting allows to decompose the growth rate of GDP (Y) into the contribution
of capital accumulation (αK), the change in labor input ((1-α)L) and the contribution of
technical change (A).
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Basic concepts and tools: growth accounting (2)
 Limitations of growth accounting
Technological progress is determined residually. However, TFP (hence the rate of change of TFP) does
not only depend on technical knowledge. TFP depends on a long list of an economy’s characteristics, like
the tax system, the degree of economic integration, the sectoral structure, etc.
The results are often very sensitive w.r.t. measurement of inputs and outputs.
Only the proximate sources of growth (like technical change and capital accumulation) are identified.
The deep determinants of economic growth cannot be made visible.
Bosworth, Barry P. and Susan M. Collins, The Empirics of Growth: An Update, Brookings Papers on Economic Activity 2:
2003, 113-206.
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Basic concepts and tools: growth regressions (1)
 Growth regressions are due to Barro (1991) and Mankiw, Romer, Weil (1992). The last
mentioned authors have estimated the following cross-sectional growth regression
Remarks: Sample size: 98 countries; t-values in brackets; estimation procedure: OLS
Mankiw, N. Gregory, David Romer, and David N. Weil, A Contribution to the Empirics of Economic Growth, The Quarterly
Journal of Economics, Vol. 107, No. 2. (May, 1992), pp. 407-437.
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Basic concepts and tools: growth regressions – limitations (2)
 Endogeneity of right hand side variables
 The right hand side variables are often determined together with the dependent variable.
As a consequence, estimation results are likely to be biased.
 Way out: instrumental variables approach.
 Model uncertainty  Results are often highly sensitive w.r.t. to the underlying empirical model (i.e. number and
type of explanatory variables).
 “The true empirical model is not known.”
 Way out: robustness checks and model averaging procedure.
Hemmer, Hans-Rimbert und Andreas Lorenz, Wachstumsempirie, Vahlen-Verlag, 2004.
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Methodical slide (1)
 The growth rate of a time-dependent variable x(t) with t∈ is defined as follows
 Consider the following dependent variable (time index t is suppressed)
 Question: What is the growth rate of y in terms of x1 and x2?
Answer: The growth rate reads as follows (reasoning: next slide)
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Methodical slide (1a)
 Reasoning (1): Differentiate both side of y=x1αx2β w.r.t. time
 Subsequently, divide both sides by y=x1αx2β to get
 Reasoning (2): Form the natural logarithm of y=x1αx2β to get
 Subsequently, take the derivative w.r.t. time on both sides
 Noting
 Gives
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Notation and abbreviations
Notation
Abbreviations
0<α<1 constant technology parameter
A technology parameter (either TFP or labor
efficiency)
CD
Cobb-Douglas
DE
differential equation
K physical capital
FDI
foreign direct investment
L labor supply (in units of time) equal to
labor input
GDP
gross domestic product
r interest rate
IRS
increasing returns to scale
OLS
ordinary least squares
PDV
present discounted value
PWT
Penn World Tables
TFP
total factor productivity
i.i.d.
independent identically distributed
w.r.t.
with respect to
t∈[0,...,∞] time index
u(C) instantaneous utility function
V:=dV/dt
derivative of V w.r.t. time
V:=V/V
growth rate of V
w wage rate
Y
final output
δ>0 capital depreciation rate
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