why thinking about “economic growth”? kaldor facts – old ... · institut für theoretische...

Institut für Theoretische VolkswirtschaftslehreMakroökonomik

1. Motivation and Basic Concepts

Why thinking about “economic growth”?

Kaldor facts – old and new

Basic tools and concepts

Prof. Dr. Thomas StegerEconomic Growth | Lecture | WS 13/14


2Winter Term 13/14 Economic Growth (Master Economics)

Motivation and Basic Concepts

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.





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).





"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)

0

5000

10000

15000

20000

25000

1950 1953 1956 1959 1962 1965 1968 1971 1974 1977 1980 1983 1986 1989 1992 1995 1998 2001 2004

Real GDP pe

r cap

ita (C

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t Pric

es: C

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South Korea Niger





How long does it take until x(t) is twice its initial value?

Solve x0egt=2x0 for t to get t=ln(2)/g.

g=0.01

g=0.02

g=0.1




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.

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.

Fact #4 is implied by #1&#2. Fact #5 is implied by #3&#4.




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 theory1. 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.





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.





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.





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.





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).




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.





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 highly-educated 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 skill-biased? 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 highly-educated labor tilts technical change in its own direction.




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




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




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).




Basic concepts and tools: growth accounting (2)

Limitations of growth accountingTechnological 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.




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.




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.




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)




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




Notation and abbreviations

Notation

0<α<1 constant technology parameter

A technology parameter (either TFP or labor efficiency)

K physical capital

L labor supply (in units of time) equal to labor input

r interest rate

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

Abbreviations

CD Cobb-Douglas

DE differential equation

FDI foreign direct investment

GDP gross domestic product

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

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