Transcript Lecture5

Economics 216:
The Macroeconomics of Development
Lawrence J. Lau, Ph. D., D. Soc. Sc. (hon.)
Kwoh-Ting Li Professor of Economic Development
Department of Economics
Stanford University
Stanford, CA 94305-6072, U.S.A.
Spring 2000-2001
Email: [email protected]; WebPages: http://www.stanford.edu/~ljlau
Lecture 5
Cross-Country Growth Regressions
Lawrence J. Lau, Ph. D., D. Soc. Sc. (hon.)
Kwoh-Ting Li Professor of Economic Development
Department of Economics
Stanford University
Stanford, CA 94305-6072, U.S.A.
Spring 2000-2001
Email: [email protected]; WebPages: http://www.stanford.edu/~ljlau
The Basic Methodology of Cross-Country
Regressions



Real output (GDP) (per capita) at a given time t is assumed to
depend and only depend on initial conditions (per capita) (including
initial real GDP, endowments (capital stock), etc., perhaps even
savings and investment rates) at time 0, policy and environmental
variables (e.g., degree of openness), possibly external variables, and
elapsed time
The explanatory variables are assumed to be pre-determined or
exogenous
Variables that may be regarded as endogenous, e.g., the levels and
the rates of growth of the population and the capital stock, etc. are in
general not included in the list of explanatory variables
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The Basic Methodology:
A Dynamic Reduced Form Approach
 Thus,
for example, ln Yt = F(Y0, X0, Z0, t)
 where Yt
and Y0 are the real GDP per capita of a country at time t
and time 0 respectively, X0 is a vector of variables reflecting
initial conditions, and Z0 )is a vector of variables reflecting
government policy and the environment (Z0 may contain some
variables that reflect developments after time 0 to the extent that
they are exogenous to the country itself)
 Given
the level equation, the growth rate of real output per
capita between time 0 and time t may be derived as:
 gt = (ln Yt - ln Y0)/t = F(Y0, X0, Z0, t)
 The average rate of growth over t periods
therefore depends on
the same variables
 It is reasonable to assume that the average rate of growth is
independent of the length of the period under consideration
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The Basic Methodology:
The Growth Rate Equation
 In
a typical cross-country regression study, it is the growth
rate equation that is actually estimated, even though in
principle the level equation can also be estimated
 gt
= (ln Yt - ln Y0)/t = G(Y0, X0, Z0)
 t is typically chosen to be a decade or longer
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Implicit Assumptions Required by Pooling
across Countries

The economic structures of the different economies are identical or at
least similar up to at most a multiplicative factor, e.g., conditional on
the exogenous policy and environmental variables:




the production functions must be identical up to multiplicative factors across
countries
the consumption, saving and investment behavior must be identical across
countries
no external variables are available if all countries are included (except
sunspots)
no individual country fixed effects are allowable (although group fixed effects
based on geography--latitude, land-lockedness, cultural or language affinity,
common colonial heritage, etc. are possible)
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Implicit Assumptions Required by Pooling
across Countries




The dynamic structure, that is, the leads and lags in the economies
are also identical
The differences in institutions across countries are either unimportant
or can be captured through explanatory variables
The stochastic structure is such that the stochastic disturbances at
each instant of time have no permanent or lasting impact
Individual fixed country effects cannot be identified unless there are
truly long time-series so that there can be several non-overlapping
decade-long growth rates for the same country
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The Formulation of Robert Barro
gt = (ln Yt - ln Y0)/t = F(ln Y0, ln Y*)
 where Yt and Y0 are the real outputs per capita at time t
and 0 respectively, and Y* is the target or steady-state
value of real output per capita, which in turn depends on
other explanatory variables
 The (initial) savings rate is not included as an exogenous
variable
 Endogeneity of the exogenous/predetermined variables
 Evidence of conditional convergence

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The Hypothesis of Conditional Convergence
 Other
things being equal, countries with lower levels of per
capita real GDP tend to grow faster
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The Barro Formulation (Estimation Results)
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The Barro Formulation (Figure)
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Differences between Production FunctionBased Approaches and Growth Regressions
 The
questions addressed
 Effects
of alternative economic development strategies and
policies versus the relationship between output and inputs
 The
assumptions
 A high
degree of similarity of technology and tastes (conditional)
 Exogeneity of policy and environmental variables
 The existence of a steady state
 The functional form
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Alternative Concepts of Convergence
 Convergence
in the levels of real output per capita
 Convergence in the rates of growth of real output per
capita
 Convergence
in the levels eventually implies convergence in the
rates of growth, but not vice versa
 Conditional
convergence (given initial conditions, policy
variables and environmental variables)
 Convergence in technology (given the same measured
inputs, outputs of different countries converge to the same
levels)
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Convergence in the Levels of Real Output per
Capita
Figure 1.1: GDP per Capita of the Group-of-Seven (G-7) Countries
30,000
Canada
25,000
France
W. Germany
20,000
Japan
U.K.
U.S.A.
15,000
10,000
5,000
0
19
50
19
52
19
54
19
56
19
58
19
60
19
62
19
64
19
66
19
68
19
70
19
72
19
74
19
76
19
78
19
80
19
82
19
84
19
86
19
88
19
90
19
92
19
94
19
96
U.S. Dollars per Person
Italy
Year
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Convergence in the Levels of Real Output per
Capita
Figure1.1: GDP per Capita of the Group-of-Seven (G-7) Countries Relative to U.S.A.
1.1
1
0.9
0.8
0.6
0.5
Canada
France
W. Germany
Italy
Japan
U.K.
U.S,A.
0.4
0.3
0.2
0.1
Lawrence J. Lau,Year
Stanford University
1997
1995
1993
1991
1989
1987
1985
1983
1981
1979
1977
1975
1973
1971
1969
1967
1965
1963
1961
1959
1957
1955
0
1953
U.S.A.=1.0
0.7
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The Term Rate of Growth &
the Initial Level of Real GDP per Capita
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Convergence in the Rates of Growth of Real
Output per Capita
Average Annual Rate of Growth of Real GNP per Capita over Each Decade
vs. Real GNP per Capita at the Beginning of That Decade (in 1995 US$)
15
Percent per annum
10
5
0
100
1000
10000
100000
-5
1960-1970
1970-1980
1980-1990
1990-1998
-10
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Stanford University
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Convergence in the Rates of Growth of Real
Output per Capita
Average Annual Rate of Growth of Real GNP per Capita over Various Periods
vs. Real GNP per capita at 1960 (in 1995 US$)
16
1960-1970
1960-1980
1960-1990
1960-1998
Percent per annum
12
8
4
US$
0
100
1,000
10,000
100,000
-4
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Instantaneous Rate of Growth &
the Initial Level of Real GDP per Capita (1960)
The Instantaneous Annual Rate of Growth of Real GNP per Capita
versus Real GNP per capita of 1960 (in 1995 US$)
30
20
Percent per annum
10
0
0
5000
10000
15000
20000
25000
US$
30000
-10
-20
-30
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Instantaneous Rate of Growth &
the Initial Level of Real GDP per Capita (1970)
The Instantaneous Annual Rate of Growth of Real GNP per Capita
versus Real GNP per capita of 1970 (in 1995 US$)
30
20
Percent per annum
10
0
0
10000
20000
30000
40000
50000
60000
US$
70000
-10
-20
-30
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Instantaneous Rate of Growth &
the Initial Level of Real GDP per Capita (1980)
The Instantaneous Annual Rate of Growth of Real GNP per Capita
versus Real GNP per capita of 1980 (in 1995 US$)
30
20
Percent per annum
10
0
0
5000
10000
15000
20000
25000
30000
35000
40000
45000
US$
50000
-10
-20
-30
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Instantaneous Rate of Growth &
the Initial Level of Real GDP per Capita (1990)
The Instantaneous Annual Rate of Growth of Real GNP per Capita
versus Real GNP per capita of 1990 (in 1995 US$)
30
20
Percent per annum
10
0
0
10000
20000
30000
40000
50000
US$
60000
-10
-20
-30
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Convergence in Technology: Hypothetical
Levels of Real Output (Boskin & Lau (2000))
Hypothetical Output Level of Countries with Measured Inputs of the U.S.
8
6
CAN
FRA
WGER
JAP
UK
US
ITA
5
4
3
2
1
Lawrence J. Lau, Stanford University
1996
1994
1992
1990
1988
1986
1984
1982
1980
1978
1976
1974
1972
1970
1968
1966
1964
1962
0
1960
Trillions of Constant 1990 US Dollar
7
23
Convergence in Technology: Relative
Productive Efficiencies (Boskin & Lau (2000))
Productive Efficiency Relative to the U.S. (U.S.=100)
110
100
90
70
60
50
CAN
FRA
WGER
ITA
JAP
UK
US
40
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1996
1994
1992
1990
1988
1986
1984
1982
1980
1978
1976
1974
1972
1970
1968
1966
1964
1962
30
1960
Percent
80
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Tests of the Maintained Hypotheses of
Growth Regressions
 Identical
across countries, e.g., division into groups and
tests of identical parameters across groups
 Non-existence of fixed country effects
 Replicability over time, e.g., origin-shifting growth
regressions
 Linearity (or logarithmic linearity) of the functional form
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The Negative Relationship between the Growth
Rate & Initial Real GDP
 Is
it true?
 What are possible explanations of the negative
relationship?
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Is a Slowdown of the Measured Rate of Growth
of Real GNP Inevitable?
 Problems
of measurement
 At
low levels of real GNP/GDP per capita, marketization alone
can result in larger measured increases in real GNP; however, the
marketization effect is a one-time phenomenon and is expected to
disappear as an economy completes its process of marketization
(e.g., monetization of in kind compensation and consumption;
market transactions instead of barter; household work)
 With the onset of economic development, the price of land tends
to rise rapidly; to the extent that profits from the appreciation of
land values are not separated or separable from total profits, there
will be an over-estimation of value added or GNP/GDP. Again,
this is expected to be less of a problem as an economy matures,
asset prices stabilize, and accounting practices improve.
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Is a Slowdown of the Measured Rate of Growth
of Real GNP Inevitable?
 The
law of diminishing returns
 Given
a stationary or slowly growing labor force, and a much
faster rate of growth of the tangible capital stock, the law of
diminishing returns is going to set in for additional tangible
investments--the marginal productivity of capital may be
expected to decline. Since the investment rate cannot be
increased indefinitely to offset the decline in the marginal
productivity of capital, the rate of growth is therefore likely to
decline over time.
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Is a Slowdown of the Measured Rate of Growth
of Real GNP Inevitable?
 The
rising demand for leisure
 At
high levels of real GNP/GDP per capita, more and more
leisure is likely to be consumed voluntarily (leisure has a high
income elasticity of demand). Since leisure is not directly valued
in GNP and only goods and services are included, the growth of
measured GNP in terms of the value of goods and services (other
than leisure) produced is likely to slow.
 The
importance of the quality of life
 At
high levels of real GNP/GDP per capita, more and more
resources are likely to be devoted to the improvement of the
quality of life (education, public health, environmental protection
and preservation, etc.) rather than to the direct increase of real
GNP.
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Is a Slowdown Inevitable? The Catching-Up
Factor
 The
“Late-Comer” advantage--the further away an
economy is from the technological frontier, the more
potential improvements in technical efficiency (total factor
productivity) are possible
 Economies
with low levels of real GNP/GDP per capita are most
likely operating well within the production possibilities frontier
and hence have greater potential for a higher rate of economic
growth, exploiting innovations made by more advanced
economies. Economies with high levels of real GNP/GDP per
capita can grow more rapidly only by pushing out the production
possibilities frontier, which in turn requires significant investment
of new resources
 This effect depends on technology being freely available and
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exploitable by low-income
countries
Interpretation of the Negative Relationship
between the Growth Rate & Initial Real GDP
 Two
economies have identical exogenous and policy
variables, differing only in initial real GDP per capita
 Assumption: Aggregate production functions exhibit
constant returns to scale and neutral technical progress and
are identical up to a positive multiplicative constant (Thus,
the rates of technical progress are also identical).
 Case 1: Suppose initial capital stocks per capita and
savings rates are the same
 Case 2: Suppose initial capital stocks per capita are
different but savings rates are the same
 Case 3: Suppose both initial capital stocks per capita and
savings rates are different,
but the growth regressions are31
Lawrence J. Lau, Stanford University
not controlled for savings rates
Case 1: Initial Capital Stocks per Capita and
Savings Rates are Identical
 Then
initial real GDP per capita is higher in one economy
than the other because of either (1) stochastic disturbances
(transient) or (2) unmeasured factor of production or
technical efficiency (permanent)
 Under scenario (1), the economy with a higher initial real
GDP per capita will have a higher capital stock per capita
in the second period and hence a higher real output per
capita in the second period, other things being equal
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Case 1: Initial Capital Stocks per Capita and
Savings Rates are Identical
Y/L = A(t)f(K/L)
y = A(t) f(k)
ln y = ln f(k) + ln A(t)
d ln y d ln f d ln k d ln A( t )



dt
d ln k dt
dt
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Case 1: Initial Capital Stocks per Capita and
Savings Rates are Identical
 For
an economy with a higher initial real GDP per capita
but the same initial capital stock per capita and savings
rate, the elasticity of output per capita with respect to
capital stock per capita should be the same and the rate of
growth of capital should be higher, thus the rate of growth
of per capita real GDP should not be lower
 It can be lower only if either the elasticity of output with
respect to capital stock declines sufficiently sharply with
the higher rate of growth of capital (which is unlikely) or it
is simply the statistical artifact of a higher initial level of
real GDP per capita and hence a lower measured rate of
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growth
Case 1: Initial Capital Stocks per Capita and
Savings Rates are Identical
 Under
scenario (2), the higher initial real GDP per capita
can be attributed to permanent factors, I.e., a higher level
of A(0). However, since the relative efficiency between
the two economies remains the same over time, the rates of
growth (as opposed to the levels) of the two economies
should also remain the same.
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Case 2: Savings Rates are Identical
 Since
initial capital stocks per capita need not be the same,
it is reasonable to assume that the economy with the higher
initial real GDP per capita is also the one with the higher
initial capital stock per capita
 Growth could well be slower in the economy with the
higher initial real GDP per capita if its initial capital stock
were sufficiently high to result in a lower elasticity of
output with respect to capital
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Case 2: Savings Rates are Identical
y11 = A(1) f(k11)
y21 = A(1) f(k21)
y11/y10 = A(1) f(k11)/y10
y21/y20 = A(1) f(k21)/y20
(y11/y10)/(y21/y20) = [f(k11)/f(k21)]/(y10/y20)
Now, k11>k21; y10>y20; thus, f(k11)>f(k21). In order for the rate of growth
of economy 1 to be less than the rate of growth of economy 2, it must be
the case that the proportional increase in output due to the higher savings
per capita is less than the proportional difference in initial real output per
capita.
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Case 3: Initial Capital Stocks per Capita and
Savings Rates are Different
 It
is assumed here that the differences in the savings rate
are not controlled for in the growth regressions. In this
case it is reasonable to suppose that the higher initial real
GDP per capita is associated with higher initial capital
stock per capita and higher savings rate. A sufficiently
rapid decline in the output elasticity of capital with respect
to increases in the capital stock per capita can result in a
negative correlation with the rate of growth and the initial
level of real GDP per capita
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