Download Document

Major Currents
in Contemporary Economics
New Developments
in Growth Theory
Mariusz Próchniak
Department of Economics II
Warsaw School of Economics
1
Time
Models of economic growth: An overview
Models of economic growth
Neoclassical models
The Solow model (1956)
The Ramsey model (1928, 1965)
The Diamond model (1965)
Endogenous models
 The Romer learning-by-doing
model (1986)
 The Lucas model (1988)
 R&D models
 Neoclassical revival: the Mankiw-Romer-Weil (augmented Solow)
model (1992)
2
Time
The Harrod-Domar model (1939, 1946)
 Harrod (1939) and Domar (1946) tried to combine the Keynesian
analysis with the elements of economic growth.
 Economic growth is proportional to the investment rate
(equal to the savings rate) and inversely depending
on the marginal capital intensity of production.
 The growth rate of GDP is described by the following equation:
s
gy 
k
where:
gy – real GDP growth rate,
s – the investment rate (the savings rate),
k – the capital intensity of production (investment outlays
per unit increase in national income).
3
Time
The neoclassical growth theory: General characteristics
 The neoclassical production function:
 constant returns to scale,
 diminishing marginal product of capital.
 Neoclassical models do not explain well the long-run economic
growth.
 Long-run economic growth depends on technological progress
which is exogenous.
 The desired property would be to endogenize technical
progress, so that economic growth could be explained
within the model.
4
Time
The neoclassical growth theory: General characteristics (cont.)
 Neoclassical models confirm the existence of conditional 
convergence.
 Convergence (-type) means that less developed countries
(with lower GDP per capita) tend to grow faster than
more developed ones.
 The catching-up process confirmed by neoclassical models
is conditional because it only occurs if the economies tend
to reach the same steady-state.
5
Time
The Solow model
The Solow model, also called the Solow-Swan model:
 Robert Solow (1956),
 Trevor Swan (1956).
(1) Assumptions
 F – the production function.
 Inputs to production:
 physical capital K(t),
 effective labour A(t)L(t): the product of the level
of technology A(t) and population (labour force) L(t).
F  K t  , A t  L t 
6
Time
The Solow model (cont.)
 The production function exhibits:
 constant returns to both inputs (capital and effective labour),
 diminishing marginal product of capital.
 One of the functions satisfying these assumptions
is the Cobb-Douglas production function:
F  K  t  , A  t  L  t    K  t   A  t  L  t 

1
where 0 <  < 1.
7
Time
The Solow model (cont.)
 Technology and population both grow at constant exogenous
rates:
L t 
L t 
n
A t 
A t 
a
 The increase in capital stock equals investment (savings) minus
depreciation:
K  t   sF  K  t  , A  t  L  t     K  t 
s – the exogenous savings rate,
 – the capital depreciation rate.
8
Time
The Solow model (cont.)
(2) Dynamics
 The dynamics of the economy is analysed in terms of capital
and output per unit of effective labour:
K
k
AL
f k  
F  K , AL 
AL


 K AL 

F
,

F
k
,1

f
k
   



AL
AL




 To find the equation describing the dynamics of the economy,
we differentiate the definition of k with respect to time:
k  sf  k    n  a    k
9
Time
The Solow model (cont.)
k  sf  k    n  a    k
 The above equation is the basic formula describing
the dynamics of the economy in the Solow model.
 The increase in capital per unit of effective labour equals actual
investment sf(k) minus replacement investment (n + a + )k.
10
Time
The Solow model (cont.)
(3) Steady-state
f k 
f  k*
c*
n  a    k
sf  k 
f  k  0
k
k
k
k  0
sf  k*
k 1
k  2
k*
k
Figure 1
The transition period and the steady-state in the Solow model
 The long-run equilibrium (steady-state) occurs at the point
of intersection between sf(k) and (n + a + )k.
 In the steady-state, output and capital per unit of effective
labour are constant over time.
11
Time
The Solow model (cont.)
 What is the growth rate of total GDP (Y = F(K,AL))
and GDP per capita (Y/L) in the steady-state?
 We have to differentiate Y ≡ f(k)AL and Y/L ≡ f(k)A
with respect to time:
Y f k  A L

 
Y f k  A L
Y / L f k  A


Y / L f k  A
 In the steady-state, output per unit of effective labour
is constant, while technology and population both grow
at constant rates (a and n).
12
Time
The Solow model (cont.)
We have obtained two important implications of the Solow model.
In the steady-state (long-run equilibrium):
 the growth rate of GDP equals technological
progress plus population growth,
 the growth rate of per capita GDP equals
technological progress.
13
Time
The Solow model (cont.)
 The steady-state in the Solow model is stable: regardless
of the initial capital stock, the economy always tends towards
the steady-state.
 During the transition period, economic growth is higher
than in the steady-state because capital and output per unit
of effective labour both increase.
 The Solow model confirms the existence of conditional 
convergence.
14
Time
The Solow model (cont.)
 The steady-state may be dynamically inefficient: long-run
equilibrium needn’t be Pareto optimal. This results from
the exogenous savings rate. Too high savings rate leads
to excessive capital accumulation.
 The savings rate does not affect the pace of economic growth
in the steady-state, but it influences the equilibrium level
of income (higher savings rate means a higher position of sf(k)
function and consequently a higher level of k*). The impact
of a change in the savings rate on GDP growth is temporary –
higher savings rate accelerates economic growth during
the transition period.
15
Time
The Ramsey model
 The Ramsey-Cass-Koopmans model: Frank Ramsey (1928),
David Cass (1965), Tjalling Koopmans (1965).
 The main difference: the savings rate. In the Ramsey model,
it is endogenous and results from optimal decisions made
by utility-maximizing individuals.
Similarities as compared with the Solow model:
 In the steady-state, GDP growth rate equals the sum
of technological progress and population growth
(the variables exogenously given) while the growth rate
of per capita GDP equals technological progress.
 The Ramsey model confirms the conditional  convergence.
Differences as compared with the Solow model:
 The Ramsey model is Pareto optimal. Endogenous savings
prevent excessive accumulation of physical capital
 dynamic inefficiency does not appear.
16
Time
Endogenous models of economic growth
 Endogenous models explain the economic growth
in an endogenous manner, i.e. within the model.
 This feature contrasts with neoclassical growth theory
where long-run growth depended on exogenous technological
progress, introduced along with other assumptions.
 Achieving endogenous growth is possible due to abandoning
the neoclassical production function which assumes diminishing
returns to accumulable inputs and constant returns to scale.
 Endogenous models assume that there are at least
constant returns to accumulable inputs.
17
Time
The AK model
 The mechanism of endogenous growth can be explained
by introducing into the Solow model the production function:
Y  t   AK  t 
 This function exhibits constant returns to capital, the only
accumulable factor of production.
 Given (Y = C + I = C + dK/dt) and (I = sY), the economic
growth rate is:
Y
 sA
Y
 The economy is continuously growing at the rate of sA.
 The increase in the savings rate is sufficient to accelerate
permanently the long-run rate of economic growth.
18
Time
Endogenous models of economic growth
 Endogenous growth occurs by eliminating the assumption
of diminishing returns to accumulable inputs.
 Introduction of (at least) constant returns takes various forms.
 The Romer learning-by-doing model: a one-sector model,
in which long-run growth is achieved due to increasing
returns to accumulable factors at the whole economy level.
 The Rebelo and Lucas models: endogenous growth is
possible due to the existence of two sectors, each of which
exhibiting constant returns.
 Models with an expanding variety of products and models
with an improving quality of products are known as R&D
models: long-run economic growth is obtained by
endogenizing technical progress, which is the output
of the R&D sector.
19
Time
The Romer learning-by-doing model
 Romer (1986)
 Knowledge, which is the only accumulable factor of production,
exhibits increasing returns at the social (whole economy) level.
 Knowledge, being created through investment of individual
firms, can spread freely throughout the economy and can be
used by all firms without incurring additional costs
(learning-by-doing).
 Due to increasing returns, the Romer model reveals
an accelerating and permanent economic growth
without introducing exogenous variables.
20
Time
The Romer learning-by-doing model (cont.)
 The production function of an individual firm:
fi  ai , ki , A
ai – the level of knowledge of an individual firm,
ki – other factors of production (capital, labour, etc.),
A – the general level of knowledge in the economy.
 Other inputs are constant (ki = const.)  knowledge is the only
accumulable factor of production.
 The production function exhibits increasing returns with respect
to all inputs (a, k, A) and constant returns with respect to a and k:
f  a, k ,  A   f  a, k , A
f  a, k , A   f  a, k , A
 The marginal product of knowledge at the social level is increasing
while from the firm’s point of view it is decreasing or constant.
21
Time
The Romer learning-by-doing model (cont.)
 There is no steady-state in the Romer model.
 At the optimal trajectory, a perfectly competitive economy
reveals a permanent and accelerating economic growth.
 The Romer model does not confirm the existence
of convergence. It suggests rather divergence trends: the rate
of economic growth increases with income meaning that more
developed countries grow faster than less developed ones.
 Perfectly competitive economy is not Pareto optimal. This is
because investments in knowledge made by a single firm lead
to the increase of the overall level of knowledge. But a single
company in its investment decisions does not take into account
these positive externalities.
22
Time
The Lucas model
 Also: Uzawa-Lucas model (Lucas, 1988; Uzawa, 1964, 1965).
 A two-sector model: physical capital and human capital.
 Endogenous growth is achieved due to the existence of two
sectors that both exhibit constant returns.
 The Lucas model explains well the differences in income levels
between countries. The economies, which at a starting point
are capital scarce, achieve long-run equilibrium with low level
of capital. The economies which are initially richer tend
to steady-state characterized by higher capital level.
 The Lucas model does not confirm the convergence
– in terms of both the comparison of various steady-states
and the comparison of transition periods.
 Steady-states: GDP growth rate does not depend on income level.
 Transition periods: less developed countries may grow faster or slower than more
developed ones.
23
Time
Neoclassical revival: the Mankiw-Romer-Weil (augmented Solow) model
 Mankiw, Romer, Weil (1992)
 The MRW model includes human capital. The production function:
Y  K  H   AL 
  
where  > 0,  > 0,  +  < 1.
 The production function shares all the neoclassical properties:
the diminishing marginal product of each input and constant
returns to scale.
 Output may be devoted to consumption, accumulation
of physical capital, or accumulation of human capital.
 The time paths for physical capital and human capital are:
K  sK Y   K
H  sH Y   H
24
Time
The Mankiw-Romer-Weil (augmented Solow) model (cont.)
 Capital and output per unit of effective labour:
K
k
AL
H
h
AL
y
Y

AL
K  H   AL 
  
AL
 k  h
 Equations describing the dynamics of the economy:
k  sK y   n  a    k  s K k  h    n  a    k
h  sH y   n  a    h  s H k  h    n  a    h
 In the steady-state, the capital per unit of effective labour
is constant.
 Setting the above equations to zero, we get the stock
of physical and human capital in the long-run equilibrium:
1  
K
H
 s s 
k*  

n

a




1
1  
 1
 s s

h*   K H 
 n  a  
1
1  
25
Time
The Mankiw-Romer-Weil (augmented Solow) model (cont.)
k
B
h0
C
k 0
k*
E
D
A
h*
h
Figure 2
The transition period and the steady-state in the augmented Solow model
 The steady-state is at the point of intersection between
dk/dt = 0 and dh/dt = 0 functions (point E).
 The long-run equilibrium is stable: from any starting point
the economy is moving towards the steady-state.
26
Time
The Mankiw-Romer-Weil (augmented Solow) model (cont.)
 In the steady-state, physical capital, human capital,
consumption, and output per unit of effective labour
are all constant.
In the steady-state (long-run equilibrium):
 the growth rate of GDP equals technological
progress plus population growth,
 the growth rate of per capita GDP equals
technological progress.
 The Mankiw-Romer-Weil model, like other neoclassical models,
confirms the existence of conditional convergence.
27
Time
Growth empirics: Growth determinants
 We use correlation and regression analysis.
 Correlation coefficient shows the relationship between
the GDP growth rate and a variable tested as an economic
growth determinant.
 In the regression equation, it is possible to test simultaneously
many variables that are economic growth determinants:
ggdpt  0  1 x1t   2 x2t 
  n xnt  1initialgdpt  2 dummyt   t
 The explained variable (ggdpt) is the GDP growth rate.
 The explanatory variables (x1t, x2t, …, xnt) are economic growth
determinants.
 The regression equation may include the GDP per capita
from the previous period (initialgdpt) to control the influence
of initial conditions; and/or dummy variables (dummyt)
to assess the impact of a single shock on economic growth.
28
Time
Growth empirics: Growth determinants (cont.)
Table 1. Empirical models of economic growth for the CEE-10 countries, 1993-2009
Variable
MODEL 1
Gross capital formation (% of GDP)
General government balance (% of GDP)
Lending interest rate (%)
Private sector share in GDP (%)
GDP per capita at PPP (constant 2005 US$) from the previous period
Dummy (=1 for the 2008-2009 period; =0 otherwise)
Constant
n = 54
R2 = 0.6347
R2 adjusted = 0.5881
MODEL 2
Gross capital formation (% of GDP)
Market capitalization of listed companies (% of GDP)
General government balance (% of GDP)
CPI inflation (%)
GDP per capita at PPP (constant 2005 US$) from the previous period
Dummy (=1 for the 2008-2009 period; =0 otherwise)
Constant
n = 55
R2 = 0.6246
R2 adjusted = 0.5777
MODEL 3
Gross capital formation (% of GDP)
General government balance (% of GDP)
CPI inflation (%)
Private sector share in GDP (%)
GDP per capita at PPP (constant 2005 US$) from the previous period
Dummy (=1 for the 2008-2009 period; =0 otherwise)
Constant
n = 56
R2 = 0.6033
R2 adjusted = 0.5547
Coefficient
t-statistics
p-value
0.1572
1.81
0.2427
2.05
–0.0569
–3.16
0.0696
1.65
–0.0002
–2.02
–7.1788
–5.21
–0.1681
–0.05
F = 13.61 (p-value for F = 0.000)
0.076
0.046
0.003
0.105
0.049
0.000
0.962
0.1985
2.47
0.0620
1.63
0.2688
2.28
–0.0241
–3.66
–0.0002
–1.89
–4.6624
–3.92
2.0208
0.93
F = 13.31 (p-value for F = 0.000)
0.017
0.111
0.027
0.001
0.064
0.000
0.355
0.1510
1.78
0.2732
2.26
–0.0234
–3.37
0.0971
2.40
–0.0002
–1.56
–5.5737
–4.64
–3.0093
–1.03
F = 12.42 (p-value for F = 0.000)
0.082
0.029
0.001
0.020
0.126
0.000
0.308
29
Time
Growth empirics: Convergence
 In empirical analyses, two most popular concepts
of income-level convergence usually are tested:
 absolute -convergence,
 -convergence.
 Absolute -convergence exists when less developed
economies grow faster than more developed ones.
 -convergence appears when income differentiation
between economies decreases over time.
30
Time
Growth empirics: Convergence (cont.)
 To verify the absolute -convergence hypothesis, we estimate:
1 yT
ln
  0  1 ln y0
T y0
 The explained variable is the average growth rate of real GDP per capita
between period T and 0.
 The explanatory variable is the log GDP per capita in the initial period.
 If 1 is negative and significant, -convergence exists.
 To verify the -convergence hypothesis, we estimate the trend
line of dispersion in income levels:
sd  ln yt   0  1t
 The explained variable usually is the standard deviation
of log GDP per capita levels between countries.
 The explanatory variable is the time variable.
 If 1 is negative and significant, -convergence exists.
31
Time
Growth empirics: Convergence (cont.)
Annual growth rate of real GDP per
capita, 1993-2009
0,05
EST
LAT
POL
SLK
IRE
LIT
0,04
SLV
EU10
ROM
0,03
CZE
HUN
GRE
0,00
8,65
R = 0.5485
SWE
SPA
EU10 (average) & EU15 (average)
EU10
EU15
Trend line: EU10 and EU15
Trend line: EU10 (average) & EU15 (average)
8,85
LUX
2
0,02
0,01
g y = -0.0164y 0 + 0.1850
FIN
BGR
9,05
9,25
POR
UK
EU15
BEL
NET
AUS
DEN
FRA
GER
ITA
g y = -0.0226y 0 + 0.2424;
9,45
9,65
9,85
10,05
Log of real 1993 GDP per capita
10,25
2
R =1
10,45
10,65
10,85
Figure 3
GDP per capita growth rate over the period 1993-2009
and the initial GDP per capital level
32
Time
Growth empirics: Convergence (cont.)
Standard deviation of log of real GDP.
per capita
0,60
0,56
sd(y ) = -0.0100t + 0.6031
2
R = 0.8693
0,52
0,48
0,44
0,40
25 countries
2 regions
0,36
Trend line: country differentiation
Trend line: regional differentiation
sd(y ) = -0.0118t + 0.5441
2
R = 0.9251
0,32
1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009
Year
Figure 4
Standard deviation of GDP per capita, 1993-2009
33
Time
Growth empirics: Growth accounting – total factor productivity (TFP)
 We differentiate the production function:
F  A, L, K 
F  A, L, K 
F  A, L, K 
A
L
K
Y
A
L
K
A
L
K



Y
Y
A
Y
L
Y
K
 We further assume:
 Hicks-neutral technological progress: F(A,L,K) = Af(L,K).
 The technological share in income (∂F/∂A)A/Y is simply 1.
 All markets are perfectly competitive and there are no
externalities.  The marginal social product of capital ∂F/∂K
equals the price of capital r; similarly for labour: ∂F/∂L = w.
Let sK be the capital share in income (rK/Y),
and sL – the labour share in income (wL/Y).
 Total income is obtained from labour and capital
(Y = wL + rK).  sK + sL = 1.
34
Time
Growth empirics: Growth accounting – TFP (cont.)
Y A
K
L
  sK  1  sK 
Y A
K
L
 The above equation is the basic equation in standard growth
accounting.
 From this equation, we can calculate the TFP growth rate
as the difference between the GDP growth rate and the
weighted average growth rate of labour and physical capital:
A Y  K
L
TFP growth rate     sK  1  sK  
A Y  K
L
35
Time
Growth empirics: Growth accounting – TFP (cont.)
Table 2
Labour (L), physical capital (K), and TFP contribution to economic growth in Poland, 2000-2008
2000
2001
2002
2003
2004
2005
2006
2007
2008
contr.
contr.
contr.
contr.
contr.
contr.
contr.
contr.
contr.
growth
contr. growth
contr. growth
contr. growth
contr. growth
contr. growth
contr. growth
contr. growth
contr. growth
contr.
(%
(%
(%
(%
(%
(%
(%
(%
(%
(%)
(%) (%)
(%) (%)
(%) (%)
(%) (%)
(%) (%)
(%) (%)
(%) (%)
(%) (%)
(%)
points)
points)
points)
points)
points)
points)
points)
points)
points)
L
K
TFP
GDP
–1.6
–0.8
–19.1
–2.2
–1.1
–99.1
–3.0
–1.2
–0.6
–15.7
1.2
0.6
11.3
2.2
1.1
31.2
3.2
1.6
25.8
4.4
2.2
32.4
3.8
1.9
38.0
4.6
2.3
55.3
4.3
2.2
195.5
2.9
–1.5 –107.1
1.4
103.4
2.0
1.0
26.8
2.0
1.0
18.7
2.2
1.1
30.5
2.3
1.1
18.4
3.2
1.6
23.5
4.3
2.1
43.0
2.7
2.7
63.8
0.0
0.0
3.5
1.5
1.5
103.7
3.4
3.4
88.9
3.7
3.7
70.0
1.3
1.3
38.3
3.5
3.5
55.8
3.0
3.0
44.2
1.0
1.0
19.0
4.2
4.2
100.0
1.1
1.1
100.0
1.4
1.4
100.0
3.8
3.8
100.0
5.3
5.3
100.0
3.5
3.5
100.0
6.2
6.2
100.0
6.8
6.8
100.0
5.0
5.0
100.0
contr. = contribution.
36
Time
Summary
1.
The models of economic growth can be divided into two groups:
neoclassical and endogenous models. The first ones are characterized
by a neoclassical production function which exhibits diminishing
returns to accumulable inputs and constant returns to scale. The
endogenous models assume at least constant returns to accumulable
inputs. The most important neoclassical approaches include the
Solow, Ramsey, and Diamond models. The basic endogenous theories
are the Romer learning-by-doing model, the Lucas model, and models
with an expanding variety or an improving quality of products. The
new growth theory also includes the Mankiw-Romer-Weil (augmented
Solow) model.
2.
Neoclassical growth theory does not explain well the determinants
of long-run economic growth. According to these models, long-run
economic growth depends on technological progress which is
exogenously given.
3.
The conditional -convergence is confirmed by all neoclassical models.
Endogenous growth models, however, do not confirm the existence
of convergence. Some of them even indicate that economic growth
increases with income suggesting rather divergence trends.
37
Time
References
• Barro R. and X. Sala-i-Martin (2003), Economic Growth,
Cambridge – London: The MIT Press.
• Mankiw N.G., D. Romer, and D.N. Weil (1992), A Contribution
to the Empirics of Economic Growth, “Quarterly Journal
of Economics”, 107, pp. 407-437.
• Romer D. (2006), Advanced Macroeconomics, New York:
McGraw-Hill. Polish translation: Romer D. (2000),
Makroekonomia dla zaawansowanych, Warszawa: Wydawnictwo
Naukowe PWN.
38
Time
Additional references
• Aghion P. and P. Howitt (1992), A Model of Growth through Creative Destruction, “Econometrica”, 60, pp. 323-351.
• Arrow K. (1962), The Economic Implications of Learning by Doing, “Review of Economic Studies”, 29, pp. 155-173.
• Barro R. and X. Sala-i-Martin (1995), Economic Growth, New York – St. Louis – San Francisco: McGraw-Hill.
• Cass D. (1965), Optimum Growth in an Aggregative Model of Capital Accumulation, “Review of Economic Studies”, 32,
pp. 233-240.
• Diamond P.A. (1965), National Debt in a Neoclassical Growth Model, “American Economic Review”, 55, pp. 1126-1150.
• Domar E.D. (1946), Capital Expansion, Rate of Growth, and Employment, “Econometrica”, 14, pp. 137-147.
• Grossman G.M. and E. Helpman (1991), Quality Ladders in the Theory of Growth, “Review of Economic Studies”, 58,
pp. 43-61.
• Harrod R. (1939), An Essay in Dynamic Theory, “Economic Journal”, 49, pp. 14-33.
• Inada K.-I. (1963), On a Two-Sector Model of Economic Growth: Comments and a Generalization, “Review of Economic
Studies”, 30, pp. 119-127.
• Kaldor N. and J.A. Mirrlees (1962), A New Model of Economic Growth, “Review of Economic Studies”, 29, pp. 174-192.
• Koopmans T.C. (1965), On the Concept of Optimal Economic Growth, in: The Econometric Approach to Development
Planning, Amsterdam: North Holland.
• Lucas R.E. (1988), On the Mechanics of Economic Development, “Journal of Monetary Economics”, 22, pp. 3-42.
• Matkowski Z. and M. Próchniak (2010), Real Convergence or Divergence in GDP Per Capita, in: Poland. Competitiveness
Report 2010. Focus on Clusters (ed. M.A. Weresa), Warsaw: World Economy Research Institute, Warsaw School
of Economics, pp. 42-56.
• Próchniak M. (2010a), Economic Growth Determinants in the 10 Central and Eastern European Countries, 1993-2009.
Paper presented at the EuroConference 2010 „Challenges and Opportunities in Emerging Markets”, organised
by the Society for the Study of Emerging Markets, Milas (Turkey), 16-18 July.
• Próchniak M. (2010b), Total Factor Productivity, in: Poland. Competitiveness Report 2010. Focus on Clusters
(ed. M.A. Weresa), Warsaw: World Economy Research Institute, Warsaw School of Economics, pp. 171-179.
39
Time
Additional references (cont.)
• Ramsey F. (1928), A Mathematical Theory of Saving, “Economic Journal”, 38, pp. 543-559.
• Rapacki R. and M. Próchniak (2006), Charakterystyka wzrostu gospodarczego w krajach postsocjalistycznych w latach
1990-2003 [The Characteristics of Economic Growth in Post-Socialist Countries, 1990-2003], “Ekonomista”, 6, pp. 715-744.
• Rapacki R. and M. Próchniak (2010), Wpływ rozszerzenia Unii Europejskiej na wzrost gospodarczy i realną konwergencję
krajów Europy Środkowo-Wschodniej [The Impact of EU Enlargement on Economic Growth and Real Convergence
of the CEE Countries], “Ekonomista”, 4, pp. 523-546.
• Rebelo S. (1991), Long-Run Policy Analysis and Long-Run Growth, “Journal of Political Economy”, 99, pp. 500-521.
• Romer P.M. (1986), Increasing Returns and Long-Run Growth, “Journal of Political Economy”, 94, pp. 1002-1037.
• Romer P.M. (1990), Endogenous Technological Change, “Journal of Political Economy”, 98, pp. S71-S102.
• Shell K. (1966), Toward a Theory of Inventive Activity and Capital Accumulation, “American Economic Review”, 56,
pp. 62-68.
• Sheshinski E. (1967), Optimal Accumulation with Learning by Doing, in: Essays on the Theory of Optimal Economic Growth
(ed. K. Shell), Cambridge, MA: The MIT Press, pp. 31-52.
• Solow R.M. (1956), A Contribution to the Theory of Economic Growth, “Quarterly Journal of Economics”, 70, pp. 65-94.
• Solow R.M. (1957), Technical Change and the Aggregate Production Function, “Review of Economics and Statistics”, 39,
pp. 312-320.
• Swan T.W. (1956), Economic Growth and Capital Accumulation, “Economic Record”, 32, pp. 334-361.
• Uzawa H. (1964), Optimal Growth in a Two-Sector Model of Capital Accumulation, “Review of Economic Studies”, 31,
pp. 1-24.
• Uzawa H. (1965), Optimal Technical Change in an Aggregative Model of Economic Growth, “International Economic
Review”, 6, pp. 18-31.
40
Time
Thank you very much
for the attention!!!
41
Time