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Inequality and the Process of Development ¨ Omer ¨ Ozak Department of Economics Southern Methodist University Economic Growth and Comparative Development ¨ Omer ¨ Ozak Inequality and Growth Growth & Comparative Development 1 / 73
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Page 1: Inequality and the Process of Development · Inequality is bene cial for growth (in the post-industrialization stage) Keynes (1920), Kaldor (1957) ... to save is higher =)increases

Inequality and the Process of Development

Omer Ozak

Department of EconomicsSouthern Methodist University

Economic Growth and Comparative Development

Omer Ozak Inequality and Growth Growth & Comparative Development 1 / 73

Page 2: Inequality and the Process of Development · Inequality is bene cial for growth (in the post-industrialization stage) Keynes (1920), Kaldor (1957) ... to save is higher =)increases

From the Classical to the Modern Perspective The Classical Paradigm

The Classical Theory

Inequality is beneficial for growth (in the post-industrialization stage)

Keynes (1920), Kaldor (1957)

The marginal propensity to save increases with income

Inequality channels resources towards individuals whose marginal propensity

to save is higher

=⇒ increases aggregate savings & capital accumulation

=⇒ enhances the development process

Omer Ozak Inequality and Growth Growth & Comparative Development 2 / 73

Page 3: Inequality and the Process of Development · Inequality is bene cial for growth (in the post-industrialization stage) Keynes (1920), Kaldor (1957) ... to save is higher =)increases

From the Classical to the Modern Perspective The Classical Paradigm

The Classical Theory

Inequality is beneficial for growth (in the post-industrialization stage)

Keynes (1920), Kaldor (1957)

The marginal propensity to save increases with income

Inequality channels resources towards individuals whose marginal propensity

to save is higher

=⇒ increases aggregate savings & capital accumulation

=⇒ enhances the development process

Omer Ozak Inequality and Growth Growth & Comparative Development 2 / 73

Page 4: Inequality and the Process of Development · Inequality is bene cial for growth (in the post-industrialization stage) Keynes (1920), Kaldor (1957) ... to save is higher =)increases

From the Classical to the Modern Perspective The Classical Paradigm

The Classical Theory

Inequality is beneficial for growth (in the post-industrialization stage)

Keynes (1920), Kaldor (1957)

The marginal propensity to save increases with income

Inequality channels resources towards individuals whose marginal propensity

to save is higher

=⇒ increases aggregate savings & capital accumulation

=⇒ enhances the development process

Omer Ozak Inequality and Growth Growth & Comparative Development 2 / 73

Page 5: Inequality and the Process of Development · Inequality is bene cial for growth (in the post-industrialization stage) Keynes (1920), Kaldor (1957) ... to save is higher =)increases

From the Classical to the Modern Perspective The Classical Paradigm

The Classical Theory

Inequality is beneficial for growth (in the post-industrialization stage)

Keynes (1920), Kaldor (1957)

The marginal propensity to save increases with income

Inequality channels resources towards individuals whose marginal propensity

to save is higher

=⇒ increases aggregate savings & capital accumulation

=⇒ enhances the development process

Omer Ozak Inequality and Growth Growth & Comparative Development 2 / 73

Page 6: Inequality and the Process of Development · Inequality is bene cial for growth (in the post-industrialization stage) Keynes (1920), Kaldor (1957) ... to save is higher =)increases

From the Classical to the Modern Perspective The Classical Paradigm

The Classical Theory

Inequality is beneficial for growth (in the post-industrialization stage)

Keynes (1920), Kaldor (1957)

The marginal propensity to save increases with income

Inequality channels resources towards individuals whose marginal propensity

to save is higher

=⇒ increases aggregate savings & capital accumulation

=⇒ enhances the development process

Omer Ozak Inequality and Growth Growth & Comparative Development 2 / 73

Page 7: Inequality and the Process of Development · Inequality is bene cial for growth (in the post-industrialization stage) Keynes (1920), Kaldor (1957) ... to save is higher =)increases

From the Classical to the Modern Perspective The Classical Paradigm

The Classical Theory

Inequality is beneficial for growth (in the post-industrialization stage)

Keynes (1920), Kaldor (1957)

The marginal propensity to save increases with income

Inequality channels resources towards individuals whose marginal propensity

to save is higher

=⇒ increases aggregate savings & capital accumulation

=⇒ enhances the development process

Omer Ozak Inequality and Growth Growth & Comparative Development 2 / 73

Page 8: Inequality and the Process of Development · Inequality is bene cial for growth (in the post-industrialization stage) Keynes (1920), Kaldor (1957) ... to save is higher =)increases

From the Classical to the Modern Perspective The Neoclassical Viewpoint

The Neoclassical Paradigm

The Representative Agent Approach

Rejects the role of heterogeneity, and thus income distribution, in eco-nomic growth

Growth Process ⇒ Income Distribution

Income Distribution ; Growth Process

Omer Ozak Inequality and Growth Growth & Comparative Development 3 / 73

Page 9: Inequality and the Process of Development · Inequality is bene cial for growth (in the post-industrialization stage) Keynes (1920), Kaldor (1957) ... to save is higher =)increases

From the Classical to the Modern Perspective The Neoclassical Viewpoint

The Neoclassical Paradigm

The Representative Agent Approach

Rejects the role of heterogeneity, and thus income distribution, in eco-nomic growth

Growth Process ⇒ Income Distribution

Income Distribution ; Growth Process

Omer Ozak Inequality and Growth Growth & Comparative Development 3 / 73

Page 10: Inequality and the Process of Development · Inequality is bene cial for growth (in the post-industrialization stage) Keynes (1920), Kaldor (1957) ... to save is higher =)increases

From the Classical to the Modern Perspective The Neoclassical Viewpoint

The Neoclassical Paradigm

The Representative Agent Approach

Rejects the role of heterogeneity, and thus income distribution, in eco-nomic growth

Growth Process ⇒ Income Distribution

Income Distribution ; Growth Process

Omer Ozak Inequality and Growth Growth & Comparative Development 3 / 73

Page 11: Inequality and the Process of Development · Inequality is bene cial for growth (in the post-industrialization stage) Keynes (1920), Kaldor (1957) ... to save is higher =)increases

From the Classical to the Modern Perspective The Neoclassical Viewpoint

The Neoclassical Paradigm

The Representative Agent Approach

Rejects the role of heterogeneity, and thus income distribution, in eco-nomic growth

Growth Process ⇒ Income Distribution

Income Distribution ; Growth Process

Omer Ozak Inequality and Growth Growth & Comparative Development 3 / 73

Page 12: Inequality and the Process of Development · Inequality is bene cial for growth (in the post-industrialization stage) Keynes (1920), Kaldor (1957) ... to save is higher =)increases

From the Classical to the Modern Perspective The Neoclassical Viewpoint

The Neoclassical Paradigm

The Representative Agent Approach

Rejects the role of heterogeneity, and thus income distribution, in eco-nomic growth

Growth Process ⇒ Income Distribution

Income Distribution ; Growth Process

Omer Ozak Inequality and Growth Growth & Comparative Development 3 / 73

Page 13: Inequality and the Process of Development · Inequality is bene cial for growth (in the post-industrialization stage) Keynes (1920), Kaldor (1957) ... to save is higher =)increases

The Modern Perspective

The Modern Perspective: Origins

Galor and Zeira (1988, 1993)

Unlike the Neoclassical Paradigm

Income Distribution ⇒ the growth process

Unlike the Classical Perspective

Underlined the adverse effect of Inequality on the growth process

Omer Ozak Inequality and Growth Growth & Comparative Development 4 / 73

Page 14: Inequality and the Process of Development · Inequality is bene cial for growth (in the post-industrialization stage) Keynes (1920), Kaldor (1957) ... to save is higher =)increases

The Modern Perspective

The Modern Perspective: Origins

Galor and Zeira (1988, 1993)

Unlike the Neoclassical Paradigm

Income Distribution ⇒ the growth process

Unlike the Classical Perspective

Underlined the adverse effect of Inequality on the growth process

Omer Ozak Inequality and Growth Growth & Comparative Development 4 / 73

Page 15: Inequality and the Process of Development · Inequality is bene cial for growth (in the post-industrialization stage) Keynes (1920), Kaldor (1957) ... to save is higher =)increases

The Modern Perspective

The Modern Perspective: Origins

Galor and Zeira (1988, 1993)

Unlike the Neoclassical Paradigm

Income Distribution ⇒ the growth process

Unlike the Classical Perspective

Underlined the adverse effect of Inequality on the growth process

Omer Ozak Inequality and Growth Growth & Comparative Development 4 / 73

Page 16: Inequality and the Process of Development · Inequality is bene cial for growth (in the post-industrialization stage) Keynes (1920), Kaldor (1957) ... to save is higher =)increases

The Modern Perspective

The Modern Perspective: Origins

Galor and Zeira (1988, 1993)

Unlike the Neoclassical Paradigm

Income Distribution ⇒ the growth process

Unlike the Classical Perspective

Underlined the adverse effect of Inequality on the growth process

Omer Ozak Inequality and Growth Growth & Comparative Development 4 / 73

Page 17: Inequality and the Process of Development · Inequality is bene cial for growth (in the post-industrialization stage) Keynes (1920), Kaldor (1957) ... to save is higher =)increases

The Modern Perspective

The Modern Perspective: Origins

Galor and Zeira (1988, 1993)

Unlike the Neoclassical Paradigm

Income Distribution ⇒ the growth process

Unlike the Classical Perspective

Underlined the adverse effect of Inequality on the growth process

Omer Ozak Inequality and Growth Growth & Comparative Development 4 / 73

Page 18: Inequality and the Process of Development · Inequality is bene cial for growth (in the post-industrialization stage) Keynes (1920), Kaldor (1957) ... to save is higher =)increases

The Modern Perspective

The Modern Perspective: Origins

Galor and Zeira (1988, 1993)

Unlike the Neoclassical Paradigm

Income Distribution ⇒ the growth process

Unlike the Classical Perspective

Underlined the adverse effect of Inequality on the growth process

Omer Ozak Inequality and Growth Growth & Comparative Development 4 / 73

Page 19: Inequality and the Process of Development · Inequality is bene cial for growth (in the post-industrialization stage) Keynes (1920), Kaldor (1957) ... to save is higher =)increases

The Modern Perspective The Credit market imperfection Channel

The Credit Market Imperfections Approach: Assumptions

Main assumptions:

Credit market imperfections

Differences in the interest rates for borrowers and lenders

and either

Fixed investment cost in education or in other individual-specific projects

or

Saving and bequest rates are increasing function of wealth (Moav, (2002) Galor and

Moav (2004))

Omer Ozak Inequality and Growth Growth & Comparative Development 5 / 73

Page 20: Inequality and the Process of Development · Inequality is bene cial for growth (in the post-industrialization stage) Keynes (1920), Kaldor (1957) ... to save is higher =)increases

The Modern Perspective The Credit market imperfection Channel

The Credit Market Imperfections Approach: Assumptions

Main assumptions:

Credit market imperfections

Differences in the interest rates for borrowers and lenders

and either

Fixed investment cost in education or in other individual-specific projects

or

Saving and bequest rates are increasing function of wealth (Moav, (2002) Galor and

Moav (2004))

Omer Ozak Inequality and Growth Growth & Comparative Development 5 / 73

Page 21: Inequality and the Process of Development · Inequality is bene cial for growth (in the post-industrialization stage) Keynes (1920), Kaldor (1957) ... to save is higher =)increases

The Modern Perspective The Credit market imperfection Channel

The Credit Market Imperfections Approach: Assumptions

Main assumptions:

Credit market imperfections

Differences in the interest rates for borrowers and lenders

and either

Fixed investment cost in education or in other individual-specific projects

or

Saving and bequest rates are increasing function of wealth (Moav, (2002) Galor and

Moav (2004))

Omer Ozak Inequality and Growth Growth & Comparative Development 5 / 73

Page 22: Inequality and the Process of Development · Inequality is bene cial for growth (in the post-industrialization stage) Keynes (1920), Kaldor (1957) ... to save is higher =)increases

The Modern Perspective The Credit market imperfection Channel

The Credit Market Imperfections Approach: Assumptions

Main assumptions:

Credit market imperfections

Differences in the interest rates for borrowers and lenders

and either

Fixed investment cost in education or in other individual-specific projects

or

Saving and bequest rates are increasing function of wealth (Moav, (2002) Galor and

Moav (2004))

Omer Ozak Inequality and Growth Growth & Comparative Development 5 / 73

Page 23: Inequality and the Process of Development · Inequality is bene cial for growth (in the post-industrialization stage) Keynes (1920), Kaldor (1957) ... to save is higher =)increases

The Modern Perspective The Credit market imperfection Channel

The Credit Market Imperfections Approach: Assumptions

Main assumptions:

Credit market imperfections

Differences in the interest rates for borrowers and lenders

and either

Fixed investment cost in education or in other individual-specific projects

or

Saving and bequest rates are increasing function of wealth (Moav, (2002) Galor and

Moav (2004))

Omer Ozak Inequality and Growth Growth & Comparative Development 5 / 73

Page 24: Inequality and the Process of Development · Inequality is bene cial for growth (in the post-industrialization stage) Keynes (1920), Kaldor (1957) ... to save is higher =)increases

The Modern Perspective The Credit market imperfection Channel

The Credit Market Imperfections Approach: Mechanism

Inequality affects occupational choices: skilled vs. unskilled workers or en-

trepreneurs vs. workers

Non-poor economies:

Inequality =⇒ under-investment in human capital (inv’t projects)that is transmitted across generations =⇒ lower output growth inthe short-run and in the long-run

Poor economies:

Inequality permits some investment in HC (inv’t projects) and maythus promote output growth

The human capital channel is consistent with evidence (Perotti (1996))

Omer Ozak Inequality and Growth Growth & Comparative Development 6 / 73

Page 25: Inequality and the Process of Development · Inequality is bene cial for growth (in the post-industrialization stage) Keynes (1920), Kaldor (1957) ... to save is higher =)increases

The Modern Perspective The Credit market imperfection Channel

The Credit Market Imperfections Approach: Mechanism

Inequality affects occupational choices: skilled vs. unskilled workers or en-

trepreneurs vs. workers

Non-poor economies:

Inequality =⇒ under-investment in human capital (inv’t projects)that is transmitted across generations =⇒ lower output growth inthe short-run and in the long-run

Poor economies:

Inequality permits some investment in HC (inv’t projects) and maythus promote output growth

The human capital channel is consistent with evidence (Perotti (1996))

Omer Ozak Inequality and Growth Growth & Comparative Development 6 / 73

Page 26: Inequality and the Process of Development · Inequality is bene cial for growth (in the post-industrialization stage) Keynes (1920), Kaldor (1957) ... to save is higher =)increases

The Modern Perspective The Credit market imperfection Channel

The Credit Market Imperfections Approach: Mechanism

Inequality affects occupational choices: skilled vs. unskilled workers or en-

trepreneurs vs. workers

Non-poor economies:

Inequality =⇒ under-investment in human capital (inv’t projects)that is transmitted across generations =⇒ lower output growth inthe short-run and in the long-run

Poor economies:

Inequality permits some investment in HC (inv’t projects) and maythus promote output growth

The human capital channel is consistent with evidence (Perotti (1996))

Omer Ozak Inequality and Growth Growth & Comparative Development 6 / 73

Page 27: Inequality and the Process of Development · Inequality is bene cial for growth (in the post-industrialization stage) Keynes (1920), Kaldor (1957) ... to save is higher =)increases

The Modern Perspective The Credit market imperfection Channel

The Credit Market Imperfections Approach: Mechanism

Inequality affects occupational choices: skilled vs. unskilled workers or en-

trepreneurs vs. workers

Non-poor economies:

Inequality =⇒ under-investment in human capital (inv’t projects)that is transmitted across generations =⇒ lower output growth inthe short-run and in the long-run

Poor economies:

Inequality permits some investment in HC (inv’t projects) and maythus promote output growth

The human capital channel is consistent with evidence (Perotti (1996))

Omer Ozak Inequality and Growth Growth & Comparative Development 6 / 73

Page 28: Inequality and the Process of Development · Inequality is bene cial for growth (in the post-industrialization stage) Keynes (1920), Kaldor (1957) ... to save is higher =)increases

The Modern Perspective The Credit market imperfection Channel

The Credit Market Imperfections Approach: Mechanism

Inequality affects occupational choices: skilled vs. unskilled workers or en-

trepreneurs vs. workers

Non-poor economies:

Inequality =⇒ under-investment in human capital (inv’t projects)that is transmitted across generations =⇒ lower output growth inthe short-run and in the long-run

Poor economies:

Inequality permits some investment in HC (inv’t projects) and maythus promote output growth

The human capital channel is consistent with evidence (Perotti (1996))

Omer Ozak Inequality and Growth Growth & Comparative Development 6 / 73

Page 29: Inequality and the Process of Development · Inequality is bene cial for growth (in the post-industrialization stage) Keynes (1920), Kaldor (1957) ... to save is higher =)increases

The Modern Perspective The Political Economy Channel

The Political Economy Approach

Echoes the hypothesis of the CMI Approach

Inequality is harmful for the growth process

Inequality =⇒ political pressure for redistribution

Higher (distortionary) taxation =⇒ lower investment and slowereconomic growth

Alesina and Rodrik, (1994) Persson and Tebelini (1994)

This channel is inconsistent with evidence (Perotti (1996))

Omer Ozak Inequality and Growth Growth & Comparative Development 7 / 73

Page 30: Inequality and the Process of Development · Inequality is bene cial for growth (in the post-industrialization stage) Keynes (1920), Kaldor (1957) ... to save is higher =)increases

The Modern Perspective The Political Economy Channel

The Political Economy Approach

Echoes the hypothesis of the CMI Approach

Inequality is harmful for the growth process

Inequality =⇒ political pressure for redistribution

Higher (distortionary) taxation =⇒ lower investment and slowereconomic growth

Alesina and Rodrik, (1994) Persson and Tebelini (1994)

This channel is inconsistent with evidence (Perotti (1996))

Omer Ozak Inequality and Growth Growth & Comparative Development 7 / 73

Page 31: Inequality and the Process of Development · Inequality is bene cial for growth (in the post-industrialization stage) Keynes (1920), Kaldor (1957) ... to save is higher =)increases

The Modern Perspective The Political Economy Channel

The Political Economy Approach

Echoes the hypothesis of the CMI Approach

Inequality is harmful for the growth process

Inequality =⇒ political pressure for redistribution

Higher (distortionary) taxation =⇒ lower investment and slowereconomic growth

Alesina and Rodrik, (1994) Persson and Tebelini (1994)

This channel is inconsistent with evidence (Perotti (1996))

Omer Ozak Inequality and Growth Growth & Comparative Development 7 / 73

Page 32: Inequality and the Process of Development · Inequality is bene cial for growth (in the post-industrialization stage) Keynes (1920), Kaldor (1957) ... to save is higher =)increases

The Modern Perspective The Political Economy Channel

The Political Economy Approach

Echoes the hypothesis of the CMI Approach

Inequality is harmful for the growth process

Inequality =⇒ political pressure for redistribution

Higher (distortionary) taxation =⇒ lower investment and slowereconomic growth

Alesina and Rodrik, (1994) Persson and Tebelini (1994)

This channel is inconsistent with evidence (Perotti (1996))

Omer Ozak Inequality and Growth Growth & Comparative Development 7 / 73

Page 33: Inequality and the Process of Development · Inequality is bene cial for growth (in the post-industrialization stage) Keynes (1920), Kaldor (1957) ... to save is higher =)increases

The Modern Perspective The Political Economy Channel

The Political Economy Approach

Echoes the hypothesis of the CMI Approach

Inequality is harmful for the growth process

Inequality =⇒ political pressure for redistribution

Higher (distortionary) taxation =⇒ lower investment and slowereconomic growth

Alesina and Rodrik, (1994) Persson and Tebelini (1994)

This channel is inconsistent with evidence (Perotti (1996))

Omer Ozak Inequality and Growth Growth & Comparative Development 7 / 73

Page 34: Inequality and the Process of Development · Inequality is bene cial for growth (in the post-industrialization stage) Keynes (1920), Kaldor (1957) ... to save is higher =)increases

The Modern Perspective The Political Economy Channel

The Political Economy Approach

Echoes the hypothesis of the CMI Approach

Inequality is harmful for the growth process

Inequality =⇒ political pressure for redistribution

Higher (distortionary) taxation =⇒ lower investment and slowereconomic growth

Alesina and Rodrik, (1994) Persson and Tebelini (1994)

This channel is inconsistent with evidence (Perotti (1996))

Omer Ozak Inequality and Growth Growth & Comparative Development 7 / 73

Page 35: Inequality and the Process of Development · Inequality is bene cial for growth (in the post-industrialization stage) Keynes (1920), Kaldor (1957) ... to save is higher =)increases

The Modern Perspective The Political Economy Channel

The Political Economy Approach: An Alternative Channel

Inequality is harmful for the growth process

Inequality =⇒ incentive for better endowed agents (landowners) toblock redistribution

Efficient redistribution policies are not implemented

Benabou, (2000), Galor-Moav-Vollrath (2009)

Omer Ozak Inequality and Growth Growth & Comparative Development 8 / 73

Page 36: Inequality and the Process of Development · Inequality is bene cial for growth (in the post-industrialization stage) Keynes (1920), Kaldor (1957) ... to save is higher =)increases

The Modern Perspective The Political Economy Channel

The Political Economy Approach: An Alternative Channel

Inequality is harmful for the growth process

Inequality =⇒ incentive for better endowed agents (landowners) toblock redistribution

Efficient redistribution policies are not implemented

Benabou, (2000), Galor-Moav-Vollrath (2009)

Omer Ozak Inequality and Growth Growth & Comparative Development 8 / 73

Page 37: Inequality and the Process of Development · Inequality is bene cial for growth (in the post-industrialization stage) Keynes (1920), Kaldor (1957) ... to save is higher =)increases

The Modern Perspective The Political Economy Channel

The Political Economy Approach: An Alternative Channel

Inequality is harmful for the growth process

Inequality =⇒ incentive for better endowed agents (landowners) toblock redistribution

Efficient redistribution policies are not implemented

Benabou, (2000), Galor-Moav-Vollrath (2009)

Omer Ozak Inequality and Growth Growth & Comparative Development 8 / 73

Page 38: Inequality and the Process of Development · Inequality is bene cial for growth (in the post-industrialization stage) Keynes (1920), Kaldor (1957) ... to save is higher =)increases

The Modern Perspective The Political Economy Channel

The Political Economy Approach: An Alternative Channel

Inequality is harmful for the growth process

Inequality =⇒ incentive for better endowed agents (landowners) toblock redistribution

Efficient redistribution policies are not implemented

Benabou, (2000), Galor-Moav-Vollrath (2009)

Omer Ozak Inequality and Growth Growth & Comparative Development 8 / 73

Page 39: Inequality and the Process of Development · Inequality is bene cial for growth (in the post-industrialization stage) Keynes (1920), Kaldor (1957) ... to save is higher =)increases

The Modern Perspective Socio-Political Instability

The Socio-Political Instability Approach

Echoes the hypothesis of the CMI Approach

Inequality is harmful for the growth process

Inequality =⇒ Socio-Political instability

Socio-Political instability =⇒ reduces the security of property rights=⇒ lower investment and slower economic growth (Alesina and Perotti (1996))

This channel is consistent with evidence (Perotti (1996))

Omer Ozak Inequality and Growth Growth & Comparative Development 9 / 73

Page 40: Inequality and the Process of Development · Inequality is bene cial for growth (in the post-industrialization stage) Keynes (1920), Kaldor (1957) ... to save is higher =)increases

The Modern Perspective Socio-Political Instability

The Socio-Political Instability Approach

Echoes the hypothesis of the CMI Approach

Inequality is harmful for the growth process

Inequality =⇒ Socio-Political instability

Socio-Political instability =⇒ reduces the security of property rights=⇒ lower investment and slower economic growth (Alesina and Perotti (1996))

This channel is consistent with evidence (Perotti (1996))

Omer Ozak Inequality and Growth Growth & Comparative Development 9 / 73

Page 41: Inequality and the Process of Development · Inequality is bene cial for growth (in the post-industrialization stage) Keynes (1920), Kaldor (1957) ... to save is higher =)increases

The Modern Perspective Socio-Political Instability

The Socio-Political Instability Approach

Echoes the hypothesis of the CMI Approach

Inequality is harmful for the growth process

Inequality =⇒ Socio-Political instability

Socio-Political instability =⇒ reduces the security of property rights=⇒ lower investment and slower economic growth (Alesina and Perotti (1996))

This channel is consistent with evidence (Perotti (1996))

Omer Ozak Inequality and Growth Growth & Comparative Development 9 / 73

Page 42: Inequality and the Process of Development · Inequality is bene cial for growth (in the post-industrialization stage) Keynes (1920), Kaldor (1957) ... to save is higher =)increases

The Modern Perspective Socio-Political Instability

The Socio-Political Instability Approach

Echoes the hypothesis of the CMI Approach

Inequality is harmful for the growth process

Inequality =⇒ Socio-Political instability

Socio-Political instability =⇒ reduces the security of property rights=⇒ lower investment and slower economic growth (Alesina and Perotti (1996))

This channel is consistent with evidence (Perotti (1996))

Omer Ozak Inequality and Growth Growth & Comparative Development 9 / 73

Page 43: Inequality and the Process of Development · Inequality is bene cial for growth (in the post-industrialization stage) Keynes (1920), Kaldor (1957) ... to save is higher =)increases

The Modern Perspective Socio-Political Instability

The Socio-Political Instability Approach

Echoes the hypothesis of the CMI Approach

Inequality is harmful for the growth process

Inequality =⇒ Socio-Political instability

Socio-Political instability =⇒ reduces the security of property rights=⇒ lower investment and slower economic growth (Alesina and Perotti (1996))

This channel is consistent with evidence (Perotti (1996))

Omer Ozak Inequality and Growth Growth & Comparative Development 9 / 73

Page 44: Inequality and the Process of Development · Inequality is bene cial for growth (in the post-industrialization stage) Keynes (1920), Kaldor (1957) ... to save is higher =)increases

The Modern Perspective Socio-Political Instability

The Socio-Political Instability Approach

Echoes the hypothesis of the CMI Approach

Inequality is harmful for the growth process

Inequality =⇒ Socio-Political instability

Socio-Political instability =⇒ reduces the security of property rights=⇒ lower investment and slower economic growth (Alesina and Perotti (1996))

This channel is consistent with evidence (Perotti (1996))

Omer Ozak Inequality and Growth Growth & Comparative Development 9 / 73

Page 45: Inequality and the Process of Development · Inequality is bene cial for growth (in the post-industrialization stage) Keynes (1920), Kaldor (1957) ... to save is higher =)increases

The Modern Perspective Gender Inequality

Gender Inequality

Gender inequality is harmful for the growth process

Galor-Weil (AER 1996)

Gender inequality reduces the opportunity cost of raising children more than

it reduces household income

=⇒ increases fertility

=⇒ reduces human capital investment (quantity-quality trade-off)

=⇒ lowers female labor force participation

=⇒ slows the growth process

Omer Ozak Inequality and Growth Growth & Comparative Development 10 / 73

Page 46: Inequality and the Process of Development · Inequality is bene cial for growth (in the post-industrialization stage) Keynes (1920), Kaldor (1957) ... to save is higher =)increases

The Modern Perspective Gender Inequality

Gender Inequality

Gender inequality is harmful for the growth process

Galor-Weil (AER 1996)

Gender inequality reduces the opportunity cost of raising children more than

it reduces household income

=⇒ increases fertility

=⇒ reduces human capital investment (quantity-quality trade-off)

=⇒ lowers female labor force participation

=⇒ slows the growth process

Omer Ozak Inequality and Growth Growth & Comparative Development 10 / 73

Page 47: Inequality and the Process of Development · Inequality is bene cial for growth (in the post-industrialization stage) Keynes (1920), Kaldor (1957) ... to save is higher =)increases

The Modern Perspective Gender Inequality

Gender Inequality

Gender inequality is harmful for the growth process

Galor-Weil (AER 1996)

Gender inequality reduces the opportunity cost of raising children more than

it reduces household income

=⇒ increases fertility

=⇒ reduces human capital investment (quantity-quality trade-off)

=⇒ lowers female labor force participation

=⇒ slows the growth process

Omer Ozak Inequality and Growth Growth & Comparative Development 10 / 73

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The Modern Perspective Gender Inequality

Gender Inequality

Gender inequality is harmful for the growth process

Galor-Weil (AER 1996)

Gender inequality reduces the opportunity cost of raising children more than

it reduces household income

=⇒ increases fertility

=⇒ reduces human capital investment (quantity-quality trade-off)

=⇒ lowers female labor force participation

=⇒ slows the growth process

Omer Ozak Inequality and Growth Growth & Comparative Development 10 / 73

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The Modern Perspective Gender Inequality

Gender Inequality

Gender inequality is harmful for the growth process

Galor-Weil (AER 1996)

Gender inequality reduces the opportunity cost of raising children more than

it reduces household income

=⇒ increases fertility

=⇒ reduces human capital investment (quantity-quality trade-off)

=⇒ lowers female labor force participation

=⇒ slows the growth process

Omer Ozak Inequality and Growth Growth & Comparative Development 10 / 73

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The Modern Perspective Gender Inequality

Gender Inequality

Gender inequality is harmful for the growth process

Galor-Weil (AER 1996)

Gender inequality reduces the opportunity cost of raising children more than

it reduces household income

=⇒ increases fertility

=⇒ reduces human capital investment (quantity-quality trade-off)

=⇒ lowers female labor force participation

=⇒ slows the growth process

Omer Ozak Inequality and Growth Growth & Comparative Development 10 / 73

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The Modern Perspective Gender Inequality

Gender Inequality

Gender inequality is harmful for the growth process

Galor-Weil (AER 1996)

Gender inequality reduces the opportunity cost of raising children more than

it reduces household income

=⇒ increases fertility

=⇒ reduces human capital investment (quantity-quality trade-off)

=⇒ lowers female labor force participation

=⇒ slows the growth process

Omer Ozak Inequality and Growth Growth & Comparative Development 10 / 73

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The Modern Perspective The Unified Approach

A unified theory of inequality and economic development

Galor and Moav (2004):

Captures the changing role of inequality in the growth process

Unifies the Classical and the Modern Paradigms

Provides an intertemporal reconciliation between conflicting viewpoints

about the effect of inequality on economic growth

Underlines the role of inequality in triggering socio-political transition

(Galor-Moav-Vollrath (2009), Galor-Moav (2006))

Omer Ozak Inequality and Growth Growth & Comparative Development 11 / 73

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The Modern Perspective The Unified Approach

A unified theory of inequality and economic development

Galor and Moav (2004):

Captures the changing role of inequality in the growth process

Unifies the Classical and the Modern Paradigms

Provides an intertemporal reconciliation between conflicting viewpoints

about the effect of inequality on economic growth

Underlines the role of inequality in triggering socio-political transition

(Galor-Moav-Vollrath (2009), Galor-Moav (2006))

Omer Ozak Inequality and Growth Growth & Comparative Development 11 / 73

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The Modern Perspective The Unified Approach

A unified theory of inequality and economic development

Galor and Moav (2004):

Captures the changing role of inequality in the growth process

Unifies the Classical and the Modern Paradigms

Provides an intertemporal reconciliation between conflicting viewpoints

about the effect of inequality on economic growth

Underlines the role of inequality in triggering socio-political transition

(Galor-Moav-Vollrath (2009), Galor-Moav (2006))

Omer Ozak Inequality and Growth Growth & Comparative Development 11 / 73

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The Modern Perspective The Unified Approach

A unified theory of inequality and economic development

Galor and Moav (2004):

Captures the changing role of inequality in the growth process

Unifies the Classical and the Modern Paradigms

Provides an intertemporal reconciliation between conflicting viewpoints

about the effect of inequality on economic growth

Underlines the role of inequality in triggering socio-political transition

(Galor-Moav-Vollrath (2009), Galor-Moav (2006))

Omer Ozak Inequality and Growth Growth & Comparative Development 11 / 73

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The Modern Perspective The Unified Approach

A unified theory of inequality and economic development

Galor and Moav (2004):

Captures the changing role of inequality in the growth process

Unifies the Classical and the Modern Paradigms

Provides an intertemporal reconciliation between conflicting viewpoints

about the effect of inequality on economic growth

Underlines the role of inequality in triggering socio-political transition

(Galor-Moav-Vollrath (2009), Galor-Moav (2006))

Omer Ozak Inequality and Growth Growth & Comparative Development 11 / 73

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The Modern Perspective The Unified Approach

A unified theory of inequality and economic development

Galor and Moav (2004):

Captures the changing role of inequality in the growth process

Unifies the Classical and the Modern Paradigms

Provides an intertemporal reconciliation between conflicting viewpoints

about the effect of inequality on economic growth

Underlines the role of inequality in triggering socio-political transition

(Galor-Moav-Vollrath (2009), Galor-Moav (2006))

Omer Ozak Inequality and Growth Growth & Comparative Development 11 / 73

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The Modern Perspective The Unified Approach

A Unified Theory of Inequality and Development

A unified theory of the dynamic implications of inequality on the growthprocess

Places the dominating modern theories within a broader unified struc-ture

Provides an intertemporal reconciliation between the Classical view-point and the Modern perspective

Omer Ozak Inequality and Growth Growth & Comparative Development 12 / 73

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The Modern Perspective The Unified Approach

A Unified Theory of Inequality and Development

A unified theory of the dynamic implications of inequality on the growthprocess

Places the dominating modern theories within a broader unified struc-ture

Provides an intertemporal reconciliation between the Classical view-point and the Modern perspective

Omer Ozak Inequality and Growth Growth & Comparative Development 12 / 73

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The Modern Perspective The Unified Approach

A Unified Theory of Inequality and Development

A unified theory of the dynamic implications of inequality on the growthprocess

Places the dominating modern theories within a broader unified struc-ture

Provides an intertemporal reconciliation between the Classical view-point and the Modern perspective

Omer Ozak Inequality and Growth Growth & Comparative Development 12 / 73

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The Modern Perspective The Unified Approach

A Unified Theory of Inequality and Development

A unified theory of the dynamic implications of inequality on the growthprocess

Places the dominating modern theories within a broader unified struc-ture

Provides an intertemporal reconciliation between the Classical view-point and the Modern perspective

Omer Ozak Inequality and Growth Growth & Comparative Development 12 / 73

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The Modern Perspective The Unified Approach

Main Hypothesis

The replacement of physical capital accumulation by human capital accu-

mulation as a prime engine of economic growth has changed the qualitative

impact of inequality on the process of development

Early stages of industrialization: physical capital accumulation is a main en-

gine of growth =⇒Inequality enhanced development by channeling resources towardsindividuals whose marginal propensity to save is higher

Later stages of development: the return to human capital increases due to

capital-skill complementarity and human capital became the prime engine of

growth =⇒Inequality, due to credit constraints, is harmful for growth

Omer Ozak Inequality and Growth Growth & Comparative Development 13 / 73

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The Modern Perspective The Unified Approach

Main Hypothesis

The replacement of physical capital accumulation by human capital accu-

mulation as a prime engine of economic growth has changed the qualitative

impact of inequality on the process of development

Early stages of industrialization: physical capital accumulation is a main en-

gine of growth =⇒Inequality enhanced development by channeling resources towardsindividuals whose marginal propensity to save is higher

Later stages of development: the return to human capital increases due to

capital-skill complementarity and human capital became the prime engine of

growth =⇒Inequality, due to credit constraints, is harmful for growth

Omer Ozak Inequality and Growth Growth & Comparative Development 13 / 73

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The Modern Perspective The Unified Approach

Main Hypothesis

The replacement of physical capital accumulation by human capital accu-

mulation as a prime engine of economic growth has changed the qualitative

impact of inequality on the process of development

Early stages of industrialization: physical capital accumulation is a main en-

gine of growth =⇒Inequality enhanced development by channeling resources towardsindividuals whose marginal propensity to save is higher

Later stages of development: the return to human capital increases due to

capital-skill complementarity and human capital became the prime engine of

growth =⇒Inequality, due to credit constraints, is harmful for growth

Omer Ozak Inequality and Growth Growth & Comparative Development 13 / 73

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The Modern Perspective The Unified Approach

Main Hypothesis

The replacement of physical capital accumulation by human capital accu-

mulation as a prime engine of economic growth has changed the qualitative

impact of inequality on the process of development

Early stages of industrialization: physical capital accumulation is a main en-

gine of growth =⇒Inequality enhanced development by channeling resources towardsindividuals whose marginal propensity to save is higher

Later stages of development: the return to human capital increases due to

capital-skill complementarity and human capital became the prime engine of

growth =⇒Inequality, due to credit constraints, is harmful for growth

Omer Ozak Inequality and Growth Growth & Comparative Development 13 / 73

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The Modern Perspective The Unified Approach

Main Hypothesis

The replacement of physical capital accumulation by human capital accu-

mulation as a prime engine of economic growth has changed the qualitative

impact of inequality on the process of development

Early stages of industrialization: physical capital accumulation is a main en-

gine of growth =⇒Inequality enhanced development by channeling resources towardsindividuals whose marginal propensity to save is higher

Later stages of development: the return to human capital increases due to

capital-skill complementarity and human capital became the prime engine of

growth =⇒Inequality, due to credit constraints, is harmful for growth

Omer Ozak Inequality and Growth Growth & Comparative Development 13 / 73

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The Modern Perspective The Unified Approach

Main Hypothesis

The replacement of physical capital accumulation by human capital accu-

mulation as a prime engine of economic growth has changed the qualitative

impact of inequality on the process of development

Early stages of industrialization: physical capital accumulation is a main en-

gine of growth =⇒Inequality enhanced development by channeling resources towardsindividuals whose marginal propensity to save is higher

Later stages of development: the return to human capital increases due to

capital-skill complementarity and human capital became the prime engine of

growth =⇒Inequality, due to credit constraints, is harmful for growth

Omer Ozak Inequality and Growth Growth & Comparative Development 13 / 73

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The Modern Perspective The Unified Approach

Central Argument

Fundamental asymmetry between:

Human capital accumulation

Physical capital accumulation

Omer Ozak Inequality and Growth Growth & Comparative Development 14 / 73

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The Modern Perspective The Unified Approach

Central Argument

Fundamental asymmetry between:

Human capital accumulation

Physical capital accumulation

Omer Ozak Inequality and Growth Growth & Comparative Development 14 / 73

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The Modern Perspective The Unified Approach

Central Argument

Fundamental asymmetry between:

Human capital accumulation

Physical capital accumulation

Omer Ozak Inequality and Growth Growth & Comparative Development 14 / 73

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The Modern Perspective The Unified Approach

Central Argument

Fundamental asymmetry between:

Human capital accumulation

Physical capital accumulation

Omer Ozak Inequality and Growth Growth & Comparative Development 14 / 73

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The Modern Perspective The Unified Approach

Human Capital vs. Physical Capital Accumulation

Human capital is embodied in humans =⇒

Physiological constraints subjects its accumulation at the individuallevel to diminishing returns

The accumulation of human capital would be larger if it would bewidely distributed among individuals in society

Physical capital is not embodied in humans =⇒

Physical capital accumulation may benefit from the concentration ofwealth among individuals whose marginal propensity to save is larger

Omer Ozak Inequality and Growth Growth & Comparative Development 15 / 73

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The Modern Perspective The Unified Approach

Human Capital vs. Physical Capital Accumulation

Human capital is embodied in humans =⇒

Physiological constraints subjects its accumulation at the individuallevel to diminishing returns

The accumulation of human capital would be larger if it would bewidely distributed among individuals in society

Physical capital is not embodied in humans =⇒

Physical capital accumulation may benefit from the concentration ofwealth among individuals whose marginal propensity to save is larger

Omer Ozak Inequality and Growth Growth & Comparative Development 15 / 73

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The Modern Perspective The Unified Approach

Human Capital vs. Physical Capital Accumulation

Human capital is embodied in humans =⇒

Physiological constraints subjects its accumulation at the individuallevel to diminishing returns

The accumulation of human capital would be larger if it would bewidely distributed among individuals in society

Physical capital is not embodied in humans =⇒

Physical capital accumulation may benefit from the concentration ofwealth among individuals whose marginal propensity to save is larger

Omer Ozak Inequality and Growth Growth & Comparative Development 15 / 73

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The Modern Perspective The Unified Approach

Human Capital vs. Physical Capital Accumulation

Human capital is embodied in humans =⇒

Physiological constraints subjects its accumulation at the individuallevel to diminishing returns

The accumulation of human capital would be larger if it would bewidely distributed among individuals in society

Physical capital is not embodied in humans =⇒

Physical capital accumulation may benefit from the concentration ofwealth among individuals whose marginal propensity to save is larger

Omer Ozak Inequality and Growth Growth & Comparative Development 15 / 73

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The Modern Perspective The Unified Approach

Human Capital vs. Physical Capital Accumulation

Human capital is embodied in humans =⇒

Physiological constraints subjects its accumulation at the individuallevel to diminishing returns

The accumulation of human capital would be larger if it would bewidely distributed among individuals in society

Physical capital is not embodied in humans =⇒

Physical capital accumulation may benefit from the concentration ofwealth among individuals whose marginal propensity to save is larger

Omer Ozak Inequality and Growth Growth & Comparative Development 15 / 73

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The Modern Perspective The Unified Approach

Human Capital vs. Physical Capital Accumulation

Human capital is embodied in humans =⇒

Physiological constraints subjects its accumulation at the individuallevel to diminishing returns

The accumulation of human capital would be larger if it would bewidely distributed among individuals in society

Physical capital is not embodied in humans =⇒

Physical capital accumulation may benefit from the concentration ofwealth among individuals whose marginal propensity to save is larger

Omer Ozak Inequality and Growth Growth & Comparative Development 15 / 73

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The Modern Perspective The Unified Approach

Inequality and Physical and Human Capital Accumulation

Inequality is conducive for physical capital accumulation, as long asthe marginal propensity to save rises with income

Inequality is harmful for human capital accumulation, as long ascredit constraints are binding

Omer Ozak Inequality and Growth Growth & Comparative Development 16 / 73

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The Modern Perspective The Unified Approach

Inequality and Physical and Human Capital Accumulation

Inequality is conducive for physical capital accumulation, as long asthe marginal propensity to save rises with income

Inequality is harmful for human capital accumulation, as long ascredit constraints are binding

Omer Ozak Inequality and Growth Growth & Comparative Development 16 / 73

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The Modern Perspective The Unified Approach

Inequality and Physical and Human Capital Accumulation

Inequality is conducive for physical capital accumulation, as long asthe marginal propensity to save rises with income

Inequality is harmful for human capital accumulation, as long ascredit constraints are binding

Omer Ozak Inequality and Growth Growth & Comparative Development 16 / 73

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The Modern Perspective The Unified Approach

Inequality and Growth in Different Stages of Development

Inequality stimulates economic growth in stages of development inwhich physical capital accumulation is the prime engine of growth

Inequality is harmful for economic growth in stages of development inwhich human capital accumulation is the prime engine of economicgrowth and credit constraints are still binding

Omer Ozak Inequality and Growth Growth & Comparative Development 17 / 73

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The Modern Perspective The Unified Approach

Inequality and Growth in Different Stages of Development

Inequality stimulates economic growth in stages of development inwhich physical capital accumulation is the prime engine of growth

Inequality is harmful for economic growth in stages of development inwhich human capital accumulation is the prime engine of economicgrowth and credit constraints are still binding

Omer Ozak Inequality and Growth Growth & Comparative Development 17 / 73

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The Modern Perspective The Unified Approach

Inequality and Growth in Different Stages of Development

Inequality stimulates economic growth in stages of development inwhich physical capital accumulation is the prime engine of growth

Inequality is harmful for economic growth in stages of development inwhich human capital accumulation is the prime engine of economicgrowth and credit constraints are still binding

Omer Ozak Inequality and Growth Growth & Comparative Development 17 / 73

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The Galor-Zeira Model

The Galor-Zeira Model

Overlapping-Generations economy

t = 0, 1, 2, 3, ...

One good

3 factors:

K ≡ Physical capital

Ls ≡ Skilled Labor

Lu ≡ Unskilled Labor

Omer Ozak Inequality and Growth Growth & Comparative Development 18 / 73

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The Galor-Zeira Model

The Galor-Zeira Model

Overlapping-Generations economy

t = 0, 1, 2, 3, ...

One good

3 factors:

K ≡ Physical capital

Ls ≡ Skilled Labor

Lu ≡ Unskilled Labor

Omer Ozak Inequality and Growth Growth & Comparative Development 18 / 73

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The Galor-Zeira Model

The Galor-Zeira Model

Overlapping-Generations economy

t = 0, 1, 2, 3, ...

One good

3 factors:

K ≡ Physical capital

Ls ≡ Skilled Labor

Lu ≡ Unskilled Labor

Omer Ozak Inequality and Growth Growth & Comparative Development 18 / 73

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The Galor-Zeira Model

The Galor-Zeira Model

Overlapping-Generations economy

t = 0, 1, 2, 3, ...

One good

3 factors:

K ≡ Physical capital

Ls ≡ Skilled Labor

Lu ≡ Unskilled Labor

Omer Ozak Inequality and Growth Growth & Comparative Development 18 / 73

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The Galor-Zeira Model

The Galor-Zeira Model

Overlapping-Generations economy

t = 0, 1, 2, 3, ...

One good

3 factors:

K ≡ Physical capital

Ls ≡ Skilled Labor

Lu ≡ Unskilled Labor

Omer Ozak Inequality and Growth Growth & Comparative Development 18 / 73

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The Galor-Zeira Model

The Galor-Zeira Model

Overlapping-Generations economy

t = 0, 1, 2, 3, ...

One good

3 factors:

K ≡ Physical capital

Ls ≡ Skilled Labor

Lu ≡ Unskilled Labor

Omer Ozak Inequality and Growth Growth & Comparative Development 18 / 73

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The Galor-Zeira Model

The Galor-Zeira Model

Overlapping-Generations economy

t = 0, 1, 2, 3, ...

One good

3 factors:

K ≡ Physical capital

Ls ≡ Skilled Labor

Lu ≡ Unskilled Labor

Omer Ozak Inequality and Growth Growth & Comparative Development 18 / 73

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The Galor-Zeira Model

The Galor-Zeira Model

Overlapping-Generations economy

t = 0, 1, 2, 3, ...

One good

3 factors:

K ≡ Physical capital

Ls ≡ Skilled Labor

Lu ≡ Unskilled Labor

Omer Ozak Inequality and Growth Growth & Comparative Development 18 / 73

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The Galor-Zeira Model

Production

Total output producedYt = Y s

t + Y ut

Production in the skilled-intensive sector:

Y st = F (Kt , L

st ) ≡ Lst f (kt); kt ≡ Kt/L

st

Production in the unskilled-intensive sector:

Y ut = aLut

Omer Ozak Inequality and Growth Growth & Comparative Development 19 / 73

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The Galor-Zeira Model

Production

Total output producedYt = Y s

t + Y ut

Production in the skilled-intensive sector:

Y st = F (Kt , L

st ) ≡ Lst f (kt); kt ≡ Kt/L

st

Production in the unskilled-intensive sector:

Y ut = aLut

Omer Ozak Inequality and Growth Growth & Comparative Development 19 / 73

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The Galor-Zeira Model

Production

Total output producedYt = Y s

t + Y ut

Production in the skilled-intensive sector:

Y st = F (Kt , L

st ) ≡ Lst f (kt); kt ≡ Kt/L

st

Production in the unskilled-intensive sector:

Y ut = aLut

Omer Ozak Inequality and Growth Growth & Comparative Development 19 / 73

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The Galor-Zeira Model

Production

Total output producedYt = Y s

t + Y ut

Production in the skilled-intensive sector:

Y st = F (Kt , L

st ) ≡ Lst f (kt); kt ≡ Kt/L

st

Production in the unskilled-intensive sector:

Y ut = aLut

Omer Ozak Inequality and Growth Growth & Comparative Development 19 / 73

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The Galor-Zeira Model

Inverse Demand for Factors

Capital:rt = f ′(kt) ≡ r(kt)

Skilled labor:w st = f (kt)− f ′(kt)kt ≡ w s(kt)

Unskilled labor:wut = a ≡ wu

Omer Ozak Inequality and Growth Growth & Comparative Development 20 / 73

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The Galor-Zeira Model

Inverse Demand for Factors

Capital:rt = f ′(kt) ≡ r(kt)

Skilled labor:w st = f (kt)− f ′(kt)kt ≡ w s(kt)

Unskilled labor:wut = a ≡ wu

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The Galor-Zeira Model

Inverse Demand for Factors

Capital:rt = f ′(kt) ≡ r(kt)

Skilled labor:w st = f (kt)− f ′(kt)kt ≡ w s(kt)

Unskilled labor:wut = a ≡ wu

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The Galor-Zeira Model

Factor Prices

Small open economy

World interest = r

=⇒rt = r

kt = f ′−1(r) ≡ k

w st = w s(k) ≡ w s

=⇒(rt ,w

st ,w

ut ) = (r ,w s ,wu) ∀t

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The Galor-Zeira Model

Factor Prices

Small open economy

World interest = r

=⇒rt = r

kt = f ′−1(r) ≡ k

w st = w s(k) ≡ w s

=⇒(rt ,w

st ,w

ut ) = (r ,w s ,wu) ∀t

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The Galor-Zeira Model

Factor Prices

Small open economy

World interest = r

=⇒rt = r

kt = f ′−1(r) ≡ k

w st = w s(k) ≡ w s

=⇒(rt ,w

st ,w

ut ) = (r ,w s ,wu) ∀t

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The Galor-Zeira Model

Factor Prices

Small open economy

World interest = r

=⇒rt = r

kt = f ′−1(r) ≡ k

w st = w s(k) ≡ w s

=⇒(rt ,w

st ,w

ut ) = (r ,w s ,wu) ∀t

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The Galor-Zeira Model Individuals

Individuals

Continuum of measure 1

Each Individual has 1 parent and 1 child

Identical in:

Preferences

Innate abilities

Differ in:

Parental income ⇒ Inv’t in HC

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The Galor-Zeira Model Individuals

Individuals

Continuum of measure 1

Each Individual has 1 parent and 1 child

Identical in:

Preferences

Innate abilities

Differ in:

Parental income ⇒ Inv’t in HC

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The Galor-Zeira Model Individuals

Individuals

Continuum of measure 1

Each Individual has 1 parent and 1 child

Identical in:

Preferences

Innate abilities

Differ in:

Parental income ⇒ Inv’t in HC

Omer Ozak Inequality and Growth Growth & Comparative Development 22 / 73

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The Galor-Zeira Model Individuals

Individuals

Continuum of measure 1

Each Individual has 1 parent and 1 child

Identical in:

Preferences

Innate abilities

Differ in:

Parental income ⇒ Inv’t in HC

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The Galor-Zeira Model Individuals

Individuals

Continuum of measure 1

Each Individual has 1 parent and 1 child

Identical in:

Preferences

Innate abilities

Differ in:

Parental income ⇒ Inv’t in HC

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The Galor-Zeira Model Individuals

Member of Generation t: Period of Life

First period of life (Period t):

[invest in HC] or [work as unskilled]

Second period of life (Period t + 1):

[work as unskilled / no inv’t in HC] or [work as skilled / inv’t in HC in1st period]

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The Galor-Zeira Model Individuals

Member of Generation t: Period of Life

First period of life (Period t):

[invest in HC] or [work as unskilled]

Second period of life (Period t + 1):

[work as unskilled / no inv’t in HC] or [work as skilled / inv’t in HC in1st period]

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The Galor-Zeira Model Individuals

Member of Generation t: Period of Life

First period of life (Period t):

[invest in HC] or [work as unskilled]

Second period of life (Period t + 1):

[work as unskilled / no inv’t in HC] or [work as skilled / inv’t in HC in1st period]

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The Galor-Zeira Model Individuals

Member of Generation t: Endowment and Preferences

Time endowment:

1 units of time in each period

Capital endowment:

bt ≡ capital inherited in 1st period

Preferences:

ut = α ln ct+1 + (1− α) ln bt+1 α ∈ (0, 1)

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The Galor-Zeira Model Individuals

Member of Generation t: Endowment and Preferences

Time endowment:

1 units of time in each period

Capital endowment:

bt ≡ capital inherited in 1st period

Preferences:

ut = α ln ct+1 + (1− α) ln bt+1 α ∈ (0, 1)

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The Galor-Zeira Model Individuals

Member of Generation t: Endowment and Preferences

Time endowment:

1 units of time in each period

Capital endowment:

bt ≡ capital inherited in 1st period

Preferences:

ut = α ln ct+1 + (1− α) ln bt+1 α ∈ (0, 1)

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The Galor-Zeira Model Individuals

Member of Generation t: Endowment and Preferences

Time endowment:

1 units of time in each period

Capital endowment:

bt ≡ capital inherited in 1st period

Preferences:

ut = α ln ct+1 + (1− α) ln bt+1 α ∈ (0, 1)

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The Galor-Zeira Model Individuals

Member of Generation t: Budget Constraint

Second period budget constraint:

ct+1 + bt+1 ≤ ωt+1

ct+1 ≡ consumption

bt+1 ≡ transfers to offspring

ωt+1 ≡ wealth in period t + 1

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The Galor-Zeira Model Individuals

Member of Generation t: Budget Constraint

Second period budget constraint:

ct+1 + bt+1 ≤ ωt+1

ct+1 ≡ consumption

bt+1 ≡ transfers to offspring

ωt+1 ≡ wealth in period t + 1

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The Galor-Zeira Model Individuals

Member of Generation t: Budget Constraint

Second period budget constraint:

ct+1 + bt+1 ≤ ωt+1

ct+1 ≡ consumption

bt+1 ≡ transfers to offspring

ωt+1 ≡ wealth in period t + 1

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The Galor-Zeira Model Individuals

Member of Generation t: Budget Constraint

Second period budget constraint:

ct+1 + bt+1 ≤ ωt+1

ct+1 ≡ consumption

bt+1 ≡ transfers to offspring

ωt+1 ≡ wealth in period t + 1

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The Galor-Zeira Model Individuals

Member of Generation t: Optimization

{ct+1, bt+1} = arg max[α ln ct+1 + (1− α) ln bt+1]

s.t. ct+1 + bt+1 ≤ ωt+1

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The Galor-Zeira Model Individuals

Member of Generation t: Optimization

bt+1 = (1− α)ωt+1

ct+1 = αωt+1

Indirect Utility: =⇒

v t = α lnαωt+1 + (1− α) lnωt+1

= [α lnα + (1− α) ln(1− α)] + lnωt+1

=⇒ v t is monotonic increasing in 2nd period wealth, ωt+1

=⇒ maximization of ωt+1, is the basis of occupational choices

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The Galor-Zeira Model Individuals

Member of Generation t: Optimization

bt+1 = (1− α)ωt+1

ct+1 = αωt+1

Indirect Utility: =⇒

v t = α lnαωt+1 + (1− α) lnωt+1

= [α lnα + (1− α) ln(1− α)] + lnωt+1

=⇒ v t is monotonic increasing in 2nd period wealth, ωt+1

=⇒ maximization of ωt+1, is the basis of occupational choices

Omer Ozak Inequality and Growth Growth & Comparative Development 27 / 73

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The Galor-Zeira Model Individuals

Member of Generation t: Optimization

bt+1 = (1− α)ωt+1

ct+1 = αωt+1

Indirect Utility: =⇒

v t = α lnαωt+1 + (1− α) lnωt+1

= [α lnα + (1− α) ln(1− α)] + lnωt+1

=⇒ v t is monotonic increasing in 2nd period wealth, ωt+1

=⇒ maximization of ωt+1, is the basis of occupational choices

Omer Ozak Inequality and Growth Growth & Comparative Development 27 / 73

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The Galor-Zeira Model Individuals

Member of Generation t: Optimization

bt+1 = (1− α)ωt+1

ct+1 = αωt+1

Indirect Utility: =⇒

v t = α lnαωt+1 + (1− α) lnωt+1

= [α lnα + (1− α) ln(1− α)] + lnωt+1

=⇒ v t is monotonic increasing in 2nd period wealth, ωt+1

=⇒ maximization of ωt+1, is the basis of occupational choices

Omer Ozak Inequality and Growth Growth & Comparative Development 27 / 73

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The Galor-Zeira Model Individuals

Member of Generation t: Optimization

bt+1 = (1− α)ωt+1

ct+1 = αωt+1

Indirect Utility: =⇒

v t = α lnαωt+1 + (1− α) lnωt+1

= [α lnα + (1− α) ln(1− α)] + lnωt+1

=⇒ v t is monotonic increasing in 2nd period wealth, ωt+1

=⇒ maximization of ωt+1, is the basis of occupational choices

Omer Ozak Inequality and Growth Growth & Comparative Development 27 / 73

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The Galor-Zeira Model Occupational Choice

Fundamental Assumptions

Imperfect Capital Markets:r < i (A1)

r ≡ interest rate for lender

i ≡ interest rate for borrowers (for inv’t in HC)

Fixed cost of education (Indivisibility of inv’t in HC) Weighted average of the

payments to teachers, administrators, and maintenance workers in the school system (i.e., weighted average of the

wages skilled and unskilled workers):

CH = θw s + (1− θ)wu ≡ h > 0 θ ∈ [0, 1] (A2)

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The Galor-Zeira Model Occupational Choice

Fundamental Assumptions

Imperfect Capital Markets:r < i (A1)

r ≡ interest rate for lender

i ≡ interest rate for borrowers (for inv’t in HC)

Fixed cost of education (Indivisibility of inv’t in HC) Weighted average of the

payments to teachers, administrators, and maintenance workers in the school system (i.e., weighted average of the

wages skilled and unskilled workers):

CH = θw s + (1− θ)wu ≡ h > 0 θ ∈ [0, 1] (A2)

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The Galor-Zeira Model Occupational Choice

Income: Unskilled Individuals

ωut+1 = (wu + bt)(1 + r) + wu

= wu(2 + r) + (1 + r)bt

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The Galor-Zeira Model Occupational Choice

Income: Unskilled Individuals

ωut+1 = (wu + bt)(1 + r) + wu

= wu(2 + r) + (1 + r)bt

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The Galor-Zeira Model Occupational Choice

Income: Unskilled Individuals

ωut+1 = (wu + bt)(1 + r) + wu

= wu(2 + r) + (1 + r)bt

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The Galor-Zeira Model Occupational Choice

Income: Skilled Individuals

ωst+1 =

w s − (h − bt)(1 + i) if bt ≤ h

w s + (bt − h)(1 + r) if bt ≥ h

=⇒

ωst+1 =

w s − (1 + i)h + (1 + i)bt if bt ≤ h

w s − (1 + r)h + (1 + r)bt if bt ≥ h

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The Galor-Zeira Model Occupational Choice

Income: Skilled Individuals

ωst+1 =

w s − (h − bt)(1 + i) if bt ≤ h

w s + (bt − h)(1 + r) if bt ≥ h

=⇒

ωst+1 =

w s − (1 + i)h + (1 + i)bt if bt ≤ h

w s − (1 + r)h + (1 + r)bt if bt ≥ h

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The Galor-Zeira Model Occupational Choice

Assumptions

Investment in human capital is not beneficial for individuals who mustfinance the entire cost of education via borrowing

w s − (1 + i)h < 0 (A3)

Investment in human capital is beneficial for individuals who canfinance the entire cost of education without borrowing

w s − (1 + r)h > wu(2 + r) (A4)

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The Galor-Zeira Model Occupational Choice

Assumptions

Investment in human capital is not beneficial for individuals who mustfinance the entire cost of education via borrowing

w s − (1 + i)h < 0 (A3)

Investment in human capital is beneficial for individuals who canfinance the entire cost of education without borrowing

w s − (1 + r)h > wu(2 + r) (A4)

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The Galor-Zeira Model Occupational Choice

Income from Being Unskilled Worker

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The Galor-Zeira Model Occupational Choice

Income from Being Unskilled Worker

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The Galor-Zeira Model Occupational Choice

Income from Being Skilled Worker: Borrowers

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The Galor-Zeira Model Occupational Choice

Income from Being Skilled Worker: Borrowers

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The Galor-Zeira Model Occupational Choice

Income from Being Skilled Worker: Borrowers

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The Galor-Zeira Model Occupational Choice

Income from Being Skilled Worker: Borrowers

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The Galor-Zeira Model Occupational Choice

Income from Being Skilled Worker: Lenders

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The Galor-Zeira Model Occupational Choice

Bequest and Occupational Choice

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The Galor-Zeira Model Occupational Choice

Bequest and Occupational Choice

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The Galor-Zeira Model Occupational Choice

Bequest and Occupational Choice

bt

< f → xut+1 > x st+1 (individual t becomes unskilled)

> f → xut+1 < x st+1 (individual t becomes skilled)

where

f =wu(2 + r)− [w s − (1 + i)h]

i − r> 0

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The Galor-Zeira Model Occupational Choice

Bequest and Occupational Choice

bt

< f → xut+1 > x st+1 (individual t becomes unskilled)

> f → xut+1 < x st+1 (individual t becomes skilled)

where

f =wu(2 + r)− [w s − (1 + i)h]

i − r> 0

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The Galor-Zeira Model Bequest Dynamics

Bequest Dynamics

bt+1 = (1− α)xt+1

bt+1 =

(1− α)[wu(2 + r) + (1 + r)bt ] bt ∈ [0, f ]

(1− α)[w s − (1 + i)h + (1 + i)bt ] bt ∈ [f , h]

(1− α)[w s − (1 + r)h + (1 + r)bt ] bt ∈ [h,∞]

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The Galor-Zeira Model Bequest Dynamics

Bequest Dynamics

bt+1 = (1− α)xt+1

bt+1 =

(1− α)[wu(2 + r) + (1 + r)bt ] bt ∈ [0, f ]

(1− α)[w s − (1 + i)h + (1 + i)bt ] bt ∈ [f , h]

(1− α)[w s − (1 + r)h + (1 + r)bt ] bt ∈ [h,∞]

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The Galor-Zeira Model Bequest Dynamics

Bequest Dynamics: Sufficiet Conditions for Multiplicity of Steady-Sate

(1− α)(1 + r) < 1

(1− α)(1 + i) > 1(A5)

(1− α)w s > h (A6)

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The Galor-Zeira Model Bequest Dynamics

Bequest Dynamics

Omer Ozak Inequality and Growth Growth & Comparative Development 44 / 73

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The Galor-Zeira Model Bequest Dynamics

Bequest Dynamics: Multiple Steady-State Equilibrium

Omer Ozak Inequality and Growth Growth & Comparative Development 45 / 73

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The Galor-Zeira Model Bequest Dynamics

Bequest Dynamics: Stability of High Bequest Equilibrium

Omer Ozak Inequality and Growth Growth & Comparative Development 46 / 73

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The Galor-Zeira Model Bequest Dynamics

Bequest Dynamics: Stability of Steady- State Equilibria

Omer Ozak Inequality and Growth Growth & Comparative Development 47 / 73

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The Galor-Zeira Model Inequality and Skill Composition

The Distribution of the Inheritance in Period t

Omer Ozak Inequality and Growth Growth & Comparative Development 48 / 73

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The Galor-Zeira Model Inequality and Skill Composition

Income Distribution and the Long Run Decomposition of the Labor Force

ξt(bt) ≡ Distribution of inheritance at time t

=⇒

Lt =

∫ ∞0

ξ(bt)dbt ≡ 1

Omer Ozak Inequality and Growth Growth & Comparative Development 49 / 73

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The Galor-Zeira Model Inequality and Skill Composition

The Distribution of the Inheritance in Period t

Omer Ozak Inequality and Growth Growth & Comparative Development 50 / 73

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The Galor-Zeira Model Inequality and Skill Composition

Income Distribution of the Long Run Decomposition of the Labor Force

limt→∞ lut =∫ g

0 ξt(bt)dbt ≡ lu

limt→∞ l st =∫∞g ξt(bt)dbt ≡ l s

where∂ l s/∂g < 0

and

g =(1− α)[(1 + i)h − w s ]

(1− α)(1 + i)− 1> 0

Omer Ozak Inequality and Growth Growth & Comparative Development 51 / 73

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The Galor-Zeira Model Inequality and Skill Composition

Income Distribution of the Long Run Decomposition of the Labor Force

limt→∞ lut =∫ g

0 ξt(bt)dbt ≡ lu

limt→∞ l st =∫∞g ξt(bt)dbt ≡ l s

where∂ l s/∂g < 0

and

g =(1− α)[(1 + i)h − w s ]

(1− α)(1 + i)− 1> 0

Omer Ozak Inequality and Growth Growth & Comparative Development 51 / 73

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The Galor-Zeira Model Inequality and Skill Composition

Income Distribution of the Long Run Decomposition of the Labor Force

limt→∞ lut =∫ g

0 ξt(bt)dbt ≡ lu

limt→∞ l st =∫∞g ξt(bt)dbt ≡ l s

where∂ l s/∂g < 0

and

g =(1− α)[(1 + i)h − w s ]

(1− α)(1 + i)− 1> 0

Omer Ozak Inequality and Growth Growth & Comparative Development 51 / 73

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The Galor-Zeira Model Inequality and Skill Composition

Income Distribution of Skill Composition

Omer Ozak Inequality and Growth Growth & Comparative Development 52 / 73

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The Galor-Zeira Model Inequality and Skill Composition

Income Distribution of Skill Composition

Omer Ozak Inequality and Growth Growth & Comparative Development 53 / 73

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The Galor-Zeira Model Skill Composition and Income Per Capita

Income Per Capita in the Long Run

Income of a skilled individual in the second period of life (wage and capital

income)

I s2 = w s + (bs − h)r

Income of an unskilled individual in the second period of life (wage and

capital income)

I u2 = wu + (bu + wu)r

Income of an unskilled individual in the first period of life (only wage income)

I u1 = wu

Omer Ozak Inequality and Growth Growth & Comparative Development 54 / 73

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The Galor-Zeira Model Skill Composition and Income Per Capita

Income Per Capita in the Long Run

Income of a skilled individual in the second period of life (wage and capital

income)

I s2 = w s + (bs − h)r

Income of an unskilled individual in the second period of life (wage and

capital income)

I u2 = wu + (bu + wu)r

Income of an unskilled individual in the first period of life (only wage income)

I u1 = wu

Omer Ozak Inequality and Growth Growth & Comparative Development 54 / 73

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The Galor-Zeira Model Skill Composition and Income Per Capita

Income Per Capita in the Long Run

Income of a skilled individual in the second period of life (wage and capital

income)

I s2 = w s + (bs − h)r

Income of an unskilled individual in the second period of life (wage and

capital income)

I u2 = wu + (bu + wu)r

Income of an unskilled individual in the first period of life (only wage income)

I u1 = wu

Omer Ozak Inequality and Growth Growth & Comparative Development 54 / 73

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The Galor-Zeira Model Skill Composition and Income Per Capita

Income Per Capita in the Long Run

Aggregate income in the steady-state

Y = I s2 ls + I u2 l

u + I u1 lu

Aggregate income (note: l s + lu = 1)

Y = [w s − rh + r bs ]l s + [wu(2 + r) + r bu](1− l s)

= wu(2 + r) + r bu + [(w s − rh)− wu(2 + r) + (bs − bu)]l s

Income per capitay = Y /2

Omer Ozak Inequality and Growth Growth & Comparative Development 55 / 73

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The Galor-Zeira Model Skill Composition and Income Per Capita

Income Per Capita in the Long Run

Aggregate income in the steady-state

Y = I s2 ls + I u2 l

u + I u1 lu

Aggregate income (note: l s + lu = 1)

Y = [w s − rh + r bs ]l s + [wu(2 + r) + r bu](1− l s)

= wu(2 + r) + r bu + [(w s − rh)− wu(2 + r) + (bs − bu)]l s

Income per capitay = Y /2

Omer Ozak Inequality and Growth Growth & Comparative Development 55 / 73

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The Galor-Zeira Model Skill Composition and Income Per Capita

Income Per Capita in the Long Run

Aggregate income in the steady-state

Y = I s2 ls + I u2 l

u + I u1 lu

Aggregate income (note: l s + lu = 1)

Y = [w s − rh + r bs ]l s + [wu(2 + r) + r bu](1− l s)

= wu(2 + r) + r bu + [(w s − rh)− wu(2 + r) + (bs − bu)]l s

Income per capitay = Y /2

Omer Ozak Inequality and Growth Growth & Comparative Development 55 / 73

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The Galor-Zeira Model Skill Composition and Income Per Capita

Skill Composition and Income Per Capita in the Long Run

An increase in the fraction of skilled workers increases income percapita in the steady-state

∂y

∂ l s= [(w s − rh)− wu(2 + r) + (bs − bu)]/2 > 0

sincew s − (1 + r)h > wu(2 + r)

bs > bu

An increase in g reduces income per capita in the steady-state

∂y

∂g=∂y

∂ l s∂ l s

∂g< 0

Omer Ozak Inequality and Growth Growth & Comparative Development 56 / 73

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The Galor-Zeira Model Skill Composition and Income Per Capita

Skill Composition and Income Per Capita in the Long Run

An increase in the fraction of skilled workers increases income percapita in the steady-state

∂y

∂ l s= [(w s − rh)− wu(2 + r) + (bs − bu)]/2 > 0

sincew s − (1 + r)h > wu(2 + r)

bs > bu

An increase in g reduces income per capita in the steady-state

∂y

∂g=∂y

∂ l s∂ l s

∂g< 0

Omer Ozak Inequality and Growth Growth & Comparative Development 56 / 73

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The Galor-Zeira Model Skill Composition and Income Per Capita

Skill Composition and Income Per Capita in the Long Run

An increase in the fraction of skilled workers increases income percapita in the steady-state

∂y

∂ l s= [(w s − rh)− wu(2 + r) + (bs − bu)]/2 > 0

sincew s − (1 + r)h > wu(2 + r)

bs > bu

An increase in g reduces income per capita in the steady-state

∂y

∂g=∂y

∂ l s∂ l s

∂g< 0

Omer Ozak Inequality and Growth Growth & Comparative Development 56 / 73

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Inequality and Economic Development

Inequality and Development: Rich Economies

Omer Ozak Inequality and Growth Growth & Comparative Development 57 / 73

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Inequality and Economic Development

Rich Economies: Inequality is Harmful for Development

Inequality reduces human capital formation

Omer Ozak Inequality and Growth Growth & Comparative Development 58 / 73

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Inequality and Economic Development

Rich Economies: Inequality is Harmful for Development

Omer Ozak Inequality and Growth Growth & Comparative Development 59 / 73

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Inequality and Economic Development

Rich Economies: Inequality is Harmful for Development

Omer Ozak Inequality and Growth Growth & Comparative Development 60 / 73

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Inequality and Economic Development

Inequality and Development: Poor Economies

Omer Ozak Inequality and Growth Growth & Comparative Development 61 / 73

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Inequality and Economic Development

Poor Economies: Inequality may Benefit Development

Inequality stimulates human capital formation

Omer Ozak Inequality and Growth Growth & Comparative Development 62 / 73

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Inequality and Economic Development

Poor Economies: Inequality may Benefit Development

Omer Ozak Inequality and Growth Growth & Comparative Development 63 / 73

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Inequality and Economic Development Robustness

Robustness

The qualitative results are robust to:

Education cost that is indexed to wages

Labor augmenting technical change

Shocks the outcome of investment in human capital, as long as wagesare endogenous

Concave production function of human capital (Moav (EL, 2002),

Galor-Moav (RES, 2004))

Omer Ozak Inequality and Growth Growth & Comparative Development 64 / 73

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Inequality and Economic Development Robustness

Robustness

The qualitative results are robust to:

Education cost that is indexed to wages

Labor augmenting technical change

Shocks the outcome of investment in human capital, as long as wagesare endogenous

Concave production function of human capital (Moav (EL, 2002),

Galor-Moav (RES, 2004))

Omer Ozak Inequality and Growth Growth & Comparative Development 64 / 73

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Inequality and Economic Development Robustness

Robustness

The qualitative results are robust to:

Education cost that is indexed to wages

Labor augmenting technical change

Shocks the outcome of investment in human capital, as long as wagesare endogenous

Concave production function of human capital (Moav (EL, 2002),

Galor-Moav (RES, 2004))

Omer Ozak Inequality and Growth Growth & Comparative Development 64 / 73

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Inequality and Economic Development Robustness

Robustness

The qualitative results are robust to:

Education cost that is indexed to wages

Labor augmenting technical change

Shocks the outcome of investment in human capital, as long as wagesare endogenous

Concave production function of human capital (Moav (EL, 2002),

Galor-Moav (RES, 2004))

Omer Ozak Inequality and Growth Growth & Comparative Development 64 / 73

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Inequality and Economic Development Robustness

Robustness: Technological Progress and Endogenous Education Cost

Labor Augmenting Technological Progress: increases the productivity of

workers in both the skilled-intensive and the unskilled intensive sector.

Production in the skilled-intensive sector

Y st = F (Kt ,AtL

st ) ≡ AtL

st f (kt); kt ≡ Kt/AtL

st

Production in the unskilled-intensive sector

Y ut = AtaL

ut

Technological progress

At+1 = (1 + λ)At λ > 0.

Omer Ozak Inequality and Growth Growth & Comparative Development 65 / 73

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Inequality and Economic Development Robustness

Robustness: Technological Progress and Endogenous Education Cost

Labor Augmenting Technological Progress: increases the productivity of

workers in both the skilled-intensive and the unskilled intensive sector.

Production in the skilled-intensive sector

Y st = F (Kt ,AtL

st ) ≡ AtL

st f (kt); kt ≡ Kt/AtL

st

Production in the unskilled-intensive sector

Y ut = AtaL

ut

Technological progress

At+1 = (1 + λ)At λ > 0.

Omer Ozak Inequality and Growth Growth & Comparative Development 65 / 73

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Inequality and Economic Development Robustness

Robustness: Technological Progress and Endogenous Education Cost

Labor Augmenting Technological Progress: increases the productivity of

workers in both the skilled-intensive and the unskilled intensive sector.

Production in the skilled-intensive sector

Y st = F (Kt ,AtL

st ) ≡ AtL

st f (kt); kt ≡ Kt/AtL

st

Production in the unskilled-intensive sector

Y ut = AtaL

ut

Technological progress

At+1 = (1 + λ)At λ > 0.

Omer Ozak Inequality and Growth Growth & Comparative Development 65 / 73

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Inequality and Economic Development Robustness

Robustness: Technological Progress and Endogenous Education Cost

Factor Prices

w st = At [f (k)− f ′(k)k] ≡ Atw

s

wut = Ata ≡ Atw

u

rt = r

Omer Ozak Inequality and Growth Growth & Comparative Development 66 / 73

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Inequality and Economic Development Robustness

Cost of Education

Weighted average of the payments to teachers, administrators, and

maintenance workers in the school system

⇒ Weighted average of the wages skilled and unskilled workers

CHt = θAtw

s + (1− θ)Atwu ≡ Ath

Omer Ozak Inequality and Growth Growth & Comparative Development 67 / 73

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Inequality and Economic Development Robustness

Cost of Education

Weighted average of the payments to teachers, administrators, and

maintenance workers in the school system

⇒ Weighted average of the wages skilled and unskilled workers

CHt = θAtw

s + (1− θ)Atwu ≡ Ath

Omer Ozak Inequality and Growth Growth & Comparative Development 67 / 73

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Inequality and Economic Development Robustness

Cost of Education

Weighted average of the payments to teachers, administrators, and

maintenance workers in the school system

⇒ Weighted average of the wages skilled and unskilled workers

CHt = θAtw

s + (1− θ)Atwu ≡ Ath

Omer Ozak Inequality and Growth Growth & Comparative Development 67 / 73

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Inequality and Economic Development Robustness

Income: Unskilled Individuals

xut+1 = (Atwu + bt)(1 + r) + At+1w

u

= Atwu(2 + r + λ) + (1 + r)bt

Omer Ozak Inequality and Growth Growth & Comparative Development 68 / 73

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Inequality and Economic Development Robustness

Income: Unskilled Individuals

xut+1 = (Atwu + bt)(1 + r) + At+1w

u

= Atwu(2 + r + λ) + (1 + r)bt

Omer Ozak Inequality and Growth Growth & Comparative Development 68 / 73

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Inequality and Economic Development Robustness

Income: Skilled Individuals

x st+1 =

At+1w

s − (Ath − bt)(1 + i) if bt ≤ Ath

At+1ws + (bt − Ath)(1 + r) if bt ≥ Ath

=⇒

x st+1 =

At [w

s(1 + λ)− (1 + i)h] + (1 + i)bt if bt ≤ Ath

At [ws(1 + λ)− (1 + r)h] + (1 + r)bt if bt ≥ Ath

Omer Ozak Inequality and Growth Growth & Comparative Development 69 / 73

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Inequality and Economic Development Robustness

Income: Skilled Individuals

x st+1 =

At+1w

s − (Ath − bt)(1 + i) if bt ≤ Ath

At+1ws + (bt − Ath)(1 + r) if bt ≥ Ath

=⇒

x st+1 =

At [w

s(1 + λ)− (1 + i)h] + (1 + i)bt if bt ≤ Ath

At [ws(1 + λ)− (1 + r)h] + (1 + r)bt if bt ≥ Ath

Omer Ozak Inequality and Growth Growth & Comparative Development 69 / 73

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Inequality and Economic Development Robustness

Threshold level of Bequest for Becoming Skilled Worker in Period t

f =At{wu(2 + r)− [w s − (1 + i)h]− λ(w s − wu)}

(i − r)

ftAt

=At{wu(2 + r)− [w s − (1 + i)h]− λ(w s − wu)}

(i − r)≡ f > 0

for

wu(2 + r) > [w s−(1 + i)h] + λ(w s−wu)

Omer Ozak Inequality and Growth Growth & Comparative Development 70 / 73

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Inequality and Economic Development Robustness

Threshold level of Bequest for Becoming Skilled Worker in Period t

f =At{wu(2 + r)− [w s − (1 + i)h]− λ(w s − wu)}

(i − r)

ftAt

=At{wu(2 + r)− [w s − (1 + i)h]− λ(w s − wu)}

(i − r)≡ f > 0

for

wu(2 + r) > [w s−(1 + i)h] + λ(w s−wu)

Omer Ozak Inequality and Growth Growth & Comparative Development 70 / 73

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Inequality and Economic Development Robustness

Threshold level of Bequest for Becoming Skilled Worker in Period t

f =At{wu(2 + r)− [w s − (1 + i)h]− λ(w s − wu)}

(i − r)

ftAt

=At{wu(2 + r)− [w s − (1 + i)h]− λ(w s − wu)}

(i − r)≡ f > 0

for

wu(2 + r) > [w s−(1 + i)h] + λ(w s−wu)

Omer Ozak Inequality and Growth Growth & Comparative Development 70 / 73

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Inequality and Economic Development Robustness

Bequest Dynamics

bt+1 =

(1− α){Atw

u(2 + r + λ) + (1 + r)bt} bt∈ [0, f ]

(1− α){At [ws(1 + λ)− (1 + i)h] + (1 + i)bt} bt∈ [f ,Ath]

(1− α){At [ws(1 + λ)− (1 + r)h] + (1 + r)bt} bt∈ [Ath,∞]

Omer Ozak Inequality and Growth Growth & Comparative Development 71 / 73

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Inequality and Economic Development Robustness

Bequest Dynamics

Let bt+1 ≡ bt+1At+1

bt+1 =

[1−α1+λ

]{wu(2 + r + λ) + (1 + r)bt} bt∈ [0, (f )]

[1−α1+λ

]{[w s(1 + λ)− (1 + i)h] + (1 + i)bt} bt∈ [f , h]

[1−α1+λ

]{[w s(1 + λ)− (1 + r)h] + (1 + r)bt} bt∈ [h,∞]

⇒ The dynamical system is unaffected qualitatively by labor-augmenting

technological progress

Omer Ozak Inequality and Growth Growth & Comparative Development 72 / 73

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Inequality and Economic Development Robustness

Bequest Dynamics

Let bt+1 ≡ bt+1At+1

bt+1 =

[1−α1+λ

]{wu(2 + r + λ) + (1 + r)bt} bt∈ [0, (f )]

[1−α1+λ

]{[w s(1 + λ)− (1 + i)h] + (1 + i)bt} bt∈ [f , h]

[1−α1+λ

]{[w s(1 + λ)− (1 + r)h] + (1 + r)bt} bt∈ [h,∞]

⇒ The dynamical system is unaffected qualitatively by labor-augmenting

technological progress

Omer Ozak Inequality and Growth Growth & Comparative Development 72 / 73

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Inequality and Economic Development Robustness

Sufficient Conditions for Multiple Steady-States

(1− α)(1 + r) < (1 + λ)

(1− α)(1 + i) > (1 + λ)

w s(1 + λ)− (1 + i)h < 0

⇒ The system is characterized by multiple steady-state, where theunstable equilibrium

g =(1− α)[(1 + i)h − w s(1 + λ)]

[(1− α)(i + i)− (1 + λ)]> 0

Omer Ozak Inequality and Growth Growth & Comparative Development 73 / 73


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