Inequality and the Process of Development. Lecture II: A Uni ed Theory of Inequality and Development

Transcription

1 The Classical Approach The Modern Approach CICSE Lectures, Naples Lecture II: of Inequality and Development June 9, 2009

2 Objectives The Classical Approach The Modern Approach A uni ed theory of inequality and economic development (Galor and Moav (2004): Captures the changing role of inequality in the growth process Uni es the Classical and the Modern Paradigms Provides an intertemporal reconciliation between con icting viewpoints about the e ect of inequality on economic growth Generates novel testable predictions that may resolve empirical disputes about the relationship between inequality and growth

3 The Classical Approach The Classical Approach The Modern Approach Inequality is bene cial for growth 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

4 The Classical Approach The Modern Approach The Credit Market Imperfections Approach: Inequality is harmful for growth CMI increases the cost of investment in human capital for less endowed individuals Inequality increases the fraction of society for which investment in human capital is suboptimal =) reduces human capital accumulation =) slows down the development process

5 Main Hypothesis Central Argument Mechanism Reconciliation between Various Approaches of A uni ed theory of the dynamic implications of inequality on the growth process Places the dominating modern theories within a broader uni ed structure Provides an intertemporal reconciliation between the Classical viewpoint and the Modern perspective

6 Main Hypothesis Objectives Main Hypothesis Central Argument Mechanism Reconciliation between Various Approaches The replacement of physical capital accumulation by human capital accumulation 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 engine of growth =) Inequality enhanced development by channeling resources towards individuals 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

7 Central Argument Objectives Main Hypothesis Central Argument Mechanism Reconciliation between Various Approaches Fundamental asymmetry between: Human capital accumulation Physical capital accumulation

8 Main Hypothesis Central Argument Mechanism Reconciliation between Various Approaches Human Capital vs. Physical Capital Accumulation Human capital is embodied in humans =) Physiological constraints subjects its accumulation at the individual level to diminishing returns The accumulation of human capital would be larger if it would be widely distributed among individuals in society Physical capital accumulation may bene t from the concentration of wealth among individuals whose marginal propensity to save is larger

9 Main Hypothesis Central Argument Mechanism Reconciliation between Various Approaches Inequality and Physical and Human Capital Accumulation Inequality is conducive for physical capital accumulation, as long as the marginal propensity to save rises with income Inequality is harmful for human capital accumulation, as long as credit constraints are binding

10 Main Hypothesis Central Argument Mechanism Reconciliation between Various Approaches Inequality and Growth in Di erent Stages of Development Inequality stimulates economic growth in stages of development in which physical capital accumulation is the prime engine of growth Inequality is harmful for economic growth in stages of development in which human capital accumulation is the prime engine of economic growth and credit constraints are still binding

11 Early Stages of Industrialization Main Hypothesis Central Argument Mechanism Reconciliation between Various Approaches Labor (and thus human capital) is abundant and physical capital is scarce The return to physical capital is higher than the return to human capital Physical capital accumulation is the main engine of growth =) Inequality is conducive for growth

12 Later Stages of Development Main Hypothesis Central Argument Mechanism Reconciliation between Various Approaches Physical capital accumulation complements human capital The return to human capital increases su ciently so as to induce human capital accumulation (Nelson and Phelps (1966), Shultz (1975), Foster and Rosenzweig (1996)) Investment in human capital is sub-optimal due to CMI ) the return to human capital is higher than on physical capital Human capital accumulation is the main engine of growth =) Inequality is harmful for growth

13 Main Hypothesis Central Argument Mechanism Reconciliation between Various Approaches Reconciliation: The Classical and Modern Approaches A positive e ect of inequality on growth underlined by the Classical Approach re ects early stages of industrialization when physical capital accumulation was the prime engine of growth A negative e ect of inequality on growth underlined by the Modern Approach re ects later stages of development when human capital accumulation becomes a prime engine of growth, and credit constraints are still binding

14 Production Individuals Dynamics The Basic Structure of the Model Overlapping-Generations economy t = 0; 1; 2; 3; ::: One good Two factors: Physical capital (PC) Human Capital (HC)

15 Production Individuals Dynamics The Basic Structure of the Model Output per-capita grows over time due to the accumulation of factors of production. The stock of physical capital: Output produced in the preceding period net of consumption and HC investment The level of HC: Outcome of education decisions, subject to borrowing constraint

16 Production of Final Output Production Individuals Dynamics The output produced at time t : Y t = F (K t ; H t ) H t f (k t ) K t H t - PC - HC (e ciency units) k t K t =H t

17 Factor Prices Objectives Production Individuals Dynamics Demand for factors of production at time t r t = f 0 (k t ) r(k t ) w t = f (k t ) f 0 (k t )k t w(k t )

18 Individuals Objectives Production Individuals Dynamics Continuum of measure 1 Individuals have 1 parent and 1 child Identical in: Preferences Innate abilities Di er in: Parental income ) Inv t in HC

19 Individuals of Generation t Production Individuals Dynamics First period of life (Period t): Human capital formation Second period of life (Period t + 1): Supply their e ciency units of labor Allocate income & inheritance to: (a) Consumption (b) Transfers to children Transfers are allocated to: Finance of o spring s education Saving for o spring s future wealth

20 Production Individuals Dynamics Individual i of Generation t: Wealth Second period wealth: I i t+1 = w t+1 h i t+1 + x i t+1 w t+1 wage h i t+1 e ciency units of labor x i t+1 inheritance

21 Production Individuals Dynamics Individual i of Generation t: Budget Constraint Second Period budget constraint: c i t+1 + b i t+1 I i t+1 c i t+1 b i t+1 consumption transfers to the o spring

22 Production Individuals Dynamics Individual i of Generation t: Intergenerational Transfers Transfer to o spring, bt+1 i, is allocated between: Finance of o spring s education - e i t+1 Saving for o spring s future wealth s i t+1 = b i t+1 e i t+1 Inheritance x i t+1 = s i tr t+1 = (b i t e i t)r t+1

23 Production Individuals Dynamics Individual i of Generation t: Human capital formation E ciency units of labor in period t + 1 h i t+1 = h(e i t) e i t expenditure on education

24 Production Individuals Dynamics Individual i of Generation t: Human capital formation h t+1 h(e t ) 1 e t

25 Production Individuals Dynamics Optimal Inv t in Education of Member i of Generation t In the absence of borrowing constraints: e i t = arg max[w t+1 h(e i t) + (b i t e i t)r t+1 ] e t is unique and identical across members of generation t

26 Production Individuals Dynamics Optimal Inv t in Education of Member i of Generation t e t = 0 if R t+1 > w t+1 h 0 (0) R t+1 w t+1 h(e t ) w t+1 et = 0 e t

27 Production Individuals Dynamics Optimal Inv t in Education of Member i of Generation t e t > 0 if w t+1 h 0 (e t ) = R t+1 w t+1 h(e t ) R t+1 w t+1 e t e t

28 Production Individuals Dynamics Optimal Inv t in Education of Member i of Generation t ~ R(k) ~ w(k)h(e t ) ~ w(k) et = 0 e t

29 Production Individuals Dynamics Optimal Inv t in Education of Member i of Generation t 8 < e t = e(k t+1 ) : = 0 if k t+1 e k > 0 if k t+1 > e k where e 0 (k t+1 ) > 0 if k t+1 > e k

30 Production Individuals Dynamics Borrowing Constraint of Member i of Generation t Individuals cannot borrow to nance the education expenditure of their o spring: e i t = min[e(k t+1 ); b i t]

31 Production Individuals Dynamics Preferences and Transfers of Member i of Generation t Preferences: u i t = (1 ) log c i t+1 + log( + b i t+1) Optimal transfer to o spring: 8 < bt+1 i = b(it+1) i : (I i t+1 ) if I i t+1 0 if I i t+1 where (1 )=

32 Production Individuals Dynamics Optimal transfer of a member i of generation t b i t+1 b i t+1(i i t+1) θ β I i t+1

33 Production Individuals Dynamics Saving of Member i of Generation t 8 < b st i t i if k t+1 k e = : bt i et i if k t+1 > k e Saving rate st+1 i = I t+1 i is increasing in I i t+1

34 Initial Wealth Distribution Production Individuals Dynamics The economy consists of two groups in period 0: Capitalists (R) Fraction of all adult individuals Equally own the initial capital stock Workers (P) Fraction 1 of all adult individuals No ownership over the initial capital stock

35 Factor Accumulation Objectives Production Individuals Dynamics K t+1 = Z 1 0 s i tdi = (b R t e R t ) + (1 )(b P t e P t ) = K(b R t ; b p t ; k t+1 ) H t+1 = Z 1 0 h i t+1di = h(e R t ) + (1 )h(e P t ) = H(b R t ; b P t ; k t+1 )

36 The Capital-Labor Ratio Production Individuals Dynamics k t+1 = K t+1 H t+1 = K(bR t ; b P t ; k t+1 ) H(b R t ; b P t ; k t+1 ) =) k t+1 = (b R t ; b P t )

37 Production Individuals Dynamics The Evolution of Transfers within group i = R,P b i t+1 = maxf[w t+1 h(e i t) + (b i t e i t)r t+1 ]; 0g =) b i t+1 = (b i t; k t+1 ) There exists b k, a critical level of k below which individuals who do not receive parental transfers (i.e., b i t = e i t = 0) do not transfer income to their o spring: w( b k) = b i t+1 = (0; k t+1 ) 8 < : = 0 if k t+1 b k > 0 if k t+1 > b k

38 Production Individuals Dynamics The Evolution of Transfers within Group i =R,P b i t+1 = (bi t; k t+1 ) = (b i t; (b R t ; b P t )) i (b R t ; b P t )

39 The dynamical system Production Individuals Dynamics fb P t ; b R t g 1 t=0 such that: b P t+1 = P (b R t ; b P t ) b R t+1 = R (b R t ; b P t )

40 The Process of Development The Process of Development Testable implications Implications for DC and LDCs References Regime I: PC Accumulation (k e k) Regime II: HC Accumulation (k > k) e Stage I of Regime II ( ~K < K ^K) Stage II of Regime II ( ^K < K < K ) Stage III of Regime II (K > K )

41 The Process of Development Testable implications Implications for DC and LDCs References Regime I: Physical Capital Accumulation Early stages of development (k e k) K is the main engine of growth: HC < K No investment in education No Transfers within Group P Transfers within Group R " Wages " Income inequality "

42 The Process of Development Testable implications Implications for DC and LDCs References The Conditional Dynamical System: Regime I b i t+1 φ(b i t ;k) 45 0 Group P Group R Poverty Trap b(k) b i t

43 Regime I: E ect of Inequality The Process of Development Testable implications Implications for DC and LDCs References Inequality enhances the process development A transfer of wealth from Group R to P =) Aggregate consumption " Aggregate intergenerational transfers # Rate of capital accumulation #

44 The Process of Development Testable implications Implications for DC and LDCs References Regime II: Human Capital Accumulation Mature stages of development: (k > e k) HC is the engine of growth: HC K

45 The Process of Development Testable implications Implications for DC and LDCs References Stage I of Regime II: HC Accumulation by group R Stage I of Regime II ( ~K < K ^K) Members of group P No intergenerational transfers No investment in education Members of group R Wages " Transfers " Expenditure on education " Income inequality "

46 The Process of Development Testable implications Implications for DC and LDCs References The Conditional Dynamical System: Stage I of Regime II b i t+1 φ(b i t ;k) 45 0 Group P Group R Poverty Trap b(k) b i t

47 The Process of Development Testable implications Implications for DC and LDCs References Stage II of Regime II : HC Accumulation by the Poor Stage II of Regime II ( ^K < K < K ) Members of group P (credit constrained): HC > K Start to transfers Start to acquire education Members of group R (not credit constrained): HC = K Invest optimally in human and physical capital

48 The Process of Development Testable implications Implications for DC and LDCs References Conditional Dynamical System: Stage II-III of Regime II b i t φ(b i t ;k) b i t

49 The Process of Development Testable implications Implications for DC and LDCs References Stage II of Regime II: E ect of Inequality More equality is bene cial for the process development A transfer of wealth from group R to group P allows (due to credit constraint) a more e cient allocation of aggregate investment between HC and PC

50 The Process of Development Testable implications Implications for DC and LDCs References Stage III of Regime II : Credit Constraints are not Binding All individuals are not credit constrained: R HC = R K Inequality has no e ect on the process of development

51 The Process of Development Testable implications Implications for DC and LDCs References The changing Role of Inequality in the Development Process 0 ~k Regime I K > H Regime II K H K only engine HC main engine Inequality (+) Inequality (-)

52 E ect of Inequality in Regime II The Process of Development Testable implications Implications for DC and LDCs References ~k ^k k Stage I Stage II Stage III K < H p K < H P K = H K = H R K = H R 2 engines HC main engine 2 engines Inequality (-)

53 Testable Implications The Process of Development Testable implications Implications for DC and LDCs References The CMI approach The e ect on inequality depends on the country s level of income. Inequality is bene cial for poor economies and harmful for rich ones The Uni ed Approach The e ect of inequality on growth depends on the relative return to human and physical capital. The higher is the relative return to human capital the more harmful is inequality for economic growth

54 Implications for DC and LDCS The Process of Development Testable implications Implications for DC and LDCs References The replacement of physical capital accumulation by human capital accumulation as a prime engine of economic growth has changed the impact of inequality on the process of development Inequality stimulates economic growth in stages of development in which physical capital accumulation is the prime engine of growth Inequality is harmful for economic growth in stages of development in which human capital accumulation is the prime engine of economic growth Int l capital in ow to LDCs and the adoption of skilled-biased technologies may place economies directly in the second stage in which inequality is harmful

55 References Objectives The Process of Development Testable implications Implications for DC and LDCs References Main Source: Galor, Oded and Omer Moav, 2004, "From Physical to Human Capital Accumulation:," Review of Economic Studies, 71(4), Related Papers: Galor, Oded and Omer Moav, 2006, "Das Human-Kapital: A Theory of the Demise of the Class Structure," Review of Economic Studies, 73(1), Galor, Oded and Joseph Zeira, 1993, "Income Distribution and Macroeconomics," Review of Economic Studies, 60(1), Galor, Oded and Omer Moav, and Dietrich Vollrath, 2009, "Inequality in Landownership, Human Capital Promoting Institutions and the Great Divergence" Review of Economic Studies, 76(1),