Growth or equality ? Losers and gainers from financial reform - PowerPoint PPT Presentation

Growth or equality ? Losers and gainers from financial reform Costas Azariadis David de la Croix 1

Introduction – general view point Trends towards less regulation of financial markets for household debt: • Liberalization in the OECD in the 80s (e.g. higher loan-to-value ratio, competition between banks and mortgage institution) • In Least Developed Countries (LDC), some argue that less regulation of financial sector could be good for growth. Promoting institutions that can lend to households. • In Eastern Europe, financial reform is under way. Question: What are the consequences of financial reforms ? What are the pros and cons ? Would any group of people object to such reforms ? 2

Introduction – what we do Aim: To understand the welfare effects of liberalizing the market for household debt. Method: Take a model economy where households are prevented from borrowing. Liberalization amounts to an anticipated lifting of all borrowing constraints on households. Look at the consequences on growth, inequality, and on the welfare of particular social groups indexed by age and ability. 3

Introduction – what we know already Japelli and Pagano (QJE, 1994). The level effect of financial deregulation reduces net household saving, slows down physical capital accumulation, and raises yields. Financial deregulation in the eighties has contributed to the decline in national saving and growth rates in the OECD countries. De Gregorio (JME,1996). The growth effect refers to the rise in borrowing for investments in human skills, and the corresponding boost to long-run growth (in small open societies which rely on human capital as their growth engine). Evidence for this channel appears to be mixed. 4

Introduction – specificity of our approach Borrowing limits do not necessarily ration the poor, as it is assumed in the literature. They ration instead the most efficient accumulators of human skills, that is, households with high potential income growth. Physical and human capital need to be studied jointly both because they oppose each other (they compete for funding - if young households go to school longer, they will save less) and because they interact in subtle ways. 5

Introduction – the paper (1) 1. OLG model with heterogeneous households, one consumption good, and two reproducible inputs – physical capital and human capital. + Cobb-Douglas technology and logarithmic utility 2. Models with a perfect loan market and with credit rationing; 3. We prove that the return on capital is always higher in the economy with perfect markets. Effect on output and inequality depends on how common credit rationing was before credit market liberalization; 6

Introduction – the paper (2) 4. Calibration in line with the long-run economic performance of a panel of less developed countries in the 1960’s. Dynamic simulation experiments of financial deregulation. 5. Robustness analysis to changes in technology (CES production). Study whether lifting of borrowing constraints may redirect economic growth towards a poverty trap. 6. Conclusion: sums up the costs and benefits from financial reform. 7

The model – households (1) Time is discrete and goes from 0 to + ∞ . Each generation consists in a continuum of households, with mass expanding at rate n > − 1 . The households of the same generation differ in their innate ability to work when young, ε Y , and when old, ε O . Each individual lives for two periods, youth and old-age. Their utility function: ln c t + β ln d t + 1 , β ∈ R + . 8

The model – households (2) Each young person studies a share λ t of his/her time. First-period budget constraint: ε Y ( 1 − λ t ) w t ¯ h t = c t + s t . (1) Old-age human capital: ψ ′ > 0, ψ ′′ < 0. h t + 1 = ε O ψ ( λ t ) ¯ (2) h t , Old agents consume both labor earnings and capital income: d t + 1 = R t + 1 s t + w t + 1 h t + 1 . (4) 9

The model – households (3) 3 2.5 2 1.5 1 0.5 0.2 0.4 0.6 0.8 1 10

The model – notation We denote the relative wage by: w t + 1 x t ≡ . w t R t + 1 From (1), (2) and (4), lifecycle income is proportional to the inherited human capital ¯ h t : � � ¯ ε Y ( 1 − λ t ) + x t ε O ψ ( λ t ) Ω t = w t h t . We first consider the perfect market equilibrium 11

Perfect market equilibrium – optimal schooling The optimal length of schooling maximizes lifecycle income: ε Y ψ ′ ( λ t ) = . (5) ε O x t Inverting equation (5) we obtain: ϕ ′ > 0, ϕ ( 0 ) = 0. λ t = ϕ ( ε O x t / ε Y ) , From this we compute the growth rate of average human capital g p ( x t ) : � ∞ � ∞ ¯ h t + 1 ε O ψ ( ϕ ( ε O x t / ε Y )) d G ( ε Y , ε O ) . = 1 + g p ( x t ) = (6) ¯ h t 0 0 12

Perfect market equilibrium – optimal saving Optimal savings are computed by max utility s.t. budget constraints (1) and (4): � � w t ¯ βε Y ( 1 − λ t ) − x t ε O ψ ( λ t ) ( 1 + β ) s t = h t . (7) Savings are positive if, and only if, β ( 1 − λ t ) ψ ′ ( λ t ) > ψ ( λ t ) this inequality defines a critical value for schooling, ˜ λ , separating borrowers from lenders: λ t < ˜ λ ⇔ s t > 0. 13

Perfect market equilibrium – the threshold Since λ t is a monotone function ϕ ( . ) of ability, we can define the threshold as bearing on relative ability ε O / ε Y : ε O ε Y < ˜ µ t ⇔ s t > 0. with µ t = ϕ − 1 ( ˜ λ ) ≡ B ˜ . (10) x t x t 14

Perfect market equilibrium – Aggregate savings � ∞ � ∞ β 1 + β w t ¯ s t d G ( ε Y , ε O ) = s t = ¯ h t S p ( x t ) . (11) 0 0 where the function S p ( x t ) is defined as: � ∞ � ∞ ε Y � � 1 − Φ ( ε O x t / ε Y ) d G ( ε Y , ε O ) . S p ( x t ) = 0 0 15

Perfect market equilibrium – firms Constant return to scale technology F ( K t , H t ) Capital – labor ratio: k t = K t / H t Intensive production function f ( k t ) Equilibrium factor prices: f ( k t ) − k t f ′ ( k t ) = ω ( k t ) , w t = f ′ ( k t ) = R ( k t ) . = R t Relative wage x t as a function of ( k t , k t + 1 ) : ω ( k t + 1 ) x t = ω ( k t ) R ( k t + 1 ) . (12) 16

Perfect market equilibrium – equilibrium Average labor supply (per young person) H t is obtained by averaging over young and old: H t = H p ( x t ) ¯ h t . (13) where the function H p ( x t ) is defined as: � ∞ � ∞ 1 ε Y � � 1 − ϕ ( ε O x t / ε Y ) d G ( ε Y , ε O ) . H p ( x t ) = 1 + n + 0 0 17

Perfect market equilibrium – equilibrium The equilibrium condition for financial market: s t ¯ K t + 1 = k t + 1 H t + 1 = 1 + n , Using (6), (11) and (13): S p ( x t ) ( 1 + β ) k t + 1 1 H p ( x t + 1 ) = (14) βω ( k t ) 1 + g p ( x t ) 1 + n 18

Perfect market equilibrium – characterization ( k 0 , ¯ h 0 ) , Given initial conditions a perfect foresight equilibrium can be characterized by a non-negative sequence ( x t , k t + 1 , ¯ h t + 1 ) t � 0 which solves equations (6), (12) and (14). 19

Perfect market equilibrium – Cobb-Douglas This dynamical system becomes recursive when the production function is Cobb- Douglas, f ( k t ) = Ak α t , with complete depreciation of capital. k t + 1 ω ( k t + 1 ) α α ω ( k t ) = ω ( k t ) R ( k t + 1 ) = 1 − α x t , 1 − α Eq.(14) becomes a first-order difference equation in x t : S p ( x t ) ( 1 + β ) α ( 1 − α ) β H p ( x t + 1 ) = 1 1 1 + n . x t 1 + g p ( x t ) 20

Equilibrium with credit rationing Young households cannot credibly commit their future labor income as a collateral against current loans. Individuals are allowed to borrow up to the point where they are indifferent between repaying the loans or defaulting. Since everyone dies at the end of the second period, default is individually optimal since it carries no penalties. The borrowing constraint then takes a very simple form: s t � 0 . 21

Equilibrium with credit rationing – households (1) Rationed households will not participate to the credit market, maximizing instead an autarkic utility function: ln ( 1 − λ t ) + β ln ( ψ ( λ t )) + constants . First order condition: ψ ( λ t ) = βψ ′ ( λ t )( 1 − λ t ) . This defines a unique solution ˜ λ , which does not depend on prices, nor on ability type. Same as the threshold ˜ λ defined earlier. 22

Equilibrium with credit rationing – households (2) Proposition 1 Households whose ability profiles do not rise fast, i.e. ε O / ε Y < ˜ µ t , save a positive amount given by equation (7); their investment in education λ t equals ϕ ( ε O x t / ε Y ) and depends positively on ε O / ε Y . Households with fast rising ability profiles, i.e. ε O / ε Y > ˜ µ t , are credit rationed, and invest the same amount in education, i.e. λ t = ˜ λ = ϕ ( ˜ µ t x t ) . Households with a steep potential earnings profile would like to borrow to afford to study longer, but credit rationing prevents then from doing so. The threshold ˜ µ t depends on prices through equation (10). the proportion of rationed people depends on prices and varies over time. 23

The model – households (3) 0.15 0.2 0.125 0.1 0.1 1 2 3 4 5 0.075 -0.1 0.05 -0.2 0.025 -0.3 -0.4 1 2 3 4 5 24