“Cheap Children and the “Cheap Children and the Persistence of Poverty” Persistence of Poverty” Omer Moav Omer Moav The Economic Journal, 115 The Economic Journal, 115 (January 2005) (January 2005)
INTRODUCTION INTRODUCTION To explain persistence of Theory of fertility and poverty within and across child educational countries choice Evidence: high fertility rates offspring are • Poor households also poor low invest. education • High-income low fertility rates offspring families with high high invest. education income Econ 602 Nelyda Campos Requena
INTRODUCTION INTRODUCTION Key assumption: Individual’s productivity as teachers increases with their own human capital. Minimum time cost of raising a child regardless of the child’s quality is not affected by parental education. price of child quantity Result: ↑ with individuals wage ' price of child quality Econ 602 Nelyda Campos Requena
INTRODUCTION: Value Added INTRODUCTION: Value Added • Simple model: dynasties within a country can converge to one of two equilibria. – Low education – high fertility – High education – low fertility • Extended model: amplifies effect of quality choice on income per-capita capturing diluting effect of fertility on the accumulation of physical capital. • Countries can converge to two different levels of income per capita. – Negative cross-country relationship between fertility-growth – Positive cross-country relationship between education- growth Econ 602 Nelyda Campos Requena
INTRODUCTION: Value Added INTRODUCTION: Value Added Becker et.al .(1990) • Representative agent model • Trade-off between quantity and quality of their offspring • Multiple steady states return to education is lower in poor countries. • Theoretical and empirical limitations: – Poverty trap equ. is a result of a market failure. – Fertility choices may amplify the negative impact of low education investment on income per capita, but they are not the source of multiple equilibria. – In poor economies all families eventually converge to a low- educational equilibrium. Econ 602 Nelyda Campos Requena
INTRODUCTION: Value Added INTRODUCTION: Value Added In this paper • OLG model • Multiple steady states comparative advantage of educated workers in the production of educated children • No restrictive assumptions. • Correlation of education-income within a dynasty is testable. • Educated individuals would invest highly in their offspring’s education, even in poor countries. • Poverty can persist in rich countries, and educated individuals can exist in the long run in poor countries. Econ 602 Nelyda Campos Requena
Importance Importance • From the model we can have an explanation of a fact that we observe in many countries around the world: persistence of poverty with high fertility rates. • Evaluation of policies. Econ 602 Nelyda Campos Requena
Simple Model Simple Model • OLG model over infinite discrete time • Single homogeneous good produced in the economy under CRS technology and using human capital. • Individuals live 2 periods: – First: acquire human capital Child rearing – Second: endowed with 1 unit time Part. labor force Econ 602 Nelyda Campos Requena
Simple Model Simple Model • Preferences: ( ) ( ) u i = 1 − β log c i + β log n i + θ log wh i t t t t + 1 where: β : relative weight given to children (quantity and quality) θ : relative weight given to child quality n i : number of children in a household t w : wage rate per efficiency unit of labor ( ) h + i : level of human capital of each child; h i = h e i t 1 t + 1 t + 1 i e + : level of investment in education of individual i at t. t 1 i c : consumption level t Econ 602 Nelyda Campos Requena
Simple Model Simple Model • Budget constraint: ( ) n w i τ h i + e i + c i ≤ wh i t t t + 1 t t where: τ : min. time cost required for raising a child wh i : full income t i we + : real cost of investment in education (quality) t 1 w h τ i : opp. cost of raising a child (cost of child quantity) t The cost of child quantity increases with h. Econ 602 Nelyda Campos Requena
Simple Model Simple Model ( ) ( ) • Problem: i i i Max 1 − β log c + β log n + θ log wh + t t t 1 ( ) i τ i + i + i ≤ i n w h e c wh t t t + 1 t t s t . i = h h e ( ) t + 1 t + 1 Choice variables: number and quality of children, and consumption. ( ) [ ] ( ) ( ) • Solution: i i i c : c = 1 − β wh = 1 − β wh e t t t t ( ) θ i h e ' ≤ 0 if e i = 0 1 [ ] t + 1 e : − t + 1 = ( ) ( ) + t 1 i > 0 if e 0 h e i τ h e i + e i t + 1 t + 1 t t + 1 β τ $ i ≤ if e e ( ) [ ] ( ) i i t n : n = n e = β i h e t t t $ i > t if e e ( ) ( ) t i i τ h e + φ e t t = $ i ≤ 0 if e e ( ) i i t e = φ e where: t + 1 t $ > i > 0 if e e t Econ 602 Nelyda Campos Requena
Dynamic System Simple Model Dynamic System Simple Model e + t 1 ( ) φ e t e T $ e t e e convergence to high-education, high-income, and low fertility SS e i > e T ⇒ 0 Econ 602 Nelyda Campos Requena
Main Results Simple Model Main Results Simple Model • Lower parent’s education cheaper the children parent’s choice shifts to higher fertility rates lower investment in offspring’s human capital • (quantity cost) relative cost of quantity ↑ τ move to child quality Econ 602 Nelyda Campos Requena
Extended Model Extended Model • Introduce endogenous physical capital accumulation capture effect of fertility on capital per worker amplify effect of quality choice on econ. growth • Explain cross-country income differences and club convergence. • Allow bequeath capital to offspring • 2 inputs: physical and human capital ( ) ( ) = − α α w k 1 Ak ( ) ( ) t H Ak α Y = F K , H = H f k = t t t t t t t ( ) = α α − 1 r k Ak t Econ 602 Nelyda Campos Requena
Extended Model Extended Model ( ) ( ) ( ) • Problem: Max 1 − β log c + β log n + log w h + r s t t t + 1 t + 1 t + 1 t + 1 ( ) n w τ h + w e + s + c ≤ w h + r s t t t t t + 1 t + 1 t t t t t s t . = h h e ( ) t + 1 t + 1 Choice variables: number and quality of children, consumption, and quantity of physical capital transferred to each child. • Solution: ) ( ) [ ] ( c : c = 1 − β w h + r s t t t t t t > 0 if s = 0 ( ) t + 1 h e w = [ ] [ ) t + 1 t + 1 − ∈ ∞ s : r 0 if s 0, ( ) t + 1 t + 1 t + 1 τ h + e w < + t t 1 t → ∞ 0 if s t + 1 ( ) h e ≥ = 0 if e 0 [ ] ( ) t + 1 e : − h e ' t + 1 t + 1 t + 1 τ h + e = 0 if e > 0 t t + 1 t + 1 Econ 602 Nelyda Campos Requena
Dynamic System Extended Model Dynamic System Extended Model k t ee ee kk ( ) e > e ∀ e ∈ e T , e t + 1 t t e < e ∀ e < e T and e > e t + 1 t t t ( ) > ∀ < SS k k k k e t + 1 t t t ( ) k < k ∀ k > k SS e t + 1 t t t e e = = T 0 $ e e = t e e e Econ 602 Nelyda Campos Requena
Main Results Extended Model Main Results Extended Model • Lower parent’s education cheaper the children parent’s choice shifts to higher fertility rates amplified reallocation from child quality to quantity • (quantity cost) relative cost of quantity ↑ τ move to child quality (amplified by the diluting effect on physical capital. Econ 602 Nelyda Campos Requena
Conclusions and Implications Conclusions and Implications • Model offers explanation for the persistence of poverty consistent with the relationship fertility-education, and the cross-country relationship fertility-education-economic growth. • Generation of multiple steady states based on the trade- off between child quality and quantity without imposing restrictive assumptions. • Poor countries fail to catch up with the rich because of insufficient progress in education due to high fertility rates. Econ 602 Nelyda Campos Requena
Conclusions and Implications Conclusions and Implications • Dynamic system generates a poverty trap along with a high-income equilibrium. poor (rich) dynasties with income below (above) a threshold level converge to the low-income (high-income) steady state. if initial average income in society is above the threshold, then in a more equal society, more individuals are above the threshold and more dynasties converge to the high SS • Inequality affects economic growth negatively via its interaction with fertility choice. Econ 602 Nelyda Campos Requena
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