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Introduction Economy Equilibrium From Malthus to Modern Growth From Malthus to Modern Growth Omar Licandro European University Institute April 2009 1 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth Aims 2 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth Aims • Evidence: From Malthusian stagnation to modern growth 2 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth Aims • Evidence: From Malthusian stagnation to modern growth • In Western Europe and until the 19th century, income and population where no growing, then 2 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth Aims • Evidence: From Malthusian stagnation to modern growth • In Western Europe and until the 19th century, income and population where no growing, then • Industrial Revolution: Income growth rates increase substantially 2 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth Aims • Evidence: From Malthusian stagnation to modern growth • In Western Europe and until the 19th century, income and population where no growing, then • Industrial Revolution: Income growth rates increase substantially • Demographic Transition: Population growth initially increases, then reduces 2 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth Aims • Evidence: From Malthusian stagnation to modern growth • In Western Europe and until the 19th century, income and population where no growing, then • Industrial Revolution: Income growth rates increase substantially • Demographic Transition: Population growth initially increases, then reduces • Related issue: Exceptionality of the industrial revolution 2 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth Aims • Evidence: From Malthusian stagnation to modern growth • In Western Europe and until the 19th century, income and population where no growing, then • Industrial Revolution: Income growth rates increase substantially • Demographic Transition: Population growth initially increases, then reduces • Related issue: Exceptionality of the industrial revolution • Theory: Galor and Weil (2000) unify (be more precise) • Malthus theory 2 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth Aims • Evidence: From Malthusian stagnation to modern growth • In Western Europe and until the 19th century, income and population where no growing, then • Industrial Revolution: Income growth rates increase substantially • Demographic Transition: Population growth initially increases, then reduces • Related issue: Exceptionality of the industrial revolution • Theory: Galor and Weil (2000) unify (be more precise) • Malthus theory • Modern growth theory: Solow 2 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth Aims • Evidence: From Malthusian stagnation to modern growth • In Western Europe and until the 19th century, income and population where no growing, then • Industrial Revolution: Income growth rates increase substantially • Demographic Transition: Population growth initially increases, then reduces • Related issue: Exceptionality of the industrial revolution • Theory: Galor and Weil (2000) unify (be more precise) • Malthus theory • Modern growth theory: Solow • Becker’s population theory 2 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth 3 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth Population 4 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth Population • Discrete time model of successive generations 4 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth Population • Discrete time model of successive generations • Individuals live two periods, childhood and adulthood • but, have no independent activity during childhood 4 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth Population • Discrete time model of successive generations • Individuals live two periods, childhood and adulthood • but, have no independent activity during childhood • Notation: 4 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth Population • Discrete time model of successive generations • Individuals live two periods, childhood and adulthood • but, have no independent activity during childhood • Notation: • Cohort t is adult at time t 4 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth Population • Discrete time model of successive generations • Individuals live two periods, childhood and adulthood • but, have no independent activity during childhood • Notation: • Cohort t is adult at time t • The size of adult population is Nt , with Nt+1 = nt Nt 4 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth Population • Discrete time model of successive generations • Individuals live two periods, childhood and adulthood • but, have no independent activity during childhood • Notation: • Cohort t is adult at time t • The size of adult population is Nt , with Nt+1 = nt Nt • nt is the fertility rate (number of kids by adult) 4 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth Preferences 5 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth Preferences • Preferences are, δ > 0, ut = ln(ct ) + δ ln(nt wt+1 ht+1 ) 5 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth Preferences • Preferences are, δ > 0, ut = ln(ct ) + δ ln(nt wt+1 ht+1 ) • The adult member of cohort t cares about: • its own consumption ct , assumed to be larger than a ˜ subsistence level c > 0 • the number of children nt and child earnings wt+1 ht+1 [wages times human capital] 5 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth Preferences • Preferences are, δ > 0, ut = ln(ct ) + δ ln(nt wt+1 ht+1 ) • The adult member of cohort t cares about: • its own consumption ct , assumed to be larger than a ˜ subsistence level c > 0 • the number of children nt and child earnings wt+1 ht+1 [wages times human capital] • Altruism: Diﬀerent from Barro’s dynasties 5 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth Production technology 6 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth Production technology Production technology ct + nt et = (1 − nt φ) At ht working time 6 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth Production technology Production technology ct + nt et = (1 − nt φ) At ht working time • Production • ht is human capital per worker • At is the state of technology • Individuals oﬀer inelastically one unit of the labor endowment • Raising a kid takes a fraction φ ∈ (0, 1) of parents time 6 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth Production technology Production technology ct + nt et = (1 − nt φ) At ht working time • Production • ht is human capital per worker • At is the state of technology • Individuals oﬀer inelastically one unit of the labor endowment • Raising a kid takes a fraction φ ∈ (0, 1) of parents time • Production is allocated to • Consumption • Educating kids: et is education by kid 6 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth Production technology Production technology ct + nt et = (1 − nt φ) At ht working time • Production • ht is human capital per worker • At is the state of technology • Individuals oﬀer inelastically one unit of the labor endowment • Raising a kid takes a fraction φ ∈ (0, 1) of parents time • Production is allocated to • Consumption • Educating kids: et is education by kid Per capita growth At − At−1 ht − ht−1 gt ≡ + At−1 ht−1 TFP human capital 6 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth Technical progress 7 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth Technical progress • Deﬁnition: Technical progress is At − At−1 gAt ≡ At−1 7 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth Technical progress • Deﬁnition: Technical progress is At − At−1 gAt ≡ At−1 • Assumption: βet−1 ¯ gAt = gA (et−1 ) = g + ρ 1 + βet−1 ¯ g > 0 but small, β > 0 and ρ > 0 7 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth Technical progress • Deﬁnition: Technical progress is At − At−1 gAt ≡ At−1 • Assumption: βet−1 ¯ gAt = gA (et−1 ) = g + ρ 1 + βet−1 ¯ g > 0 but small, β > 0 and ρ > 0 ¯ • Exogenous learning makes technical progress positive, gAt ≥ g 7 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth Technical progress • Deﬁnition: Technical progress is At − At−1 gAt ≡ At−1 • Assumption: βet−1 ¯ gAt = gA (et−1 ) = g + ρ 1 + βet−1 ¯ g > 0 but small, β > 0 and ρ > 0 ¯ • Exogenous learning makes technical progress positive, gAt ≥ g • Technical progress results from an externality (education) 7 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth Technical progress • Deﬁnition: Technical progress is At − At−1 gAt ≡ At−1 • Assumption: βet−1 ¯ gAt = gA (et−1 ) = g + ρ 1 + βet−1 ¯ g > 0 but small, β > 0 and ρ > 0 ¯ • Exogenous learning makes technical progress positive, gAt ≥ g • Technical progress results from an externality (education) ¯ • Technical progress is bounded by g + ρ 7 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth Human capital technology 8 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth Human capital technology Education technology: ht+1 = µ(θ + et )η µ > 0, θ > 0 and η ∈ (0, 1) 8 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth Human capital technology Education technology: ht+1 = µ(θ + et )η µ > 0, θ > 0 and η ∈ (0, 1) • There is a minimum level of human capital µθ η 8 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth Human capital technology Education technology: ht+1 = µ(θ + et )η µ > 0, θ > 0 and η ∈ (0, 1) • There is a minimum level of human capital µθ η • In the limit, when e → ∞, gh = ηg 8 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth Structure of the solution 9 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth Structure of the solution Generation t receives {At , ht } from the previous generation and transfers {At+1 , ht+1 } to the following generation 9 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth Structure of the solution Generation t receives {At , ht } from the previous generation and transfers {At+1 , ht+1 } to the following generation [the dynamics is purely backward] 9 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth Structure of the solution Generation t receives {At , ht } from the previous generation and transfers {At+1 , ht+1 } to the following generation [the dynamics is purely backward] The economy, depending on per capita income, At ht , may be in diﬀerent regimes 9 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth Structure of the solution Generation t receives {At , ht } from the previous generation and transfers {At+1 , ht+1 } to the following generation [the dynamics is purely backward] The economy, depending on per capita income, At ht , may be in diﬀerent regimes ˜ • Modern regime: ct > c and et > 0 9 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth Structure of the solution Generation t receives {At , ht } from the previous generation and transfers {At+1 , ht+1 } to the following generation [the dynamics is purely backward] The economy, depending on per capita income, At ht , may be in diﬀerent regimes ˜ • Modern regime: ct > c and et > 0 ˜ • Post-Malthusian regime: ct = c and et > 0 9 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth Structure of the solution Generation t receives {At , ht } from the previous generation and transfers {At+1 , ht+1 } to the following generation [the dynamics is purely backward] The economy, depending on per capita income, At ht , may be in diﬀerent regimes ˜ • Modern regime: ct > c and et > 0 ˜ • Post-Malthusian regime: ct = c and et > 0 ˜ • Malthusian regime: ct = c and et = 0 9 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth Individual behavior 10 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth Individual behavior The representative adult of cohort t max ln(ct ) + δ ln(nt ) + δη ln(θ + et ) {ct ,nt ,et } s.t. ct + nt et + nt φAt ht = At ht ˜ ct ≥ c et ≥ 0 given At , ht 10 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth Individual behavior The representative adult of cohort t max ln(ct ) + δ ln(nt ) + δη ln(θ + et ) {ct ,nt ,et } s.t. ct + nt et + nt φAt ht = At ht ˜ ct ≥ c et ≥ 0 given At , ht [At equilibrium, wages are equal to At ] 10 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth Individual behavior The representative adult of cohort t max ln(ct ) + δ ln(nt ) + δη ln(θ + et ) {ct ,nt ,et } s.t. ct + nt et + nt φAt ht = At ht ˜ ct ≥ c et ≥ 0 given At , ht [At equilibrium, wages are equal to At ] Trade-oﬀ between fertility and education 10 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth Individual behavior The representative adult of cohort t max ln(ct ) + δ ln(nt ) + δη ln(θ + et ) {ct ,nt ,et } s.t. ct + nt et + nt φAt ht = At ht ˜ ct ≥ c et ≥ 0 given At , ht [At equilibrium, wages are equal to At ] Trade-oﬀ between fertility and education θ ˜ Assumption: c < ηφ < (1 + δ)˜ c 10 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth Modern growth 11 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth Modern growth When per capita income is large enough, At ht ≥ (1 + δ)˜, the c solution is interior 11 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth Modern growth When per capita income is large enough, At ht ≥ (1 + δ)˜, the c solution is interior • A constant fraction of income is allocated to consumption At ht ct = ˜ ≥c 1+δ 11 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth Modern growth When per capita income is large enough, At ht ≥ (1 + δ)˜, the c solution is interior • A constant fraction of income is allocated to consumption At ht ct = ˜ ≥c 1+δ • A property of log preferences 11 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth Modern growth When per capita income is large enough, At ht ≥ (1 + δ)˜, the c solution is interior • A constant fraction of income is allocated to consumption At ht ct = ˜ ≥c 1+δ • A property of log preferences ˜ • ct = c at the optimum when At ht = (1 + δ)˜ c 11 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth Modern growth When per capita income is large enough, At ht ≥ (1 + δ)˜, the c solution is interior • A constant fraction of income is allocated to consumption At ht ct = ˜ ≥c 1+δ • A property of log preferences ˜ • ct = c at the optimum when At ht = (1 + δ)˜ c • The complement is allocated to raising and educating kids δ nt et + nt φAt ht = At ht 1+δ 11 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth Becker’s fertility theory 12 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth Becker’s fertility theory Richer parents prefer less, but more educated kids 12 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth Becker’s fertility theory Richer parents prefer less, but more educated kids • Quantity vs quality: The ratios of marginal costs and marginal beneﬁts equalize et + φAt ht 1/nt = nt η/(θ + et ) 12 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth Becker’s fertility theory Richer parents prefer less, but more educated kids • Quantity vs quality: The ratios of marginal costs and marginal beneﬁts equalize et + φAt ht 1/nt = nt η/(θ + et ) • Education ηφAt ht − θ et = >0 1−η 12 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth Becker’s fertility theory Richer parents prefer less, but more educated kids • Quantity vs quality: The ratios of marginal costs and marginal beneﬁts equalize et + φAt ht 1/nt = nt η/(θ + et ) • Education ηφAt ht − θ et = >0 1−η • Number of kids −1 δ θ nt = (1 − η) φ− >0 1+δ At ht 12 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth Becker’s fertility theory Richer parents prefer less, but more educated kids • Quantity vs quality: The ratios of marginal costs and marginal beneﬁts equalize et + φAt ht 1/nt = nt η/(θ + et ) • Education ηφAt ht − θ et = >0 1−η • Number of kids −1 δ θ nt = (1 − η) φ− >0 1+δ At ht [Assumption: having kids requires parents time, but education not] 12 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth Post-Malthusian regime 13 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth Post-Malthusian regime θ When per capita income ηφ ≤ At ht < (1 + δ)˜ c 13 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth Post-Malthusian regime θ When per capita income ηφ ≤ At ht < (1 + δ)˜ c ˜ • Consumption is at the subsistence level ct = c 13 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth Post-Malthusian regime θ When per capita income ηφ ≤ At ht < (1 + δ)˜ c ˜ • Consumption is at the subsistence level ct = c • Additional income is allocated to having more kids ˜ At ht − c nt = (1 − η) φAt ht − θ 13 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth Post-Malthusian regime θ When per capita income ηφ ≤ At ht < (1 + δ)˜ c ˜ • Consumption is at the subsistence level ct = c • Additional income is allocated to having more kids ˜ At ht − c nt = (1 − η) φAt ht − θ • and provide them with more education ηφAt ht − θ et = >0 1−η 13 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth Post-Malthusian regime θ When per capita income ηφ ≤ At ht < (1 + δ)˜ c ˜ • Consumption is at the subsistence level ct = c • Additional income is allocated to having more kids ˜ At ht − c nt = (1 − η) φAt ht − θ • and provide them with more education ηφAt ht − θ et = >0 1−η • et = 0 at the optimum when At ht = θ ηφ 13 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth Post-Malthusian regime θ When per capita income ηφ ≤ At ht < (1 + δ)˜ c ˜ • Consumption is at the subsistence level ct = c • Additional income is allocated to having more kids ˜ At ht − c nt = (1 − η) φAt ht − θ • and provide them with more education ηφAt ht − θ et = >0 1−η • et = 0 at the optimum when At ht = θ ηφ Population grows when per-capita income is high 13 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth Malthusian regime 14 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth Malthusian regime θ ˜ When per capita income is in c ≥ At ht < ηφ 14 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth Malthusian regime θ ˜ When per capita income is in c ≥ At ht < ηφ ˜ • Consumption is at the subsistence level ct = c 14 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth Malthusian regime θ ˜ When per capita income is in c ≥ At ht < ηφ ˜ • Consumption is at the subsistence level ct = c • There is no education et = 0, implying ht = µθ η > 0 14 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth Malthusian regime θ ˜ When per capita income is in c ≥ At ht < ηφ ˜ • Consumption is at the subsistence level ct = c • There is no education et = 0, implying ht = µθ η > 0 • Any additional income is allocated to having more kids ˜ At ht − c nt = φAt ht 14 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth Malthusian regime θ ˜ When per capita income is in c ≥ At ht < ηφ ˜ • Consumption is at the subsistence level ct = c • There is no education et = 0, implying ht = µθ η > 0 • Any additional income is allocated to having more kids ˜ At ht − c nt = φAt ht Population grows when per-capita income is high 14 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth Dynamics 15 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth Dynamics The model is purely backward 15 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth Dynamics The model is purely backward • In the Malthusian regime 15 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth Dynamics The model is purely backward • In the Malthusian regime ¯ • gt = g > 0, implying that At is permanently growing • The economy moves slowly to the following regime 15 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth Dynamics The model is purely backward • In the Malthusian regime ¯ • gt = g > 0, implying that At is permanently growing • The economy moves slowly to the following regime • In the Post-Malthusian regime 15 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth Dynamics The model is purely backward • In the Malthusian regime ¯ • gt = g > 0, implying that At is permanently growing • The economy moves slowly to the following regime • In the Post-Malthusian regime ¯ • Positive education raises gt > g and makes human capital grow 15 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth Dynamics The model is purely backward • In the Malthusian regime ¯ • gt = g > 0, implying that At is permanently growing • The economy moves slowly to the following regime • In the Post-Malthusian regime ¯ • Positive education raises gt > g and makes human capital grow • The economy moves to the following regime faster 15 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth Dynamics The model is purely backward • In the Malthusian regime ¯ • gt = g > 0, implying that At is permanently growing • The economy moves slowly to the following regime • In the Post-Malthusian regime ¯ • Positive education raises gt > g and makes human capital grow • The economy moves to the following regime faster • Modern growth regime 15 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth Dynamics The model is purely backward • In the Malthusian regime ¯ • gt = g > 0, implying that At is permanently growing • The economy moves slowly to the following regime • In the Post-Malthusian regime ¯ • Positive education raises gt > g and makes human capital grow • The economy moves to the following regime faster • Modern growth regime ¯ • Converges monotonically to a BGP with gA = g + ρ and η gh = 1−η (¯ + ρ) g 15 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth Key assumption 16 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth Key assumption • An adult generation leaves for 25 years 16 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth Key assumption • An adult generation leaves for 25 years • The initial time t = 0 is year 400, the end of the Roman Imperium 16 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth Key assumption • An adult generation leaves for 25 years • The initial time t = 0 is year 400, the end of the Roman Imperium • The economy is initially at the Malthusian regime 16 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth Key assumption • An adult generation leaves for 25 years • The initial time t = 0 is year 400, the end of the Roman Imperium • The economy is initially at the Malthusian regime • Education becomes positive in year 1650, t = 50 16 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth Key assumption • An adult generation leaves for 25 years • The initial time t = 0 is year 400, the end of the Roman Imperium • The economy is initially at the Malthusian regime • Education becomes positive in year 1650, t = 50 • The modern regime is reached in year 1850, t = 58 16 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth The mechanics of transition 17 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth The mechanics of transition ¯ • Learning makes gt = g > 0 from the beginning 17 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth The mechanics of transition ¯ • Learning makes gt = g > 0 from the beginning • Initially, additional income is spent on more kids [Malthus] 17 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth The mechanics of transition ¯ • Learning makes gt = g > 0 from the beginning • Initially, additional income is spent on more kids [Malthus] • Around 1650, individuals can aﬀord positive education 17 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth The mechanics of transition ¯ • Learning makes gt = g > 0 from the beginning • Initially, additional income is spent on more kids [Malthus] • Around 1650, individuals can aﬀord positive education • Human capital and technical progress slightly accelerate 17 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth The mechanics of transition ¯ • Learning makes gt = g > 0 from the beginning • Initially, additional income is spent on more kids [Malthus] • Around 1650, individuals can aﬀord positive education • Human capital and technical progress slightly accelerate • But, people are still constrained by subsistence [Malthus] 17 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth The mechanics of transition ¯ • Learning makes gt = g > 0 from the beginning • Initially, additional income is spent on more kids [Malthus] • Around 1650, individuals can aﬀord positive education • Human capital and technical progress slightly accelerate • But, people are still constrained by subsistence [Malthus] • Around 1850, consumption becomes interior and the Beckerian mechanism starts working 17 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth The mechanics of transition ¯ • Learning makes gt = g > 0 from the beginning • Initially, additional income is spent on more kids [Malthus] • Around 1650, individuals can aﬀord positive education • Human capital and technical progress slightly accelerate • But, people are still constrained by subsistence [Malthus] • Around 1850, consumption becomes interior and the Beckerian mechanism starts working • Stationary population: Parameters are chosen st. nt → 1 when t → ∞ 17 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth Calibration 18 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth Calibration ˜ • c = 1.25 18 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth Calibration ˜ • c = 1.25 • The time allocated to raising kids is φ = 1 4 and the total 1 weight of kids in utility is δ = 2 18 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth Calibration ˜ • c = 1.25 • The time allocated to raising kids is φ = 1 4 and the total 1 weight of kids in utility is δ = 2 • η= 1 4 to n be unity at steady state 18 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth Calibration ˜ • c = 1.25 • The time allocated to raising kids is φ = 1 4 and the total 1 weight of kids in utility is δ = 2 • η= 1 4 to n be unity at steady state • θ = ηφ(1 + δ − 1/8)˜ ≃ 0.107 to respect Assumption 1 c 18 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth Calibration ˜ • c = 1.25 • The time allocated to raising kids is φ = 1 4 and the total 1 weight of kids in utility is δ = 2 • η= 1 4 to n be unity at steady state • θ = ηφ(1 + δ − 1/8)˜ ≃ 0.107 to respect Assumption 1 c • Initial conditions: A0 = 1 and h0 chosen to n1 = 1 18 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth Calibration ˜ • c = 1.25 • The time allocated to raising kids is φ = 1 4 and the total 1 weight of kids in utility is δ = 2 • η= 1 4 to n be unity at steady state • θ = ηφ(1 + δ − 1/8)˜ ≃ 0.107 to respect Assumption 1 c • Initial conditions: A0 = 1 and h0 chosen to n1 = 1 • µ ≃ 2.9 makes h0 = µθ η [consistent with e1 = 0] 18 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth Calibration ˜ • c = 1.25 • The time allocated to raising kids is φ = 1 4 and the total 1 weight of kids in utility is δ = 2 • η= 1 4 to n be unity at steady state • θ = ηφ(1 + δ − 1/8)˜ ≃ 0.107 to respect Assumption 1 c • Initial conditions: A0 = 1 and h0 chosen to n1 = 1 • µ ≃ 2.9 makes h0 = µθ η [consistent with e1 = 0] ¯ • g ≃ 0.0615% makes the economy converge to the Post-Malthusian regime in year 1650 18 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth Calibration ˜ • c = 1.25 • The time allocated to raising kids is φ = 1 4 and the total 1 weight of kids in utility is δ = 2 • η= 1 4 to n be unity at steady state • θ = ηφ(1 + δ − 1/8)˜ ≃ 0.107 to respect Assumption 1 c • Initial conditions: A0 = 1 and h0 chosen to n1 = 1 • µ ≃ 2.9 makes h0 = µθ η [consistent with e1 = 0] ¯ • g ≃ 0.0615% makes the economy converge to the Post-Malthusian regime in year 1650 • β = 0.3 such that the economy reaches modern growth in year 1850 18 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth Calibration ˜ • c = 1.25 • The time allocated to raising kids is φ = 1 4 and the total 1 weight of kids in utility is δ = 2 • η= 1 4 to n be unity at steady state • θ = ηφ(1 + δ − 1/8)˜ ≃ 0.107 to respect Assumption 1 c • Initial conditions: A0 = 1 and h0 chosen to n1 = 1 • µ ≃ 2.9 makes h0 = µθ η [consistent with e1 = 0] ¯ • g ≃ 0.0615% makes the economy converge to the Post-Malthusian regime in year 1650 • β = 0.3 such that the economy reaches modern growth in year 1850 • ρ = 0.25 implies a yearly rate of technical progress of around 1% at steady state 18 / 19 Introduction Economy Equilibrium From Malthus to Modern Growth From Malthus to modern growth.nb 1 g n 1.3 0.3 1.25 0.25 1.2 0.2 0.15 1.15 0.1 1.1 0.05 1.05 time time 1750 1850 1950 2050 1750 1850 1950 2050 19 / 19

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posted: | 5/30/2010 |

language: | English |

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