复旦大学：《宏观经济学》博士生课程教学资源（讲义）Politico-Economic Equilibrium and Economic Growth

Politico-Economic Equilibrium and Economic Growth 复9大学经学院

Politico-Economic Equilibrium and Economic Growth

Part 1: Background Data show that growth g performances are very different cross countries g. There are at least three approaches to explain the differences &s Endowment Approach(e.g Acemoglu and Zilibotti, 2001 QJE ss Multiple Equilibria Approach (e. g 复回火学经济院 Azariadis and Drazen, 1990, QJE

Part 1: Background ❖ Data show that growth performances are very different cross countries. ❖ There are at least three approaches to explain the differences. ❖ Endowment Approach (e.g. Acemoglu and Zilibotti, 2001, QJE) ❖ Multiple Equilibria Approach (e.g. Azariadis and Drazen, 1990, QJE) Policy Approach (e.g. Barro

Policy Approach s Public policies may have huge g impacts on economic growth For example, increasing capital tax rate drops the interest rate and then depresses physical capital accumulation. Higher wage tax rate has the same effect on human capital accumulation &The following question comes naturally: why countries adopt o different public policies (or non-5 optimal policy)?

Policy Approach ❖ Public policies may have huge impacts on economic growth. ❖ For example, increasing capital tax rate drops the interest rate and then depresses physical capital accumulation. Higher wage tax rate has the same effect on human capital accumulation. ❖ The following question comes naturally: why countries adopt different public policies (or non￾optimal policy)?

Political Economy .Public Policy is endogenously generated from political economy rather than an abstract benevolent government &A number of theories tell us how public policies are determined in a political economy (a survey see Persson and Tabellini'si book, 2000, MIT so The"Median Voter Theorem"is the most popular one to pin 4 down the politico-economic i equilibrium

Political Economy ❖ Public Policy is endogenously generated from political economy rather than an abstract benevolent government. ❖ A number of theories tell us how public policies are determined in a political economy (a survey see Persson and Tabellini’s book, 2000, MIT). ❖ The “Median Voter Theorem” is the most popular one to pin down the politico-economic equilibrium

Part 2: A Basic Model &Environment: Consider a Three go Period economy. Only one generation lives in each period Every generation consists of a skillful and a unskillful family(S and U henceforth). S in the current period gives birth to S in the next period, so as UN Generations familv or periods Skillful Unskillful Skillful Unskillful 123 Skillful Unskillful 复9大学经学院

Part 2: A Basic Model ❖ Environment: Consider a Three￾Period economy. Only one generation lives in each period. Every generation consists of a skillful and a unskillful family (S and U henceforth). S in the current period gives birth to S in the next period, so as U. Skillful Skillful Skillful Unskillful Unskillful Unskillful Family 1 Generations (or periods) 2 3

Preference sS is altruistic towards her children (also skillful) in the following generations, so as U. Therefore, S and u in the first two generations would like to leave bequest to the their own children in the following generations 复9大学经学院

Preference ❖ S is altruistic towards her children (also skillful) in the following generations, so as U. Therefore, S and U in the first two generations would like to leave bequest to the their own children in the following generations

Capital, Technology and Policy Capital: The first generation is born with certain level of capital Their bequests form the capital held by the second generation whose bequest consequently form the capital held by the last generation ss Technology: Assume small open i economy so that interest rate and 3 wage rate are both exogenously x gIven o Policy Set: Flat-rate capital income tax is collected to balance 学经学院 the transfer payment, which is

Capital, Technology and Policy ❖ Capital: The first generation is born with certain level of capital. Their bequests form the capital held by the second generation, whose bequest consequently form the capital held by the last generation. ❖ Technology: Assume small open economy so that interest rate and wage rate are both exogenously given. ❖ Policy Set: Flat-rate capital income tax is collected to balance the transfer payment, which is equally distributed between S and

Backward Solution: 1 9 The Third Generations Programming maX c3) st 23-k=M4+(-x3)k3+xyk3 yields The Second Generations Programming max n(2)+A(2) st c2+k-k2=+(1-2)yk2+z2rk2 yields: C2=C22,k2,T2, t3 复9大学经学院

The Third Generation’s Programming max ( ) . . 3 u c st i ( ) 3 3 3 1 3 3 3 c k w rk rk i i i i − = + − + yields: ( ) 3 3 3 3 3 c c k ,k , i i i = The Second Generation’s Programming max ( ) ( ) . . 2 3 u c u c st i i +  ( ) 2 2 3 2 2 2 2 c k k w 1 rk rk i i i i i + − = + − + yields: ( ) 2 2 2 2 2 3 c c k ,k , , i i i = ( ) 3 3 3 3 3 c c k ,k , i i i = Backward Solution: 1

Backward Solution: 2 The First Generations Programming max ulC+ Bulc2 +Bul st +k2k1=+(1-c1)k+k k 252423 y、0m121,z2,z2)经

max ( ) ( ) ( ) . . 3 2 1 2 u c u c u c st i i i +  +  ( ) 1 1 2 1 1 1 1 1 c k k w rk rk i i i i i + − = + − + The First Generation’s Programming ( ) 2 2 2 2 2 3 c c k ,k , , i i i = ( ) 3 3 3 3 3 c c k ,k , i i i = yields: ( ) 1 1 1 1 1 2 3 c c k ,k , , , i i i = Backward Solution: 2

Backward Solution: 3 Note that in order to mimic the competitive equilibrium, we assume there is no strategic behavior between S and U in each period The model is closed by k.= S +h Finally, we can get three generations indirect utility functions (k1,k 1515233 22253 k3,k3 复9大学经学院

( ) 2 2 2 2 2 3 v v k ,k , , i i i = ( ) 3 3 3 3 3 v v k ,k , i i i = ( ) 1 1 1 1 1 2 3 v v k ,k , , , i i i = u t s kt = kt + k Backward Solution: 3 • Note that in order to mimic the competitive equilibrium, we assume there is no strategic behavior between S and U in each period. • The model is closed by: • Finally, we can get three generations’ indirect utility functions: