Macroeconomics Chapter 81 An Equilibrium Business-Cycle Model C h a p t e r 8

Macroeconomics Chapter 82 Cyclical Behavior of Real GDP— Recessions and Booms  Real GDP = trend real GDP + cyclical part of real GDP  Cyclical part of real GDP Coming from the business cycle Short-term economic fluctuations.

Macroeconomics Chapter 83 Cyclical Behavior of Real GDP— Recessions and Booms

Macroeconomics Chapter 84 Cyclical Behavior of Real GDP— Recessions and Booms

Macroeconomics Chapter 85 Cyclical Behavior of Real GDP— Recessions and Booms

Macroeconomics Chapter 86 An Equilibrium Business-Cycle Model

Macroeconomics Chapter 87 An Equilibrium Business-Cycle Model  Conceptual Issues Assuming that these fluctuations reflect shocks to the economy.  Change in level of technology Y= A · F( K, L)  An increase in A means that the economy is more productive.  A decrease in A means that the economy is less productive.

Macroeconomics Chapter 88 An Equilibrium Business-Cycle Model  Uses equilibrium conditions to determine how the shocks affect real GDP, Y, and other macroeconomic variables, such as consumption, C, investment, I, and the quantity of labor input, L.  RBC model  Finn Kydland & Edward Prescott （ 2004 Nobel Laureates ）

Macroeconomics Chapter 89 An Equilibrium Business-Cycle Model  The Model Y= A · F( K, L)  the capital stock, K, as fixed in the short run,  the labor input, L, is fixed. Changes in Y will reflect only changes in A.  When A rises, Y rises,  When A falls, Y falls.

Macroeconomics Chapter 810 An Equilibrium Business-Cycle Model  The Model The marginal product of labor and the real wage rate  An increase in the technology level, A, raises the marginal product of labor, MPL, for given inputs of capital, K, and labor, L.

Macroeconomics Chapter 811 An Equilibrium Business-Cycle Model

Macroeconomics Chapter 812 An Equilibrium Business-Cycle Model

Macroeconomics Chapter 813 An Equilibrium Business-Cycle Model  The Model Marginal product of capital, real rental price, and the interest rate  An increase in the technology level, A, raises the marginal product of capital, MPK, for given inputs of capital, K, and labor, L

Macroeconomics Chapter 814 An Equilibrium Business-Cycle Model

Macroeconomics Chapter 815 An Equilibrium Business-Cycle Model

Macroeconomics Chapter 816 An Equilibrium Business-Cycle Model Marginal product of capital, real rental price, and the interest rate  i = R/P − δ  i = MPK(evaluated at given K and L) − δ The model predicts that an economic boom will have a relatively high interest rate, whereas a recession will have a relatively low interest rate.

Macroeconomics Chapter 817 An Equilibrium Business-Cycle Model  Consumption, saving, and investment Aggregate household budget constraint  Given the markets for bonds, labor, and capital services clear: C + ∆K = Y − δ K

Macroeconomics Chapter 818 An Equilibrium Business-Cycle Model  C+ ∆K = A · F( K, L) −δ K depreciation, δK, is fixed in the short run, An increase in A raises real GDP for given K and L, we see that a rise in A raises overall real income.

Macroeconomics Chapter 819 An Equilibrium Business-Cycle Model  Consumption, saving, and investment income effect ： The increase in real income motivates households to raise current consumption and future consumption. Intertemporal-substitution effect ： The increase in the interest rate tends to reduce current consumption. The net change depends on whether the income effect is stronger or weaker than the intertemporal-substitution effect.

Macroeconomics Chapter 820 An Equilibrium Business-Cycle Model  Consumption, saving, and investment Assume that the change in A is permanent.  the increases in real income tend also to be permanent. The propensity to consume out of higher income would be close to one. When the increase in A is permanent, current consumption will rise. However, as long as the intertemporal-substitution operates at all, the increase in current consumption will be less than the increase in real GDP.

Macroeconomics Chapter 821 An Equilibrium Business-Cycle Model  Consumption, saving, and investment Since current consumption, C, rises, but by less than the increase in real GDP, Y. Therefore, net investment, ∆K, must increase - the increase in real GDP shows up partly as more C and partly as more K. Since net investment, ∆K, equals real saving, this result is consistent with our finding that real saving increased.

Macroeconomics Chapter 822 Matching the Theory with the Facts  Consumption and Investment When a variable fluctuates in the same direction as real GDP that variable is procyclical.  A procyclical variable moves in the same direction as the business cycle — it tends to be high relative to its trend in a boom and low relative to its trend in a recession.

Macroeconomics Chapter 823 Matching the Theory with the Facts  Consumption and Investment A variable that fluctuates in the opposite direction from real GDP is countercyclical. One that has little tendency to move in a particular direction during a business cycle is acyclical.

Macroeconomics Chapter 824 Matching the Theory with the Facts 相关系数 0.88

Macroeconomics Chapter 825 Matching the Theory with the Facts 相关系数 0.92

Macroeconomics Chapter 826 Matching the Theory with the Facts  消费和投资都是顺周期变量。  实际消费的波动幅度大于实际 GDP 的波动； 而投资的波动比 GDP 的大很多。

Macroeconomics Chapter 827 Matching the Theory with the Facts  The Real Wage Rate The model predicts that the real wage rate, w/P, will be relatively high in booms and relatively low in recessions.

Macroeconomics Chapter 828 Matching the Theory with the Facts 相关系数 0.58

Macroeconomics Chapter 829 Matching the Theory with the Facts  The Real Rental Price The model predicts that the real rental price of capital, R/P, will be relatively high in booms and relatively low in recessions.

Macroeconomics Chapter 830 Matching the Theory with the Facts 相关系数 0.52

Macroeconomics Chapter 831 Matching the Theory with the Facts  The Interest Rate The model predicts that booms will have a high interest rate, i, whereas recessions will have a low interest rate.

Macroeconomics Chapter 832 Temporary Changes in the Technology Level  A decrease in A due to a harvest failure or a general strike would be temporary.  To allow for these cases, we now assume that the change in A is temporary.

Macroeconomics Chapter 833 Temporary Changes in the Technology Level  If A increases temporarily, real GDP, A · F (K, L), still rises for fixed values of K and L.  The marginal product of capital, MPK, and the interest rate, i, also rise as before.  The intertemporal-substitution effect from the higher i still motivates households to reduce current consumption, C, and raise current real saving.

Macroeconomics Chapter 834 Temporary Changes in the Technology Level  The model therefore predicts that economic boom would feature high real GDP and investment. Consumption would rise by a small amount.  A recession would have low real GDP and investment. Consumption would decline by a modest amount.

Macroeconomics Chapter 835 Variations in Labor Input  Labor Supply More labor supplied means less leisure time for the family. Assume that households also like more leisure time. As with consumption and saving, the choice of L s involves substitution and income effects.

Macroeconomics Chapter 836 Variations in Labor Input

Macroeconomics Chapter 837 Variations in Labor Input C 1-L

Macroeconomics Chapter 838 Variations in Labor Input  The substitution effect for leisure and consumption A higher real wage rate, w/P, raises the quantity of labor supplied, L s

Macroeconomics Chapter 839 Variations in Labor Input  Income effects on labor supply A higher w/P means higher real wage income, (w/P) · L s Household spends the extra income on consumption and leisure time. A higher w/P leads to a smaller quantity of labor supplied, L s.

Macroeconomics Chapter 840 Variations in Labor Input  Income effects on labor supply Resolve the ambiguity by considering whether the income effect is strong or weak C 1 + C 2 /(1+i 1 ) + C 3 /[( 1+i 1 ) · (1+i 2 ) ] + · · · = (1 + i 0 ) · (B 0 /P+K 0 ) + (w/P) 1 · L s 1 +(w/P) 2 · L s 2 /(1+i 1 ) + (w/P) 3 · L s 3 /[(1+i1) · (1+i 2 )]+ · · ·

Macroeconomics Chapter 841 Variations in Labor Input  Income effects on labor supply A permanent increase in real wage rates results in a large income effect. If the change in year 1 ’ s real wage rate, (w/P) 1, is temporary, the income effect is small. The income effect will be weaker than the substitution effect.

Macroeconomics Chapter 842 Variations in Labor Input  Intertemporal-substitution effects on labor supply C 1 + C 2 /(1+i 1 ) + C 3 /[( 1+i 1 ) · (1+i 2 ) ] + · · · = ( 1 + i 0 ) · (B 0 /P+K 0 ) + (w/P) 1 · L s 1 +(w/P) 2 · L s 2 /(1+i 1 ) + (w/P) 3 · L s 3 /[(1+i 1 ) · (1+i 2 )] + · · ·

Macroeconomics Chapter 843 Variations in Labor Input  Intertemporal-substitution effects on labor supply. If i 1 rises, a unit of year 2 ’ s real wage income, (w/P) 2 · L s 2, becomes less valuable as a present value compared to a unit of year 1 ’ s real wage income, (w/P) 1 · L s 1. The household would increase L s 1 and decrease L s 2 as the interest rate increases.

Macroeconomics Chapter 844 Variations in Labor Input  用数字说话：劳动供给的跨期替代效应的 实证 Alogoskoufis(1987b) Mulligan (1995) 的两个 “ 自然实验 ”

Macroeconomics Chapter 845 Variations in Labor Input

Macroeconomics Chapter 846 Variations in Labor Input  The cyclical behavior of labor input: theory Increase in A will lead to:  The real wage rate increases  Labor inputs increase.

Macroeconomics Chapter 847 Variations in Labor Input  Fluctuations in Labor Input Measures of labor input are procyclical: they move in the same direction as real GDP during booms and recessions.  Employment  Total hours worked

Macroeconomics Chapter 848 Variations in Labor Input 相关系 数 0.81

Macroeconomics Chapter 849 Variations in Labor Input 相关系 数 0.88

Macroeconomics Chapter 850 Variations in Labor Input  The cyclical behavior of labor productivity Measures of labor productivity,  Y/L, is real GDP per worker,  Real GDP per worker-hour.  Labor productivity turns out to be procyclical in both cases.

Macroeconomics Chapter 851 Extra ： labor supply model  For simplicity: the household has only one member and he lives only for one period and has no initial wealth.  FOC:

Macroeconomics Chapter 852 Extra ： labor supply model  Intuition: In one period, the income and substitution effects of a change in the wage offset each other.

Macroeconomics Chapter 853 Extra ： labor supply model Two periods: FOC:

Macroeconomics Chapter 854 Extra ： labor supply model Intuition: intertemporal substitution in labor supply