Intermediate Macroeconomics Lecture 5 - An Equilibrium Business Cycle Model Zsófia L. Bárány Sciences Po 2011 October 5
What is a business cycle? business cycles are the deviation of real GDP from its trend Y t is the trend Y t is the actual real GDP Y t = Y t Y t Y t is the absolute deviation of the real GDP from its trend what is more interesting, is the percentage deviation from trend: Y t Y t by taking the natural logarithm of this we get log Y t log Y t
Actual US real GDP
Actual and trend US real GDP
Percentage deviation from trend of US real GDP
Some terminology when a variable fluctuates in the same direction as real GDP that variable is pro-cyclical a pro-cyclical 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 a variable that fluctuates in the opposite direction from real GDP is counter-cyclical a counter-cyclical variable moves in the opposite direction as the business cycle - it tends to be low relative to its trend in a boom and high relative to its trend in a recession a variable that has little tendency to move in a particular direction during a business cycle is acyclical
Business cycle facts C: less volatile than GDP, highly pro-cyclical (correlation 0.9) I : much more volatile than GDP, highly pro-cyclical (0.9) G pretty volatile, mildly pro-cyclical (0.15) does not support the idea that the cause of BC is government spending working hours: same volatility, highly pro-cyclical (0.9) employment: less volatile, less pro-cyclical (0.8) w P : much less volatile, mildly pro-cyclical (0.16) total factor productivity (TFP): very volatile, highly pro-cyclical debate: cause or consequence of business cycles?
Business cycle modelling - reminder describe a stochastic world, where shocks hit the economy the models are based on competitive markets optimising agents the economy is in EQUILIBRIUM micro-founded models fluctuations do not mean dis-equilibrium, this is the reaction of the economy to an outside shock short-term analysis
Business cycle modelling goal: develop a model capable of explaining and predicting these patterns no consensus has been reached yet there is consensus however, that the theory should be based on microeconomic foundations one of the first models to fully incorporate the insights of microeconomic theory to explain movements in macroeconomic aggregates
Baseline real business cycle model fluctuations in the real GDP reflect technological shocks to the economy Y t = A t F (K t, L t ) an increase in A t means that the economy is more productive a decrease in At means that the economy is less productive use equilibrium conditions to determine how the shocks affect Y and other macroeconomic variables such as C, I and L assume for now that K t = K and L t = L, i.e. they are constant when At rises, Y t rises when At falls, Y t falls
Effect on the marginal product of labour (MPL) an increase in A t increases the marginal product of labour at given input levels L and K MPL }{{} = Y t = A t L t }{{} F L(K, L) }{{}
Effect on the marginal product of labour (MPL) an increase in A t increases the marginal product of labour at given input levels L and K MPL }{{} = Y t = A t F L t }{{} L (K, L) }{{} constant reminder: labour demand L d such that: MPL = w P at a given real wage rate, the demand for labour increases however, labour supply L s is fixed the wage rate has to increase
MPL increases
MPL increases, but Ls fixed, w P increases
Y and w P in the data
Effect on the marginal product of capital (MPK) an increase in A t increases the marginal product of capital at given input levels L and K MPK }{{} = Y t = A t K t }{{} F K (K, L) }{{}
Effect on the marginal product of capital (MPK) an increase in A t increases the marginal product of capital at given input levels L and K MPK }{{} = Y t = A t F K t }{{} K (K, L) }{{} constant reminder: capital services demand K d such that: MPK = R P at a given real rental rate, the demand for capital services increases however, capital supply K s is fixed the rental rate has to increase i = R P δ economic boom will have relatively high interest rates recessions will have relatively low interest rates
MPK increases
MPK increases, but K s fixed, R P increases
Y and R P in the data
Predictions so far The model with fixed capital and labour predicts that the real wage rate, w P, is pro-cyclical the real interest rate, i = R P δ, is pro-cyclical they both increase during a boom and decrease in a recession these changes affect the household s budget constraint a technological shock will have an impact on the consumption and saving decision
Consumption and savings I. the aggregate household budget constraint (using that B = B = 0): C + K = w P L + ik from homogeneity of degree 1 of the production function and competitive markets we know that profits are exhausted: Y = A F (K, L) = w P L + R P K subtracting depreciation from both sides we get: Y δk = A F (K, L) δk = w P L + R P K δk = w P L + ik combining with the BC: C + K = A F (K, L) δk
Consumption and savings II. the aggregate household budget constraint: C t + K t = A t F (K t, L t ) δk t an increase in A t raises real GDP for given K t and L t K t is capital at the beginning of period t fixed at period t L t is assumed to be fixed for now a rise in A t increases overall real income
Consumption and savings II. the aggregate household budget constraint: C t + K t = A t F (K t, L t ) δk t an increase in A t raises real GDP for given K t and L t K t is capital at the beginning of period t fixed at period t L t is assumed to be fixed for now a rise in A t increases overall real income positive income effect current & future consumption
Consumption and savings II. the aggregate household budget constraint: C t + K t = A t F (K t, L t ) δk t an increase in A t raises real GDP for given K t and L t K t is capital at the beginning of period t fixed at period t L t is assumed to be fixed for now a rise in A t increases overall real income positive income effect current & future consumption a rise in A t increases the interest rate
Consumption and savings II. the aggregate household budget constraint: C t + K t = A t F (K t, L t ) δk t an increase in A t raises real GDP for given K t and L t K t is capital at the beginning of period t fixed at period t L t is assumed to be fixed for now a rise in A t increases overall real income positive income effect current & future consumption a rise in A t increases the interest rate intertemporal substitution effect current C, future C positive income effect current & future consumption
Consumption and savings II. the aggregate household budget constraint: C t + K t = A t F (K t, L t ) δk t an increase in A t raises real GDP for given K t and L t K t is capital at the beginning of period t fixed at period t L t is assumed to be fixed for now a rise in A t increases overall real income positive income effect current & future consumption a rise in A t increases the interest rate intertemporal substitution effect current C, future C positive income effect current & future consumption net effect on current consumption depends on the relative strength of the income and intertemporal substitution effect
Consumption and savings III. if the change in A is permanent the increase in the real income tends to be permanent as well in this case since the income effect is permanent the propensity to consume out of this higher income would be close to one however, the intertemporal substitution effect will also be at play the increase in current consumption < increase in real GDP current savings increase by the difference of the above two K t, net investment increases K t+1 increases model prediction: C and I are pro-cyclical
Y and C in the data
Y and I in the data
Temporary changes in A a decrease in A due to a harvest failure or a general strike would be temporary 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 savings taking the income effect into account the model predicts that in a boom: investment would rise significantly consumption would rise only by a small amount
Variations in labour input I. until now we assumed that households supply their one unit of labour inelastically in reality households allocate their time between labour and leisure why would people work less than they can? they derive utility from leisure time cost of leisure: lower income benefit of leisure: higher utility there is both a substitution effect and an income effect in play when the real wage rate increases there is an intertemporal substitution effect in play when the interest rate increases
Variations in labour input - due to the change in real wages I. Income effect higher w P the same amount of labour supply provides a higher income people become richer they spend the extra income on consumption and leisure higher w P Substitution effect labour supply decreases one extra working hour w P more units of income higher w P better trade-off between leisure and consumption household responds by working more labour supply increases
Variations in labour input - due to the change in real wages II. Which one dominates: the income or the substitution effect? C 1 + C 2 (1+i 1 )(1+i 2 ) +... = w 0 + w 1 P Ls 1 + w 2 P Ls 2 1 1+i 1 + w 3 P Ls 1 2 (1+i 1 )(1+i 2 ) +... 1+i 1 + if the change in the wage rate is permanent, then the income effect is large, and it overpowers the substitution effect if the change in the wage rate is temporary, i.e. only w 1 P changes, then the income effect is small, and the substitution effect is stronger if the change in A is not fully permanent, then the substitution effect is likely to dominate C 3
Clearing of the labour market
Variations in labour input - due to the change in the interest rate Intertemporal substitution after an increase in i 1 C 1 + C 2 (1+i 1 )(1+i 2 ) +... = w 0 + w 1 P Ls 1 + w 2 P Ls 2 1 1+i 1 + w 3 P Ls 1 2 (1+i 1 )(1+i 2 ) +... 1+i 1 + if the interest rate i 1 rises, then the present value of a unit of period 2 s hour worked becomes less valuable compared to a unit of period 1 s hour worked the household should react by increasing L s 1 and reducing Ls 2 C 3
Y and employment in the data
Y and hours worked in the data
Predictions of the model with variable labour input an increase in A leads to an increase in the real wage rate & an increase in the labour inputs labour inputs are pro-cyclical in the data measured as total hours worked or as total employment real wages are only mildly pro-cyclical, this is a problem labour productivity also increases in the data measured as real GDP per worker or as real GDP per worker hour
Summary baseline real business cycle model main assumption: flexible prices so that markets clear GDP and employment fluctuations are caused by temporary technology shocks, which changes the marginal product of resources a temporary increase in A leads to an increase in the demand for labour and capital pro-cyclical variations in real wages, interest rates pro-cyclical variation of labour input temporary nature of shock mild pro-cyclical movement in consumption large pro-cyclical movement in investment