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Real Business Cycles. Motivation The Model Solving the Model Predictions Fiscal Policy. Readings. "Understanding Real Business Cycles" by C. Plosser, Journal of Economic Perspectives 3, No. 3: 51-77 (Summer 1989)

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real business cycles

Real Business Cycles

Motivation

The Model

Solving the Model

Predictions

Fiscal Policy

readings
Readings
  • "Understanding Real Business Cycles" by C. Plosser, Journal of Economic Perspectives 3, No. 3: 51-77 (Summer 1989)
  • “Real Business Cycles: A New Keynesian Perspective” by N. Gregory Mankiw, Journal of Economic Perspectives, Vol 3, No 3, pp 79-90 (Summer 1989)
  • Williamson, Ch 11.
motivation
Motivation
  • Prior to RBC theory the mainstream idea was that aggregate demand caused business cycles (e.g. Keynesian IS-LM model)
  • Can a dynamic competitive equilibrium (CE) model provide an explanation of business cycles?
  • In CE without investment, there is no persistence (HW assignment #3)
  • Investment provides a stronger link of economic decisions over time.
  • RBC model is the CE model with (i) shocks to productivity and (ii) uncertainty and rational expectations.
slide4
Real Business Cycle (RBC) theory originates with:

(i) F. Kydland and E. Prescott

- 2004 Nobel Winners in Economics

- “Time to Build and Aggregate Fluctuations”

(Econometricia, 1982)

(ii) J. Long and C. Plosser

“Real Business Cycles” (Journal of Political Economy, 1983)

slide5
Productivity for the US economy can be calculated using the Cobb-Douglas PF:

y = f(K,N) = zK0.3N0.7 z = y/K0.3N0.7

  • Historically, the growth rate of productivity (z) fluctuates with the business cycle.
slide9
RBC model says that business cycles are caused by temporary but persistent productivity shocks:

where 0 < r < 1 is degree of persistence.

  • Productivity shocks are the impulse and investment is the propagation mechanism.
  • Rational Expectations: Households/Firms know all variables up to time t and the random process for and .
numerical example
Numerical Example
  • Consider t = 20 periods
  • There is a one-time shock to et in period 1 where e1 = 10 and et = 0 for all other time periods:
slide11
Notice the effect on ztdepends on the value of r which measures the amount of persistence for the shock e.

r = 0  purely temporary

r = 0.80  temporary but

persistent

timing
Timing
  • Households & Firms are infinitely lived
  • In each period t:

(i) Kt is known from last period.

zt shock is observed.

(ii) A rational expectation of zt+1 is formed.

(ii) Firms hire labor Ntd and buy capital Kt+1.

(cost of capital = rt + d)

(iii) Households supply labor Nts and consume ct.

(wages wt are paid)

(iv) Markets clear (labor, goods). Firm profits paid to households.

households
Households
  • In each period t households choose {ct+j,lt+j} to

subject to

firms
Firms
  • In each period t firms choose {Ndt,Kt+1} to
  • FOC for Profit Maximization
market clearing
Market Clearing
  • Goods
  • Labor
social planner
Social Planner
  • Since solution to CE is Pareto Optimal it is equivalent to the social planner’s problem:

subject to

productivity shocks
Productivity Shocks
  • Temporary Positive Shock

Supply  higher ND and z shifts Ys right. Decreases r* and shifts NS left  N* ambiguous but increase in w.

Demand  Higher w increases c*  Yd shifts right. No change in future MPK  no (direct) effect on I.

Overall  Increase in y* and decrease in r*

(C and I increases)

slide20
There will be persistence: Higher I today  Higher future output.
  • Future Positive Shock

Supply  Current z unchanged  Ys fixed.

Demand  Increases c* (from PIH) and increase in I  Yd shifts right.

Overall  Increase in y* and increase in r*

functional forms
Functional Forms
  • Cobb-Douglas (log) Utility

Cobb-Douglas Technology

where 0 < q < 1 and 0 < a < 1 are the elasticities of substitution in utility and production functions.

special case d 1
Special Case: d = 1
  • 100% depreciation  It = Kt+1
  • Guess: Nt = N constant
  • “Method of Undetermined Coefficient” plug into equilibrium conditions and verify guess by solving for N, f1, and f2.
predictions of special case
Predictions of Special Case
  • Persistent Cycles in GDP
  • Volatility of C and I

MODELDATA

C,I procyclical C,I procyclical

Var (ct) < Var (yt) Var (ct) < Var (yt)

Var (It) < Var (yt) Var (It) > Var (yt) (X)

Labor Market

Average Productivity: (yt/N) is procyclical,

Real Wages: wt = zFN(Kt,N) procyclical

slide26
Real interest rate r is countercyclical.
  • Problem: No fluctuations in N!
  • Can be resolved by d < 1:

Substitution effect > income effect

Higher MPK magnifies productivity shock.

  • No analytical solution. Need to use numerical methods.
form of solution
Form of Solution
  • In each period t, the model’s state variables are:
  • Solution for each period t are functions of the model’s state variables given K0 , , and et:
steps to solving rbc model
Steps to Solving RBC Model

(1) Solve for solutions of c(K,z), n(K,z), k(K,z)

(2) Calibrate Parameters: d = 0.25, a = 0.3, b = 0.99 (4% annual real interest rate), persistence r = 0.8,ect.

(3) Simulate Model to Generate Artificial Data

(4) Compare Artificial Economy with Real Economy.

compare with bc facts
Compare with BC Facts
  • Explains persistent fluctuations in Y, C, I.
  • C and I are procyclical, C is less volatile than Y, I more volatile than Y.
  • N is procyclical but model still understates volatility.
  • Labor productivity (Y/N) is procyclical (too much)
  • Price Level is countercyclical (?)
  • Correlation between N and productivity (and w) is close to one (too large).
table 11 1 data versus predictions of the real business cycle model with productivity shocks
Table 11.1 Data Versus Predictions of the Real Business Cycle Model with Productivity Shocks
shortcomings
Shortcomings
  • Still not enough volatility in N. Need higher intertemporal substitution effect relative to income effect.
  • N and w correlation too large.
  • Money is neutral.
adding government spending shocks to rbc model
Adding Government Spending Shocks to RBC Model
  • Firms:
  • Households:

and

  • Government BC:
slide42
Market-Clearing:

Labor: Nd = Ns

Goods: yt = Ct + It + Gt

temporary d g
Temporary DG
  • Supply Side Effects

* Increase in G  Increase in T

* Small decrease in PDV of lifetime income

* Small shift of NS and Ys right

  • Demand Side Effects

* Higher G  shifts Yd right by DG/(1-MPC).

* Higher T  small negative income effect (consumption smoothing)  Yd left by MPC*DT/(1-MPC).

* Since DT = DG, Shift Yd = DG

  • Overall: Shift Yd > Shift Ys Increase Y* and r*  lower C and I
slide44
Evidence:

(1) Procyclical G

(2) Wartime government spending and Interest Rates

(3) G and I

slide51

Suggested Reading:

  • G. Hansen and R. Wright

V. Li, “Can Market-Clearing Models Explain U.S. Labor Market Fluctuations?” Economic Review, Federal Reserve Bank of St. Louis (July 1999).

rbc debate plosser vs mankiw
RBC Debate: Plosser vs Mankiw
  • Interpretation of Productivity Shocks (Solow Residuals)

* Labor Hoarding

* Aggregate Demand Shocks affect Productivity

  • Labor Supply Elasticity of Substitution
  • Optimality of Business Cycles

- Stabilization policy

  • Cyclical behavior of prices and neutrality of money Shocks:
    • Are prices pro or counter-cyclical?
    • Phillips Curve trade-off
  • Internal vs External Consistency