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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Solving the Model
(i) F. Kydland and E. Prescott
- 2004 Nobel Winners in Economics
- “Time to Build and Aggregate Fluctuations”
(ii) J. Long and C. Plosser
“Real Business Cycles” (Journal of Political Economy, 1983)
y = f(K,N) = zK0.3N0.7 z = y/K0.3N0.7
where 0 < r < 1 is degree of persistence.
r = 0 purely temporary
r = 0.80 temporary but
(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.
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)
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*
where 0 < q < 1 and 0 < a < 1 are the elasticities of substitution in utility and production functions.
C,I procyclical C,I procyclical
Var (ct) < Var (yt) Var (ct) < Var (yt)
Var (It) < Var (yt) Var (It) > Var (yt) (X)
Average Productivity: (yt/N) is procyclical,
Real Wages: wt = zFN(Kt,N) procyclical
Substitution effect > income effect
Higher MPK magnifies productivity shock.
(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.
Labor: Nd = Ns
Goods: yt = Ct + It + Gt
* Increase in G Increase in T
* Small decrease in PDV of lifetime income
* Small shift of NS and Ys right
* 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
(1) Procyclical G
(2) Wartime government spending and Interest Rates
(3) G and I
V. Li, “Can Market-Clearing Models Explain U.S. Labor Market Fluctuations?” Economic Review, Federal Reserve Bank of St. Louis (July 1999).
* Labor Hoarding
* Aggregate Demand Shocks affect Productivity
- Stabilization policy