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Real Business Cycles

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

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  1. Real Business Cycles Motivation The Model Solving the Model Predictions Fiscal Policy

  2. 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.

  3. 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.

  4. 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)

  5. 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.

  6. Figure 4.20 The Solow Residual for the United States

  7. Figure 5.11 Deviations from Trend in Real GDP and the Solow Residual

  8. Table 3.1The Production Function of the United States, 1980–2004

  9. 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 .

  10. 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:

  11. 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

  12. r = 1  permanent

  13. 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.

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

  15. FOC for Utility Maximization:

  16. Firms • In each period t firms choose {Ndt,Kt+1} to • FOC for Profit Maximization

  17. Market Clearing • Goods • Labor

  18. Social Planner • Since solution to CE is Pareto Optimal it is equivalent to the social planner’s problem: subject to

  19. 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)

  20. 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*

  21. 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.

  22. A CE is {ct,Nt,Kt+1} solving

  23. 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.

  24. Result:

  25. 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

  26. 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.

  27. 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:

  28. Effect of One Time Productivity Shock

  29. 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.

  30. Figure 10.3Small shocks and large cycles

  31. GDP

  32. Consumption

  33. Investment

  34. Employment

  35. 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).

  36. Figure 11.3 Average Labor Productivity with Total Factor Productivity Shocks

  37. Table 11.1 Data Versus Predictions of the Real Business Cycle Model with Productivity Shocks

  38. Hours-Wage Correlation

  39. 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.

  40. Adding Government Spending Shocks to RBC Model • Firms: • Households: and • Government BC:

  41. Market-Clearing: Labor: Nd = Ns Goods: yt = Ct + It + Gt

  42. 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

  43. Evidence: (1) Procyclical G (2) Wartime government spending and Interest Rates (3) G and I

  44. The Growth Rate of U.S. Real Gross Domestic Product since 1870

  45. Figure 4.5Gross and net investment, 1929–2002

  46. Government Expenditures & Investment

  47. RBC Model w/ Government Spending Shocks

  48. Hours-Wage Correlation

  49. Hours-Wage Correlation

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