1 The full dynamic short-run model

2 The Dynamic Model A nice new addition to Mankiw. Combines - IS - LM (changed to reflect central bank targeting) - Phillips curve Closed economy Short-run of business cycles Keynesian rather than classical

3 Monetary policy rule Taylor rule: i t = π t + θ π (π t - π*) +θ Y (Y t - Y* ) Rationale: a rule that incorporates both real and inflation targets But, also one that has good stability properties Derived from minimizing loss function such as L = θ π (π t - π*) 2 +θ Y (lnY t - lnY* ) 2 [This version has loss function the same as the Taylor run. It seems more likely that the optimal Y* would be above potential output.]

4 Fedfunds* = pi *(pi – 2) -.25*(u – nairu) pi = 4 quarter PCE core inflation Why is rate below target today?

5 Algebra of Dynamic AS-AD analysis Key equations: 1. Demand for goods and services: Y t = Y* - α (r t –r*) + μG + ε t 2. Cost of capital: r t = i t – π e t + risk premium 3. Phillips curve: π t = π e t + φ(Y t - Y* ) + v t 4. Inflation expectations: π e t = π t-1 5. Monetary policy: i t = π t + θ π (π t - π*) +θ Y (Y t - Y* ) Notes: Equation (1) is just our IS-LM solution Phillips curve substitutes output by Okun’s Law Mankiw uses slightly different version of (4) Mankiw doesn’t consider risk premium, so ignore for now We have added “G” to show the impact of fiscal policy

6 Solve for AS and AD AD: Y t = -[ α θ π /(1+ α θ Y )] π t + μ /(1+ α θ Y )] G +… AS: π t = π t-1 + φ(Y t - Y* ) + v t NOTE: AD is like IS-LM equilibrium except is substitutes the Fed response for a fixed money supply AS is Phillips curve with substituting for expected inflation Note that we have moved up one derivative from intro AD-AD because of Phillips curve.

7 π Y = real output (GDP) AD Yt*Yt* AS The graphics of dynamic AS-AD πt*πt*

8 Inflationary shock π Y = real output (GDP) AD Y* AS

9 Example by simulation model This will be available on course web page. You might download and do some experiments to see how it works. New kind of economics: computerized modeling. [The screen shots are ones that were used in class. The model posted on the course web site is slightly changed from that version.]

10

11 Parameters

12 Numerical simulation in base run

13 Graph of base case

14 Very big negative demand shock

15 Other examples 1.Supply shocks (e-sup = 1) 2.Financial crisis (shock r = 1) 3.Inflation targeting without output targets: much deeper recessions with demand shocks (ECB) 4.Unstable monetary policy where insufficient response to shocks (Great Inflation discussion) 5.Liquidity trap

16 Summary This now finishes our treatment of closed-economy business cycles. Key elements are - IS elements in I, C, fiscal policy, and trade - Financial markets and monetary policy - Inflation dynamics Can we abolish the business cycle?