1 The full dynamic short-run model Chairman Bernanke J. M. Keynes2 Paper topic • Last problem is short paper (1000 words + tables, figures) • Due in reading week (exact date to follow) • Broad latitude on particular topic, but must be macro • Get approval from TF or me for topic • Examples (verbally, but will be in posted assignment) • Good style is important • References must be acceptable (not Internet junk) • Don’t wait until last moment.3 The full Keynesian model of the business cycle 3 IS-MP Y Potential output = AF(K,L) Ypot u πe π i r4 The Dynamic Model This is state-of-the-art modern Keynesian model Combines - IS - MP - Phillips curve Closed economy Short-run model of business cycles Keynesian rather than classical5 LM Bid farewell, hopefully never to see again…6 Monetary policy rule with inflation Taylor rule: i t = πt + r* + θ π (πt - π*) +θY (Yt - Y* ) Has both normative and predictive power. Theoretical point: Can be derived from minimizing loss function such as L = λ π (πt - π*) 2 + λ Y (lnYt - lnY* ) 27 Econometric estimate (for info purposes) Dependent Variable: FYFF Method: Least Squares Date: 11/04/10 Time: 18:50 Sample: 1988Q1 2008Q4 Included observations: 84 Variable Coefficient Std. Error t-Statistic Prob. C 1.458217 0.350366 4.161983 0.0001 PIPCECORE4Q(-1) 1.402713 0.131758 10.64615 0.0000 LHUR(-1)-NAIRU(-1) -1.811719 0.162368 -11.15810 0.0000 R-squared 0.735891 Mean dependent var 4.648889 Adjusted R-squared 0.729370 S.D. dependent var 2.192419 S.E. of regression 1.140542 Akaike info criterion 3.135946 Sum squared resid 105.3678 Schwarz criterion 3.222761 Log likelihood -128.7097 Hannan-Quinn criter. 3.170845 F-statistic 112.8460 Durbin-Watson stat 0.142920 Prob(F-statistic) 0.000000 FYFF = federal funds rate PIPCECORE4Q = rate of core inflation, consumption deflator, 4 quarter LHUR = unemployment rate NAIRU = natural rate of unemployment (-1) = lagged one quarter8 Fed funds =π +1.458 + 0.402*(π – 2) – 1.811*(u – natural rate) π = 4 quarter PCE core inflation -6-4-2024681088 90 92 94 96 98 00 02 04 06 08 10Actual Fed FundsTaylor rule forecastWhy is rate below target today!?!9 Algebra of Dynamic AS-AD analysis Key equations: 1. Demand for goods and services: Yt = Y* - α (rt –r*) + μG + εt 2. Cost of capital: rt = it – π e t + σt 3. Phillips curve: π t = π e t + φ(Yt - Y* ) + ηt 4. Inflation expectations: π e t = π t-1 5. Monetary policy: i t = πt + r* + θ π (πt - π*) +θY (Yt - Y* ), i > 0 Notes: • Equation (1) is our IS curve • Phillips curve substitutes output for u by Okun’s Law • We add premium to capture long v. short rates and financial crises (σt ) • Mankiw uses slightly different version of (4) with rational expectations • Mankiw doesn’t consider risk premium, so ignore for now10 Solve for AS and AD AD: Yt -Y* = -[α /(1+ α θ Y )] [(1+ θ π )π t + σt - π t-1 +…] + [ 1/(1+ α θ Y )](μG + εt ) or AD: Yt -Y* = - k1 π t - k2 σt + k3 π t-1 + k4 G + εt AS: π t = π t-1 + φ(Yt - Y* ) + ηt NOTE: AD is like IS-MP equilibrium AS is Phillips curve with substitution for expected inflation Note that we have moved up one derivative from prices to inflation from introductory AS-AD because Phillips curve related to inflation.11 π Y = real output (GDP) AD(π*, G , εt , σt ) Yt* AS(π t-1 , Y* , ηt ) The graphics of dynamic AS-AD πt*12 Inflationary shock π Y = real output (GDP) AD AS AS’ Yt** πt**13 Financial shock or cut in G π Y = real output (GDP) AD AS Yt** πt** AD’14 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.15 Screen shot16 Parameters17 Numerical simulation in base run18 Graph of base case Forecast19 Some policy approaches What should the Fed do today? Has run out of conventional bullets. Unconventional tools are “quantitative easing 2” (QE), Operation Pancake, Operation Risk Reduction, Operation Forward Guidance.20 Vice-Chair Janet Yellen (Yale Ph. D.) General stance: “Since the onset of the financial crisis, the Federal Reserve has employed a wide array of policy tools to foster our statutory objectives of maximum employment and price stability. In particular, with conventional policy having pushed short-term nominal interest rates close to zero, the FOMC … has provided additional monetary accommodation by modifying our forward policy guidance and by adjusting our securities holdings.” Forward guidance: “At our August meeting, the FOMC decided to provide more-specific information about the likely time horizon by substituting the phrase 'at least through mid-2013' for the phrase 'for an extended period.' This clarification appears to have reduced market uncertainty about the Committee's current policy expectations.” Pancake: “At our recent September meeting, the FOMC announced that we intend to extend the average maturity of our securities holdings over coming months by selling $400 billion of short-term Treasury securities and purchasing an equivalent amount of long-term Treasury securities. This maturity extension program should exert downward pressure on longer-term interest rates, thereby supporting a stronger economic recovery. “ http://www.federalreserve.gov/newsevents/speech/yellen20111021a.htm21 Some policy approaches What should the Fed do today? Has run out of conventional bullets. Unconventional tools are “quantitative easing 2” (QE), Operation Pancake, Operation Risk Reduction, Operation Forward Guidance. Impact: - Remember, r = i – π + Expected future i + risk and term premiums - Point of Pancake is to lower term premium - Estimates are in the range of 50 basis points maximum on long-term rates.22 Quantitative easing (lowers r by 50 basis points) Forecast (base + QE2)23 What about raising inflation target? Some have argued that Fed should raise target. (Krugman in his scholarly writings) Would keep i at zero for longer period. My view (and that of the model) is that it would have small effect (see below).24 Impact of higher inflation premium* Forecast (base + raise inflation target to 3 percent) * Works by lowering the expected future short rates through Taylor rule and then building that into current long rates by