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Lucas Critique and the Essence of New Classical Approach: Rational expectation Consider the IS curve or the AD curve as derived by the Keynesian economists. The parameters a, b q, k, nu, I0 are estimated using the structural model and time series observations on variables. IS: AD: a bT I qr G 0 Y 1 b 1 M a bT I q kY G 0 P Y 1 b Policies such as G and M based on these models are already known to individuals. It is internalised in their decisions. Macroeconomic Themes:3 1 There are five essential features in a New Classical model 1. 2. 3. 4. 5. It has a supply side based on optimisation. It assumes that market clears at every instance, no glut or voluntary unemployment. Rational expectations. Natural rate hypothesis. Policy irrelevance. Macroeconomic Themes:3 2 Aggregate Supply and Technology Shock AD-As in the short run Shocks to Technology and Fluctuations Macroeconomic Themes:3 3 A Simple long run new classical macro economic model with the productivity shock (very similar to Ramsey (1927) problem) Preference of a representative consumer: Max tU Ct Ct t 0 Budget constraint Ct It Gt X t M t zt F K , Lt , At t 1 Evolution of the capital stock: Boundary conditions: Kt 1 K t 1 It K 0 and K 0 T 0 Macroeconomic Themes:3 4 Aggregate supply Yt Y * Pt Pte ets (1) t 1 Where t 1Pte is the price in period t as expected in Pte E Pt | I t 1 t 1 where It 1 is the information set which includes past values of all endogenous variables and parameters. ets is the supply shock, Y * is the target output, Yt and Pt are the actual prices and outputs. period t-1, Macroeconomic Themes:3 5 Price Movement and Monetary Policy Rule Price moves according to the money supply and a demand shock Pt M t etd (2) where etd is the demand shocks and the money supply rule is given by M t Y * Y etm (3) 0 1 t 1 where etm is the policy error or unanticipated money supply, with Eetm 0 and a constant variance. Macroeconomic Themes:3 6 Expected and Actual Prices Rational expectation implies that expected price does not contain any policy error and will be given by the systematic part of (2) e * * Pt Y Y Y Y (4) 0 1 t 1 0 1 t 1 But the actual price will contain systematic as well as the error parts Pt Y * Y etm etd 0 1 t 1 Macroeconomic Themes:3 (5) 7 Policy Irrelevance Proposition The errors in the expectation of the prices are given by the differences between the expected and actual prices Pte Pt etm etd (6) Substitution (6) into (1) we get * m d Yt Y et et ets etm etd ets Macroeconomic Themes:3 (7) 8 Policy Irrelevance Proposition The errors in the expectation of the prices is given by the differences between the expected and actual prices Pte Pt etm etd (6) Substitution (6) into (1) we get output in terms of errors Yt Y * etm etd ets etm etd ets (7) Policy variable does not determine the output. Macroeconomic Themes:3 9 How to Test a Rational Expectation Model? UM t M t M t where UMt is unanticipated money supply, M t is the actual money supply and M t is the anticipated money supply, given by a trend. Now to find whether the unanticipated money supply will have a real impact regress the following model. Yt M t M t et 0 1 In case of persistence take the unanticipated money supply for several years in the past, such as Yt M t M t M M et 0 1 2 t 1 t 1 Macroeconomic Themes:3 10 What do other economists think of this conclusion? New Keynesian consider that the conclusion of policy irrelevance coming out of the New Classical model is dangerous because if policy makers think that way it may have serious welfare consequences due to lack of economic policies to contain unemployment and inflation in recession or in hyperinflation. Mankiw (1989) has explicitly stated that the New classical paradigm will be discarded as an analysis of economy as the micro foundation to the Keynesian models becomes more solid. Macroeconomic Themes:3 11 Adaptive Expectation People learn by mistake and adjust their expectations accordingly Pte P e P P e t 1 t 1 t 1 (1) Here Pte is the expected price and is the adjustment parameter between zero and 1, 0 1 . There is no observation available about the expected price,Pte . How can it be used in a model? . The trick is to solve (1) for Pte and eliminate it using observed variables. First (1) can be written as Pte P 1 P e t 1 t 1 Macroeconomic Themes:3 (2) 12 Adaptive Expectation By one step backward iterations (2) can be written as Pe P 1 Pe t 2 t 1 t 2 (3) Now use (3) into (2) Pte P 1 P 1 Pe = t 1 t 2 t 2 2 P 1 P 1 Pe (4) t 1 t 2 t 2 Now further iterate (3) and substitute the result back in (4) 2 3 Pte P 1 P 1 P 1 Pe t 1 t 2 t 3 t 3 (5) Macroeconomic Themes:3 13 Adaptive Expectation If this process continues (5) can be written as 2 n e e Pt P 1 P 1 P ... 1 Pt n t 1 t 2 t 3 (6) n e Lim 0 1 1 P Since , 0 . Therefore (6) t n n can be written only in terns of the observed values of the actual price, Pt i . Macroeconomic Themes:3 14 References 1. K. A.Chrystal and Simon Price (1994) Controversies in Macroeconomics, Harvester Wheatsheaf, 2. 3. 4. 5. 6. chapter 4. Lucas, Robert Jr. and Sargent, After Keynesian Macroeconomics, Spring 1979, Federal Reserve Bank of Monneapolis Quarterly Review. Mankiw N.G. (1989) Real Business cycle: A New Keynesian Perspective, Journal of Economic Perspectives, vol. 3, no. 3 pp. 79-90. Plosser Charles I (1989) Understanding Real Business Cycle, Journal of Economic Perspectives, vol. 3, no. 3 pp. 51-77. Ramsey, F.P. (1928) “A Mathematical Theory of Saving,” Economic Journal 38, 543-559. Sargent, Thomas J. and Wallace, Neil (1975) “Rational” Expectations, the Optimal Monetary Instrument, and the Optimal Money Supply Rule, Journal of Political Economy, pp. 241254. Macroeconomic Themes:3 15