Traditional Keynesian Theories of Fluctuations (From Romer, chapter 6 part A, section 7.8) Microfundations The IS-LM-AD model The liquidity trap and the post 2008 crisis The supply curve The open economy and exchange rate overshooting The Phillips curve The natural rate of unemployment The Canonical New-Keynesian model Introduction

Structure of a Keynesian model Aggregate demand IS curve (flow equilibrium: the Keynesian cross) LM curve (stock equilibrium, financial market, money market) Aggregate supply Labour market Production function P AS AD Y AS curve not vertical

IS-LM model with fixed prices Nominal rigidities are given (fixed prices) Time is discrete capital is fixed, closed economy, no government to start with The production function is:

Household optimization problem Fixed number of infinitely lived households They get utility from consumption, holding money, and disutility from working We ignore population growth and normalize the number of household to 1

Household objective function is

Utility functions (C and M) are CRRA The assumption that Money enter the utility function is a short cut Observationally equivalent to transaction purpose (Fenstra 1986)

Money and Bonds: Two assets The two assets are substitute Bonds bears interest rate but are not liquid (i.e., in the U function)

For households, paths of P, W, and I are given Path of C and M are chosen in order to maximize 6.2 subject to (6.5) and the No-Ponzi game condition For the moment, L is exogenous Path of M is set by the central bank

New Keynesian IS curve Following Romer intuitive methodology to derive the Euler equation (last paragraph of page 240) with the real interest rate is:

Y(t+1) is added to the traditional IS curve With uncertainty, we have instead E(Y(t+1) Inverse relationship between Y(t) and r(t). Relationship is strengthen with the introduction of capital and investment (chapter 9 of book)

LM curve Again following Romer approach to optimization (bottom of page 241 do it yourself). First order condition for money holding (an increase in m increase utility of money holding but decrease return on bond holding and consumption (6.9)

The LM curve in increasing in output and decreasing in the nominal interest rate (explanation) Interest rate rule is the modern approach to close the system

i LM(P0) LM(P1) The aggregate demand curve IS Y P P0 P1 AD Y

i LM(P0) IS(G1) IS(G0) Y AS P AS AD1 AD0 Y

The liquidity trap In this case: LM(P0) LM(P1) i IS Y Yn

-What is the shape of the AD curve in this case? What happen if the AS curve is vertical (classical) What about the Pigou effect? This is related to Summers (1991)

Source : Orphanides (2003) Monetary Policy in Deflation: The Liquidity Trap in History and Practice. Miméo, FED

Source : Orphanides (2003) Monetary Policy in Deflation: The Liquidity Trap in History and Practice. Miméo, FED

The remedy should come, I suggest, from a general recognition that the rate of investment need not be beyond our control, if we are prepared to use our banking systems to effect a proper adjustment of the market-rate of interest. It might be sufficient merely to produce a general belief in the long continuance of a very low rate of short-term interest. The change, once it has begun, will feed on itself. ... The Bank of England and the Federal Reserve Board ... should pursue bank-rate policy and open-market operations a outrance ... [t]hat is to say, they should combine to maintain a very low level of the short-term rate of interest, and buy long-dated securities ... until the short-term market is saturated.

The aggregate supply curve Alternative assumptions about wage and price rigidity section 5.3 Four cases studied: 1) Rigid nominal wages (Keynes’s model) W/P LS A decrease in the price level (AD shock) E A W/P1 W/P0 W/P counter-cyclical rejected by facts W/P moderately pro-cyclical LD L

P AS Y

Case 2: Sticky Prices, Flexible Wages, Competitive Labour Market AD And Y is determined by AD, the effective demand for labour is determined by AD Y

LD LS W/P The effective demand for labour E Pro-cyclical real wage L F-1(Y)

is the efficiency-wage LD LS W/P One reason for this is the efficiency-wage E If w flatter than LS, u↑ w(L) L F-1(Y) Case 3: Sticky Prices, Flexible wages, Real Labour Market Imperfections

Case 4: Sticky Wages, Flexible Prices, Imperfect Competition Markup function If μ is fixed, W/P counter cyclical as in case 1 However, if μ is countercyclical (strong evidences), the real wage can be acyclical or procyclical.