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The New Keynesian Model - University of Notre Dameesims1/new_keynesian_slides.pdfThe IS and LM...

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The New Keynesian Model ECON 30020: Intermediate Macroeconomics Prof. Eric Sims University of Notre Dame Fall 2016 1 / 38
Transcript
  • The New Keynesian ModelECON 30020: Intermediate Macroeconomics

    Prof. Eric Sims

    University of Notre Dame

    Fall 2016

    1 / 38

  • New Keynesian Models

    I At risk of oversimplification, New Keynesian models are theleading alternative to the neoclassical / RBC model

    I “New” Keynesian: neoclassical backbone to these models.Just a twist on neoclassical model, not a fundamentallydifferent framework. In the “medium run”/“long run” modelsare the same

    I Basic difference: nominal rigidities. Wages and/or prices areimperfectly flexible

    I Means:

    1. Money is non-neutral2. Demand shocks matter3. Equilibrium of the model is inefficient4. There is therefore scope for policy to improve outcomes in

    short run

    2 / 38

  • Demand and Supply

    I The demand side of the neoclassical and New Keynesianmodels are the same

    I Differences arise on the supply side

    I Two basic variants (or mixture of the two): wage stickinessand/or price stickiness

    I Mathematically, what we are going to assume is that eitherthe nominal wage or price level are predetermined (i.e.exogenous)

    I This will require some change in the labor market – either thefirm (price stickiness) or household (wage stickiness) is off itsdemand or supply schedule

    I Because it works out to be a bit simpler, we will focus on thesticky price model in class, though book covers both

    3 / 38

  • Review: Neoclassical Model:I Equilibrium conditions:

    Ct = Cd (Yt − Gt ,Yt+1 − Gt , rt)

    Nt = Ns(wt , θt)

    Nt = Nd (wt ,At ,Kt)

    It = Id (rt ,At+1, qt ,Kt)

    Yt = AtF (Kt ,Nt)

    Yt = Ct + It + Gt

    Mt = PtMd (it ,Yt)

    rt = it − πet+1

    I Pt is endogenousI Nominal wage, Wt , is Wt = wtPt , and is also therefore

    endogenous

    4 / 38

  • New Keynesian Model

    I Sticky price model:I Pt = P̄t is now exogenous, rather than endogenousI Extreme form of price stickiness: price level completely

    pre-determinedI Replace labor demand curve with Pt = P̄t . Firm (which sets

    price), has to hire labor to meet demand at P̄t rather than tomaximize its value

    I Sticky wage model:I Wt = W̄t is now exogenous, rather than endogenousI Extreme form of wage stickiness: wage set “in advance,”

    worker has to supply as much labor as is demanded at thiswage

    I This means that we replace the labor supply curve with thecondition wt = W̄t/Pt

    5 / 38

  • Graphing the EquilibriumI We will use the AD (aggregate demand) and AS (aggregate

    supply) curves to summarize the equilibriumI AD: stands for aggregate demand. Summarizes the following

    conditions:

    Ct = Cd (Yt − Gt ,Yt+1 − Gt , rt)

    It = Id (rt ,At+1, qt ,Kt)

    Yt = Ct + It + Gt

    Mt = PtMd (it ,Yt)

    rt = it − πet+1

    I Differently than before, AD curve summarizes both realdemand (the first three equations) and nominal demand (thelast two)

    I Classical dichotomy will no longer hold, so cannot separatelyanalyze real and nominal sides of the economy

    6 / 38

  • The IS and LM Curves

    I The IS curve is identical to before: set of (rt ,Yt) pairs wherethe first three of the conditions hold

    I LM curve (liquidity = money) plots combinations of (rt ,Yt)where last two equations hold

    I LM curve is upward-sloping in (rt ,Yt) space. Basic idea:holding Mt and Pt fixed, if rt goes up, Yt must go up formoney demand to equal money supply

    I Go through graphical derivation

    I LM curve will shift if Mt , Pt , or πet+1 change

    I Rule of thumb: LM curve shifts in the same direction as realbalances, MtPt

    7 / 38

  • Deriving the LM Curve

    𝑀𝑀𝑡𝑡 𝑌𝑌𝑡𝑡

    𝑟𝑟𝑡𝑡 𝑃𝑃𝑡𝑡

    𝑀𝑀0,𝑡𝑡

    𝑃𝑃0,𝑡𝑡 𝑟𝑟0,𝑡𝑡

    𝑌𝑌0,𝑡𝑡

    𝑀𝑀𝑠𝑠 𝐿𝐿𝑀𝑀

    𝑃𝑃𝑡𝑡𝑀𝑀𝑑𝑑�𝑟𝑟0,𝑡𝑡 + 𝜋𝜋𝑡𝑡+1𝑒𝑒 ,𝑌𝑌0,𝑡𝑡� = 𝑀𝑀𝑑𝑑�𝑟𝑟1,𝑡𝑡 + 𝜋𝜋𝑡𝑡+1𝑒𝑒 ,𝑌𝑌1,𝑡𝑡�

    𝑌𝑌1,𝑡𝑡

    𝑃𝑃𝑡𝑡𝑀𝑀𝑑𝑑(𝑟𝑟0,𝑡𝑡 + 𝜋𝜋𝑡𝑡+1𝑒𝑒 ,𝑌𝑌1,𝑡𝑡)

    𝑟𝑟1,𝑡𝑡

    8 / 38

  • The AD Curve

    I The AD curve is the set of (Pt ,Yt) pairs where the economyis on both the IS and LM curves

    I Basic idea: Pt determines position of LM curve, whichdetermines a Yt where the LM curve intersects the IS curve.A higher Pt means the LM curve shifts in, which results in alower Yt

    I Hence, the AD curve is downward-sloping

    I Go through graphical derivation

    9 / 38

  • Deriving the AD Curve

    𝑌𝑌𝑡𝑡

    𝑟𝑟𝑡𝑡

    𝑌𝑌𝑡𝑡

    𝑃𝑃𝑡𝑡

    𝐼𝐼𝐼𝐼

    𝐿𝐿𝐿𝐿(𝑃𝑃0,𝑡𝑡,𝐿𝐿0,𝑡𝑡)

    𝐿𝐿𝐿𝐿(𝑃𝑃1,𝑡𝑡,𝐿𝐿0,𝑡𝑡)

    𝐿𝐿𝐿𝐿(𝑃𝑃2,𝑡𝑡,𝐿𝐿0,𝑡𝑡)

    𝑃𝑃0,𝑡𝑡

    𝑃𝑃1,𝑡𝑡

    𝑃𝑃2,𝑡𝑡

    𝑟𝑟0,𝑡𝑡

    𝑟𝑟1,𝑡𝑡

    𝑟𝑟2,𝑡𝑡

    𝐴𝐴𝐴𝐴

    10 / 38

  • Shifts of the AD Curve

    I The AD curve will shift if either the IS or LM curves shift (forreason other than Pt)

    I This means that the AD curve will shift right if:I At+1, qt , or Gt increase (IS shifts); Mt or π

    et+1 increase (LM

    shifts)I Gt+1 decreases (IS shift)

    I Note: we could use the AD curve to summarize the demandside of the neoclassical model as well

    I Was just convenient to not since this emphasized classicaldichotomy in the neoclassical model

    11 / 38

  • The Supply Side

    I Generically, the AS curve is the set of (Pt ,Yt) pairs (i)consistent with the production function, (ii) some notion oflabor market equilibrium, and (iii) any exogenous restrictionon nominal price or wage adjustment

    I Can use the AS curve to summarize the neoclassical model aswell as the New Keynesian model:

    Nt = Ns(wt , θt)

    Nt = Nd (wt ,At ,Kt)

    Yt = AtF (Kt ,Nt)

    I Since Pt does not appear in these equations, the AS curvewould be vertical in the neoclassical model

    12 / 38

  • The Neoclassical AS Curve

    𝑤𝑤𝑡𝑡 𝑃𝑃𝑡𝑡

    𝑌𝑌𝑡𝑡 𝑌𝑌𝑡𝑡

    𝑌𝑌𝑡𝑡

    𝑌𝑌𝑡𝑡

    𝑁𝑁𝑡𝑡

    𝑁𝑁𝑡𝑡

    𝐴𝐴𝐴𝐴

    𝑤𝑤𝑡𝑡

    𝑌𝑌0,𝑡𝑡 𝑁𝑁0,𝑡𝑡

    𝑁𝑁𝑑𝑑(𝑤𝑤𝑡𝑡,𝐴𝐴𝑡𝑡 ,𝐾𝐾𝑡𝑡)

    𝐴𝐴𝑡𝑡𝐹𝐹(𝐾𝐾𝑡𝑡,𝑁𝑁𝑡𝑡)

    𝑌𝑌𝑡𝑡 = 𝑌𝑌𝑡𝑡

    𝑃𝑃0,𝑡𝑡

    𝑁𝑁𝑠𝑠(𝑤𝑤𝑡𝑡 ,𝜃𝜃𝑡𝑡)

    𝑃𝑃1,𝑡𝑡

    𝑃𝑃2,𝑡𝑡

    13 / 38

  • Neoclassical IS-LM-AD-AS Equilibrium

    𝑤𝑤𝑡𝑡 𝑃𝑃𝑡𝑡

    𝑌𝑌𝑡𝑡 𝑌𝑌𝑡𝑡

    𝑌𝑌𝑡𝑡

    𝑌𝑌𝑡𝑡

    𝑌𝑌𝑡𝑡

    𝑁𝑁𝑡𝑡

    𝑁𝑁𝑡𝑡

    𝐴𝐴𝐴𝐴

    𝐼𝐼𝐴𝐴

    𝑤𝑤𝑡𝑡

    𝑟𝑟0,𝑡𝑡

    𝑌𝑌0,𝑡𝑡 𝑁𝑁0,𝑡𝑡

    𝑁𝑁𝑑𝑑(𝑤𝑤𝑡𝑡,𝐴𝐴𝑡𝑡 ,𝐾𝐾𝑡𝑡)

    𝐿𝐿𝐿𝐿(𝐿𝐿𝑡𝑡 ,𝑃𝑃0,𝑡𝑡)

    𝐴𝐴𝑡𝑡𝐹𝐹(𝐾𝐾𝑡𝑡,𝑁𝑁𝑡𝑡)

    𝑌𝑌𝑡𝑡 = 𝑌𝑌𝑡𝑡

    𝑟𝑟𝑡𝑡

    𝐴𝐴𝐴𝐴

    𝑃𝑃0,𝑡𝑡

    𝑁𝑁𝑠𝑠(𝑤𝑤𝑡𝑡 ,𝜃𝜃𝑡𝑡)

    14 / 38

  • Sticky Price Model

    I In sticky price model, assume that Pt = P̄t is predeterminedand hence exogenous (think something like menu costs)

    I Replace labor demand with this condition: firm has to meetdemand at Pt , cannot optimally choose labor conditional onthis

    I Conditions:

    Nt = Ns(wt , θt)

    Pt = P̄t

    Yt = AtF (Kt ,Nt)

    I The AS curve will just be horizontal at P̄t . Can only shift ifP̄t changes exogenously

    15 / 38

  • The Sticky Price AS Curve

    𝑌𝑌𝑡𝑡

    𝑌𝑌𝑡𝑡

    𝑌𝑌𝑡𝑡

    𝑌𝑌𝑡𝑡

    𝑁𝑁𝑡𝑡

    𝑁𝑁𝑡𝑡

    𝑤𝑤𝑡𝑡 𝑃𝑃𝑡𝑡

    𝑃𝑃�𝑡𝑡

    𝑌𝑌𝑡𝑡 = 𝑌𝑌𝑡𝑡

    𝑌𝑌𝑡𝑡 = 𝐴𝐴𝑡𝑡𝐹𝐹(𝐾𝐾𝑡𝑡 ,𝑁𝑁𝑡𝑡)

    𝑁𝑁𝑠𝑠(𝑤𝑤𝑡𝑡,𝜃𝜃𝑡𝑡)

    𝐴𝐴𝐴𝐴

    16 / 38

  • Sticky Price IS-LM-AD-AS Equilibrium

    𝑤𝑤𝑡𝑡 𝑃𝑃𝑡𝑡

    𝑌𝑌𝑡𝑡 𝑌𝑌𝑡𝑡

    𝑌𝑌𝑡𝑡

    𝑌𝑌𝑡𝑡

    𝑌𝑌𝑡𝑡

    𝑁𝑁𝑡𝑡

    𝑁𝑁𝑡𝑡

    𝐴𝐴𝐴𝐴

    𝐼𝐼𝐴𝐴

    𝑟𝑟0,𝑡𝑡

    𝑌𝑌0,𝑡𝑡 𝑁𝑁0,𝑡𝑡

    𝑁𝑁𝑠𝑠(𝑤𝑤𝑡𝑡 ,𝜃𝜃𝑡𝑡)

    𝐿𝐿𝐿𝐿(𝐿𝐿𝑡𝑡 ,𝑃𝑃0,𝑡𝑡)

    𝐴𝐴𝑡𝑡𝐹𝐹(𝐾𝐾𝑡𝑡,𝑁𝑁𝑡𝑡)

    𝑌𝑌𝑡𝑡 = 𝑌𝑌𝑡𝑡

    𝑟𝑟𝑡𝑡

    𝐴𝐴𝐴𝐴

    𝑃𝑃�0,𝑡𝑡 𝑤𝑤0,𝑡𝑡

    17 / 38

  • Increase in Mt

    I Whereas in the neoclassical model Yt is supply determined, inthe New Keynesian model output is demand determined

    I First, figure out what Yt is, and then figure out what Nt mustbe to support that

    I In an increase in Mt shifts the LM curve to the right, andhence the AD curve to the right as well

    I With a horizontal (as opposed to vertical) AS curve, thisresults in a higher Yt and lower rt

    I The lower rt stimulates It ; lower rt plus higher Yt means Ct ishigher

    I To support higher Yt , Nt must rise

    I To induce workers to work more, wt must rise

    18 / 38

  • Increase in Mt : Graphically

    𝑤𝑤𝑡𝑡

    𝑃𝑃𝑡𝑡

    𝑌𝑌𝑡𝑡 𝑌𝑌𝑡𝑡

    𝑌𝑌𝑡𝑡

    𝑌𝑌𝑡𝑡

    𝑌𝑌𝑡𝑡

    𝑁𝑁𝑡𝑡

    𝑁𝑁𝑡𝑡

    𝐴𝐴𝐴𝐴

    𝐼𝐼𝐴𝐴

    𝑟𝑟0,𝑡𝑡

    𝑌𝑌0,𝑡𝑡 𝑁𝑁0,𝑡𝑡

    𝑁𝑁𝑠𝑠(𝑤𝑤𝑡𝑡 ,𝜃𝜃𝑡𝑡)

    𝐿𝐿𝐿𝐿(𝐿𝐿0,𝑡𝑡,𝑃𝑃0,𝑡𝑡)

    𝐴𝐴𝑡𝑡𝐹𝐹(𝐾𝐾𝑡𝑡,𝑁𝑁𝑡𝑡) 𝑌𝑌𝑡𝑡 = 𝑌𝑌𝑡𝑡

    𝑟𝑟𝑡𝑡

    𝐴𝐴𝐴𝐴

    𝑃𝑃�0,𝑡𝑡 𝑤𝑤0,𝑡𝑡

    𝐿𝐿𝐿𝐿(𝐿𝐿1,𝑡𝑡,𝑃𝑃0,𝑡𝑡)

    𝑌𝑌1,𝑡𝑡

    𝑤𝑤1,𝑡𝑡

    𝑁𝑁1,𝑡𝑡

    𝐴𝐴𝐴𝐴′

    𝑟𝑟1,𝑡𝑡

    0 subscript: original

    1 subscript: post-shock

    Original

    Post-shock

    19 / 38

  • Increase in Mt : Graphically in Neoclassical Model

    𝑤𝑤𝑡𝑡 𝑃𝑃𝑡𝑡

    𝑌𝑌𝑡𝑡 𝑌𝑌𝑡𝑡

    𝑌𝑌𝑡𝑡

    𝑌𝑌𝑡𝑡

    𝑌𝑌𝑡𝑡

    𝑁𝑁𝑡𝑡

    𝑁𝑁𝑡𝑡

    𝐴𝐴𝐴𝐴

    𝐼𝐼𝐴𝐴

    𝑤𝑤𝑡𝑡

    𝑟𝑟0,𝑡𝑡

    𝑌𝑌0,𝑡𝑡 𝑁𝑁0,𝑡𝑡

    𝑁𝑁𝑑𝑑(𝑤𝑤𝑡𝑡,𝐴𝐴𝑡𝑡 ,𝐾𝐾𝑡𝑡)

    𝐿𝐿𝐿𝐿�𝐿𝐿0,𝑡𝑡,𝑃𝑃0,𝑡𝑡� = 𝐿𝐿𝐿𝐿(𝐿𝐿1,𝑡𝑡,𝑃𝑃1,𝑡𝑡)

    𝐴𝐴𝑡𝑡𝐹𝐹(𝐾𝐾𝑡𝑡,𝑁𝑁𝑡𝑡)

    𝑌𝑌𝑡𝑡 = 𝑌𝑌𝑡𝑡

    𝑟𝑟𝑡𝑡

    𝐴𝐴𝐴𝐴

    𝑃𝑃0,𝑡𝑡

    𝑁𝑁𝑠𝑠(𝑤𝑤𝑡𝑡 ,𝜃𝜃𝑡𝑡)

    𝐿𝐿𝐿𝐿(𝐿𝐿1,𝑡𝑡,𝑃𝑃0,𝑡𝑡)

    𝐴𝐴𝐴𝐴′

    𝑃𝑃1,𝑡𝑡

    Original

    Post-shock

    Post-shock, indirect effect of 𝑃𝑃𝑡𝑡 on LM

    0 subscript: original

    1 subscript: post-shock

    20 / 38

  • IS Shock

    I Increase in qt , At+1, Gt , or decrease in Gt+1: shifts IS curveto the right

    I Results in AD curve shifting to the right, which means higherYt

    I Higher Yt means that Nt must rise

    I Again, compare results to neoclassical model

    21 / 38

  • Sticky Price Model: IS Shock

    𝑤𝑤𝑡𝑡

    𝑃𝑃𝑡𝑡

    𝑌𝑌𝑡𝑡 𝑌𝑌𝑡𝑡

    𝑌𝑌𝑡𝑡

    𝑌𝑌𝑡𝑡

    𝑌𝑌𝑡𝑡

    𝑁𝑁𝑡𝑡

    𝑁𝑁𝑡𝑡

    𝐴𝐴𝐴𝐴

    𝐼𝐼𝐴𝐴

    𝑟𝑟0,𝑡𝑡

    𝑌𝑌0,𝑡𝑡 𝑁𝑁0,𝑡𝑡

    𝑁𝑁𝑠𝑠(𝑤𝑤𝑡𝑡 ,𝜃𝜃𝑡𝑡)

    𝐿𝐿𝐿𝐿(𝐿𝐿𝑡𝑡 ,𝑃𝑃0,𝑡𝑡)

    𝐴𝐴𝑡𝑡𝐹𝐹(𝐾𝐾𝑡𝑡,𝑁𝑁𝑡𝑡) 𝑌𝑌𝑡𝑡 = 𝑌𝑌𝑡𝑡

    𝑟𝑟𝑡𝑡

    𝐴𝐴𝐴𝐴

    𝑃𝑃�0,𝑡𝑡 𝑤𝑤0,𝑡𝑡

    𝐴𝐴𝐴𝐴′

    𝑟𝑟1,𝑡𝑡

    𝑌𝑌1,𝑡𝑡

    𝑤𝑤1,𝑡𝑡

    𝑁𝑁1,𝑡𝑡

    𝐼𝐼𝐴𝐴′ 0 subscript: original

    1 subscript: post-shock

    Original

    Post-shock

    22 / 38

  • Increase in At

    I Since P̄t doesn’t change, in the sticky price model an increasein At has no effect on Yt

    I Mechanically, this means that Nt must fall

    23 / 38

  • Increase in At : Graphically

    𝑤𝑤𝑡𝑡 𝑃𝑃𝑡𝑡

    𝑌𝑌𝑡𝑡 𝑌𝑌𝑡𝑡

    𝑌𝑌𝑡𝑡

    𝑌𝑌𝑡𝑡

    𝑌𝑌𝑡𝑡

    𝑁𝑁𝑡𝑡

    𝑁𝑁𝑡𝑡

    𝐴𝐴𝐴𝐴

    𝐼𝐼𝐴𝐴

    𝑟𝑟0,𝑡𝑡

    𝑌𝑌0,𝑡𝑡 𝑁𝑁0,𝑡𝑡

    𝑁𝑁𝑠𝑠(𝑤𝑤𝑡𝑡 ,𝜃𝜃𝑡𝑡)

    𝐿𝐿𝐿𝐿(𝐿𝐿𝑡𝑡 ,𝑃𝑃0,𝑡𝑡)

    𝐴𝐴0,𝑡𝑡𝐹𝐹(𝐾𝐾𝑡𝑡,𝑁𝑁𝑡𝑡)

    𝑌𝑌𝑡𝑡 = 𝑌𝑌𝑡𝑡

    𝑟𝑟𝑡𝑡

    𝐴𝐴𝐴𝐴

    𝑃𝑃�0,𝑡𝑡 𝑤𝑤0,𝑡𝑡

    𝑤𝑤1,𝑡𝑡

    𝑁𝑁1,𝑡𝑡

    𝐴𝐴1,𝑡𝑡𝐹𝐹(𝐾𝐾𝑡𝑡,𝑁𝑁𝑡𝑡)

    0 subscript: original

    1 subscript: post-shock

    Original

    Post-shock

    24 / 38

  • Comparing Neoclassical and New Keynesian Models

    I Useful rule of thumb: demand shocks have bigger effects inNew Keynesian model and supply shocks smaller effectsrelative to neoclassical model

    I For productivity shock in particular, it is “contractionary” insense of lowering hours worked

    I Some empirical debate on this:I Gali (1999) and Basu, Fernald, and Kimball (2006): positive

    productivity shock lowers hours in the short run (i.e. the NewKeynesian model) and raises hours in the medium run (i.e. theneoclassical model)

    I Nevertheless, there is some debate about these empiricalfindings

    25 / 38

  • Increase in P̄t

    I This is the only exogenous variable which will shift the AScurve in the sticky price model

    I Real world interpretation: increase in prices of intermediateinputs (e.g. price of oil)

    I Results in AS shifting up, Yt falling, and Pt rising. Sometimescalled “stagflation” – prices (inflation) rising and output(employment) declining

    26 / 38

  • Graphical Effects: Increase in P̄t

    𝑤𝑤𝑡𝑡 𝑃𝑃𝑡𝑡

    𝑌𝑌𝑡𝑡 𝑌𝑌𝑡𝑡

    𝑌𝑌𝑡𝑡

    𝑌𝑌𝑡𝑡

    𝑌𝑌𝑡𝑡

    𝑁𝑁𝑡𝑡

    𝑁𝑁𝑡𝑡

    𝐴𝐴𝐴𝐴

    𝐼𝐼𝐴𝐴

    𝑟𝑟0,𝑡𝑡

    𝑌𝑌0,𝑡𝑡 𝑁𝑁0,𝑡𝑡

    𝑁𝑁𝑠𝑠(𝑤𝑤𝑡𝑡 ,𝜃𝜃𝑡𝑡)

    𝐿𝐿𝐿𝐿(𝐿𝐿𝑡𝑡 ,𝑃𝑃0,𝑡𝑡)

    𝐴𝐴𝑡𝑡𝐹𝐹(𝐾𝐾𝑡𝑡,𝑁𝑁𝑡𝑡)

    𝑌𝑌𝑡𝑡 = 𝑌𝑌𝑡𝑡

    𝑟𝑟𝑡𝑡

    𝐴𝐴𝐴𝐴

    𝑃𝑃�0,𝑡𝑡 𝑤𝑤0,𝑡𝑡

    𝐴𝐴𝐴𝐴′ 𝑃𝑃�1,𝑡𝑡

    𝑁𝑁1,𝑡𝑡 𝑌𝑌1,𝑡𝑡

    𝑤𝑤1,𝑡𝑡

    𝑟𝑟1,𝑡𝑡

    𝐿𝐿𝐿𝐿(𝐿𝐿𝑡𝑡 ,𝑃𝑃1,𝑡𝑡)

    0 subscript: original

    1 subscript: post-shock

    Original

    Post-shock

    Post-shock, indirect effect of 𝑃𝑃𝑡𝑡 on LM

    27 / 38

  • Summarizing Qualitative Effects in the Sticky Price Model

    Exogenous ShockVariable ↑ Mt ↑ IS curve ↑ At ↑ θt ↑ P̄tYt + + 0 0 -

    Nt + + - 0 -

    wt + + - + -

    rt - + 0 0 +

    it - + 0 0 +

    Pt 0 0 0 0 +

    28 / 38

  • Dynamics

    I The New Keynesian model is a special case of the neoclassicalmodel – we simply swap labor demand with a fixed nominalprice

    I Call Y ft the “flexible price” level of output – the level ofoutput which would emerge in the neoclassical model

    I If firm could adjust price, it would do so that it is on its labordemand curve, which would entail Yt = Y ft

    I Refer to Yt − Y ft as the output gap – the gap between actualoutput and what it would be in the absence of price stickiness

    I To see this graphically, draw in a hypothetical AS curve forthe neoclassical model – call this AS f

    29 / 38

  • A Negative Output Gap

    𝑤𝑤𝑡𝑡 𝑃𝑃𝑡𝑡

    𝑌𝑌𝑡𝑡 𝑌𝑌𝑡𝑡

    𝑌𝑌𝑡𝑡

    𝑌𝑌𝑡𝑡

    𝑌𝑌𝑡𝑡

    𝑁𝑁𝑡𝑡

    𝑁𝑁𝑡𝑡

    𝐴𝐴𝐴𝐴

    𝐼𝐼𝐴𝐴

    𝑟𝑟0,𝑡𝑡

    𝑌𝑌0,𝑡𝑡 𝑁𝑁0,𝑡𝑡

    𝑁𝑁𝑠𝑠(𝑤𝑤𝑡𝑡 ,𝜃𝜃𝑡𝑡)

    𝐿𝐿𝐿𝐿(𝐿𝐿𝑡𝑡 ,𝑃𝑃0,𝑡𝑡)

    𝐴𝐴𝑡𝑡𝐹𝐹(𝐾𝐾𝑡𝑡,𝑁𝑁𝑡𝑡)

    𝑌𝑌𝑡𝑡 = 𝑌𝑌𝑡𝑡

    𝑟𝑟𝑡𝑡

    𝐴𝐴𝐴𝐴

    𝑃𝑃�0,𝑡𝑡 𝑤𝑤0,𝑡𝑡

    𝑁𝑁0,𝑡𝑡𝑓𝑓 𝑌𝑌0,𝑡𝑡

    𝑓𝑓

    𝑁𝑁𝑑𝑑(𝑤𝑤𝑡𝑡,𝐴𝐴𝑡𝑡 ,𝐾𝐾𝑡𝑡)

    𝐴𝐴𝐴𝐴𝑓𝑓

    𝑤𝑤0,𝑡𝑡𝑓𝑓

    Sticky price model

    Hypothetical flexible price model

    𝑃𝑃0,𝑡𝑡𝑓𝑓

    0 subscript: equilibrium value

    f superscript: hypothetical flexible price equilibrium

    𝐿𝐿𝐿𝐿(𝐿𝐿𝑡𝑡 ,𝑃𝑃0,𝑡𝑡𝑓𝑓 )

    𝑟𝑟0,𝑡𝑡𝑓𝑓

    30 / 38

  • Transition from Short Run to Medium Run

    I If the firm is producing less than it would like, it will facepressure to lower its price

    I Hence, as we transition from short run (price fixed) tomedium run (price flexible), the firm will lower its price, P̄t

    I This will cause the AS curve to shift down, and output to rise

    I This pressure will persist until “the gap is closed”

    31 / 38

  • Closing the Gap

    𝑤𝑤𝑡𝑡 𝑃𝑃𝑡𝑡

    𝑌𝑌𝑡𝑡 𝑌𝑌𝑡𝑡

    𝑌𝑌𝑡𝑡

    𝑌𝑌𝑡𝑡

    𝑌𝑌𝑡𝑡

    𝑁𝑁𝑡𝑡

    𝑁𝑁𝑡𝑡

    𝐴𝐴𝐴𝐴

    𝐼𝐼𝐴𝐴

    𝑟𝑟0,𝑡𝑡

    𝑌𝑌0,𝑡𝑡 𝑁𝑁0,𝑡𝑡

    𝑁𝑁𝑠𝑠(𝑤𝑤𝑡𝑡 ,𝜃𝜃𝑡𝑡)

    𝐿𝐿𝐿𝐿(𝐿𝐿𝑡𝑡 ,𝑃𝑃0,𝑡𝑡)

    𝐴𝐴𝑡𝑡𝐹𝐹(𝐾𝐾𝑡𝑡,𝑁𝑁𝑡𝑡)

    𝑌𝑌𝑡𝑡 = 𝑌𝑌𝑡𝑡

    𝑟𝑟𝑡𝑡

    𝐴𝐴𝐴𝐴

    𝑃𝑃�0,𝑡𝑡 𝑤𝑤0,𝑡𝑡

    𝑁𝑁1,𝑡𝑡= 𝑁𝑁0,𝑡𝑡

    𝑓𝑓 𝑌𝑌1,𝑡𝑡= 𝑌𝑌0,𝑡𝑡

    𝑓𝑓

    𝑁𝑁𝑑𝑑(𝑤𝑤𝑡𝑡,𝐴𝐴𝑡𝑡 ,𝐾𝐾𝑡𝑡)

    𝐴𝐴𝐴𝐴𝑓𝑓

    𝑤𝑤1,𝑡𝑡 = 𝑤𝑤0,𝑡𝑡𝑓𝑓

    Sticky price model

    Hypothetical flexible price model

    𝑃𝑃�1,𝑡𝑡 = 𝑃𝑃0,𝑡𝑡𝑓𝑓

    0 subscript: equilibrium value

    f superscript: hypothetical flexible price equilibrium

    1 subscript: equilibrium value after price adjustment

    𝐿𝐿𝐿𝐿�𝐿𝐿𝑡𝑡 ,𝑃𝑃0,𝑡𝑡𝑓𝑓 �

    = 𝐿𝐿𝐿𝐿(𝐿𝐿𝑡𝑡 ,𝑃𝑃1,𝑡𝑡)

    𝑟𝑟1,𝑡𝑡 = 𝑟𝑟0,𝑡𝑡𝑓𝑓

    𝐴𝐴𝐴𝐴′

    Sticky price model, post price adjustment

    32 / 38

  • Dynamic Response to Shocks

    I Can use this approach to think about effects of shocks in bothshort run and medium run

    I In short run, AS curve is fixed, and we determine endogenousvariables with that fixed AS curve

    I In the medium run, the AS curve adjusts to “close the gap.”Can graphically do this by thinking about a hypotheticalvertical “medium run” AS curve (AS f ).

    33 / 38

  • Phillips Curve

    I This analysis suggests that there ought to exist a positiverelationship between the output gap, Yt − Y ft , and theinflation rate, πt (the change in prices)

    I Positive output gaps put upward pressure on prices, andnegative gaps downward pressure on prices

    I The Phillips Curve formalizes this idea. Something like:

    πt = γ(Yt − Y ft ), γ > 0

    34 / 38

  • Empirical Relationship Between Inflation and the OutputGap

    -2

    0

    2

    4

    6

    8

    10

    12

    14

    -.08 -.06 -.04 -.02 .00 .02 .04 .06

    Output Gap

    Infla

    tion

    Inflation - Output Gap Scatter Plot1960 - 2016

    I Masks sub-sample differencesI Ambiguity about how to measure Y ft empirically

    35 / 38

  • Can Monetary Policy Permanently Engineer HigherOutput?

    I No

    I Can temporarily raise output by increasing Mt , but in mediumrun this puts upward pressure on prices and the effect goesaway

    I Continually trying to raise output will only result in moreinflation

    I Further, it may cause the firm to anticipate the change in Mt ,which could cause the AS curve to shift simultaneously withthe AD shift, resulting in no effect of monetary expansion onoutput

    I It is really only unanticipated monetary expansion that canstimulate output, and even then only for a while

    36 / 38

  • Fully Anticipated Increase in Mt , so that P̄t also rises

    𝑤𝑤𝑡𝑡 𝑃𝑃𝑡𝑡

    𝑌𝑌𝑡𝑡 𝑌𝑌𝑡𝑡

    𝑌𝑌𝑡𝑡

    𝑌𝑌𝑡𝑡

    𝑌𝑌𝑡𝑡

    𝑁𝑁𝑡𝑡

    𝑁𝑁𝑡𝑡

    𝐴𝐴𝐴𝐴

    𝐼𝐼𝐴𝐴

    𝑟𝑟0,𝑡𝑡 = 𝑟𝑟1,𝑡𝑡

    𝑌𝑌0,𝑡𝑡= 𝑌𝑌1,𝑡𝑡

    𝑁𝑁0,𝑡𝑡= 𝑁𝑁1,𝑡𝑡

    𝑁𝑁𝑠𝑠(𝑤𝑤𝑡𝑡 ,𝜃𝜃𝑡𝑡)

    𝐿𝐿𝐿𝐿�𝐿𝐿0,𝑡𝑡,𝑃𝑃0,𝑡𝑡� =

    𝐿𝐿𝐿𝐿�𝐿𝐿1,𝑡𝑡,𝑃𝑃1,𝑡𝑡�

    𝐴𝐴𝑡𝑡𝐹𝐹(𝐾𝐾𝑡𝑡,𝑁𝑁𝑡𝑡)

    𝑌𝑌𝑡𝑡 = 𝑌𝑌𝑡𝑡

    𝑟𝑟𝑡𝑡

    𝐴𝐴𝐴𝐴

    𝑃𝑃�0,𝑡𝑡 𝑤𝑤0,𝑡𝑡 = 𝑤𝑤1,𝑡𝑡

    𝐿𝐿𝐿𝐿(𝐿𝐿1,𝑡𝑡,𝑃𝑃0,𝑡𝑡)

    𝐴𝐴𝐴𝐴′

    𝐴𝐴𝐴𝐴′ 𝑃𝑃�1,𝑡𝑡

    0 subscript: initial equilibrium

    1 subscript: post-shock equilibrium where 𝐿𝐿𝑡𝑡 increases but this is anticipated and reflected in 𝑃𝑃�𝑡𝑡

    Original

    Post-shock

    Indirect of price on position of LM

    37 / 38

  • Costless Disinflation

    I Can central bank lower prices (disinflation) without incurringan output loss?

    I Conventional wisdom for 1980-1982 recession was that it wascaused by Fed trying to get inflation under control (negativemonetary shock)

    I Suppose that the Fed announces in advance that it is going toreduce Mt . If firms believe this, they may adjust prices downin anticipation, causing AS curve to shift down at same timethe AD shifts in

    I In principle, this allows for a reduction in Pt with no change inYt – i.e. costless disinflation

    I Underscores importance of central bank credibility andcommunication: for this to work, people must believe thecentral bank, and the central bank must clearly communicateits objectives

    38 / 38


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