The New Keynesian Model ECON 30020: Intermediate

Prof. Eric Sims

University of Notre Dame

Fall 2016

1 / 38 New Keynesian Models

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

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

I Basic difference: nominal rigidities. and/or are imperfectly flexible I Means: 1. is non-neutral 2. shocks matter 3. Equilibrium of the model is inefficient 4. 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 Keynesian models are the same

I Differences arise on the supply side I Two basic variants (or mixture of the two): stickiness and/or stickiness

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

I This will require some change in the labor – either the firm (price stickiness) or (wage stickiness) is off its demand or supply schedule

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

3 / 38 Review: Neoclassical Model:

I Equilibrium conditions: d Ct = C (Yt − Gt , Yt+1 − Gt , rt ) s Nt = N (wt , θt ) d Nt = N (wt , At , Kt ) d It = I (rt , At+1, qt , Kt )

Yt = At F (Kt , Nt )

Yt = Ct + It + Gt d Mt = Pt M (it , Yt ) e rt = it − πt+1

I Pt is endogenous I Nominal wage, Wt , is Wt = wt Pt , and is also therefore endogenous

4 / 38 New Keynesian Model

I Sticky price model: I Pt = P¯t is now exogenous, rather than endogenous I Extreme form of price stickiness: price level completely pre-determined I Replace labor with Pt = P¯t . Firm (which sets price), has to hire labor to meet demand at P¯t rather than to maximize its I Sticky wage model: I Wt = W¯ t is now exogenous, rather than endogenous I Extreme form of wage stickiness: wage set “in advance,” worker has to supply as much labor as is demanded at this wage I This means that we replace the labor supply curve with the condition wt = W¯ t /Pt

5 / 38 Graphing the Equilibrium

I We will use the AD () and AS () curves to summarize the equilibrium I AD: stands for aggregate demand. Summarizes the following conditions: d Ct = C (Yt − Gt , Yt+1 − Gt , rt ) d It = I (rt , At+1, qt , Kt )

Yt = Ct + It + Gt d Mt = Pt M (it , Yt ) e rt = it − πt+1

I Differently than before, AD curve summarizes both real demand (the first three equations) and nominal demand (the last two) I will no longer hold, so cannot separately analyze 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 where the 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 for money demand to equal

I Go through graphical derivation e I LM curve will shift if Mt , Pt , or πt+1 change I Rule of thumb: LM curve shifts in the same direction as real balances, Mt Pt

7 / 38 Deriving the LM Curve

𝑠𝑠 𝑀𝑀 , + , , 𝑃𝑃𝑡𝑡 𝑟𝑟𝑡𝑡 𝐿𝐿𝐿𝐿 = 𝑑𝑑 , + 𝑒𝑒 , , 𝑃𝑃𝑡𝑡𝑀𝑀 �𝑟𝑟0 𝑡𝑡 𝜋𝜋𝑡𝑡+1 𝑌𝑌0 𝑡𝑡� , 𝑑𝑑 𝑒𝑒 1 𝑡𝑡 1 𝑡𝑡 𝑀𝑀 �𝑟𝑟 𝜋𝜋𝑡𝑡+1 𝑌𝑌 � 𝑟𝑟1 𝑡𝑡 ,

, ( , + , , ) 𝑟𝑟0 𝑡𝑡 0 𝑡𝑡 𝑑𝑑 𝑒𝑒 𝑃𝑃 𝑃𝑃𝑡𝑡𝑀𝑀 𝑟𝑟0 𝑡𝑡 𝜋𝜋𝑡𝑡+1 𝑌𝑌1 𝑡𝑡

, , , 0 𝑡𝑡 0 𝑡𝑡 𝑌𝑌 1 𝑡𝑡 𝑡𝑡 𝑀𝑀 𝑀𝑀𝑡𝑡 𝑌𝑌 𝑌𝑌 8 / 38 The AD Curve

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

I Basic idea: Pt determines position of LM curve, which determines a Yt where the LM curve intersects the IS curve. A higher Pt means the LM curve shifts in, which results in a lower Yt I Hence, the AD curve is downward-sloping I Go through graphical derivation

9 / 38 Deriving the AD Curve

( , , , )

2 𝑡𝑡 0 𝑡𝑡 𝐿𝐿𝐿𝐿 𝑃𝑃 𝑀𝑀 ( , , , ) 𝑡𝑡 𝑟𝑟 𝐿𝐿𝐿𝐿 𝑃𝑃0 𝑡𝑡 𝑀𝑀0 𝑡𝑡

( , , , )

, 𝐿𝐿𝐿𝐿 𝑃𝑃1 𝑡𝑡 𝑀𝑀0 𝑡𝑡 𝑟𝑟2 𝑡𝑡

,

𝑟𝑟0 𝑡𝑡

,

𝑟𝑟1 𝑡𝑡

𝐼𝐼𝐼𝐼

𝑌𝑌𝑡𝑡

𝑃𝑃𝑡𝑡

,

𝑃𝑃2 𝑡𝑡 ,

𝑃𝑃0 𝑡𝑡 ,

𝑃𝑃1 𝑡𝑡

𝐴𝐴𝐴𝐴

𝑌𝑌𝑡𝑡

10 / 38 Shifts of the AD Curve

I The AD curve will shift if either the IS or LM curves shift (for reason other than Pt ) I This means that the AD curve will shift right if: e I At+1, qt , or Gt increase (IS shifts); Mt or πt+1 increase (LM shifts) I Gt+1 decreases (IS shift) I Note: we could use the AD curve to summarize the demand side of the neoclassical model as well

I Was just convenient to not since this emphasized classical dichotomy 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 of labor market equilibrium, and (iii) any exogenous restriction on nominal price or wage adjustment

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

s Nt = N (wt , θt ) d Nt = N (wt , At , Kt )

Yt = At F (Kt , Nt )

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

12 / 38

The Neoclassical AS Curve

𝑡𝑡 𝑤𝑤 ( , ) 𝑡𝑡 𝑠𝑠 𝑃𝑃 𝐴𝐴𝐴𝐴 𝑁𝑁 𝑤𝑤𝑡𝑡 𝜃𝜃𝑡𝑡 ,

𝑃𝑃2 𝑡𝑡 , 𝑤𝑤𝑡𝑡 𝑃𝑃0 𝑡𝑡 ,

𝑃𝑃1 𝑡𝑡

( , , ) 𝑑𝑑 𝑡𝑡 𝑡𝑡 𝑡𝑡 𝑁𝑁 𝑤𝑤 𝐴𝐴 𝐾𝐾

𝑌𝑌𝑡𝑡 𝑡𝑡 𝑁𝑁 = 𝑡𝑡 𝑌𝑌 𝑡𝑡 𝑌𝑌 𝑌𝑌𝑡𝑡 𝑌𝑌𝑡𝑡 ( , )

𝐴𝐴𝑡𝑡𝐹𝐹 𝐾𝐾𝑡𝑡 𝑁𝑁𝑡𝑡

, , 0 𝑡𝑡 𝑡𝑡 𝑁𝑁 𝑁𝑁𝑡𝑡 𝑌𝑌0 𝑡𝑡 𝑌𝑌

13 / 38 Neoclassical IS-LM-AD-AS Equilibrium

( , , ) 𝑡𝑡 𝑟𝑟 𝐿𝐿𝐿𝐿 𝑀𝑀𝑡𝑡 𝑃𝑃0 𝑡𝑡

,

𝑟𝑟0 𝑡𝑡

𝐼𝐼𝐼𝐼

𝑡𝑡 𝑡𝑡 𝑌𝑌 𝑤𝑤 ( , ) 𝑡𝑡 𝑠𝑠 𝑃𝑃 𝐴𝐴𝐴𝐴 𝑁𝑁 𝑤𝑤𝑡𝑡 𝜃𝜃𝑡𝑡

, 𝑤𝑤𝑡𝑡 𝑃𝑃0 𝑡𝑡

( , , ) 𝐴𝐴𝐴𝐴 𝑑𝑑 𝑡𝑡 𝑡𝑡 𝑡𝑡 𝑁𝑁 𝑤𝑤 𝐴𝐴 𝐾𝐾

𝑌𝑌𝑡𝑡 𝑡𝑡 𝑁𝑁 = 𝑡𝑡 𝑌𝑌 𝑡𝑡 𝑌𝑌 𝑌𝑌𝑡𝑡 𝑌𝑌𝑡𝑡 ( , )

𝐴𝐴𝑡𝑡𝐹𝐹 𝐾𝐾𝑡𝑡 𝑁𝑁𝑡𝑡

, , 0 𝑡𝑡 𝑡𝑡 𝑁𝑁 𝑁𝑁𝑡𝑡 𝑌𝑌0 𝑡𝑡 𝑌𝑌 14 / 38 Sticky Price Model

I In sticky price model, assume that Pt = P¯t is predetermined and hence exogenous (think something like menu costs)

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

I Conditions:

s Nt = N (wt , θt )

Pt = P¯t

Yt = At F (Kt , Nt )

I The AS curve will just be horizontal at P¯t . Can only shift if P¯t changes exogenously

15 / 38 The Sticky Price AS Curve

( , ) 𝑤𝑤𝑡𝑡 𝑡𝑡 𝑠𝑠 𝑃𝑃 𝑁𝑁 𝑤𝑤𝑡𝑡 𝜃𝜃𝑡𝑡

𝑃𝑃�𝑡𝑡 𝐴𝐴𝐴𝐴

𝑌𝑌𝑡𝑡 𝑁𝑁𝑡𝑡 = 𝑌𝑌𝑡𝑡 𝑌𝑌𝑡𝑡 = ( , ) 𝑌𝑌𝑡𝑡 𝑌𝑌𝑡𝑡

𝑌𝑌𝑡𝑡 𝐴𝐴𝑡𝑡𝐹𝐹 𝐾𝐾𝑡𝑡 𝑁𝑁𝑡𝑡

𝑌𝑌𝑡𝑡 𝑁𝑁𝑡𝑡

16 / 38 Sticky Price IS-LM-AD-AS Equilibrium

( , , ) 𝑡𝑡 𝑟𝑟 𝐿𝐿𝐿𝐿 𝑀𝑀𝑡𝑡 𝑃𝑃0 𝑡𝑡

,

𝑟𝑟0 𝑡𝑡

𝐼𝐼𝐼𝐼

( , ) 𝑡𝑡 𝑡𝑡 𝑌𝑌 𝑤𝑤 𝑠𝑠 𝑁𝑁 𝑤𝑤𝑡𝑡 𝜃𝜃𝑡𝑡 𝑃𝑃𝑡𝑡

, , 0 𝑡𝑡 𝑤𝑤 𝑃𝑃�0 𝑡𝑡 𝐴𝐴𝐴𝐴

𝐴𝐴𝐴𝐴

𝑌𝑌𝑡𝑡 𝑡𝑡 𝑁𝑁 = 𝑡𝑡 𝑌𝑌 𝑡𝑡 𝑌𝑌 𝑌𝑌𝑡𝑡 𝑌𝑌𝑡𝑡 ( , )

𝐴𝐴𝑡𝑡𝐹𝐹 𝐾𝐾𝑡𝑡 𝑁𝑁𝑡𝑡

, , 0 𝑡𝑡 𝑡𝑡 𝑁𝑁 𝑁𝑁𝑡𝑡 𝑌𝑌0 𝑡𝑡 𝑌𝑌 17 / 38 Increase in Mt

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

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

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

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

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

I To support higher Yt , Nt must rise

I To induce workers to work more, wt must rise

18 / 38 Increase in Mt: Graphically

( , , , )

𝑡𝑡 𝑟𝑟 𝐿𝐿𝐿𝐿 𝑀𝑀0 𝑡𝑡 𝑃𝑃0 𝑡𝑡 Original ( , , , ) Post-shock 𝐿𝐿𝐿𝐿 𝑀𝑀1 𝑡𝑡 𝑃𝑃0 𝑡𝑡

, 0 subscript: original 𝑟𝑟0 𝑡𝑡 1 subscript: post-shock ,

𝑟𝑟1 𝑡𝑡

𝐼𝐼𝐼𝐼 𝑤𝑤𝑡𝑡

, ( , ) 𝑡𝑡 1 𝑡𝑡 𝑌𝑌 𝑤𝑤 𝑠𝑠 𝑁𝑁 𝑤𝑤𝑡𝑡 𝜃𝜃𝑡𝑡 𝑃𝑃𝑡𝑡

, , 0 𝑡𝑡 𝑤𝑤 𝑃𝑃�0 𝑡𝑡 𝐴𝐴𝐴𝐴

𝐴𝐴𝐴𝐴 ′

𝐴𝐴𝐴𝐴

𝑌𝑌𝑡𝑡 𝑡𝑡 𝑁𝑁 = ( , ) 𝑡𝑡 𝑌𝑌 𝑡𝑡 𝑌𝑌 𝑌𝑌𝑡𝑡 𝑌𝑌𝑡𝑡 𝐴𝐴𝑡𝑡𝐹𝐹 𝐾𝐾𝑡𝑡 𝑁𝑁𝑡𝑡

, , , , 𝑡𝑡 0 𝑡𝑡 𝑡𝑡 𝑌𝑌 𝑁𝑁 𝑁𝑁1 𝑡𝑡 𝑁𝑁 𝑌𝑌0 𝑡𝑡 𝑌𝑌1 𝑡𝑡 19 / 38 Increase in Mt: Graphically in Neoclassical Model

, , , = ( , , , )

𝑟𝑟𝑡𝑡 𝐿𝐿𝐿𝐿�𝑀𝑀0 𝑡𝑡 𝑃𝑃0 𝑡𝑡� 𝐿𝐿𝐿𝐿 𝑀𝑀1 𝑡𝑡 𝑃𝑃1 𝑡𝑡 Original ( , , , ) Post-shock 𝐿𝐿𝐿𝐿 𝑀𝑀1 𝑡𝑡 𝑃𝑃0 𝑡𝑡 Post-shock, indirect effect of on LM ,

𝑡𝑡 𝑃𝑃 𝑟𝑟0 𝑡𝑡 0 subscript: original

1 subscript: post-shock

𝐼𝐼𝐼𝐼

𝑡𝑡 𝑡𝑡 𝑌𝑌 𝑤𝑤 ( , ) 𝑡𝑡 𝐴𝐴𝐴𝐴 𝑠𝑠 𝑃𝑃 𝑁𝑁 𝑤𝑤𝑡𝑡 𝜃𝜃𝑡𝑡

,

𝑃𝑃1,𝑡𝑡 𝑤𝑤𝑡𝑡 𝑃𝑃0 𝑡𝑡

( , , ) 𝐴𝐴𝐴𝐴 ′ 𝑑𝑑 𝑡𝑡 𝑡𝑡 𝑡𝑡 𝐴𝐴𝐴𝐴 𝑁𝑁 𝑤𝑤 𝐴𝐴 𝐾𝐾

𝑌𝑌𝑡𝑡 𝑡𝑡 𝑁𝑁 = 𝑡𝑡 𝑌𝑌 𝑡𝑡 𝑌𝑌 𝑌𝑌𝑡𝑡 𝑌𝑌𝑡𝑡 ( , )

𝐴𝐴𝑡𝑡𝐹𝐹 𝐾𝐾𝑡𝑡 𝑁𝑁𝑡𝑡

, , 0 𝑡𝑡 𝑡𝑡 𝑁𝑁 𝑁𝑁𝑡𝑡 𝑌𝑌0 𝑡𝑡 𝑌𝑌 20 / 38 IS Shock

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

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

I Higher Yt means that Nt must rise I Again, compare results to neoclassical model

21 / 38 Sticky Price Model: IS Shock

( , , ) Original 𝑡𝑡 𝑟𝑟 𝐿𝐿𝐿𝐿 𝑀𝑀𝑡𝑡 𝑃𝑃0 𝑡𝑡 Post-shock

, , 𝑟𝑟1 𝑡𝑡 𝑟𝑟0 𝑡𝑡 0 subscript: original 1 subscript: post-shock 𝐼𝐼𝐼𝐼′

𝐼𝐼𝐼𝐼 𝑡𝑡 𝑤𝑤 ( , ) 𝑌𝑌𝑡𝑡 , 𝑠𝑠 𝑁𝑁 𝑤𝑤𝑡𝑡 𝜃𝜃𝑡𝑡 𝑃𝑃𝑡𝑡 𝑤𝑤1 𝑡𝑡

, , 0 𝑡𝑡 𝑤𝑤 𝑃𝑃�0 𝑡𝑡 𝐴𝐴𝐴𝐴

𝐴𝐴𝐴𝐴 ′

𝐴𝐴𝐴𝐴

𝑌𝑌𝑡𝑡 𝑡𝑡 𝑁𝑁 = 𝑡𝑡 ( , ) 𝑌𝑌 𝑡𝑡 𝑌𝑌 𝑌𝑌𝑡𝑡 𝑌𝑌𝑡𝑡 𝐴𝐴𝑡𝑡𝐹𝐹 𝐾𝐾𝑡𝑡 𝑁𝑁𝑡𝑡

, , , , 0 𝑡𝑡 𝑡𝑡 𝑁𝑁 𝑁𝑁1 𝑡𝑡 𝑁𝑁𝑡𝑡 𝑌𝑌0 𝑡𝑡 𝑌𝑌1 𝑡𝑡 𝑌𝑌 22 / 38 Increase in At

I Since P¯t doesn’t change, in the sticky price model an increase in At has no effect on Yt

I Mechanically, this means that Nt must fall

23 / 38 Increase in At: Graphically

( , , ) 𝑡𝑡 𝑟𝑟 𝐿𝐿𝐿𝐿 𝑀𝑀𝑡𝑡 𝑃𝑃0 𝑡𝑡 Original

Post-shock

,

0 subscript: original 𝑟𝑟0 𝑡𝑡 1 subscript: post-shock

𝐼𝐼𝐼𝐼

( , ) 𝑡𝑡 𝑡𝑡 𝑌𝑌 𝑤𝑤 𝑠𝑠 𝑁𝑁 𝑤𝑤𝑡𝑡 𝜃𝜃𝑡𝑡 𝑃𝑃𝑡𝑡

, , 0 𝑡𝑡 𝑤𝑤 𝑃𝑃�0 𝑡𝑡 𝐴𝐴𝐴𝐴 ,

1 𝑡𝑡 𝑤𝑤

𝐴𝐴𝐴𝐴

𝑌𝑌𝑡𝑡 𝑡𝑡 𝑁𝑁 = ( , ) 𝑡𝑡 , 𝑌𝑌 𝑡𝑡 𝑌𝑌 𝑌𝑌𝑡𝑡 𝑌𝑌𝑡𝑡 𝐴𝐴1 𝑡𝑡𝐹𝐹 𝐾𝐾𝑡𝑡 𝑁𝑁𝑡𝑡 , ( , )

𝐴𝐴0 𝑡𝑡𝐹𝐹 𝐾𝐾𝑡𝑡 𝑁𝑁𝑡𝑡

, , , 0 𝑡𝑡 𝑡𝑡 𝑁𝑁1 𝑡𝑡 𝑁𝑁 𝑁𝑁𝑡𝑡 𝑌𝑌0 𝑡𝑡 𝑌𝑌 24 / 38 Comparing Neoclassical and New Keynesian Models

I Useful rule of thumb: demand shocks have bigger effects in New Keynesian model and supply shocks smaller effects relative to neoclassical model

I For productivity shock in particular, it is “contractionary” in sense 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 New Keynesian model) and raises hours in the medium run (i.e. the neoclassical model) I Nevertheless, there is some debate about these empirical findings

25 / 38 Increase in P¯t

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

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

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

26 / 38 Graphical Effects: Increase in P¯t

( , , ) ( , , ) 𝑡𝑡 𝑟𝑟 𝐿𝐿𝐿𝐿 𝑀𝑀𝑡𝑡 𝑃𝑃1 𝑡𝑡 𝐿𝐿𝐿𝐿 𝑀𝑀𝑡𝑡 𝑃𝑃0 𝑡𝑡

Original , Post-shock 𝑟𝑟1,𝑡𝑡 Post-shock, indirect effect 0 𝑡𝑡 of on LM 𝑟𝑟

𝑃𝑃𝑡𝑡 0 subscript: original

1 subscript: post-shock 𝐼𝐼𝐼𝐼

( , ) 𝑡𝑡 𝑡𝑡 𝑌𝑌 𝑤𝑤 𝑠𝑠 𝑁𝑁 𝑤𝑤𝑡𝑡 𝜃𝜃𝑡𝑡 𝑃𝑃𝑡𝑡

, �1 𝑡𝑡 , 𝑃𝑃 𝐴𝐴𝐴𝐴′ , 0 𝑡𝑡 𝑤𝑤 𝑃𝑃�0 𝑡𝑡 𝐴𝐴𝐴𝐴

,

𝑤𝑤1 𝑡𝑡 𝐴𝐴𝐴𝐴

𝑌𝑌𝑡𝑡 𝑡𝑡 𝑁𝑁 = 𝑡𝑡 𝑌𝑌 𝑡𝑡 𝑌𝑌 𝑌𝑌𝑡𝑡 𝑌𝑌𝑡𝑡 ( , )

𝐴𝐴𝑡𝑡𝐹𝐹 𝐾𝐾𝑡𝑡 𝑁𝑁𝑡𝑡

, , , , 0 𝑡𝑡 𝑡𝑡 𝑁𝑁1 𝑡𝑡 𝑁𝑁 𝑁𝑁𝑡𝑡 𝑌𝑌1 𝑡𝑡 𝑌𝑌0 𝑡𝑡 𝑌𝑌 27 / 38 Summarizing Qualitative Effects in the Sticky Price Model

Exogenous Shock Variable ↑ Mt ↑ IS curve ↑ At ↑ θt ↑ P¯t Yt + + 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 neoclassical model – we simply swap labor demand with a fixed nominal price f I Call Yt the “flexible price” level of output – the level of output which would emerge in the neoclassical model

I If firm could adjust price, it would do so that it is on its labor f demand curve, which would entail Yt = Yt f I Refer to Yt − Yt as the – the gap between actual output and what it would be in the absence of price stickiness

I To see this graphically, draw in a hypothetical AS curve for the neoclassical model – call this ASf

29 / 38 A Negative Output Gap

( , , ) 𝑡𝑡 𝑟𝑟 𝐿𝐿𝐿𝐿 𝑀𝑀𝑡𝑡 𝑃𝑃0 𝑡𝑡 ( , , ) 𝑓𝑓 𝐿𝐿𝐿𝐿 𝑀𝑀𝑡𝑡 𝑃𝑃0 𝑡𝑡 Sticky price model , Hypothetical flexible price 0 𝑡𝑡 𝑟𝑟 , model 𝑓𝑓 𝑟𝑟0 𝑡𝑡 0 subscript: equilibrium value

f superscript: hypothetical flexible price equilibrium 𝐼𝐼𝐼𝐼

( , ) 𝑡𝑡 𝑡𝑡 𝑌𝑌 𝑤𝑤 𝑠𝑠 𝑁𝑁 𝑤𝑤𝑡𝑡 𝜃𝜃𝑡𝑡 𝑃𝑃𝑡𝑡 𝑓𝑓 𝐴𝐴𝐴𝐴

, 𝑓𝑓 𝑤𝑤0 𝑡𝑡 , , 0 𝑡𝑡 0 𝑡𝑡 𝑤𝑤 𝑃𝑃�, 𝐴𝐴𝐴𝐴 𝑓𝑓 𝑃𝑃0 𝑡𝑡

( , , ) 𝑑𝑑 𝐴𝐴𝐴𝐴 𝑁𝑁 𝑤𝑤𝑡𝑡 𝐴𝐴𝑡𝑡 𝐾𝐾𝑡𝑡

𝑌𝑌𝑡𝑡 𝑡𝑡 𝑁𝑁 = 𝑡𝑡 𝑌𝑌 𝑡𝑡 𝑌𝑌 𝑌𝑌𝑡𝑡 𝑌𝑌𝑡𝑡 ( , )

𝐴𝐴𝑡𝑡𝐹𝐹 𝐾𝐾𝑡𝑡 𝑁𝑁𝑡𝑡

, , , , 𝑓𝑓 𝑓𝑓 𝑡𝑡 0 𝑡𝑡 𝑡𝑡 0 𝑡𝑡 𝑌𝑌 𝑁𝑁 𝑁𝑁0 𝑡𝑡 𝑁𝑁 𝑌𝑌 𝑌𝑌0 𝑡𝑡 30 / 38 Transition from Short Run to Medium Run

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

I Hence, as we transition from short run (price fixed) to medium run (price flexible), the firm will lower its price, P¯t 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

( , , )

𝑡𝑡 𝑡𝑡 0 𝑡𝑡 Sticky price model 𝑟𝑟 𝐿𝐿𝐿𝐿 𝑀𝑀 𝑃𝑃 Hypothetical flexible price , , model 𝑓𝑓 = ( , , ) 𝐿𝐿𝐿𝐿�𝑀𝑀𝑡𝑡 𝑃𝑃0 𝑡𝑡� Sticky price model, post price , 𝑡𝑡 1 𝑡𝑡 adjustment 𝐿𝐿𝐿𝐿 𝑀𝑀 𝑃𝑃 0 𝑡𝑡 , = 𝑟𝑟 , 0 subscript: equilibrium value 𝑓𝑓 𝑟𝑟1 𝑡𝑡 𝑟𝑟0 𝑡𝑡 f superscript: hypothetical flexible price equilibrium

1 subscript: equilibrium value after price 𝐼𝐼𝐼𝐼 adjustment

( , ) 𝑡𝑡 𝑡𝑡 𝑌𝑌 𝑤𝑤 𝑠𝑠 𝑁𝑁 𝑤𝑤𝑡𝑡 𝜃𝜃𝑡𝑡 𝑃𝑃𝑡𝑡 𝑓𝑓 𝐴𝐴𝐴𝐴

, = , 𝑓𝑓 𝑤𝑤1 𝑡𝑡 𝑤𝑤0 𝑡𝑡 , , 0 𝑡𝑡 𝑤𝑤 , = 𝑃𝑃�,0 𝑡𝑡 𝐴𝐴𝐴𝐴 𝑓𝑓 𝑃𝑃�1 𝑡𝑡 𝑃𝑃0 𝑡𝑡 𝐴𝐴𝐴𝐴′

( , , ) 𝑑𝑑 𝐴𝐴𝐴𝐴 𝑁𝑁 𝑤𝑤𝑡𝑡 𝐴𝐴𝑡𝑡 𝐾𝐾𝑡𝑡

𝑌𝑌𝑡𝑡 𝑡𝑡 𝑁𝑁 = 𝑡𝑡 𝑌𝑌 𝑡𝑡 𝑌𝑌 𝑌𝑌𝑡𝑡 𝑌𝑌𝑡𝑡 ( , )

𝐴𝐴𝑡𝑡𝐹𝐹 𝐾𝐾𝑡𝑡 𝑁𝑁𝑡𝑡

, , , , = = 𝑡𝑡 𝑁𝑁0 𝑡𝑡 𝑁𝑁1 𝑡𝑡 , 𝑡𝑡 𝑌𝑌0 𝑡𝑡 𝑌𝑌1 𝑡𝑡 , 𝑌𝑌 𝑓𝑓 𝑁𝑁 𝑓𝑓 𝑁𝑁0 𝑡𝑡 𝑌𝑌0 𝑡𝑡 32 / 38 Dynamic Response to Shocks

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

I In short run, AS curve is fixed, and we determine endogenous variables 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 hypothetical vertical “medium run” AS curve (ASf ).

33 / 38

I This analysis suggests that there ought to exist a positive f relationship between the output gap, Yt − Yt , and the inflation rate, πt (the change in prices) I Positive output gaps put upward pressure on prices, and negative gaps downward pressure on prices

I The Phillips Curve formalizes this idea. Something like:

f πt = γ(Yt − Yt ), γ > 0

34 / 38 Empirical Relationship Between Inflation and the Output Gap

Inflation - Output Gap Scatter Plot 1960 - 2016

14

12

10

8

6 4

2

0

-2 -.08 -.06 -.04 -.02 .00 .02 .04 .06

Output Gap

I Masks sub-sample differences f I Ambiguity about how to measure Yt empirically 35 / 38 Can Permanently Engineer Higher Output?

I No

I Can temporarily raise output by increasing Mt , but in medium run this puts upward pressure on prices and the effect goes away

I Continually trying to raise output will only result in more inflation

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

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

36 / 38 Fully Anticipated Increase in Mt, so that P¯t also rises

, , , =

𝑟𝑟𝑡𝑡 𝐿𝐿𝐿𝐿�𝑀𝑀0 𝑡𝑡 𝑃𝑃,0 𝑡𝑡� Original , , ( , ) 𝐿𝐿𝐿𝐿�𝑀𝑀1 𝑡𝑡 𝑃𝑃1 𝑡𝑡� , , Post-shock 𝐿𝐿𝐿𝐿 𝑀𝑀1 𝑡𝑡 𝑃𝑃0 𝑡𝑡 Indirect of price on = position of LM , , 𝑟𝑟0 𝑡𝑡 𝑟𝑟1 𝑡𝑡 0 subscript: initial equilibrium

1 subscript: post-shock equilibrium where increases but this is anticipated and reflected𝑡𝑡 in 𝑀𝑀 𝐼𝐼𝐼𝐼 𝑡𝑡 𝑃𝑃�

( , ) 𝑡𝑡 𝑡𝑡 𝑌𝑌 𝑤𝑤 𝑠𝑠 𝑁𝑁 𝑤𝑤𝑡𝑡 𝜃𝜃𝑡𝑡 𝑃𝑃𝑡𝑡

, , = , 𝑃𝑃�1 𝑡𝑡, 𝐴𝐴𝐴𝐴 ′ 0 𝑡𝑡 1 𝑡𝑡 𝑤𝑤 𝑤𝑤 𝑃𝑃�0 𝑡𝑡 𝐴𝐴𝐴𝐴

𝐴𝐴𝐴𝐴′

𝐴𝐴𝐴𝐴

𝑌𝑌𝑡𝑡 𝑡𝑡 𝑁𝑁 = 𝑡𝑡 𝑌𝑌 𝑡𝑡 𝑌𝑌 𝑌𝑌𝑡𝑡 𝑌𝑌𝑡𝑡 ( , )

𝐴𝐴𝑡𝑡𝐹𝐹 𝐾𝐾𝑡𝑡 𝑁𝑁𝑡𝑡

, , = 0 𝑡𝑡 , = , 𝑡𝑡 𝑁𝑁 𝑁𝑁𝑡𝑡 𝑌𝑌0 𝑡𝑡 𝑌𝑌 1 𝑡𝑡 𝑁𝑁 𝑌𝑌1 𝑡𝑡 37 / 38 Costless Disinflation

I Can lower prices (disinflation) without incurring an output loss?

I Conventional wisdom for 1980-1982 was that it was caused by Fed trying to get inflation under control (negative monetary shock)

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

I In principle, this allows for a reduction in Pt with no change in Yt – i.e. costless disinflation I Underscores importance of central bank credibility and communication: for this to work, people must believe the central bank, and the central bank must clearly communicate its objectives

38 / 38