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The New Keynesian Model ECON 30020: Intermediate Macroeconomics

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The New Keynesian Model ECON 30020: Intermediate Macroeconomics The New Keynesian Model ECON 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 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. Wages and/or prices are imperfectly flexible I Means: 1. Money is non-neutral 2. Demand 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): wage stickiness and/or price stickiness I Mathematically, what we are going to assume is that either the nominal wage or price level are predetermined (i.e. exogenous) I This will require some change in the labor market { either the firm (price stickiness) or household (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 , qt ) 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 − pt+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 demand curve with Pt = P¯t . Firm (which sets price), has to hire labor to meet demand at P¯t rather than to maximize its value 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 (aggregate demand) and AS (aggregate supply) 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 − pt+1 I Differently than before, AD curve summarizes both real demand (the first three equations) and nominal demand (the last two) I Classical dichotomy 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 money supply I Go through graphical derivation e I LM curve will shift if Mt , Pt , or pt+1 change I Rule of thumb: LM curve shifts in the same direction as real balances, Mt Pt 7 / 38 Deriving the LM Curve , + , , = , + , , �0 +1 0 � , 1 1 � +1 � 1 , , ( , + , , ) 0 0 0 +1 1 , , , 0 0 1 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 0 ( , , , ) 0 0 ( , , , ) , 1 0 2 , 0 , 1 , 2 , 0 , 1 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 pt+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 , qt ) 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 ( , ) , 2 , 0 , 1 ( , , ) = ( , ) , , 0 0 13 / 38 Neoclassical IS-LM-AD-AS Equilibrium ( , , ) 0 , 0 ( , ) , 0 ( , , ) = ( , ) , , 0 0 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 , qt ) 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 ( , ) � = = ( , ) 16 / 38 Sticky Price IS-LM-AD-AS Equilibrium ( , , ) 0 , 0 ( , ) , , 0 �0 = ( , ) , , 0 0 17 / 38 Increase in Mt I Whereas in the neoclassical model Yt is supply determined, in the New Keynesian model output 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 ( , , , ) 0 0 Original ( , , , ) Post-shock 1 0 , 0 subscript: original 0 1 subscript: post-shock , 1 , ( , ) 1 , , 0 �0 ′ = ( , ) , , , , 0 1 0 1 19 / 38 Increase in Mt: Graphically in Neoclassical Model , , , = ( , , , ) �0 0 � 1 1 Original ( , , , ) Post-shock 1 0 Post-shock, indirect effect of on LM , 0 0 subscript: original 1 subscript: post-shock ( , ) , 1, 0 ′ ( , , ) = ( , ) , , 0 0 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 0 Post-shock , , 1 0 0 subscript: original 1 subscript: post-shock ′ ( , ) , 1 , , 0 �0 ′ = ( , ) , , , , 0 1 0 1 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 ( , , ) 0 Original Post-shock , 0 subscript: original 0 1 subscript: post-shock ( , ) , , 0 �0 , 1 = ( , ) , 1 , ( , ) 0 , , , 0 1 0 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 ( , , ) ( , , ) 1 0 Original , Post-shock 1, Post-shock, indirect effect 0 of on LM 0 subscript: original 1 subscript: post-shock ( , ) , �1 , ′ , 0 �0 , 1 = ( , ) , , , , 0 1 1 0 27 / 38 Summarizing Qualitative Effects in the Sticky Price Model Exogenous Shock Variable " Mt " IS curve " At " qt " 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
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