Download An Economical Business-Cycle Model Pascal Michaillat and Emmanuel Saez March 2015

An Economical
Business-Cycle Model
Pascal Michaillat and Emmanuel Saez
March 2015
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Objective of the paper
develop a tractable business-cycle model to
analyze monetary policy with
variable slack (unemployment + idle labor
+ idle capacity)
stable inflation
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Slack and inflation in the US
40%
idle capacity (Census)
30%
20%
10%
idle labor (ISM)
0%
1994
1999
2004
2009
2014
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Slack and inflation in the US
40%
idle capacity
10%
30%
7.5%
20%
5%
10%
idle labor
0%
1994
1999
unemployment
(right scale)
2004
2009
2.5%
2014
0%
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Slack and inflation in the US
40%
10%
slack
30%
7.5%
20%
5%
10%
2.5%
core inflation (right scale)
0%
1994
1999
2004
2009
2014
0%
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Overview of the model
start from money-in-the-utility-function model of
Sidrauski [AER 1967]
add matching frictions on market for labor
services as in Michaillat & Saez [QJE 2015]
add utility for wealth as in Kurz [IER 1968]
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Behavior of households
ε−1
ε
max
e
·
· c ε + φ (m) + ω(a) dt
c,m,a 0
ε −1
da
s.t.
= f (x ) · k − 1 + τ(x ) · c − i · m + r · a + s
+
+
dt
Z +∞
−δ ·t
c =consumption; m =real money; a =real wealth;
x =market tightness; 1 − f (x) =unemployment rate;
τ(x) =matching cost; i/r =nominal/real interest rate;
k = supply of services; δ =discount rate; s =seignorage
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Utility for real money
utility
money bliss point
real money m
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utility
Utility for real wealth
no aggregate wealth
a=m+b=0
real wealth a
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Steady state {a, m, i, c, x, π}
no real wealth in aggregate: a = 0
monetary policy sets real money m
IS curve (consumption Euler equation)
LM curve (demand for money)
AS curve (supply and matching process)
inflation π is a fixed parameter
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nominal interest rate i
IS curve with utility of wealth
IS
consumption c
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nominal interest rate i
IS curve without utility of wealth
i=⇡+
IS
consumption c
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nominal interest rate i
LM curve away from liquidity trap
LM
consumption c
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nominal interest rate i
LM curve in liquidity trap
i=0
LM
consumption c
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nominal interest rate i
IS & LM determine AD and i
aggregate demand cAD
LM
IS
consumption c
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AD curve
market tightness x
c
AD
(x, ⇡, m) =

+⇡
(1 + ⌧ (x)) · ( 0 (m) + ! 0 (0))
✏
AD
consumption c
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AS curve
market tightness x
cAS (x) =
f (x)
·k
1 + ⌧ (x)
AS
consumption c
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AS curve
market tightness x
overheating economy
efficient economy
AS
slack economy
consumption c
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market tightness x
AS & AD determine c and x
general
equilibrium
AS
AD
consumption c
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AS & AD determine output
market tightness x
output f(x)k capacity k
matching cost
AS
AD
consumption c
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AS & AD determine unemployment
market tightness x
output capacity
unemployment
= idle labor
= idle capacity
AS
AD
consumption c
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Increase in money supply
market tightness x
AS
output capacity
low tightness
and output
depressed AD
consumption c
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nominal interest rate i
Increase in money supply
AD increases
LM
IS
consumption c
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Increase in money supply
market tightness x
output capacity
efficient tightness
AS
AD
consumption c
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Money supply in a liquidity trap
market tightness x
AS
output capacity
very low tightness
and output
very depressed AD
consumption c
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nominal interest rate i
Money supply in a liquidity trap
LM in liquidity trap
IS
LM
consumption c
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Money supply in a liquidity trap
market tightness x
output capacity
inefficiently low
tightness
AS
AD in
liquidity trap
consumption c
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Extensions in the paper
policies to stimulate IS curve: tax on wealth
+ helicopter drop of money
inflation and tightness dynamics from
directed search and price-adjustment cost
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