Do Flexible Durable Goods Prices Undermine Sticky Price Models?
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Transcript of Do Flexible Durable Goods Prices Undermine Sticky Price Models?
Do Flexible Durable Goods Prices Undermine Sticky Price Models?
Bob Barsky, Chris House, Miles Kimball.
University of Michigan
Common Features of Sticky Price Models
• One sector.
• Symmetric price rigidity.
• Often only non-durable goods.
Reality
• Not all prices are equally sticky.
• Example: Coke vs. Lettuce
What happens to sticky price models when some prices are flexible?
Guess : The model behaves as if all firms had the average degree of price rigidity.
Safe to ignore differences at the aggregate level
Model the economy as though all goods had the average degree of nominal rigidity.
This is wrong in general.
Findings:
• Durable goods are much more important in sticky price models than nondurables.
• Durables with flexible prices strong tendency for negative comovement.
• Extreme case: flexibly priced durables imply that money is neutral w.r.t. output and employment.
Durable Goods in the Data:
-4 0 4 8 160.4
0.6
0.8
1
1.2
1.4
Starts-4 0 4 8 16
0.9
0.95
1
1.05
1.1
1.15
real nonduruablesdef
Romer dateTrend
-4 0 4 8 160.8
0.9
1
1.1
1.2
1.3
real durablesdef
-4 0 4 8 160.9
0.95
1
1.05
1.1
1.15
real GDPdef
-4 0 4 8 160.6
0.8
1
1.2
Real Res Investmentdef
-4 0 4 8 160.6
0.8
1
1.2
real autocpi
Average Response of Real Production Following a Romer Date
-4 0 4 8 12 160.8
0.85
0.9
0.95
1
1.05
1.1
1.15
Avg House pr / CPI nondur-4 0 4 8 12 16
0.85
0.9
0.95
1
1.05
1.1
Med House pr/ CPI nondur
-4 0 4 8 12 160.92
0.94
0.96
0.98
1
1.02
1.04
CPI durables/ CPI nondur-4 0 4 8 12 16
0.9
0.95
1
1.05
CPI cars/ CPI nondur
Average Response of Relative Prices Following a Romer Date
Durable Goods in the Data:
Durables respond strongly to monetary policy.
The relative price of durables falls after a monetary contraction.
Framework
Representative agent seeks to maximize:
[ ]1 2 1 20
( , ,... , ...) ( )tt t t t t t
t
E u c c d d v Nb¥
=
-å
subject to:
1
n
jt jt t t tj
P x W N=
£ +På
xjt are net purchases of good j
Nondurables: cjt = xjt
Durables: dj,t = dj,t-1(1 -) + xjt
Other Features
• Labor is mobile across sectors
• Money Demand:
• Production:
t jt jtj
M P x=å
jt jtx F n
• Prices are markups over marginal cost:
,
tjt jt jt jt
N jt
WP MC
MP
Flexible price sectors jt = j.
jt : marginal utility of having an additional
unit of good j
Labor supply decision:
'( ) tt jt
jt
Wv N
Pg=
For durable goods sectors jt ≈ j
[ ]21 2
1 1
(1 ) (1 ) ...t ttjt
jt jt jt
u uu
d d dg b d b d+ +
+ +
¶ ¶¶= + - + - +¶ ¶ ¶
1. Stock / flow distinction u′(djt) djt is almost constant.
2. Durables are long-lived
Why?
The Comovement Problem
Consider a durable good with flexible prices
't
jt j jt j
jt
WP MC
F n
' tt jt
jt
Wv N
P
The Comovement Problem
Consider a durable good with flexible prices
' 'jt jt
j
v N F n
If Nt rises then njt must fall.
The comovement problem is very robust for durable goods. Demand does not rise for durables (the ’s are all constant) No income effects for durable goods. MC increase as employment rises (labor mobility).
Sticky Prices and the Neutrality of Money
If … • Durables have flexible prices.
• Labor is fully mobile
• The MPN is roughly constant in the durables sector.
Then,
money is neutral w.r.t. employment (and output).
The same steps above imply:
'Nj
t jj
MPv N
All durables must have flexible prices for neutrality.
Neutrality in a model with capital:
1c ct t tC A k n
1i it t tI A k n
1 (1 )t t tK K I
,
(1 )'( )
it
t k tit
A kv N
n
Labor supply:
Neutrality in a model with capital:
(1 )'( ) t
t kt
A Kv N
N
Calvo price setting
Price Rigidity: 1.3 changes per year (6 month ½ life of exogenous price rigidity).
Linear production
Utility:
Simulations:
, and c xt t t tC An X An
1 1
1 11 1
1 1 1
1 1
1
1 1t
c t d t
NC D
Calvo price setting
Price Rigidity: 1.3 changes per year (6 month ½ life of exogenous price rigidity).
Linear production
Simulations:
, and c xt t t tC An X An
Labor supply elasticity: = 1 Intertemporal substitution : = 1 Intratemporal substitution: = 1Symmetric 10% markup: = 1.1
50 100 150 200 250 300-1
-0.5
0
0.5
1
Output
Per
cent
dev
iatio
n fro
m s
tead
y st
ate
0 50 100 150 200 250 3000
0.2
0.4
0.6
0.8
1
1.2
1.4
prices
0 50 100 150 200 250 300-5
0
5
10
15x 10
-3
interest rates
nominalreal
0 50 100 150 200 250 300-1
0
1
2
3
4
5
Nondurables and Durables
NondurablesDurables
Symmetric Price Rigidity
50 100 150 200 250 300-1
-0.5
0
0.5
1
Output
Per
cent
dev
iatio
n fro
m s
tead
y st
ate
0 50 100 150 200 250 3000
0.5
1
1.5
2
2.5
3
3.5
4
prices
PdPc
0 50 100 150 200 250 300-0.1
-0.08
-0.06
-0.04
-0.02
0
0.02
interest rates
nominalreal
0 50 100 150 200 250 300-10
-8
-6
-4
-2
0
2
4
Non-durables and Durables
CX
Sticky Nondurables Prices and Flexible Durables Prices
50 100 150 200 250 300-1
-0.5
0
0.5
1
Output
Per
cent
dev
iatio
n fro
m s
tead
y st
ate
0 50 100 150 200 250 3000
0.2
0.4
0.6
0.8
1
1.2
1.4
prices
PdPc
0 50 100 150 200 250 3000
0.002
0.004
0.006
0.008
0.01
0.012
interest rates
nominalreal
0 50 100 150 200 250 300-1
0
1
2
3
4
Nondurables and Durables
CX
Sticky Durable Good Prices and Flexible Nondurable Prices
0 10 20 30 40 50 60 70 80 90 100
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Share of GDP that is comprised by the sticky price sector (%)
Out
put r
espo
nse
in th
e fi
rst q
uart
er
fo
llow
ing
a 1%
incr
ease
in M
Sticky Nondurables PricesSticky Durables Prices
1st Quarter Output Resposes for Different Models
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
1st Quarter Increase in Employment vs Durability
Em
ploy
men
t Inc
reas
e in
1st
Qua
rter
50 100 150 200 250 300-10
-5
0
PeriodsPer
cent
dev
iatio
n fr
om s
tead
y st
ate
CYX
50 100 150 200 250 300-10
-5
0
Periods
CYX
50 100 150 200 250 300-10
-5
0
Periods
CYX
Complementarity Between Durable and Nondurable Goods
Do durables have sticky prices? 1. Many durables are expensive on a per unit basis.
Negotiation costs are relatively small.
2. Some durables require customization.
3. Many new homes are priced for the first time once they are produced.
Inflation kth Order Autocorrelation:
Lag k: 1 2 3 4 5 6 7 8 9 10 11 12
CPI 0.73 0.69 0.71 0.60 0.55 0.51 0.45 0.35 0.37 0.35 0.31 0.30
Nondurables CPI 0.41 0.46 0.46 0.32 0.28 0.26 0.23 0.08 0.14 0.09 0.08 0.05
Durables CPI 0.66 0.58 0.64 0.49 0.46 0.50 0.41 0.39 0.45 0.35 0.33 0.31
Automobiles CPI 0.26 0.19 0.14 0.25 0.31 0.14 0.15 0.17 0.21 0.20 0.11 0.04
Avg House Price -0.37 0.21 -0.08 0.04 0.12 0.02 0.02 0.00 0.08 0.05 0.01 -0.06
Med House Price -0.37 0.09 0.06 0.05 -0.01 0.01 0.05 -0.04 0.02 0.06 -0.07 0.00
Sticky Wages / Input Prices
50 100 150 200 250 300-1
-0.5
0
0.5
1
Output
Per
cent
dev
iatio
n fr
om s
tead
y st
ate
0 50 100 150 200 250 3000
0.2
0.4
0.6
0.8
1
1.2
1.4
prices
PdPc
0 50 100 150 200 250 300-0.005
0
0.005
0.01
0.015
0.02
0.025
interest rates (.1 = 1/10 %)
nominalreal
0 50 100 150 200 250 300-1
0
1
2
3
4
Non-durables and Durables
CX
Sticky Wages and Flexible Durable Goods Prices
Related Work
• Ohanian and Stockman [1994]
• Ohanian, Stockman and Killian [1995] (and Leahy [1995])
• Bils, Klenow and Oleksiy [2003]
• Golosov and Lucas [2003]
Conclusions:
1. New Keynesian models behave “as they should” if and only if durables have sticky prices
2. Durable goods with flexible prices pose serious problems for sticky price models.