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.