p. 1/22 · 2016-05-26 · Value of a shopper or a job-seeker is H S = H U = 73.0 Value of a buyer...

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Nominal Rigidities and the Dynamic Effects of a

Shock to Monetary Policy

Lawrence J. Christiano and Martin EichenbaumNorthwestern University, National Bureau of Economic Research, and Federal Reserve Bank ofChicago

Charles L. EvansFederal Reserve Bank of Chicago

We present a model embodying moderate amounts of nominal rigid-ities that accounts for the observed inertia in inflation and persistencein output. The key features of our model are those that prevent asharp rise in marginal costs after an expansionary shock to monetarypolicy. Of these features, the most important are staggered wage con-tracts that have an average duration of three quarters and variablecapital utilization.

I. Introduction

This paper seeks to understand the observed inertial behavior of infla-tion and persistence in aggregate quantities. To this end, we formulateand estimate a dynamic, general equilibrium model that incorporatesstaggered wage and price contracts. We use our model to investigatethe mix of frictions that can account for the evidence of inertia andpersistence. For this exercise to be well defined, we must characterize

The first two authors are grateful for the financial support of a National Science Foun-dation grant to the National Bureau of Economic Research. We would like to acknowledgehelpful comments from Lars Hansen and Mark Watson. We particularly want to thankLevon Barseghyan for his superb research assistance, as well as his insightful commentson various drafts of the paper. This paper does not necessarily reflect the views of theFederal Reserve Bank of Chicago or the Federal Reserve System.

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Household

I S: Shopping, that is, searching for an appropriategoods supplier

I R: Buying under an established relationship with asupplier

I U : Seeking work

I J : Working at a job

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Household

I U : Seeking work

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Household

I U : Seeking work

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Household

I U : Seeking work

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Search and matching

Success rate for shopper: θR

Success rate for job-seeker: θJ

Success rate for retailer attracting customer: 11+θR

Success rate for producer recruiting worker: 11+θJ

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Search and matching

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Search and matching

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Search and matching

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Household Bellman system

HS = β

1 + θR

HR = α(p− p) + β [sRHS + (1− sR)HR]

HU = β

1 + θJ

HJ = w − zp + β [sJHU + (1− sJ)HJ ]

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HS = β

1 + θR

HU = β

1 + θJ

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HS = β

1 + θR

HU = β

1 + θJ

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HS = β

1 + θR

HU = β

1 + θJ

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Household optimization

HS = HU .

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Retailer’s Bellman system

FO = −kRy + β

1 + θR

FR +θR

1 + θR

FR = α(p− y) + β (1− sR)FR

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Retailer’s Bellman system

FO = −kRy + β

1 + θR

FR +θR

1 + θR

FR = α(p− y) + β (1− sR)FR

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Producer’s Bellman system

FV = −kJy + β

1 + θJ

FJ +θJ

1 + θJ

FJ = yx− w + β (1− sJ)FJ

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Producer’s Bellman system

FV = −kJy + β

1 + θJ

FJ +θJ

1 + θJ

FJ = yx− w + β (1− sJ)FJ

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Free entry to retailing and

production

FO = 0

andFV = 0.

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Calibration

sR and sJ = known value for the labor market of 3 percentper month

θR = θJ = 1, implies supplier-finding and job-finding ratesof 0.5, and an unemployment rate of 5.7 percent

α, the number of units of output purchased each period bya buyer, =4.6, from American Time Use Survey

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Calibration

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Calibration

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Calibration, continued

Disamenity of work z = 0.6

β = 0.951/12

Normalize productivity at x = 1 and the intermediateproduct price at y = 1.

Households and sellers have equal shares of the transactionsurplus and where workers and producers have equal sharesof the employment surplus.

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β = 0.951/12

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β = 0.951/12

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β = 0.951/12

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Implications

Value of a shopper or a job-seeker is HS = HU = 73.0

Value of a buyer or a worker is HR = HJ = 73.6

Value of a customer relationship or employmentrelationship FR = 0.625.

Wage w = 0.979

Product price p = 1.005

Shadow price of the product delivered to the home isp = 1.077.

Cost of maintaining a consumer opening kR = 0.063

Cost of maintaining a vacancy kJ = 0.313.

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Implications

Wage w = 0.979

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Implications

Wage w = 0.979

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Implications

Wage w = 0.979

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Implications

Wage w = 0.979

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Implications

Wage w = 0.979

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Implications

Wage w = 0.979

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Implications

Wage w = 0.979

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Homogeneity

If (p, y, w) is an equilibrium, so is (λp, λy, λw) for anypositive λ

Normalize as (p/y, w/y)

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Equilibrium wage and price

0.5 1.0 1.5 2.0

Lowest viable price

Highest viable wage

Slope = z

Equilibria given p and w

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Equilibrium wage and price,

magnified

0.97 0.99 1.01 1.03 1.05 1.07

Highest viable wage

Equilibria given p and w

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Static equilibrium set

z ≤ w

y≤ x− 1− β(1− sJ)

1− β(1− sR)

αβkR ≤ p

y≤ w

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Static equilibrium set

z ≤ w

y≤ x− 1− β(1− sJ)

1− β(1− sR)

αβkR ≤ p

y≤ w

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Real wage

z ≤ w

x− 1−β(1−sJ )β

1−β(1−sR)αβ

kR − 1

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Time allocation

sR(1 + θR)

sJ(1 + θJ

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Output and price

0.988 0.990 0.992 0.994 0.996 0.998 1.000 1.002 1.004

Intermediate product price, y

Lowest viable, p/y

Highest viable w/y

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Allocation of time

0.988 0.990 0.992 0.994 0.996 0.998 1.000 1.002 1.004

Intermediate product price, y

Working

Job-seeking

Shopping

Buying

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Dynamic model

HS,i = HU,i.

HS,i = βE

(θR,i

1 + θR,i

HR,i′ +1

1 + θR,i

HS,i′

)HR,i = α(pi − pL(i)) + βE [sRHS,i′ + (1− sR)HR,i′ ]

HU,i = βE

(θJ,i

1 + θJ,i

HJ,i′ +1

1 + θJ,i

HU,i′

)HJ,i = wL(i) − zp + βE [sJHU,i′ + (1− sJ)HJ,i′ ]

0 = −kRyi + βE

1 + θR,i

FR,i′

)FR,i = α(pL(i) − yi) + β E [(1− sR)FR,i′ ]

0 = −kJyi + βE

1 + θJ,i

FJ,i′

)FJ,i = yixC(i) − wL(i) + β E [(1− sJ)FJ,i′ ]

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Response to productivity

0.997 0.998 0.999 1.000 1.001 1.002 1.003Productivity

Labor-market tightness

Product-market tightness (right scale)

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Alternative outcomes

Lowest Low Medium High Highest

Productivity 0.998 0.999 1.000 1.001 1.002

Stabilize labor market

Labor market tightness 1.00 1.00 1.00 1.00 1.00

Product market tightness 2.2 3.3 5.0 6.7 7.8

Intermediate price 0.9993 0.9982 0.9972 0.9962 0.9951

Stabilize product market

Labor market tightness 0.88 0.93 1.00 1.07 1.12

Product market tightness 5.0 5.0 5.0 5.0 5.0

Intermediate price 0.9972 0.9972 0.9972 0.9972 0.9972

Productivity

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Central bank policy

yι = E(yi|C(i) = ι)

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Hypothetical economy

HR,ι −HS,ι = FR,ι,

HJ,ι −HU,ι = FJ,ι,

Let the price and wage in this hypothetical economy be pι

and wι

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Hawk and dove policies

Hawk: Solve the hypothetical model for the policy yH,i thatkeeps the price level pι constant across the fundamentalstates

Dove: solve for the policy yD,i that keeps θJ constant

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Hawk and dove policies

Hawk: Solve the hypothetical model for the policy yH,i thatkeeps the price level pι constant across the fundamentalstates

Dove: solve for the policy yD,i that keeps θJ constant

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Hawk policy

0.997 0.998 0.999 1.000 1.001 1.002 1.003Current productivity

3→2 4→3

2→3 3→4

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Dove policy

0.997 0.998 0.999 1.000 1.001 1.002 1.003Current productivity

3→24→3

2→33→4

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Policy frontier

yi = hyH,i + (1− h)yD,i.

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Volatility of tightness

0.0 0.2 0.4 0.6 0.8 1.0 1.2Hawkishness, h

Labor-market tightness

Product-market tightness

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Volatilities of price and wage

0.0000

0.0002

0.0004

0.0006

0.0008

0.0010

0.0012

0.0014

0.00 0.20 0.40 0.60 0.80 1.00 1.20Hawkishness, h

Price level

Wage level

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