Search with Wage Posting Under Sticky Prices Andrew Foerster Jose - - PowerPoint PPT Presentation

Introduction Model Results Conclusion

Search with Wage Posting Under Sticky Prices

Andrew Foerster Jose Mustre-del-Rio

Federal Reserve Bank of Kansas City

May 2015

The views expressed herein are solely those of the authors and do not necessarily reflect the views of the Federal Reserve Bank of Kansas City or the Federal Reserve System

Introduction Model Results Conclusion

Introduction

• After Great Recession, Sluggish Labor Market with Low Inflation
• Importance of Frictions in Pricing Behavior — Nominal Rigidities
• Importance of Frictions in Labor Market — Search Models
• Interest in Interaction Between Pricing and Labor Market Frictions
• Many Papers Include these Two
• Typical Assumption for Tractability: Split Frictions
• We Address this Assumption, Show it Matters
• Changes in Unemployment Benefits
• Response to Shocks
• Volatility of the Labor Market

Introduction Model Results Conclusion

Our Model versus an Alternative

• Objective: Compare and Contrast Models
• Alternative: Separates Frictions (Walsh (2005), Trigari (2006))
• Wholesaler Firms: Act in Labor Market, Produce Competitive Good
• Retailer Firms: Buy Wholesale Good Competitively, Act in

Product/Pricing Market with Power

• Firms Don’t Internalize the Effects of Other Friction
• Baseline Model: Develop a Framework Where Firms...
• Post Vacancies
• Offer Workers an Hours-Compensation Contract
• Make Pricing Decisions
• Internalize the Effects of All Frictions

Introduction Model Results Conclusion

Importance of Our Environment

• Bargaining: Kuester (2011), Thomas (2011), Lago Alves (2012), others
• Once Combine Frictions, What is Bargained Over Changes
• Firm has Market Power
• Worker Input into Price Setting? Firm Size?
• Perfect Consumption Insurance in Household
• Result: Contracts Look Very Different, Introducing Many Channels not

Present in the Standard Model

• Benefits of Wage Posting
• Contracts Identical in Both Models
• Eliminate Representative Household Assumption
• Other Features of Wage Posting
• Severs Link Between Compensation and Agg. Labor Market Tightness
• Posting at Least as Common as Bargaining (Hall and Krueger (2012))

Introduction Model Results Conclusion

Model Overview

• Individuals: Consume, Work, Save, Search for Employment
• Final Goods Firms: Aggregate Intermediate Goods
• Intermediate Goods Firms
• Post Vacancies and Wages
• Monopolistically Competitive with Sticky Prices
• Policy: Taylor Rule, Lump-Sum Taxes
• Alternative Model Splits Producing Firms
• Wholesale Firms: Post Vacancies and Wages, Competitive Markets
• Retail Firms: Purchase Wholesale Good, Sticky Prices
• Calibrate to Match Same Steady State Targets

Introduction Model Results Conclusion

Individuals

• Utility Function

U (ci,t, hi,t) =

• ci,t − ϕh1+1/ψ

i,t

1−γ − 1 1 − γ

• Benefits of GHH Preferences (and Assumption on Initial Condition)
• Simplifies Contracting Environment
• Prevents Counterfactual Asset/Wage Behavior (Mustre-del-Rio (2014))
• Dispatch with Large Household Assumption
• No Consumption Insurance
• Hours Optimal from Individual’s Perspective
• Still Get Nice Aggregation

Introduction Model Results Conclusion

Individuals

• Unemployed Individual

W u

i,t = max cu

i,t,B u i,t

• U
• cu

i,t, 0

+ βEt

• stW e

i,t+1 + (1 − st) W u i,t+1

• s.t. Ptcu

i,t + Bu i,t + PtTt = Ptb + Rt−1Bi,t−1 + Dt

• Employed Individual

W e

i,t = max ce

i,t,B e i,t

• U
• ce

i,t, he i,t

+ βEt (1 − δt) W e

i,t+1 + δtW u i,t+1

• s.t. Ptce

i,t + Be i,t + PtTt = Ptωi,t + Rt−1Bi,t−1 + Dt

Introduction Model Results Conclusion

Intermediate Goods Firms

• Production

Y s

j,t = Zthj,t

• Take-it-or-leave-it Contract Υj,t = (ωj,t, hj,t)

max

Υj,t

Dj,t = Pj,t Pt

• Y d

j,t − ωj,t

s.t. Y s

j,t

≥ Y d

j,t, and W u i,t ≤ W e i,t

• Optimal Contract: Worker Indifferent Between Working and Not

ωj,t = b + ϕh

1+ 1

ψ

j,t

= b + ϕ Pj,t Pt −ǫ Yt Ztnt 1+ 1

ψ

• Dispersion of (ωj,t, hj,t) via Prices

Introduction Model Results Conclusion

Optimal Contract

0.2 0.4 0.6 0.8 1 b Hours ( h j ) Compensation Wage

Introduction Model Results Conclusion

Price Setting

• Value Function of Firm

Jt (Pj,t) = Pj,t Pt

• Y d

j,t − ωj,t

+β (1 − δt) Et λt+1 λt [ζJt+1 (Pj,t) + (1 − ζ) Jt+1 (P∗

t+1)]

= Pj,t Pt 1−ǫ Yt nt − b − ϕ Pj,t Pt −ǫ Yt Ztnt 1+ 1

ψ

+β (1 − δt) Et λt+1 λt [ζJt+1 (Pj,t) + (1 − ζ) J∗

t+1]

• Re-optimizers

P∗

t = arg max Jt (Pj,t)

Introduction Model Results Conclusion

Alternative Model

• Wholesale Firms

Y w

t

= Ztht Jw

t = max ht

Pw

t

Pt Ztht − b − ϕh1+1/ψ

t

+ β(1 − δt)Et λt+1 λt Jw

t+1

• Retail Firms

Y s

j,t ≥ Y d j,t =

Pj,t Pt −ǫ Yt Jr

t (Pj,t) =

Pj,t Pt − Pw

t

Pt

• Y d

j,t + βEt

λt+1 λt [ζJr

t+1 (Pj,t) + (1 − ζ) Jr∗ t+1]

Introduction Model Results Conclusion

Model Comparison

• Free Entry Condition: Wholesaler versus Baseline (Market Power)

κ = qt βEt λt+1 λt Jw

t+1

κ = qt βEt λt+1 λt [ζJt+1 (Pt) + (1 − ζ) Jt+1 (P∗

t+1)]

• First Order Condition: Retailer versus Baseline (Shocks)

∞

∑

k=0

(βζ)k λt+k λt P∗

t

Pt+k − µPw

t+k

Pt+k

• Yt+kPǫ

t+k = 0 ∞

∑

k=0

(βζ) k

k

∏

i=1

(1 − δt+k−i) λt+k λt   P∗

t

Pt+k − µ ϕ(1 + 1/ψ)h1/ψ

j,t+k

Zt+k   Yt+k nt+k Pǫ

t+k = 0

Introduction Model Results Conclusion

Calibration

• Most Parameters Standard From Literature
• Set of Parameters to Match Consistent Targets Across Models

Parameter Description Target Baseline Alternative ϕ Disutility of labor hj,ss = 1/3 2.7 2.7 b Unemployment benefits b/ωss = 1/2 0.1 0.1 σm Matching efficiency uss = 0.11 0.7526 0.7526 κ Vacancy posting qss = 0.70 0.8895 0.6671

Introduction Model Results Conclusion

Results Overview

• Compare and Contrast Baseline and Alternative Models
• Show a Subset of Results
• Steady State Effect of Changing Unemployment Benefits
• Matters via Free Entry Condition
• Highlights Market Power
• Impulse Responses
• Baseline Model: All Shocks hit Same Firm
• Alternative: Shocks Hit Different Firms
• Highlight Sticky Prices by Considering Flexible Prices
• Labor Market Ratios
• In Aggregate and Decompose Effects of Each Shock
• Highlight Sticky Prices by Considering Flexible Prices

Introduction Model Results Conclusion

Changing Unemployment Benefits

0.45 0.5 0.55

• 4
• 3
• 2
• 1

1 2 Output (%) 0.45 0.5 0.55

• 0.02
• 0.01

0.01 0.02 0.03 Unemploy ment Benefits 0.45 0.5 0.55

• 10
• 5

5 10 15 Av erage Hourly Wage (%) 0.45 0.5 0.55

• 0.02
• 0.01

0.01 0.02 0.03 Unemploy ment Rate (pp) 0.45 0.5 0.55

• 0.04
• 0.03
• 0.02
• 0.01

0.01 0.02 0.03 Vacanc ies Rate (pp) 0.45 0.5 0.55

• 0.5

0.5 V/U Ratio (pp) Baseline Model Alternativ e Model

Introduction Model Results Conclusion

TFP Shock: Sticky Prices

5 10 1 2 3 4 Output (%) 5 10

• 1

1 2 3 Av g Hours per Worker (%) 5 10 0.5 1 1.5 Av g Hourly Wage (%) 5 10

• 0.4
• 0.2

0.2 0.4 Inflation (pp) 5 10

• 0.2
• 0.1

0.1 0.2 Nominal Rate (pp) 5 10

• 6
• 4
• 2

2 Mark up (%) 5 10

• 0.4
• 0.3
• 0.2
• 0.1

Unemploy ment (pp) 5 10 0.2 0.4 0.6 0.8 Vacancies (pp) 5 10 2 4 6 V/U Ratio (pp) Baseline Model Alternativ e Model

Introduction Model Results Conclusion

Separation Rate Shock: Flexible Prices

5 10

• 0.4
• 0.3
• 0.2
• 0.1

Output (%) 5 10

• 1
• 0.5

0.5 1 Av g Hours per Worker (%) 5 10

• 1
• 0.5

0.5 1 Av g Hourly Wage (%) 5 10

• 1
• 0.5

0.5 Inflation (pp) 5 10

• 0.6
• 0.4
• 0.2

0.2 Nominal Rate (pp) 5 10

• 1
• 0.5

0.5 1 Mark up (%) 5 10 0.1 0.2 0.3 0.4 Unemploy ment (pp) 5 10

• 0.03
• 0.02
• 0.01

Vacancies (pp) 5 10

• 3
• 2
• 1

V/U Ratio (pp) Baseline Model Alternativ e Model

Introduction Model Results Conclusion

Separation Rate Shock: Sticky Prices

5 10

• 6
• 4
• 2

2 Output (%) 5 10

• 6
• 4
• 2

2 Av g Hours per Worker (%) 5 10

• 2
• 1

1 Av g Hourly Wage (%) 5 10

• 0.6
• 0.4
• 0.2

0.2 Inflation (pp) 5 10

• 0.4
• 0.2

0.2 0.4 Nominal Rate (pp) 5 10

• 5

5 10 Mark up (%) 5 10

• 0.1

0.1 0.2 0.3 Unemploy ment (pp) 5 10

• 0.3
• 0.2
• 0.1

0.1 Vacancies (pp) 5 10

• 3
• 2
• 1

V/U Ratio (pp) Baseline Model Alternativ e Model

Introduction Model Results Conclusion

Labor Market Ratios: Flexible versus Sticky Prices

std(v /u) std(Y )

corr (u, v)

std(n) std(Y ) std(h) std(Y ) std(w ) std(Y )

Flexible Prices Baseline 11.9971

• 0.5344

0.7724 0.3176 0.2858 Alternative 12.9331

• 0.5688

0.7880 0.3113 0.2801 Sticky Prices Baseline 7.1798

• 0.1872

0.5373 0.8405 1.0325 Alternative 11.2575

• 0.5469

0.6932 0.5480 0.4932

Introduction Model Results Conclusion

Labor Market Ratios: Sticky Prices

std(v /u) std(Y )

corr (u, v)

std(n) std(Y ) std(h) std(Y ) std(w ) std(Y )

All Shocks Baseline 7.1798

• 0.1872

0.5373 0.8405 1.0325 Alternative 11.2575

• 0.5469

0.6932 0.5480 0.4932 Tech Shock Only Baseline 7.5317

• 0.8716

0.3177 0.4717 1.0854 Alternative 10.2425

• 0.9236

0.4328 0.4364 0.3928 MP Shock Only Baseline 2.0559

• 0.2291

0.0841 1.1250 0.7230 Alternative 1.1382

• 0.0101

0.0458 1.1230 1.0107 Sep Shock Only Baseline 7.6067 0.5928 0.8159 1.1353 1.0281 Alternative 17.4045

• 0.2365

1.6273 0.9610 0.8649

Introduction Model Results Conclusion

Conclusion

• Develop a Model of Search with Wage Posting under Sticky Prices
• Compare and Contrast with Alternative Model
• Contracts Identical in Two Models
• Show Combining Frictions has Important Effects
• Sensitivity to Unemployment Benefits
• Response to Shocks
• Volatility of the Labor Market
• Implications for Estimating Models