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 � � 1 − γ c i , t − ϕ h 1 + 1 / ψ − 1 i , t U ( c i , t , h i , t ) = 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 � � � + β E t � �� W u c u s t W e i , t + 1 + ( 1 − s t ) W u i , t = max U i , t , 0 i , t + 1 c u i , t , B u i , t s.t. P t c u i , t + B u i , t + P t T t = P t b + R t − 1 B i , t − 1 + D t • Employed Individual � � � + β E t � ( 1 − δ t ) W e �� W e c e i , t , h e i , t + 1 + δ t W u i , t = max U i , t i , t + 1 c e i , t , B e i , t s.t. P t c e i , t + B e i , t + P t T t = P t ω i , t + R t − 1 B i , t − 1 + D t
Introduction Model Results Conclusion Intermediate Goods Firms • Production Y s j , t = Z t h j , t • Take-it-or-leave-it Contract Υ j , t = ( ω j , t , h j , t ) � P j , t � Y d = j , t − ω j , t max D j , t P t Υ j , t s.t. Y s Y d j , t , and W u i , t ≤ W e ≥ j , t i , t • Optimal Contract: Worker Indifferent Between Working and Not �� P j , t � 1 + 1 � − ǫ Y t ψ 1 + 1 ψ ω j , t = b + ϕ h = b + ϕ j , t P t Z t n t • Dispersion of ( ω j , t , h j , t ) via Prices
Introduction Model Results Conclusion Optimal Contract Compensation Wage b 0 0.2 0.4 0.6 0.8 1 Hours ( h j )
Introduction Model Results Conclusion Price Setting • Value Function of Firm � P j , t � Y d J t ( P j , t ) = j , t − ω j , t P t λ t + 1 [ ζ J t + 1 ( P j , t ) + ( 1 − ζ ) J t + 1 ( P ∗ + β ( 1 − δ t ) E t t + 1 )] λ t �� P j , t � 1 + 1 � P j , t � 1 − ǫ Y t � − ǫ Y t ψ = − b − ϕ P t n t P t Z t n t λ t + 1 [ ζ J t + 1 ( P j , t ) + ( 1 − ζ ) J ∗ + β ( 1 − δ t ) E t t + 1 ] λ t • Re-optimizers P ∗ t = arg max J t ( P j , t )
Introduction Model Results Conclusion Alternative Model • Wholesale Firms Y w = Z t h t t P w λ t + 1 Z t h t − b − ϕ h 1 + 1 / ψ J w t J w t = max + β ( 1 − δ t ) E t t t + 1 P t λ t h t • Retail Firms � P j , t � − ǫ Y s j , t ≥ Y d j , t = Y t P t � P j , t � − P w λ t + 1 J r t Y d [ ζ J r t + 1 ( P j , t ) + ( 1 − ζ ) J r ∗ t ( P j , t ) = j , t + β E t t + 1 ] P t P t λ t
Introduction Model Results Conclusion Model Comparison • Free Entry Condition: Wholesaler versus Baseline (Market Power) λ t + 1 J w κ = q t β E t t + 1 λ t λ t + 1 [ ζ J t + 1 ( P t ) + ( 1 − ζ ) J t + 1 ( P ∗ κ = q t β E t t + 1 )] λ t • First Order Condition: Retailer versus Baseline (Shocks) � P ∗ � − µ P w ∞ ( βζ ) k λ t + k t + k t Y t + k P ǫ ∑ t + k = 0 λ t P t + k P t + k k = 0 ϕ ( 1 + 1 / ψ ) h 1 / ψ ∞ k P ∗ ( 1 − δ t + k − i ) λ t + k Y t + k j , t + k ( βζ ) k t P ǫ ∑ ∏ − µ t + k = 0 λ t P t + k Z t + k n t + k k = 0 i = 1
Introduction Model Results Conclusion Calibration • Most Parameters Standard From Literature • Set of Parameters to Match Consistent Targets Across Models Parameter Description Target Baseline Alternative h j , ss = 1 / 3 ϕ Disutility of labor 2.7 2.7 b Unemployment benefits b / ω ss = 1 / 2 0.1 0.1 u ss = 0 . 11 σ m Matching efficiency 0.7526 0.7526 κ Vacancy posting q ss = 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 Output (%) Unemploy ment Benefits Av erage Hourly Wage (%) 2 0.03 15 1 0.02 10 0 0.01 5 -1 0 0 -2 -0.01 -5 -3 -4 -0.02 -10 0.45 0.5 0.55 0.45 0.5 0.55 0.45 0.5 0.55 Unemploy ment Rate (pp) Vacanc ies Rate (pp) V/U Ratio (pp) 0.03 0.03 0.5 0.02 0.02 0.01 0.01 0 0 -0.01 0 -0.02 -0.01 -0.03 -0.02 -0.04 -0.5 0.45 0.5 0.55 0.45 0.5 0.55 0.45 0.5 0.55 Baseline Model Alternativ e Model
Introduction Model Results Conclusion TFP Shock: Sticky Prices Output (%) Av g Hours per Worker (%) Av g Hourly Wage (%) 4 3 1.5 3 2 1 2 1 0.5 1 0 0 -1 0 0 5 10 0 5 10 0 5 10 Inflation (pp) Nominal Rate (pp) Mark up (%) 0.4 0.2 2 0.2 0.1 0 0 0 -2 -0.2 -0.1 -4 -0.4 -0.2 -6 0 5 10 0 5 10 0 5 10 Unemploy ment (pp) Vacancies (pp) V/U Ratio (pp) 0 0.8 6 -0.1 0.6 4 -0.2 0.4 2 -0.3 0.2 -0.4 0 0 0 5 10 0 5 10 0 5 10 Baseline Model Alternativ e Model
Introduction Model Results Conclusion Separation Rate Shock: Flexible Prices Output (%) Av g Hours per Worker (%) Av g Hourly Wage (%) 0 1 1 -0.1 0.5 0.5 -0.2 0 0 -0.3 -0.5 -0.5 -0.4 -1 -1 0 5 10 0 5 10 0 5 10 Inflation (pp) Nominal Rate (pp) Mark up (%) 0.5 0.2 1 0 0.5 0 -0.2 0 -0.5 -0.4 -0.5 -1 -0.6 -1 0 5 10 0 5 10 0 5 10 Unemploy ment (pp) Vacancies (pp) V/U Ratio (pp) 0.4 0 0 0.3 -0.01 -1 0.2 -0.02 -2 0.1 0 -0.03 -3 0 5 10 0 5 10 0 5 10 Baseline Model Alternativ e Model
Introduction Model Results Conclusion Separation Rate Shock: Sticky Prices Output (%) Av g Hours per Worker (%) Av g Hourly Wage (%) 2 2 1 0 0 0 -2 -2 -1 -4 -4 -6 -6 -2 0 5 10 0 5 10 0 5 10 Inflation (pp) Nominal Rate (pp) Mark up (%) 0.2 0.4 10 0 0.2 5 -0.2 0 0 -0.4 -0.2 -0.6 -0.4 -5 0 5 10 0 5 10 0 5 10 Unemploy ment (pp) Vacancies (pp) V/U Ratio (pp) 0.3 0.1 0 0.2 0 -1 0.1 -0.1 -2 0 -0.2 -0.1 -0.3 -3 0 5 10 0 5 10 0 5 10 Baseline Model Alternativ e Model
Introduction Model Results Conclusion Labor Market Ratios: Flexible versus Sticky Prices std ( v / u ) std ( n ) std ( h ) std ( w ) corr ( u , v ) std ( Y ) std ( Y ) std ( Y ) 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
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