Unemployment (Fears), Precautionary Savings, and Aggregate Demand Wouter J. Den Haan (LSE/CEPR/CFM) Pontus Rendahl (University of Cambridge/CEPR/CFM) Markus Riegler (University of Bonn/CFM) June 19, 2016
What we do Show that the interaction between can 1 One friction in financial markets: incomplete risk sharing 2 Two frictions in labor markets: sticky nominal wages: dw/dp < 1 matching give rise to "aggregate demand" like propagation from supply shocks lead to novel policy implication regarding unemployment insurance (UI)
Interaction of two frictions key Complete risk sharing = Sticky nominal wages dampen effect shocks Flexible nominal wages = Incomplete risk sharing dampens effect shocks Both shocks magnify effect shocks
Key components behind these results Aggregate risk UI policy implications different without aggregate risk Asset price volatility Portfolio rebalancing towards liquid/unproductive asset during recession Nonlinearities induced by standard matching framework
Four cases 1 Complete markets and flexible wages 2 Complete markets and sticky wages 3 Incomplete markets and flexible wages 4 Benchmark:Incomplete markets and sticky wages
Case 1: flexible wages & complete markets usual matching stuff: productivity = expected future productivity = job creation = employment rate = unemployment rate = expected duration unemployment
Case 2: Sticky nominal wages & complete markets productivity = Upward pressure on prices = downward pressure on real wages = nominal wage rigidity dampens shocks!
Case 3: Flexible nominal wages & incomplete markets productivity = investment in job creation = unemployment = idiosyncratic risk = precautionary savings = reduction in job creation is smaller = incomplete markets dampens shocks
Case 4: Sticky nominal wages & incomplete markets Incomplete markets: Precautionary savings when unemp = precautionary demand for money = downward pressure on P = W/P (sticky W) = job creation investment by more not by less! = unemployment rate = precautionary savings = etc. = deflationary spiral Risk for unemployed = countercyclical W/P = volatile asset prices
Main results 1 Incomplete markets together with sticky wages amplify shocks, but on their own repress shocks 2 Increase in unemployment insurance from 50% to 55% = everybody better off not true in economy without aggregate risk
Just a little bit of empirical motivation
Euro Area A: Price level (*) 1.1 1.05 1 0.95 0.9 0.85 2000 2002 2004 2006 2008 2010 2012 2014 1.15 B: Price level (*) and nominal wage (+) 1.1 1.05 1 0.95 0.9 0.85 2000 2002 2004 2006 2008 2010 2012 2014
0.85 2000 2002 2004 2006 2008 2010 2012 2014 Euro Area 1.15 B: Price level (*) and nominal wage (+) 1.1 1.05 1 0.95 0.9 0.85 2000 2002 2004 2006 2008 2010 2012 2014 C: Price level (*) and nominal unit labor cost (o) 1.1 1.05 1 0.95 0.9 0.85 2000 2002 2004 2006 2008 2010 2012 2014
Model: Key ingredients 1 Heterogeneous households and incomplete markets 2 Nominal wages do not respond 1-for-1 with P 3 Search frictions in the labor market 4 # jobs = # firms = # shares
Existing firms One-worker firms Profits are given by Key parameter is ω P 1 D t = P t exp (z t ) W t ( zt ) ( ) ωz ωp Pt W t = ω 0 z P z P Aactive firms do not make decisions
Individual households one-worker households employed workers earn nominal wage (1 τ t ) W t unemployed earn µ (1 τ t ) W t & search for jobs idiosyncratic risk exogenous job loss probability, δ lower chance of getting a job in a recession agents can save/invest in unproductive asset: money, M i,t productive asset: equity, q i,t 0 (i.e., firm ownership/jobs)
Individual households max E t β j j=0 i,t+j 1 + χ 1 γ c1 γ ) 1 ζ P t+j 1 1 ζ ( Mi,t+1+j with respect to P t c i,t + J t (q i,t+1 (1 δ) q i,t ) + M i,t+1 = (1 τ t ) W t e i,t + µ (1 τ t ) W t (1 e i,t ) + D t q i,t + M i,t and q i,t+1 0
First-order conditions J t P t = βe t c γ i,t [ (ci,t+1 c i,t ) γ ( Dt+1 + (1 δ) J ) ] t+1 P t+1 P t+1 [ ] Pt = βe t c γ P i,t+1 + χ t+1 ( ) ζ Mi,t Marked departure from literature: Individual MRS is used in both Euler equations Inequality constraints ignored here P t
Equity market equilibrium h }{{} t + ((1 δ) q i q (e i, q i, M i ; s t )) df i A }{{} t (e i, q i, M i ) Equity creation Equity sold = (q (e i, q i, M i ; s t ) (1 δ) q i ) df i A + }{{} t (e i, q i, M i ), with Equity bought A = {i : q(e i, q i, M i ; s t ) (1 δ)q i 0}, A + = {i : q(e i, q i, M i ; s t ) (1 δ)q i 0}, "go to equity supply derivation"
Employment q t = i A+ + q (e i, q i, M i ; s t ) df t (e i, q i, M i ) i A q (e i, q i, M i ; s t ) df t (e i, q i, M i ) = (1 δ) q t 1 + h t
Money market equilibrium Equilibrium (M i M (e i, q i, M i ; s t )) df i B }{{} t (e i, q i, M i ) = Money sold (M (e i, q i, M i ; s t ) M i ) df i B + }{{} t (e i, q i, M i ), Money bought Money supply, M, is constant in the benchmark economy.
Government τ t q t W t = (1 q t ) µ (1 τ t ) W t τ t = (1 q t ) µ q t + µ (1 q t )
Calibration ω P : range of values W t = ω 0 ( zt z ) ( ) ωz ωp Pt z P P One-year post-displacement consumption drop is 34% (Kolsrud, Landais, Nilsson, & Spinnewijn 2015; Sweden) Expected unemployment duration 3.57 quarters
MODEL PROPERTIES
Money holdings Money holdings upon displacement 0.7 0.6 Cond. on expansion Cond. on recession 0.5 0.4 0.3 0.2 0.1 0-1 0 1 2 3 4 5 6 7 8 Unemployment duration (quarters)
Money demand 0 0 0.5 1 1.5 2 2.5 3 Real cash on hand Intro Empirical motivation Model Model properties Business Cycles UI Amount invested in liquid asset 0.9 0.8 0.7 Employed in expansion Unemployed in expansion Employed in recession Unemployed in recession 0.6 0.5 0.4 0.3 0.2 0.1
BUSINESS CYCLES
Type of experiment considered productivity z t Representative-agent version: P t = dw/dp = nominal-wage stickyness dampens shocks
Log deviation Log deviation Log deviation Log deviation Ppt. deviation Log deviation IRFs with sticky nominal wages 0-3 #10 Productivity 0.2 Employment -1-2 -3 0-0.2-4 -0.4-5 -6-0.6 Incompl. markets Compl. markets -7 0 10 20 30 40 50-0.8 0 10 20 30 40 50 0 Output 6-3 #10 Real wage -0.002 4-0.004 2-0.006 0-0.008-2 -0.01-4 -0.012 0 10 20 30 40 50-6 0 10 20 30 40 50 0 Asset prices 0.02 Price level -0.02 0.01-0.04 0-0.06-0.01-0.08-0.02-0.1 0 10 20 30 40 50 Time (quarters) -0.03 0 10 20 30 40 50 Time (quarters)
Log deviation Log deviation Log deviation Log deviation Ppt. deviation Log deviation IRFs with flexible nominal wages 0-1 -2-3 -4-5 -6-3 #10 Productivity 0.1 0-0.1-0.2-0.3-0.4-0.5 Employment Incompl. markets Compl. markets -7 0 10 20 30 40 50-0.6 0 10 20 30 40 50 0 Output 0-3 #10 Real wage -0.002-0.5-0.004-0.006-0.008-0.01-1 -1.5-2 -0.012 0 10 20 30 40 50-2.5 0 10 20 30 40 50 0 Asset prices 0.02 Price level -0.01-0.02 0.01-0.03 0-0.04-0.05-0.01-0.06-0.07 0 10 20 30 40 50 Time (quarters) -0.02 0 10 20 30 40 50 Time (quarters)
UNEMPLOYMENT INSURANCE
Unemployment Insurance Two unemployment insurance (UI) experiments 1 Compare economies with different replacement rates 2 Unexpectedly increase replacement rate and take into account transition Two ways to deal with effect on wages 1 wage rule not affected 2 wage rule is adjusted to keep same implied Nash bargaining weights
Unemployment insurance Mechanism emphasized in the literature Replacement rate = 1 Agents better insured = savings = employment 2 Through bargaining wage = employment This also happens in our model too, but...
Mean employment rate and higher UI... there is a strong countervailing effect arising from aggregate uncertainty: Replacement rate = 1 Asset prices less volatile = demand equity = employment 2 Employment is concave in equity prices, J = E [employment] when SD [J]
UI and employment 0.91 ω P =0.7, µ does not affect wages 0.91 0.9 0.9 Employment level 0.89 0.88 0.87 0.89 0.88 0.87 0.86 0.86 0.85 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.85 0 ω P =1, µ does not affect wages
Switch to alternative UI policy 1 Replacement rate increases from 0.5 to 0.55 2 Switch is unexpected 3 Switch is permanent 4 Agents take transition into account
Average welfare effect of change in UI 1.5 ω P =0.7, µ affects wages 1 0.5 0 0.5 1 1.5 1 0.35 0.4 0.45 0.5 0.55 0.6 0.65 ω P =1, µ affects wages
Who likes/dislikes higher UI? 1.5 µ=0.55, ω 0 unchanged 1.5 µ=0.55, ω 0 increases 1 1 Welfare gain 0.5 0.5 0 EE UU UE EU 0.5 1 1.5 2 Real cash on hand 0 0.5 1 1.5 2 Real cash on hand
Concluding comments With incomplete markets and sticky nominal wages, a decline in productivity sets off a self-reinforcing aggregate demand effect This happens despite the fact that both incomplete markets as well as sticky nominal wages in isolation repress propagation. One of the core components of this mechanism is the missing market for unemployment insurance. A rise in UI generosity can therefore increase average employment and raise welfare for all agents even the asset-rich employed
Creation of new jobs/firms/equity number of new firms created: vacancy yield: h t = ψv η t u1 η t h t v t = ψ ( ) η 1 vt u t
Supply of new equity Matching function zero-profit condition = ( ) ψ J η/(1 η) t h t = ψ u t κ P t
Creation of new jobs/firms/equity zero-profit condition = vacancies as a function of J t /P t : κ = ψ ( vt ) η 1 J t u t P t supply of new equity (job/firm creation): "back to main" ( ) ψ J η/(1 η) t h t = ψ u t κ P t
Unemployment duration 0.4 0.35 0.3 Cond. on expansion Cond. on recession Frequency 0.25 0.2 0.15 0.1 0.05 0 0 2 4 6 8 10 12 14 16 18 20 Duration of unemployment spell (quarters)
Equity holdings upon displacement 1 0.9 0.8 0.7 Cond. on expansion Cond. on recession Equity holdings 0.6 0.5 0.4 0.3 0.2 0.1 0 1 0 1 2 3 4 5 6 7 8 Unemployment duration (quarters)
Portfolio choice: fraction in liquid asset share of money in portfolio 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 employed in boom unemployed in boom employed in recession unemployed in recession 0.1 0 0 0.5 1 1.5 2 2.5 3 real cash on hand
Technical challenges Even rep-agent version not trivial to solve accurately non-linearity matching function matters suffi ciently volatile employment = volatile surplus volatile equity prices "go to accuracy graph rep-agent model" Adding moderate aggregate uncertainty to model is not a small change substantial changes in means volatile surplus and asset prices multiplicity
Log employment level 0.08 0.1 0.12 2 nd order perturbation 0.14 0.16 0.18 0.2 0.22 0.24 5th order projections method 0.26 0 50 100 150 200 250 300 350 400 450 50 "back to main"
Increase in UI & transition dynamics Increase in UI first period of recession No change in wage rule = equity less risky = average employment less deflationary spiral = recession less deep = employment Change in wage rule = the same as above + profits = average employment
Switch to higher level of unemployment benefits 0.91 Employment 0.9 0.89 0.88 0.87 0.86 µ=0.5 µ=0.55 µ=0.55, ω 0 increases 0.85 0 10 20 30 40 50 60 Time (quarters)