Understanding the Great Recession

Home , Great Recession, Phillips curve, Shock (economics)

Lawrence Christiano Martin Eichenbaum Mathias Trabandt

Conference in honor of Jim Hamilton, Federal Reserve Bank of San Francisco, 2014

. Background

GDP appears to have su§ered a permanent (10%?) fall since • 2008. Trend decline in labor force participation accelerated after the • ‘end’ of the recession in 2009. Unemployment rate persistently high • — recent fall primarily reﬂects the fall in labor force participation. Employment to population ratio fell sharply with little evidence • of recovery. Vacancies have risen, but unemployment has fallen relatively • little (‘shift in Beveridge curve’, ‘mismatch’). Investment and consumption persistently low. • Questions

What were the key forces driving U.S. economy during the • Great Recession?

Mismatch in the labor market? •

Why was the drop in inﬂation so moderate? • To answer our questions we need a model

Model must provide empirically plausible account of key • macroeconomic aggregates — employment, vacancies, labor force participation, job ﬁnding rate, unemployment rate, real wages — output, consumption, investment, ..

Novel features of labor market • — Endogenize labor force participation. — Derive wage inertia as an equilibrium outcome.

Estimate model using pre-2008 data. •

Use estimated model to analyze post-2008 data. • Questions and Answers

What forces drove real quantities in the Great Recession? • — Shocks to ﬁnancial markets key drivers, even for variables like labor force participation.

— Government shocks not important: because of size and timing (consistent with ZLB literature).

Mismatch in the labor market? • — Not a ﬁrst order feature of the Great Recession.

— We account for ‘shift’ in the Beveridge curve without resorting to structural shifts in the labor market. Questions and Answers

Why was the drop in inﬂation so moderate? • — Prolonged slowdown in TFP growth during the Great Recession.

— Rise in cost of ﬁrms’ working capital as measured by spread between corporate-borrowing rate and risk-free interest rate.

— Both forces exert countervailing pressure on inﬂation. Labor Market

Employment* E*

Unemployment* Non,par/cipa/on* U* N* 2.2. Household Maximization

Members of the household derive utility from a market consumption good and a good produced at home. The home good is produced using labor of individuals who arenít in the labor force and unemployed individuals:

H H 1 cH cH L Ct = t (1 Lt)  (Lt lt) (Lt;Lt 1; t ) (2.6)   F  L The term (Lt;Lt 1; t ) captures the idea that is costly to change the number of people F  who specialize in home production,

L L 2 (Lt;Lt 1; t )=0:5t L (Lt=Lt 1 1) Lt: (2.7) F   

We assume cH < 1 cH ; so that in steady state the unemployed contribute less to home  H L production than do people who are out of the labor force. Finally, t and t are processes that ensure balanced growth. We discuss these processes in detail below. Because workers experience no disutility from working, they supply their labor inelasti- cally. An employed worker brings home the wages that it earns. Unemployed workers re- ceives government-provided unemployment compensation which they give to the household. Unemployment beneÖts are Önanced by lump-sum taxes paid by the household. Workers maximize their expected income. By the law of large numbers, this strategy maximizes the total income of the household. Workers maximize expected income in exchange for perfect consumption insurance from the household. All workers have the same concave preferences over consumption. So the optimal insurance arrangementLabor involves allocating Market the same level of the market good and the home good to all members of the household. The representative household maximizes the objective function:

1 t E0  (C~t); Employment* (2.8) U t=0 E* X 1 where ~ " H " ! Ct = (1 !)(Ct~)1 + ! Ct ! C  1 (C~)=  ; (2.9) h U 1 " # i  and   1 ~  H H  Ct = (1 !) Ct bCt 1 + ! Ct bCt 1 :      H Here, Ct and Ct denote market consumption  and the consumption  of a good produced at Unemployment* Non,par/cipa/on* ; C CH : home. The parameter, governs the substitutabilityU* between t and t In the next draftN* of the paper we will report results for other values of .Theparameterb controls the degree of habit formation in household preferences. We assume 0 b<1: Abaroveravariable ,Household*labor*force*decision* indicates its economy-wide average value. ,Split*between*U*and*E*determined*by*job,ﬁnding*rate.*

1 2.2. Household Maximization

H H 1 cH cH L C =  (1 Lt) (Lt lt) (Lt;Lt 1;  ) (2.6) t t F t L The term (Lt;Lt 1;  ) captures the idea that is costly to change the number of people F t who specialize in home production,

L L 2 (Lt;Lt 1;  )=0:5  (Lt=Lt 1 1) Lt: (2.7) F t t L

We assume cH < 1 cH ; so that in steady state the unemployed contribute less to home H L production than do people who are out of the labor force. Finally, t and t are processes that ensure balanced growth. We discuss these processes in detail below. Because workers experience no disutility from working, they supply their labor inelasti- cally. An employed worker brings home the wages that it earns. Unemployed workers re- ceives government-provided unemployment compensation which they give to the household. Unemployment beneÖts are Önanced by lump-sum taxes paid by the household. Workers maximize their expected income. By the law of large numbers, this strategy maximizes the total income of the household. Workers maximize expected income in exchange for perfect consumption insurance from the household. All workers have the same concave preferences over consumption. So the optimal insurance arrangementLabor involves allocating Market the same level of the market good and the home good to all members of the household. The representative household maximizes the objective function:

1 t E0  (C~t); Employment* (2.8) U t=0 E* X 1 where " " 1! C~ = (1 !)(C ") + ! CHH" ! C~t =t (1 !)(Ct)t~1+! C t !!~ C 1t h (C)= ; i (2.9) H h U 1 "" ##i C =1 Lt and t ! 1  H H   C~t = (1 !) Ct bCt 1 + ! C bC : PtCt + PI;tIt + Bt+1 t t 1 H R K +(L l ) P D + l W + R B T Here, Ct and Ct denote marketK;t t consumptiont t t  andt t thet consumptiont 1 t  t of a good produced at " ! Unemployment* ! ! Non,par/cipa/on* ; C CH : home. The parameter, governs the substitutabilityU* between t and t In the next draftN* of the paper we will report results for other values of .Theparameterb controls the degree of habit formation in household preferences. We assume 0 b<1: Abaroveravariable ,Household*labor*force*decision* indicates its economy-wide average value. ,Split*between*U*and*E*determined*by*job,ﬁnding*rate.*

1 1 Labor Market

Employment* E*

Unemployment* Non,par/cipa/on* U* N*

Bargaining* Three*types*of*worker,firm*mee/ngs:* *i)*E*to*E*,*ii)*U*to*E,*iii)*N*to*E** Modified version of Hall-Milgrom Firms pay a fixed cost to meet a worker (must post vacancies, • but these are costless).

Then, workers and ﬁrms engage in alternating-o§er bargaining. • — Better o§reaching agreement than parting ways. — Disagreement leads to continued negotiations.

If bargaining costs don’t depend too sensitively on state of • economy, neither will wages. — ﬁrms su§er cost, g, when they reject an o§er by the worker and make a countero§er. — bargaining costs somewhat sensitive to state of business cycle: protracted negotiations mean lost output/wages. • rejection of an o§er risks, with probability d, that negotiations • break down completely.

After expansionary shock, rise in wages is relatively small. • Estimated Medium-Sized DSGE Model

Standard empirical NK model (e.g., CEE, ACEL, SW): • — Calvo price setting frictions, but no indexation. — Habit persistence. — Variable capital utilization. — Working capital. — Adjustment costs: investment, labor force. — Taylor rule.

Our labor market structure. •

Estimation strategy: Bayesian impulse response matching. • — Shocks to monetary policy, neutral and investment-speciﬁc technology. — Our model performs well relative to this metric. Estimated Parameters, Pre-2008 Data Estimation by impulse response matching, Bayesian methods. •

Prices change on average every 4 quarters. •

d : roughly 0.1% chance of a breakup after rejection. •

g : cost to ﬁrm of preparing countero§er roughly 0.6 times one • day’s production.

Posterior mode of hiring cost: 0.5% of GDP; replacement ratio: • 30% of wage.

Elasticity of substitution between home and market goods: 3. • — set apriori, see Aguiar-Hurst-Karabarbounis (2012). TheFigure U.S. 4: The Great Great Recession Recession in the U.S.

Log Real GDP Inflation (%, y−o−y) Federal Funds Rate (%) Unemployment Rate (%)

2.5 5 −2.76 9 4 2 8 −2.78 3 7 −2.8 1.5 2 6

−2.82 1 1 5

2002 2004 2006 2008 2010 2012 2002 2004 2006 2008 2010 2012 2002 2004 2006 2008 2010 2012 2002 2004 2006 2008 2010 2012

Employment/Population (%) Labor Force/Population (%) Log Real Investment Log Real Consumption

64 67 −5.6 −5.5 63 66 62 −5.7 −5.52

61 65 −5.8 −5.54 60 64 59 −5.56 −5.9 2002 2004 2006 2008 2010 2012 2002 2004 2006 2008 2010 2012 2002 2004 2006 2008 2010 2012 2002 2004 2006 2008 2010 2012

Log Real Wage Log Vacancies Job Finding Rate (%) G−Z Corporate Bond Spread (%) 4.62 8.4 7 70 4.6 6 8.2 5 4.58 60 4 4.56 8 3 50 4.54 7.8 2 2002 2004 2006 2008 2010 2012 2002 2004 2006 2008 2010 2012 2002 2004 2006 2008 2010 2012 2002 2004 2006 2008 2010 2012

Log TFP Log Gov. Cons.+Investment 4.64 −4.34 4.62 Data −4.36 4.6 2008Q2 4.58 −4.38 4.56 −4.4

4.54 −4.42 4.52 2002 2004 2006 2008 2010 2012 2002 2004 2006 2008 2010 2012 Quantifying the Great Recession Want a quantitative characterization of the Great Recession • — the part of the post-2008 data that did not simply involve an unwinding of pre-2008 forces. — we seek to understand the di§erence between what would have happened absent Great Recession shocks and what did happen. — want the procedure to be as simple and transparent as possible.

For each variable, we ﬁt a linear trend from date x to 2008Q2, • where x 1985Q1; 2003Q1 . 2 { } We extrapolate the resulting trend lines for each variable from • 2008Q3 to 2013Q2.

We calculate the target gaps as the di§erences between the • projected values of each variable and its actual value. U.S. Great Recession:The Great Recession Targetin the U.S. Gap Ranges Data (Min−Max) Data (Mean) GDP (%) Inflation (p.p., y−o−y) Federal Funds Rate (ann. p.p.) Unemployment Rate (p.p.) 0 0 1 −0.5 4 −5 0 −1 −1 2 −10 −1.5 −2 0 2009 2010 2011 2012 2013 2009 2010 2011 2012 2013 2009 2010 2011 2012 2013 2009 2010 2011 2012 2013 Employment (p.p.) Labor Force (p.p.) Consumption (%) Investment (%) 0 0 0 0 −1 −10 −2 −1 −5 −3 −20 −2 −4 −30 −5 −3 −10 2009 2010 2011 2012 2013 2009 2010 2011 2012 2013 2009 2010 2011 2012 2013 2009 2010 2011 2012 2013 Real Wage (%) Job Finding Rate (p.p.) Vacancies (%) G−Z Spread (ann. p.p.) 0 0 −5 0 4 −10 −5 −15 −20 2 −20 −25 −40 0 −10 2009 2010 2011 2012 2013 2009 2010 2011 2012 2013 2009 2010 2011 2012 2013 2009 2010 2011 2012 TFP (%) Gov. Cons. & Invest. (%) 0

0 −2 −5 −4 −10 −6 2009 2010 2011 2012 2009 2010 2011 2012 2013 Two Financial Market Shocks b 1 Consumption wedge, Dt : Shock to demand for safe assets (‘Flight to safety’, see e.g. Fisher 2014):

b 1 =(1 + Dt )Etmt+1Rt/pt+1

˜ k 2 Financial wedge, Dt : Reduced form of ‘risk shock’, Christiano-Davis (2006), Christiano-Motto-Rostagno (2014):

k k 1 =(1 D˜ )E m + R /p + − t t t 1 t+1 t 1

Financial wedge also applies to working capital loans: • ˆ k — Interest charge on working capital: Rt 1 + Dt — Estimated share of labor inputs financed with loans: 0.56. — Higher financial wedge directly increases cost to firms. Measurement of Shocks

˜ k 1 Financial wedge, Dt , measured using GZ spread data.

b 2 Consumption wedge, Dt , measured using the Euler equation for the risk-free asset and Etpt+1 and Rt data.

3 Neutral technology shock based on TFP data.

4 Government shock measured using G data.

Stochastic simulation starting 2008Q3 (nonlinear model, no • perfect foresight). Figure 7:Exogenous The U.S. Great Recession: Processes Exogenous Variables

Data (Min−Max Range) Data (Mean) Model

G−Z Corporate Bond Spread (annualized p.p.) Consumption Wedge (annualized p.p.)

5 7 6 4 5 3 4 2 3 1 2 0 1

−1 0 2009 2011 2013 2015 2009 2011 2013 2015

Neutral Technology Level (%) Government Consumption & Investment (%) 0

0 −0.5

−5 −1

−10 −1.5

2009 2011 2013 2015 2009 2011 2013 2015 Figure 5: Measures of Total Factor Productivity (TFP): 2001 to 2013 Log TFP Log TFP

BLS (Private Business) Fernald (Raw) 4.7 4.68 BLS (Manufacturing) Fernald (Utilization Adjusted) BLS (Total) 4.66 Penn World Tables 4.65 4.64 4.62 4.6 Assessing model’s implication4.6 for TFP 4.55 4.58 4.56 4.5 4.54 4.52

2002 2004 2006 2008 2010 2002 2004 2006 2008 2010 2012

Notes: Linear trend from 2001Q1−2008Q2 (dashed−dotted). Forecast 2008Q3 and beyond based on linear trend (dotted).

TFP (% Deviation from Trend) 2 BLS (Private Business) BLS (Manufacturing) 0 BLS (Total) Fernald (Raw) Fernald (Util. Adjusted) −2 Penn World Tables Our Model

−4

−6

−8

−10 2008Q3 2009Q1 2009Q3 2010Q1 2010Q3 2011Q1 2011Q3 2012Q1 2012Q3 2013Q1 Monetary Policy in the Great Recession

From 2008Q3 to 2011Q2: • — Taylor-type feedback rule subject to the ZLB.

After 2011Q2: ‘forward guidance’ • — following 1 year transition, ‘Evans rule’ — keep funds rate at zero until either unemployment falls below 6.5% or inﬂation rises above 2.5%. The U.S.Figure Great 8: The U.S. Recession: Great Recession: Data Data vs. Model vs. Model

Data (Min−Max Range) Data (Mean) Model

GDP (%) Inflation (p.p., y−o−y) Federal Funds Rate (ann. p.p.) 0 0 1 −0.5 −5 0 −1 −1 −10 −1.5 −2 2009 2011 2013 2015 2009 2011 2013 2015 2009 2011 2013 2015 Unemployment Rate (p.p.) Employment (p.p.) Labor Force (p.p.) 0 0

4 −2 −1

−2 2 −4 −3 0 2009 2011 2013 2015 2009 2011 2013 2015 2009 2011 2013 2015 Investment (%) Consumption (%) Real Wage (%) 0 0 0 −10 −5 −20 −5

−30 −10 −10 2009 2011 2013 2015 2009 2011 2013 2015 2009 2011 2013 2015 Vacancies (%) Job Finding Rate (p.p.) 0 0 −10 −20 −20 −40

2009 2011 2013 2015 2009 2011 2013 2015 The U.S.Figure Great 8: The U.S. Recession: Great Recession: Data Data vs. Model vs. Model

Data (Min−Max Range) Data (Mean) Model

4 −2 −1

−2 2 −4 −3 0 2009 2011 2013 2015 2009 2011 2013 2015 2009 2011 2013 2015 Investment (%) Consumption (%) Real Wage (%) 0 0 0 −10 −5 −20 −5

−30 −10 −10 2009 2011 2013 2015 2009 2011 2013 2015 2009 2011 2013 2015 Vacancies (%) Job Finding Rate (p.p.) 0 0 −10 −20 −20 −40

2009 2011 2013 2015 2009 2011 2013 2015 Decomposing What Happened into Shocks

Our shocks roughly reproduce the actual data. •

We investigate the e§ect of a shock by shutting it o§. • — Resulting decomposition is not additive because of nonlinearity.

Results: • — Financial wedge - accounts for the biggest e§ects on real quantitites.

— Consumption wedge - less important than ﬁnancial wedge.

— Government spending - relatively small role.

— TFP - plays an important role in preventing drop in inﬂation. Phillips Curve

Widespread skepticism that NK model can account for modest • decline in inﬂation during the Great Recession.

One response: Phillips curve got ﬂat or always was very ﬂat • (e.g. Christiano, Eichenbaum and Rebelo, 2011).

Alternative: standard Phillips curve misses sharp rise in costs • — Unusually high cost of credit to finance working capital. — Fall in TFP. Both raise countervailing pressure on inflation. ) Decomposition for Inflation Beveridge Curve

Much attention focused on ‘sharp’ rise in vacancies and • relatively small fall in unemployment

— It is argued that ‘ﬁsh hook’ shape is evidence of a ‘shift’ in matching function.

— Argument based on assumption that unemployment is at steady state — misleading in the context of the Great Recession.

In our model, no shift occurs in the matching technology. • — Still, our model accounts for the ‘ﬁsh hook’ shape of the Beveridge curve. The Beveridge Curve: Data vs. Model

Figure 9: Beveridge Curve: Data vs. Model −10 Data Model −15 2008Q3 −20 2013Q2

−25

−30 2011Q4

−35 2009Q1 2010Q3 −40

−45 2009Q4

−50

−55 Vacancies (% dev. from data trend or model steady state)

−60 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 Unemployment Rate (p.p. dev. from 2008Q2 data or model steady state) Model Predicts Fish Hook, Why? Simplest DMP style model • U + U =(1 r)(1 U ) f U t 1 − t − − t − t t solving for ft :

matching function (1 Ut) Ut+1 Ut Vt a ft =(1 r) − − = st( ) − Ut − Ut Ut z}|{ solving for Vt :

standard approximation sets this to zero 1/a (1 U ) U U = 2( ) t t+1 t 3 Vt 1 r −1 a −1 a − s U − − s U − 6 t t z t }|t { 7 6 7 6 7 4 5 Naturally implies a ’ﬁsh hook’ pattern (Pissarides). • Magnitude of Fish Hook in DMP Model

U.S. Beveridge Curve

4 Jan 2001 JOLTS Data (Dec 2000−Jan 2014) Stylized Model, Steady State Condition ∆U=0 Imposed Stylized Model, Steady State Condition Not Imposed

3.5

3 Jan 2014 Vacancy Rate, V, (%) 2.5

Sept 2008

4 5 6 7 8 9 10 Unemployment Rate, U, (%)

(r = 0.97, a = 0.6, s = 0.84, monthly) Conclusion Bulk of movements in economic activity during the Great • Recession due to ﬁnancial frictions interacting with the ZLB. — ZLB has caused negative spending shocks to push the economy into a prolonged recession.

Findings based on looking through lens of a NK model: • — ﬁrms face moderate degrees of price rigidities, — no sticky wages. — endogenous labor force participation, standard labor market variables.

No (or little) evidence for ‘mismatch’ in labor market. •

Modest fall in inﬂation is not a puzzle once fall in TFP and • risky working capital channel are taken into account.