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The Making Of A Great Contraction With A Liquidity Trap And A Jobless Recovery Stephanie Schmitt-Groh´ e Mart ´ ın Uribe Columbia University November 5, 2013

A jobless recovery is a situation in which: • Output growth recovers, • but employment does not. Bernanke (2009). 2

A liquidity trap is a situation in which: • The nominal interest rate is zero; and • Expected inflation is below target. 3

Two historical examples of great contractions with a liquidity trap and a jobless recovery: • Great Contraction of 2008 in the United States. • Double Dip Recession of Japan in the 1990s. 4

U.S. Real Per Capita GDP Growth: 2005-2012 5 percent per year 0 −5 −10 2006 2008 2010 2012 Source: Bureau of Economic Activity. 5

U.S. Civilian Employment-Population Ratio: 2005-2013Q1 64 63 62 percent 61 60 59 58 2006 2008 2010 2012 Source: Bureau of Labor Statistics. 6

⇒ The U.S. recovery from the Great Contraction of 2008 was jobless . 7

U.S. Federal Funds Rate: 2005-2012 6 5 4 percent 3 2 1 0 2006 2008 2010 2012 Source: Federal Reserve Board. 8

U.S. 10-Year Expected Inflation: 2005Q1-2012Q4 3 2.5 percent 2 1.5 1 2006 2008 2010 2012 Source: Federal Reserve Bank of Cleveland. 9

⇒ The Great Contraction of 2008 pushed the U.S. economy into a liquidity trap . 10

Japan The Double-Dip Recession 1989 - 2001 11

Real Per Capita GDP Growth 4qtr, Japan, 1989-2001 Real Per Capita GDP Growth 6 4 Percent Per Year 2 0 −2 1990 1992 1994 1996 1998 2000 Year 12

Japan, 1989-2001 Employment−to−Population Ratio 63 62 Percent 61 60 59 1990 1992 1994 1996 1998 2000 Year 13

Japan, 1989-2001 Unemployment Rate 5 4.5 4 Percent 3.5 3 2.5 2 1990 1992 1994 1996 1998 2000 Year 14

⇒ The recovery from the recessions of the 1990s in Japan was jobless . 15

Japan, 1989-2001 Call Rate 8 Percent Per Year 6 4 2 0 1990 1992 1994 1996 1998 2000 Year 16

Year over Year Growth of GDP Deflator, Japan, 1989-2001 Inflation 3 2 Percent Per Year 1 0 −1 −2 1990 1992 1994 1996 1998 2000 Year 17

⇒ In the 1990s Japan fell into a liquidity trap . 18

This paper develops a theoretical model that predicts that a confidence shock can lead the economy into a liquidity trap with a jobless recovery. 19

Four Key Elements of the Argument: 1. Downward Nominal Wage Rigidity. 2. Monetary Policy follows a Taylor Rule. 3. The Zero Lower Bound On Nominal Interest Rates. 4. A Downward Revision in Inflation Expectations. 20

Related Papers on Liquidity Traps: Krugman, 1998; Eggertson and Woodford, 2003; Benhabib, Schmitt-Groh´ e, and Uribe, 2001; Related Papers on Jobless Recoveries: Shimer (2012); Calvo, Coricelli, and Ottonello (2012); Related Papers on Interpreting the Great Recession as a Self-fulfilling Crisis: Aruoba and Schorfheide, 2012; Mertens and Ravn, 2012; 21

Element 1: Downward Nominal Wage Rigidity. W t ≥ γ ( u t ) W t − 1 , where • W t nominal wage rate • u t , unemployment rate Assumption: γ ′ ( u ) < 0 22

Empirical Evidence on Downward Nominal Wage Rigidity 23

Probability of Decline, Increase, or No Change in Nominal Wages Between Interviews U.S. data, SIPP panel 1986-1993, within-job changes Interviews One Year apart Males Females Decline 5.1% 4.3% Constant 53.7% 49.2% Increase 41.2% 46.5% Source: Gottschalk (2005) Note. Male and female hourly workers not in school, 18 to 55 at some point during the panel. All nominal-wage changes are within-job wage changes, defined as changes while working for the same employer. 24

Quarterly, 1996-99. Source: Barattieri, Basu, and Gottschalk (2010) 25

Distribution of Nominal Wage Changes, 2011, USA Source: Daly et al. (2012). Workers in the same industry and occupation. 26

Distribution of Nominal Wage Changes, 2011, USA Source: Elsby et al. (2013). Hourly workers in the same employer. 27

Elements 2 and 3 • Monetary Policy Follows a Taylor Rule. • The Zero Lower Bound on Nominal Interest Rates. � � π t − π ∗ � + α y ln � �� Y t 1 , R ∗ + α π R t = max Y ∗ t α π > 1 , α y > 0 28

Households Preferences: ∞ e ξ t β t U ( C t ) � E 0 t =0 Budget constraint: P t C t + B t + T t = W t h t + R t − 1 B t − 1 + Φ t Inelastic Labor Supply: h t ≤ ¯ h 29

Firms Production function: Y t = X t F ( h t ); with X t /X t − 1 = µ > 1 Labor demand: P t X t F ′ ( h t ) = W t 30

The Labor Market h t ≤ ¯ h W t ≥ γ ( u t ) W t − 1 � = 0 (¯ h − h t ) � W t − γ ( u t ) W t − 1 31

Equilibrium: Let w t ≡ W t P t X t and c t ≡ C t /X t    e ξ t +1 U ′ ( c t +1 ) e ξ t U ′ ( c t ) = ˜ βR t E t  π t +1 1 , π ∗ � � �� � π t − π ∗ � + α y ln F ( h t ) R t = max β + α π ˜ F (¯ h ) c t = F ( h t ) w t = F ′ ( h t ) ¯ w t ≥ γ ( u t ) h − h t h t ≤ ¯ and π t µ w t − 1 ; where u t ≡ h ¯ h � � w t − γ ( u t ) (¯ h − h t ) π t µ w t − 1 = 0 32

A Key Inflation Threshold π ≡ γ (0) ¯ µ π t < ¯ π ⇒ involuntary unemployment. 33

Steady State Equilibria: c t = c , h t = h , w t = w , π t = π , R t = R R = π ˜ β � � �� � π − π ∗ � + α y ln F ( h ) 1 , R ∗ + α π R = max F (¯ h ) 34

Two Steady States π t +1 π ∗ ← ˜ β R t ( π t ) ˜ β ← 45 0 -line π t ˜ π ∗ β 35

Multiple Steady States Proposition 1 (Existence of a Full-Employment Steady State) There exists a unique full-employment steady state ( u = 0 ). Moreover, at the full-employment steady state the inflation rate equals the inflation target π ∗ . Proposition 2 (Existence of an Unemployment Steady State) There exists a unique unemployment steady state ( u = ¯ u > 0 ). Moreover, at the unemployment steady state the economy is in a liquidity trap ( R = 1 and π = ˜ β < π ∗ ). 36

Element 4: A Downward Revision in Inflation Ex- pectations (or confidence shock) π 0 < π ∗ 37

Proposition 3 (Liquidity Trap) Suppose that ξ t = 0 and de- Further, assume that π 0 < π ∗ . terministic for t ≥ 0 . Then, in any perfect foresight equilibrium, if π t ≥ γ (0)  < π t < π ∗  µ π t +1 , for all t ≥ 0 . < γ (0) if π t < γ (0) < π ∗  µ µ Furthermore, there exists a finite integer T ≥ 0 such that π T < γ (0) µ . Proposition 4 (Chronic Involuntary Unemployment) Suppose that ξ t = 0 and deterministic for t ≥ 0 . Further, assume that π 0 < π ∗ . Then, in any perfect foresight equilibrium u t > 0 for all t ≥ T , where T ≥ 0 is the finite integer defined in proposition 3. 38

Calibrated Example: F ( h ) = h α ; with α = 0 . 75 u ( c ) = c 1 − σ / (1 − σ ); with σ = 2 X t = 1 . 015 1 / 4 X t − 1 ; β = 1 . 04 − 1 / 4 ; real rate of 4 percent ˜ π ∗ = 1 . 02 1 / 4 ; inflation target of 2 percent α π = 1 . 5 α y = 0 . 125 γ ( u t ) = γ 1 · (1 − u t ) γ 2 ; γ 1 = 1 . 02 1 / 4 ; γ 2 = 0 . 19. 39

Calibration of the Degree of Downward Wage Rigidity , γ ( u ) = γ 1 (1 − u ) γ 2 • Set γ 1 = 1 . 02 1 / 4 ⇒ At the full-employment steady state, nom- inal wages must grow at a rate of 2% per year or higher. Weak restriction: due to productivity growth, lower bound on nominal wages does not bind in the intended steady state. • Set γ 2 so that if unemployment is 5 percent above the natural rate, then wages can fall frictionlessly by up to 2 percent per year. This is a conservative criterion: Between 2008 and 2010, US un- employment increased from 5 to 10 percent, but nominal hourly wages did not fall. They actually grew by 3 percent per year. 40

Dynamics Under Lack of Confidence Shock Interest Rate Inflation 6 2 5 1 4 0 % annual % annual 3 −1 2 −2 1 −3 0 −4 0 10 20 30 40 50 0 10 20 30 40 50 t t Output Growth Rate Employment Rate 1.8 100 1.6 99 1.4 98 % annual 1.2 % 97 1 96 0.8 95 0.6 0.4 94 0 10 20 30 40 50 0 10 20 30 40 50 t t 41

⇒ A Lack of Confidence Shocks Leads to • A Great Contraction • A Liquidity Trap • A Jobless Recovery 42

The U.S. Great Contraction of 2008 Federal Funds Rate 10−Year Expected Inflation 6 3 5 2.5 4 percent percent 3 2 2 1.5 1 0 1 2006 2008 2010 2012 2006 2008 2010 2012 Real Per Capita GDP Growth Civilian Employment−Population Ratio 5 64 63 0 62 percent percent 61 −5 60 59 −10 58 2006 2008 2010 2012 2006 2008 2010 2012 43

The Japanese Slump of the 1990s Call Rate Inflation 3 8 2 Percent Per Year Percent Per Year 6 1 4 0 2 −1 0 −2 1990 1992 1994 1996 1998 2000 1990 1992 1994 1996 1998 2000 Year Year Real Per Capita GDP Growth Employment−to−Population Ratio 6 63 4 62 Percent Per Year Percent 2 61 0 60 −2 59 1990 1992 1994 1996 1998 2000 1990 1992 1994 1996 1998 2000 Year Year 44