Financial Markets and Fluctuations in Uncertainty Cristina Arellano, Yan Bai, and Patrick Kehoe Federal Reserve Bank of Minneapolis April 2010 Arellano, Bai, Kehoe () Fluctuations in Uncertainty April 2010 1 / 30
Motivation Recent recession has featured I Large contraction in output I Substantial increase in the dispersion of …rms’ growth Most of the recent output downturn accounted for I By a worsening of the labor wedge I Not by fall in TFP Arellano, Bai, Kehoe () Fluctuations in Uncertainty April 2010 2 / 30
Goal Develop a model with imperfect …nancial markets that connects ‡uctuations in …rm volatility to aggregate ‡uctuations Ask: Can an increase in volatility of …rms’ idiosyncratic shocks that generates observed increase in …rms’ dispersion deliver I Large contraction? I Large worsening of labor wedge? Today focus on current recession Arellano, Bai, Kehoe () Fluctuations in Uncertainty April 2010 3 / 30
Key Elements in Model Firms I Choose their scale in advance I Issue debt uncontingent on their idiosyncratic shock and can default I Firms pay an entry cost so ongoing …rms have positive future expected pro…ts Shocks I Common shocks to the volatility of …rms’ idiosyncratic productivity Arellano, Bai, Kehoe () Fluctuations in Uncertainty April 2010 4 / 30
Role of key elements Choose scale in advance I One scale for all states I In high states ‘too small’ and in low states ‘too big’ Uncontingent/unenforceable debt I If too big, might default Entry cost I In equilibrium generates costs of default = ) Trade-o¤ between short-term pro…ts and the risk of costly liquidation Arellano, Bai, Kehoe () Fluctuations in Uncertainty April 2010 5 / 30
From …rm volatility to aggregates Model: Trade-o¤ between pro…ts and liquidation Mechanism: High volatility mainly increases risk of costly liquidation I Firms reduce scale and output I Labor wedge worsens because MPL deviates more from wage Arellano, Bai, Kehoe () Fluctuations in Uncertainty April 2010 6 / 30
Our answers for current recession Can an increase in volatility of …rms’ idiosyncratic shocks that generates observed increase in …rms’ dispersion deliver Large contraction? I Model accounts for 2/3 of the output decline Large worsening of labor wedge? I The labor wedge falls by 18% in model and 15% in data Arellano, Bai, Kehoe () Fluctuations in Uncertainty April 2010 7 / 30
Model Dynamic model of heterogeneous …rms and identical households Households provide labor services and trade assets Firms use DRS technology with labor input ` and issue debt b 0 ( σ 0 ) Firms’ idiosyncratic productivity shocks z have common stochastic volatility σ Arellano, Bai, Kehoe () Fluctuations in Uncertainty April 2010 8 / 30
Firms Stochastic structure: log z t = ρ z log z t � 1 + σ t ε t log σ t = ( 1 � ρ σ ) log µ σ + ρ σ log σ t � 1 + η t Individual states: ( ` , b , z ) Aggregate states: S = ( σ , Υ ) , where Υ is measure over individual states Arellano, Bai, Kehoe () Fluctuations in Uncertainty April 2010 9 / 30
Firms Choose b 0 ( σ 0 ) and ` 0 to maximize present value of dividends d = z ` θ � w ` � b + ∑ q 0 ( σ 0 j . ) b 0 ( σ 0 ) σ 0 q ( σ 0 j . ) depends on …rms choices and aggregate states Free entry condition given …xed cost of entry ξ ξ = E z 0 , σ 0 Q ( σ 0 j S ) V 0 ( ` 0 , b 0 , z 0 , S 0 ) After entry the expected value is positive Cost of default: Firm exits so lose expected value of future pro…ts Arellano, Bai, Kehoe () Fluctuations in Uncertainty April 2010 10 / 30
Firms Firms must have non-negative dividends Debt schedule q ( σ 0 j . ) compensates for loss in case of default I Schedule contains ‘borrowing limits’ For high enough debt due, …rms must default: I Default if ( ) z ` θ � w ` � b + max q ( σ 0 j . ) b 0 ( σ 0 ) ∑ < 0 σ 0 Arellano, Bai, Kehoe () Fluctuations in Uncertainty April 2010 11 / 30
Households Identical households with standard problem Choose c , and h to maximize present value of utility, where u ( c , h ) = log ( c ) � χ h 1 + ν 1 + v Arellano, Bai, Kehoe () Fluctuations in Uncertainty April 2010 12 / 30
Simple Example Two period problem Firm loses exogenous future value V if liquidates Arellano, Bai, Kehoe () Fluctuations in Uncertainty April 2010 13 / 30
Complete …nancial markets Z ∞ 0 [ z ` θ � w ` ] φ ( z ) dz + V max ` Optimal scale chosen to maximize short term pro…ts: θ ` θ � 1 E ( z ) = w Increasing volatility while preserving E ( z ) does not change optimal scale Arellano, Bai, Kehoe () Fluctuations in Uncertainty April 2010 14 / 30
No …nancial markets Without …nancial markets …rms liquidate in low states ( z < ˆ z ) Z ∞ Z ∞ z [ z ` α � w ` ] φ ( z ) dz + max V φ ( z ) dz ` , ˆ z ˆ z ˆ subject to z ` α � w ` = 0 ˆ d ˆ z / d ` > 0 so higher ` implies higher ˆ z which generates: I Higher short term pro…ts I Lower future value Optimal scale chosen to maximize short term pro…ts and future value Arellano, Bai, Kehoe () Fluctuations in Uncertainty April 2010 15 / 30
No …nancial markets Optimal scale: θ ` θ � 1 E ( z j z � ˆ z ) φ ( ˆ z ) d ˆ z = w + V 1 � Φ ( ˆ 1 � Φ ( ˆ z ) z ) d ` Marginal cost of labor equals wage plus loss in future value When V is high enough: I scale is smaller than with frictionless …nancial markets I marginal product of labor is larger than wage = ) labor wedge Arellano, Bai, Kehoe () Fluctuations in Uncertainty April 2010 16 / 30
Increasing volatility θ ` θ � 1 E ( z j z � ˆ z ) φ ( ˆ z ) d ˆ z = w + V 1 � Φ ( ˆ 1 � Φ ( ˆ z ) z ) d ` φ ( ˆ z ) Loss in future value is larger when z ) increases with volatility : 1 � Φ ( ˆ I scale is smaller I marginal product of labor is even larger than wage = ) even larger labor wedge Arellano, Bai, Kehoe () Fluctuations in Uncertainty April 2010 17 / 30
Quantitative Exercise Parameterize process for σ t to the times series of IQR of sales growth in Compustat …rms (1970-2009) I Moments: Mean, std., and autocorrelation of IQR of sales growth I Parameters: Mean, std. and autocorrelation of σ t Current recession: Choose the sequence of σ t to match time series of IQR of sales growth Arellano, Bai, Kehoe () Fluctuations in Uncertainty April 2010 18 / 30
Current recession: IQR of sales growth 0.26 0.24 0.22 0.2 Model 0.18 Data 0.16 0.14 2007 − IV 2008 − I 2008 − II 2008 − III 2008 − IV 2009 − I 2009 − II 2009 − III Choose sequence of σ t to match time path of IQR sales growth Arellano, Bai, Kehoe () Fluctuations in Uncertainty April 2010 20 / 30
Current recession: Output 0 − 0.01 Model (average drop 2.7%) − 0.02 − 0.03 Data (average drop 4.1%) − 0.04 − 0.05 − 0.06 − 0.07 2007 − IV 2008 − I 2008 − II 2008 − III 2008 − IV 2009 − I 2009 − II 2009 − III Model output matches 66% of the output decline Arellano, Bai, Kehoe () Fluctuations in Uncertainty April 2010 22 / 30
Current recession: Labor 0.05 0 model − 0.05 data − 0.1 − 0.15 2007 − IV 2008 − I 2008 − II 2008 − III 2008 − IV 2009 − I 2009 − II 2009 − III Model labor decline matches data; last couple of quarters decline is larger Arellano, Bai, Kehoe () Fluctuations in Uncertainty April 2010 23 / 30
Current recession: Labor wedge 0.05 0 Model − 0.05 Data − 0.1 − 0.15 2007 − IV 2008 − I 2008 − II 2008 − III 2008 − IV 2009 − I 2009 − II 2009 − III The labor wedge falls by 18% in model and 15% in data Arellano, Bai, Kehoe () Fluctuations in Uncertainty April 2010 24 / 30
Conclusion Framework that combines volatility shocks with …nancial markets imperfections Generates movements in labor wedge linked to …nancial frictions Arellano, Bai, Kehoe () Fluctuations in Uncertainty April 2010 25 / 30
Business Cycles Data Model Peak- Peak- std(x) std(x) std(x) std(x) std(gdp) std(gdp) Trough Trough GDP -5.0 2.6 -3.5 1.8 Labor -5.1 3.4 1.3 -6.7 3.5 2.0 Consumption -3.1 2.5 0.7 -0.6 1.1 0.6 Labor Wedge -5.8 4.4 1.7 -7.1 4.4 2.5 TFP -1.3 1.2 0.3 1.2 0.8 0.5 Arellano, Bai, Kehoe () Fluctuations in Uncertainty April 2010 26 / 30
Aggregate Impulse Response to High Dispersion 0.01 0.01 0 0 − 0.01 − 0.01 Output Output − 0.02 − 0.02 Labor Labor − 0.03 − 0.03 1 2 3 4 5 6 7 8 9 10 1 10 20 30 40 50 60 70 80 90 100 Periods Periods Labor falls more than output Arellano, Bai, Kehoe () Fluctuations in Uncertainty April 2010 27 / 30
Aggregate Impulse Response to High Dispersion 0.01 0.01 0 Measure 0 − 0.01 − 0.01 Measure − 0.02 − 0.02 1 2 3 4 5 6 7 8 9 10 10 20 30 40 50 60 70 80 90 100 Periods Periods Measure of …rms fall Arellano, Bai, Kehoe () Fluctuations in Uncertainty April 2010 28 / 30
Aggregate Impulse Response to High Dispersion 0.01 0.01 TFP TFP 0 0 − 0.01 − 0.01 − 0.02 − 0.02 − 0.03 − 0.03 Labor Wedge Labor Wedge − 0.04 − 0.04 1 2 3 4 5 6 7 8 9 10 10 20 30 40 50 60 70 80 90 100 Periods Periods Labor wedge worsens a lot, TFP rises a bit Arellano, Bai, Kehoe () Fluctuations in Uncertainty April 2010 29 / 30
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