Financial Markets and Fluctuations in Uncertainty Cristina Arellano, - - PowerPoint PPT Presentation

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

• bserved 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 b0(σ0) Firms’ idiosyncratic productivity shocks z have common stochastic volatility σ

Arellano, Bai, Kehoe () Fluctuations in Uncertainty April 2010 8 / 30

Firms

Stochastic structure: log zt = ρz log zt1 + σtεt log σt = (1 ρσ) log µσ + ρσ log σt1 + ηt 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 b0(σ0) and `0 to maximize present value of dividends d = z`θ w` b + ∑

σ0

q0(σ0j.)b0(σ0) q(σ0j.) depends on …rms choices and aggregate states Free entry condition given …xed cost of entry ξ ξ = Ez 0,σ0Q(σ0jS)V 0(`0, b0, z0, S0) 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(σ0j.) 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 (

∑

σ0

q(σ0j.)b0(σ0) ) < 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 h1+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

max

`

Z ∞

0 [z`θ w`]φ(z)dz + V

Optimal scale chosen to maximize short term pro…ts: θ`θ1E(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) max

`,ˆ z

Z ∞

ˆ z [z`α w`]φ(z)dz +

Z ∞

ˆ z

V φ(z)dz subject to ˆ z`α w` = 0 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`θ1 E(zjz ˆ z) 1 Φ(ˆ z) = w + V φ(ˆ z) 1 Φ(ˆ z) d ˆ 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`θ1 E(zjz ˆ z) 1 Φ(ˆ z) = w + V φ(ˆ z) 1 Φ(ˆ z) d ˆ z d` Loss in future value is larger when

φ(ˆ z) 1Φ(ˆ z) increases with volatility:

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 σt 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 σt

Current recession: Choose the sequence of σt 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

2007−IV 2008−I 2008−II 2008−III 2008−IV 2009−I 2009−II 2009−III 0.14 0.16 0.18 0.2 0.22 0.24 0.26 Data Model

Choose sequence of σt to match time path of IQR sales growth

Arellano, Bai, Kehoe () Fluctuations in Uncertainty April 2010 20 / 30

Current recession: Output

2007−IV 2008−I 2008−II 2008−III 2008−IV 2009−I 2009−II 2009−III −0.07 −0.06 −0.05 −0.04 −0.03 −0.02 −0.01 Data (average drop 4.1%) Model (average drop 2.7%)

Model output matches 66% of the output decline

Arellano, Bai, Kehoe () Fluctuations in Uncertainty April 2010 22 / 30

Current recession: Labor

2007−IV 2008−I 2008−II 2008−III 2008−IV 2009−I 2009−II 2009−III −0.15 −0.1 −0.05 0.05 data model

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

2007−IV 2008−I 2008−II 2008−III 2008−IV 2009−I 2009−II 2009−III −0.15 −0.1 −0.05 0.05 Data Model

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- Trough std(x) std(x) std(gdp) Peak- Trough std(x) std(x) std(gdp) 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

1 2 3 4 5 6 7 8 9 10 −0.03 −0.02 −0.01 0.01 Output Labor Periods 1 10 20 30 40 50 60 70 80 90 100 −0.03 −0.02 −0.01 0.01 Output Labor Periods

Labor falls more than output

Arellano, Bai, Kehoe () Fluctuations in Uncertainty April 2010 27 / 30

Aggregate Impulse Response to High Dispersion

1 2 3 4 5 6 7 8 9 10 −0.02 −0.01 0.01 Measure Periods 10 20 30 40 50 60 70 80 90 100 −0.02 −0.01 0.01 Measure Periods

Measure of …rms fall

Arellano, Bai, Kehoe () Fluctuations in Uncertainty April 2010 28 / 30

Aggregate Impulse Response to High Dispersion

1 2 3 4 5 6 7 8 9 10 −0.04 −0.03 −0.02 −0.01 0.01 TFP Labor Wedge Periods 10 20 30 40 50 60 70 80 90 100 −0.04 −0.03 −0.02 −0.01 0.01 TFP Labor Wedge Periods

Labor wedge worsens a lot, TFP rises a bit

Arellano, Bai, Kehoe () Fluctuations in Uncertainty April 2010 29 / 30

IQR sales growth from 1970-2010

.1 .15 .2 .25 IQR of sales growth 1970q1 1980q1 1990q1 2000q1 2010q1 period NBER Recession/low IQR of sales growth

Arellano, Bai, Kehoe () Fluctuations in Uncertainty April 2010 30 / 30