Labor Rigidity and the Dynamics of the Value...

Labor Rigidity and the Dynamics of the ValuePremium

Roberto Marfe

Collegio Carlo Alberto

NBER Asset Pricing Summer Institute 2016

R. Marfe (Collegio Carlo Alberto) Labor Rigidity and the Dynamics of the Value Premium NBER SI 2016

1 Motivation & Aim

2 Empirical Analysis

3 A Simple Model

4 Predictions and Limitations


Motivation and Aim

- The value premium –Graham and Dodd (1934)– is the finding that assets with a highratio of price to fundamentals (growth stocks) have low expected returns relative toassets with a low ratio of price to fundamentals (value stocks).

- This finding is not necessarily surprising: the premium on value stocks could representa compensation for bearing some ‘systematic’ risk (e.g. Zhang (JF 2005), PetkovaZhang (JFE 2005)). But no consensus on the source (Clementi Palazzo (2015)).

- Dechow, Sloan, and Soliman (RAS 2004) measure cash flow duration and find thatgrowth stocks have higher duration than value stocks.

- van Binsbergen, Brandt and Koijen (AER 2012) document that the term-structures ofequity risk and premia are downward-sloping.

- Lettau and Wachter (JF 2007) propose a dynamic risk-based model that captures thevalue premium and the downward-sloping term-structure of equity in partialequilibrium.


Motivation and Aim

- This paper investigates the relation between value premium, cash-flows duration andterm-structure of equity.

- Equity is a claim on cash-flows:

Pt = Et∫ ∞

0Mt,t+τDt+τdτ

- Valuation ratio is price relative to fundamentals: Pt/Dt. Value premium is the excessreturn of low valuation ratio firms over high valuation ratio firms.

- Cash-flows duration is

Dt = 1Pt

Et∫ ∞

0τ Mt,t+τDt+τdτ

- Term-structure is risk and premium on the claim on the horizon-τ cash-flows:

Pt =

∫ ∞0

Pt,τdτ ⇒ σ2(τ) = 1dt〈 dPt,τPt,τ

〉

pr(τ) = 1dt

dPt,τPt,τ

− rt ∀ τ


Motivation and Aim

- This paper investigates the relation between value premium, cash-flows duration andterm-structure of equity.

- The aim of the paper is:

1. to understand the macroeconomic channel beyond the connection among these stylizedfacts,

2. to understand the time-series of the value premium at business cycle frequency.

- This paper argues that labor rigidity:

1. generates a term-structure effect that gives rise to a cross-sectional duration premium,

2. largely drives business cycle fluctuations of the value premium.

- The paper provides empirical evidence and a simple illustrative model.


1 Motivation & Aim


3 A Simple Model



Empirical Analysis

STEP I: Independent variable: labor-share

STEP II: Does labor-share variation explain the value premium?

STEP III: The term-structure effect of labor rigidity

STEP IV: Does labor-share variation explain the duration premium?

STEP V: Is the value premium explained by labor-share a duration premium?

STEP VI: Robustness: alternative valuation ratios


Empirical Analysis- Labor rigidity implies:

1. smooth wages,

2. operating leverage ⇒ risky payouts to shareholders

- Asset pricing implications: high equity compensation (e.g. Danthine Donanldson (RES

2002))

1. cash-flows channel

2. discount rates channel if limited market participation (Berk Walden (RAPS 2013))

- Measurement: counter-cyclical labor-share (e.g. Rıos-Rull and Santaeulelia-Llopis (JME

2010))

US nonfinancial corporate sector in post-war yearly data:

1 =var(∆ log V )var(∆ logW )

+var(∆ logW/V )var(∆ logW )

+ 2cov(∆ log V,∆ logW/V )

var(∆ logW )

III

= 124% + 25% − 49%.

(smoothing effect is twice as large at quarterly frequency)

- Labor-share is stationary in post-war data (3.5 years half-life). To avoid time-trendissues in each regression I use a de-trended version of it on the relevant sample.


Empirical Analysis








Empirical Analysis- Negative and robust contemporaneous relation between ∆W/V and HML return:

HMLt = b0 + b1∆W/Vt + b′2controlst + εt

∆ W/V? workers’ remuneration -2.95∗∗∗ -2.61∗∗ -2.50∗∗ -3.01∗∗∗ -2.98∗∗∗ -3.11∗∗∗ -3.07∗∗∗ -3.23∗∗∗ -3.35∗∗∗ -2.89∗∗

t-stat (-2.68) (-2.16) (-2.07) (-2.68) (-2.67) (-2.81) (-2.74) (-2.67) (-2.87) (-2.57)

Macro controlslag W/V? 1.02∗∗

t-stat (2.00)

∆ B/V bondholders’ remuneration -3.51t-stat (-0.74)

lag B/V 0.26t-stat (0.36)

∆ D/V shareholders’ remuneration 0.93t-stat (0.83)

lag D/V -1.89∗∗

t-stat (-2.21)

∆ I/A investment to assets -4.44t-stat (-1.33)

lag I/A 1.28t-stat (0.62)

∆ log V value added -0.24t-stat (-0.77)

∆ log Y real GDP 0.37t-stat (0.53)

adj-R2 0.06 0.08 0.06 0.05 0.06 0.08 0.06 0.06 0.06 0.06

Newey-West corrected t-statistics in parenthesesIIII


Empirical Analysis- Negative and robust contemporaneous relation between ∆W/V and HML return:

HMLt = b0 + b1∆W/Vt + b′2controlst + εt

∆ W/V? workers’ remuneration -2.95∗∗∗ -3.47∗∗∗ -2.92∗∗ -2.81∗∗ -3.01∗∗∗ -3.25∗∗∗ -2.72∗∗ -2.89∗∗ -2.90∗∗

t-stat (-2.68) (-3.36) (-2.64) (-2.33) (-2.70) (-2.83) (-2.25) (-2.61) (-2.63)

Financial controlslag HML value minus growth excess return -0.152t-stat (-1.47)

lag HML2 0.706t-stat (1.19)

lag SMB small minus big excess return 0.131t-stat (0.95)

lag SMB2 0.063t-stat (0.15)

lag MKT market excess return -0.118t-stat (-1.40)

lag MKT2 0.304t-stat (0.81)

log P/E price to earnings -0.032t-stat (-0.83)

log P/D price to dividends -0.027t-stat (-0.82)

adj-R2 0.06 0.07 0.07 0.07 0.05 0.08 0.06 0.06 0.06



Empirical Analysis

- Negative and robust contemporaneous relation between ∆W/V and HML return:

D Labor-share

Value premium

1950 1960 1970 1980 1990 2000 2010

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é Value premium

-3 -2 -1 0 1 2D WV

-2

-1

0

1

2


Empirical Analysis- Positive and robust intertemporal relation between W/V and HML return:∑n

i=1log(1 + HMLt+i) = b0 + b1W/Vt + b′2controlst + εt

1 2 3 5 7W/V? workers’ remuneration 1.26∗∗ 1.47∗∗∗ 1.55∗∗∗ 1.21∗∗∗ 0.75∗∗∗

t-stat (2.51) (3.09) (3.71) (3.67) (2.89)

adj-R2 0.02 0.09 0.16 0.18 0.11

1 2 3 5 7W/V? workers’ remuneration 0.59 1.35∗∗ 1.81∗∗∗ 1.46∗∗∗ 0.59∗∗∗

t-stat (0.96) (2.35) (3.46) (3.97) (2.71)

B/V bondholders’ remuneration -3.36∗∗ -1.54 -0.29 -0.17 -1.43∗∗∗

t-stat (-2.40) (-1.04) (-0.27) (-0.34) (-3.49)

D/V shareholders’ remuneration -2.84∗ -0.08 0.44 -0.36 -0.84∗∗

t-stat (-1.82) (-0.06) (0.39) (-0.61) (-2.24)

I/A investment to assets -2.86 -3.36 -3.87 -2.30∗ 0.14t-stat (-0.89) (-0.93) (-1.39) (-1.72) (0.13)

log P/E price to earnings 0.43∗∗∗ 0.32∗∗∗ 0.15∗ -0.03 0.07t-stat (2.70) (2.69) (1.70) (-0.27) (0.86)

log P/D price to dividends -0.26∗ -0.26∗∗ -0.16∗∗ 0.00 -0.03t-stat (-1.84) (-2.62) (-2.51) (0.03) (-0.44)

FL financial leverage 0.34 0.01 -0.39 -0.44∗∗ -0.03t-stat (0.91) (0.03) (-1.64) (-2.59) (-0.23)

CS credit spread 24.71∗∗∗ 15.35∗∗∗ 7.44∗∗∗ 2.82 7.19∗∗∗

t-stat (5.55) (3.19) (2.77) (0.91) (3.34)

TS term spread 0.97 -0.40 -1.17∗∗ -1.33∗∗∗ -0.95∗∗

t-stat (1.31) (-0.53) (-2.08) (-5.12) (-2.17)

Rf short rate 6.24 22.46 19.26 -12.91 -13.06t-stat (0.14) (0.74) (0.81) (-0.69) (-0.92)

adj-R2 0.09 0.15 0.28 0.43 0.49



Empirical Analysis

- Positive and robust intertemporal relation between W/V and HML return:

Labor-share

Value premium

1950 1960 1970 1980 1990 2000 2010

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é Value premium

-3 -2 -1 0 1 2WV

-2

-1

0

1

2

- Labor-share predicts almost all business cycle fluctuations of the HML return.


Empirical Analysis








Empirical Analysis- Labor rigidity concerns transitory shocks but not permanent shocks:

1. Gamber (JLE 1988): theory (implicit contracts) and empirical support

2. Menzio (2005): theory (search frictions) and empirical support

3. International evidence: Guiso Pistaferri Schivardi (JPE 2005), Cardoso Portela (2009),and Ellul Pagano Schivardi (2014).

- Hence, labor rigidity alters the timing of risk of payouts to shareholders:1. van Binsbergen Brandt Koijen (AER 2012): dividend strip risk and premium are

downward-sloping

2. Belo Collin-Dufresne Goldstein (JF 2015) Marfe (RF 2016): dividend risk isdownward-sloping

3. Marfe (JF 2016): labor-share explains (i) the slope of dividend risk, and (ii) risk,premium and slope of dividend strip returns.

4. In preparation: frequency analysis provides direct evidence of income insurance’sterm-structure effect.

results

- Hence, does labor rigidity lead to a cross-sectional duration premium?1. Dechow Sloan Soliman (RES 2004) Weber (2016): positive duration premium

2. Does labor-share variation play a role?


Empirical Analysis

- Labor leverage and timing of risk:

∆ log Xt = b0 + b1∆W/Vt + εt

10 years Variance RatiosXt b1 t-stat R2 ∆ log Xt fitted val. residuals

Non-Financial Corporate SectorNet value added -1.35∗∗∗ -4.06 0.19 0.763 0.421 1.277Operating surplus -6.87∗∗∗ -17.46 0.78 0.206 0.421 1.038Before tax profits -8.96∗∗∗ -7.98 0.49 0.350 0.421 0.655After tax profits -9.51∗∗∗ -8.20 0.50 0.502 0.421 0.907Dividends plus net repurchases -7.02∗∗∗ -2.67 0.09 0.393 0.421 0.308Dividends plus net repurchases ex 2005-06a -6.64∗∗ -2.48 0.08 0.690 0.247 0.362Dividends -1.83 -1.06 0.02 0.146 0.421 0.133Dividends ex 2005-06a -2.16∗∗∗ -3.73 0.12 0.690 0.247 0.646

S&P 500 IndexEarnings -9.68∗∗∗ -5.04 0.17 0.105 0.421 0.162Earnings ex 2008-09b -8.13∗∗∗ -5.66 0.20 0.315 0.313 0.250Dividends -1.56∗∗∗ -3.18 0.09 0.818 0.421 0.758

a Excluded observations 2005 and 2006 are respectively beyond -10 and 11 standard deviations around the average.b Excluded observations 2008 and 2009 are respectively beyond -6 and 4 standard deviations around the average.


Empirical Analysis








Empirical Analysis- Weber (2016) sorts portfolios by cash-flows duration (1963-2013). I verify whether

labor-share forecasts the duration premium (i.e. D1–D10 return) at several horizons.cross-sectional results∑n

i=1log(1 + DPt+i) = b0 + b1W/Vt + b′2controlst + εt


t-stat (2.17) (3.15) (3.84) (3.72) (2.81)

adj-R2 0.04 0.15 0.23 0.27 0.20

1 2 3 5 7W/V? workers’ remuneration 4.06∗∗∗ 4.22∗∗∗ 3.90∗∗∗ 3.82∗∗∗ 1.83∗∗∗

t-stat (2.71) (4.67) (5.29) (7.71) (3.24)

B/V bondholders’ remuneration -2.10 -2.96 -1.70 -1.06 -0.75t-stat (-0.43) (-0.85) (-0.70) (-0.87) (-0.53)

D/V shareholders’ remuneration -4.30 -1.58 -1.36 0.18 1.23t-stat (-1.49) (-0.75) (-0.76) (0.18) (1.13)

I/A investment to assets -5.79 -0.84 3.89 9.80∗∗∗ 8.77∗∗∗

t-stat (-0.91) (-0.16) (1.18) (4.18) (3.13)

log P/E price to earnings -0.37 -0.18 -0.35∗∗ -0.62∗∗∗ -0.26∗∗

t-stat (-0.85) (-0.65) (-2.09) (-8.80) (-2.25)

log P/D price to dividends 0.26 0.15 0.35∗ 0.58∗∗∗ 0.29∗∗∗

t-stat (0.68) (0.53) (1.99) (6.79) (2.82)

FL financial leverage -2.11∗∗ -1.42∗∗∗ -1.09∗∗∗ -0.86∗∗∗ -0.15t-stat (-2.60) (-2.77) (-3.45) (-4.39) (-0.59)

CS credit spread 0.09 0.17∗∗ 0.12∗∗ 0.02 0.09∗∗

t-stat (0.75) (2.12) (2.47) (0.62) (2.37)

TS term spread 0.01 0.01 -0.00 0.00 -0.00t-stat (0.82) (0.38) (-0.30) (0.02) (-0.58)

Rf short rate 0.203 -0.32 -0.42 -0.66 -0.81∗∗

t-stat (0.18) (-0.50) (-0.88) (-1.46) (-2.52)

adj-R2 0.08 0.33 0.44 0.68 0.40



Empirical Analysis

- Are the HML return and the D1–D10 return correlated across horizons?

∑n

i=1log(1 + HMLt+i) = b0 + b1

∑n

i=1log(1 + DPt+i) + HML⊥t,n

1 2 3 5 7DP duration premium 0.43∗∗∗ 0.51∗∗∗ 0.48∗∗∗ 0.42∗∗∗ 0.35∗∗∗

t-stat (4.06) (7.24) (9.68) (8.12) (5.62)

adj-R2 0.39 0.54 0.54 0.44 0.34


- Value premium and duration premium are highly positively correlated at businesscycle frequencies.


Empirical Analysis

- Let’s check whether the explanatory power of labor-share for future HML returns inthe sub-sample 1963-2013 is similar to the former case of post-war data:


Empirical Analysis


∑n

i=1log(1 + HMLt+i) = b0 + b1W/Vt + b′2controlst + εt


t-stat (2.08) (2.99) (3.64) (3.42) (2.71)

adj-R2 0.01 0.09 0.19 0.18 0.11


- The pattern of predictability is very similar to the case of the full post-war sample

- The pattern of predictability is also very similar to that for the duration premium


Empirical Analysis


1970 1980 1990 2000 2010

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Labor-share

Value premium

Duration premium


Empirical Analysis








Empirical Analysis- Labor-share has sizeable predictive power for both the HML return and the D1–D10

return at business cycle frequencies.

- To what extent are the two predictability patterns due to the same economicmechanism?

HML⊥t,n = b0 + b1W/Vt + εt

1 2 3 5 7W/V? workers’ remuneration 0.16 0.12 0.34 0.26 0.20t-stat (0.32) (0.29) (0.92) (0.85) (0.76)

adj-R2 -0.02 -0.02 -0.00 -0.01 -0.01


- Labor-share does not forecast the component of the HML return orthogonal wrt theD1–D10 return.

- This result supports the idea that the term-structure effect of labor rigidity canexplain the link between labor-share variation and cross-sectional returns from B/Mand duration sorted portfolios at business cycle frequency.


Empirical Analysis- Labor-share variation drives the value premium dynamics to the extent the value

premium is indeed a duration premium:

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é Value premium Hcorr = 45%L Duration premium Hcorr = 54%L

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ò Orthogonalized value premium Hcorr = 11%L

-3 -2 -1 0 1 2WV-3

-2

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0

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2

- Cross-sectional returns meet term-structures: does the term-structure effect of laborrigidity (Marfe, JF 2016) provide a macroeconomic foundation of Lettau Wachter (JF2007)’s partial equilibrium framework?


Empirical Analysis

- Labor-share variation drives the value premium dynamics to the extent the valuepremium is indeed a duration premium.

- Does the HML return feature an unspanned risk premium once controlling for theduration spread?

HMLt =α+ b1MKTt + b2SMBt + b3WMLt + b4DPt + εt,

DPt =α+ b1MKTt + b2SMBt + b3WMLt + b4HMLt + εt,

Without Duration Premium With Duration Premiumα t-stat adj-R2 α t-stat adj-R2

HML 0.048∗∗ 2.50 0.13 -0.041∗ -1.79 0.56

Without Value Premium With Value Premiumα t-stat adj-R2 α t-stat adj-R2

DP 0.185∗∗∗ 6.29 0.15 0.134∗∗∗ 6.04 0.57


Empirical Analysis








Empirical Analysis- Predictability of Devil HML and E/P and CF/P based return spreads by W/V:

1n

∑n

i=1log(1 + Xt+i) = b0 + b1W/V?t + εt,

X⊥t,n = b0 + b1W/V?t + εt

Value premium (Asness Frazzini, 2013) 1 2 3 5 7

HMLaf Asness Frazzini (2013) 1.664∗∗∗ 1.833∗∗∗ 1.800∗∗∗ 1.222∗∗∗ 0.760∗∗∗

t-stat (3.03) (3.69) (3.87) (3.43) (3.10)

adj-R2 0.06 0.13 0.19 0.15 0.09

HML⊥af Asness Frazzini (2013) 0.943∗∗ 0.606 0.506 0.259 0.255

t-stat (2.03) (1.53) (1.37) (0.85) (1.14)

adj-R2 0.01 0.01 0.01 -0.01 -0.01

Earnings to price spread 1 2 3 5 7

E/Pspread 1.613∗∗ 1.965∗∗∗ 2.023∗∗∗ 1.654∗∗∗ 1.206∗∗

t-stat (2.48) (3.59) (3.87) (2.92) (2.17)

adj-R2 0.05 0.13 0.19 0.22 0.20

E/P⊥spread 0.566 0.439 0.349 0.236 0.304

t-stat (1.09) (0.98) (0.82) (0.48) (0.65)

adj-R2 -0.01 -0.01 -0.01 -0.01 0.01

Cash-flows to price spread 1 2 3 5 7

CF/Pspread 1.257∗∗ 1.462∗∗∗ 1.387∗∗∗ 1.013∗∗ 0.877∗∗

t-stat (2.15) (3.02) (3.12) (2.65) (2.56)

adj-R2 0.03 0.09 0.12 0.15 0.19

CF/P⊥spread 0.192 0.040 -0.070 -0.115 0.107

t-stat (0.45) (0.10) (-0.21) (-0.48) (0.47)

adj-R2 -0.02 -0.02 -0.02 -0.01 -0.01


Empirical Analysis

- Do Devil HML and E/P and CF/P based return spreads feature an unspanned riskpremium once controlling for the duration spread?

Xt = α+ b1MKTt + b2SMBt + b3WMLt + b4DPt + εt

Without Duration Premium With Duration Premiumα t-stat adj-R2 α t-stat adj-R2

HMLaf 0.052∗∗∗ 2.83 0.29 -0.011 -0.56 0.54

E/Pspread 0.091∗∗∗ 4.81 0.01 0.001 0.06 0.48

CF/Pspread 0.111∗∗∗ 6.71 0.10 0.023 1.50 0.62

- Duration is a pervasive characteristic of cross-sectional returns.

- Labor rigidity provides a macroeconomic explanation.


Empirical Analysis

- Summary

1. Labor rigidity ⇒ countercyclical labor share

2.∆W/Vt

(−)=⇒ HMLt

W/Vt(+)=⇒

∑ni=1 HMLt+i

W/V ∼ I(0)

3. Why?

(a) labor leverage ⇒ high equity premium(b) term-structure effect ⇒ boost transitory risk of payout/equity(c) decreasing term-structure of equity⇒ cross-sectional duration premium? cross-sectional valuation ratios?

value premium?

4. W/Vt(+)=⇒

∑ni=1 DPt+i same predictability pattern

5. HMLt ⇐⇒ DPt high correlation (any horizon)

6. W/Vt 6=⇒ HML⊥t,n no predictability beyond duration premium

7. Spanning test: DP nullifies HML’s α

8. Robustness to valuation ratios’ definition


1 Motivation & Aim


3 A Simple Model



A Simple Model

- Goal: rationalize the above stylized facts in a parsimonious, and otherwise standard,asset pricing model.

- Main ingredient:

Workers and shareholders share asymmetrically the transitory componentof total resources

- Interpret total resources C as output after investment C = Y − I.

- C is given by permanent x and transitory z components:

d logCt = dxt − dzt

with

dxt = (µt − σ2x/2)dt+ σxdBx,t

dµt =λµ(µ− µt)dt+ σµdBµ,t

dzt =λz(z − zt)dt+ σz√zt/zdBz,t


A Simple Model

- Limited market participation: workers consume wages and do not access financialmarkets⇒ shareholders consume dividends and act as a representative agent on the stockmarket.

- Wages and dividends sum up to total resources C = W +D and are shared in such away co-integration is preserved but wages are less sensitive to transitory shocks:

Wt = Ctω(zt) and Dt = Ctδ(zt)

with|∂z logWt| < 1 < |∂z logDt|

- Convenient functional form: δ(zt) = δe−φzt

- Parameter φ > 0 captures the degree of labor rigidity and its term-structure effect:

smoothing: ∂φσW (τ) < 0 upward-sloping effect: ∂φ,τσW (τ) > 0

leverage: ∂φσD(τ) > 0 downward-sloping effect: ∂φ,τσD(τ) < 0


A Simple Model- Shareholders feature recursive utility ⇒ standard parametrization γ > 1/ψ

- Standard solution methodology: Eraker Shaliastovich (MF 2008):

d logRt = k0dt+ k1d(pdt)− (1− k1)pdtdt+ d logDt

- State-price density:

d logMt = θ log δdt− θψd logDt − (1− θ)d logRt

= − (rt + 12‖ΣΩ‖2)dt− ΩxσxdBx,t − ΩµσµdBµ,t − Ωzσz

√zt/zdBz,t

with θ = (1− γ)/(1− 1/ψ), risk-free rate:

rt = r0 + rµµt + rzzt

and prices of risk:

Ωx = γ, Ωµ = (1− θ)k1aµ, Ωz = −γ(1 + φ) + (1− θ)k1az(φ)

- Stock price:

Pt =

∫ ∞0

Et[Mt+τ

MtDt+τ

]dτ = ext+a0+d0+aµµt+(az(φ)−(1+φ))zt


A Simple Model

- Return variance and equity premium:

σ2R(t) =σ2

x + a2µσ

2µ + (az(φ)− (1 + φ))2σ2

z

( ztz

),

prR(t) = Ωxσ2x + Ωµσ

2µaµ + Ωzσ

2z(az(φ)− (1 + φ))

( ztz

)⇒ effect of labor rigidity through both the cash-flows and discount-rates channels

- Similar formulas for the dividend strips:

Pt,τ = ea0(τ)+xt+aµ(τ)µt+az(τ)zt

for any maturity τ

- The term-structure of equity premia has slope given by:

slope = (ψ − 1)((γ − 1/ψ)× LRR − φ× SRR

)III

II

⇒ for ψ > 1, labor rigidity strong enough leads to downward-sloping compensations

(a less extreme form of limited market participation results in a lower threshold for ψ)


A Simple Model- Cross-sectional returns: heterogeneous cash-flows duration.

- Simple deterministic ‘life-cycle’ as in Lettau Wachter (JF 2007, JFE 2011).

- Continuum of firms with residual life T i ∈ (0, Tmax) and hump-shaped share processof cash-flows:

Dit = Dt g(Ti)

withg(T i) =

(π

2Tmax sin(πTiTmax

))such that

∫ Tmax

0 g(T i)dT i = 1 ∀t.

- Why such a simplistic assumption?

1. monotone relation between residual life and cash-flows duration:

Di =

∫ Ti

0

Et[τMt+τ

Mt

Dt+τ g(Ti − τ)

]dτ

2. cash-flows risk is unaffected by duration:

σ(τ) = σi(τ) = σj(τ) ∀τ ≤ min(Ti, T

j)


A Simple Model

- Heterogeneous cash-flows duration but homogeneous cash-flows risk

⇒ equilibrium implications of the term-structure effect of aggregate labor rigidity

- Price of firm (or portfolio) i:

P it =

∫ Ti

0Et[Mt+τ

MtDt+τg(Ti − τ)

]dτ =

∫ Ti

0ea0(τ,i)+xt+aµ(τ,i)µt+az(τ,i)ztdτ

- Set T value T growth, the value/duration premium is:

Π(t) = prR,value(t)− prR,growth(t)

= Ωµσ2µ∂µ(logP value

t − logP growtht )

´¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¸¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¶Πµ(t), long-run risk component

+ Ωzσ2z(zt/z)∂z(logP value

t − logP growtht ).

´¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¸¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¶Πz(t), short-run risk component

- Components Πµ(t) and Πz(t) capture the differential in the price elasticities withrespect to µt and zt

- For γ > ψ > 1, component Πµ(t) is negative and component Πz(t) is positive.The latter increases with labor rigidity φ.


1 Motivation & Aim


3 A Simple Model



Predictions and Limitations

- Calibration procedure: variance ratios of fundamentals are used to match the strengthof labor rigidity and its term-structure effect

Parametersσx µ λµ σµ z λz σz δ φ

0.005 0.02 0.70 0.015 0.15 0.20 0.026 0.159 6.5

Cash-flows moments Data ModelLong-run growth 0.020 0.020One year consumption volatility 0.025 0.025One year dividends volatility 0.174 0.173Dividend-share average (D/(D+W)) 0.060 0.060Dividend-share volatility 0.016 0.016

2 4 6 8 10 12 140.0

0.5

1.0

1.5

Variance ratio

horizon HyearsL

Consumption Dividends Wages

- Model dynamics are flexible enough to match the timing of risk of macroeconomicfundamentals



- Good fit of standard asset pricing moments:

Parametersβ γ ψ

0.96 7.5 1.25

Moments Data Model1931-2009 1947-2009 φ = 6.5 φ = 0

Risk-free rate (%) 0.60 1.00 0.75 5.55Risk-free rate volatility (%) 3.00 2.70 2.57 1.27Equity premium (%) 6.20 6.30 6.35 0.18Equity volatility (%) 19.8 17.6 16.3 2.3Sharpe ratio (%) 31.3 35.8 39.0 8.0Log price-dividend ratio 3.38 3.47 3.25 3.27

- Labor rigidity over transitory risk preserves Danthine Donaldson (RES 2002)’s result:high equity premium and volatility

- Recursive utility (with conservative parameters) solves the risk-free rate / equitypremium puzzle


Predictions and Limitations- Model captures the slope of equity risk and premium and their dynamic relation with

labor-share:

2 4 6 8 100.00

0.05

0.10

0.15

0.20

Dividend strips

horizon HyearsL

Premium

Volatility

0.85 0.90 0.95 1.000.0

0.1

0.2

0.3

Dividend strips

labor share WHW+DL

- Slope magnitude: ≈ 1% over 5-years maturity as in van Binsbergen Koijen (JFE 2016)

- Slope dynamics:

1. pro-cyclical as in van Binsbergen et al. (JFE 2013) and Aıt-Sahalia et al. (2015)

2. steeper with high labor-share as in Marfe (JF 2016)


Predictions and Limitations- The term-structure effect of labor rigidity gives rise to a duration/value premium:

0 10 20 30 40 50Ti

1.0

1.5

2.0

2.5

3.0

3.5

4.0

Log price-dividend ratio

0 10 20 30 40 50Ti0

5

10

15

Cash-flows duration

0 10 20 30 40 50Ti0.155

0.160

0.165

0.170

0.175

0.180

0.185

0.190

Return volatility

0 10 20 30 40 50Ti0.060

0.065

0.070

0.075

Premium

- Model predictions consistent with partial equilibrium model by Lettau Wachter (JF2007)



- Labor-share level positively predicts the duration/value premium:

0.85 0.90 0.95 1.000.00

0.01

0.02

0.03

0.04DurationValue Premium

labor share WHW+DL

- Model prediction is in line with the empirical analysis



- Simple and parsimonious model with a number of limitations. For instance:

- Sources of duration heterogeneity?

e.g. model extension considers cross-sectional exposure to priced & unpriced transitory risk

⇒ reduced form for cross-sectional labor rigidity / financial leverage?

- Empirically inconsistent implications?

e.g. model captures real growth predictability by labor-share but leads to real growthpredictability by prices

⇒ missing ingredients? unpriced risk of fundamentals and non-fundamental risk ofprices

- Interaction with complementary economic channels?

focus here is on understanding business cycle fluctuations of value premium

⇒ do complementary explanations operate on lower/higher frequencies?


Conclusion

- Labor-share largely drives value premium dynamics at business cycle frequency.

- Explanatory power only regards the value premium component that is actually aduration premium.

- Rationale:

1. labor rigidity concerns only transitory risk

2. this boosts short-run dividend risk and the equilibrium price of transitory risk

3. in turn, the term-structure of equity is downward-sloping and a cross-sectionalduration premium obtains

4. and, under standard assumptions, firms with low price relative to fundamentals earn acompensation over firms with high price relative to fundamentals.

- A simple illustrative model captures these stylized facts.


Additional Material

2 4 6 8 10 120.0

0.5

1.0

1.5

Dividends

Ebit

Wages

Value added

Horizon HyearsL2 4 6 8 10 12

0.0

0.5

1.0

1.5

Value addedminus wages

Labor rigidity

Labor leverage

Horizon HyearsL

Marfe (JF 2016)

Wage, output and dividend risk are upward-sloping, flat, and downward-sloping.

The remainder of output minus wages recovers the negative slope of dividend risk.

back


Additional Material

1960 1970 1980 1990 2000 2010

-2

-1

0

1

2

Labor-share

VRW -VRD

5 years

Correlation: 59%

1960 1970 1980 1990 2000 2010

-2

-1

0

1

2

3

Labor-share

VRD 5 years

Correlation: -54%

Marfe (JF 2016)

Labor-share moves positively with the gap between the VR’s of wages and dividendsand negatively with the VR’s of dividends.

back


Additional Material

1996 1998 2000 2002 2004 2006 2008 2010-2

-1

0

1

2

3

Short-Term Equity Risk

Labor-share

Dividend strip return volatility

H1 year aheadL

Correlation: 86%

1996 1998 2000 2002 2004 2006 2008 2010

-2

-1

0

1

2

3

Short-Term Equity Premium

Labor-share

Dividend strip return over

risk-free rate H1 year aheadL

Correlation: 57%

Marfe (JF 2016)

Labor-share largely forecasts risk and premium (and slope) of dividend strip returns.

back


Additional Material- Frequency decomposition of log output: log Vt = v1,t + v2,t + v3,t

-6.0

0-4

.00

-2.0

00.

002.

004.

006.

00

-6.0

0-4

.00

-2.0

00.

002.

004.

006.

00

0.00 0.10 0.20 0.30 0.40 0.50Frequency

Spectral density of v1

-6.0

0-4

.00

-2.0

00.

002.

004.

006.

00

-6.0

0-4

.00

-2.0

00.

002.

004.

006.

00

0.00 0.10 0.20 0.30 0.40 0.50Frequency


-6.0

0-4

.00

-2.0

00.

002.

004.

006.

00

-6.0

0-4

.00

-2.0

00.

002.

004.

006.

00

0.00 0.10 0.20 0.30 0.40 0.50Frequency


Della Seta, Marfe, Penasse (in preparation)

- Do workers and shareholders asymmetrically share business cycle risk?

Labor-share changes ∆W/V(1) (2) (3) (4) (5)

∆ log V -0.23∗∗∗

(-9.34)∆v1 -0.28∗∗∗ -0.27∗∗∗

(-6.60) (-6.63)∆v2 -0.25∗∗∗ -0.24∗∗∗

(-8.10) (-8.09)∆v3 -0.04 0.02

(-0.43) (0.26)adj-R2 0.34 0.19 0.18 -0.00 0.36

Profit-share changes ∆D/V(1) (2) (3) (4) (5)

∆ log V 0.33∗∗∗

(6.88)∆v1 0.37∗∗∗ 0.36∗∗∗

(4.22) (4.14)∆v2 0.36∗∗∗ 0.34∗∗∗

(6.01) (6.27)∆v3 0.20 0.11

(1.19) (0.73)adj-R2 0.28 0.13 0.15 0.00 0.28

back


Additional Material

Cross-sectional predictive regressions of duration-sorted portfolios returns onlabor-share.

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Additional Material


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Labor Rigidity and the Dynamics of the Value...

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