Labor Share in the Long and the Short Run

Labor Share Decline and IPP Capital The Overshooting SVARs and Cyclical Labor Share Labor Market Dynamics and σt

Labor Share in the Long and the Short Run

Raul Santaeulalia-Llopis

MOVE-UAB and Barcelona GSE

Barcelona GSE TrobadaOctober, 2016


(1) Graduate textbooks: The labor share is relatively constantSargent and Ljungqvist, Mankiw, Romer, Chad Jones, Acemoglu, ...

(2) This notion about the constancy of labor share is not new:I Labor share is “... is one of the great constants of nature, like

velocity of light or the incest taboo.” R. Solow (1958).I The constancy of labor share is “a bit of a miracle.” J. M .

Keynes (1939).

The constancy of labor share is at the core of the Kaldor facts.


US LABOR SHARE (LS), BEA 1947-2013


ROADMAP:

(1) The Long Run: An explanation for the US labor sharedecline: IPP Capital (work with D. Koh and Y. Zheng).

(2) The Short Run: The cyclicality of the labor share matters.

(a) Labor share overshoots reducing the ability of the RBCmodel to generate fluctuations in hours (w/ J.-V. Rıos-Rull)

(b) SVARs with long-run restrictions and cyclically movingfactor shares imply a large role for productivity shocks.

(c) A countercyclical elasticity of substitution, σt, explainslabor market dynamics very well (work with D. Koh).


Labor Share Decline and Intellectual PropertyProducts Capital

Dongya Koh 1 Raul Santaeulalia-Llopis 2 Yu Zheng 3

1University of Arkansas

2MOVE-UAB and Barcelona GSE

3City University of Hong KongEuropean University Institute



One of the great fantasies of contemporary macroeconomics isfinally gone: The LS declines.

Our two findings:

(1) The LS decline is twice as large as previously reported.Previous: Elsby, Hobijn, & Sahin ’13, Karabarbounis & Neiman ’14

(2) The decline of the LS is entirely explained byIntellectual Property Products (IPP) capital.

Our findings have essential implications for the US model


US LABOR SHARE (LS), BEA 1947-2013


IPP CAPITAL AND BEA REVISIONS SINCE 1999

• Before the 1999 BEA revision, IPP items were treated asexpenditures in intermediate non-durable goods.

• Two recent BEA revisions capitalize IPP:I The 1999 revision capitalizes software.I The 2013 revision capitalizes R&D and artistic originals.

• These are important improvements in the measurementof aggregate investment, capital, and income.Corrado, Haltinwanger, and Sichel (2009), McGrattan and Prescott(2010,14), Akcigit, Celik, and Greenwood (2015).


IPP AND TRADITIONAL INVESTMENT SHARES, BEA 1947-2013


IPP DIFFERS FROM TRADITIONAL CAPITAL IN THREE DIMENSIONS

(a) Investment (b) Price of Invesment

(c) Depreciation Rate

Aggregate Effects By IPP item


DATA CONSTRUCTION OF THE AGGREGATE LS

We apply a standard definition to national income data (BEA):(e.g., Cooley and Prescott 1995, Krueger 1999, Gomme and Rupert 2007)

• Unambiguous Capital Income (UCI) = Rental Income +Corporate Profits + Net Interest + Current SurplusGovernment Enterprises

• Unambiguous Labor Income (ULI) = Compensation ofEmployees

• Unambiguous Income (UI) = UCI + DEP + ULI


DATA CONSTRUCTION OF THE AGGREGATE LS (CONTINUED)

• Ambiguous Income (AI) = Proprietors’ Income + Taxes onProduction − Subsidies + Business Current TransfersPayments + Statistical Discrepancy

• Ambiguous Capital Income (ACI) = UCI+DEPUI × AI.

• Capital Income = UCI + DEP + ACI

• Labor Share = 1− Capital Share = 1− Capital Incomey


HOW DOES IPP CAPITAL AFFECT LABOR SHARE?

(1) Labor share from the current BEA accounts:

LS = 1−RTkx

T + RIPPkxIPP

y,

where traditional capital income is RTkxT and IPP capital

income is RIPPkxIPP.

(2) Labor share without IPP capital (∼ pre-1999 BEA):

LST = 1−RTkx

Ty− RIPPkx

IPP,

where capital income has only the traditional component.


THE RATE OF RETURN TO CAPITAL

The FOCs of each type of capital j imply,

R′j =1vj(1 + r′)− 1

v′j(1− δ′j), (1)

where r is the interest rate (or net rate of return).

Recall that we know vj and δj directly from the data.


• We find r using the model definition of LS:

LS = 1−RT(r, vT, δT)kx

T + RIPP(r, vIPP, δIPP)kxIPP

y,

in which r is the only unknown (per year).

• Given r, and hence an Rj for each j, we can remove (in apurely accounting sense) the effects of IPP capital on LS as:

LST = 1−RTkx

Ty− RIPPkx

IPP,


EFFECTS OF IPP CAPITAL ON THE LS, US 1947-2013


EFFECTS OF IPP CAPITAL ON THE LS, US 1947-2013

LS 1929-2013


THE IPP CAPITAL SHARE OF INCOME

1929-2013


VINTAGE LABOR SHARE: ONLY SOFTWARE WAS CAPITALIZEDPRE-2013 BEA REVISION ERA






VINTAGE LABOR SHARE: WHEN IPP WAS NOT CAPITALIZEDPRE-1999 BEA ERA


VINTAGE LABOR SHARE: WHEN IPP WAS NOT CAPITALIZEDPRE-1999 BEA ERA


OUR TWO FINDINGS

(1) The LS decline is twice as large as previously reported.

(2) The entire decline of the LS is accounted for byIntellectual Property Products (IPP) capital.The US is undergoing a transition to a more IPP capitalintensive economy.

Decomposition and Robustness


IMPLICATIONS FOR THE US MODEL

We consider a degree of substitutability ρ between IPP and T capital:

Yt = At

αk

((K

ρ−1ρ

IPP,t + Kρ−1ρ

T,t

) ρρ−1)σ−1

σ

+ αhHσ−1σ

t

σ

σ−1

,

that we can conveniently write as,

Yt = At

(αk (CtKT,t)

σ−1σ + αhH

σ−1σ

t

) σσ−1

,

where

Ct =

((KIPP,t

KT,t

) ρ−1ρ

+ 1

) ρρ−1

,

is driven by IPP-capital deepening (w.r.t. traditional capital).Two-Stage Estimation


1975-2010 Full Sample

Elasticity σ:(a) Aggregate Model 1.139∗∗∗ 1.137∗∗∗

(b) Traditional Model 1.049 1.034

• The long-standing Cobb-Douglas paradigm is consistent withthe trendless behavior of the traditional LS... BUT this is NOTthe case anymore with IPP capital.

• IPP capital deepening generates the decline of the LS with σ > 1.


CONCLUSION

• The US LS decline is:

(1) Large and prolonged (more than you think!)

(2) Fully accounted for by the rise of IPP capital.

• Essential implications for the US Model: The LS declinereflecs an ongoing structural shift to a more IPP-capitalintensive economy.


WHAT NEXT?

• We are conducting multicountry analysis (31 OECDcountries) with promising preliminary results. Stay tuned!


STRUCTURAL SHIFT TO LARGER IPP-CAPITAL SHARECROSS-COUNTRY EVIDENCE (PRELIMINARY WORK WITH D. KOH AND S. AUM)

(a) Investment Shares (b) Depreciation Rates

(c) IPP Capital Share of Income


Redistributive Shocks and ProductivityShocks

Jose-Vıctor Rıos-Rull 1 Raul Santaeulalia-Llopis 2

1UPenn, UMinn, UCL, CAERP, CEPR, NBER




THE LABOR SHARE OVERSHOOTS

Exogenously introducing this overshooting into the standardRBC model increases the income effect and reduces the powerof productivity shocks in explaining fluctuations in hours.


How Much Are SVARs with Long-RunRestrictions Missing Without Cyclically

Moving Factor Shares

Raul Santaeulalia-Llopis

MOVE-UAB and Barcelona GSE



An interesing and more direct approach to understand theeffects of productivity shocks is Galı (1999) and Fisher (2006).

Question: What is the ability of productivity (and investment)shocks when we incorporate cyclically moving factor shares?

We do so with a redistributive shock, same identification as inRıos-Rull and Santaeulalia-Llopis (2010)


EFFECTS OF PRODUCTIVITY SHOCKS ON HOURS

-0.200

-0.100

0.000

0.100

0.200

0.300

0.400

0.500

0.600

0.700

0.800

0.900

1.000

0 5 10 15 20 25 30 35 40 45 50

SFEVD of Hours to Productivity Shocks, U.S. Pre-1973.IV

Constant Factor Shares Nonconstant Factor Shares

-0.200

-0.100

0.000

0.100

0.200

0.300

0.400

0.500

0.600

0.700

0.800

0.900

1.000

0 5 10 15 20 25 30 35 40 45 50

SFEVD of Hours to Productivity Shocks, U.S. Post-1974.I


-0.010

-0.005

0.000

0.005

0.010

0 5 10 15 20 25 30 35 40 45 50

Response of Hours to Productivity Shocks, U.S. Pre-1973.IV


-0.005

0.000

0.005

0.010

0.015

0 5 10 15 20 25 30 35 40 45 50

Response of Hours to Productivity Shocks, U.S. Post-1974.I



EFFECTS OF INVESTMENT SHOCKS ON HOURS

-0.200

-0.100

0.000

0.100

0.200

0.300

0.400

0.500

0.600

0.700

0.800

0.900

1.000

0 5 10 15 20 25 30 35 40 45 50

SFEVD of Hours to Investment Shocks, U.S. Pre-1973.IV


-0.200

-0.100

0.000

0.100

0.200

0.300

0.400

0.500

0.600

0.700

0.800

0.900

1.000

0 5 10 15 20 25 30 35 40 45 50

SFEVD of Hours to Investment Shocks, U.S. Post-1974.I


-0.010

-0.005

0.000

0.005

0.010

0 5 10 15 20 25 30 35 40 45 50

Response of Hours to Investment Shocks, U.S. Pre-1973.IV


-0.005

0.000

0.005

0.010

0.015

0 5 10 15 20 25 30 35 40 45 50

Response of Hours to Investment Shocks, U.S. Post-1974.I



CONCLUSION

• Cyclically moving labor share matters for the assessmentof the role of productivity and investment shocksidentified using long-run restrictions.

• This is not about the size of the shocks, but about thebehavior of the dynamic multipliers (a propagationmechanism). The overshooting property of labor shareplays an important role in these effects.


The Shape of the Aggregate ProductionFunction over the Business Cycle and Its

Implications for the Labor Marke

Dongya Koh 1 Raul Santaeulalia-Llopis 2

1University of Arkansas




THE SHORT-RUN AGGREGATE ELASTICITY OF SUBSTITUTIONIS COUNTERCYCLICAL

(1) (2) (3) (4)

σ 0.765*** 0.685*** 0.739*** 0.683***(0.033) (0.026) (0.031) (0.026)

γ1 -0.170* -0.276*** -0.240** -0.311***(0.097) (0.091) (0.096) (0.093)

α 0.831*** 0.801***(0.024) (0.025)

γ2 -7.379*** -4.969***(1.282) (1.293)

Obs. 264 264 264 264


OUR IDEA: A SR-LR AGGREGATE PRODUCTION FUNCTION:

The SR-LR production function is:

yt =

((1− α)

(ktk∗t

)σt−1σt

+ α(

atlta∗t l∗t

)σt−1σt

) σtσt−1

(k∗t )1−ϑ(a∗t l∗t )ϑ, if st 6= 1

(k∗t )1−ϑ(a∗t l∗t )ϑ, if st = 1

We incorporate this production function into a state-of-the-artfrictionless business cycle model.

Then, we structurally estimate this model using SMM torecover the properties of σt


Theorem 1. In a nth-order approximation around steady state:

(a) Shocks to the elasticity of substitution, σ, have no impact on f(i.e., on equilibrium allocations) through the partial derivativesof any order n > 0. Hence, σ-shocks are not a source offluctuations per se.

(b) If n > 1 then shocks to σ propagate the effects of other sources offluctuations on f (i.e., on equilibrium allocations) through thehigher-order cross partial derivatives of f between σ and x.


IDENTIFICATION OF σ


MATCHING IRFS FOR IDENTIFICATION: ψa1


MATCHING IRFS FOR IDENTIFICATION: ψa2


THE DYNAMIC EFFECTS OF THE ELASTICITY OFSUBSTITUTION, σt


CYCLICAL BEHAVIOR OF NCES(SR)-CD(LR) BUSINESSCYCLE MODEL AND U.S.1954.I–2012.III

U.S. Data NCES(SR)-CD(LR)υx ρ(y, x) ρ(x, x′) υx ρ(y, x) ρ(x, x′)

Output:y 3.31 1.00 0.87 3.28 1.00 0.72

Labor Market:eh 3.64 0.88 0.91 3.32 0.91 0.72e 2.51 0.82 0.93 3.04 0.91 0.72h 0.28 0.73 0.82 0.03 0.51 0.73w 0.84 -0.13 0.75 0.63 -0.14 0.75lp 0.81 0.15 0.73 0.58 0.19 0.70ls 0.55 -0.34 0.75 0.52 -0.35 0.80


OUR CONCLUSIONS ALSO OPEN NEW QUESTIONS

1. The long run: The decline in the U.S. labor share can beentirely explained by the rise in IPP capital income.

Open question: Is innovation also behind the rise of individualinequality? Welfare implications of this innovation-inequalitytradeoff?

2. The short run: The cyclically of labor share matters for labormarket dynamics.

Open question: What is behind σt? What are the implicationsof all this for monetary and fiscal policy?


Thanks!


Appendix


AGGREGATE EFFECTS OF IPP

(a) Investment (b) Price of Invesment

(c) Depreciation Rate

Back


(a) Depreciation Rates of Structures,Equipment and IPP

(b) Depreciation Rates of IPPComponents

Back


US LABOR SHARE, BEA 1929-2013

Back


THE IPP CAPITAL SHARE OF INCOME, BEA 1929-2013

Back


DECOMPOSITIONS AND ROBUSTNESS

1. IPP depreciation accounts for two thirds of the LS decline.Net IPP income accounts for the remaining one third.

Decomposition

2. R&D is the most important IPP component behind the LSdecline. Software increasing role since the mid 1970s.

Software, R&D and Originals

3. Private IPP is behind the LS decline. Government IPPchanges the LS level but not the trend. Private vs. Government

4. The Corporate LS (and ’Asset Basis’ BLS) decline.Corporate LS

5. By industry level. The manufacturing sector is definitelythe most affected. By Industry

6. Extentions of IPP capital (e.g., advertising). More IPP

Back to Main Findings


DECOMPOSITION OF TOTAL EFFECTS

• Reformulate IPP capital income as

RIPP,tkxIPP,t =

(1 + rt

vIPP,t−1− 1

vIPP,t

)kx

IPP,t︸︷︷︸Net IPP Capital Income

+δIPP,t

vIPP,tkx

IPP,t︸︷︷︸IPP depreciation

• Recompute the aggregate LS without IPP depreciation bysetting the second term to zero.


DECOMPOSITION OF TOTAL EFFECTS

Back


SOFTWARE, R&D, AND ARTISTIC ORIGINALS

R&D is the most important IPP component behind the early LSdecline. Software increasing role since the mid 1970s.

Back


PRIVATE AND GOVERNMENT IPP

Private IPP is behind the LS decline. Government IPP changesthe LS level but not the trend.

Back


INVESTMENT SHARES IN THE CORPORATE SECTOR


CORPORATE LS AND ’ASSET BASIS’ BLS





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LS AND IPP CAPITAL INTENSITY BY INDUSTRY


... BY SUB-INDUSTRY

Back


ADDING ADVERTISING TO BEA IPP ACCOUNTS

Back


More Stuff


CAPITAL INCOME TO LABOR INCOME RATIO


CAPITAL TO LABOR RATIO


ROBUSTNESS TO SAMPLE PERIOD, AGGREGATE LS


THE TRADITIONAL LS AND THE PRICE OF INVESTMENT


THE NET RATE OF RETURN, DIFFERENT VINTAGES


PROPRIETORS’ INCOME AND TAXES (% OF OUTPUT)


CORPORATE SHARE OF OUTPUT


PRE- VS. POST-2013 NATIONAL INCOME DATA

(a) Capital Income (b) Labor Income

(c) Ambiguous Income


LS DECLINE BY INDUSTRY

(a) Information (b) Services (c) Manufacturing:Nondurable goods

(d) Manufacturing:Durable goods

(e) Wholesale Trade (f) Retail Trade


IPP CAPITAL AND THE US MODEL

Note that our production function is equivalent to:

Yt =(αk (BtKT,t)

σ−1σ + αh (AtHt)

σ−1σ

) σσ−1

With our technology, the interpretaiton of At and Bt are”

1. At represents labor-augmenting technical change.

2. Bt = Ct At represents capital-augmenting technical change.

That is, Ct =BtAt

represents the differential growth betweencapital- and labor-augmenting technical change.

3. If Ct = 1 (or KIPP,t = 0), then At is simply Hicks neutral.

This is equivalent to the Acemoglu’s (2002, 2003) formulation but wegive a specific interpretation to Ct through IPP capital deepening.


TWO-STEP ESTIMATION OF THE PRODUCTION FUNCTION

In a first step, we estimate ρ as:

lnRIPP,tKIPP,t

RT,tKT,t=ρ− 1ρ

lnKIPP,t

KT,t,

The Elasticity of Substitution Between IPP and Traditional Capital

Elasticity ρ 5.787∗∗∗


Then, given the observable series for KIPP,t and KT,t, and theestimated ρ, we can recover Ct as:

Ct =

((KIPP,t

KT,t

) ρ−1ρ

+ 1

) ρρ−1

.


Ct AND ρ


TWO-STEP ESTIMATION OF THE PRODUCTION FUNCTION

In the second step, having recovered Ct, we estimate, σ as:

(1) Aggregate model:

lnRT,tKT,t + RIPP,tKIPP,t

wtHt= ln

αk

αh+σ − 1σ

lnCtKT,t

Ht

(2) Traditional model that omits IPP capital from the model (Ct = 1)and from the national income (KIPP,t = 0):

lnRT,tKT,t

wtHt= ln

αk

αh+σ − 1σ

lnKT,t

Ht

Remark: By directly identifying Ct, we circumvent the jointidentification impossibility of σ and Ct in Diamond et al. (1978).

Back


STRUCTURAL SHIFT TO LARGER IPP-CAPITAL SHARECROSS-COUNTRY EVIDENCE (PRELIMINARY WORK WITH D. KOH AND S. AUM)

(a) Investment Shares (b) Depreciation Rates

(c) IPP Capital Share of Income

Economy & Finance

Labor Share in the Long and the Short Run