THE GLOBAL DECLINE OF THE LABOR SHARE

Transcription

1 THE GLOBAL DECLINE OF THE LABOR SHARE Shi Zhengyang, Huang Yiguo, Ma Chengchao, Xie Yuchen June 5, 208

2 Auhor-Loukas Karabarbounis Academic Posiion Associae professor, Deparmen of Economics, Universiy of Minnesoa Research Area Macroeconomics, Labor Economics Publicaion Ø Capial Allocaion and Produciviy in Souh Europe. Quarerly Journal of Economics, 32(4), , November 207. (Wih Gia Gopinah, Sebnem Kalemli-Ozcan, and Carolina Villegas-Sanchez.) Ø The Global Rise of Corporae Saving. Journal of Moneary Economics, 89, -9, Augus 207. Lead Aricle. (Wih Peer Chen and Bren Neiman.) Ø The Cyclicaliy of he Opporuniy Cos of Employmen. Journal of Poliical Economy, 24(6), , December 206. (Wih Gabriel Chodorow-Reich.) Ø Home Producion, Labor Wedges, and Inernaional Business Cycles. Journal of Moneary Economics, 64, 68-84, May 204. Ø The Labor Wedge: MRS vs. MPN. Review of Economic Dynamics, 7(2), , April 204. Ø The Global Decline of he Labor Share. Quarerly Journal of Economics, 29(), 6-03, February 204. Winner of he Emerald Ciaion of Excellence Award. (Wih Bren Neiman.)

3 Auhor-Bren Neiman Academic Posiion Professor, Booh School of Business, Universiy of Chicago Research Area Macroeconomics, Inernaional Finance Publicaion Ø The Global Rise of Corporae Saving (wih Peer Chen and Loukas Karabarbounis) Journal of Moneary Economics, 207, 89, p.- 9. Lead Aricle. Ø Trade and he Global Recession (wih Jonahan Eaon, Sam Korum, and John Romalis) American Economic Review, 206, 06(), p Ø Currency Unions, Produc Inroducions, and he Real Exchange Rae (wih Albero Cavalloand Robero Rigobon) Quarerly Journal of Economics, 204, 29(2), p Ø The Global Decline of he Labor Share (wih Loukas Karabarbounis) Quarerly Journal of Economics, 204, 29(), p.6-03.

4 Conen: Ø Inroducion Ø Model Ø Esimaion of Elasiciy Ø Conclusion and Implicaion

5 Inroducion Y = AK % L '(% E * E = α E * : Expendiure on Labor, E: Toal Expendiure Moivaion: A significan decline of global labor share since 980s A significan decline in relaive price of invesmen goods.

6 Trends in Labor Share Daa : Counry-level saisics in he corporae secor Sources: BEA, UN, OECD, KLEMS Time Period: Counry: 59 counries ha have a leas 5 years of daa

7 Trends in Labor Share

8 Trends in Labor Share

9 Trends in Labor Share

10 Trends in Labor Share

11 Trends in Labor Share

12 Trends in Labor Share Labor share change: Changing size of indusries wih differen level of labor share Changes in labor shares wihin indusry ω /, :indusry k = s share in coury i = s value added S */, : labor share in counr i = s indusry k

13 Trends in Labor Share

14 Trends in Relaive Price of Invesmen Goods Daa : Counry-level Sources: PWT, WDI, KLEMS Time Period:

15 Trends in Relaive Price of Invesmen Goods

16 A Model of The Labor Share

17 A. Final Consumpion Good 0 ε ε C = ( c( z) dz) 0 ε ε ε ε c P = ( p ( z) dz) = p ( z) ε c( z) = ( ) C c P Proof for cos minimizaion: c 0 π = P C p ( z) c ( z) dz π c ε ε ε ε ( ) ε ε d dc z = P C c ( z ) p ( z ) = 0

18 B. Final Invesmen Good ε ε ( ( ) ε ) ε 0 X = x z dz ξ x ε ε = ξ( ( ) ) 0 = P p z dz p ( z) ε ε x ( z) = ξ ( ) X = ξ p ( z) X c P ξ

19 C. Producers of Inermediae Inpus Given: y ( z) = F( k ( z), n ( z)) CapialàR H LaboràW H Aggregae Demand: Y = C +ξ X max Π ( z) = p ( z) y ( z) Rk ( z) Wn ( z) ε.. ( ) ( ) ( ) ( ) ε s y z = c z + x z = p z ( C + ξ X ) = p( z) Y

20 C. Producers of Inermediae Inpus The firs order condiion wih respec o capial: Proof: p ( z) F ( z) = µ W n, p ( z) F ( z) = µ R k, ε µ = ε Y ε ε ε y ( z) Π ( z) = ( ) y ( z) Rk ( z) Wn ( z) = Y y ( z) Rk ( z) Wn ( z) Π( z) Y = ( )( ) Fk, ( z) R = 0 k ( z) ε y ( z) ε

21 D. Household 0 max β VC (, N; χ ) s.. = 0 K = ( δ ) K + X + C + ξ X + B ( + r ) B = ( W n ( z) + R k ( z) +Π ( z)) dz + 0 N K = = 0 0 n ( z) dz k ( z) dz The firs order condiion wih respec o capial: R = ξ ( + r ) ξ ( δ) Vc( C, N) + r + = βv ( C, N ) c + +

22 Lagrange L 0 = β V( C, N ; χ ) + = 0 λ K+ + ( δ ) K ( Π ( ) ( ) 0 z dz + WN + RK + + r B B+ C ξ L C = β 0 V ( C, N ) + λ / ξ = 0 C L K = λ + λ( δ R / ξ) = 0

23 Hamilon H λ 0 = β V( C, N ; χ ) + δk + ( Π ( ) ( ) 0 z dz + WN + RK + + r B B+ C ξ H C = β 0 V ( C, N ) λ / ξ = 0 C H K = λ ( δ + R / ξ ) = λ λ

24 Bellman UC (,{ n( z)}, X, K, B ) = max VC (, N, χ ) + βvc (, N, χ ) U VC (, N, χ ) C VC (, N, χ ) C = + β K C K C K = V ( C, N ) ξ + βv ( C, N )[ R ξ ( δ )] = 0 C C

25 E. Equilibrium c p ( z) = P =, k ( z) = K, n ( z) = N, c ( z) = C, x ( z) = ξ X, y ( z) = C + ξ X, Y = F( K, N ) s s s L, K, Π, WN WN = = Y µ WN + RK RK RK = = Y µ WN + RK Π = = Y µ Where sl, + sk, + s Π, =

26 F. The Producion Funcion σ σ σ σ σ σ = (, ) = ( αk( K, ) + ( αk)( N, ) ) Y F K N A K A N Y F A R σ σ σ K, = α k K, ( ) = µ K Y F A W σ σ σ N, = ( α k) N, ( ) = µ N

27 G. The Labor Share σ A sl, µ = α k ( ) µ R ' = K, σ σ A sl,' µ ' = α k ( ) µ R Z Z Z K,' σ ' ' + AK ( sl( + s! L) µ ( + µ )) = ( ) s µ ( + µ )( + R) L σ

28 IV. The Elasiciy of Subsiuion A. Relaive Price of Invesmen B. Markups C. Capial-Augmening Technological Progress D. Skilled versus Unskilled Labor

29 A. Relaive Price of Invesmen + AK ( sl( + s! L) µ ( + µ )) = ( ) slµ ( + µ )( + R) R = ξ ( + δ ) β Se μ =, μo = 0, AL K =0 Firs-order approximaion: s L, s L, sˆ = γ + ( σ ) ˆ ξ + u L, σ s L,=ln s L,, ξl=ln ξ

30 A. Resuls

31 A. Visualizaion

32 B. Markups L, K, µ = = s s + s π, L, K, = ξ ( + δ ) β RK ξ X / β + δ = = Y Y δ ˆ µ = µ ( s sˆ + s sˆ ) L, L, K, K, ( ˆ ) sl, µ (( + sˆ )( + ˆ µ ) ) = γ + ( σ ) ξ + ˆ µ + u s µ s R K = X δ L,

33 B. Resuls

34 C. Capial-Augmening Technological Progress + AK ( sl( + s! L) µ ( + µ )) = ( ) s µ ( + µ )( + R) L σ Se μ =,μ = 0 Firs-order approximaion: sl, sˆ ˆ ˆ, = γ + ( σ ) ξ + ( σ) A, + u s L, L K

35 C. Capial-Augmening Technological Progress ( ˆ ˆ ) K,! σ σ = ( σ) corr A, ξ ( ˆ ) K ( ˆ ξ ) sd A sd! σ =.25 σ =.20

36 D. Skilled versus Unskilled Labor How o nes he hree inpus: skilled labor, unskilled labor and he capial sock? () (2) (3) σ ρ σ σ ρ ρ ρ σ σ ρ ρ σ = φ φ2 + ( φ2 ) + ( φ) Y K U S s ˆ ( ) ˆ U s = γ + σ ξ + κ + u L, L, s L, K σ ρ σ σ ρ ρ ρ σ σ ρ ρ σ = φ φ2 + ( φ2 ) + ( φ) Y K S U s (, ) N = N S U ˆ ( ) ˆ S s = γ + σ ξ + κ + u L, L, s L, K ^ ^

37 D. Resuls

38 V. The Decline in he Labor Share

39 Ⅵ. Conclusion Offer an explanaion for he decline of global labor share Esimae he shape of he producion funcion Explore he macroeconomic and welfare implicaions

40 Implicaion How does S change wih μ, A, R ˆ ( ˆ + A S ) ( ˆ L + S µ + µ ) = S ( ˆ )( ˆ Lµ + µ + R) σ = ˆ S = + ˆ µ σ > ( + ˆ ) ( + ˆ ) σ ˆ + A ( SLµ ) ( + ˆ µ ) ( + Rˆ ) Sˆ = S µ µ L σ + Aˆ σ ( SLµ ) ˆ ( ˆ ) ( Rˆ ds + µ + ) = 2 d ˆ µ S µ µ L σ dsˆ + Aˆ = 0 ˆ µ = d ˆ µ Rˆ + σ ( SLµ )

41 Thank you