,, 43 ( ) 2015 7 18 ( ) E-mail: sasaki@econ.kyoto-u.ac.jp 1 / 39
1. 2. (Rowthorn, 2014) 3. 4. 5. 6. 7. 2 / 39 1
( 1). ( 2). = +. 1. g. r. r > g ( 3).. 3 / 39 2
50% Figure I.1. Income inequality in the United States, 1910-2010 Share of top decile in national income 45% 40% 35% 30% 25% 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 The top decile share in U.S. national income dropped from 45-50% in the 1910s-1920s to less than 35% in the 1950s (this is the fall documented by Kuznets); it then rose from less than 35% in the 1970s to 45-50% in the 2000s-2010s. Sources and series: see piketty.pse.ens.fr/capital21c. 4 / 39
800% Figure I.2. The capital/income ratio in Europe, 1870-2010 vate capital (% national income) 700% 600% 500% 400% Germany France United Kingdom Market value of pri 300% 200% 100% 1870 1890 1910 1930 1950 1970 1990 2010 Aggregate private wealth was worth about 6-7 years of national income in Europe in 1910, between 2 and 3 years in 1950, and between 4 and 6 years in 2010. Sources and series: see piketty.pse.ens.fr/capital21c. 5 / 39
6% Figure 10.9. Rate of return vs. growth rate at the world level, from Antiquity until 2100 rate of return or rate of growth Annual 5% 4% 3% 2% Pure rate of return to capital r (pre-tax) Growth rate of world output g 1% 0% 0-1000 1000-1500 1500-1700 1700-1820 1820-1913 1913-1950 1950-2012 2012-2050 2050-2100 The rate of return to capital (pre-tax) has always been higher than the world growth rate, but the gap was reduced during the 20th century, and might widen again in the 21st century. Sources and series: see piketty.pse.ens.fr/capital21c 6 / 39
国民所得 賃金 利潤 賃金 利潤 資本分配率 = 利潤 国民所得 の上昇 7 / 39
2. (Rowthorn, 2014) β: (K/Y) ( 2). α: (rk/y). β α ( 4)., σ 1, β α., α β, σ 1.3 1.6. 8 / 39 3
40% Figure 6.5. The capital share in rich countries, 1975-2010 35% al income (% national income) Capit 30% 25% 20% U.S. Germany Japan France 15% U.K. Italy Canada Australia 10% 1975 1980 1985 1990 1995 2000 2005 2010 Capital income absorbs between 15% and 25% of national income in rich countries in 1970, and between 25% and 30% in 2000 2010. Sources and series: see piketty.pse.ens.fr/capital21c 9 / 39
. Y = [δk σ 1 σ + (1 δ)e σ 1 σ ] σ σ 1. (1) Y:, K:, E:, σ:, δ:. r, α g α. g α = ( ) σ 1 g K/Y. (2) σ, g K/Y. σ > 1, g α g K/Y. 10 / 39 4
理論的には? 資本所得比率の上昇 かつ 1 より大きい代替の弾力性 資本分配率の上昇 資本所得比率の低下 かつ 1 より小さい代替の弾力性 資本分配率の上昇 11 / 39
, K/Y, W/Y., β = W Y = vk Y, v W K. (3), v ( Q ). β. g β = g K/Y + g v. (4) g v = 0, g β = g K/Y. 12 / 39 5
, K/Y, ( 5)., g v > 0 ( 6)., g K/Y 0 g v > 0, g v > g K/Y, g β > 0., σ 1, g α > 0. σ < 1. 13 / 39 6
500% Figure A133: Simulated private wealth / national income ratios in the absence of capital gains, 1970-2010 450% 400% 350% 300% 250% 200% USA Europe (weighted) 150% 100% 1970 1980 1990 2000 2010 14 / 39
160% Figure 5.6. Market value and book value of corporations Ratio between marke et value and book value of corporations 140% U.S. Japan 120% Germany France 100% U.K. Canada 80% 60% 40% 20% 0% 1970 1975 1980 1985 1990 1995 2000 2005 2010 Tobin's Q (i.e. the ratio between market value and book value of corporations) has risen in rich countries since the 1970s-1980s. Sources and series: see piketty.pse.ens.fr/capital21c. 15 / 39
, g β > 0 g β = g K/Y > 0 g α > 0 with σ > 1. (5), g β > 0 g β = g K/Y /0 + g v + > 0 g α > 0 with σ < 1. (6), g α > 0,,. 16 / 39 7
ピケティの観察した事実 資産 所得比率の上昇 ピケティの解釈 1 資本 所得比率の上昇 21 より大きい代替の弾力性 3 評価比率は一定 より正しい解釈 1 資本 所得比率の低下 21 より小さい代替の弾力性 いずれにしても資本分配率は上昇 3 評価比率の上昇 17 / 39
3...,,.,,.,,.,. 18 / 39 8
生産関数が CES 型のとき因果関係あり 新古典派成長モデルにおける因果関係 生産関数がコブ = ダグラス型だと因果関係なし 経済成長 所得分配 古典派成長モデルとカレツキ派成長モデルにおける因果関係 所得分配 経済成長 19 / 39
4. ( ),,,.. Y = min{ae, bk}. (7), a = Y/E, b = Y/K.. w:, r:. Y = we + rk. (8) 20 / 39 9
α. α = rk Y = Y we Y = 1 w a. (9), w a,,.. r = Y we K = ( 1 w ) b = αb. (10) a,. 21 / 39 10
: s c.,. S = s c rk, 0 < s c < 1. (11) S = I.,. g s c r = s c bα. (12) 22 / 39 11
,., ( ).,. (= ) 23 / 39 12
: s w. S = s w we + s c rk, 0 < s w < 1. (13). g = [s w (1 α) + s c α]b. (14) 24 / 39 13
. dg dα = b(s c s w ). (15) s c > s w,. s c = s w,. 25 / 39 14
s w s c 0.03 0.61 0.1 0.4 0.09 0.48 0.17 0.52 0.12 0.5 0.15 0.72 0.12 0.38 0.12 0.34 0.16 0.5 0.02 0.62 0.05 0.49 0.04 0.47 0.1 0.5 Table 1: (Storm and Naastepad, 2012) 26 / 39 15
5. ( ),,,.. Y = min{ae, ubk}, (16) = min{ae, uk}. (17) : b = Y /K = 1. u = Y/Y = Y/K:. r = Y we K = u ( 1 w ) a = αu. (18) 27 / 39 16
. p = (1 + µ) ω a. (19) µ:, ω: (ω = pw).,,, 1 α = w a = 1 1 + µ. (20) α = 1 w a = 1 1 1 + µ = µ 1 + µ. (21) 28 / 39 17
. g d = γ + ϕu, γ > 0, ϕ > 0. (22).. g s = s c r = s c αu. (23).. g d = g s = γ + ϕu = s c αu. (24) 29 / 39 18
. u = g = γ s c α ϕ, (25) γs cα s c α ϕ (26) α,.,. ( ) ( ) 30 / 39 19
s w. g s = [s w (1 α) + s c α]u (27), u = g = γ [s w (1 α) + s c α] ϕ, (28) [s w(1 α) + s c α]γ [s w (1 α) + s c α] ϕ. (29) 31 / 39 20
s c > s w,. s c = s w = s, u = g = γ s ϕ, (30) sγ s ϕ. (31) α. 32 / 39 21
. g d = γ + ϕu + ψα, γ > 0, ϕ > 0, ψ > 0. (32),,,.,. 33 / 39 22
古典派とカレツキ派の違い 古典派 資本分配率の上昇 経済成長率の上昇 カレツキ派 資本分配率の上昇 経済成長率の低下 あるいは 経済成長率の上昇 34 / 39
.,,.,,,.,. α = 1 w a. (33) w, a, α. 35 / 39 23
36 / 39 24
労使交渉 国際価格競争 市場占有度 金融政策 経済成長 所得分配率 経済成長 フィードバック効果 37 / 39
6.... 38 / 39 25
7. (2014) 21,. Rowthorn, R. (2014) A Note on Piketty s Capital in the Twenty-First Century, Cambridge Journal of Economics 38, pp. 1275 1284. Sasaki, H. (2014) Growth, Cycles, and Distribution: Approach, Kyoto: Kyoto University Press. A Kaleckian Storm, S. and Naastepad, C. W. M. (2012) Macroeconomics Beyond the NAIRU, Cambridge MA: Harvard Univeristy Press. 39 / 39 26