Public Pension and Immigration The Effects of Immigration on Welfare Inequality The immigration of unskilled workers has been analyzed by a considerab

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2 Public Pension and Immigration The Effects of Immigration on Welfare Inequality The immigration of unskilled workers has been analyzed by a considerable amount of research, which has noted an ability distribution. Many of the papers, however, have not analyzed this immigration with the endogenous fertility rate. In this paper, we assume that households have different preferences about having children. This assumption leads to differences in the predicted number of children for households. In our model, three types of households exist: households with some children and no savings, those with some children and savings, and those with no children and some savings. On the basis of this assumption, this paper analyzes the effectiveness of immigration. Since both interest and wage rates are fixed in the small open economy, an acceptance of immigrants would improve welfare. A closed economy, on the other hand, would lower the capital-labor ratio and lead to a decline in wage rates. Consequently, it has been shown that the closed economy would downgrade welfare. The acceptance of immigration, moreover, has led to a higher coefficient of variation, which implies that it expands the differential of economic welfare. Without considering the differential of wage rate, this paper shows that the acceptance of immigration enlarges the gap of economic welfare. Toshiyuki Uemura and Masatoshi Jinno JELH5, J13, J61 * 2008 ** *** 149

3 64 3 Key words Public Pension, Admitting Immigrants, Disparity of Economic Welfare, Endogenous Fertility, Difference in the Preference for Children 1 1) 10 1)

4 Razin and Sadka1999 2) Razin and Sadka1999 Razin and Sadka2000 Casarico and Devillanova2003 2) Razin, Sadka and Swagel

5 64 3 Poutvaara 2007Poutvaara Razin and Sadka 1999 Razin and Sadka

6 t t t c i,y t Ut i = α ln(c i,y t ) + β ln(c i,o t+1) + γ ln(n i t D i ) (1) c i,o t n i t αβγ i i y o D i D i D i D i [ D, D] 3) t N t D i d h t d = (D D)/I I d 3) D i D w t / (E t w t + θ t ) 153

7 64 3 h t = N t /(D D) h t t N t N t = DX D=D d h t(d i ) = I d h t (2) C R 4) C R (1 φ t) φ t Ew t w t C R (1 φ t) Ew t θ t C R (1 φ t) + Ew t (1 En i t) w t p t b t t c i,y t = (1 p)(1 n i te)w t n i tc R s i t (3) c i,o t+1 = b t+1 + (1 + r t+1 ) s i t (4) s i t p b t r t+1 (3) (4) (1) 4) C R 154

8 α 1 c i,y t α 1 c i,y t+1 1 θ t + β n i t D = 0 (5) i + β (1 + r t+1) c i,o t+1 = 0 (6) n s 5) n i t = s i t (α + β) (1 + rt+1) (1 p) Di wt + bt+1 + γ (7) (1 + r t+1) θ t = θ t βdi + (α + γ)b t+1 + β (1 + r t+1 ) (1 p) w t (1 + r t+1 ) α + β + γ D i D n D s D n t γ (1 + r t+1) (1 p) w t + b t+1 (a + β) (1 + r t+1 ) θ t (9) D s t β (1 + rt+1) (1 p) wt (α + γ)bt+1 β (1 + r t+1) θ t (10) (9) D n D i (10) D s D i D n t (8) < D s t D i 1 3 6) 5) b t < (1 p)w t β(1+r t+1) (α+γ) 6)

9 Dt i Di Dt n Dt n < D i < Dt s Dt s D i n nos s noc 8 0 D D i Dt n >< n i t = < Dt i < Dt s (11) n i t D n t s i t = >: α α+γ Di + γ (1 p)wt (α+γ)θ t n nos Dt s Dt i D 8 αb t+1 (α+β)(1+r t+1 ) >< α+β s noc D D i Dt n s i t Dt n < D i < Dt s (12) >: 0 D s t D i D t ˆn ŝ ˆn t = 1 I ŝ t = 1 I DX D i =D DX D i =D n i t (D i ) (13) s i t (D i ) (14) 3.2 t IM t t P t = N t + IM t (15) 156

10 t 1 MN t IM t =MN tn t 1 (13) P t = (ˆn t 1+MN t) N t 1 t IM t = DX D=D d im t(d i ) = I d im t (16) im t(d i ) t D i im t (2) (16) t P t = I d (h t + im t ) (17) t j IMT j t IMT 1 t = IMT 2 t = D n t X D i =D D s t X D i =D n t im t (D i ) (18-1) im t(d i ) (18-2) IMT 3 t = DX im t(d i ) (18-3) D i =D s t 3.3 = Y t Y t = ψk a t L 1 a t (19) a ψ K t t L t t 157

11 64 3 K t = ŝ t 1N t 1 = d (h t 1 + im t 1) L t = d (h t + im t ) DX D i t =D h 1 n i t DX D i =D `Di Ei s i t 1(D i ) (20-a) (20-b) t t 1 t t 1 r w (1 + r t) = a Yt K t w t = (1 a) Y t L t (21-a) (21-b) t 1 b t 1 = ˆn t 1p (1 ˆn te) w t 1 1 P W t = 1 I DX D i =D P T W 1 t = 1 IT 1 t P T W 2 t = 1 IT 2 t P T W 3 t = 1 IT 3 t U i t D n t X D i =D D s t X n `Di o c i t,y`di, c i t+1,o`di, n i t U i t U i t D i =Dt n DX Ut i D i =D s t n `Di o c i t,y`di, c i t+1,o`di, n i t n `Di o c i t,y`di, c i t+1,o`di, n i t n `Di o c i t,y`di, c i t+1,o`di, n i t 158 (22) (23-a) (23-b) (23-c)

12 P W t 1 P T W j t j 1 j IT j t d (h t + im t )IT j t t j 1 P SW t P SWt τ = 1 Xt+τ DX n `Di o Ut i c i t,y`di, c i t+1,o`di, n i t (24) I j=t D i =D t t + τ τ t 1 MN t 2 7) 3 7) a 2007 p % % 3 6.3% 4 3.4%

13 α 2.5 β 1.25 γ 0.95 D D 2.30 D D 2.00 E 0.2 C R 2.8 Ψ 20.0 a (K/L) % ( N/N) 8) (%) (L/N) % ( Y/Y ) (%) (w) (r) [(1 p)(1 ˆnE)w] (c y ) (b) (c o ) % % % 3 4.1% 4 8) ( N/N)( Y/Y ) X(X = N, Y ) X % % 160

14 MN 1 1 Razin and Sadka

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18 1 5 MN t

19 Casarico and Devillanova

20 2008, 43 4,pp Casarico, A. and Devillanova, C.2003 Social security and migration with endogenous skill Upgrading, Journal of Public Economic, Vol. 87, pp Poutvaara, P.2007 Social security incentives, human capital investment and mobility of labor, Journal of Public Economics, Vol. 91, pp Razin, A. and Sadka, E.1999 Migration and pension with international capital mobility, Journal of Public Economic, Vol. 74, pp Razin, A. and Sadka, E.2000 Unskilled Migration: A Burden or a Boon for the Welfare State?, Scandinavian Journal of Economics, Vol. 102, pp Razin, A., Sadka, E., and Swagel, P.2002 Tax burden and migration: a political economy theory and evidence, Journal of Public Economic, Vol. 85, pp

税制改正にともなう家計の所得弾性値 : 高齢者パネルデータによる実証分析

Kwansei Gakuin University Rep Title Author(s) 税制改正にともなう家計の所得弾性値 : 高齢者パネルデータによる実証分析 Uemura, Toshiyuki, 上村, 敏之 ; Kitamura Takayuki, 金田, 陸幸 Citation 経済学論究, 69(4): 1-16 Issue Date 2016-3-20 URL http://hdl.handle.net/10236/14671