The Dynamic Effect of Openness on Income Distribution and Long-Run Equilibrium Tatsuya ASAMI Graduate School of Economics, Kobe University (D1) azutotatsu@gmail.com The Japan Society of International Economics Kansai July 21, 2018
Introduction Trade and Inequality in Different Income Level Figure 1 : Trade (% GDP) and Gini Index in 2010 Source: World Bank (2018) https://data.worldbank.org/ 2 / 29
Introduction Long-Run Difference Figure 2 : Two countries are open at 1960 Source: World Bank (2018) https://data.worldbank.org/ 3 / 29
Introduction Literature Empirical analysis: Feenstra and Hanson (1996, A.E.R.) Outsourcing inequality in U.S. Meschi and Vivarelli (2009, World Dev.) Trade inequality in developing countries Theoretical analysis: Galor and Zeira (1993, R.E. Stud.) Initial wealth distribution Long-run distribution Falvey et al. (2010, J.I.E.) Delay of trade liberalization Benefit from trade Aghion and Bolton (1997, R.E. Stud.) Development process Inequality Galor and Moav (2004, R.E. Stud.) Inequality Development process 4 / 29
Introduction Position in the Literature steady state transition closed opening Galor and Zeira (1993) Falvey et al. (2010) Aghion and Bolton (1997) Galor and Moav (2004) This paper 5 / 29
Introduction Contribution Main Results Inequality open regimes > closed economy (less developed) closed economy > open regimes (developing) What determines long-run equilibrium? Galor and Zeira (1993): Initial wealth distribution (exogenous) This paper: Wealth distribution at market opening (endogenous) 6 / 29
The Model Setting Setup Households Lifetime: one period Continuum heterogeneous Individuals in terms of ability (a [0, 1]): efficiency as skilled labor Intergeneration: transfer Initial transfer: independent of ability Productions Three factors; K, L and H Two final goods: Y A (L) and Y M (K, H) Perfectly competitive markets 7 / 29
The Model Setting Overview (Household a) : "&' 629 Education Investment Working Consumption Transfer : " 629 QB7 Q Q57 8 / 29
The Model Setting Overview (Productions)! " ( " ) + " ) Individuals at t Education # " + " * % "&' ( " * $ " % " 9 / 29
The Model Setting Productions and Factor Prices Y A (L) = AL, Y M (K, H) = M [ αk (σ 1)/σ + (1 α)h (σ 1)/σ] σ/(σ 1) (1). w L = Ap, w H = w H (k), r = r(k), p: price of Y A in units of Y M k = K/H 10 / 29
The Model Setting Problem of Individual a max (1 β) [ γ ln c A t + (1 γ) ln c M t ] + β ln bt, (2) s.t. p t c A t + c M t + b t = I t (a). (3) For given income I t (a), FOCs are, c A t (a) = [ (1 β)γ/p t ] It (a), c M t (a) = (1 β)(1 γ)i t (a), b t (a) = βi t (a). (4) 11 / 29
The Model Setting Working, Education and Income No education, " -./01 2 =3 " 4 56758 " 9: " 629! " $ " Banks Education without borrowing, " /01;<">.1"?.@ 629=23 " A 5 758 " : "&' 2 BC Education with borrowing, " /01;<">?.@ 629=23 " A B 758 " 0 CB: "&' 2 # " r d t = r t + z. (5) 12 / 29
The Model Setting Borrowing and Education Choice Income of individuals depends education borrowing for education cost e { max{i I t (a) = max{i no edu t no edu t I cutoff ability a e t I edu without bor (a), It (a)}, if b t 1 (a) e. edu with bor (a), It (a)}, if b t 1 (a) < e. (6) no edu t no edu t (a) = I or (a) = I edu without bor t edu with bor t (a) (a) 13 / 29
The Model Dynamic Equilibrium Aggregate Supplies Factor supplies at t: K ( a e (p t, k t, {b t 1 (a)} a [0,1] ), B t 1 ) = Bt 1 [ 1 G ( a e ( ) )] e, H ( a e (p t, k t, {b t 1 (a)} a [0,1] ) ) = 1 a e ( ) L ( a e (p t, k t, {b t 1 (a)} a [0,1] ) ) = G ( a e ( ) ), a dg(a), (7) where B t 1 = 1 0 b t 1(a) dg(a). Goods supplies at t: Y A (L( )) and Y M (K( ), H( )). Aggregate supplies are functions of p t, k t and {b t 1 (a)} a [0,1]. 14 / 29
The Model Dynamic Equilibrium Aggregate Demands Aggregate demands of goods at t: C A( p t, k t, {b t 1 (a)} a [0,1] ) = 1 (1 β)γ I(r t, wt L, wt H, b t 1 (a); a) dg(a). p t 0 C M( ) p t, k t, {b t 1 (a)} a [0,1] = (1 β)(1 γ) 1 Transfer of agents at t 0 I(r t, w L t, w H t, b t 1 (a); a) dg(a). (8) b t (a) = βi ( r t, w L t, w H t, b t 1 (a); a ), for all a [0, 1]. (9) Aggregate demands are functions of p t, k t and {b t 1 (a)} a [0,1]. 15 / 29
The Model Dynamic Equilibrium Dynamic Equilibrium Definition 1 For all t = 1, 2,..., and for given b 0, ( p t, k t, {b t 1 (a)} a [0,1] ) satisfies factors ( market equilibrium condition ) k t = K ae (p t,k t,{b t 1 (a)} a [0,1] ),B t 1 ). H ( a e (p t,k t,{b t 1 (a)} a [0,1] ) goods market equilibrium condition Y A[ L ( a e (p t, k t, {b t 1 (a)} a [0,1] ) )] = C A( p t, k t, {b t 1 (a)} a [0,1] ). Transition of transfer b t (a) = βi ( r(k t ), w L (p t ), w H (k t ), b t 1 (a); a ) for all a [0, 1]. 16 / 29
Steady States Steady States Definition 2 We call dynamic equilibrium as steady state if b t 1 (a) = b t (a) for all a [0, 1]. Proposition 3 (Existence) There exist steady state(s) if [ ] β lim k 1 γ+βγ 1 + r(k) 1 b 0 > 0 s.t. b 1 (0) > b 0 With imcomplete credit market r d > r, there may exist multiple steady states. 17 / 29
Steady States Possibility of Multiple Steady States b (p, k; a) = { b no edu (p, k) if a < a e, b edu without bor (p, k; a) if a a e, (10) : " : " =: "&' : /01;<">.1"?.@ 6LMNO2 P/01;<">?.@ 9 : /01;<">.1"?.@ 6LMNO2 P?.@ 9 : P-./01 6LMN9 K C : "&' 18 / 29
Steady States Multiple Steady States Transfer and Cutoff Abilities b no edu (p, k), b edu with bor (p, k; a), b edu without bor (p, k; a): transfer at steady states (b t (a) = b t 1 (a)). Three cutoff abilities: borrowing a bor (p, k) b edu without bor (p, k; a) = e, education a edu with bor (p, k) b no edu (p, k) = b edu with bor (p, k; a), a edu without bor (p, k) b no edu (p, k) = b edu without bor (p, k; a). 19 / 29
Transitional Dynamics Closed Economy Transition of Endogenous Variables (1) Early stage: b t (a) > b t 1 (a) for all a, Supply side (education and working) education (a e ) L Y A Demand side Aggregate income C A p (= p A /p M ) (Proposition 6) k (K ) unless r d >> r w L (p), w H (k) and r(k) 20 / 29
Transitional Dynamics Closed Economy Transition of Endogenous Variables (2) Late stage: B t > B t 1, b t (a) < b t 1 (a) for some a, Supply side (education and working) I(a e ) (a e ) L Y A Demand side Aggregate income C A p (= p A /p M ) k (K ) unless r d >> r w L (p), w H (k) and r(k) 21 / 29
Transitional Dynamics Dynamic Effect of Openness Market Opening on Prices home country: during transition world economy: steady state parameter is common p w > p, k w > k Table 1 : Market opening and prices p w L w H r Free trade (goods only) depending on k depending on k + Capital movement 22 / 29
Numerical Examples Transition of Fundamentals Numerical Examples Parameters we use are cited from Harris and Robertson (2013, J.I.E.) and Lim and McNelis (2016, Econ. Modelling). Table 2 : Parameters A M α β γ σ δ e z 3 3 0.5 0.5 0.5 1.2 0.04, 2, 0.5 The initial condition: b 0 (a) = 0.2 for all a. 23 / 29
Numerical Examples Opening and Inequality Transition of Inequality 0.04 Gini index 0.03 0.02 Closed economy Free trade Capital movement 0.01 0.00 0 20 40 60 t 24 / 29
Numerical Examples Opening and Inequality Inequality and Market Opening The key factors of inequality: difference in ability (skill premium). difference in received transfer (rental rate). In the early stage of development, Transfer is less accumulated ability is main factor Inequality: open regimes > closed economy During development, Transfer is accumulated enough received transfer is main factor Inequality: closed economy > open regimes 25 / 29
Numerical Examples Timing of Opening and Long-Run Outcome Timing of Opening and Long-Run Outcome Suppose a small country; r d r is large Earlier free trade leads to more accumulation of b due to increase in aggregate income r and revenue from capital H and w H Earlier capital movement leads to more capital accumulation due to inflow of capital r and revenue from capital H 26 / 29
Conclusion Concluding Remark In closed and developing countries, Inequality In the least developed economy, open regimes > closed economy; higher skill premium. In developing economy, closed economy > open regimes; higher rental rate. Long-run outcome Earlier market opening may leads to poor steady state smaller rental rate (free trade) outflow of rental revenue (capital movement) 27 / 29
References Aghion, P. and Bolton, P. (1997). A theory of trickle-down growth and development. Review of Economic Studies, 64(2):151-172. Falvey, R., Greenaway, D., and Silva, J. (2010). Trade liberalisation and human capital adjustment. Journal of International Economics, 81(2):230-239. Feenstra, R. C. and Hanson, G. H. (1996). Globalization, outsourcing, and wage inequality. American Economic Review, 86(2):240-245. Galor, O. and Moav, O. (2004). From physical to human capital accumulation: Inequality and the process of development. Review of Economic Studies, 71(4):1001-1026. Galor, O. and Zeira, J. (1993). Income distribution and macroeconomics. Review of Economic Studies, 60(1):35-52.
Harris, R. G. and Robertson, P. E. (2013). Trade, wages and skill accumulation in the emerging giants. Journal of International Economics, 89(2):407-421. Lim, G. C. and McNelis, P. D. (2016). Income growth and inequality: The threshold effects of trade and financial openness. Economic Modelling, 58:403-412. Meschi, E. and Vivarelli, M. (2009). Trade and income inequality in developing countries. World Development, 37(2):287-302.