capital markets integration, growth and income distribution

European Economic Review 46 (2002) 301}327

Capital markets integration, growthand income distribution

Jean-Marie Viaene��*, Itzhak Zilcha�

�Department of Economics, H8-8, Erasmus University and Tinbergen Institute, P.O. Box 1738,3000 DR Rotterdam, Netherlands

�The Eitan Berglas School of Economics, Tel-Aviv University, Tel-Aviv, Israel

Received 1 December 1999; accepted 1 November 2000

Abstract

The paper considers a two-country model of overlapping generation heterogenouseconomies with intergenerational transfers carried out in the form of bequest andinvestment in human capital. We examine in competitive equilibrium the transitory andlong-run e!ects of capital markets integration. First, we explore how the regime of publiceducation a!ects the dynamics of the integrated economy. Second, we study the e!ects ofcapital markets integration, in equilibrium, on the intragenerational income distributionin both the host and investing country. � 2002 Elsevier Science B.V. All rights reserved.

JEL classixcation: D9; E2; F2; J2

Keywords: Altruism; Growth; Human capital; Income distribution; Capital markets integration

1. Introduction

Although "nancial markets progressed gradually towards a competitiveglobal industry during the 1980s, the integration of these markets gatheredspeed during the 1990s. The European Community's single market in "nancialservices and the banking reforms in major advanced countries contributed

*Corresponding author. Tel.: #31-10-4081397; fax: #31-10-4089146.E-mail address: [email protected] (J.-M. Viaene).

0014-2921/02/$ - see front matter � 2002 Elsevier Science B.V. All rights reserved.PII: S 0 0 1 4 - 2 9 2 1 ( 0 1 ) 0 0 0 9 7 - 6

largely to this process. Consequently, gross #ows of portfolio and foreign directinvestment more than tripled between the mid-1980s and the mid-1990s and thecross-border transactions in bonds and equities currently surpass the value ofmost advanced countries' GDP (see, e.g., International Monetary Fund (IMF),1998). Given these facts, and in the light of the recent Asian "nancial crisis, thestudy of the e!ects of free capital movements assumes increasing signi"cance.The main objective of this paper is to examine the dynamic e!ects of the capitalmarkets integration (CMI) upon:

(a) Aggregate production and its allocation between countries.(b) The distribution of incomes in the capital-importing and capital-exporting

countries.

The framework we shall use to analyze these issues is a two-country overlap-ping generations (OLG) economies with intergenerational links.� There are twomain features in our economies: (a) Intergenerational transfers, motivated byaltruism between parents and their o!spring, exist and are accomplished viatransfers of physical capital and investment in educating the younger genera-tion; (b) Heterogeneity of consumers in each generation. The signi"cance ofthese intergenerational transfers to capital accumulation and growth has beenextensively studied in the literature in the last two decades. Let us mention fewexamples, out of many: Kotliko! and Summers (1981), Becker and Tomes(1986), Gale and Scholz (1994), Bernheim (1991), Lord and Rangazas (1991) andHorioka et al. (2000). Intergenerational transfers, in their various forms, areamong the signi"cant factors a!ecting inequality in the distribution of income,hence our model includes this feature. The main reason for considering hetero-genous population is our aim to study the impact of CMI on inequality indistribution of intragenerational income in the `domestic countrya, from which(by assumption) initially capital #ows, and the `foreign countrya which enjoysincoming capital. These issues have not been explored in the literature, parti-cularly not in a dynamic framework.� As capital integration a!ects wages andinterest rates in di!erent countries in di!erent ways, the relative sizes of invest-ment in education and bequest transfers change di!erently across countries andacross individuals. Equilibrium levels of physical capital, e!ective labor andoutput will therefore di!er between integrated economies. Heterogeneity results

�OLG models have been used to highlight di!erent features of capital markets integration. Forexample, see Buiter (1981) for the response of international capital movements to country di!erencesin pure rate of time preferences and Yoon (1998) for the bequest accumulation (or reduction) e!ectscaused by capital mobility.

�The evolution of human capital and its impact on income distribution has been studiedextensively in di!erent contexts (see also Loury, 1981; Galor and Zeira, 1993; Eckstein and Zilcha,1994; Park, 1996; Fernandez and Rogerson, 1998).

302 J.-M. Viaene, I. Zilcha / European Economic Review 46 (2002) 301}327

from two sources: intergenerational transfers vary across families and thehuman capital is distributed across individuals in a nondegenerate way (hencelabor earnings di!er).Due to investments in human capital, which is a factor of production,

the economy exhibits endogenous growth. As in Lucas (1988), Azariadis andDrazen (1990), Fischer and Serra (1996), van Marrewijk (1999) and others,production is constrained by education and work experience. Models in whichboth physical capital and human capital are used in production, as in our case,are abound. However, we shall concentrate on comparison, period by period, ofnon-stationary competitive equilibria of two countries once under autarky andthen under (full) capital mobility which takes place at date 0.�In this paper we concentrate on public provision of education that local

governments "nance by taxing wage income. Though we could have dealt withprivate education equally well, our choice accounts for the large contribution, inmost countries, of the public sector to education and to the enhancement ofhuman capital. It was shown by Glomm and Ravikumar (1992) that majorityvoting results in a public educational system as long as the income distributionis negatively skewed. Cardak (1999) strengthens this result by consideringa voting mechanism where the median preference for education expenditure,rather than median income household, is the decisive voter. The analysis wepresent here suggests a distinction between the input for education (the timespent teaching) and education spending by governments. In our case, the formeris equal to the labor income tax while the latter is endogenous. In essence, thisre#ects the coordinated education policy of the European Union after introduc-ing the European Credit and Transfer System based on educational require-ments like curriculum, teaching material and contact hours. The distinction isimportant since in an open regime where markets for physical capital areintegrated, there exists upward pressure on wages in the country poor inphysical capital and makes it therefore more costly to "nance a similar level ofhuman capital. By assuming that local governments "nance education by taxinglabor earnings, the immobile factor, we allow for an e$cient zoning policy. A taxon mobile capital would have the additional di$culty that can cause anine$cient distribution of public goods across regions because of positive andnegative externalities associated with investment in#ows and out#ows (see, e.g.,Wilson, 1987).There are three main motivations for our analysis. First, to analyze the

e!ects of CMI on income equality. Evidence of a rise in income inequality hasbeen observed in a large number of OECD countries. There is a widely heldbelief that this rise is driven by events like progress in information technology,

� In a di!erent framework, Dellas and de Vries (1995) examine integration under a precipitouspace versus a piecemeal integration of economies and "nd some long-run implications to income.

J.-M. Viaene, I. Zilcha / European Economic Review 46 (2002) 301}327 303

globalization of world trade and "nancial markets. Others believe that socialnorms are crucial determinants of earnings inequality (e.g., Atkinson, 1999).Given this debate it seems important to us to determine the changes in incomeinequality resulting from capital markets integration. Second, to study thedynamic e!ect of CMI on growth. A recent literature discusses the factors thatincrease the rate at which poor and rich countries converge. For example, Barroet al. (1995) consider capital mobility in a neoclassical growth model. Fischerand Serra (1996) study how trade changes the rate of income convergence underendogenous growth. A di!erent issue, though related to income convergence, isthe relationship between national gains and free capital movements. Here, onedistinguishes between the gains from trade e!ect and the growth e!ect of CMI.A large part of the literature has been devoted to the "rst question, mostly instatic models (e.g., Ru$n, 1985). We shall discuss both issues in this paper.Third, to look at the partition of gains between the capital importing and thecapital exporting countries. The bulk of international capital #ows takes placebetween industrialized countries while capital #ows to developing countries fallshort of the #ows predicted by the theory. In this regard, it is important to derivethe determinants of each country's share in the limited global capital availablefor investments. While we are aware of previous research on di!erences incross-country returns to capital (see, e.g., Lucas, 1990; Leiderman and Razin,1994), we have not seen in the literature theoretical results regarding the alloca-tion of world output among countries following capital markets integration.We consider two countries with given initial capital holdings and human

capital distributions. Comparing the equilibrium path under autarky with theequilibrium obtained when capital markets are integrated, we derive the follow-ing results: (a) Aggregate output in the integrated economy is higher in allsubsequent periods; (b) We "nd how production and capital are allocatedamong participating countries, following CMI, and identify an implementationparadox: "rst generations gain in terms of welfare from CMI and, in spite oftheir altruism, they will decide in favor of integration even if later generationslose; (c) Inequality in intragenerational income distributions, following CMI,changes in all dates. If the two countries di!er only in initial intergenerationaltransfers and human capital distributions (hence aggregate capital stocks di!er),intragenerational income distributions change according to the #ow of capital inthe xrst period: more equality in the distribution of the &wealthier country'and less equality for the capital-receiving country. However, if the two countriesdi!er only in the initial aggregate capital stock then integration yields equallydistributed incomes in each subsequent period, contrary to the case of autarkicequilibrium. These theoretical results are new to the economic literature.The rest of the paper is organized as follows. The next section presents the

two-country OLG economies, under public education regime, and characterizesthe autarky equilibrium. Section 3 studies the e!ects that capital marketsintegration will have on production, capital stocks and human capital levels.


Section 4 considers the e!ects of CMI on intragenerational income distribu-tions. Section 5 concludes the paper. The appendix contains the proofs.

2. Autarky equilibrium

2.1. Preferences and technology

Consider an overlapping generations economy with no population growth.Individuals are economically active during two periods } a working periodfollowed by a retirement period. At the end of the "rst period, every individualgives birth to one o!spring. Denote by G

�the set of individuals born at the

outset of period t and refer to these individuals as generation t. The economystarts at t"0, where G

��individuals live their retirement period, consuming

their savings. Denote by � the set of families in each generation; � is timeindependent since there is no population growth. Although our analysis can becarried out for any "nite �, to simplify our notation we assume a continuum ofindividuals (or families) in each generation, hence we take �"[0, 1]. Thus, eachindividual in G

�is characterized by its family name �3[0, 1].

In this economy parents care about the well being of their o!spring; morespeci"cally, we assume that parents derive utility from the future lifetime incomeof their child. Thus, intergenerational transfers are driven by two means: (a)Improving the earning capability of the o!spring via education; (b) the &joy ofgiving' or direct transfer of physical capital. The levels of human and physicalcapital transfers together with the relevant interest rate and wages determine theo!spring's total income. Denote by b

�(�) the transfer of physical capital by

�3G�to his/her o!spring and by e

�(�) the level of education (measured in units

of time) provided to him/her. The human capital of individual � in G��

,denoted h

��(�), depends upon e

�(�) and the parent's level of human capital

h�(�). To simplify the subsequent analysis, we take the evolution process of

human capital as follows. For some constants �'1, �'0 and �'0, we have

h��

(�)"�[e�(�)]�[h

�(�)]�, t"0,1,2,2 . (1)

The constant � represents the e$ciency of the process which generates humancapital and is a!ected by the organization of schools, the neighborhood, theattitude to learning, etc.� Lifetime preferences of individual �3G

�are assumed

to be a Cobb}Douglas utility function:

;"c��(�)��c

��(�)��y

��(�)�� , (2)

�The evolution of human capital has attracted a lot of attention in the economic literature duringthe last decade. See, for example, OECD (1997) for a list of 41 indicators that describe and comparethe process and achievements across countries. Besides e$ciency of public education, familybackground is found to play a powerful role in educational attainment (Lillard and Willis, 1994;Altonji and Dunn, 1996).


where ��are known parameters and �

�'0 for i"1,2,3; c

��and c

��denote,

respectively, consumption in the "rst and second period of the individual's life;y��

is the income of the o!spring. We assume that each individual supplies oneunit of labor inelastically. Under public provision of education in each date t forall young individuals �3G

�we assume that e

�(�)"e

�, which is "nanced by

taxing the wage income of the &older' generation. Denote by ��the tax rate on

labor income, r��

and w��

be the interest rate and the wage in period t#1,respectively. Then, the lifetime income of �3G

��is given by

y��

(�)"(1#r��

)b�(�)#(1!�

��)w

��h��

(�). (3)

The tax rate ��on wage earning "nances public education at level e

�and it is

determined by the government. Denote the average human capital of generationt by hK

�. To provide education at level e

�to the young generation a proportion

e�of the &working generation' G

�needs to be engaged in education. We assume

that those individuals engaged in education are chosen randomly from G�, hence

their average human capital is hK�as well. Since the taxes cover the cost of public

education we obtain that

��

w�h�(�) d�(�)"w

�hK�e�, (4)

Where � denotes the Debeque measure on�. Hence, e�"�

�for all t. Thus, the

aggregate e!ective labor used in the production of goods is given by

¸��"��

[1h�(�)!hK

�e�] d�(�)"(1!�

�)¸

�,

where ¸�"�� h

�(�) d�(�) is the aggregate e!ective labor available in the

economy.Since our economy considers two types of intergenerational transfers, phys-

ical capital and human capital, we take the aggregate production function todepend on both sorts of capital. Production in this economy is carried out bycompetitive "rms that use &e!ective' labor and capital to produce a singlecommodity. This commodity serves for consumption as well as physical capitalinput. We assume full depreciation of the physical capital. The aggregate level ofhuman capital at each date t has a direct e!ect upon the production possibilitiesat that period. In particular, we take the aggregate production function to be

Q�"F(K

�,¸�

�), (5)

where K�is the aggregate capital stock. F( ) , ) ) is assumed to exhibit constant

returns to scale, it is strictly increasing, concave, continuously di!erentiable andsatis"es F

�(0,¸� )"R, F

�(K, 0)"R, F(0,¸� )"F(K, 0)"0.


2.2. Competitive equilibrium

Throughout this paper we assume that the political process which determinesthe levels of public provision of education is given exogenously. However, ourwhole analysis does not depend on these positive public education levels e

�. In

particular, if e��

is determined by maximizing some social welfare functionall the subsequent results hold. Production at each date t is carried out bycompetitive "rms which borrow capital at date t!1 and hire labor services atdate t. Thus, the factor prices are given, in equilibrium, by the marginalproducts. Since the human capital of a worker is observable, the wage paymentswill depend upon the e!ective labor supply of the worker, i.e., w

�h�where

w�"F

�(K

�,¸�

�) is the wage rate. Heterogeneity within each G

�emanates from

two sources: intergenerational transfers, represented by b��

(�), and the humancapital distribution, given by the function h

�(�). The economy starts at period 0

with some initial distributions b��

(�) and h(�) of capital transfers and human

capital endowments. Both functions evolve in equilibrium from these initialdistributions and from the market conditions.Given the intergenerational transfers at date t, b

��(�), the stock of human

capital, h�(�), the e!ective wage rates w

�, w

��for dates t and t#1, interest rates

r�, r

��for dates t and t#1, the levels of public provision of education e

�, an

individual �3G�chooses the levels of saving, s

�(�), bequest transfer, b

�(�), so as

to maximize

Max c��(�)��c

��(�)��[ y

��(�)]�� , (6)

subject to constraints

c��(�)"y

�(�)!s

�(�)!b

�(�)50, (7)

c��(�)"(1#r

��)s�(�)50, (8)

h��

(�)"�e��[h

�(�)]�, (9)

where y�(�) and y

��(�) are de"ned by (3). Given the aggregate capital stockK

,

the initial distributions b��

(�) and h(�) at the outset of period 0, and the

education provision plan over time e��

, a competitive equilibrium is asequence of functions [c

��(�), c

��(�), s

�(�), b

�(�)]�

��and a sequence of prices

(w�, r

�)��

such that for t"0,1,2,2

(a) Given the above prices, for all �3G�, [c

��(�), c

��(�), s

�(�),b

�(�)] is the

optimum for (6)}(9).(b) The market clearing conditions hold:

w�"F

�(K

�,¸�

�), (10)

1#r�"F

�(K

�,¸�

�), (11)


K��

"��

[s�(�)#b

�(�)] d�(�). (12)

Condition (12) is a market clearing condition for the physical capital at period tequating the aggregate capital stock to the aggregate savings and transfers ofphysical capital. After substituting the constraints, the "rst-order conditionsthat lead to the necessary and su$cient conditions for optimum are

c��(�)

c��(�)

"

��

��(1#r

��), (13)

c��(�)

y��

(�)"

��

��(1#r

��). (14)

From (8), (13) and (14) we also obtain that

y��

(�)"��

��

(1#r��

)s�(�). (15)

Using (3), (7), (8), and (14), we obtain

b�(�)"

��

��

s�(�)!

(1!��

)w��

(1#r��

)h��

(�). (16)

To simplify the subsequent analysis we assume in Sections 2 and 3 only thatthe aggregate production function in our economy has the Cobb}Douglas form:

F(K�,¸�

�)"AK�

�¸��

�. (17)

In equilibrium the following expressions are therefore obtained: (1#r�)"

�A(K�/¸�

�)�� and w

�"(1!�)A(K

�/¸�

�)�. Using this information, (12) and (16)

we derive

��

s�(�) d�(�)"

��

�(��#�

�)K

��, (18)

��

b�(�) d�(�)"

(�(��#�

�)!�

�)

�(��#�

�)

K��

. (19)

To ensure that the aggregate intergenerational transfers are positive we shallmake the following assumption about the parameters:

�(��#�

�)5�

�.


Such condition holds, for example, if the capital share in production and thealtruism parameter are not small. Substituting (16) and (18) in (7), while makinguse of (8) and (12), we obtain an expression for the economy's aggregate incomeat date t:

��

y�(�) d�(�)"�1#

��

�(��#�

�)�K

��. (20)

However, using (15) and (18), we can also express aggregate income at anydate t as a proportion of aggregate output at the same date:

��

y�(�) d�(�)"�

��

��#�

��Q�

. (21)

This indicates the part of aggregate output which &young' members inG

�allocate between current consumption, saving and bequest. The remaining

part is consumed by the &old' in G��

.

2.3. Economic growth

Our main purpose now is to compare two economies in autarky which areassumed to di!er only in initial distributions of physical capital and humancapital. We shall consider competitive equilibria, given the government educa-tion policy e

�, and compare the dynamic paths in terms of the levels of capital,

e!ective labor and output at each date. It is useful to start by expressing thegrowth factor of e!ective aggregate labor. Using (1):

¸��¸�

"

��[h�(�)]� d�(�)

��h�(�) d�(�)

�e��,�

�. (22)

Observe that the evolution process of human capital of a dynasty can bewritten as follows:

h�(�)"�

�[h

(�)]��, (23)

where ��"��2��

��[e�

�]��. The human capital of a family �3G

�is the

product of two exponential functions, the "rst one representing the contributionof public education, the other representing the family history. Assuming that thehuman capital scale is chosen such that h

(�)51, it is clear from (23) that the

magnitudes of both ��and � are key determinants of h

�. Substitution of (23) in

(22) gives rise to an alternative expression for ��:

��,

��[h(�)]�� d�(�)

��h(�)��d�(�)

��, (24)


where ��"��

��[e

��]��. The growth factor of e!ective labor is now

dependent on the initial distribution of human capital and the parametersdescribing the evolution of a family's human capital. One can see from the ratioof integrals in (24) that the contribution of the initial human capital distributionto growth depends on the value of �. The growth factor �

�is independent of time

only if �"1 and e�"e for all t, where it is equal to �e�. Moreover, if �e�

�(1 for

all t, and if �41 then ��41 for all t. In this case, the stock of human capital

declines until &most' h�are smaller than 1.

Let us consider the e!ect of a more dispersed initial distribution ofhuman capital on the growth rate. We say that h�

(�) is more dispersed

than h(�) if it is obtained from h

(�) by a mean-preserving spread (MPS).

The following result can be derived directly from (24) and it is stated withouta proof.

Proposition 1. Assume that 0(�(1. A more dispersed initial distribution ofhuman capital h

(�) results in a lower growth factor �

�in all subsequent periods.

It is important to add that when �'1 the result of this proposition isreversed: �

�'��

�for all k. When �"1 growth is unrelated to the distribution of

human capital. Proposition 1 and its discussion advance a testable hypothesiswith regard to the relationship between the growth rate of an economy and thedistribution of human capital. It depends on the value of �, that is on the extentthat the process describing the acquisition of human capital incorporatesexternalities. Since a &less equal' human capital distribution contributes to a lessequal income distribution the result of Proposition 1 is compatible with someempirical observations that income inequality is harmful to economic growth(see, e.g., Persson and Tabellini, 1994).In the sequel we shall assume that the tax rates "nancing the provision of

public education ��

are given. We shall not attempt in this work to derivesome &optimal' levels of taxes (and, hence, education provision): this has beendone in Viaene and Zilcha (2001). However, it should be pointed out that all thesubsequent analysis holds for any such sequence of positive taxes. Consider nowtwo economies in autarky: the domestic economy and the foreign economywhose variables are marked with &*'. We assume throughout this work that thetwo countries have identical tax in each date. Denote by GH

�members of

generation t in the foreign country. At date t"0, the following variables aredetermined historically: s

��(�), b

��(�) and h

(�) for the domestic economy;

sH��

(�), bH��

(�) and hH(�) for the foreign economy. Denote the domestic equilib-

rium by (c��, c

��, s

�,b

�), (w

�, r

�), the equilibrium abroad by (cH

��, cH

��, sH

�, bH

�),

(wH�, rH

�). Given this, we now prove two propositions comparing two economies

that di!er only in initial conditions, "rst in the stocks of physical capital andthen in the levels of human capital. There are, however, integration exampleslike NAFTA and the EU expansion to the South where the incumbent has more


of both types of capital. The total e!ect on growth will be a combination of bothpropositions and whether one dominates will depend very much on initialconditions.The "rst proposition assumes that the domestic economy is initially endowed

with more physical capital. Consider, for example, East and West Germanybefore their union, Eastern and Western Europe in general where the discerningdi!erence is clearly the availability of physical capital while individual endow-ments of human capital are fairly similar. Under this assumption the growthfactor in (24) is the same for both economies, �

�"�H

�. Hence, ¸

�"¸H

�for all t.

From (20) and (21) we obtain

K��K

�

"

��A

(��#�

�#�

�/�) �

¸��

K��

��.

Dividing by (22):

K��

¸��

"

��A(1!�

�)��

��(�

�#�

�#�

�/�) �

K�

¸��

�. (25)

This describes the dynamic path of the capital}labor ratio of each economy inautarky. As (25) holds for both economies, K

/¸

'KH

/¸H

implies

K�/¸

�'KH

�/¸H

�for all t. Hence, K

�'KH

�and Q

�'QH

�for all t. Thus, the

economy which starts from higher capital stock, while other parameters areequal, attains higher output in all subsequent periods. Summing up:

Proposition 2. Consider the domestic and foreign economies in autarky under theassumptions h

(�)"hH

(�) for all � and K

'KH

. Then Q

�'QH

�and K

�'KH

�for all dates t.

Consider now the other case where countries di!er in individual endowmentsof human capital while keeping similar the stocks of physical capital. A fairrepresentation of this situation is The Philippines which, when compared tocountries like Indonesia, Malaysia and Thailand, enjoys higher endowments ofhuman capital.�

Proposition 3. Assume that 0(�(1. In autarky assume that h(�)'hH

(�) for all

� and K"KH

. Then:

(a) The human capital growth factors satisfy: ��4�H

�.

(b) If �e��'1 for all t, then 14�

�4�H

�for all large t.

(c) If �e��(1 for all t, then �

�4�H

�41.

(d) If for the given e�, Lim

��exists and it is xnite, then the aggregate labor

¸�and capital stock K

�converge to some xnite ¸H, KH.

�See Table 2.10 at theWorld Bank site (http://www.worldbank.org/data) for various indicators ofhuman capital.


Proof. See the appendix.

Thus, the economy which, ceteris paribus, starts from higher individualendowments of human capital will experience a lower growth rate of e!ectivelabor when 0(�(1. Part (c) describes a shrinking economy because thefunding level for education is too low. This is not a mere theoretical curiosum.World Bank education indicators single out many transition economies of theformer Soviet Republic and isolated developing countries like the Republic ofCongo, Iraq and Syria that witnessed large drops in secondary enrollment ratiosand substantial cumulative falls in output.Although our analysis considers non-stationary equilibria starting at date

t"0, let us consider brie#y the long-run equilibria of this economy. Thus, weshall assume for a moment that �

�"� for all t. It is straightforward to see that

the growth factor of e!ective labor is either �"�e� when �"1 or, if �(1, itconverges to �"1. In contrast, when �'1, � can be unbounded. In this briefattention to the stationary equilibria we do not intend to pursue the case where�'1, hence, we shall assume that 0(�41.In the long run K

��/¸

��"K

�/¸

�"K/¸. From Propositions 2 and 3, we

obtain the long-run capital}labor ratio:

K

¸

"��A

�(��#�

�#�

�/�)�

� ��(1!�). (26)

This is obtained regardless of the initial distribution of human capital and ofintergenerational transfers. Let us apply a one-period lead to (21) and then,divide by (20) to obtain the expression for output and aggregate income growth:

Q��Q

�

"

��y��

(�) d�(�)��y

�(�) d�(�)

"

��A

(��#�

�#�

�/�)�

K��

(1!�)¸��

��. (27)

The substitution of (26) in (27) shows that, in the long run, economic growth inautarky coincides with �, the growth factor of e!ective labor. Our model in thestationary state is therefore an AK-type endogenous growth model where allvariables grow at the same rate (�!1). An implication is that any two econo-mies which di!er only in the initial conditions will grow in the long run at thesame endogenous growth rate (�!1).

3. Capital markets integration

Assume that at date t"0 the domestic and foreign economies integrate toform a single commodity market and a single capital market (while laborremains internationally immobile). The two countries are assumed identical inall respects (hence, �

�"�H

�for all t) except for the initial distributions of human


and/or physical capital transfers. Upon the integration of capital markets,physical capital will #ow from the low return to the high return country untilinterest rates are equalized in the integrated economy. The type of internationalcapital movement we consider, involves a change in the location but not theownership of physical capital. In the sequel, post-integration variables will bedistinguished from their autarky counterparts by the mark &!'.

3.1. Two-country equilibrium

Distinguish between the capital stock used in the production in the homecountry, KM

�and the stock of physical capital, located at home and abroad,

owned by domestic residents, ¹M�. Hence, (12) becomes

¹M��

"��

[ s��(�)#bM

�(�)] d�(�). (28)

Similarly, we de"ne ¹M H�for the foreign country. A positive di!erence (¹M

�!KM

�)

corresponds to a net out#ow of domestic capital abroad. At any date t, thefollowing international identity must hold:

¹M�#¹M H

�"KM

�#KM H

�. (29)

Hence, the above di!erence corresponds also to a foreign in#ow of capital,(KM H

�!¹M H

�). After substituting (28) and making use of (29), the "rst-order condi-

tions for both countries under integration lead to

��

[ s��(�)#s� H

�(�)] d�(�)"

��

�(��#�

�)(KM

��#KM H

��), (30)

��

[bM�(�)#bM H

�(�)] d�(�)"

[�(��#�

�)!�

�]

�(��#�

�)

(KM��

#KM H��

). (31)

These two equations are the analogs of (18) and (19) for the integratedeconomy. As for the autarky equilibrium, we obtain

��

[y��(�)#y� H

�(�)] d�(�)"�1#

��

�(��#�

�)� (KM ��

#KM H��

), (32)

��

[y��(�)#y� H

�(�)] d�(�)"�

��

��#�

�� (QM �#QM H

�). (33)


It is worth noting that Eqs. (30)}(33) that describe the dynamic path of theintegrated economy are similar to those attained for the autarky case. Thegrowth factor of e!ective labor of the integrated economy is given by

�M̧��

# M̧ H��

M̧�# M̧ H

��"�

��#�H

�(1!�

�), (34)

where ��"��[h

(�)]�� d�(�)/��[h(�)]��d�(�)#��[hH

(�)]��d�(�). It is a

weighted average of the autarky growth factors where the weights ��depend on

the distribution of human capital of both countries. Over time ��converges to

1/2 if �(1. Hence, capital markets integration is unable to a!ect the long-rungrowth rate when compared to autarky. Only parameters which describes theprovision of public education can a!ect these rates.

Remark. It is tempting to blame our assumption of public education for theinability of CMI to a!ect the long-run growth rate. Consider parental educationinstead. Set e

�"0 and replace (1) by h

��(�)"�e

�(�)h

�(�) where e

�now

represents the parents' e!ort, measured in time, invested in educating o!springs.Replace (2) by ;"c

��(�)��c

��(�)��y

��(�)��(1!e

�(�))�� where (1!e

�) repres-

ents leisure (where each individual has 1 unit of non-labor time). Applying thesame steps of Section 2 to this particular problem one can show that (22) nowbecomes �"�(1!�)(�

�#�

�)/[�

�#(1!�)(�

�#�

�)]. Hence, if the two econ-

omies di!er only in the initial conditions, they will grow in the long run at thesame endogenous growth rate. Again the latter remains una!ected by CMI.During the transition periods capital mobility a!ects economic development.

More precisely, two main questions can be raised: What are the bene"ts, if any,resulting from liberalizing capital markets? And, what is the division of the gainsbetween the capital importing country and capital exporting country? Thesequestions are examined in the following two propositions.�

Proposition 4. Total output of the integrated economy after capital markets integra-tion is higher than the sum of outputs of the autarkic economies at all dates.


This proposition extends to a dynamic framework the static result thatinternational capital mobility increases production (Ru$n, 1985). In addition todynamic gains from trade, the proof shows that aggregate capital stocks arehigher following integration in all dates subsequent to period 0. What can besaid about the partition of output of the integrated economy? To show that,

�The extent of the gains that participating countries expect to realize after integrating their capitalmarkets has been examined in dynamic frameworks di!erent from ours (see Stokey, 1996).


consider the equality of returns to capital, and its implication for capital}laborratios:

KM�

M̧ ��

"

KM H�

M̧ �H�

"

KM�#KM H

�M̧ ��# M̧ �H

�

, t"0,1,2,2 .

From the assumptions of identical and linear homogenous production func-tions:

QM�

KM�

"

QM H�

KM H�

"

QM�#QM H

�KM

�#KM H

�

, t"0,1,2,2 . (35)

Combining these two expressions, we obtain

QM�

QM�#QM H

�

"

KM�

KM�#KM H

�

"

M̧ ��

M̧ ��# M̧ �H

�

, t"0,1,2,2, (36)

which proves our next claim.

Proposition 5. Following capital market integration, each country's share of outputand share of physical capital stock in the integrated economy is equal to its share inthe stock of human capital.

Remarks. (a) This result can be generalized to the case where technologies di!erin scale (i.e., AOAH). In such a case the stocks of human capital should benormalized.(b) Proposition 5 holds for a broader class of production functions including

the CES with homogeneity of degree one.(c) With similar regimes of public education (�

�"�H

�for all dates), each

country's share in the stock of human capital is given by ��in (34). Thus, each

country's share in total aggregate output and physical capital in each period isfully predetermined by �, the tax rates and the initial distributions of domesticand foreign human capital.�

3.2. Implementation

With the help of numerical simulations we are able to compute the dynamicpaths of the domestic and foreign economies for the cases of autarky andof capital markets integration. We consider a representative agent in each

�This result could be modi"ed if labor supply were allowed to vary, though the dynamics is notobvious. As capital #ows out of the domestic country, one would expect the marginal product oflabor to decrease, so agents would devote less time to production and more to leisure. CMI, ofcourse, has consequences for the future marginal product of labor as well. Altruistic individuals maythen wish to o!set the decrease in the younger generation's income by working more in order totransfer larger amounts of physical capital to this younger generation.


Fig. 1. Capital market integration under public education: (1) changes in variable brought about bycapital market integration as a percentage of its autarky value; (2) smooth lines refer to the domesticeconomy, dotted lines to the foreign one.

economy, who is endowed with perfect foresight and attains his optimalconsumption-bequest in three steps: First, the paths of w

�, r

�, ¸

�and K

�are

solved for. Second, given these parameters, each agent can compute his incomey�and his human capital, h

�. Finally, given this information, the paths of

c��, c

��, s

�and b

�and the utility can be computed. Numerical simulations under

public education must satisfy e�"�

�"�. Simulations under capital markets

integration must satisfy Eqs. (28), (29) and (36) as well.Fig. 1 plots the change in utility and income following capital markets

integration as a percentage of their autarky values under public education.Initial values were taken to be: �

�"�

�"�

�"1, �

�"2, �"0.5,

�"�"1, �"2.70, ��"�H

�"0.4, A"4.0, K

"2, KH

"1, ¸

"¸H

"1. We

observe from Fig. 1 that the "rst generation of both countries Gand GH

are

better o! after CMI. Foreign individuals are worse o! in all generations t, t51,following CMI. Under public education, as integration does not a!ect the pathof human capital and public education, as the foreign country is by assumption


poorer at the outset, the channel of e!ects comes from the decrease in interestrates abroad compared to autarky.

Remarks. (a) The simulation results can be generalized to a very broad range ofparameter values. The pattern of country responses to CMI is, however, onlysensitive to the choice of capital share �. For the parameter values given above,the changes in foreign national income in Fig. 1(b) become all negative when � isbelow the cut-o! point of 0.44.(b) It is important to stress that independently of parameter values gains from

CMI are always attained.

The simulated dynamic paths give rise to two other important issues. First,the results of Fig. 1 identify an implementation paradox: As "rst generations gainin terms of utility, while being altruistic, they will decide in favor of integrationeven if later generations lose. Second, since after integration the aggregateincomes increase for all periods t, some transfer system can achieve Paretodominating allocation, namely, make individuals in both countries better o!following capital markets integration. This is not necessarily the case if thecompetitive mechanism acts solely.

4. Income distribution and capital markets integration

Income distribution is a key economic issue and this importance is forcingeconomists and policymakers to improve their understanding of how incomedistribution and the globalization of markets for capital interact. A general viewis that the relationship between distributional equity and economic growthdepends on the education policies each government follows and on the condi-tions in each country. Given this, the focus of this section is to consider theinequality in the intragenerational income distributions for the domestic andforeign countries. To limit the number of possibilities we assume that thedomestic economy is initially more endowed in physical capital, examples ofwhich are discussed in conjunction with Proposition 2. The preceding sectionsdemonstrated that, under a public provision of education (and keeping theassumption that results in e

�"�

�unchanged), a nation's distribution of human

capital is una!ected by the extent to which its capital market is integrated withthe rest of the world. An important implication is that any e!ect of CMI on theincome distributions will therefore be dominated by the relative factor returnsand by the heterogeneity of individuals' holding of physical capital.Let X and= be two random variables with values in a bounded interval in

(!R,R) and let m�and m

�denote their respective means. De"ne XK "X/m

�and=K "=/m

�. Denote by F

�and F

�the cumulative distribution functions of


XK and=K , respectively. Let [a, b] be the smallest interval containing the supportsof XK and =K .

Dexnition. F�is more equal than F

�if, for all t3[a, b],��

[F

�(s)!F

�(s)] ds40.

Thus, F�is more equal than F

�if F

�dominates in the second-degree stochas-

tic dominance F�. This de"nition, due to Atkinson (1970), is equivalent to the

requirement that the Lorenz curve corresponding toX is everywhere above thatof=. We say that X is more equal than= if the c.d.f. of XK and=K satisfy: F

�is

more equal than F�. Henceforth, the relationX is more equal than= is denoted

X<=. We say thatX is equivalent to=, and denote this relation byX&=, ifX<= and =<X.Let us emphasize here that the results in this section do not depend on the

functional form of the production function F(K,¸) made in Section 2, i.e. theCobb}Douglas form. Without loss of generality let us take �

�#�

�#�

�"1.

We shall use the relations that were derived in earlier sections to obtain thefollowing expression for the income at date t#1, y

��(�), in terms of y

�(�) and

the human capital level h�(�). First, rewriting (3) we have

y�(�)"(1#r

�)�b��

(�)#(1!�

�)w

�1#r

�

h�(�)�. (37)

Using Eqs. (13)}(16) we obtain after few manipulations:

y��

(�)"��(1#r

��)�y� (�)#�

(1!��

)w��

1#r��

h��

(�)�. (38)

We shall examine the impact of capital markets integration on the intra-generational income distribution assuming that education is provided publiclywith �

�"�H

�for all t. Then, (38) becomes

y��

(�)"��(1#r

��)�y� (�)#�

w��

1#r�� (1!�

��)�

��[h

(�)]��.

(39)

Now, we prove the following result assuming public provision of education.

Proposition 6. Given the initial distributions in both countries at date 0, assumethat K

'KH

. Integration of capital markets results in a more equal intragenera-

tional income distribution in the domestic country and less equal income distribu-tion in the foreign country in all generations.



Inequality in our economy results from two sources: unequal human capitaldistribution and unequal intergenerational transfers starting at t"0. In thedomestic economy CMI results in higher interest rates and lower wage rates inall subsequent periods, hence, we obtain lower labor to capital price ratios alongthe equilibrium path (while higher ratios in the foreign case). As a result, incomedi!erences between families resulting from labor earnings (i.e., due to humancapital inequality) will be reduced while di!erences emanating from intergenera-tional transfers are magni"ed due to CMI. However, by the proof of Proposition 6,in the domestic country the "rst e!ect dominates. Since the ratio of the wage rateto the interest factor declines (see (37) and Corollary 1 in the appendix), this willresult in a more equal distribution of income. The opposite happens in thecapital-importing country.�Does capital markets integration imply more equality in income distribution

between the wealthier country and the capital importing country? The followingproposition highlights the role played by capital markets integration towardsequalizing the inequality in income distributions of two similar economies whichdi!er in initial capital stocks only. Without this integration the foreign econ-omy's income distribution is more equal.

Proposition 7. Assume that initial transfers and human capital distributions satisfy:b��

(�)&bH��

(�) and h(�)"hH

(�), while K

'KH

, then:

(a) In the autarky equilibrium we have: yH�(�)<y

�(�) for t"0,1,2,2 .

(b) Under capital markets integration inequality in the income distributions is thesame for all periods, namely, y�

�(�)&y� H

�(�) for all t.


The result of this proposition should be related to that of Proposition 6.Initially, in the absence of CMI the foreign economy, due to lower capitalholdings, has a more equal income distribution. By Proposition 6, CMI resultsin more equality in the domestic economy and in less equality in the foreign one.This proposition claims that if intergenerational transfers, at t"0, are distrib-uted in the two economies with the same level of equality (keeping the humancapital distributions to be the same), then CMI yields an equilibrium with thesame equality in income distributions in all subsequent periods. On the other

�This result does not necessarily extend to free trade because bene"cial trade is a consequence ofcomparative cost di!erences whereas bene"cial factor movements result from absolute productivitydi!erences. For example, Fischer and Serra (1996) show that trade raises inequality as compared toautarky in the rich country while it has the opposite e!ect on the poor country. In their frameworkthere is one accumulating factor of production and the rich country is de"ned as the country with thehigher average human capital stock. In our analysis, we have two accumulating factors and the richcountry is initally endowed with more physical capital. Also we have no direct investment of parentsin the education of their o!spring.


hand, if transfers in the two countries are initially unequally distributed, then theresult of Proposition 7 does not hold: Capital integration does not equalize theinequality in income distributions.

Proposition 8. Let the initial distributions of intergenerational transfers and humancapital satisfy: b

��(�)<bH

��(�), h

(�)"hH

(�), while K

'KH

. Following capi-

tal markets integration domestic income distributions are more equal than theforeign ones, i.e., y�

�<y� H

�, for all periods t.

The proof of this proposition follows from the same arguments used inproving Propositions 6 and 7: Since our assumptions guarantee y�

<y� H

it can

be shown that y��<y� H

�for all t51. We shall not bring a complete proof here.

Remark. Similar result to that brought in Proposition 8 can be derived when weswitch from unequal transfers at date 0 to unequal human capital distribution indate 0. Consider the following case: intergenerational transfers are the same inboth economies at date 0, namely, b

��(�)"bH

��(�), but the domestic country

has more equal distribution of the human capital, namely: h(�)<hH

(�). Again,

it can be shown that in equilibrium under CMI the domestic economy will havemore equal intragenerational income distribution, i.e., y�

�<y� H

�for all t. This

result does not obtain without the capital markets integration.

5. Discussion

Considering OLG economies with heterogenous populations and inter-generational transfers, we have shown how capital markets integration a!ectsthe dynamic equilibrium path of the participating countries. This integrationa!ects the dynamics of wages and interest rates, hence it a!ects the return tohuman capital relative to that of savings and intergenerational capital transfersacross generations.Assuming a public provision of education we derive: (a) International capital

mobility increases total production in a dynamic framework; (b) under ourassumptions, capital markets integration is unable to a!ect the long-run growthrate of the integrated economy when compared to the autarkic case; (c) ournumerical simulations (for homogenous models) suggest an implementationparadox: whatever the type of country (hosting vs. investing) the "rst-generationgains in terms of utility. Although individuals in our model are altruistic, sincethey derive utility from the future income of their o!springs, they will decide infavor of capital markets integration even if later generations lose; (d) capitalmarkets integration a!ects intragenerational income distributions according tothe #ow of capital in the "rst period: more equality in the distribution of thewealthier country and less equality for the capital receiving country.


Since our model makes some speci"c assumptions let us discuss the robust-ness issue. First, the selection of functional forms was strongly motivated byempirics. For example, the incorporation of physical capital and e!ective laborin a Cobb}Douglas production function has repeatedly been shown to haveempirical relevance in the USA and other industrial countries (see, e.g., Mankiwet al., 1992). Though Proposition 5 has been demonstrated in this context itholds for a broader class of production functions including the CES withhomogeneity of degree one. Second, we consider a human capital evolutionprocess that incorporates externalities that do not yield increasing returns toscale to parents' human capital. Though increasing returns have not been oftenobserved (except in China, see, e.g., Knight and Shi, 1996), such an assumptionmay give rise to poverty traps for families whose human capital falls short ofa certain threshold. Issues of indeterminacy of equilibrium may then arise (see,e.g., Benhabib and Farmer, 1994). Third, we assumed that world capital marketsare close to free and complete and that capital #ows were su$ciently large toobtain factor price equalization. However, such a situationmight not be optimalfor a large capital-exporting country since it may restrict out#ows and therebysecure monopoly rents. Fourth, in a world of largely immobile labor, policiesa!ecting the accumulation of human capital have a large potential.We considered public provision of education only, ignoring the education

that the younger generation receives from relatives and social environment. Wealluded to parental education in a remark in Section 3 and, as a matter of fact,the analysis carried out in this paper could be repeated in such a framework.When dealing with income inequality a di$culty arises, however, in that �

��in

(39), which is exogenously given to the individuals under public education,becomes endogenous with private education included.This paper indicates that integration of capital markets between economies

does not necessarily increase the long-run rate of economic growth. In thisregard, the "nding contradicts a common belief in international economics.However, even in trade theory, the result that trade in goods a!ects the rate ofgrowth is not robust (see, e.g., Grossman and Helpman, 1991; Rivera-Batiz andRomer, 1991). Generally, trade models with physical capital in R&D activities,or with trade policies that increase the stock of knowledge, show changes in therate of growth. Here, one is tempted to modify our framework in order togenerate growth e!ects of capital markets integration. However, in contrast tothe R&D activities case, a large share of public spending on education "nancesthe human capital involved in the process.

Acknowledgements

We are grateful to S. Goyal, E. Janeba, M. Janssen, C. vanMarrewijk, S. Roy,and seminar participants at El Colegio de Mexico, Munich (CES), Stockholm


(IIES), the Tinbergen Institute, and at the meetings of the Midwest InternationalEconomics Association (Bloomington, 1997), ERWIT (Rotterdam, 1998), theEuropean Economic Association (Berlin, 1998) and the Econometric Society(Santiago de Compostela, 1999) for their bene"cial remarks. Itzhak Zilcha thanksthe Tinbergen Institute for its hospitality and Erasmus University for "nancialassistance. Research assistance from N. Plaisier and L.W. Punt is gratefullyacknowledged. The current version has considerably bene"ted from the criticalremarks by K. Schmidt, our Editor in charge, and by three anonymous referees.

Appendix

Proof of Proposition 3. It can be veri"ed that whenever 0(�(1 andh�(�)'hH

�(�) for all � then we have

��[h�(�)]�d�(�)

��h�(�) d�(�)

4

��[hH�(�)]� d�(�)

��hH�(�) d�(�)

, (A.1)

which proves, under our assumptions, that ��4�H

�, the equality being obtained

when tPR. Parts (b) and (c) follow from Eqs. (24) and (A.1). The integrals ratioconverges to 1 as tPR, for any �'0. It is less than 1 since hH

(�)51 for all �.

The proof of (b) follows from (A.1) and, since �e��'1, requires t to be su$ciently

large. Proof of (c) follows from (A.1) and [�e��]��41 for all t. Now turning to part

(d), observe from (1) that the human capital level of each dynasty � convergesover time. If �

�converges over time to some �H then for all � the human capital

h�(�) converges to �H. Using Eqs. (20) and (21), we can replace the limit (over

time) output QH, which is the limit of Q�as t converges to in"nity, by KH and

¸H and derive the above expression for KH. �

Proof of Proposition 4. For the sake of simplicity, let us delete the &e' superscriptin ¸�

�but keep in mind that, in this proof, the relevant variable is aggregate

e!ective labor used in the production of goods.At date t"0, we have K

#KH

"KM

#KM H

. With integration we have

M̧/KM

" M̧ H

/KM H

"( M̧

# M̧ H

)/(KM

#KM H

). Denote �

�"K

�/(K

�#KH

�) for

t"1,2,2 . Since, at date t"0, ¸" M̧

and ¸H

" M̧ H

are given we can write

M̧

KM

"�

¸

K

#(1!�)¸H

KH

.

Therefore, by the concavity of the production function:

Q#QH

K

#KH

"�F�1,

¸

K�#(1!�

)F�1,

¸H

KH�

(F�1, �¸

K

#(1!�)¸H

KH�"F�1,

M̧

KM�"F�1,

M̧ H

KH�.


Thus,

Q#QH

K

#KH

(

QM

KM

"

QM H

KM H

"

QM#QM H

KM

#KM H

.

However, since K#KH

"KM

#KM H

then Q

#QH

(QM

#QM H

. This im-

plies that (see (33)), ��[ y(�)#yH

(�)] d�(�)(��[y� (�)#y� H

(�)] d�(�). There-

fore (see (32)), K�#KH

�(KM

�#KM H

�. But, since aggregate e!ective labor supply

is una!ected by integration we have

Q�#QH

�K

�#KH

�

"��F�1,

¸�

K��#(1!�

�)F�1,

¸H�

KH��

(F�1,��¸

�K

�

#(1!��)¸H

�KH

��"F�1,

¸�#¸H

�K

�#KH

��.

Rewriting this expression:

Q�#QH

�(F(K

�#KH

�,¸

�#¸H

�)(F(KM

�#KM H

�, M̧

�# M̧ H

�).

Dividing both sides by (KM�#KM H

�):

Q�#QH

�KM

�#KM H

�

(F�1,M̧�# M̧ H

�KM

�#KM H

��"F�1,

M̧�

KM��"F�1,

M̧ H�

KM H��

"

QM�

KM�

"

QM H�

KM H�

"

QM�#QM H

�KM

�#KM H

�

.

Hence, Q�#QH

�(QM

�#QM H

�, which implies that K

�#KH

�(KM

�#KM H

�. This

process continues for all t"2,3,4,2 proving our claim thatQ

�#QH

�(QM

�#QM H

�. �

Proof of Proposition 6. We shall need the following two Lemmas.

Lemma 1. Consider two random variables XI and >I with values in [a, b], 0(a(b(R. Let XM "EXI , >M "E>I and dexne for �'0, Z(�)"(XI #�>I )/(XM #�>M ). Then, �'�K implies that Z(�K )<Z(�).

Denote by XI (>I 6a) the random variable XI conditioned on (>I 6a). This isXI if XI and >I are statistically independent.

Lemma 2. Let the nonnegative random variables XI ,>I ,XK satisfy:XI (>I 4a) dominates (in the second degree) XK (>I 4a) for all a, denoted

XI (>I 4a)'�XK (>I 4a), then Z"XI #>I '

�ZK "XK #>I .

Corollary 1. Under the assumptions of Lemma 2: XI #�>I '�XK #��>I for any

positive ��'�.


Proof of Lemma 1. Di!erentiating Z(�) with respect to � we obtain

Z�(�)"�XM

(XM #�>M )��>I (�)!>MXM

XI (�)�.Thus, for any �(�)"(>M /XM )X(�) we see that Z�(0 if >(�)(�(�) while

Z�'0 if >(�)'�(�). Moreover �Z�(�)�(�Z�(�K )� whenever >(�)O�(�) andZ�"0 as �(�)">(�). Thus, for any s70,

ProbZ(�K )6s�XI "�6ProbZ(�)6s�XI "�.

This inequality holds for any value of XI . This implies that for any s70,

ProbZ(�K )6s6ProbZ(� )6s.

Namely, Z(�K ) dominates "rst-degree stochastic dominance Z(�), hence itdominates in the second degree stochastic dominance, which proves the claim(see Atkinson, 1970). �

Proof of Lemma 2. Denote the c.d.f. for XI , XK , etc. by F�( ) ), F

�(( ) ). Then,

F�(s)"ProbXI #>I 6s

"Prob>I "� and XI 6s!� for 06�6s

"��

F��(�)F

�(s!�) d�.

Therefore, for �70,

��

[F�(s)!F

�((s)] ds

"��

�

�

F��(�) [F

�(s!� �>"�)!F

�((s!� �>"�)] d�ds

"��

��

�

�F��(�) [F

�(s!� �>"�)!F

�((s!� �>"�)] ds�d�

"��

F��(�)��

��

[F�(s �>"�)!F

�((s �>"�)] ds�d�

6��

F��(�) [H(�!� �>"�)!HK (�!� �>"�)] d�40,

where H(r)"��F�(�) d�, and similarly HK (r) is de"ned; since it is given that

H(r)6HK (r). �


Proof of Proposition 6. Given the initial distributions and the conditionK

'KH

we obtained earlier that for all t, t"1,2,32, we have: K

�/¸

�'KM

�/ M̧

�and KH

�/¸H

�(KM

�/ M̧

�. Thus, w

�/(1#r

�) declines while wH

�/(1#rH

�) increases after

the capital market integration. Using Eq. (39) for t"0, sinceb��

(�)"bM��

(�), h(�)"hM

(�) and �

/(1#r

)'��

/(1#r�

) we obtain by

Lemma 1 that y�(�)<y

(�). Now, we shall use Lemma 2 and Eq. (39) to obtain

by induction that y��<y

�and w

��/(1#r

��)'w�

��/(1#r�

��) imply that

y��

<y��

(�). Thus, capital market integration results in more equal distribu-tion of incomes in all coming generations in the domestic country.Now we shall use wH

�/(1#rH

�)(w� H

�/(1#r� H

�) for all t in the above proof to

derive that yH(�)<y� H

(�). Again by induction if yH

�(�)<y� H

�(�) by Eq. (39) and

Corollary 1 we obtain that

yH�(�)#

wH��

1#rH��

(1!��

)��

[h(�)]��

<y� H�(�)#

w��

1#r��

(1!��

)��

[h(�)]��.

Hence, yH��

(�)<y� H��

(�). �

Proof of Proposition 7. (a) As before K'KH

implies that w

/(1#r

)'

wH/(1#rH

) hence from (39) for t"0, using Corollary 1 in the appendix

we derive that y� H(�)<y

(�). Now, we can use Eq. (38) (for t"0) to obtain by

Corollary 1 in the appendix, that yH�<y

�. This process can be continued

by induction since w�/(1#r

�)'wH

�/(1#rH

�) for all t51. Assume that yH

�<y

�.

We apply now: h�(�)"hH

�(�) for all t and �

�"�H

�"e

�"eH

�(which implies that

��"�H

�for all t). Again, Corollary 1 in the appendix is applied to the expres-

sions of y��

(�) and yH��

(�) in (39) to derive that yH��

<y��

, which completesthe induction step.(b) Assume that capital markets integration is introduced at the outset of

period 0. As a result the factor price ratios are equated in the two countries, i.e.,w��/(1#r�

�)"w� H

�/(1#r� H

�) for all t. Given that b

(�)&bH

(�) and h

(�)"hH

(�)

we obtain that yH(�)&y� H

(�). By Eq. (39), since �

�"�H

�for all t, we obtain

y��&y� H

�. Again by induction we prove that y�

�&y� H

�for all t'1. �

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