THE ECONOMIC RECORD. VOL. 73. NO. 221. JUNE 1997. 1X-124

International Labour Migrations and the Pseudoconvergence of National Living Standards*

HARRY CLARKE School of Business, La Trobe University,

Bundoora, Victoria 3083

International labour immigrations between competitive econo- mies promote divergence in international living standards though conventional per capita income measures suggest Convergence. Observed convergence due to such immigrations is therefore a pseudoconvergence. Pseudoconvergence arises regurdless of good and productive factor numbers but need not arise if competitive imperfections arise from increasing returns or sticky real wages.

I Introduction The contribution of trade and factor mobility to

international living standard convergence has been much discussed. A consequence of factor price equalization in Heckscher-Ohlin-Samuelson trade theory is that, under certain conditions. by equal- izing factor prices, trade promotes income equal- ity: see Samuelson (1948). (1949). Trade based on factor endowments intensifies demand for rela- tively abundant factors and. through import substitution for domestic outputs, diminishes demands for scarce factors. This promotes factor return equalization and hence international (per capita) income equality.

International factor flows promote equality of factor returns more directly. Labour migrates from low to high wage countries fostering international wage equality. Capital flows, by promoting a single international capital market. encourage the equality of capital returns.

The dominant view is, therefore, that factor flows will accelerate trade-based convergence by generating additional pressures toward equaliza- tion of factor returns and incomes. This view is implicit in literature concerned with international convergence (Gerschenkron ( 1962). Maddison (1982). Barro and Sala-i-Martin ( 1992)) and has

* While I thank two anonymous referees for their comments. the views expressed here are my own.

been the subject of empirical tests on the effects of factor mobility on regional convergence in Quah ( 1994). Indeed Lucas ( 1988) takes i t as self- evident that international trade will make econo- mies converge and that this process is accelerated by factor flows. The difficult issue for Lucas was to explain why divergence in living standards, due to persistent growth differences, might ever occur:

In the absence of differences in pure tech- nology then. and under the assumption of no factor mobility, the neoclassical model predicts a strong tendency to income equality and equal- ity in growth rates, tendencies we can observe within countries and, perhaps within the wealth- iest taken as a group, but which simply cannot be seen in the world at large. When factor mobility is permitted, this prediction is power- fully reinforced (op. cit. pp. 15- 16).

This last clause seems to be the conventional wisdom on the effects of factor mobility on inter- national income convergence. This paper ques- tions this presumption and makes a contrary claim with respect to labour immigrations. Provided markets are competitive we show that when labour immigration effects are assessed using con- ventional national accounting procedures they provide a false indication of convergence of inter- national living standards. Real living standards

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1997. The Economic Society of Australia. ISSN 0013-0249.

I997 LABOUR MIGRATIONS AND CONVERGENCE 121

diverge with such migrations though measured per head incomes converge. Such apparent conver- gence is therefore a pseudoconvergence.

Section I1 below models the pseudoconvergence finding in a simple setting. Section 111 provides a graphical and numerical illustration of the phe- nomenon. Section IV discusses extensions and limitations of the basic result and makes some final remarks.

II The Model To analyze the rationale for pseudoconvergence

consider two countries ( I . 2) each producing output in quantities Y , and Y2 using (possibly dif- ferent) though nonincreasing-returns-to-scale technologies F , ( L , , K , P , ) and F2(L2.K2.R2). The Li. Ki and Ri ( i = 1.2) refer to respective national stocks of labour, capital and a vector of other internationally non-traded factors while F,. F2 are the respective production functions. There can be any pattern of (perhaps restricted) international trade in outputs between countries but:

a) Country 2 is 'developed' and Country I 'developing' in the sense that wages and per capita incomes are initially lower in I than in 2; b) labour migration occurs purely in pursuit of higher wages: c ) Country 2 maintains higher wages by a restrictive migration quota; d) capital is non-traded internationally and immigrants from I own none of 1's capital; e) all commodity and factor prices are flexible so that, within each economy, there is instantaneous adjustment to full employment of all resources.

Assumption a) is plausible if not inevitable-it is possible for 2 to have higher wages than 1 but lower per capita incomes, however this is empir- ically uninteresting-low income countries are invariably low wage countries. Assumption b) is basic to economic theories of immigration. Assumption c) is restrictive but provides a base for assessing impacts of induced capital flows on the welfare implications of labour migrations-a generalization discussed below. Assumptions d) and e) are also restrictive but the implications of relaxing them easy to establish. This framework is standard in economic analyses of labour migra- tions: see Berry and Soligo (1969), Bhagwati and Srinivasan ( 1983, chapter 29).

Suppose Country 2 partially relaxes its migra- tion quota and admits AL immigrants from Country I . By 'partially' we mean the relaxation is insufficient to generate wage equalization between I and 2. Then country 2's labour force

rises to L + AL. and 1's falls to L - AL with other factor stocks remaining as before. What are the welfare effects of this change?

Because Country 2 has more labour its aggre- gate income rises while its wages fall. Standard theory however shows that residents pre-existing in 2 before the migration are now better off in income terms. The gains they derive on their fixed assets exceed their wage losses: see Berry and Soligo ( I 969). Migrants are unambiguously better off because they now gain higher wages and originally owned no other factors of production.

Note however that, if the labour force in Country 2 rises, output there increases less than proportionately since 2's technology is non- increasing returns. Thus income per head in 2 falls as its workforce expands though both preexisting residents and new migrant arrivals are better off. This is an instance of Parfit's (1984) mere addi- tion paradox-the introduction of additional people has not inflicted Pareto losses on any group (migrants or original residents) but average economy-wide income falls.' The paradox was originally designed to illustrate a counterintuitive consequence of using average utility to assess population changes. The paradox was Seen LS

something pathological that established the inad- equacy of using avenge utility to indicate welfare consequences of population change. This paradox, however, always arises in the standard economic analysis of immigration impacts: see Clarke ( 1995).

In Country I reverse changes occur. Residents left after the emigration are worse off for Berry and Soligo reasons but now, since only a single input has been withdrawn. aggregate output falls proportionately by less than the workforce decrease. Per capita income in I rises although citizens in I are worse off in income terms.

Note that in this setting wage convergence does occur-wages rise in I and fall in 2. Wages are, however, only one component of income and. by themselves. an inadequate welfne indicator. Use of unadjusted per capita incomes. however, raises its own problems. Per capita incomes fall in 2 and rise in 1 suggesting that international income con- vergence has occurred. But the welfare of both immigrants and original residents in 2 rises with

'This paradox shows why i t is invalid to explicitly evaluate the welfare consequences of international labour migrations using per capita Millian criteria as in Quibria (1990).

I22 ECONOMIC RECORD JUNE

migration while the welfare of those not migrating from 1 falls so there is international welfare diver- gence. To summarize: Proposition: With assumptions a) to e) labour immigrations between competitive open econo- mies imply convergence of measured GNP per head across economies though there is (as a con- sequence of these immigrations) invariably welfare divergence.

Thus such income convergence is a pseudocon- vergence since it does not imply living standard convergence. To the contrary, migration increases welfare inequality even though measured per capita incomes converge. It is therefore mislead- ing to assume that, because wages tend to equality with international migration, the same is true for welfare measured by per capita income-under standard competitive assumptions this is not so.

Ill A Graphical and Numerical Illustration The preceding argument can be illustrated using

an adaptation of the one good-two country model of Bhagwati and Srinivasan (1983, p. 305)-an adaptation allowing for incomplete labour market liberalization. Let output of Country I (the 'UK') be Y, and output of Country 2 ('Australia') be Y2. Suppose both economies are competitive with those migrating from I owning no capital any- where. Consider Figure 1 which graphs labour's marginal product in Countries I and 2 given respective labour forces.

Here 0 I P denotes the initial workforce of 2 and 02P that for I . The respective marginal products are MP,. MP, with initial wages being w , , w2 in 1. 2 respectively. When a migration PP occurs from I to 2 wages rise to wI in 1 and fall to w2 in 2--so wage convergence occurs. Looking at areas under the respective marginal product curves, incomes accruing to original residents of 2 rise by area A while those attributable to non- emigrating residents of I fall by area E. Those migrating to 2 are better off because their wages rise and they own no other inputs. Thus. those finally living in Country 2 are better off while those finally living in Country I are worse off. There is welfare divergence. With diminishing marginal products the observed rise in income in 2 (inclusive of newcomers) is less than propor- tionate to its increased workforce while the observed fall in income in I (accruing to those living there) is less than proportionate to its work- force decline. Thus observed per capita incomes fall in Country 2 and rise in Country 1. Thus there

FIGURE I

Pseudoconvergence in a Two-Country World

d

4'

wl

01 P P is measured income convergence. Thus pseudo- convergence occurs.

Take a numerical instance. Suppose, for the UK, Y, .=. 106L,.6 K , . 2 with its population of 1.05 million consisting of one million workers (who own no capital) and 50000 capital and resource owners who are not simultaneously workers. Suppose there is a capital stock of 50 OOO machines and a (fixed. nondepletable) resource stock of 1. Assume for Australia, Y2 = lo6Ly.6 K2.2 R2.2 with population of 105 OOO and capital stock of 50000 machines and a (fixed. nondepletable) resource stock of 4. With factors paid their marginal products the UK real wage is $20 794 and the Australian real wage $68 922. If 50 OOO emigrants leave the UK for Australia the UK real wage increases to $21 225 and the Aus- tralian wage falls to $58 603. Tables 1-3 show the effect of this emigration on per capita incomes when averages are calculated, respectively, for people currently living in a country, those origi- nally living in a country who remain there and finally for those who originally lived in the country.

These tables illustrate points made so far. Table 1 shows that labour immigration causes measured per capita income convergence-meas- ured UK per capita incomes increase as a pmpor- tion of Australian incomes. Table 2 shows that, including only non-migrating populations, there is per capita income divergence not convergence. Those who migrated are better off since their wages rise and they own no capital. This shows that i t is entirely misleading to infer from Table I that living standards in the two countries have converged. Both immigrants and pre-existing res-

I997 LABOUR MIGRATIONS AND CONVERGENCE I23

TABLE I Per Capita Incomes (Measured Actual)

UK Australia Ratio UK/ Australia

Pre-Immigration 33 007 109 400 ,302 Post-Immigration 33 607 94 521 .356

TABLE 2 Per Capita Incomes of Non-Migraring Citi:ens

UK Australia Ratio UW Australia

Pre-Immigration 33 617 109 400 ,307 Post-Immigration 33 607 I 1 I 624 .30 I

T A e L E 3 Per Cupiru Incomes of Originul Residrnts

U K Australia Ratio UK/ Australia

Pre-Immigration 33 007 109 400 ,302 Post Immigration 34 797 I I I 624 .312

idents in the destination economy are better off while non-emigrants in the source country are worse off. Table 3 shows that if emigrants com- pensate those left behind in the source country? by sharing the income gains they make with them, then there is convergence in the sense that per capita incomes converge.

IV Generalizations and Final Remarks How general is the pseudoconvergence argu-

ment? The assumption that countries produce only a single output is for simplicity only. Pseudocon- vergence arises with arbitrarily (finitely) many goods and productive factors3 even should markets have monopolistic elements: proof uses general 'gains from trade' arguments adapted for factor flows: see Kemp (1993). The core insight is that, subject to standard assumptions made by

'Or equivalently if those left behind display altruism

%ovided there exists at least one fixed factor. towards those departing.

Kemp, with migration from Country I . possible internal 'gains-from-trade' decline there while pre-existing residents of Country 2 have expanded trade opportunities because of the new migrant presence. With non-increasing returns, output losses in the immigrant source Country I are less than proportionate to population loss. The output gains in the migration destination Country 2 are less than proportionate to workforce gains again due to non-increasing returns." Thus the result is more general than exposited.

There are three issues however which make the analysis more intricate: (i) migrant holdings of human or nonhuman capital; (ii) increasing returns and (iii) factor price (for example wage) rigidity in one or both economies. These issues do modify the argument.

(i) If migrants own freely-internationally-traded factors, for example. capital when there is perfect capital mobility, then the above conclusion remains valid because prices of such factors do not then change when migration occurs. Capital inflows accompanying migration lead directly to corresponding o ~ t f l o w s . ~ Suppose migrants own internationally nontnded factors such as human capital. Then the earlier pseudoconvergence con- clusion remains valid provided Country 2's post- migration human capital to labour endowment ratio is not higher than pre-migration. This is so whenever migrants bring in quantities of other factors not exceeding the average resident endow- ment: see also Clarke (1995). If migrants bring with them a package of factors equal to the average resident endowment then, with constant returns-to-scale. output per head does not change.

4~herefore per capita output in the source counuy rises even though welfare falls there while per capita output in the destination country falls even though there are welfare gains to pre-existing residents and newcomers.

5Suppose capital inflows are induced by labour immi- grations rather than being brought in by immigrants. This occurs if labour inflows, by reducing wages. make investment in immigration-destination countries more attractive. Such inflows provide gains from trade for standard reasons (see e.g. Clarke 1995) but these gains now accrue to the augmented society inclusive of migranu. This acts to raise income per head in desti- nation countries and to reduce it in immigrant-source countries. This reduces pseudoconvergence bias but to an extent depending on the degree of capital mobility and the scale of the initial labour migration. Measured income per head remains a biased assessor of average welfare but the extent of bias is reduced.

124 ECONOMIC RECORD JUNE

Note that issues of how residents spend the income they receive from their factor endowment package is irrelevant to the qualitative implica- tions of gains-from-migration theory-as Kemp (1993) shows, profits can be repatriated to source countries or spent locally. Provided that there are non-increasing returns to scale, the same general welfare implications hold.

(ii) With increasing returns in one or both econ- omies labour migration can possibly (not inevi- tably) lead to income divergence reflecting a growing real disparity in living standards. Pseudo- convergence of incomes need not be observed- real divergence can arise reflecting reduced inter- national welfare equality. Conversely, observed divergence of per capita incomes with migration is consistent with increasing returns.

(iii) With unemployment in Country 2 and migrants drawing sustenance from social security coffers, a decline in per capita incomes will be observed with migration which reflects a decline in per capita incomes of the pre-existing residents of 2. That migrants voluntarily come suggests they are better off. If there is simultaneously unemployment in Country I due to an inflexible wage, then living standards can improve there with emigration while on avenge they fall in 2. Again pseudoconvergence is not inevitable-all original residents of 1 are now better off while original residents of 2 are worse off by having to fund the social security benefits of additional unemployed. Convergence is observed reflecting real improvements in international welfare equality.

Without such imperfections, factor price convergence will be accompanied by real per capita income pseudoconvergence with labour immigration.

These findings suggest a need for caution in accounting for economic welfare change in an economy subject to immigration (or general population growth). Note however that standard Heckscher-OhlinSamuelson factor price equal- ization and income convergence conclusions are

unaffected by the above analysis. With cornmod- ity trade, convergence obtains because all factors are indirectly internationally traded when goods are traded. Hence trade liberalization does not promote pseudoconvergence even though liberal- ization of international labour markets, by pro- moting living standard divergence, does.

REFERENCES

B u m , R.J. and Sala-i-Martin, X. (1992). 'Regional Growth and Migration: A Japan-United States Com- parison'. Journal of thr Japanese and Intrrnutionul Economies 6. 4. 3 12-46,

Berry, R. and Soligo. R. (1969). 'Some Welfare Aspects of International Migration'. Journal of Politicul

Bhagwati. J.N. and Srinivasan, T.N. (1983). Lectures on international Trade, MIT Press, Cambridge.

Clarke, H.R. ( 1995). 'International Labor-cum-Capital Migrations: Theory, Welfare Implications and Empir- ical Evidence', Oprn Economies Rrvirw 6, 3 2 3 4 .

Gerschenkron. A. ( 1962). Economic Backwardnrss in Hisroricol Perspective, Harvard University Press, Cambridge. Massachusetts.

Kemp, M.C. (1993). 'The Welfare Gains from Inter- national Migration', Krio Economic Studies 30 ( I ) ,

Lucas. R.E. ( 1988). 'On the Mechanics of Economic Development'. Journal of Monetary Economics 22. 342 .

Maddison, A. ( 1982). Phases of Capitulisr Devrlop- ment. Oxford University Press, Oxford.

Parfit. D. (1984). Reasons and Persons, Cambridge University Press. Cambridge.

Quah, D. (1994). 'Convergence Across Europe', London School o f Economics, mimeo.

Quibria. M.D. (1990). 'On International Migration and the Social Welfare Function', Bulletin of Economic Research 42, 141-53.

Samuelson. P.A. (1948). 'International Trade and the Equalisation of Factor Prices', Economic Journal 49, 33641.

Samuelson. P.A. ( 1949). 'International Factor-Price Equalisation Once Again', Economic Journal 59,

Economy n. 778-94.

1-5.

I8 1-97.