- Email: [email protected]
Foreign competition, immigration and structural adjustment
Journal
of International
Economics
FOREIGN
14 (1983) 381-394.
North-Holland
Publishing
COMPETITION, IMMIGRATION STRUCTURAL ADJUSTMENT
Company
AND
Andrk SAPIR* University of Wisconsin-Madison, Madison, WI 53706, USA CEME, Received
March
University of Brussels, Belgium
1982, revised version
received
November
1982
The paper uses the Ricardo-Viner (R-V) model to investigate the relationship, in a capitalabundant economy, between trade competition and immigration. In doing so, it derives new results for the R-V model, especially on the welfare implications of migration with and without an initial tariff.
1. Introduction During the 1960s and 1970s employment of foreign labor became an important aspect of Western European economies. The facts suggest that immigration policies might have been used by Western European capitalists in structurally weak sectors as a means of remaining competitive. Indeed, one way for industries to resist the competition from less-developed laborabundant countries is to try to reduce their labor costs. This paper therefore investigates the potential relationship, in a capital-abundant economy, between trade competition and immigration from labor-abundant countries. Alternative trade models may be utilized towards this end: the HeckscherOhlin-Samuelson model, the Haberler-Brecher model with sticky wages, or the Ricardo-Viner sector-specific model. While Bhagwati (1982) has used these models in his analysis of the choice between protectionism and labor immigration as a response to shifting comparative advantage, he concentrated his main analysis on the Heckscher-Ohlin-Samuelson (H-O-S) model, whereas here we analyze in greater depth the Ricardo-Viner (R-V) model.’ *The paper was originally written while I was visiting the University of Leuven. I am grateful to Jagdish Bhagwati, Robert Baldwin, Jan Gunning, Rachel McCulloch, Francisco Rivera-Batiz and Ear-yiu gong for helpful discussions and suggestions. I also wish to thank workshop participants at the University of Boston, Brussels, Leuven, Minnesota, Wisconsin and the World Bank for useful comments. ‘The work on this paper was finished before Bhagwati’s (1982) contributions came to the author’s attention. 0022~1996/83/$03.00
0
1983 Elsevier Science Publishers
B.V. (North-Holland)
382
A. Sapir, Foreign competition
and immigration
The plan of the paper is as follows. In section 2 we briefly present the assumptions of the R-V model. In section 3 we examine the interaction between foreign competition and immigration, as well as their effects on output levels and factor rewards. In addition, we take a look at the impact of labor migration on the process of structural adjustment which takes place in response to shifting comparative advantage. Section 4 analyzes the welfare implications of the results of section 3. In section 5 we extend some results of section 4 to the case of a tariff-ridden economy. The final section of the paper suggests some possible avenues which appear to warrant further research.
2. Equilibrium in the RicardwViner
model
Consider an economy producing two goods, X and Y with two factors of production, labor L and capital K. Perfect competition prevails and factors are fully employed. The economy is assumed to be incompletely specialized. All prices are expressed in terms of good E; the numeraire. In addition, under the small country assumption, the domestic commodity price ratio P is equal to the international terms of trade, assuming there are no tariffs. The production functions are given by:
X = W, , K,),
(14
Y = G(L,, KY).
(lb)
These functions are assumed to be linear homogeneous, twice differentiable with positive and declining marginal physical products. Initially, the economy is in long-run equilibrium, with both labor and capital fully mobile between sectors. Therefore, for each factor, the value of the marginal product is equalized between sectors. This is, indeed, the case of the Heckscher-Ohlin-Samuelson model. Given the technology, factor endowments E and K, and relative prices PO, the production equilibrium is at Qk on the long-run production possibilities frontier (PPF) denoted by MM’ in fig. 1. It is assumed that X is L-intensive and Y K-intensive, and that the country is K-abundant. Therefore, the consumption equilibrium is above Qk on the budget line passing through Qi, i.e. Y is the exportable and X the importable industry. ‘Following Mayer (1974), we draw a short-run PPF, denoted by NN’, which is tangent to MM’ at Qt. This corresponds to the case of sectorspecific capital. Equilibrium in the labor market can then be written: PF, = w,
(24
A. Sapir, Foreign competition
GOOD X
383
and immigration
i
I
I
I
M N
N’
0
M’
GOOD Y
Fig. 1.
GL=w, L,+L,=L,
(24
where w denotes the wage rate expressed market equilibrium is given by:
in terms
of good
E: The capital-
PF, = rx,
W-4
where R, and R, are the amounts the long-run equilibrium Qk, and expressed in terms of good Y; This K, and KY) Ricardo-Viner model.
of capital employed in each industry in and rr are their respective returns case corresponds to the three-factor (L, In this model, a change in the terms of rx
A. Sapir, Foreign competition and immigration
384
trade, a change in factor endowments or any other exogenous disturbance will have an initial short-run impact with fixed inter-sectoral allocation of capital. Only with the passage of time will there by a reallocation of capital between sectors that will lead to a new long-run equilibrium. The solution of the model may also be depicted with the help of fig. 2. In the left part of this figure, the initial equilibrium is shown as A, which represents the intersection of the original value marginal product of labor (VMPL) curves for sectors X and Y This intersection determines the initial wage rate as well as the allocation of labor between the two sectors. For expository purposes it will also prove convenient to depict the factor-price frontier (FPF) for sector X in the right part of fig. 2. Given the wage rate, the capital rental in sector X is determined via the equilibrium point B, on the factor-price frontier. AL
w
W
1 X
0’
0,
AL
TX
-Lx-
-L,Fig. 2.
3. Foreign competition
and immigration
Let us assume that, in the first phase, the industrialized (capital-abundant) home country is disturbed from its long-run equilibrium position Qh by a competitive pressure from (labor-abundant) newly industrializing countries.’ As previous authors have shown, with sector-specific capital, the shift in comparative advantage against the Lintensive sector X (i.e. dP < 0) produces the following effects: (a) 011 output: a decrease (increase) in the production of good X (good Y); and (b) on factor rewards: a decrease in wages expressed in terms of good Y (i.e. w) and an increase in wages expressed in terms of good X (i.e. w/P), and a decrease (increase) in capital rentals expressed in terms of either good in sector X (sector Y).3 *This pressure might result from factors %ee Mayer (1974) and Mussa (1974).
like skill accumulation
and know-how
acquisition
A. Sapir, Foreign competition
and immigration
385
The output effect is indicated in fig. 1. The change in the terms of trade from P, to P, (Pr
dL,
dY = (- PF,,G,/A)
(4a)
dL,
(4b)
where A = - (PF,, + G,,). Combining s=
(4a) and (4b), the slope of the RS-locus can be written GLLFL -----0. PFLLGL
4The relaxation JIE
G
of both of these assumptions
as follows:
(5) will be discussed
below
A. Sapir, Foreign competition and immigration
386
Differentiating S with respect to L indicates that the slope of RS may be increasing or decreasing for different values of L. Therefore, in general, it may only be stated that RS is monotonically increasing. If the production function in both sectors is Cobb-Douglas, then (5) becomes:
s=
u-w, P(l -YL’
where y and 6 are the respectively. Differentiating dS
(l-6)(y--6)~
dL=
P(l-y)dLC
distributive shares of labor S with respect to L yields:
in sector
X
and
E:
’
which is always positive (negative) if sector X is L-intensive (K-intensive). Therefore, with Cobb-Douglas production functions, RS is a convex increasing curve in our case. Returning to our main argument, we observe that immigration increases the rates of return to capital in both sectors by lowering wage rates. Therefore, capitalists should always favor and workers always oppose an inflow of foreign labor. Accordingly, if we postulate that the government is dedicated to preserving ‘social justice’, we should generally find that it is reluctant to grant capitalists freer access to immigrant labor. Nevertheless, the attitude of the government might be affected by the pressing demand of the capitalists in the labor-intensive sector whose income suffers from falling terms of trade. However, in order to minimize the ensuing wage cuts, the government would probably wish to adopt what we will call a ‘compensating immigration policy’. Such a policy would involve delivering the exact number of labor permits required to restore the economic situation of capitalists in the structurally weak sector at the initial level which prevailed before the change in the terms of trade. For the moment, we will make the simplifying assumption that the economic situation of the capitalists is equivalent to their income. 3.1. The short-run equilibrium with compensating immigration Let us now combine phase one - the change in the terms of trade - and phase two the compensating immigration policy and compare the resulting new short-run equilibrium with the initial equilibrium Qi. Two cases can be distinguished according to whether we express the capitalists’ income in terms of good X (i.e. rx/P) or good Y (i.e. rx). We begin with the former case.
A. Sapir, Foreign competition
and immigration
387
We differentiate totally system (2) along with eq. (3a), holding K, and K, constant; moreover, we set d(r,/P) =0 in accordance with the governmental policy of exact compensation for capital-earners in sector X. We obtain a system of five equations in five unknowns (dL,, dL,, dL, dw and dr,). Solving for dL, and dL, yields dL,=O, dLr> 0, and therefore dX =0 and dY > 0. Consequently, the new short-run equilibrium, Qz, lies in fig. 1 on RS at the same level as Qt. The number of immigrants is given by dL=dL,. Moreover, the policy yields a loss in income for workers as dw 0, i.e. at Q: we have rr > rx. We could similarly characterize Q:, the short-run equilibrium corresponding to the case where the compensating immigration policy is aimed at restoring the income of sector X capitalists measured in terms of good Y However, it will prove more useful to examine this case with the help of fig. 2.5 The change in comparative advantage against sector X reduces P and shifts sector X’s value marginal product of labor schedule proportionately from VMPL$ to VMPL;. The corresponding schedule for sector Y is unaffected. At the same time, there is a downward shift in the factor-price frontier for sector X from FPF$ to FPF;. Therefore, starting from the equilibrium position (A,,&,), we move to a new equilibrium (A,,B,) with a lower wage rate and a lower rental rate for sector-X capitalists, both expressed in terms of good Y In view of this situation, our policy implies the immigration of labor so as to compensate the capitalists’ income in sector X. In the right part of fig. 2 this policy means a shift along FPF$ from B, to B,, where rx is back at its original level. Using the left part of fig. 2, it is now easy to determine AL, the amount of foreign labor required to achieve compensation. This is done by shifting VMPL, uniformly to the left up to A, where the equilibrium wage rate is the same as at B,. Thus, AL is given by A,H. Comparing (A,,B,) with (A,,&), we find that employment and output have increased in both sectors. In addition, the wage rate has fallen in terms of both goods while rental rates have all increased except, obviously, for rx which has remained the same. These results may be summarized as follows: Proposition I. Consider a situation where, with short-run capital specificity, the returns to capital fall in the labor-intensive importable sector due to a shift in comparative advantage. One can always design an immigration policy that will compensate the capitalists in that sector for their loss of income. Such a policy will increase output in the capital-intensive sector and either increase or keep constant output in the labor-intensive sector. 5The diagrammatic
treatment
was partly
suggested
by Kar-yiu
Wong.
388
A. Sapir, Foreign competition
and immigration
3.2. Structural adjustment with compensating immigration Over time, the rental differential between sectors that prevails at Q? will induce a reallocation of capital from sector X to sector I: Eventually, a longrun equilibrium with immigration will be reached at Qt. This equilibrium point lies on the Rybczynski line RL which originates at Qi, the long-run equilibrium with no immigration corresponding to the price ratio Pi. The trajectory of the economy from Qh to Qi is indicated by the darker line in fig. l6 With no immigration allowed, the shift in comparative advantage would have implied a process of structural adjustment involving a continuous decrease in the production of good X and increase in the production of good I: Indeed, in a first stage the economy would have shifted from Qf; to Qs, along with intersectoral labor migration and capital rigidity. Thereafter capital would have followed the same path as labor, moving from sector X to sector Y and output would have gone from Qf to Qi. The adjustment process is somewhat different with the policy of compensatory migration. In this case, the economy first shifts from Qk to Qz along with the international labor migration and inter-sectoral capital rigidity. This implies an increase in the production of good Y and a constant level in the production of good X. From Q”, to Q$ there is then a reallocation of capital from sector X to sector Y implying a further increase in the production of good Y‘ and a decrease in the production of good X. Therefore, at Qi the production of good Y (good X) is necessarily larger (smaller) than at Qh. This change in the structure of production towards good Y is similar, although to a lesser extent, to what would have occurred if there had been no immigration. 4. Welfare considerations
In this section we examine what happens to welfare as we move first from Qk to Qy,then from Qf to Qs and finally from Q$ to Qi. For each of these three phases we distinguish between two cases. In the first one we assume that each of the three groups of factor owners - workers, capitalists in sector X, and capitalists in sector Y - has a distinct welfare function. In contrast, the second case postulates a unique welfare function for society as a whole. 4.1. Phase I: From Qk to Qs
With separate welfare functions, our previous discussion clearly indicates that the deterioration in the terms of trade against sector X generates a loss %
is left to the reader
to examine
the trajectory
that would obtain
via @i.
A. Sapir, Foreign competition
and immigration
389
(gain) for capitalists in sector X (sector Y). However, the situation of the workers is ambiguous since they lose in terms of good Y but gain in terms of good X. This ambiguity for labor (the fully mobile factor), which was first pointed out by Mussa (1974), will be further explored. Let us assume that the workers seek to maximize their welfare,
subject to their budget constraint: (9) where Cr and Cy are consumption of good X and Y; respectively, by the workers and Zw is their income. The first-order condition ZJy/ZJy = P and the budget constraint yield:
cy =aZW/P,
(loa)
c? = (1 - a)ZW,
(lob)
where c( is the share of their income which workers allocate to the consumption of good X.’ Differentiating totally (8), dividing through by LJy and using the first-order condition, one obtains after manipulations: dUW/Uy = L dw - C: dP = q(Zw/P) dP + (- cr)(Zw/P)dP,
(11)
where q is the elasticity of w with respect to P derived with L, K, and K, being held constant. Expression (11) indicates that the change in the workers’ welfare is the sum of two competing factors, each representing a different role played by workers in the economy. The first term, which is negative, indicates the loss for labor due to its status as a production factor. The second one, which is positive, reflects the gain of labor as a consumer. This result can be summarized as follows:’ Proposition 2. With sector-specijic capital, a deterioration in the terms of trade against the importable labor-intensive good improves (worsens) the welfare level of the workers if their consumption share of that good is larger (smaller) than the elasticity of their wage with respect to the terms of trade.g ‘Obviously, this share is constant only if we postulate a Cobb-Douglas utility function. ‘After this research was completed, it came to my attention that a similar result was derived earlier by R&in and Jones (1977). ‘Mussa (1974) has shown that 0 < q< 1.
A. Sapir, Foreign competition and immigration
390
In the case where we postulate a single welfare function for society as a whole, the shift in comparative advantage against the importable sector would necessarily improve welfare. This can be seen from fig. 1 by comparing the budget lines passing through Qk (for P = PO) and Qf (for P = PI),
4.2. Phase II: From Qs to Qs We begin by assuming that each of the three groups of factor owners has a distinct welfare function. For this case, the discussion of section 3 indicates that labor immigration benefits both groups of capitalists, but hurts the workers.” With a single welfare function for society as a whole, the national welfare level (defined over the pre-immigration home population) will generally increase with immigration unless there were no foreign workers originally and the number of immigrants is infinitesimal. This increase in welfare follows from the fact that, as we have seen in the previous section, an inflow of labor drives down the domestic wage rate. Indeed, let us write I as the national income of the host country: I=PX+Y-WE,
(12)
where E is the number of foreign workers from an infinitesimal change in I! that:
in the home
country.
It follows
(dl/dE) = P(dX/dLf) + (d Y/d,?!) - w - L!(dw/dE) = - L’(dw/dl!),
(13)
where the last step results from the fact that foreign labor is paid its marginal product. If there were no foreign workers originally (L! =O), then, with an initinitesimal change, we would have dI=O. In order to study the effect on welfare of a non-infinitesimal change in E, we turn to the left part of fig. 2. National income at A, (corresponding to Q$ is given by the combined area under both curves VMPL; and VMPL:. With the inflow of AL foreign workers, the equilibrium becomes A, and national income increases as the wage falls from w1 to w2.11 This increase is represented by the two shaded areas below the curves VMPL$ and VMPLF.
we.
“In our earlier discussion, assumedthat capitalists in sector X seek to maintain their economic situation as reflected by their income. More generally, we could consider that they are seeking to preserve their utility level Ux and set dUX=O. Using the budget constraint, this is equivalent to setting dr,=j?(r,/P)dP, where b is the share of their income which capitalists in sector X devote to good X. It can easily be shown that in this case we would obtain an intermediate situation between Qs and Q7. “I am grateful to Francisco Rivera-Batiz for drawing my attention to this important point.
A. Sapir, Foreign competition
and immigration
391
4.3. Phase III: From Q”, to Qi In this final phase toward the new long-run equilibrium, there is a reallocation of capital from sector X to sector I: This implies a loss (gain) for capitalists in sector Y (sector X), as well as a gain for labor. With a unique societal welfare criterion, it is clear that the move toward the long run may or may not be beneficial. Indeed, as Mayer (1974) has shown, the welfare level corresponding to Qs is necessarily inferior to that associated with Qf; the difference being the loss caused by the short-run capital specificity. On the other hand, as we have just seen, the welfare level at Qs will generally also be higher than at Qs. Therefore, since welfare levels at Qf and Qf: are identical, we cannot conclude anything about the relative desirability of Q$ and Q’;. However, if there were no foreign worker already in the country and the number of migrants is infinitesimal, then welfare levels are equal at Qs and Q”,, and Qi would unambiguously be superior to Q2. Finally, we compare the initial (Qf;) and final (Qi) equilibrium points. From the Stolper-Samuelson Theorem, we conclude that the welfare of workers deteriorates and that of capitalists improves as we move from Qk to Qf. Moreover, the welfare of each group remains the same along RL, and thus between Qf and Q$. When we consider national welfare, our previous results indicate that it improves from Qh to Qf and Q”,, and, possibly, further from Qs to Qi. 5. An important digression: Welfare considerations
in a tariff-ridden economy
In the previous section, we have seen that in phase II the national welfare level generally increases with immigration, unless there were no foreign workers already in the home country and the number of immigrants is infinitesimal. In addition, it was assumed that the home country is not tariffridden. An interesting possibility arises in the presence of an initial tariff. Let us assume that the labor-intensive importable sector (X) in the home country is protected by a tariff. As is well known, in this situation immigration would reduce national welfare if capital were freely mobile across domestic sectowl In this section we will show that, on the contrary, an inflow of labor into a tariff-ridden economy in which capital is sector-specific can be beneficial. There are two reasons for this: a positively-sloping short-run Rybczynski locus and a decline in the wage rate as foreign workers flow in. The former reason is valid for both finite and infinite changes, whereas the latter is effective for finite inflow or for infinite inflow and an initial presence of foreign workers. “See Bhagwati (1973) and Brecher and Diaz-Alejandro (1977). For further. discussion on the long-run welfare effects of various trade policies in the presence of foreign-owned factors of production, see Bhagwati and Brecher (1980) and Brecher and Bhagwati (1981).
392
A. Sapir, Foreign competition
and immigration
Let P* be the international (free-trade) price ratio. Assuming that the labor-intensive importable sector is protected therefore means P>P*. For simplicity, throughout the remainder of this section we will postulate infinitesimal changes while at the same time allowing for an initial presence of foreign workers.r3 We begin with the situation in which foreign workers are paid exclusively in terms of the exportable good I: The national income of the host country valued at international prices can be written: I* = PTX + Y - WE.
(14)
Differentiating (14) totally yields: (dI*/dLf) = P*(dX/dE) + (dY/dE) - w -E(dw/dLf) = P(dX/dZ.!) + (d Y/dLf)- w + (P* - P)(dX/dE)-
Lf(dw/dE)
= (P* - P)(dX/dE) - E(dw/dLf) 2 0,
(15)
where the first term is negative (since X increases along Rs) and the second is positive. On the other hand, if foreign workers were paid entirely in terms of the importable good X, we would have: I* = P*x + Y - (P*/P)wE,
(16)
and therefore, from an infinitesimal change in E, it follows that: (dl*/dI!) = P*(dX/dLf) + (d Y/d,!!) -(P*/P)w - (P*/P)E(dw/dI!) = (P* -P)[P(dX/dE)
- w]/P -(P*/P)E(dw/dE)
= (P* - P)( - d Y/dL!)/P - (P*/P)E(dw/dE) > 0,
(17)
where both the first (since Y increases along Rs) and second terms are positive. These results can be summarized as follows: Proposition 3. Within the R-V model, a host country protecting its importable sector might experience a welfare gain or loss from an inflow of foreign labor which receives its full (tax-free) marginal product. If workers are paid only in terms of the importable good there will be a gain; if they are paid ‘only in terms of the exportable good there might be either a loss or a gain. Moreover, these results hold regardless of whether the host country is labor- or capital-abundant. 13Hence, from the viewpoint
of the impact
on wages, this is equivalent
to finite changes.
A. Sapir, Foreign competition
and immigration
393
In addition, in the ‘absence of initial foreign workers (and with infinitesimal changes) immigration will be immiserizing when foreign workers are paid exclusively in terms of good I: Also, in this case it can easily be verified that I* would remain unaffected by the arrival of foreign labor if it consumed (or were paid in terms of) the two goods in the same proportion as it produces them. Finally, we briefly extend our analysis to deal with the effect of an inflow of foreign capital in a labor-abundant economy. Thus, let the home country be labor-abundant, exporting the Lintensive good X and importing the Kintensive good Y Specialization is incomplete and the K-intensive sector is protected by a tariff. To begin with, suppose that there is an inflow of foreign capital in the protected sector I: With short-run capital-specificity, we have dX < 0, d Y > 0 and dr, < 0. Therefore, along the lines of the above discussion we have that the change in national income at international prices due to an infinitesimal capital inflow with full (tax-free) payments of foreign profits in terms of either goods is negative (positive or negative) in the absence (presence) of initial foreign capital. On the other hand, if the inflow of foreign capital took place in sector X, one would have dX >O, dY
6. Concluding remarks There are several directions which could be explored in further research. First, we could distinguish between skilled and unskilled labor and allow for the immigration of unskilled labor to be sector-specific. A further addition to the specification of the labor market could be the introduction of a discriminatory mechanism implying that only domestic workers are allowed to move across sectors or up the skill ladder.14 The latter point raises the question of dynamic extensions of the model in terms of accumulation of either physical or human capital. Finally, except for a brief comment, we have exclusively focused our attention on labor immigration. However, in our model the same effects that were obtained with an inflow of foreign labor could have been reached instead with an outflow of capital from the injured labor-intensive sector.15 Indeed, a yet unexplored facet of the R-V model is the fact that it naturally suggests the possibility of intra-sectoral international movements of capital. IdPorter (1978) discusses a similar situation for the Southern African-type economy. 15For an illuminating discussion of the choice between labor and capital mobility good two-country model, see Bhagwati and Srinivasan (1983).
in a one-
394
A. Sapir, Foreign competition
and immigration
References Bhagwati, J.N., 1973, The theory of immiserizing growth: Further applications, in: M.B. Connolly and A.K. Swoboda, eds., International trade and money (University of Toronto Press, Toronto) 45-54. Bhagwati, J.N., 1982, Shifting comparative advantage, protectionist demands, and policy response options, Paper presented at the Ford Foundation-N.B.E.R. Conference on Import Competition and Adjustment: Theory and Policy, 8-11 May 1980, Cambridge, Massachusetts; in: J. Bhagwati, ed., Import competition and response (Chicago University Press, 1982). Bhagwati, J.N. and R.A. Brecher, 1980, National welfare in an open economy in the presence of foreign-owned factors of production, Journal of International Economics 10, 103-116. Bhagwati, J.N. and T.N. Srinivasan, 1983, On the choice between capital and labour mobility, Journal of International Economics 14, this issue. Brecher, R.A. and J.N. Bhagwati, 1981, Foreign ownership and the theory of trade and welfare, Journal of Political Economy 89, 497-511. Brecher, R.A. and C.F. Diaz-Alejandro, 1977, Tariffs, foreign capital and immiserizing growth, Journal of Political Economy 82, 317-322. Mayer, W., 1974, Short-run and long-run equilibrium for a small open economy, Journal of Political Economy 82, 955-967. Mussa, M., 1974, Tariffs and the distribution of income: The importance of factor specificity, substitutability, and intensity in the short and long run, Journal of Political Economy 82, 1191-1203. Porter, R.C., 1978, A mode1 of the Southern African-type economy, American Economic Review 68, 743-755. Ruffin, R. and R.W. Jones, 1977, Protection and real wages: The neo-classical ambiguity, Journal of Economic Theory 14, 337-348.
of International
Economics
FOREIGN
14 (1983) 381-394.
North-Holland
Publishing
COMPETITION, IMMIGRATION STRUCTURAL ADJUSTMENT
Company
AND
Andrk SAPIR* University of Wisconsin-Madison, Madison, WI 53706, USA CEME, Received
March
University of Brussels, Belgium
1982, revised version
received
November
1982
The paper uses the Ricardo-Viner (R-V) model to investigate the relationship, in a capitalabundant economy, between trade competition and immigration. In doing so, it derives new results for the R-V model, especially on the welfare implications of migration with and without an initial tariff.
1. Introduction During the 1960s and 1970s employment of foreign labor became an important aspect of Western European economies. The facts suggest that immigration policies might have been used by Western European capitalists in structurally weak sectors as a means of remaining competitive. Indeed, one way for industries to resist the competition from less-developed laborabundant countries is to try to reduce their labor costs. This paper therefore investigates the potential relationship, in a capital-abundant economy, between trade competition and immigration from labor-abundant countries. Alternative trade models may be utilized towards this end: the HeckscherOhlin-Samuelson model, the Haberler-Brecher model with sticky wages, or the Ricardo-Viner sector-specific model. While Bhagwati (1982) has used these models in his analysis of the choice between protectionism and labor immigration as a response to shifting comparative advantage, he concentrated his main analysis on the Heckscher-Ohlin-Samuelson (H-O-S) model, whereas here we analyze in greater depth the Ricardo-Viner (R-V) model.’ *The paper was originally written while I was visiting the University of Leuven. I am grateful to Jagdish Bhagwati, Robert Baldwin, Jan Gunning, Rachel McCulloch, Francisco Rivera-Batiz and Ear-yiu gong for helpful discussions and suggestions. I also wish to thank workshop participants at the University of Boston, Brussels, Leuven, Minnesota, Wisconsin and the World Bank for useful comments. ‘The work on this paper was finished before Bhagwati’s (1982) contributions came to the author’s attention. 0022~1996/83/$03.00
0
1983 Elsevier Science Publishers
B.V. (North-Holland)
382
A. Sapir, Foreign competition
and immigration
The plan of the paper is as follows. In section 2 we briefly present the assumptions of the R-V model. In section 3 we examine the interaction between foreign competition and immigration, as well as their effects on output levels and factor rewards. In addition, we take a look at the impact of labor migration on the process of structural adjustment which takes place in response to shifting comparative advantage. Section 4 analyzes the welfare implications of the results of section 3. In section 5 we extend some results of section 4 to the case of a tariff-ridden economy. The final section of the paper suggests some possible avenues which appear to warrant further research.
2. Equilibrium in the RicardwViner
model
Consider an economy producing two goods, X and Y with two factors of production, labor L and capital K. Perfect competition prevails and factors are fully employed. The economy is assumed to be incompletely specialized. All prices are expressed in terms of good E; the numeraire. In addition, under the small country assumption, the domestic commodity price ratio P is equal to the international terms of trade, assuming there are no tariffs. The production functions are given by:
X = W, , K,),
(14
Y = G(L,, KY).
(lb)
These functions are assumed to be linear homogeneous, twice differentiable with positive and declining marginal physical products. Initially, the economy is in long-run equilibrium, with both labor and capital fully mobile between sectors. Therefore, for each factor, the value of the marginal product is equalized between sectors. This is, indeed, the case of the Heckscher-Ohlin-Samuelson model. Given the technology, factor endowments E and K, and relative prices PO, the production equilibrium is at Qk on the long-run production possibilities frontier (PPF) denoted by MM’ in fig. 1. It is assumed that X is L-intensive and Y K-intensive, and that the country is K-abundant. Therefore, the consumption equilibrium is above Qk on the budget line passing through Qi, i.e. Y is the exportable and X the importable industry. ‘Following Mayer (1974), we draw a short-run PPF, denoted by NN’, which is tangent to MM’ at Qt. This corresponds to the case of sectorspecific capital. Equilibrium in the labor market can then be written: PF, = w,
(24
A. Sapir, Foreign competition
GOOD X
383
and immigration
i
I
I
I
M N
N’
0
M’
GOOD Y
Fig. 1.
GL=w, L,+L,=L,
(24
where w denotes the wage rate expressed market equilibrium is given by:
in terms
of good
E: The capital-
PF, = rx,
W-4
where R, and R, are the amounts the long-run equilibrium Qk, and expressed in terms of good Y; This K, and KY) Ricardo-Viner model.
of capital employed in each industry in and rr are their respective returns case corresponds to the three-factor (L, In this model, a change in the terms of rx
A. Sapir, Foreign competition and immigration
384
trade, a change in factor endowments or any other exogenous disturbance will have an initial short-run impact with fixed inter-sectoral allocation of capital. Only with the passage of time will there by a reallocation of capital between sectors that will lead to a new long-run equilibrium. The solution of the model may also be depicted with the help of fig. 2. In the left part of this figure, the initial equilibrium is shown as A, which represents the intersection of the original value marginal product of labor (VMPL) curves for sectors X and Y This intersection determines the initial wage rate as well as the allocation of labor between the two sectors. For expository purposes it will also prove convenient to depict the factor-price frontier (FPF) for sector X in the right part of fig. 2. Given the wage rate, the capital rental in sector X is determined via the equilibrium point B, on the factor-price frontier. AL
w
W
1 X
0’
0,
AL
TX
-Lx-
-L,Fig. 2.
3. Foreign competition
and immigration
Let us assume that, in the first phase, the industrialized (capital-abundant) home country is disturbed from its long-run equilibrium position Qh by a competitive pressure from (labor-abundant) newly industrializing countries.’ As previous authors have shown, with sector-specific capital, the shift in comparative advantage against the Lintensive sector X (i.e. dP < 0) produces the following effects: (a) 011 output: a decrease (increase) in the production of good X (good Y); and (b) on factor rewards: a decrease in wages expressed in terms of good Y (i.e. w) and an increase in wages expressed in terms of good X (i.e. w/P), and a decrease (increase) in capital rentals expressed in terms of either good in sector X (sector Y).3 *This pressure might result from factors %ee Mayer (1974) and Mussa (1974).
like skill accumulation
and know-how
acquisition
A. Sapir, Foreign competition
and immigration
385
The output effect is indicated in fig. 1. The change in the terms of trade from P, to P, (Pr
dL,
dY = (- PF,,G,/A)
(4a)
dL,
(4b)
where A = - (PF,, + G,,). Combining s=
(4a) and (4b), the slope of the RS-locus can be written GLLFL -----0. PFLLGL
4The relaxation JIE
G
of both of these assumptions
as follows:
(5) will be discussed
below
A. Sapir, Foreign competition and immigration
386
Differentiating S with respect to L indicates that the slope of RS may be increasing or decreasing for different values of L. Therefore, in general, it may only be stated that RS is monotonically increasing. If the production function in both sectors is Cobb-Douglas, then (5) becomes:
s=
u-w, P(l -YL’
where y and 6 are the respectively. Differentiating dS
(l-6)(y--6)~
dL=
P(l-y)dLC
distributive shares of labor S with respect to L yields:
in sector
X
and
E:
’
which is always positive (negative) if sector X is L-intensive (K-intensive). Therefore, with Cobb-Douglas production functions, RS is a convex increasing curve in our case. Returning to our main argument, we observe that immigration increases the rates of return to capital in both sectors by lowering wage rates. Therefore, capitalists should always favor and workers always oppose an inflow of foreign labor. Accordingly, if we postulate that the government is dedicated to preserving ‘social justice’, we should generally find that it is reluctant to grant capitalists freer access to immigrant labor. Nevertheless, the attitude of the government might be affected by the pressing demand of the capitalists in the labor-intensive sector whose income suffers from falling terms of trade. However, in order to minimize the ensuing wage cuts, the government would probably wish to adopt what we will call a ‘compensating immigration policy’. Such a policy would involve delivering the exact number of labor permits required to restore the economic situation of capitalists in the structurally weak sector at the initial level which prevailed before the change in the terms of trade. For the moment, we will make the simplifying assumption that the economic situation of the capitalists is equivalent to their income. 3.1. The short-run equilibrium with compensating immigration Let us now combine phase one - the change in the terms of trade - and phase two the compensating immigration policy and compare the resulting new short-run equilibrium with the initial equilibrium Qi. Two cases can be distinguished according to whether we express the capitalists’ income in terms of good X (i.e. rx/P) or good Y (i.e. rx). We begin with the former case.
A. Sapir, Foreign competition
and immigration
387
We differentiate totally system (2) along with eq. (3a), holding K, and K, constant; moreover, we set d(r,/P) =0 in accordance with the governmental policy of exact compensation for capital-earners in sector X. We obtain a system of five equations in five unknowns (dL,, dL,, dL, dw and dr,). Solving for dL, and dL, yields dL,=O, dLr> 0, and therefore dX =0 and dY > 0. Consequently, the new short-run equilibrium, Qz, lies in fig. 1 on RS at the same level as Qt. The number of immigrants is given by dL=dL,. Moreover, the policy yields a loss in income for workers as dw
treatment
was partly
suggested
by Kar-yiu
Wong.
388
A. Sapir, Foreign competition
and immigration
3.2. Structural adjustment with compensating immigration Over time, the rental differential between sectors that prevails at Q? will induce a reallocation of capital from sector X to sector I: Eventually, a longrun equilibrium with immigration will be reached at Qt. This equilibrium point lies on the Rybczynski line RL which originates at Qi, the long-run equilibrium with no immigration corresponding to the price ratio Pi. The trajectory of the economy from Qh to Qi is indicated by the darker line in fig. l6 With no immigration allowed, the shift in comparative advantage would have implied a process of structural adjustment involving a continuous decrease in the production of good X and increase in the production of good I: Indeed, in a first stage the economy would have shifted from Qf; to Qs, along with intersectoral labor migration and capital rigidity. Thereafter capital would have followed the same path as labor, moving from sector X to sector Y and output would have gone from Qf to Qi. The adjustment process is somewhat different with the policy of compensatory migration. In this case, the economy first shifts from Qk to Qz along with the international labor migration and inter-sectoral capital rigidity. This implies an increase in the production of good Y and a constant level in the production of good X. From Q”, to Q$ there is then a reallocation of capital from sector X to sector Y implying a further increase in the production of good Y‘ and a decrease in the production of good X. Therefore, at Qi the production of good Y (good X) is necessarily larger (smaller) than at Qh. This change in the structure of production towards good Y is similar, although to a lesser extent, to what would have occurred if there had been no immigration. 4. Welfare considerations
In this section we examine what happens to welfare as we move first from Qk to Qy,then from Qf to Qs and finally from Q$ to Qi. For each of these three phases we distinguish between two cases. In the first one we assume that each of the three groups of factor owners - workers, capitalists in sector X, and capitalists in sector Y - has a distinct welfare function. In contrast, the second case postulates a unique welfare function for society as a whole. 4.1. Phase I: From Qk to Qs
With separate welfare functions, our previous discussion clearly indicates that the deterioration in the terms of trade against sector X generates a loss %
is left to the reader
to examine
the trajectory
that would obtain
via @i.
A. Sapir, Foreign competition
and immigration
389
(gain) for capitalists in sector X (sector Y). However, the situation of the workers is ambiguous since they lose in terms of good Y but gain in terms of good X. This ambiguity for labor (the fully mobile factor), which was first pointed out by Mussa (1974), will be further explored. Let us assume that the workers seek to maximize their welfare,
subject to their budget constraint: (9) where Cr and Cy are consumption of good X and Y; respectively, by the workers and Zw is their income. The first-order condition ZJy/ZJy = P and the budget constraint yield:
cy =aZW/P,
(loa)
c? = (1 - a)ZW,
(lob)
where c( is the share of their income which workers allocate to the consumption of good X.’ Differentiating totally (8), dividing through by LJy and using the first-order condition, one obtains after manipulations: dUW/Uy = L dw - C: dP = q(Zw/P) dP + (- cr)(Zw/P)dP,
(11)
where q is the elasticity of w with respect to P derived with L, K, and K, being held constant. Expression (11) indicates that the change in the workers’ welfare is the sum of two competing factors, each representing a different role played by workers in the economy. The first term, which is negative, indicates the loss for labor due to its status as a production factor. The second one, which is positive, reflects the gain of labor as a consumer. This result can be summarized as follows:’ Proposition 2. With sector-specijic capital, a deterioration in the terms of trade against the importable labor-intensive good improves (worsens) the welfare level of the workers if their consumption share of that good is larger (smaller) than the elasticity of their wage with respect to the terms of trade.g ‘Obviously, this share is constant only if we postulate a Cobb-Douglas utility function. ‘After this research was completed, it came to my attention that a similar result was derived earlier by R&in and Jones (1977). ‘Mussa (1974) has shown that 0 < q< 1.
A. Sapir, Foreign competition and immigration
390
In the case where we postulate a single welfare function for society as a whole, the shift in comparative advantage against the importable sector would necessarily improve welfare. This can be seen from fig. 1 by comparing the budget lines passing through Qk (for P = PO) and Qf (for P = PI),
4.2. Phase II: From Qs to Qs We begin by assuming that each of the three groups of factor owners has a distinct welfare function. For this case, the discussion of section 3 indicates that labor immigration benefits both groups of capitalists, but hurts the workers.” With a single welfare function for society as a whole, the national welfare level (defined over the pre-immigration home population) will generally increase with immigration unless there were no foreign workers originally and the number of immigrants is infinitesimal. This increase in welfare follows from the fact that, as we have seen in the previous section, an inflow of labor drives down the domestic wage rate. Indeed, let us write I as the national income of the host country: I=PX+Y-WE,
(12)
where E is the number of foreign workers from an infinitesimal change in I! that:
in the home
country.
It follows
(dl/dE) = P(dX/dLf) + (d Y/d,?!) - w - L!(dw/dE) = - L’(dw/dl!),
(13)
where the last step results from the fact that foreign labor is paid its marginal product. If there were no foreign workers originally (L! =O), then, with an initinitesimal change, we would have dI=O. In order to study the effect on welfare of a non-infinitesimal change in E, we turn to the left part of fig. 2. National income at A, (corresponding to Q$ is given by the combined area under both curves VMPL; and VMPL:. With the inflow of AL foreign workers, the equilibrium becomes A, and national income increases as the wage falls from w1 to w2.11 This increase is represented by the two shaded areas below the curves VMPL$ and VMPLF.
we.
“In our earlier discussion, assumedthat capitalists in sector X seek to maintain their economic situation as reflected by their income. More generally, we could consider that they are seeking to preserve their utility level Ux and set dUX=O. Using the budget constraint, this is equivalent to setting dr,=j?(r,/P)dP, where b is the share of their income which capitalists in sector X devote to good X. It can easily be shown that in this case we would obtain an intermediate situation between Qs and Q7. “I am grateful to Francisco Rivera-Batiz for drawing my attention to this important point.
A. Sapir, Foreign competition
and immigration
391
4.3. Phase III: From Q”, to Qi In this final phase toward the new long-run equilibrium, there is a reallocation of capital from sector X to sector I: This implies a loss (gain) for capitalists in sector Y (sector X), as well as a gain for labor. With a unique societal welfare criterion, it is clear that the move toward the long run may or may not be beneficial. Indeed, as Mayer (1974) has shown, the welfare level corresponding to Qs is necessarily inferior to that associated with Qf; the difference being the loss caused by the short-run capital specificity. On the other hand, as we have just seen, the welfare level at Qs will generally also be higher than at Qs. Therefore, since welfare levels at Qf and Qf: are identical, we cannot conclude anything about the relative desirability of Q$ and Q’;. However, if there were no foreign worker already in the country and the number of migrants is infinitesimal, then welfare levels are equal at Qs and Q”,, and Qi would unambiguously be superior to Q2. Finally, we compare the initial (Qf;) and final (Qi) equilibrium points. From the Stolper-Samuelson Theorem, we conclude that the welfare of workers deteriorates and that of capitalists improves as we move from Qk to Qf. Moreover, the welfare of each group remains the same along RL, and thus between Qf and Q$. When we consider national welfare, our previous results indicate that it improves from Qh to Qf and Q”,, and, possibly, further from Qs to Qi. 5. An important digression: Welfare considerations
in a tariff-ridden economy
In the previous section, we have seen that in phase II the national welfare level generally increases with immigration, unless there were no foreign workers already in the home country and the number of immigrants is infinitesimal. In addition, it was assumed that the home country is not tariffridden. An interesting possibility arises in the presence of an initial tariff. Let us assume that the labor-intensive importable sector (X) in the home country is protected by a tariff. As is well known, in this situation immigration would reduce national welfare if capital were freely mobile across domestic sectowl In this section we will show that, on the contrary, an inflow of labor into a tariff-ridden economy in which capital is sector-specific can be beneficial. There are two reasons for this: a positively-sloping short-run Rybczynski locus and a decline in the wage rate as foreign workers flow in. The former reason is valid for both finite and infinite changes, whereas the latter is effective for finite inflow or for infinite inflow and an initial presence of foreign workers. “See Bhagwati (1973) and Brecher and Diaz-Alejandro (1977). For further. discussion on the long-run welfare effects of various trade policies in the presence of foreign-owned factors of production, see Bhagwati and Brecher (1980) and Brecher and Bhagwati (1981).
392
A. Sapir, Foreign competition
and immigration
Let P* be the international (free-trade) price ratio. Assuming that the labor-intensive importable sector is protected therefore means P>P*. For simplicity, throughout the remainder of this section we will postulate infinitesimal changes while at the same time allowing for an initial presence of foreign workers.r3 We begin with the situation in which foreign workers are paid exclusively in terms of the exportable good I: The national income of the host country valued at international prices can be written: I* = PTX + Y - WE.
(14)
Differentiating (14) totally yields: (dI*/dLf) = P*(dX/dE) + (dY/dE) - w -E(dw/dLf) = P(dX/dZ.!) + (d Y/dLf)- w + (P* - P)(dX/dE)-
Lf(dw/dE)
= (P* - P)(dX/dE) - E(dw/dLf) 2 0,
(15)
where the first term is negative (since X increases along Rs) and the second is positive. On the other hand, if foreign workers were paid entirely in terms of the importable good X, we would have: I* = P*x + Y - (P*/P)wE,
(16)
and therefore, from an infinitesimal change in E, it follows that: (dl*/dI!) = P*(dX/dLf) + (d Y/d,!!) -(P*/P)w - (P*/P)E(dw/dI!) = (P* -P)[P(dX/dE)
- w]/P -(P*/P)E(dw/dE)
= (P* - P)( - d Y/dL!)/P - (P*/P)E(dw/dE) > 0,
(17)
where both the first (since Y increases along Rs) and second terms are positive. These results can be summarized as follows: Proposition 3. Within the R-V model, a host country protecting its importable sector might experience a welfare gain or loss from an inflow of foreign labor which receives its full (tax-free) marginal product. If workers are paid only in terms of the importable good there will be a gain; if they are paid ‘only in terms of the exportable good there might be either a loss or a gain. Moreover, these results hold regardless of whether the host country is labor- or capital-abundant. 13Hence, from the viewpoint
of the impact
on wages, this is equivalent
to finite changes.
A. Sapir, Foreign competition
and immigration
393
In addition, in the ‘absence of initial foreign workers (and with infinitesimal changes) immigration will be immiserizing when foreign workers are paid exclusively in terms of good I: Also, in this case it can easily be verified that I* would remain unaffected by the arrival of foreign labor if it consumed (or were paid in terms of) the two goods in the same proportion as it produces them. Finally, we briefly extend our analysis to deal with the effect of an inflow of foreign capital in a labor-abundant economy. Thus, let the home country be labor-abundant, exporting the Lintensive good X and importing the Kintensive good Y Specialization is incomplete and the K-intensive sector is protected by a tariff. To begin with, suppose that there is an inflow of foreign capital in the protected sector I: With short-run capital-specificity, we have dX < 0, d Y > 0 and dr, < 0. Therefore, along the lines of the above discussion we have that the change in national income at international prices due to an infinitesimal capital inflow with full (tax-free) payments of foreign profits in terms of either goods is negative (positive or negative) in the absence (presence) of initial foreign capital. On the other hand, if the inflow of foreign capital took place in sector X, one would have dX >O, dY
6. Concluding remarks There are several directions which could be explored in further research. First, we could distinguish between skilled and unskilled labor and allow for the immigration of unskilled labor to be sector-specific. A further addition to the specification of the labor market could be the introduction of a discriminatory mechanism implying that only domestic workers are allowed to move across sectors or up the skill ladder.14 The latter point raises the question of dynamic extensions of the model in terms of accumulation of either physical or human capital. Finally, except for a brief comment, we have exclusively focused our attention on labor immigration. However, in our model the same effects that were obtained with an inflow of foreign labor could have been reached instead with an outflow of capital from the injured labor-intensive sector.15 Indeed, a yet unexplored facet of the R-V model is the fact that it naturally suggests the possibility of intra-sectoral international movements of capital. IdPorter (1978) discusses a similar situation for the Southern African-type economy. 15For an illuminating discussion of the choice between labor and capital mobility good two-country model, see Bhagwati and Srinivasan (1983).
in a one-
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A. Sapir, Foreign competition
and immigration
References Bhagwati, J.N., 1973, The theory of immiserizing growth: Further applications, in: M.B. Connolly and A.K. Swoboda, eds., International trade and money (University of Toronto Press, Toronto) 45-54. Bhagwati, J.N., 1982, Shifting comparative advantage, protectionist demands, and policy response options, Paper presented at the Ford Foundation-N.B.E.R. Conference on Import Competition and Adjustment: Theory and Policy, 8-11 May 1980, Cambridge, Massachusetts; in: J. Bhagwati, ed., Import competition and response (Chicago University Press, 1982). Bhagwati, J.N. and R.A. Brecher, 1980, National welfare in an open economy in the presence of foreign-owned factors of production, Journal of International Economics 10, 103-116. Bhagwati, J.N. and T.N. Srinivasan, 1983, On the choice between capital and labour mobility, Journal of International Economics 14, this issue. Brecher, R.A. and J.N. Bhagwati, 1981, Foreign ownership and the theory of trade and welfare, Journal of Political Economy 89, 497-511. Brecher, R.A. and C.F. Diaz-Alejandro, 1977, Tariffs, foreign capital and immiserizing growth, Journal of Political Economy 82, 317-322. Mayer, W., 1974, Short-run and long-run equilibrium for a small open economy, Journal of Political Economy 82, 955-967. Mussa, M., 1974, Tariffs and the distribution of income: The importance of factor specificity, substitutability, and intensity in the short and long run, Journal of Political Economy 82, 1191-1203. Porter, R.C., 1978, A mode1 of the Southern African-type economy, American Economic Review 68, 743-755. Ruffin, R. and R.W. Jones, 1977, Protection and real wages: The neo-classical ambiguity, Journal of Economic Theory 14, 337-348.