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The welfare effects of illegal immigration
Journal of International Economics 23 (1987) 315-328. North-Holland
THE WELFARE
EFFECTS
OF ILLEGAL IMMIGRATION
Eric W. B O N D The Pennsylvania State University, University Park, PA 16802, USA
Tain-Jy CHEN* Drexel University, Philadelphia, PA 19104, USA
Received January 1985, revised version received March 1987 This paper extends the work of Ethier on illegal immigration by examining the optimal level of enforcement for the labor-importing country in a two-country model and by considering the effects of allowing capital mobility. We derive a formula for the optimal level of enforcement against firms that hire illegal workers, and show that the presence of enforcement costs makes the policy less efficient than a wage tax. With capital mobility, foreign workers gain from an increase in enforcement in the home country because capital is driven out of the home country.
i. Introduction Ethier (1986) has recently presented a m o d e l of illegal i m m i g r a t i o n to analyze the effects of enforcement policies designed to reduce the level of this i m m i g r a t i o n . Ethier's m o d e l b r e a k s new g r o u n d by analyzing the effects of b o r d e r enforcement a n d internal enforcement using a crime-theoretic analysis [in the spirit of Becker (1968)] in which w o r k e r s or firms must be c o m p e n s a t e d for the expected level of costs they incur in the event they are caught in an illegal activity. Ethier used this m o d e l to e x a m i n e how a small c o u n t r y could use d o m e s t i c enforcement policies of catching w o r k e r s at the b o r d e r or penalizing firms that e m p l o y illegal w o r k e r s to achieve d o m e s t i c policy targets c o n c e r n i n g the level of illegal i m m i g r a t i o n or the d i s t r i b u t i o n of income. The p u r p o s e of this p a p e r is to extend Ethier's m o d e l a n d to analyze some issues not considered in his work. First, we consider a t w o - c o u n t r y model, a n d e x a m i n e the level of enforcement that maximizes the welfare of the l a b o r - i m p o r t i n g country. Since firms m u s t be c o m p e n s a t e d for the expected level of fines they will bear if they hire illegal workers, the expected penalty has an effect on illegal w o r k e r s similar to that of a wage tax. The difference *We thank anonymous referees for helpful comments. All remaining errors are ours. 0022-1996/87/$3.50 © 1987, Elsevier Science Publishers B.V. (North-Holland)
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is that the presence of enforcement costs means that only part of the wedge between the cost of illegal workers to firms and the wages earned by illegal workers goes to the government. Thus, the formula for the optimal enforcement level will be similar to that for the optimal wage tax, although enforcement will be a less efficient form of improving the terms of trade and the optimal level could be zero. Also, we consider how the optimal penalty will be affected if firms are unable to distinguish legal workers from illegal workers. Second, we consider the effect of allowing capital to be mobile internationally. The mobility of capital is shown to alter the income distribution effects of enforcement, since with capital mobility foreign workers actually gain from an increase in the level of enforcement. This occurs because the increase in enforcement causes capital to leave the home country and hire workers in the foreign country, which in the stable case must raise the total demand (legal plus illegal) for foreign workers. Also, it is shown that when the optimal penalty on illegal workers is in place, it might pay the home country to export capital. This result could not occur when there is a tax on imported labor, as has been recently shown by Jones, Coelho and Easton (1986), because the optimal policy in that case is to import both labor and capital. However, since the enforcement is less efficient than the optimal labor tax, the simultaneous import of labor and export of capital might be desirable in the present model. Section 2 of the paper analyzes the effect of enforcement against illegal immigration in a one-sector model in which capital and labor are the only factors of production, and capital is not mobile between countries. We consider enforcement which involves fining firms that are caught employing illegal workers. We initially consider the case in which firms can distinguish illegal workers from legal workers, and then show how the results are modified if firms are unable to distinguish them. In section 3 we analyze the comparative statics effects of an increase in enforcement, given that capital is mobile internationally. We then examine whether it is in the interest of the home country to allow capital to be exported, given that the optimal enforcement level is in place. Section 4 offers some concluding remarks. 2. The model
In this section we develop a simple two-country model of illegal immigration. There are two factors in each country, capital and labor, that are combined in each country to produce a single output using a constant returns to scale technology. Technologies are allowed to differ between countries, with the production functions at home and abroad denoted F(L, K) and F*(L*,K*), respectively. The labelling of countries is chosen so that in the absence of factor mobility, the home wage rate, w, exceeds the
E.W. Bond and Z-J. Chen, We!fareeffects of illegal immigration
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foreign wage rate, w*. The output good is chosen to be the numeraire in this analysis. Legal barriers to movements of factors are assumed to exist that prevent the free flow of labor and capital between countries. Foreign workers may move to the home c o u n t r y and work illegally in home country firms, although home firms will be subject to penalties if they are caught employing illegal workers. Foreign country workers are assumed to be indifferent between working in the foreign country and working illegally in the home country, so that the wage earned by illegal workers will be w* in equilibrium. The analysis could easily be extended to allow illegal workers to require a wage differential between illegal work and legal work in the foreign country to compensate the illegal workers for the risk of being caught and deported and for the psychic costs of leaving their native country. We abstract from these costs because we assume that the level of border enforcement is held constant t h r o u g h o u t the analysis. The tool of government policy will be the level of enforcement against firms that hire illegal workers in the home country. I 2.1. Factor market equilibrium
We start with a derivation of the factor demands for a representative producer in a competitive industry employing unauthorized workers under the risk of being caught and penalized. Firms choose employment of legal labor, illegal labor, and capital to minimize the cost of producing output (including the expected fines resulting from being caught with illegal workers). It is assumed that illegal workers and legal workers are perfect substitutes in the production process. It should be noted that since illegal immigrants are likely to be primarily unskilled workers, it may be appropriate to think of skilled labor as being aggregated with capital in the production process. We assume that firms are able to distinguish whether workers are legal or illegal, and that firms are risk neutral. The fine that the firm pays for each illegal worker it is caught with is denoted as z. 2 The level of the fine is taken to be exogenously determined by ~Ethier (1986) analyzes the case of border enforcement, and shows that increases in border enforcement must decrease national welfare. As Ethier points out, the difference between border enforcement and penalizing firms is that in the former case the illegal workers earn the same wage as legal workers once they have successfully crossed the border, whereas in the latter case the firms pay illegal workers a lower wage than legal workers because of the risk of being penalized for illegal workers. In the border enforcement case, the country is essentially giving up the revenue it obtains in the case of penalizing workers. 2Changes in the levels of the penalties could be used to alter the expected cost of employing illegal workers without raising the level of resources devoted to catching illegal workers. However, it would also increase the incentive to bribe officials responsible for catching illegals, requiring increases in the monitoring of these officials. Since we have not developed a full model of this aspect of the enforcement process, we will assume that z (and therefore the incentive for bribery) is held constant throughout the analysis.
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E.W.. Bond and T.-J. Chen, Welfare effects of illegal immigration
social considerations such as the 'fairness' of the penalty level for the crime, and the penalty level will be held constant throughout the analysis. Following Ethier (1986), we assume that the percentage of illegal workers who are caught is an increasing function of the level of expenditure on enforcement, E. The probability of detection is denoted p(E), with p(0)=0, p < 1, p ' > 0 and p"
w=w* +p(E)z.
(I)
The objective of firms is to choose the levels of capital and labor inputs to minimize the cost of producing a given level of output. Under the assumption of constant returns to scale, the production function for home firms can be written as F(L,K)=Kf(2), where 2=L/K and f ' > 0 , f " < 0 . The solution to the cost-minimization problem for the firm facing given factor prices for capital and labor, r and w, yields the well-known first-order conditions:
f'(2) = w,
(2a)
f(2)-2w=r.
(2b)
The first condition involves equating the marginal physical product of labor to the real wage, and the second condition gives the value of r necessary to assure zero profits for the firm. The first condition can therefore be inverted to yield the optimal labor/capital ratio as a function of the price of labor services:
2=2(w), 2'= 1/f"<0.
(3)
From total differentiation of (2b) and (1), we obtain the relationship between the return to capital and the cost of labor (given that 2 is chosen optimally): dr = - 2 dw = - 2(dw* + p'zdE).
(4)
Increases in the cost of labor, due either to increases in wage costs or nonwage costs of labor, will reduce the return to capital. In the foreign country, firms choose the levels of capital and labor to minimize costs given foreign wage rates and rentals on capital, w* and r*. The cost minimization problem requires that marginal products be equated to real factor prices in the foreign country, yielding relations similar to (3)
E.W. Bond and T.-J. Chen, Welfare effects of illegal immigration
319
and (4) for the foreign country: 2"=2"(w*),
2*'= I / f * " < 0 ,
dr* = - 2* dw*.
(5a) (5b)
Having determined these demand functions for firms facing given factor prices, we now turn to the determination of the equilibrium values of factor prices. The home country is assumed to have fixed supplies of capital, K, and domestic labor, L Define a = I/(L+ I) to be the fraction of the home country work force that is illegal, where I is the level of illegal immigration. The equilibrium condition in the home factor markets requires that the values of w* and a be such that the demand for domestic labor (K(1-a)2) equal the supply. This condition is /~(1 - a))o(w* + p(E)z) = L.
(6)
Equilibrium in the foreign country factor markets requires that the demand for labor in the foreign country, K*2*, plus the demand for illegal workers in the home country, K'a2, equal the endowment of foreign country labor. Substituting in this relationship from the factor market demands (1), (3) and (5a) yields:
2*(w*)g* + a2(w* +
p ( E ) z ) K = L*.
(7)
Eqs. (6) and (7) will determine the equilibrium values of a and w*, given the level of enforcement. We now consider the effects of an increase in the enforcement level E, which must raise the wage differential between home and foreign workers. Totally differentiating (6) and (7) and solving for the effects of an increase in E yields: dw* - K 2 K 2 ' p ' z dE- A <0, da dE
(1-a)Kp'K*2*'2'z
A
(8a)
<0,
(8b)
where A = / ( 2 [ / ( 2 ' + K ' * 2 * ' ] < 0 . The increase in the expected penalty associated with the use of foreign labor must cause a decrease in w*, since the demand for foreign labor declines. This will cause a decline in the percentage of the labor force that is illegal. There are two opposing effects on the home
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E.W. Bond and T.-J. Chert, Welfare effects of illegal immigration
wage rate, since the penalty on illegal labor is rising but the foreign wage rate is falling. We have from (1) and (8a): (9)
d w _ d w * t_p,z=l"~ z l~.zpZ>O" dE dE A
The increase in penalties must protect domestic labor, which will cause a decline in the labor/capital ratio in the home country and a decline in the return to capital from (4). Thus, the burden of penalties will fall on home country capital and foreign labor in the case in which there is no capital mobility. 2.2. Optimal penalty levels
" "
We now examine the level of enforcement, E, that maximizes home country welfare. National income in the home country will equal the sum of payments to domestic factors plus the fines paid by firms to the government, less the real resource costs of the enforcement policy: Y = w L + rK, + (w - w* - vp(E))l - E,
(1 O)
where v denotes the real resource costs associated with the return of illegal workers to the foreign country and the collection of fines from firms, while E is the cost of catching illegal workers. Differentiating this expression with respect to E and making use of (4) yields: (d Y / d E ) = - l ( d w * / d E ) + (w - w* - v p ) ( d l / d E ) - (vp'l + 1).
(11)
Increases in the level of enforcement have a favorable effect on national welfare because they reduce the price at which illegal labor is purchased from the foreign country. However, the resulting decline in government revenue from the outflow of illegal workers ( d U d E < O ) and the increased resource costs of enforcement and returning illegal workers reduces national welfare. If (1 1) is evaluated at E = 0 , we have p ( E ) = 0 and a necessary condition for the optimal enforcement level to the positive is that - ( v p ' l + 1 ) - l ( d w * / d E ) > O . In order for penalties to improve welfare, the host country must be large enough to have an effect on the foreign wage, and the marginal costs of enforcement must be sufficiently low. The optimal enforcement level will involve choosing the level of the fine at which these marginal costs and benefits are equated. This can be expressed as the optimal markup rate of domestic wages above foreign wages, net of the real resource cost, of p(z-v) w*
l ( d w * / d E ) + ( v p ' l + 1) w*( d l /dE)
(12)
E.W. Bond and T.-J. Chen, Welfare effects of illegal immigration
321
The formula in (12) is similar to the one that would be obtained from the optimal wage tax on foreign labor. There are two differences between an optimal wage tax and an optimal penalty, which arise because of the real resource costs associated with catching illegal workers. First, the wedge between the wage of domestic workers and that of illegal workers exceeds the net receipts of the government, due to the resource cost o per worker caught. Second, the term (vp'l + 1) i,', the numerator captures the increase in resource costs associated with higher enforcement levels. Using the comparative statics results (8) and the fact that d 1 = ( ( L + l ) / ( 1 - a ) ) d a , (12) can be rewritten to express the optimal penalty rate as
p(z-v) w*
],
FI vp'l+l - L q -~ wg-~l~-E) J
(13)
where q = -(g~*2*'w*/l*) is the elasticity of the supply curve of illegal labor. In the case in which the tax on foreign labor takes the form of a wage tax with no enforcement costs, the second term in brackets equals zero. Expression (131 then states that the optimal wedge between home and foreign wages is equal to the inverse of the elasticity of supply of illegal labor. In the presence of enforcement costs, the expression in brackets will be less than the inverse of the supply elasticity (dl/dE
2.3. No discernment case The previous discussion has assumed that employers are able to distinguish illegal workers from legal workers. In this sub section we illustrate how the results of the previous sub section are modified if firms are unable to distinguish legal workers from illegal workers. We assumed that the government has access to information that is superior to that available to firms, which allows it to identify illegal workers as part of the enforcement process. If firms cannot distinguish legal workers from illegal workers, then all workers must earn the same wage (which will be denoted by w*). The expected cost of a worker to firms will be w*+ap(E)z, since the firm views the probability that a worker is illegal as being equal to the portion of the total work force that is illegal. The equilibrium conditions in this case will be given by the two labor market equilibrium conditions (6) and (7), with w*+ p(E)z replaced by w*+ ap(E)z in the no discernment case. Totally differentiating these conditions yields the effect of enforcement on wages to be dw* dE
- a2K22'zp ' <0. /(222' + / ( / ( * ( 2 2 " - - (1 --a)2'2*'pz)
(14)
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E.W. Bond and T.-J. Chen, Welfare effects of illegal immigration
An increase in expenditures on enforcement must reduce the wage of foreign workers. The difference is that in the no discernment case this will also mean a reduction in the wage of domestic workers. Also, starting from an initial point of no enforcement, enforcement will have a larger effect on wages when there is discernment than when there is no discernment. This is established by the fact that the numerator of (8a) is larger and the denominator smaller (in absolute value) than that of(14). The expression for national income when there is no discernment will be identical to that given by (10), since national income is also the sum of factor incomes of the domestic factors plus the net earnings from the enforcement program. Totally differentiating this expression, and making use of the costminimizing condition ( L + l ) d w + K d r = O and the relationship between firm labor costs and worker wages, yields: d Y = (az - v)p d l - I dw* - (vp'l + 1) dE.
(15)
Comparing this expression with (11), we see that the only difference is that the wedge between the value of illegal labor to firms and the social cost of illegal labor (w*+ vp) is reduced from ( z - v ) p in (11) to ( a z - v ) p in (15). Enforcement is less likely to be a desirable policy from the point of view of national welfare in the case of no discernment in the sense that the condition for a small increment of enforcement to improve welfare is less likely to be satisfied. Evaluating (15) at p = 0 , we obtain the condition for enforcement to improve welfare to be - l ( d w * / d E ) - ( v p ' + 1)=0. This condition is identical to the one obtained in the case of discernment, but is less likely to be satisfied because (dw*/dE) is smaller in the case of no discernment, as noted above. Penalties against illegal workers are less likely to improve welfare when there is no discernment because the penalties are less effective at improving the terms of trade in this case.
3. Capital mobility 3.1. Penalties on illegal labor
We now consider the case in which capital is mobile between countries, and examine how the mobility of capital alters the results concerning the effects of a change in penalties on illegal labor. We assume in this section that technologies are the same in both locations. If there were no barriers to capital mobility, capital would enter the foreign country until returns equalized in the two locations. This would also lead to equalization of wage rates and there would be no illegal immigration. Therefore, we assume that there is a tax on capital located in the foreign country such that the net return to home capital located in the foreign country is r * ( 1 - t ) , where t is
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323
the tax rate. This allows there to be both capital movements and illegal labor flows in equilibrium. Home capital will move to the foreign country until the after-tax returns are equalized: r=r*(1 - t ) .
(16)
Equivalently, the tax on capital could represent other types of barriers that make location in the foreign country less attractive, so that returns to capital do not equalize between the two markets. We analyze below whether it would ever be in the interest of the home country to erect barriers to capital movements. The amount of home country capital located in the foreign country is denoted KF. With capital mobility, the labor market equilibrium conditions in the home and foreign countries become: (/~ -- KF)(I - a ) 2 = L ,
(17a)
(K* + Kv)2* + (/~ - K v ) a 2 = L*,
(17b)
which are obtained by replacing the endowments of capital in the two countries in (6) and (7) for the no capital mobility case by the amounts of capital located in the respective countries with capital mobility. Eqs. (16) and (17) determine the equilibrium values of a, w* and KF. The link between home country and foreign country wages created by capital mobility can be seen by totally differentiating condition (16), making use of (4) and (5b): [2*( 1 - t) - 2] dw* = r* d( 1 - t) + 2p'z dE.
(18)
An increase in the tax rate on capital will reduce the wages of foreign workers as long as ( 2 " ( 1 - t ) - 2 ) > 0. Under the assumption that technologies are identical in the two countries, we know that 2*> 2 as long as wages are higher in the home country. However, this does not guarantee that the condition 2 " ( I - 0 - 2 > 0 is satisfied. It will be shown below that the case in which 2 * - 2 and 2 " ( 1 - t ) - 2 have opposite signs is analogous to the case in which the physical factor intensities differ from the value factor intensities, which has been shown to lead to perverse comparative statics results and market instability in two-sector models [Jones (1971) and Neary (1978)]. Therefore, it will be assumed that this condition is satisfied. Note that from (18) this condition leads to the surprising result that an increase in expenditure on enforcement must raise the wages of foreign workers. This occurs because the increase in expected penalties causes capital to move from the home country to the foreign country. Home country capital avoids the
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E.W. Bond and T.-J. Chen, Welfare effects of illegal immigration
penalties by purchasing labor legally in the foreign country rather than illegally in the home country. The reason that the overall effect falls on capital is that the home country is the capital-intensive location for production in a value sense whenever 2 " ( 1 - 0 - 2 > 0 . The home country wage rate will rise by more than the foreign wage rate, since the expected penalty on foreign workers is also increasing and the home wage rate is determined by condition (1). Totally differentiating the labor market equilibrium conditions and eliminating dw using (1) yields the three-equation system:
( K - K F ) ( 1 ~a)).'
-(K-KF)2
*+KF)2*'+a2(K,--KF)
(/( -- KF)2
-(l-a)2
2"--a2 ._J
da
K
I_ -r*dt+2p'zdE J (g-Kv)(1-a))~p'zdE . - (K - Kv)a2 p z dE
(19)
The determinant of the system (19) will be D =(2"(1 - t ) - 2 ) ( ( K - K v ) ( 2 - 2")2), where D will be negative if 2 " ( 1 - t ) - 2 > 0 , which will be assumed, as noted above. The requirement that D be negative is equivalent to the requirement that an increase in labor endowments decrease the equilibrium wage. The effect of an increase in the level of enforcement on the levels of a and Kv can be obtained from (19) to be ddE-PZ[-2 a_ , ,2 (1 - t ) ( l - a ) ( g - K v ) 2 ' - 2 2 ( 1
a)(K*+KF)2*']/D
dKv = p'z[2*2( 1 - t)(K" - dE
KF)22 ' + (/( --
K F)(/(* +
KF)J.2J.*']/D> O. (20b)
Since the increase in enforcement taxes capital located in the home country, more capital will move to the foreign country and the fraction of alien labor in the home country will fall. The total level of immigration must also fall, since by definition dl=(L+l)da/(1-a).
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These results indicate that the presence of capital mobility alters the conclusions concerning the effects of penalties on income distribution. With capital mobility, the burden of the penalty is shifted onto capital in all locations, while foreign workers benefit. 3.2. The welfare effects of capital outflows
The above analysis has examined the effect of penalties on illegal labor in the presence of capital mobility. We conclude this section by examining whether it is in the interest of the host country to allow capital exports, given that there are penalties on illegal labor. A recent paper by Jones, Coelho and Easton (1986) has shown that in the two-factor model, with both labor and capital mobile, the optimal policy for the capital abundant home country is to import both capital and labor. In this section we examine whether this conclusion continues to hold when the tax on imported labor is replaced by penalties against illegal labor. In the presence of capital mobility, national income will be equal to (14) plus the tax revenue earned from capital located in the foreign country: Y = wE + r/( + p(z - v)l + (r* - r)K F - E.
(21)
Differentiating this expression with respect to K v and substituting from (4) we obtain: dY dK v -
I dw* dr* dl dKv+Kv~-~v+p(z--v)-~v+(r*--r).
(22)
The effect of the capital outflow on national income will depend on three factors: the change in the prices of factor services exchanged with the foreign country, the change in revenue from penalties due to changes in the level of illegal migration, and the differential between home and foreign returns to capital. We will concentrate on capital flows from an initial point of KF=O, where the second term in (22) is equal to zero. From total differentiation of the equilibrium conditions (6) and (7) using d K v = d / ( * = - d / ( , we obtain the comparative statics results: dw* dK F dl dKv
i
-(2*-2)/(2 >0, d
(23a)
/(2 da 1-adKv
(23b)
-K2(K).*2'+/(*22*') <0, A
with d given from eq. (8). The capital outflow must raise the foreign country
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326
wage and reduce the level of illegal immigration. From (22), the increase in the wage rate reduces domestic welfare by raising the cost of illegal labor, and the reduction in immigration reduces welfare by reducing the revenue collected from fines for the use of illegal workers. However, the capital outflow provides a benefit because capital earns a higher return in the foreign country than it does in the home country. The overall effect will depend on the relative magnitude of these three terms. To evaluate these effects, suppose that the home country has imposed the optimal enforcement against illegal immigration given by (13). Will an outflow of capital improve home country welfare starting from this position? Substituting into (22) from (23) yields: dY dKv
K2 A
x [-- ( w - w* - vp)(/('2*2' + / ( ' 2 2 " ) + 1(2" - 2 ) - ( r - r*)(K2'+ g'*2*')]. Substituting I = - / ( * 2 * ' ( w - w* - vp) +(vp'I + 1)(/(2'+ K*2*')/K2'p'z from the formula for the optimal enforcement level (13), this expression can be simplified to
,F-o - =L
~
l/ -(w-w*-op)2*-(r -r*t]
(24)
The first term must be negative, and will tend to reduce national welfare. From cost minimization with identical technologies, it must be the case that ( w - w * ) 2 * + ( r - r * ) > O . If there are no resource costs as part of the wedge between home and foreign wages, then the sum of the remaining terms must also be negative and the capital outflow will reduce welfare. This corresponds to the case in which the wedge between home and foreign wages is due to a tax on imported labor, and the loss of revenue due to decreased immigration must more than offset the higher return to capital obtained abroad. However, the penalties on illegal workers may be a less efficient form of tax on imported labor. If part of the gap between w and w* is made up of the resource costs of returning illegal workers, then the loss in revenue from fines when capital moves overseas may be so small that the sum of the last two terms is positive. If the sum of the last two terms is positive and sufficiently large, it might be in the interest of the home country to tax capital exports while penalties are in place on illegal immigrants. To summarize these results, the capital outflow has offsetting effects on national welfare. The decline in expected revenue from detecting illegal aliens tends to reduce national welfare. However, this could be offset by the fact that taxation of capital exports is a relatively more efficient way of capturing
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revenue for the g o v e r n m e n t since the g o v e r n m e n t c a p t u r e s all of the wedge r * - r , but only part of the wedge w - w * . 3 It should be noted that this c o m p a r i s o n rests on the a s s u m p t i o n that the g o v e r n m e n t can costlessly enforce the t a x a t i o n of capital exports. If it is costly to enforce the t a x a t i o n of capital, then the g o v e r n m e n t m a y not c a p t u r e all of the differential r - r * . Let b d e n o t e the real resource cost of collecting revenues from firms caught a v o i d i n g taxes. A necessary c o n d i t i o n for a capital outflow to i m p r o v e h o m e welfare will be ( w - w * - v p ) 2 * + ( r - r * + b ) < O , which requires that the costs associated with the collection of capital tax revenues are less than those for enforcement of l a b o r penalties (per unit capital). 4 This result can also be related to R a m a s w a m i ' s (1968) conclusion that l a b o r i m p o r t i n g is preferred to capital e x p o r t i n g by a capital a b u n d a n t e c o n o m y . R a m a s w a m i finds the o p t i m a l tax on l a b o r i m m i g r a t i o n yields higher welfare than the o p t i m a l tax on capital exports, because under the former tax the c a p i t a l / l a b o r ratio is the same for all h o m e c o u n t r y factors. In the present p r o b l e m , it is not possible to c o m p a r e the extreme cases of l a b o r i m p o r t alone and capital e x p o r t alone because of the inability of the h o m e c o u n t r y to c o m p l e t e l y shut off i m m i g r a t i o n . H o w e v e r , the fact that capital e x p o r t i n g m a y be desirable in the n e i g h b o r h o o d of the o p t i m a l enforcement level (which c a n n o t occur with l a b o r taxes) suggests that l a b o r i m p o r t i n g is relatively less desirable when the t a x a t i o n takes the form of penalizing firms that e m p l o y illegal workers.
4. Conclusions This p a p e r has a d d r e s s e d the n a t i o n a l welfare effects of penalties on the e m p l o y m e n t of illegal w o r k e r s by host c o u n t r y firms. Previous w o r k on illegal i m m i g r a t i o n by Ethier (1986) has been generalized by e x a m i n i n g the effects of allowing capital to be m o b i l e when penalties are imposed. First, it was shown that a n o n - z e r o enforcement level for catching illegal l a b o r m a y exist that m a x i m i z e s n a t i o n a l welfare if terms of t r a d e effects are large e n o u g h a n d m a r g i n a l cost of enforcement is sufficiently low. The o p t i m a l 3It is the latter effect that leads to results different than those obtained by Jones, Coelho and Easton (1986) for the case of labor taxes. Jones, Coelho and Easton find that if foreign workers are paid the home country wage (no discrimination between home and foreign workers is possible in taxation), the optimal policy is to restrict capital exports and allow no labor movements. The case in which foreign workers are paid the home wage is similar to the case z=t, in the present paper, since the home country earns no revenue from foreign workers. However, elimination of labor flows is not possible in the present case because all labor flows are illegal. '*Avoidance of taxes on long term capital flows could take the form of manipulating transfer prices (if the capital flow occurs through direct foreign investment) or of underreporting foreign dividend and interest income. Although no data on relative collection costs are available, it seems plausible that the costs would be higher for illegal labor flows. Note that it is the cost varying with the number of workers caught (v) rather than the enforcement cost itself (E) that is relevant for comparison.
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level of enforcement is m o r e likely to be zero if h o m e country firms cannot distinguish illegal workers from legal workers. Second, it was shown that the effects of the penalties on income distribution are sensitive to the ability of h o m e country capital to escape the penalty by m o v i n g to the foreign country. With capital mobility, capital in both countries loses from the penalties while foreign labor gains. Without capital mobility, foreign workers lose and foreign capitalists gain. Finally, the analysis of optimal policy indicated that it m a y be optimal for a country to both penalize illegal immigrants and allow capital export. This simultaneous inflow of labor and outflow of capital cannot be optimal when labor inflows are restricted using a wage tax.
References Becker, Gary, 1968, Crime and punishment: An economic approach, Journal of Political Economy 76, 169-217. Ethier, Wilfred J., 1986, Illegal immigration, American Economic Review 76, 56--71. Jones, Ronald W., 1971, Distortions in factor markets and the general equilibrium model of production, Journal of Political Economy 79, 437--459. Jones, Ronald W., lsaias Coelho and Steven Easton, 1986, The basic model of international factor flows, Journal of International Economics 20, 313-329. Neary, Peter J., 1978, Dynamic stability and the theory of factor market distortions, American Economic Review 68, 671-682. Ramaswami, V.K., 1968, International factor movements and the national advantage, Economica 35, 309-310.
THE WELFARE
EFFECTS
OF ILLEGAL IMMIGRATION
Eric W. B O N D The Pennsylvania State University, University Park, PA 16802, USA
Tain-Jy CHEN* Drexel University, Philadelphia, PA 19104, USA
Received January 1985, revised version received March 1987 This paper extends the work of Ethier on illegal immigration by examining the optimal level of enforcement for the labor-importing country in a two-country model and by considering the effects of allowing capital mobility. We derive a formula for the optimal level of enforcement against firms that hire illegal workers, and show that the presence of enforcement costs makes the policy less efficient than a wage tax. With capital mobility, foreign workers gain from an increase in enforcement in the home country because capital is driven out of the home country.
i. Introduction Ethier (1986) has recently presented a m o d e l of illegal i m m i g r a t i o n to analyze the effects of enforcement policies designed to reduce the level of this i m m i g r a t i o n . Ethier's m o d e l b r e a k s new g r o u n d by analyzing the effects of b o r d e r enforcement a n d internal enforcement using a crime-theoretic analysis [in the spirit of Becker (1968)] in which w o r k e r s or firms must be c o m p e n s a t e d for the expected level of costs they incur in the event they are caught in an illegal activity. Ethier used this m o d e l to e x a m i n e how a small c o u n t r y could use d o m e s t i c enforcement policies of catching w o r k e r s at the b o r d e r or penalizing firms that e m p l o y illegal w o r k e r s to achieve d o m e s t i c policy targets c o n c e r n i n g the level of illegal i m m i g r a t i o n or the d i s t r i b u t i o n of income. The p u r p o s e of this p a p e r is to extend Ethier's m o d e l a n d to analyze some issues not considered in his work. First, we consider a t w o - c o u n t r y model, a n d e x a m i n e the level of enforcement that maximizes the welfare of the l a b o r - i m p o r t i n g country. Since firms m u s t be c o m p e n s a t e d for the expected level of fines they will bear if they hire illegal workers, the expected penalty has an effect on illegal w o r k e r s similar to that of a wage tax. The difference *We thank anonymous referees for helpful comments. All remaining errors are ours. 0022-1996/87/$3.50 © 1987, Elsevier Science Publishers B.V. (North-Holland)
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E.W. Bond and T.-J. Chen, Welfare effects of illegal immigration
is that the presence of enforcement costs means that only part of the wedge between the cost of illegal workers to firms and the wages earned by illegal workers goes to the government. Thus, the formula for the optimal enforcement level will be similar to that for the optimal wage tax, although enforcement will be a less efficient form of improving the terms of trade and the optimal level could be zero. Also, we consider how the optimal penalty will be affected if firms are unable to distinguish legal workers from illegal workers. Second, we consider the effect of allowing capital to be mobile internationally. The mobility of capital is shown to alter the income distribution effects of enforcement, since with capital mobility foreign workers actually gain from an increase in the level of enforcement. This occurs because the increase in enforcement causes capital to leave the home country and hire workers in the foreign country, which in the stable case must raise the total demand (legal plus illegal) for foreign workers. Also, it is shown that when the optimal penalty on illegal workers is in place, it might pay the home country to export capital. This result could not occur when there is a tax on imported labor, as has been recently shown by Jones, Coelho and Easton (1986), because the optimal policy in that case is to import both labor and capital. However, since the enforcement is less efficient than the optimal labor tax, the simultaneous import of labor and export of capital might be desirable in the present model. Section 2 of the paper analyzes the effect of enforcement against illegal immigration in a one-sector model in which capital and labor are the only factors of production, and capital is not mobile between countries. We consider enforcement which involves fining firms that are caught employing illegal workers. We initially consider the case in which firms can distinguish illegal workers from legal workers, and then show how the results are modified if firms are unable to distinguish them. In section 3 we analyze the comparative statics effects of an increase in enforcement, given that capital is mobile internationally. We then examine whether it is in the interest of the home country to allow capital to be exported, given that the optimal enforcement level is in place. Section 4 offers some concluding remarks. 2. The model
In this section we develop a simple two-country model of illegal immigration. There are two factors in each country, capital and labor, that are combined in each country to produce a single output using a constant returns to scale technology. Technologies are allowed to differ between countries, with the production functions at home and abroad denoted F(L, K) and F*(L*,K*), respectively. The labelling of countries is chosen so that in the absence of factor mobility, the home wage rate, w, exceeds the
E.W. Bond and Z-J. Chen, We!fareeffects of illegal immigration
317
foreign wage rate, w*. The output good is chosen to be the numeraire in this analysis. Legal barriers to movements of factors are assumed to exist that prevent the free flow of labor and capital between countries. Foreign workers may move to the home c o u n t r y and work illegally in home country firms, although home firms will be subject to penalties if they are caught employing illegal workers. Foreign country workers are assumed to be indifferent between working in the foreign country and working illegally in the home country, so that the wage earned by illegal workers will be w* in equilibrium. The analysis could easily be extended to allow illegal workers to require a wage differential between illegal work and legal work in the foreign country to compensate the illegal workers for the risk of being caught and deported and for the psychic costs of leaving their native country. We abstract from these costs because we assume that the level of border enforcement is held constant t h r o u g h o u t the analysis. The tool of government policy will be the level of enforcement against firms that hire illegal workers in the home country. I 2.1. Factor market equilibrium
We start with a derivation of the factor demands for a representative producer in a competitive industry employing unauthorized workers under the risk of being caught and penalized. Firms choose employment of legal labor, illegal labor, and capital to minimize the cost of producing output (including the expected fines resulting from being caught with illegal workers). It is assumed that illegal workers and legal workers are perfect substitutes in the production process. It should be noted that since illegal immigrants are likely to be primarily unskilled workers, it may be appropriate to think of skilled labor as being aggregated with capital in the production process. We assume that firms are able to distinguish whether workers are legal or illegal, and that firms are risk neutral. The fine that the firm pays for each illegal worker it is caught with is denoted as z. 2 The level of the fine is taken to be exogenously determined by ~Ethier (1986) analyzes the case of border enforcement, and shows that increases in border enforcement must decrease national welfare. As Ethier points out, the difference between border enforcement and penalizing firms is that in the former case the illegal workers earn the same wage as legal workers once they have successfully crossed the border, whereas in the latter case the firms pay illegal workers a lower wage than legal workers because of the risk of being penalized for illegal workers. In the border enforcement case, the country is essentially giving up the revenue it obtains in the case of penalizing workers. 2Changes in the levels of the penalties could be used to alter the expected cost of employing illegal workers without raising the level of resources devoted to catching illegal workers. However, it would also increase the incentive to bribe officials responsible for catching illegals, requiring increases in the monitoring of these officials. Since we have not developed a full model of this aspect of the enforcement process, we will assume that z (and therefore the incentive for bribery) is held constant throughout the analysis.
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E.W.. Bond and T.-J. Chen, Welfare effects of illegal immigration
social considerations such as the 'fairness' of the penalty level for the crime, and the penalty level will be held constant throughout the analysis. Following Ethier (1986), we assume that the percentage of illegal workers who are caught is an increasing function of the level of expenditure on enforcement, E. The probability of detection is denoted p(E), with p(0)=0, p < 1, p ' > 0 and p"
w=w* +p(E)z.
(I)
The objective of firms is to choose the levels of capital and labor inputs to minimize the cost of producing a given level of output. Under the assumption of constant returns to scale, the production function for home firms can be written as F(L,K)=Kf(2), where 2=L/K and f ' > 0 , f " < 0 . The solution to the cost-minimization problem for the firm facing given factor prices for capital and labor, r and w, yields the well-known first-order conditions:
f'(2) = w,
(2a)
f(2)-2w=r.
(2b)
The first condition involves equating the marginal physical product of labor to the real wage, and the second condition gives the value of r necessary to assure zero profits for the firm. The first condition can therefore be inverted to yield the optimal labor/capital ratio as a function of the price of labor services:
2=2(w), 2'= 1/f"<0.
(3)
From total differentiation of (2b) and (1), we obtain the relationship between the return to capital and the cost of labor (given that 2 is chosen optimally): dr = - 2 dw = - 2(dw* + p'zdE).
(4)
Increases in the cost of labor, due either to increases in wage costs or nonwage costs of labor, will reduce the return to capital. In the foreign country, firms choose the levels of capital and labor to minimize costs given foreign wage rates and rentals on capital, w* and r*. The cost minimization problem requires that marginal products be equated to real factor prices in the foreign country, yielding relations similar to (3)
E.W. Bond and T.-J. Chen, Welfare effects of illegal immigration
319
and (4) for the foreign country: 2"=2"(w*),
2*'= I / f * " < 0 ,
dr* = - 2* dw*.
(5a) (5b)
Having determined these demand functions for firms facing given factor prices, we now turn to the determination of the equilibrium values of factor prices. The home country is assumed to have fixed supplies of capital, K, and domestic labor, L Define a = I/(L+ I) to be the fraction of the home country work force that is illegal, where I is the level of illegal immigration. The equilibrium condition in the home factor markets requires that the values of w* and a be such that the demand for domestic labor (K(1-a)2) equal the supply. This condition is /~(1 - a))o(w* + p(E)z) = L.
(6)
Equilibrium in the foreign country factor markets requires that the demand for labor in the foreign country, K*2*, plus the demand for illegal workers in the home country, K'a2, equal the endowment of foreign country labor. Substituting in this relationship from the factor market demands (1), (3) and (5a) yields:
2*(w*)g* + a2(w* +
p ( E ) z ) K = L*.
(7)
Eqs. (6) and (7) will determine the equilibrium values of a and w*, given the level of enforcement. We now consider the effects of an increase in the enforcement level E, which must raise the wage differential between home and foreign workers. Totally differentiating (6) and (7) and solving for the effects of an increase in E yields: dw* - K 2 K 2 ' p ' z dE- A <0, da dE
(1-a)Kp'K*2*'2'z
A
(8a)
<0,
(8b)
where A = / ( 2 [ / ( 2 ' + K ' * 2 * ' ] < 0 . The increase in the expected penalty associated with the use of foreign labor must cause a decrease in w*, since the demand for foreign labor declines. This will cause a decline in the percentage of the labor force that is illegal. There are two opposing effects on the home
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E.W. Bond and T.-J. Chert, Welfare effects of illegal immigration
wage rate, since the penalty on illegal labor is rising but the foreign wage rate is falling. We have from (1) and (8a): (9)
d w _ d w * t_p,z=l"~ z l~.zpZ>O" dE dE A
The increase in penalties must protect domestic labor, which will cause a decline in the labor/capital ratio in the home country and a decline in the return to capital from (4). Thus, the burden of penalties will fall on home country capital and foreign labor in the case in which there is no capital mobility. 2.2. Optimal penalty levels
" "
We now examine the level of enforcement, E, that maximizes home country welfare. National income in the home country will equal the sum of payments to domestic factors plus the fines paid by firms to the government, less the real resource costs of the enforcement policy: Y = w L + rK, + (w - w* - vp(E))l - E,
(1 O)
where v denotes the real resource costs associated with the return of illegal workers to the foreign country and the collection of fines from firms, while E is the cost of catching illegal workers. Differentiating this expression with respect to E and making use of (4) yields: (d Y / d E ) = - l ( d w * / d E ) + (w - w* - v p ) ( d l / d E ) - (vp'l + 1).
(11)
Increases in the level of enforcement have a favorable effect on national welfare because they reduce the price at which illegal labor is purchased from the foreign country. However, the resulting decline in government revenue from the outflow of illegal workers ( d U d E < O ) and the increased resource costs of enforcement and returning illegal workers reduces national welfare. If (1 1) is evaluated at E = 0 , we have p ( E ) = 0 and a necessary condition for the optimal enforcement level to the positive is that - ( v p ' l + 1 ) - l ( d w * / d E ) > O . In order for penalties to improve welfare, the host country must be large enough to have an effect on the foreign wage, and the marginal costs of enforcement must be sufficiently low. The optimal enforcement level will involve choosing the level of the fine at which these marginal costs and benefits are equated. This can be expressed as the optimal markup rate of domestic wages above foreign wages, net of the real resource cost, of p(z-v) w*
l ( d w * / d E ) + ( v p ' l + 1) w*( d l /dE)
(12)
E.W. Bond and T.-J. Chen, Welfare effects of illegal immigration
321
The formula in (12) is similar to the one that would be obtained from the optimal wage tax on foreign labor. There are two differences between an optimal wage tax and an optimal penalty, which arise because of the real resource costs associated with catching illegal workers. First, the wedge between the wage of domestic workers and that of illegal workers exceeds the net receipts of the government, due to the resource cost o per worker caught. Second, the term (vp'l + 1) i,', the numerator captures the increase in resource costs associated with higher enforcement levels. Using the comparative statics results (8) and the fact that d 1 = ( ( L + l ) / ( 1 - a ) ) d a , (12) can be rewritten to express the optimal penalty rate as
p(z-v) w*
],
FI vp'l+l - L q -~ wg-~l~-E) J
(13)
where q = -(g~*2*'w*/l*) is the elasticity of the supply curve of illegal labor. In the case in which the tax on foreign labor takes the form of a wage tax with no enforcement costs, the second term in brackets equals zero. Expression (131 then states that the optimal wedge between home and foreign wages is equal to the inverse of the elasticity of supply of illegal labor. In the presence of enforcement costs, the expression in brackets will be less than the inverse of the supply elasticity (dl/dE
2.3. No discernment case The previous discussion has assumed that employers are able to distinguish illegal workers from legal workers. In this sub section we illustrate how the results of the previous sub section are modified if firms are unable to distinguish legal workers from illegal workers. We assumed that the government has access to information that is superior to that available to firms, which allows it to identify illegal workers as part of the enforcement process. If firms cannot distinguish legal workers from illegal workers, then all workers must earn the same wage (which will be denoted by w*). The expected cost of a worker to firms will be w*+ap(E)z, since the firm views the probability that a worker is illegal as being equal to the portion of the total work force that is illegal. The equilibrium conditions in this case will be given by the two labor market equilibrium conditions (6) and (7), with w*+ p(E)z replaced by w*+ ap(E)z in the no discernment case. Totally differentiating these conditions yields the effect of enforcement on wages to be dw* dE
- a2K22'zp ' <0. /(222' + / ( / ( * ( 2 2 " - - (1 --a)2'2*'pz)
(14)
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E.W. Bond and T.-J. Chen, Welfare effects of illegal immigration
An increase in expenditures on enforcement must reduce the wage of foreign workers. The difference is that in the no discernment case this will also mean a reduction in the wage of domestic workers. Also, starting from an initial point of no enforcement, enforcement will have a larger effect on wages when there is discernment than when there is no discernment. This is established by the fact that the numerator of (8a) is larger and the denominator smaller (in absolute value) than that of(14). The expression for national income when there is no discernment will be identical to that given by (10), since national income is also the sum of factor incomes of the domestic factors plus the net earnings from the enforcement program. Totally differentiating this expression, and making use of the costminimizing condition ( L + l ) d w + K d r = O and the relationship between firm labor costs and worker wages, yields: d Y = (az - v)p d l - I dw* - (vp'l + 1) dE.
(15)
Comparing this expression with (11), we see that the only difference is that the wedge between the value of illegal labor to firms and the social cost of illegal labor (w*+ vp) is reduced from ( z - v ) p in (11) to ( a z - v ) p in (15). Enforcement is less likely to be a desirable policy from the point of view of national welfare in the case of no discernment in the sense that the condition for a small increment of enforcement to improve welfare is less likely to be satisfied. Evaluating (15) at p = 0 , we obtain the condition for enforcement to improve welfare to be - l ( d w * / d E ) - ( v p ' + 1)=0. This condition is identical to the one obtained in the case of discernment, but is less likely to be satisfied because (dw*/dE) is smaller in the case of no discernment, as noted above. Penalties against illegal workers are less likely to improve welfare when there is no discernment because the penalties are less effective at improving the terms of trade in this case.
3. Capital mobility 3.1. Penalties on illegal labor
We now consider the case in which capital is mobile between countries, and examine how the mobility of capital alters the results concerning the effects of a change in penalties on illegal labor. We assume in this section that technologies are the same in both locations. If there were no barriers to capital mobility, capital would enter the foreign country until returns equalized in the two locations. This would also lead to equalization of wage rates and there would be no illegal immigration. Therefore, we assume that there is a tax on capital located in the foreign country such that the net return to home capital located in the foreign country is r * ( 1 - t ) , where t is
E.W. Bond and T.-J. Chert, Welfare effects of illegal immigration
323
the tax rate. This allows there to be both capital movements and illegal labor flows in equilibrium. Home capital will move to the foreign country until the after-tax returns are equalized: r=r*(1 - t ) .
(16)
Equivalently, the tax on capital could represent other types of barriers that make location in the foreign country less attractive, so that returns to capital do not equalize between the two markets. We analyze below whether it would ever be in the interest of the home country to erect barriers to capital movements. The amount of home country capital located in the foreign country is denoted KF. With capital mobility, the labor market equilibrium conditions in the home and foreign countries become: (/~ -- KF)(I - a ) 2 = L ,
(17a)
(K* + Kv)2* + (/~ - K v ) a 2 = L*,
(17b)
which are obtained by replacing the endowments of capital in the two countries in (6) and (7) for the no capital mobility case by the amounts of capital located in the respective countries with capital mobility. Eqs. (16) and (17) determine the equilibrium values of a, w* and KF. The link between home country and foreign country wages created by capital mobility can be seen by totally differentiating condition (16), making use of (4) and (5b): [2*( 1 - t) - 2] dw* = r* d( 1 - t) + 2p'z dE.
(18)
An increase in the tax rate on capital will reduce the wages of foreign workers as long as ( 2 " ( 1 - t ) - 2 ) > 0. Under the assumption that technologies are identical in the two countries, we know that 2*> 2 as long as wages are higher in the home country. However, this does not guarantee that the condition 2 " ( I - 0 - 2 > 0 is satisfied. It will be shown below that the case in which 2 * - 2 and 2 " ( 1 - t ) - 2 have opposite signs is analogous to the case in which the physical factor intensities differ from the value factor intensities, which has been shown to lead to perverse comparative statics results and market instability in two-sector models [Jones (1971) and Neary (1978)]. Therefore, it will be assumed that this condition is satisfied. Note that from (18) this condition leads to the surprising result that an increase in expenditure on enforcement must raise the wages of foreign workers. This occurs because the increase in expected penalties causes capital to move from the home country to the foreign country. Home country capital avoids the
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E.W. Bond and T.-J. Chen, Welfare effects of illegal immigration
penalties by purchasing labor legally in the foreign country rather than illegally in the home country. The reason that the overall effect falls on capital is that the home country is the capital-intensive location for production in a value sense whenever 2 " ( 1 - 0 - 2 > 0 . The home country wage rate will rise by more than the foreign wage rate, since the expected penalty on foreign workers is also increasing and the home wage rate is determined by condition (1). Totally differentiating the labor market equilibrium conditions and eliminating dw using (1) yields the three-equation system:
( K - K F ) ( 1 ~a)).'
-(K-KF)2
*+KF)2*'+a2(K,--KF)
(/( -- KF)2
-(l-a)2
2"--a2 ._J
da
K
I_ -r*dt+2p'zdE J (g-Kv)(1-a))~p'zdE . - (K - Kv)a2 p z dE
(19)
The determinant of the system (19) will be D =(2"(1 - t ) - 2 ) ( ( K - K v ) ( 2 - 2")2), where D will be negative if 2 " ( 1 - t ) - 2 > 0 , which will be assumed, as noted above. The requirement that D be negative is equivalent to the requirement that an increase in labor endowments decrease the equilibrium wage. The effect of an increase in the level of enforcement on the levels of a and Kv can be obtained from (19) to be ddE-PZ[-2 a_ , ,2 (1 - t ) ( l - a ) ( g - K v ) 2 ' - 2 2 ( 1
a)(K*+KF)2*']/D
dKv = p'z[2*2( 1 - t)(K" - dE
KF)22 ' + (/( --
K F)(/(* +
KF)J.2J.*']/D> O. (20b)
Since the increase in enforcement taxes capital located in the home country, more capital will move to the foreign country and the fraction of alien labor in the home country will fall. The total level of immigration must also fall, since by definition dl=(L+l)da/(1-a).
E.W. Bond and T.-J. Chen, Welfare effects of illegal immigration
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These results indicate that the presence of capital mobility alters the conclusions concerning the effects of penalties on income distribution. With capital mobility, the burden of the penalty is shifted onto capital in all locations, while foreign workers benefit. 3.2. The welfare effects of capital outflows
The above analysis has examined the effect of penalties on illegal labor in the presence of capital mobility. We conclude this section by examining whether it is in the interest of the host country to allow capital exports, given that there are penalties on illegal labor. A recent paper by Jones, Coelho and Easton (1986) has shown that in the two-factor model, with both labor and capital mobile, the optimal policy for the capital abundant home country is to import both capital and labor. In this section we examine whether this conclusion continues to hold when the tax on imported labor is replaced by penalties against illegal labor. In the presence of capital mobility, national income will be equal to (14) plus the tax revenue earned from capital located in the foreign country: Y = wE + r/( + p(z - v)l + (r* - r)K F - E.
(21)
Differentiating this expression with respect to K v and substituting from (4) we obtain: dY dK v -
I dw* dr* dl dKv+Kv~-~v+p(z--v)-~v+(r*--r).
(22)
The effect of the capital outflow on national income will depend on three factors: the change in the prices of factor services exchanged with the foreign country, the change in revenue from penalties due to changes in the level of illegal migration, and the differential between home and foreign returns to capital. We will concentrate on capital flows from an initial point of KF=O, where the second term in (22) is equal to zero. From total differentiation of the equilibrium conditions (6) and (7) using d K v = d / ( * = - d / ( , we obtain the comparative statics results: dw* dK F dl dKv
i
-(2*-2)/(2 >0, d
(23a)
/(2 da 1-adKv
(23b)
-K2(K).*2'+/(*22*') <0, A
with d given from eq. (8). The capital outflow must raise the foreign country
E.W. Bond and T.-J. Chen, Welfare effects of illegal immigration
326
wage and reduce the level of illegal immigration. From (22), the increase in the wage rate reduces domestic welfare by raising the cost of illegal labor, and the reduction in immigration reduces welfare by reducing the revenue collected from fines for the use of illegal workers. However, the capital outflow provides a benefit because capital earns a higher return in the foreign country than it does in the home country. The overall effect will depend on the relative magnitude of these three terms. To evaluate these effects, suppose that the home country has imposed the optimal enforcement against illegal immigration given by (13). Will an outflow of capital improve home country welfare starting from this position? Substituting into (22) from (23) yields: dY dKv
K2 A
x [-- ( w - w* - vp)(/('2*2' + / ( ' 2 2 " ) + 1(2" - 2 ) - ( r - r*)(K2'+ g'*2*')]. Substituting I = - / ( * 2 * ' ( w - w* - vp) +(vp'I + 1)(/(2'+ K*2*')/K2'p'z from the formula for the optimal enforcement level (13), this expression can be simplified to
,F-o - =L
~
l/ -(w-w*-op)2*-(r -r*t]
(24)
The first term must be negative, and will tend to reduce national welfare. From cost minimization with identical technologies, it must be the case that ( w - w * ) 2 * + ( r - r * ) > O . If there are no resource costs as part of the wedge between home and foreign wages, then the sum of the remaining terms must also be negative and the capital outflow will reduce welfare. This corresponds to the case in which the wedge between home and foreign wages is due to a tax on imported labor, and the loss of revenue due to decreased immigration must more than offset the higher return to capital obtained abroad. However, the penalties on illegal workers may be a less efficient form of tax on imported labor. If part of the gap between w and w* is made up of the resource costs of returning illegal workers, then the loss in revenue from fines when capital moves overseas may be so small that the sum of the last two terms is positive. If the sum of the last two terms is positive and sufficiently large, it might be in the interest of the home country to tax capital exports while penalties are in place on illegal immigrants. To summarize these results, the capital outflow has offsetting effects on national welfare. The decline in expected revenue from detecting illegal aliens tends to reduce national welfare. However, this could be offset by the fact that taxation of capital exports is a relatively more efficient way of capturing
E.W. Bond and T.-J. Chen, Welfareeffects of illegal immigration
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revenue for the g o v e r n m e n t since the g o v e r n m e n t c a p t u r e s all of the wedge r * - r , but only part of the wedge w - w * . 3 It should be noted that this c o m p a r i s o n rests on the a s s u m p t i o n that the g o v e r n m e n t can costlessly enforce the t a x a t i o n of capital exports. If it is costly to enforce the t a x a t i o n of capital, then the g o v e r n m e n t m a y not c a p t u r e all of the differential r - r * . Let b d e n o t e the real resource cost of collecting revenues from firms caught a v o i d i n g taxes. A necessary c o n d i t i o n for a capital outflow to i m p r o v e h o m e welfare will be ( w - w * - v p ) 2 * + ( r - r * + b ) < O , which requires that the costs associated with the collection of capital tax revenues are less than those for enforcement of l a b o r penalties (per unit capital). 4 This result can also be related to R a m a s w a m i ' s (1968) conclusion that l a b o r i m p o r t i n g is preferred to capital e x p o r t i n g by a capital a b u n d a n t e c o n o m y . R a m a s w a m i finds the o p t i m a l tax on l a b o r i m m i g r a t i o n yields higher welfare than the o p t i m a l tax on capital exports, because under the former tax the c a p i t a l / l a b o r ratio is the same for all h o m e c o u n t r y factors. In the present p r o b l e m , it is not possible to c o m p a r e the extreme cases of l a b o r i m p o r t alone and capital e x p o r t alone because of the inability of the h o m e c o u n t r y to c o m p l e t e l y shut off i m m i g r a t i o n . H o w e v e r , the fact that capital e x p o r t i n g m a y be desirable in the n e i g h b o r h o o d of the o p t i m a l enforcement level (which c a n n o t occur with l a b o r taxes) suggests that l a b o r i m p o r t i n g is relatively less desirable when the t a x a t i o n takes the form of penalizing firms that e m p l o y illegal workers.
4. Conclusions This p a p e r has a d d r e s s e d the n a t i o n a l welfare effects of penalties on the e m p l o y m e n t of illegal w o r k e r s by host c o u n t r y firms. Previous w o r k on illegal i m m i g r a t i o n by Ethier (1986) has been generalized by e x a m i n i n g the effects of allowing capital to be m o b i l e when penalties are imposed. First, it was shown that a n o n - z e r o enforcement level for catching illegal l a b o r m a y exist that m a x i m i z e s n a t i o n a l welfare if terms of t r a d e effects are large e n o u g h a n d m a r g i n a l cost of enforcement is sufficiently low. The o p t i m a l 3It is the latter effect that leads to results different than those obtained by Jones, Coelho and Easton (1986) for the case of labor taxes. Jones, Coelho and Easton find that if foreign workers are paid the home country wage (no discrimination between home and foreign workers is possible in taxation), the optimal policy is to restrict capital exports and allow no labor movements. The case in which foreign workers are paid the home wage is similar to the case z=t, in the present paper, since the home country earns no revenue from foreign workers. However, elimination of labor flows is not possible in the present case because all labor flows are illegal. '*Avoidance of taxes on long term capital flows could take the form of manipulating transfer prices (if the capital flow occurs through direct foreign investment) or of underreporting foreign dividend and interest income. Although no data on relative collection costs are available, it seems plausible that the costs would be higher for illegal labor flows. Note that it is the cost varying with the number of workers caught (v) rather than the enforcement cost itself (E) that is relevant for comparison.
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level of enforcement is m o r e likely to be zero if h o m e country firms cannot distinguish illegal workers from legal workers. Second, it was shown that the effects of the penalties on income distribution are sensitive to the ability of h o m e country capital to escape the penalty by m o v i n g to the foreign country. With capital mobility, capital in both countries loses from the penalties while foreign labor gains. Without capital mobility, foreign workers lose and foreign capitalists gain. Finally, the analysis of optimal policy indicated that it m a y be optimal for a country to both penalize illegal immigrants and allow capital export. This simultaneous inflow of labor and outflow of capital cannot be optimal when labor inflows are restricted using a wage tax.
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