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Economic effects of immigrants on native and foreign-born workers: complementarity, substitutability, and other channels of influence.

13. Greenwood, Michael J., and John M. McDowell, "The Factor-Market Consequences of U.S. Immigration." Journal of Economic Literature, December 1986, 1738-72.

14. Greenwood, Michael J., Gary L. Hunt, Dan S. Rickman, and George I. Treyz, "Migration, Regional Equilibrium, and the Estimation of Compensating Differentials." American Economic Review, December 1991, 1382-90.

15. Grossman, Jean B., "The Substitutability of Natives and Immigrants in Production." Review of Economics and Statistics, November 1982, 596-603.

I. Introduction

Do immigrant workers cause the reduction of domestic wage rates and displace domestic workers from jobs? This question is central to the current debate regarding the economic consequences of U.S. immigration. Moreover, it has been a key issue in the U.S. for over 100 years. As discussed in Greenwood and McDowell [13], the economic consequences of U.S. immigration are highly debatable. On one side of the debate are those who argue that immigrants take jobs that would otherwise be filled by other U.S. workers, depress domestic wages, and worsen working conditions. To the extent that the immigrants are poorly trained and lack education, they have negative impacts on those Americans with whom they compete in the labor market, such as blacks, Hispanics, youths, and others (including prior immigrants) whose incomes tend to be low and whose unemployment rates tend to be high.

On the other side of the debate are those who argue that immigration has positive impacts on other workers. Such effects supposedly are due primarily to the innovative and entrepreneurial abilities of the immigrants and to the increased rate of capital accumulation they foster. Others argue that less-skilled immigrants fill jobs that domestic workers find undesirable and thus do not directly decrease the employment opportunities and wages of native labor.

Empirical findings to date reflect this uncertainty regarding the effects of immigrants on native workers. For example, Grossman concludes that both second-generation and foreign workers are substitutes for native workers, but the relevant elasticities are sufficiently small that "large inflows of immigrants . . . do not pose serious economic threats to natives" [15, 602]. These findings are consistent with Borjas's [3] conclusion that during the 1970s male immigrants had a small negative influence on the earnings of native white men. More recent research reaches similar conclusions [7; 20; 21]. Work reported by Altonji and Card [1] is qualitatively comparable, but the estimated impacts on less-skilled natives under their preferred estimation method is somewhat higher than other estimates.

On the contrary, focusing on the effect of first-generation Hispanics on the earnings of second- and third-generation Hispanic workers, King, Lowell, and Bean [18] find little support for the substitutability hypothesis. Only for the subsample of workers classified as laborers does their evidence suggest a competitive influence of immigrants on native wages, and even then the influence is slight.

Although the results of the various studies are somewhat sensitive to the country of origin of the immigrants, to the specific groups of native workers studied, to whether the immigrants are legal or illegal, and to other factors, in general they suggest that if immigrants are substitutes for native workers, the degree of substitution is small. However, a major problem with existing studies is that they focus on a single channel of immigrant influence, namely, the production structure channel. That is, they are concerned with whether immigrants and natives are substitutes or complements in production. However, immigrants may also influence native workers through a number of other channels, and these additional influences may offset or reinforce those exerted through the production structure channel. In this paper, we develop a structural model of immigrant/native labor demand and labor supply that allows us to distinguish the effects of immigrants in such a way as to identify the channels through which wages and employment are influenced. We show that although immigrants and natives are substitutes in production, when other channels of influence are taken into account, immigrants can positively affect the employment and wages of native workers. However, they cause somewhat lower wages among other immigrants.

II. Channels of Influence and the Model

Channels of Influence

Several distinct channels are evident through which the location of immigrants can influence the employment and wages of other U.S. residents. The approach that we implement incorporates several main channels. It is useful first to give a qualitative description of the various channels of influence that the approach will treat before we introduce the equations required by our approach.

Production Structure Channel. An increase in the number of immigrants in an area increases the supply of immigrant labor, which will decrease immigrant wage rates, ceteris paribus. If immigrants and natives are substitutes in production, immigrant employment will increase and native employment will fall, ceteris paribus. The magnitudes will depend on the relevant own-and cross-price elasticities. If immigrants and natives are complements in production, then this implies substitutability with respect to capital (given three input factors). Under conditions of native-immigrant complementarity, a fall in immigrant wage rates will lead to the substitution of immigrant labor for capital and an increase in immigrant employment. An induced increase in native employment will also occur.

Local Demand Channel. The production structure effect can lead to either a decrease or an increase in aggregate labor income depending on whether immigrants and natives are complements or substitutes and the size of the elasticities. Consequently, this effect can lead to higher or lower levels of local final demand in an area. Moreover, the larger the per capita wealth of the immigrants, the larger their sources of non-labor income, and therefore the greater will be the stimulation of local final demand in the area due to their entry. Many attempts to model the effects of immigrants on native workers assume that if the immigrants own capital, they leave it behind. This seems like an unrealistic assumption, but the relative magnitude of the effect of the assumption is an empirical question. Given the area's propensity to import goods to satisfy local final demand, the enhanced local final demand will result in additional local output and therefore in additional labor demand. The net effect of this channel of influence will depend on whether the change in aggregate labor income and non-labor income is positive or negative.

Net Export$Demand Channel. An increased supply of immigrants and the resulting fall in immigrant wage rates will lead to reduced unit production costs, ceteris paribus. This reduction should make the area more competitive in national and international markets, which should in turn lead to an increase in the quantity of area net exports demanded and to increases in area labor demand.

Labor Force Participation Channel. If labor force participation rates are sensitive to real wage rates, and if increased immigration causes wage rates to fall (rise), then part of the adjustment will occur through employment reductions (increases) in contrast to wage changes bearing all of the adjustment.

Migration Channel. If lower (higher) real wage rates induce net out-migration (in-migration), then this channel also transfers some of the adjustment from wage rates to employment. The net export demand channel is labor demand enhancing. The local demand channel is as well in areas that have aggregate real labor income gains. The labor force participation and migration channels shift part of the adjustment of more immigrants from wage rates to employment. The basic idea that underlies the model developed below is to assess the relative importance of each channel of influence discussed above. Whether immigration represents a net cost or a net benefit to the original U.S. workers is then determined in light of the various channels through which immigrants might affect others.

The Model

Depending on the relative strengths of these various channels of influence, the location of immigrants in an area could result in better or worse economic conditions for existing residents of the area. To get at the relative strengths of the various influences, we estimated an empirical model comprised of the following equations:

Unit cost function:

c = c([w.sub.1], [w.sub.2], [w.sub.3]) (1)

Input demand functions:

[Mathematical Expression Omitted]

[Mathematical Expression Omitted]

[Mathematical Expression Omitted]

Output demand function:

[q.sup.d] = [q.sup.d](p, Y/Np, N) (5)

Local price:

p = [Phi]c (6)

Input supply functions:

[Mathematical Expression Omitted]

[Mathematical Expression Omitted]

Capital supply function (exogenous):

[w.sub.3] = [W.sub.3] (rcok) (9)

Income identity:

Y [equivalent] [w.sub.1][x.sub.1] + [w.sub.2][x.sub.2] + [YNL.sub.1][N.sub.1] + [YNL.sub.2][N.sub.2] (10)

Factor market equilibrium:

[Mathematical Expression Omitted]

[Mathematical Expression Omitted]

[Mathematical Expression Omitted]

Output market equilibrium:

[q.sup.s] = [q.sup.d] = q. (14)

Equation (1) is the unit cost function. Unit cost and the input demand functions are derived from a three-input cost function incorporating native labor, foreign-born labor, and capital. Constant returns-to-scale (CRTS) is imposed as a maintained hypothesis. Unit costs depend positively on the three factor prices: [w.sub.1], [w.sub.2], [w.sub.3]. Additional regularity conditions theoretically required for equation (1) to be a true unit cost function are discussed in the Model Estimation section.

Input demand functions are derived via Shephard's lemma from the cost function. Equations (2)-(4) are the factor demand equations. Labor demand for each class of labor (i.e., foreign-born and native) and for capital is specified to be a function of own (-) and other factor prices (+, -) and output (+).

Aggregate demand for local output, which is a function of real per capita income (+), population (+), and local prices (-), is given in equation (5). Local prices are assumed to be proportional ([Phi]) to unit costs in equation (6). The aggregate demand curve slopes downward for several reasons. First, as local prices fall, area residents substitute locally-produced goods for imports. Also, as local prices fall, real income rises. Finally, lower local prices increase inter-regional and international export sales. Given transport costs, lower production costs lead to lower free-on-board prices, and therefore to a larger trade area and higher demand for area exports. Additional properties of this equation are discussed in the Model Estimation section.

Labor supply functions given in equations (7) and (8) are written as the product of the respective labor force participation rates (defined as the employment-to-population ratios) and populations. Participation rate functions are required because the measure of labor force that we use is number of persons and not number of hours. Sign expectations are: wage rates (+), local prices (-), and non-labor income (-).

The supply of capital in equation (9) is assumed to be perfectly elastic at the nationally or internationally determined price of capital services, [W.sub.3], adjusted for relative regional capital taxation differences. The price of capital goods is assumed to be determined outside the region. Tax structure differences are therefore reflected in regional variations in the cost of capital (i.e., supply price of capital services).(1)

Equation (10) is the identity for aggregate income.

We assume input factor and goods market equilibrium in our model, and the equilibrium conditions are given in equations (11)-(14). The assumption of labor market equilibrium permits us to use equations (2), (3), (7), and (8) to solve for native and immigrant equilibrium wage rates and employment. The assumption of output market equilibrium and proportionality between price and unit costs permits us to solve for output and prices. We have done this in equations (1), (5), (6), and (14). Once prices are determined, output is determined from the output demand equation. Because we have assumed constant returns in the aggregate technology, output does not appear in equation (1). This appears to imply that output supply is perfectly elastic. However, if factor inputs are not supplied perfectly elastically, then as area output increases factor prices will rise causing unit costs to rise and therefore output price to rise.

We have assumed that the supply price of capital services is fixed at a level reflecting both international capital market conditions and the regional structure of capital taxation. Both are assumed to be exogenous to the region. Consequently, [w.sub.3] is exogenously given to the local area economy. Capital is therefore supplied perfectly elastically to an area at the regional supply price, which will be higher (lower) than the international supply price if regional capital taxation is higher (lower) than that existing internationally. Regions with above (below) average capital taxation will have above (below) average cost of capital. The quantity of capital services used in production is determined by the demand equation for capital services given the exogenously determined regional supply price of capital services.

Due to data constraints, we have not explicitly specified a native migration equation. To handle migration, we assume that in the long run any real wage rate differentials across space will be arbitraged by migration if they differ from compensating differentials. We further assume that the real wage rate differentials that existed in 1980 are approximately equilibrium compensating differentials following the findings of Greenwood, Hunt, Rickman, and Treyz [14]. If immigration causes a change in native real wage rates from 1980 baseline levels, we compute migration as the change in native population required in an area to put real wage levels back to baseline levels.

The model explicitly contains nine endogenous variables: c, [x.sub.1], [x.sub.2], [x.sub.3], [w.sub.1], [w.sub.2], q, p, and Y. Implicitly, net migration flows and population for natives are also endogenous and therefore total population as well. Performing the appropriate substitutions implied by the factor and output market equilibrium conditions and the exogenous capital supply function, we obtain exactly nine equations corresponding to the nine endogenous variables in our model. Altogether, the model contains seven exogenous variables: [w.sub.3], A (four amenities), [YNL.sub.1], [YNL.sub.2]. The four amenity variables are arguments in the implicit migration functions.(2)

III. The Data

The wide variation that exists in immigrant concentrations across the U.S. provides the rationale for using cross-sectional data on Standard Metropolitan Statistical Areas to estimate the model described above. For 24 selected SMSAs, Table I gives the percent foreign-born employment in 1980 and the percent of 1980 foreign-born who immigrated between 1970 and 1980. Miami had almost 41 percent of its employment accounted for by the foreign-born. About 65 percent of Houston's 1980 foreign-born population had immigrated since 1970. While these are extreme values, note that the data range widely even in those areas with relatively high concentrations of immigrants.

The primary source of data employed in this study is the 1980 Census Public Use Microdata files. The 1980 microdata have been drawn from the B Sample. Every SMSA for which 1970 data were available was included in the sample. The total number of areas is 123; this number includes every major metropolitan area in the country.(3)

Nominal Output

We use a value-added output concept in our model. Nominal output data on a value-added basis have been compiled by the Bureau of Economic Analysis in the form of gross regional product data at the state level, but not at the SMSA level. Our strategy is to estimate SMSA level nominal output by stepping down state level nominal output to the area level using SMSA and state personal income data by major industry division.(4)
Table I. Selected Characteristics of Selected SMSAs, 1980


 Percent Foreign- Percent 1980 Foreign-Born
SMSA Born Employment Who Immigrated 1970-80


Boston 9.3% 32.0%
New York 23.2 39.1
Jersey City 26.9 40.7
Paterson 17.1 38.6
Washington, D.C. 8.6 53.6
Miami 40.9 36.1
Detroit 6.0 22.0
Chicago 11.8 41.8
Houston 8.8 65.1
San Antonio 7.3 35.1
El Paso 22.4 39.1
Denver 4.7 44.9
Las Vegas 9.0 45.5
Tucson 6.0 31.7
San Diego 12.8 46.1
Los Angeles 23.9 58.2
Anaheim 14.4 52.7
Fresno 11.5 42.9
Riverside 8.6 36.3
Santa Barbara 11.3 37.1
Salinas 20.8 45.0
San Francisco 16.4 42.9
San Jose 14.0 47.6
Honolulu 15.4 52.1


Real Output

Nominal output for each area was deflated by a local price index to obtain an aggregate quantity (or real output) index. The local price index used is the fitted unit cost for each area based on an estimated CRTS translog cost function. Estimation is presented in the next section. Unit costs can be estimated up to a factor of proportionality with a CRTS translog cost function and factor price and quantity data as discussed in detail by Hunt [17].

Price (User Cost) of Capital Services ([w.sub.3])

The user cost of capital is given by

[w.sub.3] = [W.sub.3](rcok) (15)

where [W.sub.3] is the 1980 nominal value of the Jorgensonian user cost of capital for the U.S. as a whole and rcok is a 123 x 1 vector of SMSA user costs of capital relative to the U.S. value incorporating local tax structure features. The area's relative user cost of capital is the value for the state in which the area is located; [w.sub.3] is a 123 x 1 vector. The source of the rcok vector is Regional Economic Models, Inc. The methodology is described in Treyz and Stevens [24]. The U.S. value of the user cost of capital was computed by the Jorgensonian formula:

[W.sub.3] = {[1 - k - uz][(1 - u)i + [Delta]][p.sub.k]}/(1 - u), (16)

where k is the investment tax credit, u is the combined federal and state marginal tax rate on capital income (inclusive of local deductibility), z is the present value of one dollar's worth of depreciation allowances, i is the financial cost of capital, [Delta] is the economic depreciation rate, and [p.sub.k] is the implicit deflator for investment output. All data are weighted averages of structures and equipment.

Capital

By definition, capital income ([C.sup.*]) is equal to the quantity of capital ([x.sub.3]) times its rental price ([w.sub.3]):

[C.sup.*] = [x.sub.3][w.sub.3]. (17)

Given our assumption of CRTS, capital income from each area is equal to nominal output less labor income. An index of the quantity of capital is therefore given by:

[x.sub.3] = [C.sup.*]/[w.sub.3]. (18)

Other Required Data

A number of other variables are required to estimate the structural model presented in section II. For the most part, these variables were drawn from the census microdata files. Data for the cost variable are the sum of nominal values of labor income and capital income. This is consistent with our assumption of CRTS and our definition of output as value added in production. A glossary of variable terms is given in Table II and summary statistics appear in Table III.

IV. Model Estimation

Given the aggregate nature of the model, simultaneous equations estimators are employed to estimate the parameters of the model. Where theoretical restrictions on the parameter space exist, these are explicitly accounted for in the estimation. The seven exogenous variables plus natural logarithms of the two exogenous non-labor income variables and a constant term are used as instrumental variables. The three additional instruments arise from the specification of the functional forms for the empirical model.

[TABULAR DATA FOR TABLE II OMITTED]
Table III. Summary Statistics


Variable Mean Standard Deviation


p 0.9797443 0.0585867
[w.sub.1] 16074.372 1197.4677
[w.sub.2] 12554.844 2779.6873
[w.sub.3] 0.1414186 0.0059987
[x.sub.1] 478.88537 546.96026
[x.sub.2] 45.700813 125.49274
[x.sub.3] 55616818 82579021
q 14389099 19490523
[N.sub.1] 996.46017 1150.7698
[N.sub.2] 93.353659 250.45325
N 1089.8138 1363.6103
HUMID 64.658537 8.5763966
ED1 11.965854 0.4816006
ED2 11.028862 1.3199461
CD 0.2357724 0.4262167
[YNL.sub.1] 2292.9399 464.27629
[YNL.sub.2] 2532.7407 979.39237
Y 9285148.9 12408038


Cost Function and Input Demand Equations

The three inputs are native labor ([x.sub.1]), foreign-born labor ([x.sub.2]), and capital ([x.sub.3]). Corresponding factor prices are [w.sub.1], [w.sub.2], and [w.sub.3]. The translog functional form is used to specify the cost function. The translog was selected because it is a flexible functional form and does not constrain the Allen elasticities a priori. This is important given our interest in the degree of substitutability or complementarity among natives and immigrants. Moreover, a CRTS translog specification permits us to compute a unit cost index based only on a knowledge of factor prices, factor quantities, and total cost (i.e., nominal output) - all of which are observable. In turn, we were able to compute a consistent index of aggregate real output.
Table IV. Unit Cost Function and Share Equations: Iterative
Three-Stage Least Squares Estimates


Parameter Estimates Parameter Estimates


[[Beta].sub.10] 0.4478691 [[Beta].sub.22] -0.1126502
 (0.0062865) (0.0194350)


[[Beta].sub.11] -0.1126502 [[Beta].sub.23] 0.0
 (0.0194350) (set)


[[Beta].sub.12] 0.1126502 [[Beta].sub.30] 0.5232807
 (0.0194350) (0.0065241)


[[Beta].sub.13] 0.0 [[Beta].sub.33] 0.0
 (set) (set)


[[Beta].sub.20] 0.0288502
 (0.0024787)


Notes: Asymptotic standard errors appear in parentheses. Number of
observations is 123. The parameters [[Beta].sub.13],
[[Beta].sub.23], and [[Beta].sub.33] were all restricted to a value
of zero.


Linear homogeneity in factor prices, symmetry in cross-price effects, and CRTS are imposed a priori. The monotonicity and concavity regularity conditions are checked ex post with the estimated cost function.

Applying Shephard's lemma to the cost function, we obtain the share equations. The share equations are each identified and are estimated by iterative three-stage least squares (I3SLS), which is equivalent to maximum likelihood [9]. The equations are estimated jointly to exploit the cross-equation parameter restrictions present. The singularity of the complete system of three share equations requires that we estimate only two of the equations. Given that we use a maximum likelihood estimator, our estimates are invariant to the equation dropped.

The translog cost function with CRTS imposed is as follows:

[Mathematical Expression Omitted],

where the [[Beta].sub.ij]'s are elements of a square symmetric matrix of parameters (i.e., [[Beta].sub.ij] = [[Beta].sub.ji], i [not equal to] j). The share equations derived via Shephard's lemma are:

[s.sub.i] = [[Beta].sub.io] + [summation of] [[Beta].sub.ij] ln[w.sub.j] where j=1 to 3 + [[Epsilon].sub.i], i = 1,2,3 (20)

where the [[Epsilon].sub.i]'s are stochastic disturbance terms.

Unit costs are derived by subtracting ln q from both sides of equation (19) and then exponentiating. Final estimates of the parameters are reported in Table IV.

Initial estimates suggested that [[Beta].sub.13] = [[Beta].sub.23] = 0. A Wald test for these restrictions yielded a [[Chi].sup.2] value of 0.73 with a corresponding probability of 0.69. Therefore, the restrictions are not rejected. Given adding-up, linear homogeneity in factor prices, and symmetry in cross-price effects, the restriction that [[Beta].sub.13] = [[Beta].sub.23] = 0 also implies that [[Beta].sub.11] = [[Beta].sub.12], [[Beta].sub.11] = [[Beta].sub.22], and [[Beta].sub.33] = 0. All of these restrictions are reflected in Table IV.
Table V. Matrix of Price Elasticities of Factor Demand


 Native Labor Foreign-Born Labor Capital


Native Labor -.80 0.28 0.52
 (0.04) (0.04) (0.04)


Foreign-Born Labor 4.71 -5.23 0.52
 (0.63) (0.63) (0.63)


Capital 0.45 0.03 -0.48
 (0.03) (0.03) (0.03)


Note: Asymptotic standard errors appear in parentheses and are based
on the assumption of nonstochastic shares. Elasticities derived at
the sample means.


Based on the estimated parameter values and the fitted share values, the monotonicity and concavity regularity conditions are met at the overwhelming majority of sample data points. The monotonicity condition is violated for only the foreign-born share equation at 15 sample observations out of 123 total.(5) The concavity condition is met at all sample data points.(6) These results are quite supportive of our estimated specification in light of the vexing problems represented by the serious failure of many estimated structural relationships based on flexible functional forms to meet the regularity conditions [10].

The estimated parameters in Table IV generally are not of great direct interest. However, we can derive estimates of factor substitutability or complementarity from them. One intuitive set of measures is the matrix of price elasticities of factor demand. This square non-symmetric matrix of elasticities is given by:

[E.sub.ij] = [s.sub.j][[Sigma].sub.ij],i,j = 1,2,3; (21)

where [E.sub.ij] is the i,j element of the elasticity matrix, [s.sub.j] is the jth factor share and [[Sigma].sub.ij] is the i,j element of the matrix of Allen-Uzawa elasticities. Table V shows the estimated matrix of price elasticities of factor demands.

All own-price elasticities are negative as required by theory. Moreover, the row sums are zero as required by the zero homogeneity of factor demands with respect to factor prices [8, 65]. Native labor is a substitute with both foreign-born labor and capital, Foreign-born labor is a substitute with native labor. Based on the size of the estimated standard errors, we cannot conclude that foreign-born labor and capital are either substitutes or complements.(7)

[TABULAR DATA FOR TABLE VI OMITTED]

Labor Supply Equations

Estimation is done with two-stage least squares (2SLS) and three-stage least squares (3SLS and I3SLS). Each equation is identified and estimation is done with zero homogeneity imposed in wages, prices, and non-labor income. Wald tests of the restrictions fail to reject them at conventional levels. Table VI presents the results. For all estimation techniques undertaken, the native equation is well-behaved and meets a priori expectations, although the estimated real wage elasticity appears to be high. The structure of our simulation experiments, however, allows us to avoid drawing any unreasonable conclusions based on such estimates.

The foreign-born equation has the incorrect sign on the real wage; but the estimated value is never significant at conventional levels. For simulation purposes, the foreign-born labor force participation rate is exogenized. Changes in immigration therefore produce proportional changes in labor supply. This has the effect of imposing a perfectly inelastic foreign-born labor supply function for a given population.

Aggregate Demand for Local Output Equation

Aggregate demand for local output derives from three sources: (1) local demand, which is related to the size of the local population and its per capita real income, (2) the propensity to import, which depends on local output prices relative to those elsewhere, and (3) the interregional and international demand for area exports, which also depends on relative local output prices and the scale of real income in the rest of the world.
Table VII. Aggregate Demand for Local Output Equation: Two-Stage
Least Squares Estimates


 Estimates


Variable Unrestricted Restricted


ln p -1.3481 -1.1466
 (0.4802) (0.3264)


ln N 1.0396 1.0
 (0.0559) (set)


ln(Y/Np) 1.0533 1.0
 (0.3145) (set)


Constant 4.3276 4.3724
 (1.8357) (1.1270)


[R.sup.2] 0.97 0.96


Wald Test [[Chi].sup.2] -- -1.09
P-value -- 0.58


Notes: Asymptotic standard errors in parentheses. Number of
observations is 123. Parameters on ln N and ln(Y/Np) variables are
restricted to equal unity in restricted estimates.


Because we are using a cross-section to estimate this equation, the area's output price is the relative price and the scale factor for exports is constant. Therefore, we specify the aggregate demand for locally-produced output as a function of local output prices (proxied here by local unit costs generated by equation (19)), population, and nominal local income. All variables are specified as natural logarithms. The equation used is:

ln q = [[Alpha].sub.0] + [[Alpha].sub.1] ln p + [[Alpha].sub.2] ln N + [[Alpha].sub.3] ln(Y/Np) (22)

where q is real aggregate demand for locally-produced output, p is local price, N is population, and (Y/Np) is real per capita income. We expect [[Alpha].sub.2] and [[Alpha].sub.3] to be positive and close to unity in value. We expect [[Alpha].sub.1] to be negative and significantly different than zero.(8)

Table VII presents two-stage least squares estimates of Equation (22). The unrestricted estimated parameters for the log population and log real per capita income variables are close to unity, and the estimated parameter on log price term is of reasonable magnitude for the price elasticity.(9) All parameter estimates are highly significant. A Wald test fails to reject the restrictions that the parameters on the log population and log real per capita income terms are unity. This implies that the equation can be simplified by replacing the real per capita income and population terms with a real income term. This is done in the simulations.

The estimated parameter value of unity on the population and real per capita income terms seems high. Since the aggregate demand for locally-produced output depends on local demand as well as imports and exports, a change in local real income should induce less than a proportionate change in aggregate demand. Our estimates probably reflect the fact that we do not have a scale factor for exports in our equation. This situation reflects the cross-sectional data constraints that we face. Our concern with the magnitude of these parameter estimates leads us to undertake tests of the sensitivity of our simulation results to a smaller real income elasticity of aggregate demand.

V. Simulations

In order to assess the impacts of immigrants on both natives and the foreign-born, we simulate our estimated model for an exogenous 10 percent increase in foreign-born population stock. A 10 percent increase is selected so that our results can be compared with previously published ones, such as those of Grossman [15; 16].

In a nonlinear model such as ours, the simulation results can vary substantially depending on the baseline chosen as a starting point [22]. To get accurate results, we start our simulations from the actual 1980 values in each metropolitan area. The baseline must therefore represent the actual 1980 values of all endogenous and exogenous variables in the model. To be sure that this condition is met, we compute our simulations in two steps.

First, we compute an add-factored baseline solution for each of the 123 metropolitan areas. These solutions produce add-factors for each structural endogenous variable. These add-factors represent the discrepancy between the non-add-factored baseline solutions and the actual 1980 values. Therefore, the add-factored simulation replicates the actual structural endogenous variable values exactly in each of the 123 areas. Given that the structural endogenous values are replicated, any endogenous values computed by identity are also exactly replicated. We refer to these simulations as add-factored baseline simulations.

The second step in simulating the effects of 10 percent more immigrants is to resolve the model with a 10 percent increase in the foreign-born population and incorporating the add factors. This use of the add factors ensures that our alternative simulations start from a baseline that accurately reflects the values of the endogenous variables in each area. The simulation results that we report below are changes from baseline values that represent the actual 1980 values of all variables. To isolate the effects of the various channels of influence, 15 alternative simulations are done for each of the 123 areas. These results are reported in Tables VIII and IX and represent the unweighted average effects for all areas under alternative parameter assumptions. Table X reports the unweighted average effects for areas grouped by census region and for those areas with relatively large flows of immigrants during 1970-1980.

All Areas

The alternative simulations presented in Table VIII are separated into four sets distinguished by whether native labor supply is fixed or flexible and whether the pattern of immigration is spatially concentrated or dispersed. If native labor supply is fixed, then the full burden of adjustment is carried by wage rates. If native labor supply is flexible, then changes in labor force participation rates and migration can shift some of the adjustment to employment. If the spatial pattern of immigration is concentrated in a subset of all metropolitan areas, then any induced reductions in local production costs can result in interregional relative price changes and stimulate additional interregional net exports. If immigration is dispersed throughout the metropolitan system, then any induced production cost reductions may not result in changes in interregional prices and net exports. International net export demand would be affected in either case. Finally, the divergence [TABULAR DATA FOR TABLE VIII OMITTED] in native real wage rates across metropolitan areas should be greater in the spatially concentrated case. Consequently, native migration is more likely to be a component of the adjustment process in this case.(10)

Fixed Native Labor Supply/Spatially Concentrated Immigration Pattern: Production Structure Only. In this simulation only the production structure channel is allowed to operate. All other channels are blocked. This is accomplished by exogenizing price, population, output, labor supply, and income. The labor demand equations are rewritten in inverse form so that wage rates appear on the lefthand side and factor quantities on the righthand side. The quantity of foreign-born labor is increased 10 percent and the model is solved for new equilibrium wage rates.

Our production structure simulation is comparable to the approach used by Grossman [15]. She finds that a 10 percent increase in foreign-born stock leads to a -0.8% to -1.0% change in real wages of natives, and to a -2.3% change for the foreign-born. Our results indicate a similar effect on natives (-0.88%) and on the foreign-born (-2.46%). Our results are consistent with Grossman's in direction and in absolute and relative impact.

Fixed Native Labor Supply/Spatially Concentrated Immigration Pattern: Production Structure and Demand Channels. As a result of absorbing 10 percent more immigrants, foreign-born wage rates fall by 2.5 percent. Consequently, nominal earnings of the foreign-born as a group rise given that their employment rises by 10 percent. However, nominal earnings of natives as a group fall by approximately 0.9 percent. In addition to these changes in earnings due to the production structure effects on wage rates, local prices fall and this boosts real earnings and the purchasing power of non-labor income. The price decline in this spatially concentrated case also stimulates net export demand. In total, these effects are sufficient to increase the demand for locally-produced output enough to bring native real wage rates back to essentially baseline levels (+0.02%). Foreign-born real wage rate losses are cut back to -1.58 percent. These results are conservative in that they ignore any non-labor income sources that the immigrants may have. This is denoted in Table VIII with a "0%" indicating that the immigrants are assumed to have non-labor earnings equal to zero percent of the average of non-labor earnings among the area's existing foreign-born population.

When we assume that the immigrants have non-labor income equal to 50 percent or 100 percent of the average for the area's existing foreign-born population, then the real wage rate impacts become more positive for natives (+0.08% and +0.14%, respectively) and less negative for the foreign-born (-1.52% and -1.46%, respectively).

The most significant and interesting results derived from this set of simulations are that (1) our production structure results corroborate the findings of Grossman [15], and (2) adding demand-side effects (including net export demand) completely offsets any negative impacts on native real wage rates even if we assume that new immigrants have no sources of non-labor income.

Fixed Native Labor Supply/Spatially Dispersed Immigration Pattern: Production Structure Channel. This replicates the previous result and is reported to provide a benchmark against which subsequent changes can be compared.

Fixed Native Labor Supply Spatially/Dispersed Immigration Pattern: Production Structure and Demand Channels. These simulations differ from the analogous ones for the spatially concentrated case because net export demand effects are suppressed. This somewhat understates the demand effects in this case because international net export effects would still be operative. We have no way, given our data, of separately identifying such effects. Consequently, we must treat them as zero.

If immigrants have no non-labor income, our simulation predicts a relatively small decline in native real wage rates (-0.17%). This negative impact is reversed and native real wage rates rise if immigrants are assumed to have non-labor income equal to 50 percent or 100 percent of the average non-labor income of the area's existing foreign-born (0.01% and 0.18%, respectively). Foreign-born real wage rates are negatively affected, but to a progressively lesser extent as more of the demand channel is permitted to operate. The impacts range from -1.76 percent when immigrants have no non-labor income to -1.42 percent when immigrants have non-labor income equal to that of the area's existing foreign-born population.

Flexible Native Labor Supply/Spatially Concentrated Immigration Pattern: Production Structure Channel. This replicates the previous result and is reported to provide a benchmark against which subsequent changes can be compared.

Flexible Native Labor Supply/Spatially Concentrated Immigration: Production Structure and Labor Force Participation Rate (LFPR) Channels. In this simulation, wage rate changes are permitted to spillover to native LFPR changes. The native adjustment to immigration now can occur in terms of wage rates and employment. As expected, native wage rates fall less (-0.17% versus -0.88%) when they share the adjustment burden with employment. The fall in native employment due to changes in the native LFPR is -0.41%. Because native wage rates fall less when employment changes are permitted, foreign-born wage rates also fall less given that native and foreign-born labor are substitutes in production.

Flexible Native Labor Supply/Spatially Concentrated Immigration: Production Structure, LFPR, and Demand Channels. In the spatially concentrated case, the demand channel includes changes in net export demand as well as local demand. Even if we assume that the immigrants have no non-labor income, native real wages and employment are essentially unaffected (+0.01% and +0.01%, respectively). Assuming that the immigrants have non-labor income equal to 50 percent and 100 percent of that of existing area foreign-born produces positive impacts on native real wage rates (+0.05% and +0.09%, respectively) and employment (+0.11% and +0.22%, respectively). Progressively higher demand levels also reduce the negative impacts on foreign-born real wages (-1.59%, -1.54%, and -1.46%, respectively).

Flexible Native Labor Supply/Spatially Concentrated Immigration: Production Structure, LFPR, Demand, and Native Migration Channels. This simulation starts with the impacts produced by assuming that the non-labor income of immigrants is 100 percent of that of the existing area foreign-born. Given that native real wage rates are above baseline values, net in-migration will occur. To compute the amount, we exogenize the native real wage rate at the baseline level under the assumption that area real wage rates in 1980 reflect equilibrium compensating differentials. We then permit the model to increase native population and labor supply enough so that supply and demand are equated at the exogenously set native real wage rate, which will produce a maximum flow of native migrants in the model because we assume that migration is costless. Taking such costs into account would reduce the simulated native employment increase of +1.99 percent possibly to zero given that the native real wage rates are only 0.09 percent above baseline values before the migration.

The most interesting and important aspect of this set of simulation results is that 10 percent more immigrants does not make natives worse off in terms of real wage rates or employment. Depending on the demand assumptions, natives may in fact be better off although the computed positive impacts are small.

Flexible Native Labor Supply/Spatially Dispersed Immigration Patterns: Production Structure Channel. This replicates the previous result and is reported to provide a benchmark against which subsequent changes can be compared.

Flexible Native Labor Supply/Spatially Dispersed Immigration Patterns: Production Structure and LFPR Channels. This replicates the previous result and is reported to provide a benchmark against which subsequent changes can be computed.

Flexible Native Labor Supply/Spatially Dispersed Immigration Patterns: Production Structure, LFPR, and Demand Channels. These results for both natives and immigrants are more negative (or less positive) than the analogous set in the spatially concentrated case. The reason is that net export effects are blocked in the spatially dispersed case. If we assume that the immigrants have no non-labor income, the impacts on native real wages and employment are negative (-0.07% and -0.20%, respectively) but relatively small. As we increase the amount of non-labor income possessed by immigrants, the impacts are reduced. At the 50 percent level, we estimate that natives are unaffected. At the 100 percent level, native real wage rates and employment are above baseline levels (0.08% and 0.20%, respectively).

Because this set of simulations is based on a dispersed pattern of immigration, native real wage gains occur throughout the metropolitan system and consequently do not represent differentials across space that migration can arbitrage. Therefore, a native migration simulation is not applicable in this case.

All Areas: Sensitivity Analysis

The estimated elasticities of native labor supply to the real wage and aggregate demand to real income are high, as previously noted. The sensitivity of the results to lower real wage elasticities can be bracketed by comparing the fixed labor supply results to those for flexible labor supply. In the fixed supply case, the real wage elasticity is zero. This comparison shows that in either case the impacts on natives are small and can be positive.

To gauge the sensitivity of the results to the elasticity of aggregate demand for local output, we resolved the model with the elasticity reduced from unity to 0.7. These additional simulations assume a fixed native labor supply. The results are reported in Table IX. Although the impacts are more negative (or less positive), as expected, they are still small in absolute terms for natives. Relatively, the foreign-born are more adversely affected, as before.

Areas by Region and with Large Relative Immigration

The results for four of the alternative simulations are presented in Table X for areas grouped by census region and for that set of areas that had the relatively largest immigration during 19701980. For each group of areas, the reported results are unweighted averages. They are based on 27 areas in the Northeast region, 31 areas in the Midwest region, 40 areas in the South region, 24 areas in the West region, and 24 areas that experienced relatively large recent immigration as indicated in Table I. To facilitate comparison, the corresponding results for all areas are also reported.

Fixed Native Labor Supply: Production Structure Only. The results for all groups of areas are qualitatively similar to the unweighted results for all areas. Ten percent more immigrants reduce the wages of both native and foreign-born workers with the impacts greater for the foreign-born. However, the magnitude of the negative effects is larger in the Northeast and West regions and in the areas with relatively large recent immigration. The unweighted average decline in native [TABULAR DATA FOR TABLE X OMITTED] wages in the West, for example, is -1.40% which is double the impact on natives in the South (-0.70%) and more than double the impact in the Midwest (-0.58%). The impact in the areas incurring relatively large recent immigration is the largest of all with native wages falling -1.84%.

The pattern of impact on foreign-born worker wages is similar to the effects in the Northeast (-2.99%), West (-3.66%), and in areas with relatively large recent immigration (-4.58%) being more negative than those in the Midwest (-1.78%) and South (-1.90%).

Fixed Native Labor Supply: Production Structure and Local and Export Demand. These results are based on the simulations that include demand and assume that immigrants have no sources of non-labor income. They are consistent qualitatively with those for all areas. In the case of each census region and for the group of areas experiencing relatively large recent immigration, opening the local and export demand channels mitigates the adverse consequences on natives and foreign-born workers. For natives, wages are now either at baseline levels or slightly above them. It is interesting that in the West and the areas of relatively large recent immigration, the largest positive percentage gains from baseline occur for native wages. These were the areas that exhibited the most substantial decline in native wages when only production structure effects were considered. The reason for this is that these areas have the largest shares of immigrant labor income in total output. They also have the largest negative impacts from production structure effects on foreign-born wages. Consequently, unit costs decline relatively more and the competitive net export effect is larger, leading to relatively stronger labor market outcomes for natives in these areas.

The impacts on foreign-born worker wages are still negative, but the extent of the declines is mitigated substantially by the partially offsetting effects of increases in demand. The largest negative effects occur as in the previous simulation in the Northeast (-1.98%), West (-2.23%), and the areas with relatively large recent immigration (-2.74%).

Flexible Labor Supply: Production Structure Only. In these simulations, adjustments can occur in both wages and employment. The results for each of the five groups of areas are qualitatively similar to the results for all areas. As in the case of the simulations that have only the production structure channel open, these results indicate that the impacts on native wages and employment are larger in the Northeast and West regions and in the areas that experienced relatively large recent immigration. This pattern holds for the impacts on foreign-born wages as well.

Flexible Native Labor Supply: Production Structure and Local and Export Demand. As before, we assume that immigrants have no sources of non-labor income. The demand effects mitigate the production structure impacts. For natives, wages and employment return to or exceed baseline values except in the cases of wages in the Midwest (-0.01%) and employment in the Midwest (-0.02%) and South (-0.01%). These departures from baseline are extremely small, however. As in the fixed native labor supply case with demand channels open, native wages and employment are most favorably affected in the West (0.05%, 0.09%, respectively) and in those areas experiencing relatively large recent immigration (0.04%, 0.08%, respectively).

The impacts on foreign-born worker wages are reduced as well when demand effects are permitted to play a role. The largest impacts on wages are in the Northeast (-1.98%), West (-2.22%), and areas with relatively large recent immigration (-2.73%). The impacts in the South (-1.22%) and the Midwest (-1.22%) are less.

VI. Summary and Conclusions

In this study we use SMSA data constructed from 1980 census microdata files and other sources to estimate a structural model of native/foreign-born labor demand and labor supply that distinguishes the effects on real wages of each type of labor and on employment of natives. What especially sets our model apart from others is that we specify, econometrically estimate, and simulate a structural model that incorporates not only a production structure channel through which immigrants influence area real wages and employment, but also demand and native labor supply channels. These are not the only channels through which immigrants might affect native workers. Among other potentially important channels are technological change, agglomeration economies, inflation, balance of payments, remittances, tax and transfer payments, use of public services, and externalities. However, our model constitutes a step in the direction of a general equilibrium approach.

In the production structure channel, immigrants and natives are found to be substitutes in production. Immigration lowers foreign-born wage rates and leads to lower wages for natives. The negative effects of the production channel usually are ameliorated through the demand channel. Immigrants add to local demand through their earnings and potentially through non-labor income. Immigrants induce lower unit costs and local prices. This enhances real incomes and potentially net exports, and therefore the demands for local output and area labor.

Several interesting findings emerge from our simulation results based on an analysis of all areas. First, production structure results are consistent with those of Grossman [15], who finds that immigrants and natives are substitutes in production. Second, the maximum negative impact on natives is a -0.88 percent decline in real wage rates, or a -0.17 percent decline in real wage rates accompanied by a -0.41 percent drop in employment. These impacts are based on an absence of demand effects and native migration adjustments. Third, opening the demand channel almost always eliminates the negative effects on natives. The exception is in the case of a spatially dispersed immigration pattern combined with immigrants who have no non-labor income. In all other cases, the impacts on natives are zero or slightly positive. Fourth, the impacts on the foreign-born are always negative. The maximum impact is a -2.46 percent change in real wages (about two-and-one-half times the magnitude for natives). The smallest impact is a -1.13 change in real wages.

Moreover, when our simulation results are grouped by region, we find that the impacts are generally consistent qualitatively with the results for all areas. These results show that the impacts on natives and foreign-born workers through the production structure channel are larger in magnitude in the Northeast and West regions and in those areas that had relatively large recent immigration. Finally, in these regions we find more positive impacts on natives when demand effects are considered.

Whether past studies claim to show that immigrants are substitutes or complements for native labor, virtually all of them conclude that the effects on the wages and employment opportunities of native workers are quantitatively small. The greatest negative impacts appear to be on the foreign born. The present study attempts to account for channels of immigrant influence other than those that directly relate to production structure, which has been the focus of most previous attention. It too shows that the effects of immigrants are small. When demand and native labor supply channels of influence are taken into account, the effects on natives are almost always negligible or slightly positive. Moreover, foreign-born workers have the greatest negative influence on other foreign-born workers. These results hold on average across all areas in our sample and for areas grouped by region of the U.S. and for those experiencing relatively large immigration during 1970-1980.

Finally, Filer [12] argues that areas with high concentrations of immigrants were less attractive to natives as evidenced by internal migration patterns. However, Butcher and Card [7] report that native migration and immigration are positively correlated. Our results provide an explanation for this latter finding. We see at least two reasons for the finding that involve the inducement of improved native labor market outcomes. If natives and immigrants are complements in production, then additional immigrants raise native wages and attract native migrants. The problem with this explanation is that the literature consistently reports the finding that natives and immigrants are substitutes in production. A second explanation is that the negative effects on natives resulting from their substitutability with immigrants is more than offset by the demand effects of immigration. Our research provides empirical support for this more coherent explanation.

1. Ignoring taxes, the cost of capital ([W.sub.3]) is determined as

[W.sub.3] = ([Rho] + [Delta])[p.sub.k]

where [Rho] is the opportunity cost of capital, [Delta] is the depreciation rate of capital, and [p.sub.k] is the price of a unit of capital stock. This price is assumed to be determined outside the region. It is assumed that [Rho] and [Delta] are regionally invariant. Let [Phi] represent tax provisions applicable to the stock of capital and T represents those applicable to the income from capital. The national or international supply price for capital services ([W.sub.3]) is determined by the following relationship

(1 - T)[W.sub.3] = [Phi]([Rho] + [Delta])[p.sub.k]

or

[W.sub.3] = [[Phi]/(1 - T)]([Rho] + [Delta])[p.sub.k].

The region-specific cost of capital is therefore

[w.sub.3] = [[Phi]/(1- [Tau])]([Rho] + [Delta])[p.sub.k].

The corresponding relative cost of capital for a region (rcok) is obtained by dividing the region-specific cost of capital by national cost of capital. Because the opportunity cost, depreciation rate, and price of capital terms have the same value in the region as in the nation, by assumption, rcok reduces to

rcok = [w.sub.3]/[W.sub.3] = ([Phi]/[Phi])/[(1 - [Tau])/(1-T)]

2. The estimates are not significantly affected when the foreign-born share of the 1970 area population is included as an instrument. An argument for the inclusion of such a variable could be based on Bartel's [2] finding that location choices of new immigrants are significantly influenced by the spatial distribution of previous immigrants from the same country of birth. Our instruments are apparently picking up any such effect.

3. Certain aspects of the broader study of which this was part required both 1970 and 1980 PUMS data. The 1980 B Sample contains 282 distinct SMSAs and 36 paired SMSAs. However, the 1970 County Group PUMS contains information on only 125 distinct SMSAs. Thus, the availability of 1970 data ultimately determined the number of SMSAs that could be used as the observation base in this study. Two (1970) SMSAs were lost due to their being combined in 1980. Dallas and Fort Worth were combined to form the Dallas-Fort Worth SMSA, which is included in the data base as a single SMSA. Wilkes-Barre-Hazelton and Scranton were combined to form the Northeast Pennsylvania SMSA. However, since Scranton was not included in the 1970 file, this SMSA was not incorporated into the data base.

4. Nominal output for the 123 SMSAs was formed in the following way. Let nominal output (thousands of dollars) for each of the areas be stacked in a 123 x 1 vector Z. The following steps were undertaken to create Z:

Z = diag(C)

C = AB[prime]

A = [A.sub.1]/[A.sub.2] (where "/" indicates Hadamard, or element-by-element, division)

where

[A.sub.1] [equivalent] 123 x 10 matrix of 1980 Gross State Product (thousands of dollars) - 123 areas, 10 major industry divisions [5].

[A.sub.2] [equivalent] 123 x 10 matrix of 1980 state earnings (thousands of dollars) - 123 areas, 10 major industry divisions [5].

B [equivalent] 123 x 10 matrix of 1980 earnings (thousands of dollars) - 123 areas, 10 major industry divisions [6].

Data in [A.sub.1] and [A.sub.2] are the data for the states in which the 123 areas are located (e.g., data for Boston are Massachusetts data).

5. The monotonicity condition is checked by confirming that the factor shares (and therefore factor demands) predicted at each observation in the data are positive. Negative fitted foreign-born labor cost shares occur for the following areas: Utica-Rome, N.Y.; Buffalo, N.Y.; Binghamton, N.Y.; York, Pa.; Charlotte, N.C.; Chattanooga, Tenn.; Knoxville, Tenn.; Huntington, Ken.; Cincinnatti, Oh.; Pittsburgh, Pa.; South Bend, Ind.; Peoria. Ill.; Appleton-Oshkosh, Wisc.; Kansas City, Mo.; and St. Louis, Mo.

6. The concavity condition is checked by evaluating the definiteness of the Hessian. At each observation the estimated Hessian matrix has two negative and one zero eigenvalues, which implies that it is negative semi-definite as required at all sample observations.

7. The estimation of a cost function naturally yields the direct price elasticities based on the Allen-Uzawa elasticities of substitution. However, the fact that the stock of foreign-born labor is being increased indicates that the inverse price elasticities of factor demand derived from the Hicksian elasticities of complementarity are important. These Hicksian elasticities naturally are obtained from production function estimates. However, following the procedures outlined in Kohli [19], we compute the inverse price elasticities from our direct price elasticity estimates. At the average of the data for all areas, a one percent increase in foreign-born labor results in a -0.02 percent change in native wages, a -0.20 percent change in foreign-born wages, and a 0.03 percent change in the rental price of capital services. These estimates are qualitatively and quantitatively consistent with those based on the Allen-Uzawa elasticities of substitution as reported in Table V.

8. Our constant markup of price over unit cost (equation (6)) is consistent with our specification of a constant elasticity form for the demand equation. The value of the markup parameter [Phi] is implicitly incorporated in the constant term of equation (22).

9. Our estimated elasticity of 1.1 is within the range reported by Engle [11] in his study of the Boston area. It is lower than the estimate of 1.8 obtained by Treyz, Rickman, and Shao [13].

10. The spatially concentrated case is more consistent with observed immigrant location patterns [2].

References

1. Altonji, Joseph G. and David Card. "The Effects of Immigration on the Labor Market Outcomes of Less-skilled Natives," in Immigration, Trade, and the Labor Market, edited by John M. Abowd and Richard B. Freeman. Chicago: University of Chicago Press, 1991, 201-34.

2. Bartel, Ann P., "Where Do the New U.S. Immigrants Live?" Journal of Labor Economics, October 1989, 371-91.

3. Borjas, George, J., "The Sensitivity of Labor Demand Functions to Choice of Dependent Variables." Review of Economics and Statistics, February 1986, 58-66.

4. -----, "Immigration, Minorities, and Labor Market Competition." Industrial and Labor Relations Review, April 1987, 382-93.

5. Bureau of Economic Analysis. Local Area Personal Income, Volume 1, Summary, 1979-84. Washington, D.C.: U.S. Government Printing Office, August 1986.

6. -----. Local Area Personal Income, Volume 1, Summary, 1976-81. Washington, D.C.: U.S. Government Printing Office, June 1983.

7. Butcher, Kristin F. and David Card, "Immigration and Wages: Evidence from the 1980's." American Economic Review, Papers and Proceedings, May 1991, 292-96.

8. Chambers, R. G. Applied Production Analysis: A Dual Approach. Cambridge: Cambridge University Press, 1988.

9. Dhrymes, Phoebus. J., "Small Sample and Asymptotic Relations Between Maximum Likelihood and Three Stages Least Squares Estimators." Econometrica, March 1973, 357-64.

10. Diewert, W. E. and T. J. Wales, "Flexible Functional Forms and Global Curvature Conditions." Econometrica, January 1987, 43-68.

11. Engle, Robert F., "Estimation of the Price Elasticity of Demand Facing Metropolitan Producers." Journal of Urban Economics, January 1979, 42-64.

12. Filer, Randall K. "The Effect of Immigrant Arrivals on Migratory Patterns of Native Workers," in Immigration and the Work Force, edited by George J. Borjas. Chicago: University of Chicago Press, 1992, 245-69.
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Date:Apr 1, 1995
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