The Substitutability of Natives and Immigrants in Production Author(s): Jean Baldwin Grossman Source: The Review of Economics and Statistics, Vol. 64, No. 4 (Nov., 1982), pp. 596-603 Published by: The MIT Press Stable URL: http://www.jstor.org/stable/1923944 Accessed: 22/09/2010 11:12 Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at http://www.jstor.org/action/showPublisher?publisherCode=mitpress. Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission. JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact
[email protected].
The MIT Press is collaborating with JSTOR to digitize, preserve and extend access to The Review of Economics and Statistics.
http://www.jstor.org
THE SUBSTITUTABILITY OF NATIVES AND IMMIGRANTS IN PRODUCTION Jean BaldwinGrossman* 1970, the most recent year for which such data are available, to estimate aggregate production T HE United States is a countryof immigrants relationships. The resulting estimates shed light and sons and daughters of former immi- on the substitutability between the stock of imgrants. From colonial times to the 1920s, Amer- migrants in the United States at that time, and ica had an open door immigration policy. Al- the native work force. Until more is known about though the formal policy generally welcomed the employment behavior of more recent illegal immigrants, those who preceded the newcomers and legal (especially refugee) immigrants, this is have never looked kindly on the arrival of new the best that can be accomplished. immigrants. Xenophobia has been a common reaction by Americans to large scale inflows. AlII. Specification and Data though ethnocentrism undoubtedly is one reason for such isolationist feelings, fear of economic Several studies have examined the substitutdisplacement is another underlying cause.' At ability of various labor disaggregates.2 Both the center of the debates over immigration policy time-series and cross-section data have been has been the fear that the newcomers take jobs used to determine the substitutability between away from native Americans. The substitutabil- capital, non-production and production workity of natives for immigrants is critical in evaluat- ers.3 Most of these studies have concluded that ing the validity of the displacement fears. blue collar and white collar workers are substiA number of theoretical contributions, includ- tutes; and that capital is a substitute for blue ing Gerking and Mutti (1979), Grossman (1981) collar workers and a complement to white collar and Johnson (1980a) have dealt with the eco- workers. A few studies have disaggregated nomic effects of international labor inflows. workers by educational attainment.4 These studHowever, no empirical investigation of these is- ies have generally found that the labor disaggresues has been undertaken. The absence of such gates are substitutes for one another and that studies is due, at least in part, to the lack of "raw" labor and capital are also substitutes. A accurate data on the number of employed illegal last general category of labor disaggregation is by immigrants, who comprise a substantial portion age.5 Again, capital is shown to be a substitute of the immigrant stock. While it is currently not with all categories of labor and the various labor possible to develop empirical estimates of the categories are shown to be substitutes for one substitutability of illegal immigrants and natives, another. or even between the most recent wave of legal Although much has been learned from these immigrants and natives, it is nonetheless useful studies, they do not bear directly on the question to investigate the relationship in production that of the degree of substitutability of immigrants for has historically existed between immigrants and natives, which is the subject of the present paper. the domestic labor force. Table 1 presents characteristics of legal immiIn what follows, I use cross-section data for grants surveyed in the 1970 Census, and comI.
Introduction
Received for publication September 30, 1981. Revision accepted for publication February 22, 1982. Mathematica Policy Research. The author would like to thank Bryan Boulier and Daniel Hamermesh for useful comments and James Grant for providing his capital stock data for this study. I An additional social concern is whether or not immigrants constitute a net burden to the social welfare system. Simon (1980), at a macro level, and Blau (1981), at a micro level, show that immigrants are not more likely to use the transfer system. However, more research is needed in the area.
1 596 1
See Hamermesh and Grant (1979) for a critical survey of these studies. I For examples of cross-section studies see Freeman and Medoff (1982), and Chiswick ( 1978). For time-series studies see Berndt and Christensen ( 1974) and Clark and Freeman (1977). 4 Griliches (1969), Grant (1979), Johnson (1970), and Welch (1970). See Freeman ( 1979), Anderson ( 1977). and Johnson and Blakemore (1979).
SUBSTITUTABILITY
OF NATIVES AND IMMIGRANTS
pares them with those of 1970 Census natives.6 The stock of immigrants in 1970 was, on average, older and less educated than natives. However, there is no obvious correspondence between the immigrants' characteristics and the disaggregation of previous studies. To determine the production relationship among immigrants, second generation natives, and natives, we estimate a translog production function. A production function, rather than a cost function, is used to discern the underlying technology because, in this case, it is more reasonable to assume that quantities are fixed rather than prices.7 The production function from which we obtain the estimable factor share equations is a second order Taylor series approximation to Q = F(N,SG,FN,K)
TABLE
1.-SELECTED
CHARACTERISTICS
S597 OF THE
BY NATIVITY POPULATION (MALES AND FEMALES COMBINED)
Mean Years of Education Completed by Those Ages 25 to 64 Natives with native parents Natives with a foreign-born parent Foreign-born persons (immigrants)
12.1 12.2 11.2
Median Age Range of Those Ages 15 to 64 Natives with native parents Natives with a foreign-born parent Foreign-born persons (immigrants)
30-34 45-49 40-44
Percentage of Those Ages 16 to 64 Choosing a White Collar Occupation (Professional, Manager, Clerical, or Sales) Natives with native parents Natives with a foreign-born parent Foreign-born persons (immigrants)
45.6% 53.9%o 44. O%c
Source: U.S. Census of the Population: 1970, National Origin and Language PC(2)- tA.
(1)
where Q is the quantity produced, N is the number of employed native workers over 16,
SG is the number of employed second generation native workers over 16, FN is the number of employed foreign born workers over 16, and K is the capital stock. The factor share equations, derived with the
It is useful in considering the policy implications of the later results to compare the characteristics of recent immi- assumption of perfect competition, are grants, as reported in the Immigration and Naturalization Si = ?a + yi,n ln N + yi, ln SG + -yif ln FN Service Annual Reports, with those of the 1970 stock upon which the estimates are based. The median age of the immi+ Yi,k ln K grants admitted between 1971-79 is 25.0 years old, younger (2) i=n,s,f,k; than the 1970 stock, but approximately equal to the median age of immigrants admitted between 1951-60, 25.8, and where Si is the share of factor i in production, 1961-70, 25.2. Information on education is not available: i.e., wjXi/Q. Demand theory requires symmetry, the that percentindicate on occupations however, the data age of recent immigrants with white collar jobs is much less yij = yji. We also impose homogeneity, la, = 1. than that of the 1970 stock of foreign-born workers, approxiWhen assuming that quantities and not prices mately 17.6%. The younger age and lower occupational status is explained, in part, because the immigrants of the 1970s arc are exogenous, the appropriate measure of factor recent arrivals, whereas those of the 1970 stock have been ir substitutability is the Hicks elasticity of comthe United States, on average, for many years. The differencc plementarity rather than the Allen elasticity of which is likely to make the greatest economic difference is that many more of the immigrants admitted in the 1970s were substitution.8 The Hicks elasticity of comrefugees. Sixty per cent of all immigrants admitted since 1954 plementarity, Cij, is defined as the proportional were admitted between 1971-1978. Whereas 6.4% of the im change in relative wage for factor i given a promigrants admitted between 1961-1970 were refugees, 11.6QA portional change in factorj's endowment, holdwere refugees in the 1971-1978 period. Work by Chiswisl ( 1978) indicates the refugees do worse with respect to wag( ing the output price and other input quantities profiles than non-refugees, and therefore may be conclude( constant. Alternatively it can be defined as Cij = to be economically less successful than non-refugees. 7 Hamermesh and Grant (1979) discuss the assumption: FFij/FiFj, where Fi is the first derivative of the needed to justify the use of cost or production functions. Ii production function F with respect to factor i and our problem, we are dealing with input categories that canno F,j is a second derivative. In terms of the translog change very rapidly, except possibly, the immigrant cate gory. However, the number of immigrants allowed into thc coefficients, country in a given year is limited by law. As of 1965, the tota number of preference immigrants was restricted to 290,000 Cij = (1Yij+ SiSj)/ssj, The quota is always fully subscribed. To consider all the inputs as approximately fixed we must assume there is nc I Hicks (1970) and Sato and Koizumi (1973) discuss the mobility. We are using a cross-sectional approach to mak relationship between the two elasticities. more plausible. this assumption 6
THE REVIEW OF ECONOMICS AND STATISTICS
598 and
TABLE 3.-TRANSLOG
COEFFICIENTS
FOR THE PRODUCTION
FUNCTIONa
Cii
=
(yii + Sj2 - S )/S,.
Factors i and j are substitutes if Cij is negative and complements if Cij is positive. The factor share equations are estimated for nineteen SMSAs for the year 1969 since more recent information is not available.9 It is not possible to obtain the capital stock for the nonmanufacturing sectors. Hence, we must assume the total capital stock is proportional to the capital stock in the manufacturing sector. Mean values for the variables are shown in table 2. Capital's share is taken to be one minus the labor shares. The labor shares are understated because they do not account for fringe benefits or firms' Social Security contributions. This causes capital's share to be overstated. III.
Results and Discussion
In Q
In aa + Ea,1n Xi + il^yijj In X, In X,, i = n, s, f, k, andXi = N, SG, FN, K (standard errors in parentheses) Capital Included
axn
as af ak
,n-.08 tYn' 'In, f YIn,k
tyn,k
'YS^S.f 'Ys,k ,/fj 'If,.k 'Yk,k
.23 .24 .12 .40 .15
(.06) (.02) (.01) (.06) (.04) (.01) -*.02 (.005) -.05 (.04) .11 (.01) -.01 (.003) -.02 (.01) .04 (.003) -. 004 (.004) .07 (.05)
Capital Excluded .17 (.03) .23 (.01) .11 (.007) .12 (.01) -.09 (.007) -.02 (.004) .10 (.006) -.0 1 (.003) .04 (.003)
Note: The mean square error for the system with capital is 1.65 with 48 degrees of freedom, without capital it is 1.53 with 51 degrees of freedom. I Zeliner's seemingly unrelated regression technique was used to estimate the system of factor share equations. The capital share equation was deleted for estimation.
Equation (2) was estimated using Zellner's seemingly unrelated regression technique to take account of the cross-equation correlations. The three coefficients are simultaneously zero, this from labor results are presented in table 3. From the first would imply that capital is separable to be included in a does not have capital so that column of table 3, we observe that the this for F-statistic The equation. share or demand coefficients on the capital interaction terms (Y,,k, hypothesis is 1.10. Thus, we cannot reject the Ys,k, 'Yf.k) are all individually equal to zero. If the hypothesis that coefficients are simultaneously 9 1980 data by nativity will not be available for several zero. Notice that other coefficients change very years, therefore, 1970 data were used. The employment and little with the deletion of the capital stock variincome data were taken from the Nationial Origin and Lanable as would be expected if the production funcguage Sob/'ject Report. The output data were collected from the Countxt and Citx' Data Book. An SMSA's output was tion exhibited separability. defined to be sum of total local government revenues, total Most of the previous studies that have examvalue added in manufacturing, total retail sales, total service the empirical separability of capital and ined capital receipts and, total wholesale sales. The manufacturing and the data were derived from the Census ofManutJacturing labor have used time series studies data (e.g., Annuiial SurOey of MManlfa(cturing. (The author is very grateful Berndt and Christensen, 1974; and Denny and to James Grant for providing his capital stock data for this Fuss, 1977). With their disaggregations of labor study.) into broad occupational classes, these studies rejected the separability hypothesis. Grant (1979), OF THE VARIABLES TABLE 2.-MEANS using cross-section data, also found that when Mean Variable labor is disaggregated by occupational or educa.33 tional class, labor is not jointly separable from Share of natives' value-added in output .13 Share of the second generation's capital. However, if labor was disaggregated by value-added in output age, or jointly by age and education, capital was .05 Share of foreign-born's value-added in output empirically separable. His study thus reinforces .49 Share of capital's value-added in output our finding that under certain disaggregation of 607,688 Number of native workers labor, capital can be treated empirically as a (in thousands) 203,775 Number of second generation workers separable input. However, it is also clear that (in thousands) should be tested, not simply asseparability 80,545 Number of foreign-born workers since not all labor disaggregations are sumed, (in thousands) 1,404,001 Amount of capital used consistent with empirical separability. Although (in thousands of dollars) we cannot reject the hypothesis of separability,
SUBSTITUTABILITY OF NATIVES AND IMMIGRANTS we will continue to examine the coefficients from the equations where capital was included, as well as those from where it was excluded, because the power of the separability test is quite small. The elasticities of complementarity calculated using the coefficients in table 3 and the mean values of each factor share are presented in table 4. Factors are substitutes if Cij is negative and complements if positive. Both second generation workers and foreign-born workers are substitutes for native workers, but the second generation workers are much more highly substitutable for natives than are foreign-born workers. Immigrants substitute for second generation workers much more easily than for native workers. The regressions indicate that capital is complementary with all types of labor but the degree of complementarity is strongest with foreign-born workers and weakest with native workers. To relate these findings with previous work, consider the characteristics of immigrants. From table 1 we saw that foreign-born workers are slightly less educated and older than both native workers and second generation natives. Both types of adult natives had completed just over twelve years of schooling, whereas the adult immigrants had completed just over eleven years. The median age of natives with native parents was between 30-34, between 45-49 for second generation natives, and between 40-44 for immigrants. Our results show that capital seems to be more complementary with the less educated imTABLF 4.-El
599
migrants than with natives, which is somewhat contradictory to the hypothesis presented by Zvi Griliches (1969) that "education is more complementary with physical capital than with unskilled or raw labor."'0 The results also could not have been deduced from Anderson's (1977) results which show that all age groups are substitutes with capital. '' Our results are probably best compared with those of Grant (1979), because he is one of the few to estimate elasticities of complementarity and, in addition, he used 1969 cross-section data. He finds, as we do, that when labor input is disaggregated by either age or by education, capital is complementary with all labor groups.'2 He also finds that the degree of complementarity increases with age, which is conGriliches (1969), p. 465. " Anderson's (1977) results estimated that the elasticities of substitution (tiot complementarity) between capital and various age groups were 9.40 for those 16-24, 0.37 for those 25-44, and 1.38 for those over 45. 12 Grant's elasticities of complementarity of the two models are "I
By Age 14-24 yrs. 25-44 yrs. 45+ yrs. Capital
14-24 yrs.
25-44 yrs.
- 2.20
-0.12 1.03
- 0.20 -0.02 -1.19
0.36 0.51 0.60 -0.58
9-12 yrs.
12+ yrs.
Capital
3.74 -1.53 -15.04
0.25 3.15 5.46 - 3.72
By Education 0-8 yrs. 0-8 yrs. 9-12 yrs. 12+ yrs. Capital
-15.33
1.84 5.17
45+ yrs.
Capital
ASTICITIES OF FAC1-OR COMPLEMENTARITIESa
(standard errors of yij coefficients in parentheses) With Respect to the Quantity of)' N Wage of
"/K -.61 (.04)
N .SG
FN
SG w/o K
w/K
w/o K
W/K
w/o K
K
-.95 (.01)
-.92 (.01) - .26 (.01)
-1.17 (0.007) -0.52 (0.006)
-0.32 (0.005) -0.61 (0.003) -4.65 (0.003)
-0.50 (0.004) -0.69 (0.003) -4.73 (0.002)
.69 (.04) .73 (.01) .85 (.004) -.75 (.05)
EN A: I'he elasticities of factor complementarity are defined as d In(pi/pp)1d In(qlqj), or (ii
( Yi,
4-
.j
S,)i
S,S,
(tnd Cj
( yii + S
-
S,)//Si-
wher-e y,, is the translog production function coefficient and Si is the share of factor i in output. The estimates above are evaluated at the means of the S,'s. Factors are substitutes if Cij
