Asian American Women PROFESSIONALS:

DOES DISCRIMINATION EXIST?

DON MAR^*

this article examines the earnings of American-born Asian women professional using data from the 1990 Census by comparing their actual hourly wage and salary earnings to simulated earnings. The simulated earnings are obtained by using parameter estimates obtained from human capital models of white women corrected for sample selection bias.

American born Asian American women appear to have made dramatic gains in the 1970s. The 1980s and 1990s appears to be a period of relative economic parity between Asian American and white women. ( JEL J71, J15)

I. IntroDUCTION

The earnings progress experienced by American ethnic minorities and women reflects changes in the structure of economic discrimination in the United States. The degree of Asian American economic progress is marked by controversy with some researchers arguing that substantial earnings parity for American-born Japanese and Filipinos was achieved as in the 1970s. (See, for example, Hirschman and Wong, 1984.). Others believe that Asian Americans have never reached economic parity with whites and continued to face discrimination as late as the 1980s (Nee and Sanders, 1985; Duleep and Sanders, 1992 ). There have been various empirical studies provided to support each of these positions based on analyses of men. Mar (2000) found that Asian American women faced significant earnings discrimination in 1960, made substantial economic progress by 1970, and stayed at earnings parity with non-Hispanic white women in 1980 and 1990.

Although average US-born Asian American women's hourly earnings are approximately at parity for all occupational groups, there is evidence to suggest that there may be some evidence of "discrimination at the top" amongst US-born Asian professional workers. Duleep and Sanders (ibid) offer some preliminary evidence of discrimination within professional workers using 1980 Census data. One, they find that there are earnings differences among higher educated Asian men relative to non-Hispanic whites. Two, using logit analysis, they find that Asian men are less likely to be employed as managers among professional workers. King and Locke (1980) in their historical analysis of occupational change among Chinese in the United States find that Chinese with 4 years of college are less likely to be employed as professionals when compared to all US workers during the 1970s and 1980s. Finally, recent public surveys find significant resentment against Asian Americans in the workplace, particularly as supervisors and managers (Tang, 1997; SF Chronicle, 2001).

This paper examines earnings discrimination in professional occupations among Japanese, Chinese and FilipinoAmerican women, relative to non-Hispanic white women[1]. The 3 Asian groups were chosen as they are the largest groups of American born Asians. Only US-born women are studied in order to avoid problems associated with earnings estimation of foreign-born women. Data for this study comes from the 5% decennial 1990 Census Public Use Micro Samples (PUMS).

The basic methodology employed is to simulate Asian American women's earnings using parameter estimates derived from white human capital regressions. The difference between simulated earnings and actual earnings are a frequently used variation of the Oaxaca-Blinder decomposition of discrimination (Oaxaca, 1973; Blinder, 1974). This method is commonly employed as a means of studying the relative economic progress of ethnic groups over time. More recently, Neuman and Oaxaca (1998) have investigated the effects of selectivity corrections on the Oaxaca-Blinder decomposition of earnings discrimination by occupation. The methods described in Neuman and Oaxaca are applied to the Asian American professionals in this paper.

II. PAST STUDIES

Sociologists have a long tradition behind this debate sparked by the literature on racial and ethnic stratification (Warner and Srole, 1945; Gordon, 1964). Earlier studies concentrated on an assimilation model emphasizing the similarity between Asian cultural values with American cultural values as a vehicle for economic advancement (Kitano, 1969; Caudill and Devos, 1969; Petersen, 1971). Later studies argued strongly against this values based explanation, citing the persistence of discrimination and other institutional factors as limiting factors to economic advancement (Nee and Sanders, ibid; Cabezas and Kawaguchi, 1988; Duleep and Sanders, ibid).

Economists recently entered the debate, but with a slightly different flavor. Initial interest in Asian Americans centered around the labor market adaptation of Asian American immigrants to the United States. These studies concluded that immigrants were self-selected; self-selected in the sense of high motivated individuals. With additional time spent in the United States spent adapting to the labor market, higher motivation allows immigrant earnings to eventually equal and surpass native-born earnings, assuming that human capital attributes such as education and experience are equal (Chiswick, 1978, 1979, 1980). Borjas (1985, 1987, 1990) has argued that skill differences in immigrant cohorts over time account for the observed human capital results instead of labor market assimilation.

Higher motivation is also passed onto the sons and daughters of immigrants allowing the second generation of Asian Americans even higher levels of earnings (Carliner, 1980; Chiswick, 1983). Thus, economists argued not only that parity could be attained by both foreign-born and American-born Asian Americans, but also that Asian would do better than the white majority due to higher motivation as opposed to the similarity of values espoused by some of the earlier sociological studies.

There is relatively little work in estimating the earnings regressions for Asian American women. The majority of the empirical studies on Asian American earnings have focused on the earnings of men. This has been traditional in economics where problems modeling the earnings function of women have been complicated by their entry and exit from the labor market (Mincer and Polachek, 1974).

In an earlier study using Census PUMS data from 1960 through 1990, Mar (2000) found that American born Asian women faced considerable discrimination in 1960. However, dramatic earnings gains were made in the 1970s with relative economic parity between Asian American and white women from 1980.

Carlson and Swartz (1988) present a brief empirical examination of the changes in Asian American women’s earnings using the 1970 and 1980 census data as part of a larger study of women’s earnings by ethnicity. One, they find that 1979 unadjusted earnings for Chinese, Japanese, and Filipino were higher than that of white women. After adjusting for human capital differences, they find that Japanese and Filipino earnings would have been lower using the white women’s parameters. For Chinese women, adjusted earnings would have been slightly higher. Their evidence also shows some relative improvement from 1969 to 1979 for Asian American women in terms of a narrowing of the earnings gap between Asian American women and white men. One problem with the Carlson and Swartz study is their pooling of the foreign-born women with US born women.

The Human Rights Commission report (1988) also analyzes 1980 Census data to compare earnings of Asian American women to white women. The authors do separate comparisons for foreign-born women and US-born women. They find that foreign-born Filipino women have higher earnings than white immigrant women. For American-born Filipino women, foreign-born and US-born Chinese, and foreign-born and US-born Japanese women, there are no differences in earnings compared to white women.

Brown (2001) utilized 1990 Census PUMS data to find some weak evidence of discrimination against Chinese and Japanese men with high levels of education in the San Francisco Bay Area. The adjusted earnings for Chinese and Japanese with professional or doctoral degrees using white human capital coefficients were generally higher although the sample sizes were rather small.

Tang (1997) finds some evidence of a lower likelihood of Asian women being promoted to managerial or administrative positions. (See article when it arrives).

Given the problems and lack of research cited above, the earnings of Asian American women are examined using the 1990 US Census PUMS data. Careful attention is paid to self-selection issues.

III. DATA AND METHODOLOGY

The Census of Population 5% PUMS are the only large sample sources of data on Asian Americans. The Chinese, Japanese, and Filipino respondents to the decennial PUMS are extracted for analyses as well as a 1 in 10,000 sample of whites for comparative purposes. The samples are limited to US-born women between the ages of 25 and 64 with wage and salary earnings during the reference year.

The basic methodology employed in this paper is to estimate human capital earnings functions for the various ethnic groups by place of birth over time and then to simulate Asian American earnings as if they were treated as whites. The following familiar Becker (1974) type human capital earnings models are estimated:

LOG (EARNINGS) = b₀ + b_1-6*EDUCS + b₇*EXPER + b₈*EXPER2 + b₉*MARRIED

+ b₁₀*CHILDREN + b₁₁*MGR + b₁₂*MGMTREL + b₁₃*ENGSCI

+ b₁₄*HEALTH + b₁₅*TEACHER + b_16-20*REGIONS + b_21-31*INDUSTRY

+ b₃₂*PUBLIC + q*l_i + u_i

where: EARNINGS = hourly earnings; EDUCS = six dummy variables for educational attainment for high school graduate, associate degree, bachelor's degree, masters degree, professional degree and doctoral degree; EXPER = years of potential experience calculated by subtracting number of years spent in school plus 4 from age. The number of years in school was calculated by taking the Census Years of Schooling variable and assigning a number of years in the middle of the range of possible years spent in school; EXPER2 = years of experienced squared; MARRIED = dichotomous variable for married individuals; CHILDREN = number of children ever born to this individual; MGR = dichotomous variable for individuals employed in managerial occupations; MGMTREL = dichotomous variable for individuals employed in management related occupations; ENGSCI = dichotomous variable for individuals employed in engineering and science related occupations; HEALTH = dichotomous variable for individuals employed in health and medical related occupations; TEACHER = dichotomous variable for individuals employed in teaching occupations; the excluded occupational category is other professionals; REGIONS = four dichotomous regional variables for residence in an SMSA, Northeast, Midwest and West with the excluded region the South; INDUSTRY = 10 dichotomous industry variables for construction, manufacturing, wholesale, retail, FIRE, business services, personal services, professional services, public services, and transportation; l_i = the self-selection variable often referred to as the Inverse Mills Ratio. The b_i's are the estimated parameters, q is the self-selection parameter; and u_i is the error term. Hourly earnings are used rather than weekly or annual earnings to reduce problems associated with modeling hours and weeks worked.

Empirical studies of occupations in recent years often cite sample selection bias as a frequent problem in estimating wage equations (Heckman, 1979; Hirsch and Schumacher, 1992; Greene, 1997). Sample selection bias may occur in this study if men by different ethnic groups choose professional occupations based on unobserved worker characteristics. If this is the case, the sample of professionals may differ by ethnic group on these unobserved characteristics. The existence of sample selection bias means that ordinary least squares may yield inconsistent parameter estimates of the human capital equation. As a result, the Heckman procedure is utilized where l_i represents the inverse Mills ratio estimated from probit equations, and q is the self-selection parameter from the earnings regressions. The probit equations use all of the variables in the wage model except for the occupational variables. Past studies of Asian American men have not accounted for sample selection bias in occupations.

Empirical studies of women’s earnings in recent years often cite sample selection bias as a frequent problem in estimating wage equations (Heckman, 1979, Greene, 1997). Sample selection bias may occur if women choose to work for wages based on a reservation wage. If this is the case, the sample consisting of women with observed market wages includes only individuals whose wage is greater than their reservation wage. This sample selection bias means that ordinary least squares may yield inconsistent parameter estimates of the human capital equation. As a result, the Heckman procedure is utilized where l_i represents the inverse Mills ratio estimated from probit equations, and q is the self-selection parameter estimated from the probit equations on whether the person is in the labor force. The probit equations^2. use a simplified model of labor force participation. Past studies of Asian American women have not accounted for sample selection bias.

The addition of the number of children variable is similar to several earnings regressions specifications. For example see James Long's study (1980) of white immigrant women as a means of controlling for movement in and out of the labor force.

IV. RESULTS

The analytic results are presented as follows. I begin with some simple descriptive comparisons of the Asian women compared to white women. Next, the adjusted earnings of all Asian American women calculated using the regression parameters for whites are presented as a measure of the relative economic progress of Asian women across decades.

Table 1 shows the unadjusted annual earnings of Asian American women compared to white women. These unadjusted earnings show that American-born Asian women’s earnings were greater than white women’s earnings after 1970. Foreign-born Japanese women's earnings compared to white women's earnings varied considerably over the period.

(Insert Table 1 here)

The generally higher earnings displayed by Asian American women over the period is not too surprising for a number of reasons. One, Asian American women generally possess higher endowments of human capital. Two, Asian American women lived predominantly in cities and in higher wage states out of the South. (See Table 2 for the variable means of Asian American and white women.) In order to separate out the effects of different endowments of human capital, non-human capital personal characteristics, and regional location, the earnings of Asian American women are adjusted using the human capital earnings regression parameters.

Results

The analytic results are presented as follows. The paper begins with some simple descriptive comparisons of the Asian American professionals compared to whites for the nation. Next, differences in the probability of being a professional by ethnic group are examined by simulating the probability of being a professional for Asian men using the probit parameters of white men. Differences in the adjusted earnings versus the actual earnings of Asian American men are then calculated, using the regression parameters for whites, are presented as a measure of discrimination among Asian Americans for the nation, separate regions in the US, and by various professional occupations.

Table 1 shows the percentage of Asian American men employed as professionals and the mean values of the variables compared to white men.

TABLE 1. Variable Means of White and Asian American Professional Men, 1990.

(redo)

Whites Chinese Japanese Filipinos

% Professional 31.8% 55.8% 44.7% 27.6%

EDUC 15.34 16.28 15.71 14.83

Experience 21.93 17.37 21.73 17.90

Experience² 592.96 408.11 596.97 424.38

Married 0.77 0.61 0.66 0.62

Manager 0.36 0.23 0.29 0.33

Mgmt. Related 0.07 0.06 0.07 0.08

Engineer/Scientist 0.14 0.24 0.20 0.14

Medical/Health 0.04 0.08 0.05 0.03

Teacher 0.11 0.07 0.08 0.07

Live in SMSA 0.81 0.97 0.92 0.91

Live in Northeast 0.23 0.18 0.03 0.05

Live in Midwest 0.22 0.06 0.05 0.06

Live in West 0.22 0.69 0.88 0.79

IMR(l) 0.82 0.55 0.67 0.97

Log Earnings 2.78 2.85 2.86 2.63

Chinese and Japanese Americans were more likely to employed as professionals compared to whites and Filipinos. Chinese and Japanese professional earnings were also greater than whites and Filipinos. Higher earnings for Chinese and Japanese may be partially explained by their higher education levels. White professionals were more likely to be employed as managers compared to all three Asian groups, whereas Chinese and Japanese were more likely to be employed as engineers and scientists. Finally, Asian Americans were more likely to be living in urban areas and in the western United States.

Simulated probabilities of being a professional. One way in which discrimination can manifest itself is in a lowering the number of Asian professionals. To examine the effect of discrimination on occupational choice, the probabilities of being a professional were simulated using the variables for Asian men and the probit parameters of white men. These results are shown in Table 2.

Overall, these simulations show that the Asian percentages of workers employed as professionals would have increased very little using the white parameters. The only exception may be for Filipinos. For Filipinos, the simulated percentages of professional workers was somewhat higher than actual. On the other hand, the simulated probabilities were lower for Chinese and Japanese Americans than the actual percentages of professionals.

TABLE 2. Difference between percentages of Actual Asian American Professionals and Simulated percentages from the 1990 Census PUMS.

Chinese Japanese Filipino

Actual 0.558 0.447 0.276

Simulated 0.517 0.434 0.300

Difference 0.041 0.013 -0.024

Simulated earnings. Asian American earnings are simulated using the parameters derived from the white men's regressions and the Asian Americans human capital endowments and personal characteristics. This simulates a labor market where Asian Americans are treated the same as whites. Although there is discussion over the which human capital parameter estimates to use in simulations (see, Oaxaca and Ransom, 1994) depending on the gains and losses to each ethnic or gender group, the white men's parameters were utilized for simplicity and due to the relatively small percentage of Asian American men in the labor market.

The choice of which self-selection parameter, q_w or q_a, estimated from the white and Asian human capital regressions respectively, and inverse Mills ratios, l_wor l_a, calculated from the white and Asian probit equations, has been discussed extensively by Neuman and Oaxaca (ibid). In their discussion, the self-selection parameters and inverse Mills ratio can be handled in a number of ways depending on whether self-selection is considered an endowment difference or a discrimination difference. For example, q_a and l_a may be used in simulation Asian American wages if the self-selection component is considered to be a difference based on endowments. Alternatively, q_w and l_w-est , where l_w-est is constructed from the white probits and Asian endowments, may be used if self-selection differences are considered to be based on discrimination.

In this paper, 3 different sets of simulations are performed for all professional workers in the entire US. The first set simply utilizes the OLS parameters. The second set utilizes the self-selection parameter, q_w, from the white regressions, but the inverse Mills ratio, l_a, estimated from the Asian American probit parameters. The third set again uses the self-selection parameter, q_w, from the white regressions, but the inverse Mills ratios, l_w-est, are estimated using the white probit parameters and the Asian American endowments. These choices are made for a number of reasons. One, it is useful to determine the impact of self-selection on professional earnings by comparing the OLS results with the self-selection results. Two, the self-selection parameters from the Asian regressions are generally not statistically significant so use of the white self-selection parameter may be justified based on statistical significance. Three, as the intent of the simulation is to treat Asians as whites, the use of the white self-selection parameter is in keeping with this intent. The differences between actual and simulated earnings are presented in Table 3. Negative numbers would indicate that Asian Americans would have earned more in 1990.

TABLE 3. Difference between Actual Asian American Professional Men's Log

Hourly Earnings from Simulated Log Earnings.

No Industry Variables

Chinese Japanese Filipino

OLS, No self-selection 0.0340 0.0290 -0.0548

Self-selection I 0.0163 0.0194 -0.0424

Self-selection II 0.0336 0.0286 -0.0553

With Industry Variables

Chinese Japanese Filipino

OLS, No self-selection 0.0246 0.0253 -0.0533

Self-selection I 0.0130 0.0191 -0.0447

Self-selection II 0.0246 0.0106 -0.0533 (check)

There were little differences between actual and simulated earnings for Chinese and Japanese men. Simulated earnings were slightly lower for Chinese and Japanese men in the OLS and first set of self-selection simulations. On the other hand, Filipino professional men's earnings are higher in the OLS and the self-selection simulations. Finally, the two self-selection methods of calculating earnings yield different results. The first self selection method gives numbers very close to OLS, but the second method yields higher earnings for Asian Americans, although the differences were generally small.

Regional Differences. Much of the literature (see, for example Cabezas and Kawaguchi, ibid or Sanders and Nee, 1985; Mar, 1999) argues that regional effects are important in Asian American earnings comparisons. In order to examine the regional effects, a similar analysis was performed comparing actual and simulated earnings in 5 US cities: Honolulu, Los Angeles, San Francisco, San Jose, and New York City. The cities were chosen for their large populations of Asian Americans. The regression models were revised to omit the regional dummy variables. In addition, all the occupational dummy variables were excluded except for the managerial category due to sample size limitations.

The results are shown in Table 4. One interesting result is that simulated earnings of all three Asian groups are higher in the California cities. Two, Asian American men, with the exception of Filipino men, do not appear to suffering earnings discrimination in Honolulu. In fact, actual earnings are higher for Chinese and Japanese compared to simulated earnings in Honolulu. Three, actual Chinese earnings are also higher than simulated in New York City. Four, Filipino men appear to suffer discrimination in all cities. No figures are shown for Japanese and Filipino men in New York City due to the small sample sizes of these groups.

Differences by Professional Occupational Categories. Duleep and Sanders found evidence of discrimination against Asians in managerial occupations in 1980. To examine the extent of discrimination in managerial occupations, the probabilities of Japanese, Chinese and Filipino men are calculated using probit parameters estimated from the white sample of professionals. The sample is limited to workers employed in the professional categories as managers are generally drawn from the professional ranks and the relatively small differences in the actual versus simulated percentages of Asian professions discussed earlier in the paper. For all 3 groups shown in Table 5, the simulated probabilities were less than the actual.

TABLE 5. Difference between percentages of Actual Asian American Managers and

Simulated percentages. (all workers)

Chinese Japanese Filipino

Actual 13.05 12.93 9.21

Simulated 14.95 14.15 9.97

Difference -1.90 -1.22 -0.76

TABLE 5a. Difference between percentages of Actual Asian American Managers and

Simulated percentages. (professional workers only)

Chinese Japanese Filipino

Actual c13.05 c12.93 c9.21

Simulated c14.95 c14.15 c9.97

Difference c-1.90 c-1.22 c-0.76

The final analyses examines earnings differences within the professional occupational categories. The categories of managers, engineering & science professionals, health professionals, and teachers are the largest occupations within the professional jobs category. Simulated earnings using only OLS regressions were performed on all 3 Asian groups. These results are shown in Table 6.

TABLE 6. Difference between Actual Asian American Professional Men's Log

Hourly Earnings from Simulated Log Earnings by Occupational Category.

No industry variables

Chinese Japanese Filipino

Managers -0.0401 -0.0281 -0.0691

Engineering & Science 0.0395 0.0402 -0.0211

Health -0.0003 -0.1024 -0.2201 (check)

Teaching 0.0670 0.1495 0.2085

With industry variables

Chinese Japanese Filipino

Managers -0.0410 -0.0355 -0.0875

Engineering & Science 0.0400 0.0409 -0.0143

Health 0.0089 -0.1028 -0.2200 (check)

Teaching 0.0756 0.1455 0.2152

The occupational simulations find some evidence of earnings discrimination against Asian men in the managerial occupations but none in the other 3 large occupational categories. The engineering & science category shows close parity while the teaching occupations show an advantage to Asian men.

Using the human capital parameters derived from the white women's regressions in Table 3 and the Asian Americans human capital endowments and personal characteristics allows calculation of an adjusted earnings for Asian Americans as a simulation of the labor market where Asian Americans are treated the same as whites. Since the human capital endowment of Asian American women are generally higher than whites, the traditional method of decomposing earnings differences into endowments and discrimination components is less appealing. Although there is discussion over the which human capital parameter estimates to use in simulations (Oaxaca and Ransom, 1994) depending on the gains and losses to each ethnic or gender group, the relatively small percentage of Asian American women in the labor market means that the entire market is best approximated by the white women's parameters. Finally, the choice of which inverse Mills ratios and self-selection parameters has been discussed extensively by Neuman and Oaxaca (1998). In these simulations, the self-selection parameters from the white earnings regressions are used along with the inverse Mills ratios from the Asian probits. This choice is made for a number of reasons. One, the self-selection parameters from the white regressions were almost all statistically significant in all years for both US-born and foreign-born (which was not true for many of the Asian self-selection parameters due many times to small samples). Two, as the intent of the simulation is to treat Asians as whites, the use of the white self-selection parameter is in keeping with this intent. Three, there is considerable literature on the differences in labor force participation determinants between Asians and whites. (See Reimers, 1985; Duleep and Sanders, 1997) As a result, inverse Mills ratios from the Asian probit equations were used. The difference between actual and simulated earnings are presented in Table 4. Thus, negative numbers show that Asian Americans would have earned more in a given year. The white regression results are shown in Table 3. The probit equations and earnings regressions for Asian American women are available on request from the author.

(Insert Table 3 here)

V. CONCLUSION

Conclusion

The basic thrust of the research is to examine earnings discrimination against Asian American men employed in professional occupations. Simulations on the percentages of Asian American professionals using white probit parameters find little differences from actual percentages. Simulations of hourly earnings using OLS and self-selection models show little earnings discrimination against Chinese and Japanese men, but some evidence of earnings discrimination against Filipinos in the aggregate. However, disaggregated analyses show some evidence of earnings discrimination by region and occupations within professional jobs. Professional Asian men have higher simulated earnings in California, but not in Honolulu or New York City. Filipino men appear to face discrimination in 4 cities in the study and in the aggregate. Simulated earnings are higher for all Asian men in managerial occupations but are at substantial parity in other professional job categories.

The results argue that discrimination against Asian Americans in the labor market is more complex than simply discrimination at all professional occupations and in all places. Significant regional and occupational discrimination does exist. Areas which have either very high percentage populations of Asian Americans or very low percentage populations appear to have little discrimination against Asians. Honolulu can be viewed as a relatively unique social, political, and economic context whereby Asian Americans were able to capture significant political and economic power. The New York City results are intriguing but not definitive as only Chinese professional could be examined. The California cities results are troubling in that discrimination against Asians appears to persist in the state with significant numbers of Asian Americans. Finally, Asian Americans may continue to encounter problems in managerial positions.

REFERENCES

________________________________________________________________________

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Footnotes

*This paper was presented at the Western Economics Association held in Seattle, WA on July 2002.

Mar: Professor, Department of Economics, San Francisco State University. Phone 1-415-338-2499, Fax 1-415-338-1057, E-Mail dmar@sfsu.edu. JEL codes J71, J15.

1. The probit equations were estimated based on a simple labor supply model. The dependent variable was whether the individual was working in the reference year. The independent variables were spouse's total annual earnings, years of school, age, age squared, number of children ever born, residence in an urban area, residence in California, residence in Hawaii, residence in the South for US-born women. For foreign-born women, English speaking ability, years since migration, and years since migration squared were added.

(Data and Regression Appendices)

TABLE 6. Difference between Actual Asian American Women's Log Hourly Earnings

from Simulated Asian American Women's Log Earnings by Place of Birth:

1980 - 1990, Never Married Women.

Ethnic Group 1980 1990

For. US For. US

born born born born

Japanese 0.116 0.042 -0.249 0.012

Chinese 0.051 0.094 0.088 0.051

Filipinos 0.115 -0.096 0.138 0.027

REFERENCES

________________________________________________________________________

Becker, Gary. 1975. Human Capital, 2nd edition. New York: National Bureau of Economic Research.

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Duleep, Harriet and Seth Sanders. 1992. “Discrimination at the Top: American-born Asian and White Men,” Industrial Relations 31:416-432.

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[1] For convenience, the term white will refer to non-Hispanic white for the rest of this paper.