Wealth Discrimination Theory

One approach to analyzing inequality is to compare average economic choices from a classical theoretical framework. Another approach considers the impact of the formation of society, through statutes and institutions, on average economic outcomes. This paper studies the effects of slavery on black-white wealth inequality upon the emancipation of slaves in the US using historical data. The purpose of wealth has varied from over time. From an economics perspective, wealth is the accumulation of resources that have market value and can be liquidated for present and future consumption. This study proceeds based on the most measurable assumption: households reside in a country with a mixed economy of markets and social planning, such that they have an incentive to accumulate material wealth for inter-temporal household consumption and social influence. Becker (1957) and Arrow (1972) developed the most general theories of wage discrimination and favoritism. Oaxaca (1973) and Blinder (1973) have mechanized their theories for empirical analysis. While their findings are insightful, they cannot be directly applied to studying wealth differences since wealth is a complex combination of wages and other variables. Finally, since unexplained differences in states that abolished slavery after the Civil War were 10 percent higher than unexplained effects in states that abolished slavery well before the Civil War and the magnitudes of the unexplained effects were similar over the long-run, we cannot reject the existence of a negatively bounded correlation between the duration of time from enslavement and the magnitude of unexplained differences in wealth.


Introduction
Many individuals look to a higher source of power, such as the holiness expressed in the King James Version of the Holy Bible, for a source of direction (i.e., Genesis 1:1; Genesis 1:27; Exodus 20:2-17; John 1:1; Romans 3:23-25, 1 Corinthians 6:12a), strength (i.e., Philippians 4:6,13; Hebrews 11:1), purpose (i.e., Jeremiah 29:11; 1 Corinthians 13:13), and provision (i.e.,Matthew 6:33;Philippians 4:11;Hebrews 11:6).Since the days of old, differences in creation existed, for instance, the Holy Bible reads "Servants be obedient" (Ephesians 6:5).But it also reads "ye Masters, do the same … knowing your Master also is in heaven; neither is there respect of persons with him" (Ephesians 6:9).Seemingly juxtapositional scriptures, as read, suggest the issue of inequality in provisions among creation is monitored by the divinity expressed in holy documents, such as the Holy Bible.This produces an incentive to derive robust explanations for experiential differences in observed phenomena among creation and recommendations for progress.
The following is a skeleton review of literature, with supplemental discussions in Appendix C; a definition and theory of economic discrimination, with supplemental discussions in Appendix A and Appendix B; econometrics; measurements of economic discrimination; regression decomposition results; conclusions; and references.

Literature
Entering the 21st Century, Table 1 shows Blacks, Hispanics and women still have reduced labor market experiences relative to white men.  1 on page 3147 from Altonji and Blank, "Race and Gender in the Labor Market," in Handbook of Labor Economics edited by Ashenfelter and Card, 1999;Borjas, 1999, p. 343.Modern economic progress is slowing for blacks relative to whites.Table 1 shows the unemployment rate of black males doubled the rate of white males and the unemployment rate of black females doubled the rate of white females.Juhn, Murphy and Pierce (1991) also show a slowdown in black-white wage convergence: in the Mid-1960's, Blacks earned 55% of white hourly wages; in the late 1970's: Blacks earned 70% of white hourly wages; and in the late 1980's, Blacks earned 70% of white hourly wages.
New evidence from James Curtis Jr in Figure 1 and Figure 2 demonstrates persistent black-white differences in wealth & homeownership.Figure 1 demonstrates convergence in wealth levels through most of the 20th century until the start of the 21st century, when stagnation in convergence is observed.Furthermore, Table 2 demonstrates observations by Melvin Oliver and Thomas Shapiro: large late-20th century differences in wealth among blacks and whites occurred across income groups.Juhn, Murphy and Pierce (1991) observed a sustained gap among blacks and whites with college degrees: in 1965: 13.9 percent of whites, compared to 4.6 percent of blacks had college degrees, producing a 9.3 percent gap; in 1975: 19.7 percent of whites, compared to 7.4 percent of blacks had college degrees, producing a 12.3 percent gap; and in 1985: 25.2 percent of whites, compared to 13.4 percent of blacks had college degrees, producing 11.8 percent gap.Many researchers suggest these type of schooling gaps explain differences in measured economic outcomes.However, Table 3 demonstrates large black-white wealth differences even when controlling for schooling differences.

Discrimination
Gregory Mankiw defines Discrimination as the offering of different opportunities to similar individuals who differ by color of skin, ethnicity, gender, age or other characteristic (Mankiw, 1997, p. 408).

Statistical Discrimination
Statistical Discrimination is making predictions about a person based on membership in a certain group (Stockton, 1999, p. 434), or using an individual's membership in a certain group as information on the individual's skill and productivity (Borjas, 2000, p. 357).

Economic Discrimination [Practical Labor Market Discrimination]
Practical labor market discrimination is based on observed and quantified outcomes in the economy; wide disparity in income, earnings, and wage rates among a variety of demographic groups, classified by gender, color, ethnicity and other characteristics.The disparities are systematic, persistent and considered by most observers to be inequitable (Cain, 1986, p. 694).

Economic Discrimination [Theoretical Labor Market Discrimination]
Theoretical labor market discrimination is the analysis under what conditions will essentially identical goods have different prices in the competitive markets?Discrimination in the labor market takes labor services as the good in question and the wage rate as the price.Labor services are considered essentially identical if they have the same productivity in the physical or material production process; a consideration that excludes the effect of the laborer on the psychic utility (or disutility) of his or her coworkers or employers (Cain, 1986, p. 695).

Economic Discrimination [Becker Definition of Economic Discrimination]
Gary Becker defines economic discrimination as the following: If an individual has a "taste for discrimination", he must act as if he were willing to pay something, either directly or in the form of reduced income, to be associated with some persons instead of others.Different levels of discrimination against a particular group are associated with: [a] different levels of social and physical distance from that group [which is the sociological analysis], [b] different personality types [which is the psychological analysis], and [c] separate factors of production.All persons who contribute to the production process in the same way are put into one group, such as the sale of labor services [which as the economic analysis] (Becker, 1957, p. 14).
Gary Becker presents a discrimination coefficient (d), which is defined as "tastes for discrimination" for different factors of production, employers and consumers.The money costs of a transaction do not always completely measure net costs and a discrimination coefficient acts as a bridge between money and net costs (Becker, 1957, p. 14).For instance, [a] A factor of production (or an employee) is offered a net money wage [w -d] Gary Becker also presents a market discrimination coefficient (MDC), which is the proportional difference in wage rates due to discrimination (Becker, 1957, p. 17).Consider the example of imperfect substitutes, where there are two groups, one and two, who are imperfect substitutes in the production process.Then, they may receive different wage rates even in the absence of discrimination [w 1 * ≠ w 2 * ].A more general definition of the MDC sets the MDC equal to the difference between the ratio of two group's wage rates with discrimination [w 1 ≠ w 2 ] and without discrimination (Becker, 1957, p. 17

Definition of Econometrics
Econometrics "attempts to quantify economic reality and bridge the gap between the abstract world of economic theory and the real world of human activity ... Econometrics allows us to examine data and quantify the actions of firms, consumers and governments" (Studenmund, p. 3).

Economic Theory
Economic theory tells us about the anticipated direction (+/-) of changes in the economic environment.For example, theory suggests: An increase in income increases demand for goods; an increase in price decreases demand for goods.

Econometric Modeling
Econometric modeling allows us to measure the specific amount, or the magnitude of the change.

Simple Regression Model versus the Multivariate Regression Model
The simple regression model implies a dependent variable (c) is only explained by one independent variable, which is not realistic.For example, quantity (c) consumed is not just explained by price (p).The multivariate regression model implies a dependent variable (c) is explained by more than one independent variable, which is more realistic.For example, the combination of price (p) and income (I) explain quantity consumed (c).

Slopes (B s )
The only difference between the simple and multivariate regression models is the calculation and the interpretation of the slope.The slope (B k ) from the multivariate regression model is the change in the dependent variable associated with a one-unit change in the independent variable, holding constant the other independent variables in the equation: ln When using logs of the dependent variable, a slope becomes the elasticity and units become percentages.

Hypothesis Testing
Hypothesis Testing are statistical tests, such as t-tests, on the accuracy of slopes calculated in an econometric model before accepting the results.In the way in which the FDA withholds approval of a new medication that has a side effect more frequently than expected, economists withhold "accepting" a calculated coefficient until it pasts certain statistical or hypothesis tests (Studenmund, 1999, p. 126).

Sample Survey Data
A hypothetical survey is two questions to six families: How many meals does your family consume at restaurants per year?What is you annual family income?The hypothetical results of the survey are presented in Table 4.The line that "best fits" the data minimizes difference between the fitted line and the data.Let e i be the difference between the one point on the line and one data point, then the smallest sum of e i 's seems to produce the best fitted line.But the smallest sum of e i 's can produce more than one estimate of the slope the line.Instead, by summing the square of each e i , we can obtain one estimate of the slope.Hence, the line that "best fits" the data is a "least squares" regression line that minimizes the sum of squared error.

Empirical Results
Empirical results are the output from the econometric model and statistical software (or calculations using a calculator), where c = 2.6 + 4.78 I and where estimated B o = 2.6.Thus, we can predict that families will visit restaurants 2.6 times annually even if they have zero annual income.Estimated B 1 = 4.78.Thus, we can predict that the number of annual restaurant visits increase by 4.78 with one unit (one thousand dollar) increase in annual income.

Measurements of Economic Discrimination
We can apply these lessons from econometrics to measure economic discrimination.Ronald Oaxaca (1973) mechanized empirical analysis of economics discrimination even though we do not have direct data on preferences in favor of group one, or the disutilities of employing group two.Oaxaca (1973) used Becker's (1957) market discrimination coefficient to conduct regression decomposition, known as the Oaxaca decomposition.The market discrimination coefficient (MDC) can be analyzed in terms of wages and income when members of group one and group two are perfect substitutes.Given: MDC = (w 1 -w 2 )/w 2 = w 1 /w 2 -1, then: ln (MDC) = ln (w 1 ) -ln (w 2 ).Differences in wealth can be analyzed using the MDC with additional theoretical considerations (Curtis Jr, 2002).
Using an econometric model for wages, income or wealth (w i ), then ln(w 1 ) = B o1 + B 11 Z 1 + error 1 and ln(w 2 ) = B o2 + B 12 Z 2 + error 2 where Z is a matrix of variables that determine wages, income or wealth.To form the regression decomposition, combine the log MDC and the econometric model.

Regression Decomposition Results
Empirical results of differences in economic outcomes between enfranchised groups and disenfranchised groups demonstrate significant unexplained differences in economic outcomes, even when controlling for classical choice characteristics.

Male and Female Wages
Oaxaca (1973) found 53 percent to 78 percent of wage differences among white males and white females in the United States were unexplained and 50 percent to 99 percent of wage differences among black males and black females in the United States were unexplained.

Black and White Wages
Determinants of gender and ethnic wages differences are comparable.Binder (1973) found 30 percent to 45 percent of wage differences among males and females in the United States were unexplained.Similarly, 20 percent to 35 percent of wage differences among blacks and whites in the United States were unexplained.Furthermore, Carlstom and Rollow (1998) found 37 percent to 39 percent of wage differences among blacks and whites in the United States were unexplained.
Carlstrom and Rollow (1998) also observed fair wage premium for blacks residing in non-southern states: they found 37 percent of wage differences among non-southern blacks and non-southern whites in the United States were unexplained, 44 percent of wage differences among southern blacks and southern whites in the United States were unexplained.
Nevertheless, this is preliminary evidence that the fair wage issue for females is, at least, proportional to the fair wage issue for blacks.

Black and White Housing Prices
Differences in the determinants of housing values were also observed and blacks and whites in the United States: 41 percent to 42 percent of differences in housing values among blacks and whites in the United States were unexplained (Long & Caudill, 1992).

Black and White Wealth
The analysis of differences in the determinants of the wealth by ethnicity is, at least as revealing or, more revealing than the analysis of wages and income.Becker (1957) and Arrow (1972) developed the most general theories of wage discrimination and favoritism.Oaxaca (1973) and Blinder (1973) have mechanized their theories for empirical analysis.While their findings are insightful, they cannot be directly applied to studying wealth differences since wealth is a complex combination of wages and other variables.
The purpose of wealth has varied from over time.From an economics perspective, wealth is the accumulation of resources that have market value and can be liquidated for present and future consumption.This study proceeds based on the most measurable assumption: households reside in a country with a mixed economy of markets and social planning, such that they have an incentive to accumulate material wealth for intertemporal household consumption and social influence.Appendix A contextualizes wealth regression decomposition results with models of grouped household decisions and social planner decisions.Appendix B contextualizes wealth regression decomposition results with models of a group-specific analysis of household wealth.
Most academic research has found that three out of every four US dollars of wealth held by white households represents the difference among blacks and whites in the United States which is unexplained.Blau and Graham (1990) found that 78 percent of differences in wealth among blacks and whites in the United States were unexplained in the late 20th Century.Similarly, Altonj, Doraszeski and Segal (2000) found that 70 percent to 94 percent of differences in wealth among blacks and whites in the United States were unexplained.Furthermore, Gittleman and Wolff (2000) found that 68 percent to 72 percent of differences in wealth among blacks and whites in the United States were unexplained.
James Curtis Jr (December, 2002) confirms that the source of contemporary black-white wealth differences have historical roots: 82 percent to 86 percent of differences in wealth among blacks and whites in the United States were unexplained by classical choice characteristics in the mid-19th century.Curtis Jr ( 2002) also observed a quasi-fairness wealth premium for blacks residing in non-southern states (i.e., states which abolished slavery before mass emancipation of southern slaves or states which never officially instituted slavery as a social practice): 78 percent of differences in wealth among blacks and whites in the non-southern states in the United States were unexplained while 88 percent of differences in wealth among blacks and whites in former southern slave states in the United States remained unexplained by classical choice characteristics.
Much like "the plight of the antebellum free black American, which, in hindsight, illuminated the path of the average black American after emancipation" (Curtis Jr, February, 2002), the experience of blacks in non-southern states, as early as 1870, provided insight to the experience of the contemporary Americans of diverse experiences attempting achieve the pursuit of happiness.

Reflections and Conclusions
Historical black-white differences in wealth were estimated using regression decomposition.This technique decomposes economic differences into the portion explained by differences in characteristics and the unexplained portion due to different returns to a set of characteristics (See, e.g., Blinder, 1973;Oaxaca, 1973).
Reflecting on the analyses of James Curtis Jr (2002), results confirm that we cannot reject that the claim that, when comparing the wealth of ex-slaves to the wealth whites, differences in wealth due to unexplained (or discrimination) effects dominate the portion due to classical characteristic differences.
Furthermore, the size and source of contemporary black-white wealth differences have historical roots: In 1870, at least 75 percent of white-black wealth differences were not explained by characteristic differences described by the classical model when employing the primary index.This is consistent with wealth decompositions of late twentieth century data that shows that three-quarters of white-black differences in wealth were unexplained (See, e.g., Blau & Graham, 1990).
Finally, since unexplained differences in states that abolished slavery after the Civil War were 10 percent higher than unexplained effects in states that abolished slavery well before the Civil War and the magnitudes of the unexplained effects were similar over the long-run, we cannot reject the existence of a negatively bounded correlation between the duration of time from enslavement and the magnitude of unexplained differences in wealth.

Appendix A Agent-Specific Constraints
Further, let: Further, let: Therefore, the decision becomes: Therefore, the decision becomes: Real estate value was enumerated based on guidelines specified in the Circular to Marshals.It specified that "under heading 8 insert the value of real estate owned by each individual enumerated.You are to obtain the value of real estate by inquiry of each individual who was supposed to own real estate, be the same located where it may, and insert the amount in dollars.No abatement of the value is to be made on account of any lien or encumbrance thereon in the nature of debt" (Magnuson, 1995, p347).Personal estate value (other wealth) was also enumerated based on guidelines that specified "Personal estate is to be inclusive of all bonds, stocks, mortgages, notes, live stock, plate, jewels, or furniture, but exclusive of wearing apparel" (p.349).For more on the quality of historical census data (see Wright, 1900;Steckel, 1991;Magnuson, 1995).
Note that sample includes the reported wealth of household heads.Enumerators only recorded the value of wealth if an individual had more than 100 dollars in nominal wealth.Furthermore, zero wealth is not equivalent to zero dollar-wages per hour, where one must account for the participation decision to obtain robust estimates.Instead, not having any initial wealth, savings, and assets leads to one possessing zero wealth.
, [b] Employers pays a net rental rate of capital [r + d], or [c] Consumers pay a net commodity price [p + d].
). Then: MDC = w 1 /w 2 -w 1 Equation 1a: A presentation of the arrow model of discrimination Equation 1b: The first order condition of the arrow model of discrimination for group 1 Equation 1c: The first order condition of the arrow model of discrimination for group 2 Equation 1d: The interpretation of the arrow model of discrimination Equation 1e: The profit conditions of the arrow model of discrimination 4. Econometrics Consider following example: Let: c * = [a/(a + b)] [I/p] (from utility maximization); Then, ln(c) = ln[a/(a + b)] + ln(I) -ln(p) such that the econometric or regression model is ln(c) = B o + B 1 * ln(I) -B 2 * ln(p) + error.

Figure 3 .
Figure 3.The fitted line from the hypothetical survey which minimizes the sum of squared error Source: Data Analysis from James Curtis Jr (2001).

Table 1 .
Recent labor market statistics across race, ethnicity & gender Source: Calculations from 1995 CPS data reported in Table

Table 2 .
Wealth across income & race Source: 1983-1984 CPS data reported in Table 6 on page 19 from Oliver and Shapiro, "Race and Wealth" in the Review of Black Political Economy, Spring 1989.

Table 3 .
Wealth across age, income, education & race Source: 1967 SEO data reported inTable 5 on page 376 from Terrell, Wealth Accumulation of Black and White Families: The Empirical Evidence, Journal of Finance, 1971.

Table 4 .
A Hypothetical survey of 6 families, annual income and restaurant meals/year 4.4.2Least Squares