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# Blinder-Oaxaca Decomposition Technique

ILLUSTRATION

INTERPRETATION

EXTENSIONS

BIBLIOGRAPHY

The Blinder-Oaxaca decomposition technique, or simply the Oaxaca decomposition, decomposes wage differentials into two components: a portion that arises because two comparison groups, on average, have different qualifications or credentials (e.g., years of schooling and experience in the labor market) when both groups receive the same treatment (explained component), and a portion that arises because one group is more favorably treated than the other given the same individual characteristics (unexplained component). The two portions are also called characteristics and coefficients effect using the terminology of regression analysis, which provides the basis of this decomposition technique. The coefficients effect is frequently interpreted as a measure of labor market discrimination. For a comprehensive review of issues related to labor market discrimination, see Joseph Altonji and Rebecca Blank (1999).

The Blinder-Oaxaca decomposition technique is named after two economists, Alan Blinder and Ronald Oaxaca, who introduced it to economic literature in the early 1970s. A similar version of this technique was explored in sociology during the late 1960s and early 1970s in order to examine sources of racial wage differentials (e.g., Duncan 1969; Althauser and Wigler 1972). The Blinder-Oaxaca decomposition technique has provided a practical way to apply economist Gary Beckers (1971) definition of discrimination as unequal treatment among equivalent people due to race or gender. This decomposition technique has become a basic tool for studying racial and gender wage differentials and discrimination, and it has been allowed in court litigation on discrimination (Ashenfelter and Oaxaca 1987).

## ILLUSTRATION

Suppose that only years of schooling affect the determination of wages for men and women. The illustration can be easily extended to a more complicated model in which several variables help determine wages. A linear equation is estimated using a regression technique in statistics. The two equations, the first for men and the second for women, are: WM = αM + βMSM + eM, and WF = αF + βFSF + eF, where W is wages; α and β are the intercept and the coefficient of years of schooling (S ); e is an error term; and subscript M and F are men and women, respectively. Economists usually use the natural logarithm of wages for W, while sociologists usually use level wages.

In order to examine sources of wage differentials between men and women, a counterfactual equation is constructed where women are treated as men. In other words, the intercept and coefficient in the womens equation are replaced by those of the mens equation. The counterfactual equation becomes WF* = αM + βMSF + eF. Wage differentials between men and women, on average, can be decomposed into a characteristics effect , that is, differences between mens wages and counterfactual wages, and a coefficients effect , that is,

differences between counterfactual wages and womens wages. The Blinder-Oaxaca decomposition equation is: .

Figure 1 shows the intuition behind the Blinder-Oaxaca decomposition technique. The diagram depicts a situation where men start off at higher wages without schooling (higher intercept) and receive a bigger payoff for each year of schooling (steeper slope). The wage differentials due to differences in intercepts and coefficients , that is, the increases in wages when women are treated as men, are attributed to coefficients effect or discrimination. The remaining wage differentials , the characteristics effect, arises because women have fewer years of schooling than men, although women are treated as men.

## INTERPRETATION

The existence of discrimination and its measurement using the Blinder-Oaxaca decomposition technique has been a center of controversy. Those who believe that discrimination does not exist in the labor market or that the Blinder-Oaxaca decomposition technique overestimates the degree of discrimination point out that the wage equation cannot include all relevant variables measuring skills and individual productivity; hence, observationally equivalent people based on the characteristics in the wage equation may not be equivalent. In Figure 1, for example, the same years of schooling do not guarantee that both men and women are equally productive because men may be more motivated for work; therefore, the coefficients effect is not due to discrimination but to unobserved differences in productivity between men and women. As long as people believe that the two comparison groups possess systematically different but difficult to observe characteristics, such as motivation, ability, and effort, they will argue that the measure of discrimination from the Blinder-Oaxaca decomposition technique is biased, and gross wage differentials can be explained by differences in skills and productivity between the two groups.

On the other hand, those who believe that there is prevalent discrimination or that the magnitude of discrimination is bigger than the coefficients effect itself argue that even differences in qualifications and credentials may be the result of premarket discrimination. In Figure 1, for example, it is possible that women were discouraged against pursuing higher education due to existing discriminatory barriers in the labor market (e.g., the glass ceiling) and elsewhere in the economy. Though current employers are not responsible for the different levels of schooling between men and women, society is. Therefore, those who believe in widespread discrimination in society may argue that the coefficients effect underestimates the magnitude of discrimination; hence, gross wage differentials may be an outcome of discrimination.

## EXTENSIONS

In spite of the difficulties in interpreting the Blinder-Oaxaca decomposition equation, this decomposition technique has provided a starting point for studying racial and gender wage differentials and discrimination since its introduction in the early 1970s. Although the Blinder-Oaxaca decomposition technique was introduced to decompose racial and gender wage differentials, this technique is also suitable for studying changes in wages over time. In this case, the characteristics effect represents wage growth arising from changes in qualifications and credentials over time, and the coefficients effect shows changes in wages due to structural changes in wage determination over time. In principle, the Blinder-Oaxaca decomposition technique can be applied to decomposing differentials or changes of any continuous variable, such as hours of work. The flexibility of this technique is further demonstrated by extending it to decomposing differences or changes in binary choice variables, such as the labor-market participation rate (e.g., Yun 2004), and differences or changes in wage inequality measured with variances of log wages (e.g., Yun 2006). The Blinder-Oaxaca decomposition technique has been and will continue to be widely used in studying differences and changes in various socioeconomic variables due to its simplicity and flexibility in implementation, and the insights it offers.

SEE ALSO Discrimination; Economics, Labor

## BIBLIOGRAPHY

Althauser, Robert P., and Michael Wigler. 1972. Standardization and Component Analysis. Sociological Methods and Research 1 (1): 97135.

Altonji, Joseph G., and Rebecca M. Blank. 1999. Race and Gender in the Labor Market. In Handbook of Labor Economics, Vol. 3C, eds. Orley Ashenfelter and David Card, 31433259. Amsterdam: Elsevier.

Ashenfelter, Orley, and Ronald Oaxaca. 1987. The Economics of Discrimination: Economists Enter the Courtroom. American Economic Review 77 (2): 321325.

Becker, Gary S. 1971. The Economics of Discrimination. 2nd ed. Chicago: University of Chicago Press.

Blinder, Alan S. 1973. Wage Discrimination: Reduced Form and Structural Estimates. Journal of Human Resources 8 (4): 436455.

Duncan, Otis D. 1969. Inheritance of Poverty or Inheritance of Race. In On Understanding Poverty: Perspectives from the Social Sciences, ed. Daniel P. Moynihan, 85110. New York: Basic Books.

Oaxaca, Ronald L. 1973. Male-Female Wage Differentials in Urban Labor Markets. International Economic Review 14 (3): 693709.

Yun, Myeong-Su. 2004. Decomposing Differences in the First Moment. Economics Letters 82 (2): 273278.

Yun, Myeong-Su. 2006. Earnings Inequality in USA, 19691999: Comparing Inequality Using Earnings Equations. Review of Income and Wealth 52 (1): 127144.

Myeong-Su Yun

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