View source for Blinder–Oaxaca decomposition

{{Short description|Statistical method}}
[[File:Blinder-oaxaca-decomposition-diagram.svg|thumb|alt=A graph illustrating the decomposition.|Using Blinder–Oaxaca decomposition one can distinguish between "change of mean" contribution (purple) and "change of effect" contribution]]
The '''Blinder–Oaxaca decomposition''' ({{IPAc-en|ˈ|b|l|aɪ|n|d|ər|_|w|ɑː|ˈ|h|ɑː|k|ɑː}}) or '''Kitagawa decomposition''', is a [[statistical method]] that explains the difference in the [[mean]]s of a [[dependent variable]] between two groups by decomposing the gap into within-group and between-group differences in the effect of the explanatory variable.

The method was introduced by sociologist and demographer [[Evelyn M. Kitagawa]] in 1955.<ref>{{cite journal|last=Kitagawa|first=Evelyn M.|date=1955|title=Components of a Difference Between Two Rates|jstor=2281213|journal=Journal of the American Statistical Association|volume=50|issue=272|pages=1168–1194|doi=10.2307/2281213}}</ref> [[Ronald Oaxaca]] introduced this method in economics in his doctoral thesis at [[Princeton University]] and eventually published in 1973.<ref>{{cite journal |last=Oaxaca |first=R. |title=Male-Female Wage Differentials in Urban Labor Markets |journal=[[International Economic Review]] |year=1973 |volume=14 |issue=3 |pages=693–709 |doi=10.2307/2525981 |jstor=2525981 }}</ref> The decomposition technique also carries the name of [[Alan Blinder]] who proposed a similar approach in the same year.<ref>{{cite journal | last1 = Blinder | first1 = A. S. | year = 1973 | title = Wage Discrimination: Reduced Form and Structural Estimates | journal = Journal of Human Resources | volume = 8 | issue = 4| pages = 436–455 | doi=10.2307/144855| jstor = 144855 }}</ref> Oaxaca's original research question was the wage differential between two different groups of workers (male vs. female), but the method has since been applied to numerous other topics.<ref>{{cite book |first=Owen A. |last=O'Donnell |chapter=Explaining Differences between Groups: Oaxaca Decomposition |title=Analyzing Health Equity Using Household Survey Data: A Guide to Techniques and Their Implementation |publisher=World Bank Publications |year=2008 |pages=147–158 |isbn=9780821369340 |chapter-url=https://books.google.com/books?id=8krsjfKv2vgC&pg=PA147 |display-authors=etal}}</ref>

==Method==

The following three equations illustrate this decomposition. Estimate separate linear wage [[Ordinary least squares|regressions]] for individuals ''i'' in groups ''A'' and ''B'':

: <math>
\begin{align}
(1) \qquad \ln(\text{wages}_{A_i}) & = X_{A_i} \beta_A + \mu_{A_i} \\
(2) \qquad \ln(\text{wages}_{B_i}) & = X_{B_i} \beta_B + \mu_{B_i}
\end{align}
</math>

where ''Χ'' is a vector of explanatory variables such as education, experience, industry, and occupation, ''β''<sub>''A''</sub> and ''β''<sub>''B''</sub> are vectors of coefficients and ''μ'' is an [[Errors and residuals|error term]].

Let ''b''<sub>''A''</sub> and ''b''<sub>''B''</sub> be respectively the regression estimates of ''β''<sub>''A''</sub> and ''β''<sub>''B''</sub>. Then, since the average value of [[Errors and residuals|residuals]] in a linear regression is zero, we have:

: <math>
\begin{align}
(3) \qquad & \operatorname{mean}(\ln(\text{wages}_A)) - \operatorname{mean}(\ln(\text{wages}_B)) \\[4pt]
= {} & b_A \operatorname{mean}(X_A) - b_B \operatorname{mean}(X_B) \\[4pt]
= {} & b_A (\operatorname{mean}(X_A) - \operatorname{mean}(X_B)) + \operatorname{mean}(X_B) (b_A - b_B)
\end{align}
</math>

The first part of the last line of (3) is the impact of between-group differences in the explanatory variables ''X'', evaluated using the coefficients for group ''A''. The second part is the differential not explained by these differences in observed characteristics&nbsp;''X''.

==Interpretation==
The unexplained differential in wages for the same values of explanatory variables should not be interpreted as the amount of the difference in wages due only to [[Wage discrimination|discrimination]] (against women in Oaxaca's application). This is because other explanatory variables not included in the regression (e.g. because they are unobserved) may also account for wage differences. For example, [[David Card]] and [[Alan Krueger]] found in a paper entitled, "School Quality and Black-White Relative Earnings: A Direct Assessment"<ref>{{cite journal|last1=Card|first1=David|last2=Krueger|first2=Alan|year=1992|title=School Quality and Black-White Relative Earnings: A Direct Assessment|url=http://davidcard.berkeley.edu/papers/school-quality-bw.pdf|journal=Quarterly Journal of Economics|volume=107|issue=1 |pages=151–200 |doi=10.2307/2118326|jstor=2118326 |s2cid=150859258 }}</ref> that improvements in the quality of schools for Black men born in the Southern states of the United States between 1915 and 1966 increased the return to education for these men, leading to narrowing of the black-white earnings gap.  In terms of wage regressions, the poor quality of schools for Black men had meant a lower value of the ''β'' coefficient on years of schooling for Black men than for White men. Thus, some of this lower ''β'' coefficient reflected a difference in the quality of education for Black workers which could have otherwise been interpreted as an effect of direct discrimination; differences in the quality of education for Black workers would reflect historical or 'indirect' discrimination against them.

== Differences between Kitagawa and Blinder–Oaxaca ==
Oaxaca and Sierminska argued that the Blinder–Oaxaca decomposition is a generalization of the Kitagawa decomposition.<ref>{{cite journal |last1=Oaxaca |last2=Sierminska |date=May 2023 |title=Oaxaca-Blinder Meets Kitagawa: What Is the Link? |url=https://docs.iza.org/dp16188.pdf |journal=IZA Discussion Papers |volume=IZA DP No. |issue=16188}}</ref>

== See also ==
* [[Standardization (demographics)]]

== References ==
{{Reflist}}

== Further reading ==
* {{cite web |first=David |last=Autor  |title=MIT Graduate Labor Economics 14.662 Spring 2015 Lecture Note 1: Wage Density Decompositions |publisher=Massachusetts Institute of Technology: MIT OpenCourseWare |date =January 30, 2015|url=https://ocw.mit.edu/courses/economics/14-662-labor-economics-ii-spring-2015/lecture-notes/MIT14_662S15_lecnotes1.pdf }}
* {{cite book |first=George J. |last=Borjas |chapter=Measuring Discrimination |title=Labor Economics |location=Boston |publisher=Irwin McGraw-Hill |edition=Second |year=2000 |isbn=0-07-231198-3 |pages=[https://archive.org/details/laboreconomics0000borj/page/362 362–366] |chapter-url=https://books.google.com/books?id=hODtAAAAMAAJ&pg=PA362 |url=https://archive.org/details/laboreconomics0000borj/page/362 }}
* {{cite book |first1=Pierre |last1=Cahuc |first2=Stéphane |last2=Carcillo |first3=André |last3=Zylberberg |chapter=Decomposition Methods: The Case of the Gender Wage Gap |title=Labor Economics |location=Cambridge |publisher=MIT Press |year=2014 |isbn=978-0-262-02770-0 |pages=504–514 |chapter-url=https://books.google.com/books?id=yf46BAAAQBAJ&pg=PA504 }}
* {{cite book |first1=Nicole |last1=Fortin |author-link1=Nicole Fortin |first2=Thomas |last2=Lemieux |first3=Sergio |last3=Firpo |chapter=Decomposition Methods in Economics |title=Handbook of Labor Economics |publisher=Elsevier |year=2011 |isbn=978-0-444-53450-7 |pages=1–102 |chapter-url=https://books.google.com/books?id=YYytg5ewE2wC&pg=PA1 |doi=10.1016/S0169-7218(11)00407-2 |url=http://www.nber.org/papers/w16045.pdf }}
*Kevin Guo & Guillaume Basse. 2021. "[[doi:10.1080/01621459.2021.1941053|The Generalized Oaxaca-Blinder Estimator.]]" ''Journal of the American Statistical Association''.

{{DEFAULTSORT:Oaxaca decomposition}}
[[Category:Regression analysis]]
[[Category:Observational study]]
[[Category:Causal inference]]