Utah's Wage Gap. Econometric procedures for estimating gender wage discrimination in Utah. Curtis Miller. March 6, University of Utah

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1 Utah's Wage Gap Econometric procedures for estimating gender wage discrimination in Utah Curtis Miller University of Utah March 6, 2017 Curtis Miller (University of Utah) Utah's Wage Gap March 6, / 61

2 Table of contents 1. Introduction 2. Estimating Discrimination 3. Selection Bias 4. Decomposition Estimates 5. Conclusion Curtis Miller (University of Utah) Utah's Wage Gap March 6, / 61

3 Introduction Background In 2014 I began work on a project with Voices for Utah Children, a Salt Lake nonprot advocacy organization, studying Utah's gender gap in wages. The result was a report and my Honor's thesis that earned me an HBS in Economics from the University of Utah. This project got a lot of media attention, being quoted by newspapers and local TV stations (even a Pat Bagley cartoon!). I presented my results to the Utah Commission on Women in the Economy, and also got a TV spot and gave a talk at the SLC PechaKucha Night 2015 hosted by the Utah branch of the Women in Architecture organization. I thank Prof. Cihan Bilginsoy in the University of Utah Economics department and Matthew Weinstein, my mentor at Voices for Utah Children, for their incalculable assistance in this project. Curtis Miller (University of Utah) Utah's Wage Gap March 6, / 61

4 Introduction Bagley Cartoon Curtis Miller (University of Utah) Utah's Wage Gap March 6, / 61

5 Introduction Basic Data Foreword The next few slides show basic data about gender in the Utah economy (calculated using data from the 2013 American Community Survey; not updated for recent survey data). W Here, the measure for the wage gap is f, where W W f is women's median m wages, and W m men's median wages. Curtis Miller (University of Utah) Utah's Wage Gap March 6, / 61

6 Introduction Basic Data Participation I Curtis Miller (University of Utah) Utah's Wage Gap March 6, / 61

7 Introduction Basic Data Participation II Curtis Miller (University of Utah) Utah's Wage Gap March 6, / 61

8 Introduction Basic Data Education I Curtis Miller (University of Utah) Utah's Wage Gap March 6, / 61

9 Introduction Basic Data Education II Curtis Miller (University of Utah) Utah's Wage Gap March 6, / 61

10 Introduction Basic Data Marital/Parental Status Curtis Miller (University of Utah) Utah's Wage Gap March 6, / 61

11 Introduction Basic Data Family Size Curtis Miller (University of Utah) Utah's Wage Gap March 6, / 61

12 Introduction Basic Data Overall Wage Gap I Curtis Miller (University of Utah) Utah's Wage Gap March 6, / 61

13 Introduction Basic Data Overall Wage Gap II Curtis Miller (University of Utah) Utah's Wage Gap March 6, / 61

14 Introduction Basic Data Rate of Convergence Curtis Miller (University of Utah) Utah's Wage Gap March 6, / 61

15 Introduction Basic Data Occupation Wage Gap Curtis Miller (University of Utah) Utah's Wage Gap March 6, / 61

16 Introduction Basic Data Industry Wage Gap Curtis Miller (University of Utah) Utah's Wage Gap March 6, / 61

17 Introduction Basic Data Education Wage Gap I Curtis Miller (University of Utah) Utah's Wage Gap March 6, / 61

18 Introduction Basic Data Education Wage Gap II Curtis Miller (University of Utah) Utah's Wage Gap March 6, / 61

19 Introduction Basic Data Marital/Parental Wage Gap Curtis Miller (University of Utah) Utah's Wage Gap March 6, / 61

20 Estimating Discrimination Introduction We call W f W m the raw wage gap. This metric alone does not provide a satisfactory picture about the wage gap. For example, is the disparity because: Men are better educated than women? Men choose better-paying jobs? Men are more experienced and thus have better pay? Division of labor in households? Discrimination against women? Curtis Miller (University of Utah) Utah's Wage Gap March 6, / 61

Estimating Discrimination Decomposition Methods Figure: Ronald Oaxaca Ronald Oaxaca, an economist now with the University of Arizona, is recognized, along with Alan Blinder (an economist at

21 Estimating Discrimination Decomposition Methods Figure: Ronald Oaxaca Ronald Oaxaca, an economist now with the University of Arizona, is recognized, along with Alan Blinder (an economist at Princeton), as having rst developed and applied the decomposition technique known as Oaxaca-Blinder (OB) decomposition. Despite the limitations of OB decomposition and the availability of alternatives, OB decomposition is not only the simplest technique but remains the most commonly used. Curtis Miller (University of Utah) Utah's Wage Gap March 6, / 61

22 Estimating Discrimination Framework I X a is group a's characteristics (perhaps a data matrix) Y a is the outcome of a response variable for group a (say, a vector) f a ( ) a function that determines the value of the response variable for group a, so we automatically have Y a = f a (X a ) Dene X b, Y b and f b ( ) similarly for group b. Curtis Miller (University of Utah) Utah's Wage Gap March 6, / 61

23 Estimating Discrimination Framework II Y = Y b Y a denotes the dierence in Y between group b and group a Let T be the treatment eect, the dierence between group b and a due to being applied dierent treatments, associated with f b f a Let E be the endowment eect, the dierent between group b and a due to possessing dierent characteristics, associated with X b X a We decompose Y so that Y = T + E. We wish to discover T and E. Curtis Miller (University of Utah) Utah's Wage Gap March 6, / 61

24 Estimating Discrimination Framework III Let f ( ) be a counterfactual function representing a counterfactual treatment. Ỹ a = f (X a ) is group a's counterfactual response. Ỹ b = f (X b ) is similar. Curtis Miller (University of Utah) Utah's Wage Gap March 6, / 61

25 Estimating Discrimination General Decomposition Derivation Y = Y b Y a = Y b Ỹ b + Ỹ b Ỹ a + Ỹ a Y a = f b (X b ) f (X b ) + f (X b ) f (X a ) + f (X a ) f a (X a ) = [(f b (X b ) f (X b )) + ( f (X a ) f a (X a ))] + ( f (X b ) f (X a )) Let T = T,b + T,a = [(f b (X b ) f (X b )) + ( f (X a ) f a (X a ))] and E = ( f (X b ) f (X a )). Then: [(f b (X b ) f (X b )) + ( f (X a ) f a (X a ))] + ( f (X b ) f (X a )) = [ T,b + T,a ] + E = T + E T,b is group b's premium and T,a group a's penalty. Curtis Miller (University of Utah) Utah's Wage Gap March 6, / 61

26 Estimating Discrimination Oaxaca-Blinder Decomposition I Let Y b be the mean for group b, X b a vector of mean values of group b's characteristics, and β b a vector of coecients so Y b = f b (X b ) = β T b X b. Dene Y a, X a, and β a similarly, and β serves the role of f ( ). Then: T,b = (β b β) T X b T,a = ( β β a ) T X a T = T,b + T,a E = β T (X b X a ) Curtis Miller (University of Utah) Utah's Wage Gap March 6, / 61

27 Estimating Discrimination Oaxaca-Blinder Decomposition II The Oaxaca-Blinder decomposition is Y = T + E = [(β b β) T X b + ( β β a ) T X a ] + β T (X b X a ) Curtis Miller (University of Utah) Utah's Wage Gap March 6, / 61

28 Estimating Discrimination Oaxaca-Blinder Decomposition III Ȳ b, Ȳ a are estimated mean values of Y X b and X a are estimated mean vectors ˆβ b and ˆβ a are estimators for β b and β a resp. (typically the least-squares estimators) ˆ Y = Ȳ b Ȳ a ˆ T,b = ( ˆβ b β) T X b ˆ T,a = ( β ˆβ a ) T X a ˆ T = ˆ T,b + ˆ T,a ˆ E = β T ( X b X a ) Curtis Miller (University of Utah) Utah's Wage Gap March 6, / 61

29 Estimating Discrimination Oaxaca-Blinder Decomposition IV ˆ Y = ˆ T + ˆ E = [( ˆβ b β) T X b + ( β ˆβ a ) T X a ] + β T ( ˆX b ˆX a ) Curtis Miller (University of Utah) Utah's Wage Gap March 6, / 61

30 Estimating Discrimination Oaxaca-Blinder Decomposition V Regarding the choice of β, these are common choices: β { ˆβ a, ˆβ b } If β = ˆβ b, ˆ T = ˆ T,a and ˆ T,b = 0. This equates to saying that group b has no premium; any dierence is due to group a's penalty. If β = ˆβ a, ˆ T = ˆ T,b and ˆ T,a = 0. This equates to saying that group a has no penalty; any dierence is due to group b's premium. When studying disparity in pay due to gender, economists believe that there is both a male wage premium and a female wage penalty, so choosing β this way is not considered best. β = ˆβ, where ˆβ is the function estimated upon the pooled sample, including observations from both populations a and b. ˆβ has the exact same covariates as ˆβ a and ˆβ b. β = ˆβ, where ˆβ includes the same covariates as ˆβ but an additional dummy variable tracking membership in group a and b. This was the chosen β in my research. Curtis Miller (University of Utah) Utah's Wage Gap March 6, / 61

31 Estimating Discrimination Oaxaca-Blinder Decomposition VI If β a = (β a,0, β a,1,..., β a,k ) T (β a,0 is the intercept), X a = (1, X a,1,..., X a,k ) T, and β b, X b, and β are analogous, then we use the following to nd the contribution of the k th covariate to each quantity of interest: T,b = T,a = T = E = K T,b,k = k=0 K T,a,k = k=0 K [ T,b,k + T,a,k ] k=0 K E,k = k=0 Estimated values are dened similarly. K (β b,k β k )X b,k k=0 K ( β k β a,k )X a,k k=0 K β k (X b,k X a,k ) Curtis Miller (University of Utah) Utah's Wage Gap March 6, / 61 k=0

32 Estimating Discrimination Comparing Decompositions I Suppose we wish to determine whether T or E has changed over time and how, or suppose you wish to compare T or E between regions (or any other reasonable set of groups). We can do a second decomposition to answer these questions (it's not enough to just use dierences). Here, let Yb 1 be the value of Y b for group/period 1, Yb 0 the value of Y b for group/period 0, and the operator denotes a dierence of a variable between two groups (so (Y b Y a ) = (Yb 1 Y a 1 ) (Yb 0 Y a 0 ) or β = β 1 β 0 ). Dene other variables similarly. Curtis Miller (University of Utah) Utah's Wage Gap March 6, / 61

33 Estimating Discrimination Comparing Decompositions II ( ) ( ) X 1 (Y b Y a ) = b + Xb 0 X 1 (β b β) + a + Xa 0 ( β β a ) 2 2 }{{} Pure dierence in treatment eect ( ) ( ) (β β0 a ) ( β 1 + β 0 ) ( β 1 + β 0 ) (βa 1 + βa 0 ) X b + X a 2 2 }{{} ( β1 + + β ) 0 (X b X a ) 2 }{{} Pure endowment interaction ( (X 1 + b + Xb 0) (X ) a 1 + Xa 0 ) β 2 }{{} Endowment interaction Treatment interaction Substitute in estimators ( X b, X a, ˆβ b, ˆβ a, etc.) as appropriate for estimation. Curtis Miller (University of Utah) Utah's Wage Gap March 6, / 61

34 Estimating Discrimination OB decomposition inherits any aws associated with the parameters and estimators it uses, both mathematic and economic in nature. Of particular interest: Omitted variable bias could pollute results. In particular, missing variables may lead to an inated ˆ T. Selection bias may lead to estimators not being applicable to our target group. For example, we may like to say that ˆβ a is women's estimated wage function, but in reality, at best, it's the estimated wage function for employed women, since not all women even have a wage to estimate! We cannot reach causal conclusions from OB decomposition alone. (OB decomposition looks more like an accounting for the gap.) OB decomposition applies only to the population mean/sample mean. The rest of the distribution is ignored. While failing to account for variables in which men and women may dier may cause T to be biased, we may falsely be legitimizing E ; perhaps dierences in characteristics are in response to discrimination Curtis Miller or represent (University ofdiscrimination Utah) Utah's of a Wage dierent Gap nature. March 6, / 61 Problems with OB Decomposition

35 Estimating Discrimination Defense of OB Decomposition While old, OB decomposition is common and well understood and easy to learn, while still making a lot accessible. I believe that useful information about the structure of wage dierentials is revealed by decomposition methods. Curtis Miller (University of Utah) Utah's Wage Gap March 6, / 61

36 Selection Bias Introduction Suppose we are discussing workers, or membership in the labor force. Selection bias occurs if membership of individuals in the labor force is not independent of the characteristics of the individuals and those characteristics inuence the variable under investigation. For example, if individuals who are more industrious are more likely to enter the labor force, they may earn more than those not in the labor force if those outside were forced to enter. This is termed positive selection. If individuals who are less industrious are more likely to enter the labor force, they may earn less than those not in the labor force if the outsiders earned a wage. This is termed negative selection. Curtis Miller (University of Utah) Utah's Wage Gap March 6, / 61

37 Selection Bias Challenges of Selection Bias We cannot generalize statements as we like without accounting for selection bias. In the context of accounting discrimination, if women's characteristics impact the decision to enter the labor force and those same characteristics inuence their pay, T will be contaminated by the bias and we cannot say T responds primarily to one's gender. Men usually serve the role of breadwinner and thus have less agency in the decision to participate in the labor force. We assume for men there is no selection eect. Handling selection bias is obviously tricky since unemployed individuals don't have wages, so we cannot use those wages to see the eects of selection bias! Curtis Miller (University of Utah) Utah's Wage Gap March 6, / 61

Selection Bias James Heckman Figure: James Heckman James Heckman, an economist at the University of Chicago, won the Nobel Prize in Economics for his solution to the selection bias problem.

38 Selection Bias James Heckman Figure: James Heckman James Heckman, an economist at the University of Chicago, won the Nobel Prize in Economics for his solution to the selection bias problem. Heckman showed that the selection bias problem is not only a problem with censored data but a missing variable problem. He developed a procedure referred to as Heckman regression (sometimes called a "heckit" model) that can estimate a wage function that corrects for selection bias. Curtis Miller (University of Utah) Utah's Wage Gap March 6, / 61

39 Selection Bias Heckman Procedure The Heckman procedure works as follows: 1 Estimate a probit model that describes the probability that a person is in the labor market, depending on their characteristics. 2 Use the results of the probit model to add a new variable to your wage model (varying for each person), dependent on this probability. (This quantity is related to the inverse Mills' ratio.) 3 Estimate the wage regression model as you otherwise would, with this new variable included. Once done, you have estimated a (wage) function that accounts for selection bias. Curtis Miller (University of Utah) Utah's Wage Gap March 6, / 61

40 Selection Bias Problems with Heckman Regression Heckman regression's biggest problem is deciding which variates to include in β and γ. Why does a variate in γ not belong in β? This problem is compounded by the fact that Heckman regression is very sensitive to its specication, and results can dier greatly depending on the division of variables in β and γ. To my knowledge, there is no solution to this problem. This problem resulted in my estimating ve dierent models for my project. Curtis Miller (University of Utah) Utah's Wage Gap March 6, / 61

41 Decomposition Estimates Wage Model Economists believe that the majority of a wage distribution is modeled well by a log-normal distribution, so log(wage i ) N(µ, σ 2 ). When taking the natural log of wages, the dierence of the averages can be interpreted as the dierence in proportion between the two groups, much like the cents-on-the-dollar wage gap. The preferred wage equation is: log(wage i ) = β 0 + β 1 age i + β 2 age 2 i + β 3 nohsdeg i + β 4 somecoll i + β 5 assoc i + β 6 bachelor i + β 7 graduate i + β 8 notwhite i + β 9 notcitizen i + β 10 vet i + β 11 occ i + β 12 ind i + β 13 overwork i + β 14 public i + ɛ i Curtis Miller (University of Utah) Utah's Wage Gap March 6, / 61

42 Decomposition Estimates Selection Model Let E i denote whether individual i is employed. Then our selection model is: P (E i = 1 X i ) = Φ(β 0 + β 1 age i + β 2 age 2 i + β 3 nohsdeg i + β 4 somecoll i + β 5 assoc i + β 6 bachelor i + β 7 graduate i + β 8 notwhite i + β 9 notcitizen i + β 10 vet i + β 11 married i + β 12 nhhinfant i + β 13 nhhpreschooler i + β 14 nhholdchild i + β 15 singlepar i + β 16 multiadult i + β 17 otherhhincome i + ν i ) Every numeric variable used in this study was centered. All data is from the CPS March samples. Years were pooled into roughly 5-year periods to improve sample sizes. The main period of interest is the period. Curtis Miller (University of Utah) Utah's Wage Gap March 6, / 61

43 Decomposition Estimates OB Decomposition Curtis Miller (University of Utah) Utah's Wage Gap March 6, / 61

44 Decomposition Estimates Detailed National OB Decomposition Curtis Miller (University of Utah) Utah's Wage Gap March 6, / 61

45 Decomposition Estimates Detailed Utah OB Decomposition Curtis Miller (University of Utah) Utah's Wage Gap March 6, / 61

46 Decomposition Estimates Comparative Decomposition Curtis Miller (University of Utah) Utah's Wage Gap March 6, / 61

47 Decomposition Estimates Utah vs. Nation Detailed Decomposition Curtis Miller (University of Utah) Utah's Wage Gap March 6, / 61

48 Decomposition Estimates National Change in Decomposition Curtis Miller (University of Utah) Utah's Wage Gap March 6, / 61

49 Decomposition Estimates Detailed National Change Since '92 Curtis Miller (University of Utah) Utah's Wage Gap March 6, / 61

50 Decomposition Estimates Intermountain Region Change in Decomposition Curtis Miller (University of Utah) Utah's Wage Gap March 6, / 61

51 Decomposition Estimates Utah Change in Decomposition Curtis Miller (University of Utah) Utah's Wage Gap March 6, / 61

52 Decomposition Estimates Detailed Utah Change Since '92 Curtis Miller (University of Utah) Utah's Wage Gap March 6, / 61

53 Conclusion Is There Discrimination Given all this evidence, even with the potential aws of the methods used, I do believe there is evidence for some wage discrimination at least in Utah that does cost Utah women a signicant amount. Discrimination need not be brought about by malevolent intent. It could be due to unintended bias and the only solution is to reduce subjectivity and arbitrariness in the workplace. Curtis Miller (University of Utah) Utah's Wage Gap March 6, / 61

54 Conclusion Solutions Given the larger family sizes and the younger ages women start families in Utah, there needs to be support for educated, professional mothers. We should seek solutions to make being a mother and a student or worker easier. I support paid maternity and paternity leave We need to ensure girls get a good education and stay in school We must recognize the typical prole of a family in poverty is a single mother with children in a low wage job, and provide her support especially given her disadvantage. Curtis Miller (University of Utah) Utah's Wage Gap March 6, / 61

55 Conclusion Why Should Data Scientists Care I Why should data scientists care about my work? Data scientists may be able to use the Heckman model in regression scenarios Data scientists should be aware of discrimination in their applications Curtis Miller (University of Utah) Utah's Wage Gap March 6, / 61

56 Conclusion Heckman Regression for Data Scientists While Heckman regression is a method for economists, data scientists may want to consider its use. Selection bias can appear anywhere. When trying to generalize a regression model from a subset to a larger group, perhaps the Heckman model can improve predictive accuracy. Example: Generalizing information in Twitter tweets to, say, all voters. Curtis Miller (University of Utah) Utah's Wage Gap March 6, / 61

57 Conclusion Discrimination by Big Data I Employers are looking to big data to help make decisions about employment, promotions, pay, and other aspects of workplace life. The belief that algorithms don't discriminate because they are not human is DANGEROUS! Data sets are created by humans. If your data is racist/sexist, your algorithm will learn to be racist/sexist. Opaque algorithms deployed broadly with little oversight or opportunity for recourse can reinforce rather than eliminate discrimination! There is evidence discriminatory algorithms exist and make decisions at present. Curtis Miller (University of Utah) Utah's Wage Gap March 6, / 61

58 Conclusion Discrimination by Big Data II We can easily train racist/sexist algorithms by accident! 1 Removing race/gender information from the data set is not enough. (In fact, I believe that would be the wrong approach!) 2 Race and gender are likely associated with other variables in your data set. The algorithm may learn to use those other variables as proxies for race or gender, and overweight (or underweight) them in predictions. Practitioners should be conscious of the potential for deploying an algorithm that was trained to discriminate. We need to audit algorithms and be sure they do not reinforce discrimination Curtis Miller (University of Utah) Utah's Wage Gap March 6, / 61

59 Conclusion Discrimination by Big Data III Y b Y a = [(f b (X b ) f (X b )) + ( f (X a ) f a (X a ))] + ( f (X b ) f (X a )) = [ T,b + T,a ] + E = T + E Many algorithms are "black boxes"; they may be treated as trade secrets or the resulting model may be intractable (or, often, both). Decomposition techniques may oer a starting point for auditing algorithms, even while treating them as "black boxes." Consider the following procedure: 1 Stratify a dataset according to sex or race. 2 Train separate models on dierent groups of individuals, along with the model to be deployed. 3 Perform a decomposition to identify to what degree a model is discriminatory. (Notice that f, X, and Y are all loosely specied; this decomposition should be possible, even when treating f as a "black box.") Curtis Miller (University of Utah) Utah's Wage Gap March 6, / 61

60 Conclusion In any case, practitioners should be aware of the eects of their models, especially when they will be deployed widely, have a great impact, and have little opportunity for correction. Curtis Miller (University of Utah) Utah's Wage Gap March 6, / 61

61 Conclusion References M. W. Curtis Grant Miller, Utah's gender opportunity, C. G. Miller, Explaining utah's gender gap in wages, S. F. Nicole Fortin, Thomas Lemieux, Decomposition methods in economics, R. L. Oaxaca, Male-female wage dierentials in urban labor markets, International Economic Review, vol. 14, pp , J. J. Heckman, Sample selection bias as a specication error, Econometrica, vol. 47, no. 1, pp , C. O'Neil, Weapons of Math Destruction You can also nd out more on my website/blog at ntguardian.wordpress.com. Curtis Miller (University of Utah) Utah's Wage Gap March 6, / 61

EXPLAINING UTAH S GENDER GAP IN WAGES. Curtis Miller

EXPLAINING UTAH S GENDER GAP IN WAGES by Curtis Miller A Senior Honors Thesis Submitted to the Faculty of The University of Utah In Partial Fulfillment of the Requirements for the Honors Degree in Bachelor