Estimating Income Inequality from Binned Incomes with Paul von Hippel

Starting this year, many employers will be required to report to the Equal Employment Opportunity Commission (EEOC) their employees’ pay by sex, race, and ethnicity within 12 specified pay bins. This reporting will help the EEOC improve enforcement of pay discrimination laws and may provide some insight into the persistence of wage gaps. This week’s WAPPP seminar featured Paul von Hippel, Assistant Professor of Public Affairs at the Lyndon B. Johnson School of Public Affairs, University of Texas at Austin. While many methods have been used to analyze binned incomes, little work has been done to evaluate these methods. Professor von Hippel described three statistical methods for analyzing binned data and their relative accuracy in estimating underlying income differences.

According to Professor von Hippel, there are some misunderstandings about the limitations of binned date. The general impression is that because pay bins can be $10,000-$15,000 wide, it is impossible to estimate pay differences that are smaller than the bin width. While it is difficult to accurately measure the difference in individual pay within one pay band, it is possible to discern average or median pay differences with much greater precision. Even with a bin width of $10,000, it is possible to estimate pay differences within $1,500. Despite the assumption to the contrary, bin width is actually not an obstacle to this sort of analysis.

Depending upon the desired estimate, be it average income, median income, or an index of inequality like the Gini coefficient, certain types of statistical analysis will be more precise than others. Using Census data of binned incomes and statistics on underlying non-binned income, Professor von Hippel described three statistical methods to see how close each method comes, using the binned data, to estimating the underlying non-binned data.

Robust Pareto Midpoint Estimator (RPME): This method, the simplest, sets each household income to the midpoint of its bin. While it is not the most sophisticated method, it works about as well as more complex analyses, particularly if the bins aren’t too wide. As the number of bins increases, the estimates get better and better. The only “trouble spot” with this type of analysis is the top income bin, which doesn’t have an upper bound. To solve this issue, this method estimates a Pareto distribution that fits the top two income bins and plugs in the mean of that distribution for households within those bins. There are some issues with the traditional formula when there are a large number of high-income households, but using a harmonic mean tends to resolve this difficulty. This method is very quick and can run on thousands of employers within a minute or so. The downside of this method is that it’s unrealistic to assume that every household within a given pay bin has the same pay value, and the analysis may lose something by treating each household the same.

Multi-Model Generalized Beta Estimator (MGBE): This method involves fitting continuous distributions to the given income distribution. In looking at county-level Census data, Professor von Hippel set each of 10 different continuous distributions to the income distribution for a county, took the distribution that best fit that county’s data, and then used those distributions to estimate average income, median income, and the Gini coefficient. One positive aspect of this approach is that it treats incomes as continuous, not discrete. However, on the negative side, even the best-fitting distribution may not fit that well. This is particularly true if income is bimodal.

Spline CDF Estimator: This method uses nonparametric bin smoothing to spread incomes evenly across bins. A simple step function works nicely, but the method works even better if the bins are divided recursively or a cubic spline is fit to smooth over the step function to model the distribution of incomes. Professor von Hippel credits David Hunter and McKalie Drown for their work on this method, which combines the best aspects of the other two methods: the Spline CDF Estimator models income as continuous and perfectly reproduces bin counts.

Of these three techniques, the Spline CDF Estimator is the most accurate. Between the other two, RPME works about as well as MGBE for some estimates and is much faster, particularly when estimating average income. However, it is not as accurate for median income, and estimating inequality indices is even more difficult. There are still some inaccuracies with these methods, particularly when trying to estimate trends in inequality over time, but this analysis is good news for researchers studying wage gaps. With the binned data soon to be available from the EEOC, it will be possible to estimate income differences much more precisely than the bins would seem to indicate – and with good data comes good policy! RPME and MGBE are available in both Stata and in R’s inequality package, and the Spline CDF Estimator is available in R’s binsmooth package.

The History of the "Mommy Track" with Elizabeth Singer More

In the age of Lean In, we continually interrogate the differences between men and women’s experiences at work. Do these differences arise from gender discrimination, or do working women simply have different work/family preferences than their male colleagues? These questions have a long history, and the debate over sameness and difference can help to illuminate the relationship between feminism, women, and work. This week’s WAPPP seminar feature Elizabeth Singer More, WAPPP Fellow and Associate Director of Open Circle Jewish Learning at Hebrew College. A historian of women, work, and the family, Professor More discussed the history of the “mommy track,” tracing in particular the controversy over Felice Schwartz’s 1989 Harvard Business Review article “Management Women and the New Facts of Life.”

The issue of sameness versus difference was a significant dispute for feminists in the 1970s and 1980s, and was thrown into sharp relief in the case of EEOC v. Sears Roebuck & Co. The case was brought on behalf of women who were denied commission sales jobs based on management’s assumptions about women’s preferences, personalities, and skills. Both sides in the case called experts, who alternately described the disparity between male and female employees as the result of discrimination or of women’s voluntary cultural patterns. Some women, one side argued, were “like” management men; that is, they were willing to work long hours, travel, and sacrifice time with their families in order to advance. Other women were different than their male colleagues. They wanted to work but also wanted to have children and were willing to sacrifice advancement at work to take time off and raise their families. The case went on in this vein, with one side presenting “natural” dichotomies between men and women, such as women being more concerned with nurturing and men with work, while the other maintained that women’s historical labor market behavior was established just as much by lack of opportunity as by a different set of preferences. These arguments emphasized the economic consequences of the sameness/difference question for working women.

Against this backdrop, Schwartz published her article, “Management Women and the New Facts of Life.” Schwartz was the founder of the nonprofit Catalyst Institute, which in the 1970s had worked to help housewives enter the workforce. By the 1980s, the Institute regularly advised corporations on attracting, retaining, and advancing female professionals. Schwartz saw this article as part of the same project. Addressed to executives, the article laid out a business case for hiring women, but encouraged executives to identify female employees early on as “career-primary” or “career-and-family.” “Career-primary” women should be given the same opportunities as any male employee, but these women would have to remain “single or at least childless.” If they did choose to have children, they would have to be “satisfied to have others raise them.” These women, Schwartz said, would cost corporations more to employ.

“Career-and-family” women would be relegated to the derisively-labeled “mommy track.” Corporations, Schwartz’s argument went, could better retain women in whom they had invested training if these women could be permitted to balance work and family. Women who took long maternity leaves should be encouraged to return to work; corporations should provide flex time, part-time, and job-sharing options; and companies should assist with day care. In exchange for these supports, women on the mommy track would have to accept that their ascension up the corporate ladder had halted, or at least paused. Schwartz argued that this arrangement would help women and employers – women would be able to maintain professional and family lives, and employers would accrue talented middle managers who were grateful to be where they were.

Schwartz argued that not all women have the same desires. Some want to put their careers first, and so the automatic association of women with babies is unjustified. However, by drawing on the language of sameness and of difference, Schwartz angered both sides. Painting women as ambitious non-caregivers or as complacent nurturers – combined with the assertion that management women are more costly to employ than men – caused an uproar. The Harvard Business Review printed 22 pages of letters in response to her 14 page article, most of them critical. Schwartz’s critics argued that she was incorrect in the facts or that the facts she cited were entirely unsubstantiated and that her article reinforced stereotypes that hindered women in their professional lives and men in their family lives. In trying to reconcile opposing feminist philosophies, she pleased only male executives, who loved the article.

Professor More points to an article by legal theorist Joan Williams, published the same month as Schwartz’s article, to further underscore the difficulty of reconciling feminism and market-based policymaking. Williams took issue with both sameness and difference feminism. She argued that sameness feminists don’t deal with how differences work to women’s disadvantage in a “gender-blind” system that is based on male life patterns. On the other hand, while difference feminism values women’s caregiving labor, in doing so it may perpetuate women’s economic marginalization. Williams called for the existing structures of work and family life to be totally rethought. The idea that women choose to become marginalized on the “mommy track” clouds the reality that all workers are stuck choosing between two unacceptable life patterns that we term stereotypically male or female. Where Schwartz was optimistic about negotiating on employers’ terms, Williams thought it was a feminist imperative to change the terms of work and family life.

Schwartz, for her part, was shocked and hurt by the critical reaction. Her article was dedicated to persuading corporations that it was in their own best interests to fight discrimination and institute family-friendly policies. However, her method for advocating these approaches was to argue that it was in business’s competitive advantage to be responsive to women’s needs. Whereas she had previously been forced to make an equality and justice argument – “Be fair and good to women and support us!” – she could now use a big-business logic in saying that if companies couldn’t attract, retain, and promote female talent, they would lose their competitive advantage and the bottom line would suffer. Where Schwartz saw a reasonable tradeoff for women – getting family-friendly working policies in exchange for pausing advancement – others saw institutionalized discrimination and a penalty for female workers for failing to conform to a male standard. Leaning heavily on a profit motive as an incentive to respond to women’s needs could also disadvantage women – in times of economic scarcity, female employees would lose their leverage and employers would have ready justification for firing women or favoring men.

In closing, Professor More emphasized that we cannot relinquish the justice and equality argument. We have to protect gains in equality even in times of economic weakness. As a WAPPP Fellow, Professor More will be completing her manuscript on the intellectual and political history of maternal employment in America from World War II through the mid-1990s. We look forward to hearing more from her and continuing these conversations!

Beyond the Glass Ceiling

Today my friend sent me a link to Boys Clubs Tumblr – a visual collection of “the corners of the world where women have yet to tread.” It is mind-boggling how much progress we still have to make in closing gender gaps.

At WAPPP Seminars this year we discussed some of these “corners of the world.” There are the overwhelmingly male corporate boards, the merely 18 female CEO’s of Fortune 500 companies, and the female stock brokers earning less than their male peers. But we also heard about female leaders helping their countries address inter-group conflict, female professors inspiring young women to pursue STEM careers, and the women mobilizing their communities for land rights. 

In the final seminar of the academic year, Professor Matt Huffman, of the UC Irvine Sociology Department and the Paul Merage School of Business, brought research to bear on another question – do women managers change the workplace itself?

There is some evidence that female managers do close gender gaps among their employees. One study found that wage gaps were smaller inlocal U.S. industries with many high-status females. Two other studies explored gender segregation and found that female managers increased female hiring and gender integration in the California savings and loan industry and in California’s state agencies.

Huffman set out to study these phenomena on a much larger scale, using Equal Employment Opportunity Commission’s data. EEO-1 reports, which are filed by all “medium and large” firms under the 1964 Civil Rights Act, amount to a set of longitudinal workplace data spanning decades. Each report breaks out the managerial and non-managerial occupations at a specific work site and reports on the number of women and racial minorities in each category. Because the work sites are identified by name and address, the individual files are confidential and only available to a handful of researchers. For Huffman, this presents a goldmine for empirical analysis, complete with information on industry types, organization sizes, and other potential control variables.

Since the data did not include wages, instead of focusing on wage gaps, Huffman decided to study organizational segregation – a measure of how evenly men and women were distributed across the non-managerial categories in the organization. Using regression analysis on 1975, 1986, 1995 and 2005 data, he demonstrated that organizations with a higher percentage of women in management positions were less gender-segregated in the non-managerial ranks.

Though the most recent work places were generally far less gender-segregated than the older cohorts, even without female managers, the pattern across all four points in time was similar – higher percentage of female managers meant more integrated subordinates. In other words, breaking up the boys' club at the top, helped break the barriers among departments and functional areas below. 

Huffman ran a series of other analyses to pinpoint aspects of the workplace context that amplified or diminished the gender-integrating effect of female managers on their organizations. He found that managerial formalization and company growth were both conducive to the gender integrating effect of female managers. Perhaps it is because formal structures can give women more access to power than a loose work environment might. It may also be because a female manager in a growing organization has more opportunities to hire people, altering the gender balance of her workforce.

Why does gender diversity and gender integration matter? First, women bring unique lived experiences to the workplace, and given that women are also half of the consumers, it is prudent to include their perspectives in developing and selling products and services. (Maybe if the Apple Inc. team added some women, someone would have thought that iPad could be a bit of an awkward name...). Second, companies with more female leaders make more money and women executives make venture-backed companies more successful, despite the fact that the venture capital world is still decidedly a boys club. 

Finally, gender equality is the just and the smart thing to do, which is why WAPPP's work closing gender gaps in economic opportunity, political participation, health and education is so important.

Anya Malkov is an MPP candidate at the Harvard Kennedy School, a WAPPP Cultural Bridge Fellow, and an alumna of From Harvard Square to the Oval Office.