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.

Achieving Meritocracy in the Workplace

Knowing what we do about the gender wage gap and implicit bias in the workplace, what sort of measures could we take to improve pay equity? Could a meritocratic system, with pay based strictly on performance, be the answer?

This week’s WAPPP seminar featured Emilio Castilla, NTU Professor of Management at the MIT Sloan School of Management (during his spring break, no less!). Professor Castilla’s work focuses on the social aspects of work and how social and organizational processes influence employment outcomes – with important managerial implications.

Performance-reward practices are now standard within most industries – 69% of organizations offer variable bonuses based on performance, and some type of merit pay exists in almost all companies. If these pay practices are truly meritocratic, demographics shouldn’t matter. However, the gender and racial implications of merit-based employer efforts are not well understood – do these company practices improve workplace equity and diversity?

In theory, if merit pay was based solely on performance, we would see similar levels of pay for men and women at each performance rank. However, one of Professor Castilla’s studies showed that the benefits of a higher performance rank were much greater for men than for women. A man’s performance bonus was significantly larger than a woman’s at the same performance level, and the gender gap increased the higher the performance quintile.

Skeptics may argue that women may have less experience than men, may be less productive than men, or may not ask for bonuses. To test these assertions, Professor Castilla conducted a company field study of performance rewards over time. There was no evidence in the company that women or minorities received lower starting salaries than white men within a given job and work unit. However, there was evidence of performance-reward bias. Even with the same performance scores, women and minorities with the same job, work unit, supervisor, and human capital received lower salary increases than white men. This study provides some evidence that in trying to close the gender wage gap, we should really be looking at the processes and outcomes surrounding bonus pay.

The key question in thinking about organizational processes is whether the gender gap exists because of or despite employer meritocratic efforts. What is the alternative to performance-based pay? If we eliminated merit pay, would we see no bias? Or are these results better than what we had under traditional systems?

To answer these questions, Professor Castilla took to the lab. Participants were given a limited budget of $1,000 to distribute among employees in bonuses. In the meritocratic condition, participants were given performance evaluations of each employee and were told that this was the only criterion for distributing bonuses. In the non-meritocratic condition, participants still had access to performance evaluations, but were told that it was up to the manager’s discretion to distribute bonuses. In addition, researchers varied the gender of the employees to be evaluated, who each had equal performance ratings. In the non-meritocratic condition, participants awarded male and female employees about the same level of bonus, with no statistically significant difference (on average, women received about $399 and men received $401). Shockingly, in the meritocratic condition, there was an enormous gender gap in favor of men. Men received about $420 in bonus pay in the meritocratic condition, compared to $374 for women. Professor Castilla calls this the paradox of meritocracy—in an organization that emphasizes meritocracy in its culture, without specific structures or processes in place, bias is even greater.

Demographic inequality persists despite employer merit-based efforts. This finding is consistent with “moral credentialing” – in contexts where people are led to feel unbiased, fair, or objective, they are actually more likely to then behave in biased ways. By making employees feel like they’re working in a meritocracy that strictly evaluates performance, they are more likely to unleash bias. This is true for both male and female study participants distributing bonuses!

Organizational practices and processes matter, and there is unlikely to be only one solution to bias in the workplace. Still, it is critical to investigate which employer practices help to reduce workplace inequality and increase diversity. Professor Castilla undertook one large firm-level study designed to empirically test whether introducing organizational accountability and transparency policies reduced any pay gap based on employee demographics. Performance management at this company was a three-step process: supervisors met with employees once a year to discuss their performance and provide feedback, but were not responsible for setting compensation. This step is characterized by high accountability and transparency: the supervisor is responsible for providing feedback, and the employee has to acknowledge receiving the feedback and register their reaction to it. However, steps two and three are less visible. In step two, compensation is decided at the work unit level, and in step three HR rubber stamps the work unit’s decision. The key intervention here would be to increase accountability and transparency in steps two and three.

The company created a Performance-Reward Committee that Professor Castilla emphasized was a task force in the truest sense of the term: they had a defined task and the force to intervene if they found any evidence of pay discrepancy and bias. Once compensation-setters had to be accountable and visible in terms of their process and outcome, demographic variables played no significant role in bonus pay. Instead, performance ratings became even more statistically significant.

Professor Castilla’s work illustrates some of the critical challenges faced by employers. Meritocracy is harder than it looks! Merit-based efforts can activate implicit bias above and beyond traditional processes. However, Professor Castilla emphasizes, the key lesson here is not “we shouldn’t adopt practices to increase fairness and equity.” Instead, we should pay close attention to implementation, accountability, and transparency.

Read the paper: 

The Paradox of Meritocracy in Organizations 
Authors: Emilio J. Castilla Stephan Benard 
Organizations that emphasize merit-based cultures, while intending to increase opportunities, fairness, and equity, may inadvertently be disadvantaging women.
 

What Works: Closing the Gender Wage Gap in Boston

As part of HUB Week, the Women and Public Policy Program at the Harvard Kennedy School presented a panel discussion about the public-private-academic partnership facilitated by the Office of the Mayor of Boston and the Boston Women's Workforce Council that resulted in innovative, research-based interventions to reduce the wage gap in the city. Victoria A. Budson, Executive Director, Women and Public Policy Program moderated panelists Iris Bohnet,  Professor of Public Policy and Director of the Women and Public Policy Program; Megan Costello, Executive Director of the Mayor's Office of Women's Advancement, City of Boston; Katharine Lusk, Executive Director of the Initiative on Cities, Boston University; and Michelle Wu, Councilor At-Large, Boston City Council.

The first step to look for ways to reduce the wage gap is the applicant's first contact with any employer, the recruitment process. Professor Bohnet started the panel with a discussion about reducing bias in interview processes. Bias is very difficult to eliminate, we are all biased in one way or another, "it has something to do with how our minds work... we are all affected by these biases independent of our own demographic characteristics" she explained. Her research focuses on ways to "debunk" these cognitive glitches in order to improve recruitment and interview processes. Research has shown that interviews are not particularly strong tools for predicting future on-the-job performance, "blind evaluations are great, but in most of your jobs those aren't possible." What is the next best option? There is a way to structure an interview to make it more useful: "You should force yourself to ask every job candidate the very same five questions, in the same order, and ideally... compare question by question". She shared that this is actually the way she grades papers students write for her class!

WAPPP Panel Discussion on the wage gap in Boston, part of HUB Week

Katharine Lusk, who according to Victoria Budson, "really began the transition and change around these metrics in the city" followed Professor Bohnet's intervention. She talked about what former Kennedy School Professor Samantha Power referred to as being a "bureaucratic samurai", which essentially means having the ability to defy the status quo while still being able to operate within a bureaucratic setting. In Ted Kennedy's words, it means knowing how to operationalize good intentions. Katharine was working with former Mayor Thomas Menino, when he set out, in 2013, to make Boston "the premiere city for working women". They focused on creating evidence-based policy to benefit women, including capital resources for early educators, support for women entrepreneurs and women in STEM, and of course, pay equity. They created the Women's Workforce Council in a model of collaborative governance as "a new way of solving a very old and tractable problem". This effort brought talent to the table. The Mayor's Office then formed further coalitions with businesses and with a team at Boston University, which figured out a way for employers to share sensitive wage data anonymously, in order to provide the city with information that allowed them to determine just how large the wage gap is.

Victoria Budson noted that "it's really about whether your ideas catch fire", and that enlisting stakeholders beyond those who obviously benefit from a policy, as Katharine did, is key to getting things done in government. She then introduced the next speaker, Megan Costello, who spoke about her experience as the Campaign Director for Mayor Marty Walsh and now as the Executive Director of the Mayor's Office of Women's Advancement, who works closely with the Women's Workforce Council. "We have to be intentional about diversity," she said, and explained that their approach is three-pronged: they are focusing on working with businesses so they can join the data effort previously set up by Katharine Lusk and her team; secondly, they are working with individual women setting up helpful tools for them, like free workshops on salary negotiation, and finally, they are working on supporting equal pay legislation. Their aim is to really change the culture. Ambitious but possible.

Finally, City Councilor At-Large Michelle Wu, spoke about the importance of having leaders of different perspectives sitting at the table; they can pave the way for change. She said she is convinced there is no better place in the world to be making change than in Boston, a city that is blessed with incredible resources for innovation. "Government innovation is not an oxymoron!", she exclaimed. She spoke about her efforts, working together with the Mayor's Office, to make parental leave a reality for Boston families, and other work she had been able to do as a City Councilor like putting in place a training program for the Boston Housing Authority to assist domestic violence victims, and even make the forms at the Registry friendly for all types of families, including same-sex couples. As the youngest serving member of the Council and the first Asian American to be elected as Councilor, she was a true inspiration.

The audience was very enthusiastic and put forth a number of questions and comments. A wonderful closing for a conversation full of insights, new ideas, and exciting work, all pointing towards achieving equality for women.

Boston to help you get that higher salary

From the Boston Globe, May 21, 2015

About 275 business leaders, most of them women, gathered at the Seaport Hotel Wednesday to broach a touchy subject: the fact that they earn less than men. It’s a timely topic, with the City of Boston in the midst of gathering gender-specific salary data from local companies. And the city used the Greater Boston Chamber of Commerce event to announce yet another step toward closing the wage gap.

This fall, the city plans to hold the first of hundreds of free or low-cost salary negotiation workshops, aimed at teaching women — and men if they so desire — the best ways to boost their pay.

Megan Costello , director of the city’s Office of Women’s Advancement and a panelist at the morning event, said later that she hears stories every day about women underselling themselves, worried about asking for too much “because that’s going to seem egotistical or presumptuous, all these attributes that women tend to see as negative.”

The panel, moderated by Victoria Budson , executive director of the Women and Public Policy Program at Harvard’s Kennedy School, also featured Cathy Minehan, dean of the Simmons College School of Management; Evelyn Murphy , former lieutenant governor and president of the WAGE Project; and Beth Williams , president of Roxbury Technology LLC, a manufacturer that rebuilds toner cartridges.

Williams told the group that after she agreed to be part of the citywide effort to close the wage gap, she examined her own payroll and found more men in supervisory positions. She subsequently promoted two women.

“If I could, I would hire all women,” she said, “but then I’d get in trouble on the other side.” — KATIE JOHNSTON

When Daddy is CEO - WAPPP Seminar Series

The Man: David Ross, Assistant Professor of Management, Columbia University
The Talk: Like Daughter, Like Father: How Employees’ Wages Change When CEOs Have Daughters
The Question: Do people get paid more if their CEOs have daughters?

Daddy's little girl may be a boost to his workforce -- in Denmark, at least. Recent research by David Ross of Columbia University in the country suggests that when male CEOs have daughters, they tend to on average pay their employees more than if they have boys.

Why?

It's a thorny issue. Some people (including some who attended the seminar) may balk at the idea that men think more like women once they have daughters. But these are exactly the assumptions the study uses to conduct its research. Ross's intuition based on his own experience having daughters got him thinking that:

• When anybody has a child, they tend to start thinking about the well-being of others.

• This proximity matters when it comes to leading a group of employees

• When men in particular have girls, they may be more conscious of having to protect/care for someone's well-being -- a "nurture" effect that women tend to exhibit more often.

The results of the research back up Ross's claim: On average, men pay their employees o.4% more when they have daughters. What's more:

• This only happens when have their first daughter. It doesn't happen with subsequent children.
• People who are closer in proximity to the CEO - ie, higher rank in the company - also tend to get paid more than people who know the CEO less or are a lower rank.
• The age and education of the CEO don't really matter - the effect is the same across all groups.

The limitations of the study are many, however. Chiefly, can the Danish example be extrapolated to other countries where gender parity is worse, or where parents do not share the same burden of raising a child? What if the effect is actually negative - that is, daughters don't have an effect at all, but having a son actually makes CEOs pay employees less? And since the data only analyzes numbers, we can't make a causal claim by observing behavior: our evidence is at best circumstantial.

At the very least, Ross's research backs up the idea that the wage gap persists, and that seemingly innocuous variables like the gender of a CEO's child can make a difference.


*Photo Courtesy Smithsonian Magazine


Effie-Michelle Metallidis is a guest student blogger for the Women and Public Policy Program and Master in Public Policy first-year student at Harvard Kennedy School.

How Are Women Doing? The World Bank Weighs in on Gender & Development - WAPPP Seminar Series

The Men: Sudhir Shetty, Sector Manager, Poverty Reduction and Economic Management, The World Bank; and Jishnu Das, Senior Economist in the Development Research Group, The World Bank

The Talk: World Development Report: Gender Equality and Development

The Question: Are women better or worst off than they've been in previous decades?

Not all inequalities are created equal.

At least, that's what researchers at the World Bank have concluded with the release of this year's Gender Development Gap report.

Sudhir Shetty and Jishnu Das, two economists who worked on the report, were on hand at WAPPP to present the latest findings to the Women's Leadership Board at WAPPP on how women have progressed around the world in the past few decades.

The results are positive, but reveal that there's still a long way to go.

While some areas such as education have improved dramatically, researchers says, inequality stubbornly persists in areas such as maternal mortality, HIV/AIDS infection, the wage gap, and domestic violence.

The reason, say Shetty and Das, is a complex interaction between markets, households and formal institutions that must all work together in order to ensure women are supported by every aspect of society.

For instance, curbing female mortality necessitates deep political will on the part of the government to reform its institutions. "I have never been to a district hospital in India where a doctor is not drunk after 8 o'clock," says Das. "The institutions are just not working, and these are the problems that effect female mortality."

The researchers say that there are ways to tackle these challenges. To reduce female mortality, for instance, countries must concentrate on improving clean water and sanitation so that infant girls stand a better chance of survival. A look at the historical data in the US and Europe revealed telling data to the team: as access to clean water improved at the turn of the 20th century, so too did the survival of baby girls.

Some challenges like domestic abuse, however, require a far more complex approach. Political will must drive an agenda that prioritizes the well-being of women and their children; economic opportunities such as access to land, better infrastructure, and greater emphasis on child care can all contribute to a shifting climate that empowers women within their households and in society. Buy-in from men is also a critical aspect in reducing domestic violence; as Shetty says: "This report is about gender -- not just women."

*Photo Image Courtesy of World Bank
Effie-Michelle Metallidis is a guest student blogger for the Women and Public Policy Program and Master in Public Policy first-year student at Harvard Kennedy School.

Women, Business, and the Law - WAPPP Seminar Series

The Woman: Rita Ramalho, Program Manager, Enterprise Analysis Unit, The World Bank Group

The Talk: Women, Business and the Law 2012: Removing Barriers to Economic Inclusion

The Question: How do laws in different countries affect a woman's ability to start businesses and get jobs?

A lower retirement age sounds pretty decent, right? Who wants to work into their 70s, after all? Shorter working days sound good, too. A good work-life balance is strike in this fast-paced world.

But while these may sound like job perks, they're the sorts of prohibitive laws that keep women from achieving the same economic status as men in many countries, say researchers from the World Bank.

In a recent survey of 141 economies conducted by the Enterprise Analysis Unit of the World Bank Group, researchers found that 103 countries have laws that may hinder women's economic opportunities. The laws, which range from restricting the property rights of women in the Phillipines to not paying for maternity leave in Papua New Guinea, account for disparities in income, and affect the way women make decisions about whether to enter the workforce.

"In practice, there's less women in the private sector and [less] entrepreneurs," says Rita Ramalho, the EAU's Program Manager. "We want to see what regulations play a role in that."

According to Ramalho's team, there are a lot. Legally, women can be restricted by:

• Needing permission from men to travel outside the home
• Needing a male witness to sign contracts or conduct business transactions
• Being barred from deciding on property and finance decisions if men are the only legally recognized heads of the household
• Getting married. Marriage can restrict a woman's rights to property, business transactions, and sometimes also results in her paying higher taxes.

The good news is that while gender disparity still exists on the books, many countries are amending their laws. The most active reformer has been Kenya, who amended its constitution last year to grant women equal inheritance property rights and the ability to confer citizenship onto their children. These small changes allow women greater autonomy over their property, their children's future, and the ability to decide with greater independence.

Keep up with Rita's blog to find out more about the World Bank's research on women.

*Above: A Kenyan woman learns to sew through a World Relief microfinance initiative. Courtesy world-relief.org
Top: American women assemble a B-17 bomber during World War II on an air base in Long Beach, California. Courtesy Library of Congress
Effie-Michelle Metallidis is a guest student blogger for the Women and Public Policy Program and Master in Public Policy first-year student at Harvard Kennedy School.

Men, Women, Competition, Money - WAPPP Seminar Series

The Woman: Pinar Fletcher, Doctoral Candidate in Organizational Behavior, Harvard Business School

The Talk: Gender and Incentives: An Experimental Study on Competition and Cooperation (co-authored by Iris Bohnet and Kathleen McGinn)

The Question: How does gender influence earning ability in men and women?

Do women cheat themselves out of better pay because they don't like competition?

A new study presented at WAPPP yesterday suggested that this may be the case – but only if they don't like the work they're performing. The paper, “An Experimental Study on Competition and Cooperation”, co-authored by HBS professor Kathleen McGinn WAPPP's director Iris Bohnet, sought to examine the factors that drive competition and cooperation between men and women.

The results, presented by Pinar Fletcher of the Harvard Business School last week, are mildly depressing. They suggest that gender stereotypes may hold true when it comes to understanding how men and women think they should be paid.

When tested in a series of games that asked them to compete in same-sex and mixed-sex teams, women thought they were better at verbal tasks, and felt more comfortable working with other women. Men thought they were better at math, and performed better on this subject with other men.

Critically, men performed better in competitive rather than cooperative settings, and also thought they performed better overall. “Men are more likely to think they will earn more in verbal and math competition than women do,” said Fletcher, a finding which implies that men tend to overestimate their earning ability. Conversely, women underestimate their earning ability in competition and cooperative settings. Such findings, if supported by future studies the team plans to conduct, could have a significant impact in how we understand the way men and women compete for salaries and respond to incentives in the workplace.

This may seem like a disheartening find that feeds prevailing stereotypes: women are talkers, men are number-crunchers. Women shy away from competition, but men thrive on it. But an astute audience of female scientists, statisticians and students were on hand to question the results and suggest that further studies are needed to better understand the dynamics at play.

“Did women like cooperation better because they thought they would win more money, or because they felt more comfortable making mistakes in front of other women?” one student asked, implying that motivation plays a significant role in determining cooperative behavior.

“Did you control for the preference of math or reading?” asked another audience member. The woman, who is a scientist and a mother, questioned to what degree the preference of subject matter (math vs. reading) influenced how well men and women performed such tasks in the study. “There can be a tendency to attribute aspects of personality to gender, but in fact a lot of things are not gender specific,” she said.

For now, the jury is out until the final results of the study are tabulated. But with a lingering gender wage gap that prevails across industries and a yawning wage gap by state in the US, studies such as these can help to unpack the dynamics of a woman's worth in the workplace -- and what may be keeping her from her full due.

*Photo courtesy of online.wsj.com
Effie-Michelle Metallidis is a guest student blogger for the Women and Public Policy Program and Master in Public Policy first-year student at Harvard Kennedy School.