Sunday, January 5, 2014

The real productivity competition is between familial models not between genders

Two very recent and very interesting economic papers on the gender wage gap. It has long been known based on evidence across the OECD that most of the gap is attributable to several common-sense factors: degree level, type of profession, work hour volume, sector, labor force participation continuity, and part-time/full-time. Factor in these obvious variables and the wage gap shrinks dramatically, usually to close to the margin of error of measurement.

This much has been known for the better part of ten or twenty years though it has been largely ignored in popular discussions. What has been missing from much of the research has been one further factor which has always been obvious to me in my management consulting career, both managing consulting business units around the world as well as implementing HR systems for global and national clients. That missing factor is the value of the marginal hour.

Claudia Goldin tackles this pretty directly and rather cleverly in A Grand Gender Convergence, just out today. The issue is that not all hours are created equal in all industries. In Goldin's terms, some industries have linear compensation (more hours worked yield proportionally more income on a direct linear basis) and other industries have non-linear compensation (more hours worked yield a disproportionately greater income). With a linear compensation industry, if you work 10% more hours you will see your income increase by 10%. In a non-linear compensation industry, if you work 10% more hours, you might see your income increase by 20%. Non-linear compensation is also often referred to as winner-take-all markets.

Part of the non-linear effect is based on the old adage, practice makes perfect. More hours of practice make you better and better, even if only incrementally so. Even though there might be a declining rate of improvement for each increment, in a competitive, transparent market where there are high returns to the customer, there can still be outsized returns to small increments of improvement. If you need heart surgery, what is your demand elasticity, if you have the resources, for the best surgeon? Pretty low. Obviously you would be willing to pay significantly more than the average person to obtain the best, even if the cardiac surgeon is only marginally better than the next best.

In industries characterized by high reward, high competition, high growth, high transparency, where compensation is predominantly in objective and empirical terms such as money (as opposed to status or some other murkier form of compensation) there is usually non-linear, winner-take-all compensation. Examples of non-linear, winner-take-all markets include music, sports, chess, mathematics, film, art, hard sciences, law, finance, management consulting, etc. Specialized fields within some industries also often are characterized by non-linear compensation (for example surgeons versus general practitioner MDs in the field of healthcare).

In my profession of management consulting, two professionals of equal educational attainment and experiential background might both work 50 hours a week. However, the nature of the business is such that client's demands and needs change on short notice, projects come off the tracks and other unplanned events occur. The employee who is able to pack in 60 hours one week and only 40 the next in order to fly out to deal with an emergency or spend extra time with a struggling client is worth much more than an employee who works the steady 50 hours and cannot deviate from that schedule.

This variable marginal hour value is huge in most competitive industries and it is a compounding issue. The employee who puts in the same volume of hours but deals with a broader variety of client problems gains much broader, and therefore greater value, experience than the one who simply performs the routine work that can be fit to a less flexible schedule.

In the past, this issue of marginal hour value has been substantially ignored because the data is scarce and it is hard to model. Goldin begins to water that desert.

Goldin indicates that there is little empirical data to support alternate explanations of wage gap differentials (such as discrimination) and that most of the gap is explained by the obvious issues such as full-time versus part-time, etc. She then goes on to show that much of the remaining unexplained residual gaps is attributable to the premium placed on the marginal hour value in terms of hour volume flexibility (ability to increase volume hours when necessary) and hour schedule adaptability (ability to work non-standard hours such as evenings, weekends and holidays) and schedule flexibility (ability to adjust schedule on short notice).

From her paper, footnotes omitted.
But what can explain the residual portion of the gap that now remains? There are many contenders. Some would claim that earnings differences for the same position are due to actual discrimination. To others it is due to women’s lower ability to bargain and their lesser desire to compete. And still others blame it on differential employer promotion standards due to gender differences in the probability of leaving.

A better answer, I will demonstrate, can be found in an application of personnel economics. The explanation will rely on labor market equilibrium with compensating differentials and endogenous job design.

As women have increased their productivity enhancing characteristics and as they “look” more like men, the human capital part of the wage difference has been squeezed out. What remains is largely how firms reward individuals who differ in their desire for various amenities. These amenities are various aspects of workplace flexibility. Workplace flexibility is a complicated, multidimensional concept. The term includes the number of hours to be worked and also the need to work particular hours, to be “on call,” give “face time,” be around for clients, be present for group meetings and so forth. Because these idiosyncratic temporal demands are generally more important for the highly-educated workers, I will emphasize the college educated and occupations at the higher end of the earnings distribution.


The main takeaway is that what is going on within occupations—even when there are 469 of them as in the case of the Census and ACS - is far more important to the gender gap in earnings than is the distribution of men and women by occupations. That is an extremely useful clue to what must be in the last chapter. If earnings gaps within occupations are more important than the distribution of individuals by occupations then looking at specific occupations should provide further evidence on how to equalize earnings by gender. Furthermore, it means that changing the gender mix of occupations will not do the trick.


Whenever an employee does not have a perfect substitute nonlinearities can arise. When there are perfect substitutes for particular workers and zero transactions costs, there is never a premium in earnings with respect to the number or the timing of hours. If there were perfect substitutes earnings would be linear with respect to hours. But if there are transactions costs that render workers imperfect substitutes for each other, there will be penalties from low hours depending on the value to the firm.


Individuals place different values on the amenity, “temporal flexibility,” and firms or sectors face different costs in providing the amenity.

The only drawback to the paper is that it treats non-linear industries as if it is easy and reasonable to shift from high variability schedules to planned schedules (her solution to the remaining wage gap). With changing law, regulations, technology and social standards, it is always conceivable that that might be achievable, in practice it is relatively uncommon. Goldin provides evidence for how and why it occurred in the Pharmacy sector but it is hard to see how the necessary changes could be brought about elsewhere.

The other paper is Degrees Are Forever: Marriage, Educational Investment, and Lifecycle Labor Decisions of Men and Women by Mary Ann Bronsony. Bronsony is not looking specifically at marginal hour value and non-linearity, though she covers some similar ground. She is examining, as the paper title intimates, the degree to which a college degree functions as a form of life-cycle insurance policy for women, particularly in the context of divorce. From her abstract.
Women attend college today at much higher rates than men. They also select disproportionately into low-paying majors, with almost no gender convergence along this margin since the mid-1980s. In this paper, I explain the dynamics of the gender differences in college attendance and choice of major from 1960 to 2010. I document first that changes in returns to skill over time and gender differences in wage premiums across majors cannot explain the observed gender gaps in educational choices. I then provide reduced-form evidence that two factors help explain the observed gender gaps: first, college degrees provide insurance against very low income for women, especially in case of divorce; second, majors differ substantially in the degree of work-family flexibility they offer, such as the size of wage penalties for temporary reductions in labor supply.
Her findings also tip the hat at the ever present danger of unintended consequences despite honest efforts.
My results show that some family-friendly policies increase the share of women in science and business majors substantially, while others further widen both college gender gaps.
Specifically, in an environment where there is generous paid maternity leave, "the model predicts that the policy increases both college gender gaps" and "Under the maternity leave policy women accumulate less experience by their mid to
late-thirties, and thus have lower wages later in life." For part-time work entitlement policies, "the policy has one main effect on women's lifecycle labor supply: women choose to supply less labor to the market over most of their lifetime." Finally she looks at the implications of fully-subsidized child-care. Here, "The policy increases the labor supply of college women in the model mostly in their early childbearing years." However, there is an unintended class consequence. In other words, everyone pays indirectly for the fully funded childcare but the primary beneficiaries are college educated women in science/business occupations.

You always have to be careful of complex models, economic and otherwise. The greater the complexity, the more likely it is that there are false assumptions built into them. These only manifest themselves when many parties use the models under many circumstances, over time. Any new model, regardless of the conclusions, has to be in the wait-and-see category of evidence.

Both these papers help move the knowledge frontier outwards. From my perspective it also moves us closer to an honest discussion of the variability in personal trade-off decisions which are far more sophisticated than we have allowed in the past. It also moves us towards the root issue - what policies support the rapid accumulation of an appropriate portfolio of Knowledge, Experience, Skills, Values and Behaviors that allow a person to optimize their personal productivity across a range of unique personal trade-off decisions.

Despite my caution regarding Bronsony's model and its conclusions, it should be noted that the answers are compatible with the rather ironic comparison of gender policies in the US with those in Sweden. Sweden has the lengthy guaranteed maternity leaves, affordable childcare, and access to part-time schedules that are often advocated for in the US. The consequence though is exactly the opposite of the supposed justification. These policies are supposed to make it easier for women to have both careers and children. However, compared to the US, the gender wage gap is much higher in Sweden and the labor market is much more segregated than in the US. Whereas in the US women are represented in virtually all fields including at the top of all fields, women in Sweden are heavily concentrated in Government employment and in the caring industries (education, childcare, healthcare and eldercare). These outcomes are exactly what Bronsony's model predicts. As she alludes to in the article, there is a conflict of goals. Do we want to make it easier for women to have careers or do we want to make it easier for them to have children. The policies being pursued in Sweden make it easy for them to have children. Counter-intuitively, those in the US make it easier for them to have careers.

Finally, these papers begin to move us towards a truly interesting and challenging discussion. We are accustomed to frame this as equity in terms of gender individualism, i.e. group averages of individual males and individual females. I suspect the real issue is much more complicated. We ought to be framing the discussion in terms of optimum life-time productivity for familial units. This was much the message in Charles Murray's recent book, Coming Apart.

The following graphic does not do the complexities of the issue justice but I think does capture some of the complex trade-offs. None of the bars are measured, merely indicative of relative outcomes. On the bottom axis you have education attainment (did not graduate high school, high school graduate and or some college, and college graduate and or higher) matched with familial structure (single parent, single, married). The vertical axis is life time accumulated earnings per adult person in the household by quintile where Quintile One is the top 20% of people in terms of life time earnings. I have left off the complicating issue of divorce which has a major impact on life earnings. I have also omitted, except in the furthest right column, to separate the distinctly different outcomes of married couples in terms of one earner, two equal earners or one primary and one secondary earner. Interestingly, for reasons discussed by Goldin, married with a primary and secondary income structure tend to do better than married, equal earners.

At each educational attainment level, single parenthood is a huge impediment to productivity as reflected in potential life time earnings. Single people do pretty well but married people do especially well. Interestingly, if you are married (with no children before marriage), completed high school on time and are employed at all, you have less than a 2% chance of being in poverty. The single most effective anti-poverty policy would be one that reduced the number of children born to single parents.

What all this means, and just scratching the thin surface to the complexity, is that choices about education attainment and about familial structure dominate your likely life time productivity. How early or late you make those choices and how effectively you are able to carry out those choices are also contributors.

I think the real productivity issue is not about fairness regarding gender equity or race or any of the other common demographic markers. The productivity issue hinges on the competition between familial models. Intact families with significant education attainment and investment beat all other familial productivity models hands down. But what is the role of the government in such a tangled and complex issue, if any? And what are the policies that would be likely to make a difference? Deep, fraught and complex waters

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