13 February, 20200

Skills and knowledge are crucial for finding good jobs and earning high incomes. This explains why, in spite of the increasing costs, most of us consider education as a valuable investment. However, recent research at Harvard’s Growth Lab shows that just having valuable skills oneself is insufficient. What is as, or possibly even more, important as one’s own education is how our skills relate to the skills of the people we work with.

In modern societies, most workers have become highly specialized. However, the problem of being a specialist is that you can achieve preciously little on your own. Picture an architect. This architect will have to work with structural engineers, city planners, lawyers, masons, plumbers, electricians, and many others to erect a building. In fact, the architect’s vision cannot materialize without their help. It’s not a matter of effort; it’s because the architect lacks the skills of these other specialists that are needed to get a building built.

This example shows that specialization not only means that we have important skills but also that we lack many of them. Over the course of history, this problem has become more and more pronounced. As the amount of knowledge in the world grows, it gets divided across more and more people. Relative to what we do not know, what we do know becomes vanishingly little. The solution for this conundrum is to mobilize missing skills in others, by working together with other specialists. However, this means that we become increasingly dependent on the people we work with. As a consequence, the value of what we know how to do comes to depend on what our coworkers know how to do.

Research at Harvard’s Growth Lab tested this idea by analyzing administrative data on the 9 million inhabitants of Sweden to estimate the complementarity and substitutability of coworkers in terms of hundreds of different educational specializations. This allowed determining the “skill ecosystem” – composed of the skills of coworkers – in which a worker would be most effective. The results show that coworkers can have a remarkable effect on wages: the returns to having complementary coworkers are comparable to the returns to having a college degree. Moreover, coworker complementarities help answer a number of old questions: Why can workers with the same education earn drastically different wages? Why do large cities pay such high wages? And why do workers earn higher wages in large establishments than in small establishments, even if they have similar skills? It turns out that we can provide answers to each of these questions that have to do with how complementary or substitutable a worker is to his or her coworkers.

But how can we know which coworkers can substitute or complement one another? To assess this, we construct two different networks that connect the almost 500 different educational tracks in Sweden. The first network (shown below) connects educational tracks if they are often found in the same economic establishments. That is, it connects educations if workers with these educations are often direct colleagues. The idea behind this is that firms will hire teams that combine all the know-how to make them successful. The network depicted below therefore gives an impression of how synergistic educational tracks are to one another. The nodes in the network represent educational tracks. The shape of each node corresponds to the level at which the track is taught (rounder shapes represent lower levels of education). The color represents the broad field of the education. You can explore the network by clicking on a node to see which educations are most synergistic to the one you selected. For instance, if you select the track “Other program in town planning and architecture – College” you will see that the most synergistic degrees are college-level degrees in interior design, landscape engineering, architecture and structural engineering, as well as post-secondary-level degrees in structural engineering.

However, your direct colleagues do not necessarily just complement you: firms often need several employees who have the same or very similar skills, and, as a result, colleagues can often substitute for one another. To assess this, we can construct a second network (shown below). This network captures which educations are substitutes for one another. It does so using data on the occupations, i.e., the kind of jobs, that workers have. If two educations allow workers to do the same kind of jobs, they are, by definition, substitutes for one another. The network is built in a similar way as the educational synergies network. Nodes still represent educational tracks. However, links now represent the degree to which we estimate two educations to be able to substitute for one another. You can explore this network in the same way as before. For instance, if you select the track “Other program in town planning and architecture – College”, you will see that the closest substitutes to this education are other architectural degrees and degrees in landscape engineering or interior design.

All degrees that are close substitutes for “Other program in town planning and architecture – College” turn out to be also highly synergistic. However, the paper shows that, whereas working with colleagues who have synergistic skills is typically associated with higher wages, working with colleagues who can substitute you tends to be associated with lower wages. Therefore, the ideal case is working with synergistic coworkers, who cannot easily substitute you. Such workers are labeled complementary coworkers. Below, the educational synergy and substitutability networks are shown side by side. If you select an education in one network, it will also be selected in the other. Underneath these networks, you find a table that lists the selected track’s most synergistic educations, its closest substitutes, and its closest complements. The most complementary educations to “Other program in town planning and architecture – College” turn out to be in the fields of structural, mineral and environmental engineering.

The analyses in the paper show that the degree to which workers can substitute or complement their coworkers is an important factor in wages. In general, working with a highly complementary team of coworkers tends to be associated with significantly higher wages. Unsurprisingly, workers tend to remain with such teams longer. In contrast, working in a team where most coworkers can substitute one another is associated with lower wages and higher rates of worker turnover.

The wage effects of complementarity are strong: For college-educated workers, having highly complementary coworkers is as valuable as the college degree itself. The figure below shows the close relation between wages and complementarity. The blue curve shows how complementarity to coworkers rises with work experience. This increase in complementarity is due to a combination of two factors: workers moving to establishments where more coworkers complement them and leaving establishments with many coworkers who can substitute them. The combined effect is striking: the observed complementarity between coworkers rises for a long time – as long as 20 years – after workers complete their education. Meanwhile, the red curve shows how wages grow with work experience. The two curves are remarkably similar: The increase in complementarity as workers gain work experience and find better fitting jobs slows down at a strikingly similar rate as the increase in their wages.

Workers do not only earn relatively high wages for working in complementary teams. The returns they get to their own education also depend on it. This is shown in the figure below. The vertical axis shows how much more workers with a certain level of education earn compared to workers who only have primary school degrees. For instance, college educated workers in Sweden earn on average about 60% higher wages than workers with only primary school. The figure divides workers within each level of education into five groups, corresponding to their complementarity quintile. The dark blue markers represent workers with among the 20% least complementary coworkers, the dark red workers with among the top 20% most complementary coworkers.

Let’s again look at Swedish workers with college degrees. Those who work with many complementary coworkers earn a (for Swedish standards) hefty premium: 88% higher wages than workers with only primary school degrees. In contrast, college educated workers who have few coworkers who complement them earn just 18% higher wages than workers with primary school degrees. In fact, workers in the latter group earn about the same as workers with only secondary (high school) degrees.

Complementarity does not just have an impact on wages and careers. It can also explain a number of well-known but seemingly unconnected facts about labor markets. For instance, labor economists have long known that large establishments pay workers with similar skills higher wages than small establishments. This is known as the large plant premium. However, for most workers, what really matters is not the overall size of the establishment in which they work, but rather how many workers in that establishments can complement them. A plausible explanation for this is that what makes large establishments special is that they allow for a deep division of labor. This allows their workers to concentrate on those tasks at which they excel, which, in principle, should make them more productive. However, to concentrate on specific tasks complementary coworkers must be present to handle the remaining tasks. The figure below illustrates this. It shows how the benefits (in terms of earning higher wages) of complementarity rise as establishments grow larger.

Workers do not only earn more in large establishments but also in large cities. Urban economists call this the urban wage premium. This premium is substantial. A city twice the size of another city will offer wages that are about 5% higher. However, as shown in the figure below, once again, not everyone benefits from this effect. The urban wage premium is contingent on finding coworkers with complementary skills. For workers who do, working in a large city like Boston really pays off. For these workers, the urban wage premium is 9% for each doubling of a city’s size. For workers who don’t, the wage premium is just 1%.

Overall, the research shows that in today’s complex economy, where many people are heavily specialized, having complementary coworkers is crucial. However, the benefits of working with complementary coworkers are not the same for all workers. Higher educated workers seem to benefit much more from working in complementary teams than lower educated workers. Moreover, on average, over the past 20 years, workers with college degrees or higher have been more and more able to find better matching coworkers. These trends point in a direction where the benefits of complementarity at work are shared increasingly unequally.

The fact that many people have become specialized is not surprising: the world has accumulated far more knowledge than any single individual could possibly acquire in a lifetime. In a sense, our specialization is the world economy’s way of dealing with the predicament that a society’s body of knowledge can grow seemingly without bounds, but, at the same time, it has to store this knowledge in humans whose absorptive capacity for knowledge is severely limited compared to this task. By distributing knowledge across different people, we can actually store vastly greater amounts of knowledge in a society than in a person. The flip-side of this is that people have to specialize. Moreover, to utilize this distributed knowledge, we need to coordinate different specialists into teams. These teams are still fairly limited in how much knowledge they can store. Therefore, we need to coordinate teams of teams. In a sense, this is what the global economy is doing: it is creating teams of workers who are coordinated within establishments. These establishments, in turn, are coordinated into firms, which themselves are coordinated in value chains that nowadays stretch across the globe. An exciting set of questions that are implied by but not addressed in this research revolves around how such coordination mechanisms are changing in today’s economy.

Which industries hire the most complementary teams? To explore this, the graph below shows a scatter plot that displays industries’ average synergy on the vertical axis and the average substitutability among their workers on the horizontal axis. Note that an industry’s workers are complementary if they are more synergistic than their substitutability would suggest. Exactly how synergistic we would expect two workers of a given level of substitutability to be is reflected in the regression line that is displayed in the plot. The distance to this regression line tells us how much more (or less) synergistic workers in a given industry are than we would have expected given how substitutable they are among each other. In other words, the complementarity of the average team in an industry is reflected in the distance to this regression line. For instance, skill-intensive industries that employ many college-educated workers, such as R&D in natural sciences or health care, hire highly complementary labor forces. On the other hand, there are also industries that demand mostly homogeneous skills. In these industries, most workers can substitute for one another. These industries are mostly found in the lower skill segment of the economy, such as cleaning and retail activities. However, complementarity is not only determined by the level of workers’ skills. For instance, we also see high levels of complementarity in the labor forces of construction industries. Although these workers have typically lower levels of education, they do possess specialized, complementary skill sets.

We can also look at which jobs are associated with high levels of coworker complementarity or substitutability. The scatter plot below does exactly that. It shows the average synergy and substitutability to coworkers for workers in a given occupation. The distance to the regression line once again shows how complementary the coworkers of workers in that occupation are.

Among occupations that operate in the most complementarity-rich work environments, we find professionals like doctors, nurses, dentists and lawyers, but also craft-related occupations, such as plumbers and painters. Workers that are often found in work environments with few complements and many substitutes typically hold more elementary occupations, such as cleaners, cashiers, receptionists and building caretakers.

To measure the synergies and substitutabilities between educational tracks, we rely on administrative records for Sweden. These records contain information for each of the roughly nine million inhabitants of Sweden: what they studied, for which employer they work, and in what occupation their job is. If we are willing to assume that firms will try to hire a workforce that, as a team, can carry out all necessary tasks in the firm’s production processes, we can use these data to measure synergies between coworkers. Given that workers are specialized in specific tasks, these teams would reflect skills that cover coherent knowledge bases. For instance, a car producer will hire workers that cover the gamut of car manufacturing activities, from car design, to organizing work processes, and maintaining the machinery required to make cars. In reverse, this means that workers who are typically found working together are likely to have synergistic skills.

This suggests that to measure synergy, we can count how often two educational tracks co-occur in the workforces of the same establishments. First, we need to decide what we mean when we say that an education is present (“occurs”) in an establishment. To do so, we assess whether the education is overrepresented in the establishment’s labor force. That is, we look at whether the share of workers with this educational track exceeds the share of workers with the same educational track in the economy as a whole. In the figure below, there are three educational tracks that are present in establishment 𝑝: 𝑒, 𝑒′ and 𝑒′′. As a consequence, there are three educational co-occurrences in this establishment: 𝑒−𝑒′, 𝑒−𝑒′′ and 𝑒′−𝑒′′. Because larger establishments will have more educational tracks and therefore also more educational co-occurrences, just counting co-occurrences would give a lot of weight to these large establishments. Instead, we normalize the co-occurrences such that each establishment generates a total of one co-occurrence. In the example depicted below, that generates for each observed pair of educations 1/3 of a co-occurrence. In the next step, we add up all co-occurrences across all establishments in the economy. Now we have for each pair of educations a number that tells us how often the educations co-occur in the same establishments. Finally, we ask whether these co-occurrences could have happened by chance. For this, we calculate how often we would have thought that these educational tracks would have ended up in the same establishments, had they been randomly distributed across establishments. The ratio of observed to expected co-occurrences now tells us how synergistic two educational tracks are.

By defining synergistic educations as educations that often co-occur in establishments, we risk that two educations that are synergistic are not necessarily complementary. After all, whenever there is a lot of work for workers with a certain type of skills employers will hire several workers who have these same skills. In that case, two educations co-occur in the same establishments, not because they are complementary, but because are similar to one another. Workers with similar skills, however, would be substitutes, not complements. To assess whether two educations are substitutes, we look at the tasks workers can carry out once they have completed this education. Taking occupations as bundles of tasks, we compare the jobs workers get with different educations. This strategy is visualized in the figure below. The figure shows two educations for which workers can end up in one of seven occupations. The figure shows that these educations actually have very similar occupational distributions. Most workers with either education end up in the green or pink occupations, but few workers end up in the yellow or purple occupations. The similarity of the occupational distributions can now be used as a measure of how similar – and hence how substitutable – two educations are.

Complementarity is now essentially defined as the excess synergies that cannot be explained by substitutability. That is, we call two educations complementary if workers with these educations work together more often than what we would have expected given the similarity in occupational opportunities that workers with these educations have.






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