Which Workers' Wages Track Productivity? The Role of Position Specificity and On-the-Job Search Justin Bloesch & Bledi Taska September 30, 2020 Abstract Which workers' wages track productivity regardless of the state of the labor market? Evidence suggests that wages for workers in high-wage occupations (i) have been relatively stable across the business cycles over the last two recessions and recoveries, and (ii) covary systematically with firm characteristics such as productivity or firm size. Conversely, wages in low-wage occupations have comoved more with labor market slack over the last two business cycles, and a broad literature suggests that firm characteristics, such as size or productivity, no longer have a significant relationship with wages in low- wage jobs. In this paper, we introduce a concept of position specificity to explain these differential wage patterns across occupations. Using online job posting data from Burning Glass Technologies, we construct a measure of position specificity based on jobs' posted skill requirements, using a clustering algorithm to identify occupations in which jobs are highly differentiated in their tasks from other jobs within the firm. Next, we develop a model with worker-position skill specificity and on-the-job search that can rationalize the above observations. This is achieved without imposing exogenous heterogeneity in worker bargaining power, while remaining consistent with a range of recent findings about wage setting and recruiting behavior that have challenged other popular models. We document the differential sensitivity of wages in low-wage occupations to labor market slack over the last two business cycles, and we offer preliminary evidence that position specificity may better account for these wage patterns than an occupation's relative wage. 1 Introduction The evolution of the wage distribution in the US is one of the most thoroughly researched subjects in economics. In this paper, we hope to highlight two thus-far unrelated patterns in the labor market and propose a new concept of position specificity to jointly explain 1 these observations. In doing so, we hope to contribute to understanding the dynamics of the wage distribution over the past two business cycles, while offering a novel theoretical foundation for heterogeneity in wage determination across workers. The first of these patterns is the greater sensitivity of wages in low-wage occupations to aggregate labor market slack. This pattern is well illustrated by the wage dynamics between high- and low-wage occupation during the current recovery. Using wage data from the Occupational Employment Statistics (OES), Figure 1 plots a 6-digit occupation's log median wage in 2010 against that occupation's nominal wage growth in two periods, 2010- 14 and 2014-18. These periods were chosen to avoid the large and sudden compositional changes of employment during the recession. These periods differ most notably in that throughout the earlier period, the labor market was very slack, whereas in the second period, the labor market is substantially tighter. Figure 1 shows that wage growth in high- wage occupations was nearly constant over these two periods, but wage growth in low-wage occupations was substantially lower in the early period but shows nearly perfect catch-up growth in the later period. As shown in Figure 2, it is difficult to rationalize these wage patterns of low- and high-wage occupations between 2010-2018 with changes in demand alone. Figure 2 plots employment growth by occupation over same period, showing that employment growth over these two periods are essentially identical for both high- and low-wage occupations. In addition to differences within business cycles, there is evidence that low-wage occupations' relative sensitivity to slack holds across business cycles as well. Autor (2014) shows that despite acceleration of employment in non-routine manual jobs from the decades of the 1990s to early 2000s, wage growth suddenly decelerated as the labor market became slack in the new millenium. Over the same period, the growth high-wage jobs slowed, but wage growth remained high in these high-wage jobs. Taken together, it appears that the wages in high-wage occupations are driven upwards regardless of labor market conditions, while wages in low-wage occupations are severely affected by labor market slack. The second pattern we seek to rationalize is that wages for workers in high-wage oc- cupation appear to covary more with firm characteristics, such as firm size or output per worker, and we hypothesize that these patterns may reflect true firm premia. On the other hand, wages in low-wage occupations appear to covary much less with firm characteristics, suggesting less variation in firm premia. Evidence on differential firm premia falls gener- ally into two camps. First are recent studies that the measure the passthrough of firm productivity shocks to wages. Garin & Silv´erio(2018) show using Portuguese data that shocks to firm value added per worker are passed on to workers in low-turnover industries, indicating that jobs with large barriers between internal and external labor markets fa- 2 cilitate passthrough of producitivty shocks to wages. Kline et. al (2019) show that firms with high-value patents raise wages, primarily for top quartile employees, specifically men. Lastly, Friederich et. al (2019) using Swedish data find that while temporary shocks to firm productivity pass on more to the wages of low-education workers, they find that permanent shocks to productivity are passed on much more to high-education workers. This finding is important because unlike Garin & Silv´erio(2018) and Kline et. al (2019), it says that even in the long term, skilled workers at more productive firms receive a larger firm premium than do less skilled workers. In addition to differential pay premia linked to productivity, other studies show a that large and high paying firms offer differentially higher wage premia for \higher" type workers or workers in high-wage occupations in the cross section, such as Bloom et al. (2018) and Mueller et al. (2017). Bloom et al. show that prior to 1990, the firm size premium for workers with a high school diploma or less was large, nearly 20%, but has now all but disappeared. However, for workers with a college degree or more, the wage premium for being at a large firm has held steady at around 10%. Mueller et al. find that the highest paying occupations at large firms pay substantially more than at small firms. Using data from the UK between 2004 and 2013, they detail that within-firm upper tail inequality (e.g. 90/50 ratios) grows substantially with firm size, while lower tail inequality (50/10 ratios ) does not. In the sorting/worker and firm fixed effects literature, Mogstad et al. (2019) find in the US that moving a 20th percentile from the lowest to the highest type of firm raises wages by 22%, while an equivalent move for an 80th percentile worker yields a 78% wage increase. While these cross-sectional studies do not establish a causal link between firm productivity and heterogenous wage premia, they would be consistent with such a finding if workers in high-wage occupations differentially received firm productivity premia. Together, these two patterns can be loosely described with the reduced-form relation- ship: wjt = γyyjt + γθθt; where yjt is output per worker at firm j at time t, θt is a measure of labor market tightness at time t, and γy and γθ are the weights determining the wage. In summary, our brief high low high low survey of the literature suggests that γy > γy and γθ < γθ . We seek to provide an explanation for both of these inequalities with one mechanism: heterogeneity in position specificity. This paper offers three contributions to the literature. First, we derive a model in which the wage patterns described above are determined by the specificity of skills required by a position, rather than the level of skills. The intuition for this model is that highly skilled workers are, on average, more likely to be differentiated in their tasks within the firm. Not 3 only might this imply that workers are less substitutable within the firm, but also that their horizontal differentiation increases the difficulty of finding a replacement in the case of a vacancy. Drawing on Lazear's (2009) \Skill-Weights Approach", firms with positions that require unique combinations of skills search in thinner labor markets. Hence, firms with positions defined by high specificity must have both (i) costly reallocation of workers across positions in the firm and (ii) time-consuming search (or training) processes to fill vacant positions. The second contribution is to provide a measure of position specificity. To do this, we will use data from Burning Glass Technologies, who collect and clean nearly the entire universe of online vacancy postings since 2010. These vacancy postings provide information on required skills, as well as the company name, location, and occasionally the wage of the postings. We will use this data to construct average position specificity measures by occupation. Third, we will document that some of these specificity measures successfully account for the different relationship between slack and wages for low-wage and high-wage occupations in aggregate panel regressions. In future work, we plan to developed identified tests of differential causal effects of slack on wages. A key question that arises from thinking of workers as horizontally differentiated: how should their labor inputs be aggregated into a production function? To answer this, we introduce a novel production function with two inputs: the number of positions and the fraction of positions filled. The crucial feature is that the lost product of having a position go unfilled is greater than the marginal product of adding a new position.