Technological Job Destruction and Labor Reallocation on a Job Ladder Eunsun Gil University of Wisconsin-Madison December 11, 2017 [Link to Current Version]
Abstract Technological job destruction (i.e., disappearance of jobs that have become obsolete due to technological progress) in a subset of an economy triggers labor reallocation, and its impact is transmitted to the entire economy. Using CPS data, this paper demonstrates that unemployed workers found their next jobs in adjacent industries on a wage hierarchy. If unemployed workers earned relatively low (high) wages in the previous industry, they moved to a lower-paying (higher-paying) industry. These observed reallocation patterns are consistent with vertical sorting rather than horizontal sorting; heterogeneous workers are allocated to different quality of job positions and earn different wages. I explain when positive technological shock results in job polarization, by presenting four specifications based on Stokey’s (2016) general equilibrium submarket choice model. Even when automation technology substitutes labor in the middle sector, lower employment is only observed if the demand of output is inelastic. In conclusion, complementarities determine the core sorting, output size, and employment size. When middle-wage manufacturing jobs disappear (i.e., jobs polarize), nearby sectoral labor markets are sequentially affected like a domino due to vertical reallocation. If the reallocation occurred during a recession, a time of scarcity of aggregate labor demand, positive assortative matching predicts the lowest class of workers had difficulty finding jobs regardless of a composition of employment. Keywords— Sorting, technological progress, job polarization, reallocation, jobless recovery
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1
Introduction
The 2008 Great Recession in the United States was accompanied by a historically lackluster labor market. Between 2008 and 2010, the aggregate nonfarm employment declined by 6.8 million (6.2% of the 2008 employment), the unemployment rate spiked from 5% to 10%, and the average duration of unemployment increased from 17 to 40 weeks.1 After 2010, the subsequent recovery was abnormally slow compared to other expansionary periods after recessions. It usually took two to three years to achieve the pre-recession employment peak again in the 20th century postwar era (1939–2000). For the Great Recession, however, it took seven (eight) years for the employment level (unemployment rate) to obtain the pre-recession value. Although the initial shock of the last financial crisis was severe itself, the labor market was exceptional because other markets (e.g., output, capital and financial markets) recovered more quickly from the cyclical downturn. Corporate profits returned to the pre-recession values within a year, consumption took two years, gross domestic production (GDP) took three years, and both equity price and gross investment took five years to rebound.2 This paper examines technological job destruction—a large-scale atypical phenomenon that coincided with the recent recessions—and its impact on the labor allocation. I propose that the manufacturing industry is the essential difference between the 21st century recessions and previous recessions. The decline in the durable goods manufacturing employment during the 2001 and 2008 recessions reflected technological job destruction of team assemblers and first line supervisors, instead of cyclical fluctuations. The recent dynamics in the durable goods sector, which is the intersection between jobless recovery and job polarization, is noteworthy in four respects. First, the within sector correlation between output and employment is negative. This paper views this to reflect progress in labor-saving production technology rather than a cyclical fluctuation or an industrial composition change. Most other industries exhibited positive time correlation between output and labor input, and even the durable goods manufacturing industry showed positive correlation before 2000.3 Second, only a subset of the economy permanently reduced employment, which contrasts with an aggregate temporary decline in employment (i.e., business cycles). If all submarkets reduce and recover the number of employees simultaneously, then unemployed workers have little incentive to alter their submarket choice.4 When the labor market tightness in a submarket is low (unfavorable to unemployed workers), the other submarkets are in the same condition as well. In addition, if the shock is temporary, 1
The proportion of long-term (27 weeks or more) unemployed to total unemployed persons increased from 17%
to 45%, and the share of labor compensation in GDP dropped from 61.5% to 59.5%. 2 For the equity price, the Russell 2000 returned to its December 2007 value in January 2011, the Wilshire 5000 revived in December 2012, and the S&P 500 recovered in Janurary 2013. 3 The information and the nondurable goods manufacturing industries also produce more with fewer workers since 2000, but these changes are gradual and relatively acyclical. Agriculture is the only major (two-digit) industry that had negative time correlation between output and employment even in the 20th century. 4 If a model do not have unemployment and labor reallocation is faster than the speed of the economy reaches to an equilibrium, then aggregate temporary shock makes all the workers move to the same direction on a job ladder.
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then laid-off workers can simply wait until they receive a recall offer. On the contrary, workers who are replaced have an incentive to avoid the long-lasting industry-specific shortages in labor demand; hence, they actively move to other industries. The sectoral shock provides a natural experiment in which to observe labor reallocation patterns. Third, the growth in productivity and decline in employment were episodic, as the changes mostly occurred during two recessions: 2001–2003 and 2008–2010. Because of the coincidence, analyzing employment without considering output dynamics could overlook the distinction among technological job destruction, cyclical job destruction, and composition change. For identification purposes, I focus on an industrial job ladder sorted by average wage rate. By analyzing the relationship between industry and occupation, I suggest that the industries most affected by laid-off manufacturing workers have a relatively exclusive relationship with occupational classifications.5 Finally, the magnitudes of employment drop and output growth in the durable goods industry are not negligible at the aggregate level. Real output increased by 485 billion dollars (or 78% of the 1997 durable goods output), with the number of employees reduced by 3 million (or 30% of the 1997 durable goods employment). The size of the change is effectively the same as if we eliminated the transportation industry from employment axis (2% of the 2017 aggregate nonfarm employment) but added the food services industry as an output dimension (3% of the Q2 2017 real GDP). Consequently, it is important to understand the technological job destruction in the durable goods manufacturing, but it does not neatly fit into canonical concepts of cyclical fluctuation, economic growth, or industrial composition change. The technological job destruction has inspired more researchers to understand its impact on the United States economy. From a microeconomic perspective, technological job destruction allows us to observe labor reallocation that is closely linked with the fundamental allocation mechanism. If progress in technology (or capital substituted labor) enables an industry to save labor input for the long-run targeted production level, then the decline in labor demand of the jobless sector is not expected to recover even during an expansionary phase of the economy. Jobless workers are more likely to change their job market standard and try something new to quickly settle into other submarkets. Hence, the technological job destruction induces substantive labor transitions between industries. The reallocation fills the logical gap between two empirical findings: disappearing middle wage jobs in the job polarization literature and the largest proportional loss in labor income for bottom wage workers in the income inequality studies. When middle jobs disappear, middle class workers go to other industries, leaving the workers from other industries to be unmatched with a firm. In this situation, long-term unemployment does not necessarily consist of workers from the manufacturing industry, and other types of workers may lose the largest fraction of their labor income. From a macroeconomic perspective, the technological job destruction directly contributed to the 5
Declining manufacturing employment is related with production (manual) and office (cognitive) occupations.
Declining information employment is related with office (cognitive), installation (manual), and production (manual) occupations. Details of the relationship between industry and occupation are discussed in Section 3, and details of occupational analysis are documented in Appendix A.
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slow recovery in the aggregate employment level. Three industries (i.e., the durable goods manufacturing, nondurable goods manufacturing and information industries) continuously reduced their employment size during the two recent decades; however, the growth rate in employment of other industries have increased little. It is obvious that the recovery in aggregate employment takes longer, if some of the submarkets simply do not join the recovery. In addition, the dominance of technological job destruction results in higher output with fewer employees within a sector. This induces a permanent decline in the labor input–output ratio, and the labor share of income sharply decreases as well (given the relatively stable wage dynamics).6 Leaving aside other issues for future studies, this paper investigates the reallocation of unemployed workers on an industrial job ladder sorted by average wage. First, I document that the technologically unemployed workers initiated a chain of downward industrial transitions, which I call the trickle-down effect of unemployment. The most distinctive patterns are transitions toward the one-step lower adjacent industry on a wage hierarchy: Unemployed workers from the durable goods industry find their next job in construction, construction workers move to the administrative sector, administrative workers move to retail trade, and retail trade workers move to the food services industry. Between 2007 and 2010, workers laid off from the durable goods sector successfully found jobs in lower-paying industries (e.g., construction, administrative, or retail trade) while lower-paying industries reduced their employment size. The transitions from the durable goods sector to actively hiring industries (e.g., health services or food services) were less frequent. In addition to the downward worker transitions between industries, some of the highest-wage (85th percentile) workers within the jobless industry were also laid off, but they climbed up to a higher-paying industry (the professional industry). In conclusion, workers who used to earn relatively lower wages within the previous industry have been observed to further fall down the industry ladder. The industrial transitions suggest a vertical sorting on an industry ladder, as the best workers within the jobless sector climb up the ladder while other workers climb down the ladder. Second, I show that the timing of trough, peak, and recovery points of the unemployment rate from each industry lag by a descending order of average wage, which I call the domino effect of unemployment. The fluctuation of the unemployment rate started in the durable goods sector, followed by construction, retail trade, and the food services industry, in sequence. It shows that the worker reallocation takes time, the shock spreads out to the nearest sector on the ladder, and sectors that are further away are affected later. The labor reallocation fills the logical gap from studies working on job polarization to those on in6
Declining labor share is a broader concept than technological job destruction that this paper focuses on,
because the faster growth rate of production compared to employment reduces the labor share as well. The nondurable goods manufacturing, information, wholesale trade, and finance sectors are related with the longterm downward trend in the labor share. The durable goods manufacturing industry experienced sudden but permanent drops in the labor share after the 2001 and 2008 recessions. Nominal wages grow positively every year for any occupations, but the real wages are either procyclical or acyclical (and either grow or decline) depending on the inflation measurement. Even the wage is procyclical, although the magnitude is relatively smaller than the change in employment.
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come inequality and upskilling effect: Middle-wage job positions disappear, low-wage firms hire better (middle jobless) workers and, thus, low-wage unemployed workers are damaged. In the United States, it was difficult to find jobs for the low-wage unemployed workers despite an increase in low-wage employment, while middle-wage employment decreased.7 When middle-wage jobs permanently disappear, jobless workers are more likely to win low-wage jobs rather than high-wage jobs, thereby competing with persons who were cyclically unemployed. Because a better type of counterparty is expected, firms with low-type job openings elevate their standard for hiring and target being matched with workers from the middle-wage jobless sector. Hence, it is difficult for the lowest-wage workers to get a job, even when the low-wage employment has increased. When job positions are hollowed out in the middle associated with scarce aggregate labor demand, the vertical sorting predicts that middle-type workers take lower-wage jobs and bottom workers cannot find a job; as a result, the labor income distribution shows a higher skewness. In addition, vertical sorting anticipates that the lower half of firms become pickier until the congestion caused by technological unemployment is resolved. However, we currently do not have a complete equilibrium framework to understand these unmatched bottom type of workers after the Great Recession, because a shortage in total labor demand is contradictory with the definition of the long run equilibrium.8 Therefore, the following theoretical section of this paper focuses on analyzing technological job destruction and labor reallocation in the long-run general equilibrium, except the shortage of aggregate labor demand. Theoretically, the observed labor reallocation is consistent with a vertical sorting rather than horizontal sorting, as the previous wage in the lost job is helpful in predicting the unemployed workers’ future success in the labor market. The premise for the vertical sorting is that workers were originally sorted by general human capital, skill, or learnability, and job positions are ranked by a general labor productivity.9 Vertical sorting requires two-sided heterogeneity and a common preference order of counterparty in matching. Specifically, the supermodular production function is assumed in the theory part to have positive assortative matching (PAM) as a core labor allocation.10 I use Stokey’s (2016) general equilibrium submarket choice model (with PAM) to answer following two questions: Why is labor reallocation asymmetric—in other words, why are labor transitions more likely to be downward rather than upward? Why does technological progress result in lower employment instead of higher employment within a sector? The first question is relatively easy to answer: The 7 8
Long-term unemployment and income inequality studies are summarized in Section 2. In the Walrasian market, excess labor supply and high unemployment are disequilibrium in the short run. In
the search friction market, (cyclical) unemployment can be understood as an equilibrium. However, the vacancy is a jump variable in existing search theory, which means labor demand is counter-factually over-adjusted for any type of shock in the short run. In the real world, neither the unemployment rate nor the vacancy rate is a jump variable. 9 Wage reflects a mixture of the worker type and firm type. This paper does not directly observe labor allocation, but observes labor reallocation that is consistent with vertical sorting. 10 See Becker (1973) for the theoretical background. Technically, the observed reallocation in this paper cannot distinguish between negative assortative matching (NAM) and positive assortative matching (PAM) because the firm type is not explicitly observed.
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asymmetric counterparty effect embedded in PAM makes the downward and upward transitions not necessarily symmetric to any type of shock. I demonstrate a case that labor reallocation is more downward than upward when the middle sector shows progress in productivity. Once productivity increases in a sector given complementary intermediates, marginal workers within each sector farther down the submarket ladder move to a lung one step lower, whereas agents in the upper submarkets are affected ambiguously. As productivity goes up, the general equilibrium effect causes an increase in the output demand of all sectors. The lower-ranked sectors can produce more by expanding employment size so that a relatively high type of workers newly enters the submarket. On the contrary, the upperranked sectors engage in a trade-off when they hire more workers. The number of workers increases (extensive margin), but a relatively low type of workers newly enters the sector (intensive margin). The asymmetric quality of the counterparty generates asymmetric labor reallocation patterns. The second question is not easily answered in existing theory, because the basic constant elasticity of substitution (CES) aggregator cannot make technological progress, resulting in lower employment within the middle-ranked sector (but not in other sectors). I give a rationale when the model generates technological job destruction. When a higher productivity overwhelms the additional equilibrium demand of sectoral output good, the sector ends up producing more with fewer employees. The proper setting is the decreasing elasticity of substitution (DES) preference, so that consumers are less likely to substitute (buy additional) the good they have already consumed at a high level.11 The proxy shock of the DES setup in the CES framework is the total factor productivity progress with a negative preference shock (or consumption share in the aggregator) in the middle sector. The combined shock shows that the decline in a particular class of employment does not require the productivity shock itself to be sector specific. Furthermore, emerging capital that substitutes labor itself cannot guarantee the decline in employment in equilibrium: If more firms enter the sector and produce even higher outputs, then the total sectoral employment increases, such as when the automatic gas pump resulted in a growing retail sales employment in the 1970s. The key variable that reduces employment in a particular sector is the relatively inelastic sectoral consumption with respect to income. Intuitively, the manufacturing industry in the 21st century follows the step of the agricultural industry in the 20th century: Manufacturing industry can produce even more if people in the United States wish to allocate more resources to the sector, but we prefer not to. The remainder of this paper consists of the following content. Section 2 introduces related empirical studies and theories in the labor market. The empirical scope of technological job destruction in the durable goods manufacturing industry is located at the intersection between job polarization (microeconomics) and jobless recovery (macroeconomics). Theoretically, I classify the existing labor theories by the underlying sorting premise to explain why I choose a general equilibrium submarket choice model. Section 3 illustrates the empirical evidence of technological job destruction. Section 4 conveys the empirical evidence of labor reallocation, which I call the trickle-down effect and domino effect of unemployment. Section 5 uses a general equilibrium submarket choice model to show how labor 11
Specific form of DES preferences with are in Bertoletti (2006) and Behrens and Murta (2012).
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is reallocated when technological job destruction occurs in the middle sector. Section 6’s conclusion includes contributions of this study and recommendations for future studies.
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Literature Review
The section 2.1 explains why this paper focuses on an industrial ladder sorted by average wage instead of an occupational ladder. For identification, submarket specific employment and output variables are required so that we extract the technological job destruction from cyclical job destruction or submarket composition change. This paper argue that the intersection between job polarization and jobless recovery is the dominance of technological job destruction. The section 2.2 summaries competing hypotheses about what caused technological job destruction in the manufacturing industry. Three theoretical hypotheses currently exist: automation (or capital-labor substitution), offshoring (or international trade), and superstar firms (or highly concentrated market structure). In the data, automation—more specifically, industrial robots—is the most plausible reason for the technological job destruction in the durable goods manufacturing industry. The section 2.3 categorizes existing labor market theory, depending on their core allocation; from vertical sorting to horizontal sorting. The initial allocation of labor fundamentally determines an unique pattern of labor reallocation. The section 2.4 summarizes other applied topics that are potentially related with technological job destruction and its impact on labor allocation, including labor income inequality, upskilling effect, ins and outs of unemployment, unemployment scar effect and an outward shift in the Beveridge curve.
2.1
Jobless Recovery and Job Polarization
Macroeconomic papers pay attention to a recent atypical feature in the labor market called jobless recovery, weak recovery, or slow recovery (Groshen & Potter, 2003; Elsby, Hobijn & Şahin, 2010; Stock & Watson, 2012).12 Initial studies claimed that we now experience a jobless recovery that refers to unrestored employment, despite revived output production. It sounded plausible in the early period of the 21st-century recoveries, however, the drop in total employment did not last forever. For example, the United States aggregate employment achieved the pre-2008-recession level in May of 2014 and has since grown higher. After that, more researchers preferred to use a relaxed concept of jobless recovery called slow recovery or weak recovery. The modified argument is that employment increased at a slow rate during the recent expansionary periods by comparing output growth or old-days recoveries.13 Al12
On top of the jobless recovery, numerous papers also studied the decline in the labor share of income, persistent
long-term unemployment rate, and outward shift in the Beveridge curve. Many researchers have a conjecture that some (or all) of these are connected, but the linkage is not yet well established. 13 Groshen and Potter (2003), Schreft and Singh (2003), and Jaimovich and Siu (2014) argue that the lagging start of recovery is a distinctive feature. They find that employment starts to recover within six months after the
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though the wider concept—slow recovery—is more accurate description of the fluctuations in aggregate employment, it became difficult to obtain objective criteria to determine how much slow growth in employment is noteworthy. Therefore, it is important to find a proper measuring scope to convey jobless recovery as a qualitatively different pattern, rather than a matter of degree. This paper finds a long-lasting decline in employment in the manufacturing, information, and construction industries, by observing disaggregated employment. The employment in the three industries is still far below the pre-recession values, even 10 years after the beginning of the Great Recession. The decline in employment in these industries is not short-term fluctuations; instead, it is a long-lasting change. The United States economy do experience joblessness, but it is limited in scope. On the other hand, microeconomic studies on the labor market investigate a new phenomenon called job polarization (Acemoglu, 1999; Levy & Murnane, 2004; Autor, Katz, & Kearney, 2006; Goos & Manning, 2007; Acemoglu & Autor, 2011; Autor & Dorn, 2013). They argue that the proportion of routine-skill based and middle-wage occupations to total employment has declined since the 1980s.14 Many empirical studies investigated the occupation, wages, detailed demographics, and the cause of slowly growing middle-wage jobs from a typical microeconomic perspective. However, the canonical approach does not distinguish two qualitatively different patterns of declining jobs. One is a reduction in employment from a fading industry as productivity of the sector declines, which reflects a industrial composition change. The other is a downsizing in employment from a growing industry regarding output, as human labor is replaced by non-labor inputs to produce even more. In this paper, I analyze both employment and output to distinguish between declining jobs in a fading industry and replaced jobs due to a change in production technology. Among the sectors with reduced employment over a decade, construction can be considered a fading industry. The real output for construction substantially decreased and has not fully revived until 2017. Therefore, it is less surprising that construction did not recover the employment to the pre-recession level. However, the manufacturing and information are ones of the most growing industries in terms of both sectoral real output and real output per worker. The drop in employment in these two industries should be considered as dominance of technological job destruction, rather than cyclical job destruction or composition change. I refine the intersection between jobless recovery and job polarization: it is the technological job destruction in the manufacturing and information industries. I say jobs disappeared in this paper if there is an actual decline in employment level without a significant rebound afterward, rather than a slow growth rate or a drop in a ratio. The dominance of technological job destruction in a sector exhibits both an explicit decrease in employment level and increase in output level. Naturally, the trough of output in typical business cycles, whereas it took two years to begin growth after the 2001 and 2008 recessions. Some scholars may refer to slow recovery—or the Great Moderation—as lower output growth rate itself, as compared to the old-days growth trend, but the growth rate in output is not the focus of this paper. 14 A handbook chapter written by Acemoglu and Autor (2011) summarizes the literature and major findings in job polarization (first noted in Acemoglu, 1999) and the routinization hypothesis (first raised in Autor, Levy & Murnane, 2003).
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technological job destruction is a subset of jobless recovery. The jobless recovery literature usually adopts a wider concept of disappearing jobs, by focusing on a decline in the employment share to gross production (Groshen & Potter, 2003; Aaronson, Rissman, & Sullivan, 2004) or the labor income share to total income (Rodriguez & Jayadev, 2010; Elsby, Hobijn & Şahin, 2013; Karabarbounis & Neiman, 2014). When employment grows positively but the speed is slower than the output growth, it is not technological job destruction, but it is a jobless recovery. Among others, Groshen and Potter (2003) particularly mentioned the possibility that structural changes in industrial composition caused the jobless recovery. Their conjecture is harmonized with my argument that industrial analysis is important, but the technological job destruction is not a simple industrial composition change. In the same manner, technological job destruction is also a subset of job polarization. The definition of job polarization, as known as disappearing middle-wage jobs, accurately refers to a decline in the employment share: employment in middle-wage occupations grows at a slow speed (or declines), as compared to low-wage or high-wage occupations. It does not distinguish between declining job in a less productive industry and technological job destruction in a more productive industry, as long as the wage is in the middle range. However, technological job destruction, this paper focuses on, requires both an explicit drop in employment and increase in output, which happens to be concentrated in middle-wage jobs. Routine manual middle-wage occupations includes production and construction occupations, but the construction sector is not related with technological job destruction. Office occupations in almost every industries declined, however, other industries including food services and health services increased their total industrial employment. The most declining occupations are specialized in declining industries such as photographic services, vending machine operators, taxi service, tobacco manufacturing, and apparel manufacturing, which are relatively less related with technological job destruction. Time framework matters. Jobless recovery focuses on a business cycle, and in that case, only the durable goods manufacturing industry matters because its change coincided with recessions. Job polarization analyzes long-term trend, hence all of the durable, nondurable manufacturing and information industries are equally important. Autor (2010) mentioned that job polarization accelerated during a recession. Moreover, Jaimovich and Siu (2014), Tüzeman and Willis (2014), and Foote and Ryan (2015) argue that job polarization and jobless recovery are actually the same phenomenon. Generally agreeing with the view, however, I explain that jobless recovery and job polarization do not have the same boundary. Jobless recovery includes the wholesale trade and the financial sectors, because of their slow growth in employment with fast growth in output. These sectors are not particularly related with job polarization because of steady growth rate in employment, and their wages are relatively high. Job polarization includes construction, installation, and office occupations in the other sectors except the manufacturing and information industries. These occupations in other industries are not associated with decline in employment share to output.15 Besides, a rapid decline in the highest wage occupation 15
The decline in employment of the information industry was derived by a large drop in office occupation and
installation occupation. Office occupation takes about 10% of employment in every industries, but the overall employment in other industries except the manufacturing and the information has not decreased.
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(chief executive and managers) is also noticeable in the data.16
2.2
The Cause of Technological Job Destruction
How can the manufacturing and information industries produce more with fewer employees? There are three existing hypothesis about the source of technological job destruction. First, automation and new technology could replace the labor input (Brynjolfsson and McAfee, 2012; Akst, 2013; Acemoglu and Restrepo, 2017). Second, offshoring and outsourcing through international trade could replace jobs at home country, even if the effect is relatively small (Brainard and Riker, 1997; Hanson, Mataloni & Slaughter, 2003; Muendler & Becker, 2010; Harrison & McMillan, 2011). There also exist applied studies that conclude the opposite argument: The foreign production activity stimulated overall job growth at home country (Slaughter, 2004; Borga, 2005; Desai, Foley & Hines, 2005; Mankiw and Swagel, 2006). Third, there is a rising alternative that claims enhanced market power and more concentrated market structure make production technology be less intensive in labor within industries (Barkai, 2016; De Loecker & Eeckhout, 2017; Autor, Dorn, Katz, Patterson & Van Reenen, 2017). According to the empirical evidences, it is likely that the technological job destruction in the durable goods manufacturing is caused by automation, rather than offshoring or market power. Acemoglu and Restrepo (2017) document that cities on the Great Lakes adopted industrial robots (or automatic machines) and decreased employment the most intensively in the United States.17 In their geographical analysis, industrial robots purchases are significantly associated with decline in employment, but imports from Mexico or China are insignificantly related. They also listed minor (three-digit) industries that adopted industrial robots the most intensively. I confirm that these industries contributed the technological job destruction the most as well. Four out of top five minor industries are durable goods manufacturing, and the other one is non-durable goods manufacturing. For example, the automotive vehicle industry exposed to robots and enhanced productivity the most distinctively right after reducing the numbers of workers, which coincided with recessions. There are two empirical aspects that are not favorable to offshoring hypothesis. First, technological job destruction (or jobless recovery) is measured as a sharp decline in the share of domestic employment to domestic product. If multinational corporations establish a foreign site, neither product or employment are accounted as national accounts of home country. Otherwise, domestic employment includes the international workers who are in the United States payroll system at the beginning. What I try to understand is that how domestic establishments can produce 5%-10% more in total, with 10%-15% fewer domestic workers within two years. Second, the jobless recovery is a global phenomenon. A Heckscher-Ohlin theory predicts that capital-abundant countries hire fewer workers due to compara16
The decline in the top paying occupation mitigates the job polarization. It is rather related with more
concentrated market competition in the United States, rather than job polarization. 17 Detroit, the city the hardest hit by the 2008 Great Recession, extremely adopted machines and industrial robots. The city unemployment rate spiked to 28%, and it took six years to attain the pre-recession unemployment rate.
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tive advantages, whereas labor-abundant countries hire more workers and produce more labor-intensive goods. It means that offshoring hypothesis predicts an increase in the labor share for the labor-abundant countries. However, in the data, unskilled-labor-abundant countries including Mexico, China, and India also experienced jobless recovery and their labor shares declined (Karabarbounis & Neiman, 2014). Barkai (2016) and De Loecker and Eeckhout (2017) argue that both the labor share and the capital share declined in the aggregate United States economy. A large increase in markups and market power within the industry could explain the declining input shares. However, the capital share in the durable goods manufacturing industry jumped up after 2001 and 2008 recessions by 4% each.18 In addition, the change in markups gradually occurred over the recent 30 years, and the markup even decreased (moved to the opposite direction) during the recessions. They focus on the long-run declining trend in the labor share, while this paper focuses on technological job destruction that contributes the sharp drops in the labor share right after the 2001 and 2008 recessions. One of the most important industry to understand a long-run decline in the labor share is the real estate, rental and leasing industry (subsector in the financial industry) that grows in a high speed with an extremely low labor share.
2.3
Vertical and Horizontal Sorting
How labor market reallocate labor when middle-wage employment declines for good? Suppose that a massive amount of discharges reduced the number of middle-wage employees, and the jobs were not expected to be recovered, even during an expansionary phase of the economy. Even though jobs in other industries will grow eventually, it took 7–8 years for aggregate employment level to achieve a new high for the Great Recession. The now unemployed and jobless workers should change their job market standard and try something new to quickly settle into other jobs. Which industries become their next jobs? Is there a directional labor turnover from a certain industry to another? Is previous wage in the lost job helpful to predict the worker’s labor market transition? The answers will be qualitatively different, depending on whether workers are initially allocated vertically or horizontally. Numerous models generate equilibrium wage dispersion to explain why some workers are paid higher than others. Even if we assume that labor productivity is the sole determinant of wages for simplicity, we have four categories of theories, depending on their fundamental labor allocation. Horizontal sorting is based on a belief that workers and jobs are just different and have idiosyncrasies. The most polar case is that workers and jobs are homogeneous a priori. High wage workers are merely the lucky people who have a good idiosyncratic match quality, for now. Mortensen and Pissarides’ (1994) random search model is one of the examples that generates wage dispersion from idiosyncratic productivity shocks. Including Montgomery’s (1991) directed search model, a model with one-sided heterogeneity also results in a strictly horizontal sorting if the other party is identical or randomly matched. In the polar horizontal sorting models, past wages (or productivity) provides no information about the worker’s 18
Admittedly, the measurement of capital factor share is debatable, because measuring total capital and its
price are not simple. Here, I mention the series from U.S. Bureau of Labor Statistics, Manufacturing Durable Goods Sector: Capital Factor Shares [MPU9920671].
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Figure 1: Models from Horizontal Sorting to Vertical Sorting
Determinants of Wage Dispersion
Strictly Horizontal
Labor Productivity
& On-the-job Search
Weakly Horizontal
·Montgomery (1991)
Weakly Vertical
·Roy (1951) ·Shimer & Smith (2000)
·Mortensen & Pissarides (1994) ·Postel-Vinay & Robin (2002a) ·Burdett & Coles (2003) ·Shi (2009)
Strictly Vertical
·Becker (1973) ·Stokey (2016)
·Lise & Robin (2017)
·Farber & Gibbons (1996) ·Groes, Kircher & Manovskii (2015)
& Learning
Wage Differentials ≠ Productivity Differentials Homogenous Agents
Heterogenous Agents
future payroll (or performance) in the same or a different job. A wider concept of horizontal sorting allows workers to be considered differently in terms of productivity and human capital, but the skill is firm–, career–, industry–, or occupation–specific. As long as an employee works in a similar position, his/her wage increases as a specific tenure goes up. On the job search model with two-sided heterogeneity, including Lise and Robin (2017), exhibits vertical sorting in allocation but horizontal sorting in reallocation. Workers’ outside option become nullified when they experience unemployment, so unemployed workers are willing to work at any type of job positions. In either case of horizontal sorting, industry switchers (after unemployment) due to technological job destruction in a particular submarket move to the tightest submarkets. Once they start to work in a new industry, they are more likely to be paid less than incumbent employees, because of a relatively worse fitness for the job or a lower tenure. Similarly, unemployed workers from the jobless sector are less (or at most equally) likely to win jobs in the new sector over unemployed workers who had worked in the sector. In contrast, vertical sorting views some workers as more productive (or more able to learn) than others. Some jobs are also regarded more productive (or higher paying) than other positions. The extreme version of vertical sorting predicts that the worst worker in a high-paying submarket is more productive than the best worker in a low-paying submarket. Positive Assortative Matching (PAM) in Becker’s (1973) sorting model, with a supermodular production function, is one of the examples. More able workers take better but scarce jobs receiving high wages, whereas less able workers take the remaining low-wage jobs. A relaxed version regards the average worker in a high-paying occupation is
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better than the average worker in a low-paying occupation. Roy’s (1951) occupational choice model, given a positive correlation across skills, demonstrates a weak concept of vertical sorting. All workers optimally choose their submarket, but high-wage workers are more productive than low-wage workers in any submarket on average. In either Becker model and Roy model with vertical sorting, career switchers due to a technological job destruction are moving downward on a submarket ladder. New comers from upper lung find a new job faster than unemployed who had experienced the submarket, and they receive higher wage than old-hands workers on average. Comparing to the wage in the previous jobs, industry switchers are expected to earn less in a new job. To analyze labor reallocation on a submarket ladder sorted by wage, twp streams of models that allows positive assortative matching give qualitatively identical result: Becker’s (1973) sorting model and Roy’s (1951) occupation choice model. The distinction between matching or sorting model and occupation choice model is not fundamental. Stokey (2016) presents a general equilibrium occupational choice model to anlayze when one of a particular class of jobs (or tasks) disappears. Her model is an extension of Roy’s (1951) model and it shows labor reallocation caused by a submarket specific negative shock. However, as the paper allows uni-dimensional types, so the sorting is exactly same with the Becker model, extreme vertical sorting. For a general equilibrium analysis due to a sectoral declining employment, I use Stokey (2016) submarket choice model in section 5.19 It is true that the Becker model, which is one of two origins of a matching and search model, generates extreme vertical sorting, whereas the Roy model generates weak vertical sorting. However, the fundamental difference between two models is not the sorting result. Depending on the specification, both matching and occupational choice models can generate strictly vertical, weakly vertical, or even horizontal sorting as the labor market allocation. More specifically, if the Roy model has a perfect correlation across skills, it results in strict vertical sorting. On the other hand, if the Becker model has positively correlated skills as a vector, instead of a scalar, it induces weak vertical sorting. Furthermore, both models generate horizontal sorting if the correlation between skills is close to zero, or the production function is modular. The crucial difference between the Becker’s matching model and the Roy’s occupational choice model is the role of wages in disequilibrium, which potentially affects dynamic adjustments in future research. Roy’s occupational choice model is based on the Walrasian equilibrium. Therefore, wage primarily guides the extensive margin of employment (allocation of workers to job positions). On the contrary, match surplus based on outside options determines the extensive margin of employment in the Becker’s marriage model. In this case, wages are sets secondarily, through bargaining or non-corporative alternating games, which does not alter the extensive margin. 19
Alternatively, I analyze an extended Shimer and Smith’s (2000) matching and search model in appendix I.
It explains several details in the labor reallocation relatively well, but the model analyzes partial equilibrium. In either models, the disappearing middle-wage labor demand mostly affects the lower half of the submarket ladder.
13
2.4
Income Inequality and Persistent Unemployment
The trickle-down unemployment hypothesis fills the gap between middle-wage job disappearance and the decline in income for the low-wage unemployed workers. Various data sources consistently illustrated that the bottom unemployed workers have lost the largest percentage of income during the recent recessions in the United States. Guvenen, Ozkan, and Song (2014) found that the lowest percentile of income (in the 5 years before a recession) lost the largest proportion of income during the Great Recession by analyzing a confidential dataset from the U.S. Social Security Administration. Using data form the Current Population Survey (CPS), Bitler and Hoynes (2015) argue that the Great Recession significantly increased non-elderly poverty at the bottom (lowest income-to-poverty) level. The demographic groups were not very relevant. Pfeffer, Danziger, and Schoeni (2013) document that large percentage income losses are concentrated among lowe-income households by analyzing Panel Study of Income Dynamics (PSID) and the Survey of Consumer Finances (SCF). Gil (2015) finds that disproportional losses in annual earnings among unemployed workers during the 2001 and 2008 recessions by using data from PSID as well. The loss in income for the lowest quintile unemployed workers is more related to the losses in total working hours (mostly due to longer unemployment duration), than the wage rate difference between the past and current job position. Another distinctive and unusual pattern of the Great Recession is that the long-term unemployment duration rose sharply. The share of 27 weeks or more in duration among the total unemployed persons spiked from 18% to 45% after the 2008 recession. There are two existing hypotheses that explain the persistent unemployment of which some scholars call a scarring effect. The statistical discrimination hypothesis (or stigma effect) explains that firms are reluctant to hire workers who experienced a long unemployment duration under imperfect information, as they believe that the long-term unemployed persons are generally inferior. Alternatively, the human capital deterioration hypothesis argues that a worker’s human capital becomes rusty the longer the unemployment lasts. However, neither alternative can explain the cyclical pattern of long-term unemployment—namely, how bottom unemployed workers start to exit the unemployment pool after experiencing an exceptionally long unemployment period. On contrary, the reallocation hypothesis in this paper predicts a cyclical pattern as a natural consequence. Bottom unemployment is stagnant until the unemployment congestion from the jobless sectors with higher wages is resolved. This trickle-down hypothesis is consistent with Hershbein and Kahn (2017). It analyzes skill requirements in job vacancy postings to conclude that upskilling effect reflects a restructuring of production toward labor-saving technologies during the Great Recession. The technological job destruction and labor reallocation is consistently related to other aspects of labor market as well, namely, the ins and outs of unemployment, inefficiency in matching, and an outward shift in the Beveridge curve. Ahn and Hamilton (2014) suggest that compositional changes in the inflows of the newly unemployed, and increases in permanent job losses, have caused high and persistent unemployment in the recent recessions. Barnichon and Figura (2010) document that the inefficiency in matching per vacancy became noticeably severe after the Great Recession, which means it takes longer time to hire given the unemployment and vacancy levels. Barnichon, Elsby, Hobijn, and
14
Şahin (2012) argue that the construction, trade, and Food services industries are significant for the inefficient matching and outward shift in the Beveridge curve. On the contrary, the declining labor participation rate is not directly caused by unemployed or discouraged workers from the industries with technological job destruction. The labor force participation rate was 67% before the 2001 recession; it is now 63%. The trend in the labor force participation rate was non-positive during the recent two decades. Also, most of the drop occurred right after the 2001 and 2008 recessions. However, the decreasing labor participation rate is not caused by discouraged or marginally attached workers. Discouraged and marginally attached workers who were not-in-the-laborforce co-moved with the regular unemployment rate. Thus, the rate of discouraged workers became close to the pre-recession level since 2014. The decline in the labor participation rate is caused because the number of young people aged 16 to 24 sharply declined by 16.7% in the recent two decades, which accounts for 2.8% of the total labor force participation rate.20 There is a possibility that a technological job destruction in the manufacturing industry is fundamentally related with a lower youth participation rate. When a particular skill becomes obsolete, workers who have the skills now become unskilled workers, which leads to an abundant supply of unskilled labor. It alters the education choices for youth so that they choose even higher educations to acquire high-paid skill sets. Rising college premium for younger men in the United States labor market is well documented (Card & Lemieux, 2001; Goldin & Katz, 2009). The relationship between the youth labor market participation decisions and recessions will not be discussed in this paper.21
3
Technological Job Destruction
The empirical part of this paper starts from illustrating a technological job destruction. Among 18 two-digits major industries in the United States, durable/nondurable manufacturing and information industries began to produce more with fewer workers.22 Employment permanently declined by 25–35%, whereas real output per employee increased by 45%–85%. The change in durable goods manufacturing was concentrated during the 2001 and 2008 recessions, whereas nondurable goods manufacturing and information industries have gradually changed. For all of the three major sectors, we had not observed a negative correlation between output and labor input in 20th century. The result is robust 20
I calculate the numbers based on Toossi (2015)’s labor force participation rate by demographics. The data
source is the Current Population Survey (CPS) from the Bureau of Labor Statistics (BLS). https://www.bls. gov/emp/ep_table_303.htm 21 See Kahn (2010), Bell and Blanchflower (2011), and Oreopoulous, Wachter, and Heisz (2012) for more detail about the youth labor market. 22 Construction industry contracted in both output and input from 2006 to 2010. Other major nonfarm industries has grown both in output and employment. Agricultural industry produce more with fewer workers in postwar era.
15
in occupational analysis, because the only two-digit occupation that disappeared during recessions is production occupation (routine manual), which is almost exclusively used in the manufacturing industry.23 The decline in information employment is derived by the decline in office (routine cognitive) and installation/maintenance (routine manual) occupations. The technological job destruction or jobs that replaced, which we are going to see in this section, is distinguished from traditional senses of declining jobs or business-cycle fluctuations. Declining jobs in composition change mean jobs that both employment and output gradually decrease as the productivity declines from a long-term perspective. Cyclical employment refers that employment, output, and productivity move to the same direction in a short-run, but a drop or rise vanish away over time. Both typical changes in employment predict a positive correlation between output, employment and productivity. However, we currently observe a new pattern of employment that causes a decline in employment, but an increase in real output and real output per worker. Such employees are replaced due to progress in labor-saving technology so that firms can produce more with less labor input. In the United States, a technological job destruction has occurred since 2000 in durable/nondurable goods manufacturing and information industries. Among then, the durable goods manufacturing industry is the most influential, because its size is relatively big and the change coincides recessions episodically. The main arguments in this section is that the jobs that disappeared were associated with progress in production technology. To distinguish the technological change from canonical business cycles or declining jobs in a fading industry, I adopt a mixture of macro– and micro–economic frameworks. Macro empirical papers have an advantage by analyzing employment under the context of a general equilibrium, but they commonly do not focus on the employment details. Microeconomic papers have a strength in scrutinizing the composition of jobs, however, their empirical boundary usually does not reach to the output market. Therefore, the traditional macro– or micro–economic framework have limitations to extract the technological job destruction in a specific class of employment from other cyclical job destruction. Only by overlapping two schemes, can a sudden disappearance of jobs be highlighted as a qualitatively different job destruction rather than a matter of degree. Therefore, this paper analyzes (un)employment and output together at an industry level, instead of an occupational or aggregate level.
3.1
Relationship between Industry and Occupation
Job hierarchy can be sorted by various standards depending on the purpose of a study. The most straightforward sorting criteria for workers and jobs is the hourly wage rate, weekly earnings, or annual earnings. Human capital literature sorts employment by workers’ characteristics, such as education, 23
Admittedly, office occupation (middle-wage routine cognitive) is not easily map to a single industry. However,
the decline in office occupation is distinguished from a disappearance of production occupation. The overall decline in office occupation is gradually made in three decades, and there was a large compositional change within occupation. On contrary, 86% of detailed (four-digits) production occupations decreased simultaneously, and most of the drops are concentrated during recessions.
16
age, or tenure. Job polarization literature sorts employment by job characteristics such as occupation and skill requirements. Macro papers compare industries over the business cycles and heterogeneous fluctuations in the labor market by industries are usually observed. Among them, Groes, Kircher, and Manovskii (2014) document that a vertical sorting exists along an occupational hierarchy in Danish data. Occupation captures labor supply side information successfully. It is also directly related to a specific skill that becomes obsolete after a labor-saving technological progress. However, occupation does not provide data such as output, job openings, and hiring, which is related with labor demand and output market. Because the smallest unit of measurement of output is establishment that has various type of occupations, decomposing the contribution to production by each occupation is not easily done. On the other hand, industry captures labor demand side, and aggregate market condition more effectively. This paper uses industrial hierarchy that is also vertically sorted. The downside of the industrial hierarchy is a larger within-group wage dispersion than occupation. However, industrial data include production, corporate profits, unemployment, job openings, quits, and layoffs, which are useful variables to analyze the disappearing job and subsequent worker reallocation. Also, the industrial data covers more than 95% of payroll employment in the United States, and monthly data is available in most cases whereas occupational data is annual.
Table 1: The most common occupation in each industry Industry
&
Share in industry
Share in occupation
Computer
18.5%
12.5%
Finance
Office
38.8%
13.6%
Professionals
Office
21.8%
27.0%
Healthcare
51.5%
78.7%
Construction
62.4%
58.9%
Production
51.6%
68.2%
Sales
47.4%
65.1%
Food serving
80.4%
81.3%
Information
Health Construction Manufacturing Trade Food
Occupation
Conditional proportion of industry and occupation is provided. The first row means that the proportion of computer occupation in information employment is 18.5%, while the share of information industry to the total computer occupation is 12.5%. The computer occupation is not exclusively used in information industry, and vice versa. This table is a summary of national employment matrix form BLS in 2014, which based on OES and CPS.
As the Table 1 shows, the distinction between occupational and industrial analysis in recent recessions is mild. The jobs that disappeared in the United States are characterized as information and manufacturing industries, and office and production occupations. Admittedly, it is hard to map information industry (office occupation) to a single occupation (industry). Office occupation share in
17
each industry is usually higher than 10%. However, the job suddenly but permanently dropped during a recession—which this paper focuses on—is production occupation in manufacturing industry. The 51.6% of manufacturing employment is production occupation, and 68.2% of production occupation is in manufacturing sector. The industry with the second highest production occupation is the administrative sector (one of three-digit industry in professionals group), and the occupational share is 8.7%. Trade and Food industry have less than four percent of production occupation. Similarly, the most growing job is food preparation and serving occupations in food services industry, which has a roughly exclusive relationship between occupation and industry. Therefore, either industrial or occupational dimension captures disappearing jobs without losing much information. The data sources for employment is Current Employment Statistics (CES) from the Bureau of Labor Statistics (BLS). The source of unemployment and industrial turnover is Current Population Survey (CPS) from BLS. The source of real GDP is National Income and Product Accounts (NIPA) from Bureau of Economic Analysis (BEA). Also, the source of quits, layoffs, hiring, and job openings by industry is Job Openings and Labor Turnover Survey (JOLTS) from BLS. Occupational employment and wages are from Occupational Employment Statistics (OES). I determine industrial job hierarchy by considering average wage, working hours, median weekly earnings, unemployment risk, health and pension benefits, and illness risk associated with jobs. For details of job quality beyond payroll, Injuries, Illnesses, and Fatalities (IIF), and Quarterly Census of Employment and Wages (QCEW) from BLS are also used. Information employment decreased mainly due to the decline in office, installation and production occupations within the industry. In details, communications equipment operators (office), Data entry workers (office), industrial machinery installation workers (installation), miscellaneous production workers (production) and printing workers (production) decreased the most. Similarly, the manufacturing employment decreased because of the drops in office and production occupations within the industry. Communications equipment operators (office occupation), tailors and sewers (production occupation), electrical assemblers (production occupation), secretaries (office occupation) and molders and forming machine setters (production occupation) declined the most in this sector. Among them, the occupation declined during the recessions the most intensively in the manufacturing industry are team assemblers and supervisors of the first line assembly.
3.2
Employment and Output Dynamics by Industries
In aggregate level, we trivially expect that both employment and output increases in a long-run (economic growth), and they fluctuate to the same direction around their long term trends (business cycles). Even after the 2008 great recession, the United States economy recovered the pre-recession levels of employment and output, and now achieves the highest levels in the history. However, not all of the major industries exhibit the same pattern that aggregate economy shows.24 24
In this paper, major industry means two-digit (in North American Industry Classification System (NAICS) or
Standard Industrial Classification (SIC) code) industries, and minor industry refers three-digit industry. Group
18
Figure 2: Real GDP and Employment by 13 Group Industries (1997–2016) 25,000
Government Professional and business services Educational services, health care, and social assistance
20,000
Retail trade Arts, entertainment, recreation, accommodation, and food services
Employment by Industry (Thousand)
Manufacturing: Durable goods Manufacturing: Nondurable goods
15,000
Construction Finance: Finance and insurance Wholesale trade 10,000 Transportation and warehousing Information Finance: Real estate and rental and leasing
5,000
0 0
500,000
1,000,000
1,500,000
2,000,000
2,500,000
Real GDP by Industry (Millions of chained 2009 dollars)
Figure 3: (Enlarged) Real GDP and Employment by 13 Group Industries (1997–2016) 25,000 15,000
1997
Employment by Industry (Thousand)
Employment by Industry (Thousand)
20,000
2001
10,000
2008
15,000
10,000
5,000
5,000
0 0
500,000
1,000,000
1,500,000
2,000,000
2,500,000
Real GDP by Industry (Millions of chained 2009 dollars) 0 0
500,000
1,000,000
Government
1,500,000
Professional and business services
Real GDP by Industry (Millions of chained 2009 dollars)
Educational services, health care, and social assistance
Manufacturing: Durable goods
Retail trade
Manufacturing: Nondurable goods
Arts, entertainment, recreation, accommodation, and food services Finance: Finance and insurance
Information
Wholesale trade
Construction
Transportation and warehousing Finance: Real estate and rental and leasing
∗ Light blue dot of each line represents 1997. The unit of horizontal axis guideline is 0.5 trillion real dollars, and one of the vertical axis is 5 million employees. The aggregate pattern is at the bottom right in a smaller scale. Data source of Employment is the number of employees in payroll system in Current Employment Statistics (CES) survey from Bureau of Labor Statistics (BLS). Employment at May for each year is used to match monthly data to yearly GDP data. Data source of Real GDP is Real Value Added by Industry in National Economic Accounts from Bureau of Economic Analysis (BEA).
19
25,000
25,000
20,000
20,000
Employment by Industry (thousand)
Employment by Industry (thousand)
Figure 4: Real GDP per Worker and Employment by 13 Group Industries (1997–2016)
15,000
1997
10,000
2001 2008
15,000
10,000
5,000
5,000
0
0 0
50,000
100,000
150,000
200,000
250,000
300,000
350,000
0
Real GDP per Worker by Industry (Millions of chained 2009 dollars)
50,000
100,000
150,000
200,000
Real GDP per Worker by Industry (Millions of chained 2009 dollars)
Government
Manufacturing: Durable goods
Manufacturing: Nondurable goods
Construction
Information
Professional and business services Educational services, health care, and social assistance Retail trade Arts, entertainment, recreation, accommodation, and food services Finance: Finance and insurance Wholesale trade Transportation and warehousing
Figure 5: Employment and Real GDP per Worker in Manufacturing and Information Sectors Information Industry
Manufacturing Industry
NBER Recessions
Real GDP per worker (left axis)
Employment (right axis)
NBER Recessions
Manufacturing: Durable Goods
Real GDP per worker (left axis)
2016
2015
2014
2013
2012
2011
2010
2009
2008
2007
2006
2005
2004
2003
2002
2001
2000
2,000 k
1999
$100,000
1998
10,000 k
1997
$0
2016
2,400 k
2015
$150,000
2014
12,000 k
2013
$50,000
2012
2,800 k
2011
$200,000
2010
14,000 k
2009
$100,000
2008
3,200 k
2007
$250,000
2006
16,000 k
2005
$150,000
2004
3,600 k
2003
$300,000
2002
18,000 k
2001
$200,000
2000
4,000 k
1999
$350,000
1998
20,000 k
1997
$250,000
Employment (right axis)
Manufacturing: Nondurable Goods 14,000 k
$250,000
10,000 k
$200,000
12,000 k
$200,000
8,000 k
$150,000
10,000 k
$150,000
6,000 k
$100,000
8,000 k
$100,000
4,000 k
$50,000
6,000 k
$50,000
2,000 k
$0
4,000 k
$0
NBER Recessions
Real GDP per worker (left axis)
Employment (right axis)
NBER Recessions
20
Real GDP per worker (left axis)
2016
2015
2014
2013
2012
2011
2010
2009
2008
2007
2006
2005
2004
2003
2002
2001
2000
1999
1998
0k
1997
1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016
$250,000
Employment (right axis)
We observe five patterns of output and labor input dynamics in major (two-digit) industries level. First, employment oriented growing industry has faster growth rate in employment compared to output. Health, education, and food services are examples of growing industry in employment. They gradually increase the size of worker over a long run under a roughly constant output per worker. Second, output oriented growing industry includes the wholesales trade and real estate (in financial group) sectors. Output grows rapidly, but employment size is roughly constant. Third, a declining industry means a sector of which employment and output decreases in a long-term, which includes the construction industry. Fourth, the professionals industry shows both economic growth with downward fluctuations, and its dynamics is similar with aggregate economy. Lastly, technological job destruction or jobs that replaced means an increasing output despite a decreasing employment. The nondurable manufacturing and information industries shows the negative correlation between output and employment over two recent decades, and the changes has been gradually made. The durable goods manufacturing industry exhibits an episodic job destruction, that coincides aggregate cyclical downturns. I combined adjacent major industries that show the same output-input dynamics as a single group. Figure 2 shows a trajectory by 13 group industry from 1997 to 2016 in Real GDP (x axis) and employment (y axis) space. Professional and business services sector (yellow line) shows both economic growth and business cycle in a conventional sense with procyclical employment. Education and health care service industry (skyblue line) keep grows in both employment and output without a particular declines even during a recession. Construction sector (dark blue line) is the sector moved toward origin the most intensively, as it decreased (and then increase) both employment and output. Real estate industry (grey line) grows in output without hiring substantially more workers. In summary, education and health services is a typical growing industry, real estate is a growing industry with roughly constant employment, and construction is a conventional declining industry. Meanwhile, manufacturing and information industries show unique trajectories that employment declines while production increases. Information (dark yellow line) grows in output by 93% while it decreased employment by 25% from 2001 to 2016. Durable goods manufacturing (dark orange line) cut employment size by 26%, even though its production increased by 47%. Nondurable goods manufacturing (dark grey line) reduced employment by 25% where the real output is almost the same. To highlight the improvement of productivity, figure 4 shows the same information of previous figure but having x-axis as real output per worker instead of aggregate real output. Information industry doubled real output per worker in last 16 years. Durable and nondurable goods manufacturing increased output per employee by 58% and 19%, respectively. We cannot easily characterize these jobless growing sectors as business cycle or economic growth effect, as labor input and output move to the opposite directions. Only manufacturing and information industries reduced employees and also enhanced real output per worker. Except housing finance industry, the other industries have relatively constant real output per worker: see appendix A for the other graphs. As figure 5 shows, drops in employment is occurred during a recession despite a growing output per employee. Jobs in durable goods manufacturing and industry is supersets of two-digit industries, so it conceptually corresponds to one-digit industry.
21
information industries disappeared, leading a higher real output per worker. I analyze details of industry and occupational compositions for a robustness, see Appendix A for details. In summary, among 22 major (two-digits) occupations, production occupation permanently decreased during recent two recessions, which is heavily used in manufacturing industry. Among over 700 detailed (four-digits) occupations, the most 13 growing jobs are mostly food services, health services, retail salespersons, and customer service representatives. The most 12 declining jobs includes executives, typists, sewing machine operators, packers, delivery services, and order clerks. The 85% of detailed production occupations decreased, and most of them shows a waning w pattern: the number of employees heavily dropped during recessions with little declines during expansionary periods. W pattern dynamics is appeared in team assemblers, first-line supervisors of production, and machinists.
3.3
A New Trend
A sharp decline in employment despite a higher output per worker is a new trend rather than ordinary industrial idiosyncrasy. To show the replaced jobs had never observed in the past, I analyze a longer time period for the jobless sectors. Figure 6 shows employment and output per employee from 1947 to 2016 in the durable goods, nondurable goods manufacturing and information industries. In early 50 years (1947–1996), all of the industries moved to north-east (or east). It means that they hired more workers (or maintained the same level of employment), while real output per worker increased in a long-run. Since 2000, all of three industries have moved south-east, in other words, they reduce employment even though the real output per worker is keep increasing. Especially the durable goods manufacturing reduced 3 million of workers and average real output per worker increased by $33,000 in just four years of recessions: from 2001 to 2003 and from 2008 to 2010. For reference, employment size in transportation and warehousing is about 5 million, and real output per employee in food industry is about $40,000 in 2017. The changes in the durable goods industry from 2001 to 2010 is quantitatively the same with that a small industry is added in productivity but another small industry is eliminated in employment. Given the same amount of job destruction, the timing, speed, and way of job destruction matters when we analyze unemployment dynamics. First, technological job destruction results in a permanent decline in employment, unlike to the cyclical job destruction. The job openings and net hiring during expansionary periods were low in the durable/nondurable goods manufacturing and information industries, while employment in professionals and trade sectors revived and then grow higher. Second, the job destruction in the durable goods sector was episodic contrast to the gradual declines in the nondurable or information sector. Unemployment spikes if there is an influx of labor supply as one time shock, compared to a mildly higher inflows over a long-period. Third, durable goods firms reduced employment by massive layoffs during the 2008 recession, whereas they hired less in net during the 2001 recession. Less net hiring is a passive and soft way of downsizing employment, because it causes slow outs from unemployment without high ins to unemployment. On the other hand, massive layoffs is an active and direct way of downsizing, because we have both high ins to and outs from unemployment.
22
Figure 6: A New Trend of Input-Output Dynamics (1947–2016) 15,000
Durable goods (1947-1996) Durable goods (1997-2016) Nondurable goods (1947-1996)
Employment (thousands)
Nondurable goods (1997-2016) Information (1947-1996)
2001 – 2003 (+ $16k -1.5 mil)
10,000
Infomation (1997-2016) 2008 – 2010 ( +$17k -1.5 mil)
2001 5,000
2008 2001
2008
0 $0
$50,000
$100,000
$150,000
$200,000
$250,000
$300,000
Real GDP per Employee (GDP deflator adjusted (2009=100))
Figure 7: Manufacturing Employment and Output per Worker (1947–2016) $300,000
14,000 k
12,000 k
$250,000
10,000 k $200,000 8,000 k $150,000 6,000 k $100,000 4,000 k
$50,000
2,000 k
NBER recessions
Nominal GDP per Worker
Real GDP per Worker
Employment (right axis)
23
2016
2013
2010
2007
2004
2001
1998
1995
1992
1989
1986
1983
1980
1977
1974
1971
1968
1965
1962
1959
1956
1953
1950
0k
1947
$0
Therefore, the technological job destruction in the durable goods sector during the 2008 recession was the most influential to unemployment rate, ceteris paribus. Business cycles are generally designed as a aggregate shock in total factor productivity. When an aggregate labor market consist with several submarkets (like industry, occupation, or education attainment), a recession generates cyclical job destruction for every submarkets. If submarket is optimally chosen, cyclically unemployed workers have little incentive to change their submarkets, because all of the submarkets become tight and loose simultaneously. However, technological job destruction occurred in a particular submarket. Workers now have incentive to alter their optimal submarket choice to avoid the industry-specific negative shock. In the next section, we observe industrial transitions initiated by the technological job destruction from the durable goods manufacturing industry. The time framework can be important to analyze the source and the effect of technological job destruction. First, the production occupation and the office occupation in the durable goods manufacturing industries suddenly made. Also, the timing coincided with 2001 and 2008 recessions. The rapid destruction of jobs put a large burden on the labor market to reallocate massive number of unemployed workers to scarce job positions during a short period of time. Second, we observe a gradual decline over two decades in office occupation from the information sector and production occupation in the nondurable goods manufacturing sector. In next section, I will explain that automation is the most plausible reason for the technological job destruction in the data. However, it does not eliminate the possibility, for instance, that employment in the textile industry (subsector in the nondurable goods manufacturing) is gradually diminished because of international trade. The speed and timing of a technological job destruction are important, when we analyze the impact and spillover effect of automation technology in the labor market. The manufacturing and information industries reduced 12%–18% of the employment within two years, but there were little rebounds in employment, new hiring, and job openings during subsequent recoveries over more than seven years. In the meanwhile, the most growing industries (health services and food services) increased employment by 2%–4% annually. Because the speed of disappearing jobs exceeds the growth in other job positions, aggregate employment deeply hollows out, the unemployment rate spikes, and the economy appears to slowly recover. When technological job destruction coincides cyclical job destruction, the labor market has an even larger burden of relocating massive numbers of unemployed workers, while dealing with a shortage of labor demand. The replaced jobs may unnecessarily aggravate the labor market, because it add a large negative shock at the worst time of economy. If the replacement is only possible during the recession, then policies would have limited roles. However, if firms replace workers with machines when it is the most cost-efficient time to do it, then policy may provide incentives for firms to reduce employee at the most desirable time.
24
4
Labor Reallocation
This section analyzes the empirical patterns of labor reallocation triggered by a sectional technological job destruction. A labor-saving technology replaced workers in a middle-wage industry, and thus, the particular labor demand (or job positions) disappeared permanently. It is evident that the unemployed workers from the jobless industry are directly suffering for the technological job destruction. However, once jobless workers start to move to other submarkets, it is not a simple question how other unemployed workers are affected by the joblessness in the middle. Suppose that there is no spill-over effect to other submarkets, then we can expect following three patterns as a consequence of technological job destruction in a particular submarket. First, the technologically unemployed workers should wait longer than the cyclically unemployed workers until finding new jobs on average. For example, a middle-wage employment (the durable goods manufacturing industry) declined, whereas the lowest-wage employment (the food services industry) expands after the recession. If unemployed workers stick to their original submarkets, we unambiguously predict that the unemployment rate from the middle industry have both higher ins (to unemployment) and lower outs (from unemployment). Second, the middle unemployed workers must be losing a substantial amount of long-term labor income than unemployed workers from other industries. We expect a hollowing-out in the middle of the annual earnings distribution, which is exactly the same pattern of initial shock in the distribution of labor demand. Third, recruiting firms from the jobless industry would be pickier, but not the firms in other industries. On the contrary, the empirical patterns are quite different with the no-spill-over predictions above. First, unemployment from the lowest-wage industry was more persistent and lagged, compared to the unemployment from the jobless industry. The increase in unemployment of the bottom industry caused by the slow outs in spite of no ins. The increase in unemployment from the jobless industry was fast due to high ins, but its decline was also faster due to high outs. Second, existing studies based on various data sources consistently show that the lower a worker earned before the recession, the larger percentage losses the worker get after the Great recession: see section 2.4 for the summary of literature. The change in earnings distribution is a severe negative skewness, rather than hollowing out in the middle of distribution. Third, existing literature about upskilling effect an outward shift in the Beveridge curve point out lower-wage industries, not the jobless industry.25 In this section, I focus on the Great Recession and show the unemployment recovery that is mostly determined by the speed of outs from unemployment. A rapid and preceding increase in unemployment is mostly due to high ins to unemployment, however, other industries also followed by an increasing unemployment rate despite no ins. A recovery speed is contradictory with the net employment, but it is consistently related with the wage hierarchy. For a direct evidence of trickle-down unemployment, I analyze industries and earnings of a lost job in last three years to their current industries and earnings in the CPS. I find a domino chain of industrial transitions: the durable goods workers move to construction, construction workers move to retail trade, and retail trade workers move to the food services. Even 25
See section 2.4 for a summary of literature.
25
though the construction and retail trade industries largely reduced their employment size, but upper class unemployed workers successfully settle down in the one-step-lower-paying industry. I emphasize that the direct transition from jobless sector to actively hiring sector is lower than other transitions or the same transitions in non-recession periods.
4.1
Trickle-Down Unemployment
Table 2: Change in Employment and Unemployment during the Great Recession Industry
Average Wage
Change in Employment
Range of Unemployment
$/hour
thousands (percentage)
thousands (percentage)
Information
$28.12
−349
(−11%)
+296
(2% → 12%)
Finance
$25.54
−706
(−8%)
+486
(2% → 8%)
Professionals
$24.61
−316
(−2%)
+1,130
Health (and Education)
$20.67
+1,719
(+9%)
+941
Construction
$22.98
−1,926
(−26%)
+1,882
(5% → 27%)
Durable Manufacturing
$22.43
−1,694
(−19%)
+1,038
(3% → 14%)
Nondurable Manufacturing
$19.64
−600
(−12%)
+482
(3% → 12%)
Trade (and Transportation)
$18.50
−903
(−3%)
+1,800
(4% → 11%)
Food (and Leisure)
$12.34
−181
(−1%)
+982
(7% → 14%)
(5% → 12%) (3% → 7%)
The industry for an unemployed worker refers the industry of previous job in which he/she had worked. The change in employment is the difference between employment level in 2007 and 2010 (E10 − E07 ). The range of unemployment is the maximum unemployment level minus the minimum unemployment level in 2007 to 2010. The average earnings rate represents the nominal value of May 2007, and all the wages have increased holding the same order in recent two decades.
When aggregate unemployment is split into subcategory that is not perfectly exclusive segment of the labor market, then unemployment dynamics is not the opposite of employment dynamics for each group. In addition, labor reallocation causes that the importance of inflows to unemployment is underestimated in submarket analysis for unemployment variation. Table 2 shows that unemployment rate from a particular industry goes up regardless the employment growth in the industry. Construction, manufacturing, and information industries reduced their employment size the most between 2007 to 2010. Therefore, unemployment rate for these downsizing industries spiked mostly due to the high ins to unemployment. However, the trade, professionals, and food services industries reduced their employment by relatively little percentage, and the health services sector even increased their employment size. Unemployment rate from these little affected industries by a recession also substantially increased. It suggests a possibility that the health services and food services industry hired unemployed workers from other industry instead of unemployed workers who had worked in their industries. Labor reallocation
26
is important, even the submarket is devided by a permanent trait of workers. For example, if female workers are laid off but successfully take new jobs that has done by male workers, then unemployment for men increases because of slow outflow from unemployment for men that is caused by the high inflow to unemployment for women. Figure 8 shows the unemployment level from the finance industry, which is the epicenter of the Great Recession, was less volatile than the unemployment level from the health services industry, which increased their employment size by 9% around the Great Recession. Also it shows that unemployment level from the durable goods manufacturing sector, which reflects disappearing middle-wage production occupations, is almost equally volatile with the food services industry, which reflects growing low-wage service occupations. When manufacturing workers are laid off because their skill becomes obsolete, they do not necessarily stay in the unemployment pool. Similarly, when services industry actively increase their employment size, unemployed workers from the services industry do not necessarily find new jobs faster than other unemployed.
27
Figure 8: Unemployment Level for Four Industries Differ in Employment Growth Unemployment level from the Financial and the Health Services 1,600 k
1,400 k
1,200 k
1,000 k
800 k
600 k
400 k
200 k
0k
2000
2002
2004
2006
NBER Recessions
2008
2010
Financial Activities
2012
2014
2016
2014
2016
Health Services
Unemployment level from the Durable Goods and the Food Services 2,000 k
1,800 k
1,600 k
1,400 k
1,200 k
1,000 k
800 k
600 k
400 k
200 k
0k
2000
2002
2004
2006
NBER Recessions
2008
Durable Goods
28
2010
2012
Food Services
Figure 9 shows the pre-recession trough, peak, and 1/4th, 1/2th, and 3/4th recovery points of unemployment rate from each industries for the 2001 and 2008 recessions. The rise of unemployment rate sequentially started from the information, professionals, financial activities, and health services industry. These industries have average wage rate as $28, $25, $26, and $21 respectively based on 2007. Similarly, the rise of unemployment rate sequentially occurred from durable goods manufacturing, construction, non-durable goods manufacturing, Transport, Trade, and Food services industry. The industries pays average hourly wage of $22, $23, $20, $19, $18, and $12 respectively based on 2007. Although the employment level decreased for most industries for the first three years of beginning of a recession, the health services industry increased their employment level by 9% for both recessions. The unemployment rate from the food services industry increased by 3.7% and 6.1% for each recession, while the industrial employment level increased by 3% and decreased by 1%, respectively. Table 3 shows estimates of regression:
Uk,t = βk,0 + βk,1 Et + βk,2 Vk,t + βk,3 Lk,t + βk,4 Qk,t +
K X
βk,i+4 Ui,t−1 + k,t
i=1
where k is industry ranking on a wage hierarchy, t is month, Uk,t is unemployment stock from each industry, E is aggregate employment level, Vk,t is the number of job openings, Lk,t is the number of layoffs and discharges, and Qk,t is the number of quits. The adjusted R-square is very close to one, mostly because of the unemployment in the previous month. When auto-regressive model is estimated, the unemployment rate cannot reject the non-stationary null hypothesis in the unit-root test. The unemployment is ergodic, which means the best prediction for the next month unemployment is the realized value of current unemployment, and unit root, which is non-stationary process. By including lagged unemployment rate in other industries, the unemployment level from each industry is stationary process. The coefficient of unemployment level from other industries are larger and more significant then the job opening or quits within the industry. Additional unemployed workers from the information industry industry last month increases the number of unemployed workers from the professional sector by .4728, but the converse effect is small and insignificant. Similarly, unemployed workers from the finance industry have negative externality to the trade sector with coefficient of .3600, but the converse effect is positive and insignificant. Outs from unemployment is closely related with reallocation of unemployed workers.
29
Change in Unemployment Rate (0=Trough)
Figure 9: Lagging Peak and Recovery of Unemployment from Low Wage Industries 6% 5%
Info ($28, -14%)
4%
Fin ($26, +3%)
3%
Prof ($25, -1%) 2%
Health ($21, +9%)
1% 0% 2000
2001
2002
2003
2004
2005
2006
2007
2008
Year
Change in Unemployment Rate (0=Trough)
5%
4%
Cons ($23, +1%) Durable ($22, -15%)
3%
Nondurable ($20, -12%) 2%
Transport ($19, -5%) Trade ($18, -2%)
1%
Food ($12, +3%) 0% 2000
2001
2002
2003
2004
2005
2006
2007
2008
Year Change in Unemployment Rate (0=Trough)
10% 8%
Info ($28, -11%)
6%
Fin ($26 -8%) 4%
Prof ($25, -2%)
Health ($21, +9%)
2% 0% 2007
2008
2009
2010
2011
2012
2013
2014
2015
2016
2017
2018
-2%
Year 18%
Change in Unemployment Rate (0=Trough)
16% 14%
Cons ($23, -26%)
12%
Durable ($22, -19%)
10%
Nondurable ($20, -12%)
8% 6%
Transport ($19, -3%)
4%
Trade ($18, -4%)
2%
Food ($12, -1%)
0% 2007 -2%
2008
2009
2010
2011
2012
2013
2014
Year
30
2015
2016
2017
2018
Table 3: Regression of Unemployment to Other Industrial Unemployment (1/2) Variable
Dependent
Independent Total Emp
Job Openings
Layoffs
Quits
Information
Professional
Finance
Construction
Manufacturing
Edu & Health
Transport
Other Service
Trade
Leis & Hospit
Constant
Adjusted R2
Et
Vk,t
Lk,t
Qk,t
U1,t−1
U2,t−1
U3,t−1
U4,t−1
U5,t−1
U6,t−1
U7,t−1
U8,t−1
U9,t−1
U10,t−1
Information
Professional
Finance
Construction
Manufacturing
U1,t
U2,t
U3,t
U4,t
U5,t
−.0030
−.0014
−.0009
−.0002
−.0040
(.0008)
(.0027)
(.0012)
(.0032)
(.0023)
−.2405
−.0232
−.0867
.0749
−.2403
(.0677)
(.0563)
(.0608)
(.2438)
(.1419)
.4030
.2227
.3243
1.3448
.9798
(.1857)
(.0846)
(.1232)
(.1535)
(.1297)
.0881
.0617
.0266
−.4127
−.2155
(.1540)
(.0766)
(.1020)
(.2411)
(.1628)
.4343
.4728
.0166
.0203
.2620
(.0668)
(.2179)
(.1014)
(.2679)
(.1792)
.0150
.4733
−.0122
−.1069
−.0565
(.0236)
(.0769)
(.0360)
(.0979)
(.0641)
.0051
.0528
.5728
−.1404
.2023
(.0385)
(.1373)
(.0607)
(.1607)
(.1068)
.0088
.0565
.0253
.8462
.0814
(.0121)
(.0390)
(.0178)
(.0474)
(.0327)
.0564
.0199
−.0026
−.0596
.6470
(.0177)
(.0567)
(.0270)
(.0699)
(.0525)
.0493
.0766
.0013
−.0803
.0809
(.0203)
(.0650)
(.0308)
(.0802)
(.0327)
.0187
.2746
.1648
.3174
.1787
(.0506)
(.1706)
(.0782)
(.2054)
(.1381)
−.0171
.3173
−.0054
.1675
.0663
(.0483)
(.1574)
(.0752)
(.1908)
(.1344)
−.0285
−.0584
.0226
.0130
− .0501
(.0225)
(.0748)
(.0343)
(.0912)
(.0605)
−.0430
.1223
.0678
.2033
−.0008
(.0244)
(.0803)
(.0373)
(.1023)
(.0673)
477.91
124.28
100.60
−219.24
628.53
(128.38)
(387.42)
(186.38)
(519.74)
(362.48)
.8651
.9254
.9204
.9480
.9672
N = 198. Parenthesis reports the standard error of each coefficient. Data source is JOLTS and CES from BLS from Dec 2000 to Jun 2017.
31
Table 4: Regression of Unemployment to Other Industrial Unemployment (2/2) Variable
Dependent
Independent Total Emp
Job Openings
Layoffs
Quits
Information
Professional
Finance
Construction
Manufacturing
Edu & Health
Transport
Other Service
Trade
Leis & Hospit
Constant
Adjusted R2
Et
Vk,t
Lk,t
Qk,t
U1,t−1
U2,t−1
U3,t−1
U4,t−1
U5,t−1
U6,t−1
U7,t−1
U8,t−1
U9,t−1
U10,t−1
Edu & Health
Transport
Other
Trade
Leis & Hospit
U6,t
U7,t
U8,t
U9,t
U10,t
.0015
−.0002
−.0013
−.0056
.0013
(.0023)
(.0012)
(.0012)
(.0028)
(.0028)
−.0124
.0768
−.0965
−.0455
−.2009
(.0570)
(.1052)
(.0723)
(.0893)
(.0838)
.8982
.3281
.1689
.4773
−.0771
(.1410)
(.0871 )
(.1059)
(.0814)
(.1009)
.1519
.4426
.0451
.0795
−.0830
(.1269)
(.1676)
(.1264)
(.1074)
(.0891)
.0828
−.0980
.0209
−.0406
−.4675
(.1724)
(.0964)
(.1018)
(.2242)
(.2363)
.0776
.0530
.0152
.0883
.1393
(.0621)
(.0336)
(.0367)
(.0813)
(.0890)
.1001
.1129
.0778
.3600
.1783
(.1057)
(.0577)
(.0601)
(.1364)
(.1460)
−.0306
.0363
−.0089
.0961
.0906
(.0303)
(.0166)
(.0192)
(.0401)
(.0439)
−.0549
.0395
−.0097
−.0078
.0599
(.0443)
(.0254)
(.0268)
(.0584)
(.0666)
.6192
−.0042
.0639
.2102
.3099
(.0534)
(.0297)
(.0312)
(.0706)
(.0782)
.0265
.4561
.0563
.1962
−.0377
(.1328)
(.0745)
(.0794)
(.1752 )
(.1876)
.1412
.0483
.3679
.4167
−.0943
(.1253)
(.0696)
(.0744)
(.1637)
(.1742)
.0683
−.0508
.0453
.4008
−.0634
(.0584)
(.0328)
(.0348)
(.0773)
(.0800)
.1426
.0864
.0355
−.0855
.3556
(.0629)
(.0353)
(.0379)
(.0836)
(.0909)
−432.50
−63.1074
205.31
800.24
334.09
(306.34)
(164.18)
(174.40)
(436.62)
(396.85)
.9480
.8924
.8702
.9415
.8966
N = 198. Parenthesis reports the standard error of each coefficient. Data source is JOLTS and CES from BLS from Dec 2000 to Jun 2017.
32
4.2
Industrial Transitions
Figure 10 and 11 show micro evidence of industrial transitions of unemployed workers. By using biennial questionnaire in CPS. The transition is counted if a worker lost his/her job in recent three years (such as layoffs and firm closure), and find a new job in a different industry. About half of unemployed workers found their new jobs in the same industry. For the 2007 to 2010, industrial transitions was the most frequent. The most frequent transitions are summarized in Table 5: Unemployed workers moved from the durable goods manufacturing to construction, construction workers moved to administrative, administrative workers moved to retail trade, retail workers moved to the food service industry. Furthermore, among the unemployed workers who had worked in the durable goods manufacturing industry, workers climbed up the industry ladder by moving up the professional industry had earned relatively high in the previous job, $1,589 as weekly earnings. Workers moved to construction, administrative, and retail trade industry had earned $745, $693, $700, respectively. Workers moved to the lowest paying industry had earned relatively low in the durable goods manufacturing industry, by $596.
33
Figure 10: Worker Transitions after Job Loss: Pre-recession (2005–2008) and The Great Recession(2007–2010)
34
Figure 11: Worker Transitions after Job Loss: Post-recessions (2009–2012 and 2011–2014)
35
Table 5: Weekly Earnings at the Lost Job and the Current Job Previous
Current
Industry
Industry
Mass
Previous
Current
Mass
Previous
Current
Retail
29
$987
$504
12
$559
$418
($617)
($629)
($325)
($175)
$1,589
$1,273
$1,422
$1,159
($651)
($712)
($530)
($776)
$745
$502
$918
$724
($401)
($573)
($515)
($500)
$693
$675
$611
$514
($334)
($470)
($435)
($228)
$700
$398
$658
$539
($351)
($252)
($378)
($411)
$596
$169
$396
$609
($242)
($99)
($140)
($877)
$723
$647
$540
$585
($345)
($655)
($223)
($248)
$663
$481
$618
$543
($392)
($306)
($416)
($334)
$783
$364
$532
$401
($422)
($144)
($261)
($207)
$520
$363
$461
$581
($321)
($248)
($199)
($700)
$429
$456
$370
$436
($336)
($462)
($320)
($408)
Professional →
Durable →
Professional
Construction
Administrative
Retail
Food
Construction →
Administrative
Retail
Food
Administrative →
Retail →
Total
Retail
Food
Recession (2007–2010)
38
50
44
44
28
36
41
32
32
32
2595
Control (2005–2008)
19
24
19
30
12
15
28
18
18
23
1491
The industry for unemployment refers the industry of previous job in which an unemployed worker had worked. The change in employment is the difference between employment level in 2007 and 2010 (E10 − E07 ). The range of unemployment is the maximum unemployment level minus the minimum unemployment level in 2007 to 2010. The average earnings rate represents the nominal value of May 2007, and all the wages have increased holding the same order in recent two decades. Parenthesis represents standard deviation of weekly earnings within group.
36
5
A General Equilibrium Submarket Choice Model
This paper uses a general equilibrium submarket choice model presented in Stokey (2016) to analyze labor reallocation to technological job destruction. Unlike an example in Stokey’s paper, I aim to make positive productivity shock result in lower employment in the middle sector, instead of negative productivity shock. Whether the technology shock is positive or negative matters for labor reallocation, because reinforcing general equilibrium growth effect through optimal size of industry (and the equilibrium demand of sectoral output goods) changes employment level to the opposite direction. The total number of workers and submarkets are fixed. Submarket in this paper refers to an industry that produces a single variety of intermediate good for a final consumption bundle. Workers differ in general ability, while firms differ in industry-specific capital, which includes any characteristic of a firm that contributes to production besides workers.26 Therefore, a single firm represents an entire industry without loss of generality. Consumers values variety, and the preference has constant elasticity of substitution (CES) across sectoral output goods. Within each submarket, production requires a match of a worker and a job position in the firm. Technology have constant elasticity of substitution (CES) between the quality of labor and capital. The model can be considered as an extension of Roy’s (1951) occupational choice model; This model is more general than Roy’s model because of endogenous prices and demands, while it is simpler due to uni-dimension of skills of workers. Alternatively, the model can be regarded as a general equilibrium extension of Becker’s (1973) marriage model with identical firms within submarket. Naturally, the model can be viewed as heterogeneous-worker extension from general equilibrium version of Dixit-Stiglitz (1977)’s model. I explain that the core labor allocation and employment size depends on two complementarity parameters. Even when automation technology substitutes labor in the middle sector, lower employment is only observed if the demand of output is inelastic. In other word, only the combination of sufficiently substitutable inputs and complementary outputs result in technological job destruction in the middle sector. If inputs are substitutes, then the core labor allocation is negative assortative matching: the best worker works in a job position with the lowest capital, the second best worker works in the job with second lowest capital, and so on. On the other hand, when labor and capital are complements, technological progress can result in lower employment if output goods are extremely complementary. If consumers intensively loves variety, then productivity growth in a particular sector is less valuable than general productivity growth, so redundant labors are moving out to other sectors. In such a case, the middle sector ends up to produce more with fewer workers, because it is not worth to expand industry size as the decline in output price overwhelms the increase in production. When sectoral output goods are substitutes while inputs within sector are complements, as the popular choices of calibration in existing literature, a progress in technology in the middle ranked sector always result in higher employment in the sector. 26
Heterogeneous technology of firms within industry can be an analogous extension of this model.
37
5.1
The Final Goods Market
The final good sector is perfectly competitive, it makes zero profits, and its output is used for consumption. The final consumption good is an aggregation of intermediate input yj from each industry j. There are J industries in the economy, and each sector is different in variety and also in technology sorted by an ascending order, 0 < x1 < x2 < · · · < xJ . The total mass of labor demand is normalized to one, and the share of intermediate good produced from industry j in the final good aggregator is denoted as γj . Industries produces unique variety of intermediate goods. Within an industry j, all firms are identical and perfectly competitive with a single equilibrium price of pj . The intermediate quantity from sector j is yj . The final good (yF ) is aggregated by a constant elasticity function (CES)
yF =
J X
ρ−1 ρ
γj yj
ρ ρ−1
,
(1)
j=1
where ρ > 0 is the elasticity of substitution across intermediates. If ρ > 1, then the cross partial derivatives of the final good with respect to any two sectoral intermediates is negative
∂ 2 yF ∂yj ∂yi
< 0 for
i 6= j. In other word, the final goods production has decreasing differences, or it is submodular function. By Topkis’s theorem, therefore, the intermediates are substitues: optimal yj is decreasing in yi . The price of the final consumption good is
pF =
J X
1 1−ρ
γj p1−ρ j
(2)
j=1
and demand of the intermediary good from sector j is
yj =
pj pF
−ρ
yF
(3)
for all j ∈ {1, 2, · · · , J}. The price of the final good is normalized to one, pF = 1. The middle ranked sector is denoted as k = [J/2].
5.2
Intermediate Goods Markets
The competitive firms within the industry j produce good with technology xj by hiring workers that minimize unit cost. Workers are heterogeneous in human capital h, which follows a continuous probability distribution of G(h) on a finite positive support (hmin , hmax ). The mass of population is unity, and worker’s decision is binary: work in the full time or not in the labor force. The total output in a sector j is Z
yj =
lj (h)φ(h, xj )dh
(4)
where lj (h) is the density of worker of type h hired in sector j. The productivity of a single worker of type h in a sector j is described as another CES function
φ(h, xj ) = ωh
σ−1 σ
σ−1 σ
+ (1 − ω)xj
38
σ σ−1
(5)
where ω is the relative weight on labor, 0 < ω < 1. To get a positive assortative matching as an equilibrium sorting, this production function is assumed to be supermodular. Therefore, the elasticity of substitution between labor and technology is less than unity, 0 < σ < 1.
5.3
The Labor Market
In this model, wage equals to the marginal product of labor, and the labor market is not monopsony, i.e., wage is heterogeneous even within a sector. It allows the model not to exclude complementary intermediate goods 0 < ρ < 1, because wage will be perfectly adjusted to give zero profits to firms. If a monopolistic firm exist in a sector, then intermediates are usually assumed to be substitutes (ρ > 1) so that the firm can make positive profits by paying one wage for every workers within the sector. In the monopsony labor market, wages will be reduced by the factor (ρ − 1)/ρ, but other quantities and prices will be the same. Workers maximize their wage by optimally choosing the submarket to supply their labor
w(h) = max {wp (h, xj )} = max {pj φ(h, xj )} j
j
(6)
for all h, where wp (h, xj ) is a potential wage a worker of type h would earn working in an industry j. In equilibrium, labor allocation is positive assortative matching (without a single exception), unless agents are sorted with multiple dimensions. An industry j hires workers of type h ∈ (bj−1 , bj ), with thresholds of hmin < b1 < b2 < · · · < bJ−1 < hmax .27 The lowest (highest) type of worker in industry j is indifferent between working in the current industry j and the one-step lower (upper) industry j − 1 (j + 1), which pins down the thresholds. The industrial employment share to total employment is determined by the bin size of workers’ type in each submarket.
5.4
Equilibrium
The economy consists of the final good market, intermediates market for each industry j, and the labor market. An equilibrium is a set of a final output quantity yF , sectoral outputs and prices {yj , pj }Jj=1 , a wage function w(h), and labor allocation thresholds {bj }J−1 j=1 . The market clearing condition for the final good market is equation (1) and market clearing condition for each sector is equation (3). The labor market clearing condition is Z bj
φ(h, xj )dG(h) = γj yj
(7)
bj−1
for all j. Equations (3) and (6) implies that pj+1 φ(bj , xj ) = pj φ(bj , xj+1 ) yj+1 = yj 27
pj+1 pj
!−ρ
=
φ(bj , xj+1 ) φ(bj , xj )
!ρ
See Groes, Kircher, and Manovskii (2015) and Stokey (2016) for details.
39
(8)
for all j. The indifference condition for a marginal worker, which combines the labor market clearing condition (7) and sectoral goods ratio (8), characterizes the equilibrium labor allocation. For any conjecture for bJ−1 given bJ = hmax , if the derived lowest bound is the minimum worker’s type, the the thresholds are unique stationary equilibrium: b0 = hmin . The recursive indifference formula is following Z bj
γj φ(h, xj )dG(h) = γj+1 bj−1
φ(bj , xj ) φ(bj , xj+1 )
!ρ Z
bj+1
φ(h, xj+1 )dG(h)
(9)
bj
for all j = 1, 2, · · · , J − 1. The total productivity of labor in a sector j is denoted as Ψj , so the equation (9) can be rewritten as following. γj Ψj = γj+1
φ(bj , xj ) φ(bj , xj+1 )
!ρ
Ψj+1
(9’)
for all j = 1, 2, · · · , J − 1. Once getting labor allocation thresholds {bj }J−1 j=1 , a sectoral output quantity (yj ) is determined by equation (7). yj =
1 Ψj . γj
(7’)
We calculate sectoral good prices (pj ) by guess and verify so that prices satisfy equation (8), and the final good is numeraire: pF = 1 in equation (2). Lastly, the final good’s quantity (yF ) is driven from equation (1).
5.5
Technological Job Destruction in the Middle Sector
The observed labor reallocation patterns have two distinctive features: technological job destruction in the middle sector, and heavier downward transitions than upward transitions. On the one hand, middle ranked sector let their workers out to other sectors: unemployed workers from the manufacturing industry, which pays the 4th to 5th average wage among 10–12 industries, to adjacent industries on a wage hierarchy was the most frequent. Within the manufacturing sector, real output per worker increased, total real output increased, and employment decreased. There are four possible combinations of elasticity of substitution and shock that result in higher productivity and lower employment in the middle ranked sector. First, when the capital and labor are substitutes (σ > 1), then a progress in technology in the middle ranked sector results in lower employment
∂Nk ∂xk
< 0. In this case, however, the core labor allocation to firms is negative assortative
matching (NAM): the most able worker works in an industry with the lowest technology. If other sectors have complementary inputs but the middle sector only have substitutable inputs, the core allocation is ambiguous. Second, a nested constant elasticity of substitution model can be alternative: an emergence of a specific type of capital substitutes labor, and effective labor of combination of human labor and automation is complementary with general technology of the industry. While positive assortative matching is the core allocation (σ < 1), the middle sector labor can be substituted by industry-specific automation technology. In this case, the price of automation technology is exogenous. Third, Leontief
40
production function of final good (ρ = 0) with sectoral productivity growth can results in lower employment level in the middle sector. Input substitutability can be overwelemed by the inelastic sectoral output demand. When complementarity across intermediates are not sufficiently high compared to the substitutability of inputs, the sectoral productivity growth results in non-decreasing employment level in the middle sector, because prices absorb the positive productivity shock. Lastly, decreasing elasticity of substitution (DES) preference for the final good results in additional productivity increase for a sector with relatively saturated production results in lower employment level. In conclusion, whether higher productivity in the middle sector results in lower employment or not is determined by the size and direction of two effects: substitution effect between labor and capital, and growth effect—in other word, optimal industry size effect—due to enhanced productivity. On the other hand, whether the technological job destruction is a negative shock to labor income or not depends on where the jobless workers go. If laid-off manufacturing workers quickly find their next jobs that pays higher wages, then technological job destruction may not be considered as a negative shock to the labor income. In the United States, the techonological job destruction in the durable goods manufacturing industry coincided with the 2001 and 2008 recessions. When the aggregate labor demand is scarce and core allocation is positive assortative matching, every classes of workers move downward on an industry ladder until the lowest type of workers are left unmatched. On contrary, when the aggregate labor supply is scarce given positive assortative matching, every classes of workers climb up on the ladder until the lowest type of firms are left unmatched. In the model, total factor productivity causes the same labor reallocation in the long run equilibrium. When total factor productivity increases (decreases), every classes of workers move one-step down (up) on the submarket ladder.
5.6
Calibration
Given ρ, σ, ω, G(h), {γj }Jj=1 , a steady-state general equilibrium is uniquely defined. In the model with a single wage within each sector, the elasticity of substitution across intermediates ρ with a one wage within an industry is usually set to be 6 to 10. The target estimates is the mark up (or net corporate profits share in the data) in the United States, which is in rage of 10%–20%. In this model, wages are differ by workers within the industry, therefore, firm’s profit is always zero. I simulate three cases complements (ρ = 0.5 < 1), unit elasticity (ρ = 1), and substitutes (ρ = 6 > 1). The elasticity of substitution between labor and technology within a sector σ is debatable in range of 0.1 to 1.5. Whether the value is less than one or not critically determines if the labor allocation is positive assortative matching or not. I use the elasticity of capital-labor substitution (σ) as 0.5, which is in range of 0.4–0.6, following the suggestion of Chirinko (2008). In the Cobb-Douglas limits, the weight on labor input ω is the labor share of income, so I use 2/3 for it. The weight shift in the final good aggregator assumed to be uniform: γj = 1/J. The distribution of workers type is assumed to be a normal distribution: h ∼ N (22, 52 ). Firms type for each sector is assumed to follow an uniform grid in [20, 100]. Given the parameter choice in agents type, the equilibrium wages are in range of (3, 49).
41
5.7
Simulation for Labor Reallocation
I simulate the labor reallocation when there is a sectoral technological progress in the middle sector (k = 3 and J = 5). The simulation results in table (9) assumes that intermediates (or sectoral output goods) are complementary with ρ = 0.5. On the other hand, the table (10) represents the results when intermediates are substitutes with ρ = 6. I consider three types of shocks. Shock 1 analyzes when only the middle sector become more productive without altering the hierarchy. Shock 2 compares stationary equilibrium if only the middle sector have lower labor input share and thus enhance the potential productivity for any given type of workers. Shock 3 simulates total factor productivity, when technology in all of the sectors become higher.
Figure 12: Changes in Wages: Preference Shock with Complements (Left) and Substitutes (Right)
42
Table 6: A Preference Shock Variable xk
k=1
k=2
k=3
k=4
k=5
Aggregate
20
40
60
80
100
xF
γ3 = 0.16 (decreased by 0.04) when complements (ρ = 0.5) bk−1
nk
Ψk
yk
pk
initial
15
12,063
22,711
32,637
41,846
final
11
12,581
23,679
31,634
41,392
initial
12,048
10,648
9,926
9,209
8,154
final
12,570
11,098
7,955
9,758
8,608
∆nk
522
450
−1,971
549
454
initial
201,343
255,595
284,063
302,209
315,319
final
211,226
268,540
227,620
317,754
331,437
initial
1,006,714
1,277,974
1,420,313
1,511,044
1,576,596
1,324,166
final
1,005,836
1,278,761
1,422,622
1,513,112
1,578,271
1,320,454
initial
1.2227
1.0294
0.9569
0.9171
0.8907
1
final
1.2213
1.0271
0.9541
0.9148
0.8885
1
γ3 = 0.16 (decreased by 0.04) when substitutes (ρ = 6) bk−1
nk
Ψk
yk
pk
initial
14
4,586
13,375
24,677
37,320
final
4
4,770
13,968
23,122
36,591
initial
4,572
8,789
11,302
12,643
12,680
final
4,766
9,198
9,154
13,469
13,409
∆nk
194
409
−2,148
826
729
initial
67,117
187,709
296,211
389,431
472,002
final
70,252
197,793
238,696
410,260
496,480
initial
335,598
938,547
1,481,056
1,947,157
2,360,008
1,376,643
final
334,534
941,873
1,491,852
1,953,621
2,364,196
1,375,705
initial
1.2236
1.0539
0.9868
0.9487
0.9227
1
final
1.2238
1.0530
0.9854
0.9479
0.9222
1
43
Table 7: A Combined Shock (Preference Shock and TFP Shock) Variable xk
k=1
k=2
k=3
k=4
k=5
Aggregate
20
40
60
80
100
xF
γ3 = 0.16 (decreased by 0.04) and z = 1.1 (xk increased by 10% for all k) when ρ = 0.5 (complements) bk−1
nk
Ψk
yk
pk
initial
15
12,063
22,711
32,637
41,846
final
11
12,707
23,816
31,749
41,457
initial
12,048
10,648
9,926
9,209
8,154
final
12,696
11,109
7,933
9,708
8,543
∆nk
648
461
−1,993
499
389
initial
201,343
255,595
284,063
302,209
315,319
final
219,304
274,226
230,596
320,386
333,041
initial
1,006,714
1,277,974
1,420,313
1,511,044
1,576,596
1,324,166
final
1,044,306
1,305,838
1,441,224
1,525,649
1,585,912
1,345,921
initial
1.2227
1.0294
0.9569
0.9171
0.8907
1
final
1.2045
1.0249
0.9573
0.9208
0.8965
1
γ3 = 0.16 (decreased by 0.04) and z = 1.1 (xk increased by 10% for all k) when ρ = 6 (substitutes) bk−1
nk
Ψk
yk
pk
initial
14
4,586
13,375
24,677
37,320
final
13
5,172
14,606
23,747
36,983
initial
4,572
8,789
11,302
12,643
12,680
final
5,159
9,434
9,141
13,236
13,017
∆nk
587
645
−2,161
593
337
initial
67,117
187,709
296,211
389,431
472,002
final
78,773
208,150
243,281
409,946
488,875
initial
335,598
938,547
1,481,056
1,947,157
2,360,008
1,376,643
final
375,111
991,192
1,520,508
1,952,122
2,327,978
1,394,654
initial
1.2236
1.0539
0.9868
0.9487
0.9227
1
final
1.2064
1.0476
0.9849
0.95016
0.9263
1
44
Figure 13: Changes in Wages: Combined shock (Preference Shock and TFP Shock) with Complements (Left) and Substitutes (Right)
Figure 14: Changes in Wages: Negative Productivity Shocks with Complements ρ = 0.5
45
Table 8: Negative Productivity Shocks with Complements ρ = 0.5 Variable xk
k=1
k=2
k=3
k=4
k=5
20
40
60
80
100
Aggregate
Shock 1: x3 = 50 (decreased by 10) bk−1
Empk
yk
pk
initial
15
12063
22711
32637
41846
final
21
12070
22722
32540
41802
initial
12048
10648
9926
9209
8154
final
12049
10652
9818
9262
8198
initial
1006714
1277974
1420313
1511044
1576596
1324166
final
11007157
1278580
1360999
1518593
1584428
1315993
initial
1.2227
1.0294
0.9569
0.9171
0.8907
1
final
1.2169
1.0245
0.9812
0.9101
0.8839
1
Shock 2: ω3 = 0.7 (increased by 0.03) bk−1
Empk
yk
pk
initial
15
12063
22711
32637
41846
final
35
12116
22803
32615
41836
initial
12048
10648
9926
9209
8154
final
12081
10687
9812
9221
8164
initial
1006714
1277974
1420313
1511044
1576596
1324166
final
1010958
1283668
1368706
1512754
1578376
1318077
initial
1.2227
1.0294
0.9569
0.9171
0.8907
1
final
1.2155
1.0232
0.9770
0.9135
0.8872
1
Shock 3: z = 0.9 (xk decreased by 10% for all k) bk−1
Empk
yk
pk
initial
15
12063
22711
32637
41846
final
8
11919
22552
32509
41774
initial
12048
10648
9926
9209
8154
final
11911
10633
9957
9265
8226
initial
1006714
1277974
1420313
1511044
1576596
1324166
final
963128
1246353
1398133
1495875
1566888
1294473
initial
1.2227
1.0294
0.9569
0.9171
0.8907
1
final
1.2428
1.0322
0.9534
0.9102
0.8815
1
46
Table 9: Positive Productivity Shocks with Complements ρ = 0.5 Variable xk
k=1
k=2
k=3
k=4
k=5
20
40
60
80
100
Aggregate
Shock 4: x3 = 70 (increased by 10) bk
Empk
yk
pk
initial
15
12,063
22,711
32,637
41,846
final
3
12,057
22,703
32,709
41,879
initial
12,048
10,648
9,926
9,209
8,154
final
12,054
10,646
10,006
9,170
8,121
initial
1,006,714
1,277,974
1,420,313
1,511,044
1,576,596
1,324,166
final
1,006,508
1,277,636
1,465,515
1,505,492
1,570,719
1,329,975
initial
1.2227
1.0294
0.9569
0.9171
0.8907
1
final
1.2262
1.0324
0.9389
0.9217
0.8952
1
Shock 5: ω3 = 0.6 (decreased by 0.07) bk
Empk
yk
pk
initial
15
12,063
22,711
32,637
41,846
final
22
11,963
22,522
32,687
41,869
initial
12,048
10,648
9,926
9,209
8,154
final
11,941
10,559
10,165
9,182
8,131
1,006,714
1,277,974
1,420,313
1,511,044
1,576,596
1,324,166
final
996,974
1,265,292
1,533,776
1,507,204
1,572,500
1,335,198
initial
1.2227
1.0294
0.9569
0.9171
0.8907
1
final
1.2381
1.0426
0.9163
0.9244
0.8978
1
initial
Shock 6: z = 1.1 (xk increased by 10% for all k) bk
Empk
yk
pk
initial
15
12,063
22,711
32,637
41,846
final
29
12,189
22,848
32,747
41,908
initial
12,048
10,648
9,926
9,209
8,154
final
12,160
10,659
9,899
9,161
8,092
initial
1,006,714
1,277,974
1,420,313
1,511,044
1,576,596
1,324,166
final
1,045,024
1,304,936
1,438,942
1,523,536
1,584,209
1,349,240
initial
1.2227
1.0294
0.9569
0.9171
0.8907
1
final
1.2058
1.0271
0.9600
0.9231
0.8985
1
47
Figure 15: Changes in Wages: Positive Productivity Shocks with Complements ρ = 0.5
Figure 16: Changes in Wages: Positive Productivity Shocks with Substitutes ρ = 6
48
Table 10: Positive Productivity Shocks with Substitutes ρ = 6 Variable xk
k=1
k=2
k=3
k=4
k=5
20
40
60
80
100
Aggregate
Shock 4: x3 = 70 (increased by 10) bk
Empk
yk
pk
initial
14
4,586
13,375
24,677
37,320
final
17
4,535
13,213
25,636
37,773
initial
4,572
8,789
11,302
12,643
12,680
final
4,518
8,678
12,423
12,137
12,227
initial
335,598
938,547
1,481,056
1,947,157
2,360,008
1,376,642
final
331,252
924,920
1,669,843
1,882,145
2,283,470
1,383,220
initial
1.2236
1.0539
0.9868
0.9487
0.9227
1
final
1.2268
1.0569
0.9706
0.9540
0.9278
1
Shock 5: ω3 = 0.6 (decreased by 0.07) bk
Empk
yk
pk
initial
14
4,586
13,375
24,677
37,320
final
20
4,185
12,112
26,597
38,229
initial
4,572
8,789
11,302
12,643
12,680
final
4,165
7,927
14,485
11,632
11,771
initial
335,598
938,547
1,481,056
1,947,157
2,360,008
1,376,642
final
302,223
833,418
2,017,051
1,816,386
2,206,028
1,395,465
initial
1.2236
1.0539
0.9868
0.9487
0.9227
1
final
1.2439
1.0736
0.9461
0.9595
0.9330
1
Shock 6: z = 1.1 (xk increased by 10% for all k) bk
Empk
yk
pk
initial
14
4,586
13,375
24,677
37,320
final
21
4,967
13,981
25,272
37,695
initial
4,572
8,789
11,302
12,643
12,680
final
4,946
9,014
11,291
12,423
12,305
initial
335,598
938,547
1,481,056
1,947,157
2,360,008
1,376,642
final
375,817
987,395
1,509,683
1,945,226
2,323,104
1,395,640
initial
1.2236
1.0539
0.9868
0.9487
0.9227
1
final
1.2064
1.0485
0.9862
0.9509
0.9269
1
49
6
Conclusion
This paper documents that technological job destruction in the manufacturing industry has provoked vertical labor reallocation on an industry ladder sorted by wage. In the post-war period, a negative time correlation between output and labor input in major non-farm industries is firstly observed. We now witness enhanced real output per worker associated with an overall decline in employment within the manufacturing and information industries. Although the decline in manufacturing jobs has coincided with recessions, it reflects the dominance of technological job destruction in production occupations (e.g., among team assemblers and first-line supervisors). Even though the purpose of the study is an exploration of employment dynamics, declining employment cannot be understood outside the general equilibrium context. The emergence of capital (or technology) that substitutes labor itself does not guarantee lower employment in a submarket, because the number of establishments and size of firms can be adjusted to increase the overall employment level in equilibrium. To analyze the general equilibrium effect of technological job destruction, a preference shock or non-CES preference is required so that high productivity in a sector results in lower sectoral employment. Despite the limitations in the scope of the initial technological job destruction, its impact spreads out to the entire labor market through labor reallocation. I suggest that the previous wage in the lost job was helpful for predicting the worker’s future job in the labor market. The reallocation pattern provides evidence that the core labor allocation is vertical, not horizontal. To analyze the reallocation of labor, two-sided heterogeneity in labor theory becomes increasingly essential, because a representative-agents model with idiosyncratic shock does not generate vertical sorting. Considering reallocation, answering the question of which type of workers have difficulty in finding jobs when middle-wage jobs disappear, is not simple. After the Great Recession in the United States, sectoral job destruction with enhanced productivity negatively affected the bottom half of workers in the labor market (from the jobless industry to the lowest-wage industry). In trying to understand the downward transmission of labor demand shock in the real world, we lacked three building blocks. First, the shock was technological job destruction. Higher output with less employment was related to rapid drops in the labor share of income after the 2001 and 2008 recessions. Also, permanently declining employment in the manufacturing and information sectors contributed to the slow recovery in aggregate employment. Second, the core labor allocation is vertical (or PAM, if we exclude negative assortative matching (NAM) from our consideration). Disappearing middle-wage jobs does not necessarily result in the most affected middle-wage workers. Jobless middlewage workers move to other industries, so workers and firms in other industries are secondarily affected by the technological job destruction in the manufacturing industry. Third, the shortage in aggregate labor demand (or lower aggregate employment with high unemployment) lasted for seven to eight years. This is a crucial background to why technological job destruction during the Great Recession is regarded as a negative shock instead of positive shock in the United States labor market. If high-wage jobs grew faster than the disappearance of middle-wage jobs (so that the aggregate labor demand increased), then middle-wage jobless workers could initiate a chain
50
of upward transitions without a spike in the aggregate unemployment rate. In reality, technological job destruction in the manufacturing industry was associated with little acceleration in the growth of employment in other industries. Instead, the shortage in aggregate labor demand lasted long, out of the stationary equilibrium. Whether the shortage in the aggregate labor demand is the property of technological job destruction itself or the characteristic of a recession (or a combination of both) has not been studied yet. Furthermore, we currently do not know why the durable goods manufacturing industry suddenly reformed their production technology during recessions, while the nondurable goods manufacturing industry and information industry changed gradually. One possibility is the procyclical shadow cost of capital adjustment: A recession has the lowest opportunity cost of giving up the original production, so firms invest their time to retool their facilities. At least, the PAM predicts that the lowest type of workers will be left unmatched, if the economy happens to have a shortage in aggregate labor demand. As middle-wage unemployed workers successfully take low-wage jobs, it becomes difficult for the bottom class of unemployed workers to exit unemployment. The lowest type of workers may encounter firms that suddenly require higher qualifications for the jobs that the workers previously had (some scholars call it the upskilling effect). The difficulty in finding jobs lasts until the aggregate labor demand recovers (some scholars call it the unemployment scar effect). The shortage in total labor demand results in a high unemployment rate, long-term duration of unemployment for the bottom class of workers, and higher skewness in labor income distribution. This paper provides the first two building blocks; technological job destruction and labor reallocation in general equilibrium. However, the third element, lower aggregate employment or high unemployment, is still illustrative based on partial equilibrium. In the Walrasian market, a shortage in labor demand and high unemployment are in disequilibrium. In the search friction market, we can naturally consider embedded dynamic adjustments, as Mortensen and Pissarides (1994) explained equilibrium unemployment over the business cycle. However, the vacancy is a jump variable in existing search theory, which means labor demand is counter-factually over-adjusted for any type of shock in the short run. Once we endogenize the smoothness in vacancy rate adjustment, a search model with two-sided heterogeneity as in Shimer and Smith (2000) can be a complete framework for understanding labor reallocation after the Great Recession as equilibrium dynamic adjustments.
51
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Appendices A
Detailed Industries and Occupations
A.1
Occupational Employment and Wage
Figure 17: Average Nominal Wage and Employment by 12 Group Occupations (2000–2016) 30,000,000
Computer and Mathematical Occupations 2016 2000
25,000,000
Engineering, Science, Legal
2007 2009
2002
Business, Financial, Healthcare Practitioners Education, Library, Entertainment
Employment
20,000,000
Maintenance, Installation, Protective service, Social service Sales, Transportation
15,000,000
Healthcare, Building cleaning, Farming Food Preparation and Serving Related Occupations
10,000,000
Management (OCC 11) Construction and Extraction Occupations (OCC 47)
5,000,000
Production Occupations (OCC 51) 0 $0
$10
$20
$30
$40
$50
$60
Office and Administrative Support Occupations (OCC 43)
Average Wage
∗ The aggregate employment and average wage pattern is in the right top corner. Both employment and nominal average wage are annual Occupational Employment Statistics (OES) data from BLS.
Even though this paper analyzes employment by industry, we can find a link between industry and occupation. This section characterizes the disappeared job by occupation to contrast typical growing job and declining job from disappeared job. Output production data is collected by establishment that uses various types of occupations, hence, it is hard to decompose the contribution to production by occupation within a firm. I use nominal average wage instead of real GDP in occupational analysis. Figure 17 shows how employment and average wage of each group occupations evolved from 2000 to 2016.28 First two dots of each line mark the beginning and ending of 2001 Dot-com bust and third and forth dots represents the start and finish of 2008 financial crisis. Most occupations moves to the 28
Similar to the industry, major occupation means two-digit (in Standard Occupational Classification (SOC)
code) occupations, and detailed occupation refers four-digit occupation. Group occupation is supersets of two-
58
north-east as both average wage and employment grows over time. The growth are more distinctive in non-recession periods. Meanwhile, there are five unique trajectories that are worth to mention among 22 major occupations. The highest paid occupation is managers (dark green line), and the employment have declined in early 2000 despite the fast growing average wage. Employment in sales and transportation (grey line) occupations are highly sensitive to the business cycles. The number of employees declines during a recession and increases in an expansionary phase of economy. Construction (dark blue line) and office (line with yellow triangle) occupation does not recover the employment after the 2008 Great Recession, even though it had rebounded after 2001 recession. Both occupations have a downward trend in employment despite the increasing nominal average wage. Production occupation (red line) is the most declined occupation regarding employment, and most of drops happened during recessions. Therefore, the disappeared job can be characterized as production occupation unambiguously while office occupation is hard to be defined. I scrutinize the minor occupations to see whether production occupation consist with the same unique patterns of minor occupations. Also as a control group, I sort 711 detailed occupation by the difference in employment level between 2000 and 2016 to determine most declining and growing detailed occupations. Figure 18 shows 13 most growing occupations, 12 most declining occupations, and 16 disappearing production occupations. Both growing and declining occupations have a long-term trend and such a change gradually made over time. It is even common that both growing and declining occupation coexist within a given major occupation. For example, data entry keyers (OCC 43-9021) and word processors and typists (43-9022) are top 2% most declining jobs, whereas customer service representatives (43-4051), interviewers, and medical secretaries (43-6013) are top 5% most growing jobs. All of them are in the same major occupation that is office and administrative support (43). However, many production occupations suddenly disappeared and they are not replaced by another production occupations. 68 out of 79 detailed occupations related with factory production reduced employment. The only two continuously growing production occupations are food batch-makers (513092) and water waste system operators (51-8031). Most production occupations shows waning w-shape or continuously declining pattern. Among them, team assemblers (51-2092) and first line supervisors (53-1021) workers were reduced the most. The employment adjustments are focused on two years of recessions rather than five to seven years of recovery. These disappeared production occupations are distinguished from sewing machine operators (51-6031) that decrease employment continuously over time. It means that sewing machine operators are likely to be a declining job whereas team assemblers and first line supervisors are replaced jobs.
A.2
Detailed Industries and Replaced Jobs
Once we point out production occupation as the disappearing jobs, industry and occupation are interchangeable without losing much information. The disappeared jobs are production occupations in digit occupations that are adjacent with a similar pattern in employment and wage space, so it conceptually corresponds to one-digit occupation.
59
Figure 18: Most Growing and Declining Occupations among over 700 detailed Occupations 13 Most Growing Detailed Occupations 5,000,000
4,500,000
Combined Food Preparation and Serving Workers, Including Fast Food (35) Personal and Home Care Aides (39)
2016 2000
2007 2009
2002
Customer Service Representatives (43)
Employment
4,000,000
3,500,000
Secretaries, Except Legal, Medical, and Executive (35) Cooks, Restaurant (35)
3,000,000
Retail Salespersons (41)
2,500,000
Waiters and Waitresses (35)
2,000,000
Laborers and Freight, Stock, and Material Movers, Hand (53) Registered Nurses (29)
1,500,000
Accountants and Auditors (13)
1,000,000
Employment, Recruitment, and Placement Specialists (13) Medical Assistants (31)
500,000
0 $0
$10
$20
$30
$40
$50
Average Hourly Wage
First-Line Supervisors/Managers of Food Preparation and Serving Workers (35) Laborers and Freight, Stock, and Material Movers, Hand (53)
12 Most Declining Detailed Occupations 2,000,000
Executive Secretaries and Administrative Assistants (43) Packers and Packagers, Hand (53)
2016 2000
2007 2009
2002
Chief Executives (11) Data Entry Keyers (43)
1,500,000
Employment
Telemarketers (41) Sewing Machine Operators (51) Word Processors and Typists (43) 1,000,000
Shipping, Receiving, and Traffic Clerks (43) Carpenters (47) Order Clerks (43) 500,000
Truck Drivers, Light Or Delivery Services (53) Computer Programmers (15)
0 $0
$10
$20
$30
$40
Average Hourly Wage
60
$50
16 Detailed Production Occupations (W pattern) 2,000,000
Team Assemblers First-Line Supervisors/Managers of Production and Operating Workers
2016 2000
2007 2002
2009
Inspectors, Testers, Sorters, Samplers, and Weighers Helpers--Production Workers
1,500,000
Employment
Machinists Cutting, Punching, and Press Machine Setters, Operators, and Tenders, Metal and Plastic Electrical and Electronic Equipment Assemblers
1,000,000
Sewing Machine Operators Computer-Controlled Machine Tool Operators, Metal and Plastic Tool and Die Makers Paper Goods Machine Setters, Operators, and Tenders
500,000
Grinding, Lapping, Polishing, and Buffing Machine Tool Setters, Operators, and Tenders, Metal and Plastic Extruding and Drawing Machine Setters, Operators, and Tenders, Metal and Plastic Woodworking Machine Setters, Operators, and Tenders, Except Sawing
0
Welders, Cutters, Solderers, and Brazers
$0
$10
$20
$30
$40
Average Hourly Wage
$50 Semiconductor Processors
manufacturing industry. Waning w-shape occupations are including team assemblers and first line supervisors. We investigate which minor industry is related with a sudden but permanent employment loss. As Figure 19 shows, there are three patterns in real output per worker: jump, business cycle and growth. Output per employee in Motor vehicles, Machinery, and Wood products industries jumped up a year later reducing employment size during the Great recession. Computer and electronic, Electrical equipment, Primary metals, and Miscellaneous manufacturing industries have a negative trend in employment whereas a positive trend in output per worker. Fabricated metal, Nonmetalic mineral, and Furniture products have a distinctive business cycle in output per worker, despite the permanently downsized employment. Appendix A has a combined scatter plots to compare each durable goods manufacturing industries. Acemoglu and Restrepo (2017) shows that industries adopted robots the most intensive are automotive, plastic and chemicals, metal products, electronics, and wood industries, in descending order. Among them, automotive and wood industries shows a jump in their output per worker after the Great Recession. Chemicals and electronics exhibits constant and rapid growth in output per worker while reducing employment. It is fair to mention that automotive industry also imported from Mexico the most intensively, and the electronics industry is the second. However, other industries that also show a higher production per labor are not related with Mexican imports.
B
Employment and Output by Industry 61
Figure 19: 3-digit Minor Industries in (Durable Goods) Manufacturing Manufacturing > Durable Goods > Motor vehicles, bodies and trailers, and transportation equipment
Manufacturing > Durable Goods > Machinery
$250,000
2,500 k
$200,000
2,000 k
$200,000
2,000 k
$150,000
1,500 k
$150,000
1,500 k
$100,000
1,000 k
$100,000
1,000 k
$50,000
$50,000
500 k
NBER Recessions
Real GDP per worker (left axis)
$0
Employment (right axis)
0k
NBER Recessions
Manufacturing > Durable Goods > Wood products $100,000
500 k
Real GDP per worker (left axis)
Employment (right axis)
Manufacturing > Nondurable Goods > Chemical products 1,000 k
$450,000
3,000 k
$400,000 2,500 k $350,000 $300,000 $50,000
2,000 k
$250,000
500 k
1,500 k $200,000
$150,000
1,000 k
$100,000 500 k $50,000 $0
0k
NBER Recessions
Real GDP per worker (left axis)
$0
Employment (right axis)
0k
NBER Recessions
Manufacturing > Durable Goods > Computer and electronic products
Real GDP per worker (left axis)
Employment (right axis)
Manufacturing > Durable Goods > Electrical equipment, appliances, and components
$300,000
3,000 k $200,000
$250,000
2,500 k $150,000
1,500 k
$200,000
2,000 k
$150,000
1,500 k $100,000
1,000 k
$100,000
1,000 k
2,000 k
$50,000 $50,000
500 k
500 k
$0
$0
0k
NBER Recessions
Real GDP per worker (left axis)
0k
NBER Recessions
Employment (right axis)
Manufacturing > Durable Goods > Primary metals
Real GDP per worker (left axis)
Employment (right axis)
Manufacturing > Durable Goods > Miscellaneous manufacturing
$200,000
2,000 k
$200,000
2,000 k
$150,000
1,500 k
$150,000
1,500 k
$100,000
1,000 k
$100,000
1,000 k
$50,000
500 k
$0
$50,000
$0
0k
NBER Recessions
Real GDP per worker (left axis)
500 k
0k
NBER Recessions
Employment (right axis)
62
Real GDP per worker (left axis)
Employment (right axis)
Manufacturing > Durable Goods > Fabricated metal products
Manufacturing > Durable Goods > Nonmetallic mineral products
$200,000
2,000 k
$150,000
1,500 k
$150,000
1,500 k
$100,000
1,000 k
$100,000
1,000 k
$50,000
$50,000
500 k
NBER Recessions
Real GDP per worker (left axis)
$0
Employment (right axis)
0k
NBER Recessions
Real GDP per worker (left axis)
Employment (right axis)
Manufacturing > Nondurable Goods > Plastics and rubber products
Manufacturing > Durable Goods > Furniture and related products $100,000
500 k
1,000 k
$150,000
3,000 k 2,500 k
$100,000
$50,000
2,000 k 1,500 k
500 k $50,000
1,000 k 500 k
$0
NBER Recessions
C
$0
0k
Real GDP per worker (left axis)
0k
NBER Recessions
Employment (right axis)
Real GDP per worker (left axis)
Employment (right axis)
Occupation
C.1
Wage hierarchy?
Figure (??) shows the wage distribution by 22 major (2-digit) occupations in 2000 and 2016. The ranking in average wage is robust over time, but dispersion within occupation is not negligible. The lowest wage worker in an occupation usually earn less than the highest wage worker in one-step lower occupation in terms of average wage. Data is favorable to the weak version of vertical sorting rather than the strict vertical sorting. As the speed of decline and growth is asymmetric, a sudden job disappearance deeply hollows out aggregate employment, drops the labor share, and accelerates unemployment rate. Both in 2001 and 2008 recessions, manufacturing and information industries reduced 12%–18% of employment, whereas health and food services sectors increased 2%–4% of employment. After a recession, the labor market has a large burden to relocate massive unemployed workers while dealing with a long-lasting shortage of job openings.
D
Industrial Wage Hierarchy • Average wage for all employees (2017 March) | Average wage for non-supervisory workers (2017 March) | Median weekly earnings for full time employees (2016) | Average weekly hours for all
63
Table 11: Job Positions in Occupation Group Employment Occupation
2000
2002
2007
2009
2016
OCC
Management
11
7,782,680
7,092,460
6,003,930
6,116,380
7,090,790
Computer and Mathematical
15
2,932,810
2,772,620
3,191,360
3,303,690
4,165,140
17, 19, 23
4,505,200
4,424,740
4,740,280
4,720,130
4,727,410
13, 29
5,657,940
5,850,750
7,271,170
7,372,050
8,434,030
25, 27
8,964,280
9,276,150
10,077,630
10,234,410
10,539,400
47
6,187,360
6,124,600
6,708,200
5,751,630
5,585,420
21, 33, 49
9,796,560
9,786,440
10,270,780
10,177,890
10,862,250
Production
51
12,400,080
10,726,670
10,146,560
8,927,130
9,105,650
Office and Administrative Support
43
22,936,140
22,754,570
23,270,810
22,336,450
22,026,080
41, 53
23,099,620
22,734,570
23,961,050
22,559,750
24,268,320
31, 37, 39, 45
10,518,710
10,806,700
11,816,650
12,037,280
13,448,170
35
9,955,060
10,067,080
11,273,850
11,218,260
12,981,720
Engineering, Science, Legal Business, Financial, Healthcare Practitioners Education, Library, Entertainment Construction and Extraction Maintenance, Installation, Social service
Sales, Transportation Healthcare, Building cleaning, Farming Food Preparation and Serving
64
Figure 20: Change in Employment and Output per Worker (1997–2016) CHANGE IN EMPLOYMENT AND OUTPUT PER WORKER: 1997 -2016 80%
Others
Edu & Health 60%
Manufacturing: Durable goods Manufacturing: Nondurable goods Prof
Information
40%
Change in Employment
Food
Construction Trsp
Finance: Finance and insurance
20%
Cons Gov
Retail
0% -60%
-40%
Fin
RE
-20%
0%
20%
Whole 40%
60%
80%
100%
120%
140%
160%
180%
200%
Info Util -20%
-40%
Nondur
-60%
Dur
Change in Real Output per Worker
CHANGE IN EMPLOYMENT AND OUTPUT PER WORKER: 2000 -2002 20%
CHANGE IN EMPLOYMENT AND OUTPUT PER WORKER: 2008 -2010 20%
Others
Others
Manufacturing: Durable goods Edu & Health
Manufacturing: Durable goods
Manufacturing: Nondurable goods
10%
Manufacturing: Nondurable goods 10%
Information
Information
Construction
-20%
Util
Cons
-10%
RE
0%
0%
Fin
Gov
Prof 10%
Trsp
Construction Edu & Health
Finance: Finance and insurance 20%
Whole
Change in Employment
Change in Employment
Food
30%
Info
Retail Nondur
-10%
-10%
Finance: Finance and insurance
Util
0% -20%
0%
Gov
10%
Trsp
Info RE
Prof
Nondur
Dur -20%
-20%
Cons
Dur
-30%
-30%
Change in Real Output per Worker
Change in Real Output per Worker
employee (2017 March) 1. Tier 1 (30 mil workers, 22% of total employment) • Information
$37.56 | $30.47 | $1,143 | 36.3 hours
. Information: NAICS 51 Employment: −1.00 mil workers (2008–11) +.13 mil (2011–17) 13% of decline in employment during the Great Recession has recovered
65
30%
Fin
Whole -10%
20%
Retail
Food
Figure 21: Employment and Real GDP per Worker in Other Group Industries Total Private Industries
Government
$250,000
124,000 k
$250,000
24,000 k
122,000 k
120,000 k
$200,000
22,000 k
$200,000
118,000 k 20,000 k
116,000 k $150,000
114,000 k
$150,000 18,000 k
112,000 k 110,000 k
$100,000
$100,000
16,000 k
108,000 k 106,000 k $50,000
$50,000
14,000 k
104,000 k 102,000 k $0
NBER Recessions
Real GDP per worker (left axis)
12,000 k
2016
2015
2014
2013
2012
2011
2010
2009
2008
2007
2006
2005
2004
2003
2002
2001
2000
1999
1998
100,000 k
1997
$0
NBER Recessions
Employment (right axis)
Education Services, Health Care, and Social Assistance $250,000
Employment (right axis)
Arts, Entertainment, Recreation, Accommodation, and Food Services 24,000 k 22,000 k
$200,000
Real GDP per worker (left axis)
$250,000
18,000 k 16,000 k
$200,000
20,000 k $150,000
14,000 k $150,000
18,000 k $100,000
12,000 k $100,000
16,000 k $50,000
14,000 k
$0
10,000 k $50,000
12,000 k
NBER Recessions
Real GDP per worker (left axis)
8,000 k
$0
Employment (right axis)
6,000 k
NBER Recessions
Real GDP per worker (left axis)
Professional and business services $250,000
Construction 22,000 k 20,000 k
$200,000
Employment (right axis)
$250,000
12,000 k
10,000 k
$200,000
8,000 k
18,000 k $150,000
$150,000
6,000 k
16,000 k $100,000
$100,000
4,000 k
14,000 k $50,000
12,000 k
NBER Recessions
Real GDP per worker (left axis)
Real GDP per worker (left axis)
2016
2015
2014
2013
2012
2011
2010
2009
2008
2007
2006
2005
2004
2003
2002
2001
2000
NBER Recessions
Employment (right axis)
Employment (right axis)
Finance: Real estate and rental and leasing
Finance: Finance and Insurace $250,000
0k
1999
$0
10,000 k
1997
$0
2,000 k
1998
$50,000
12,000 k
$1,100,000
12,000 k
$1,050,000
10,000 k
10,000 k
$200,000
$1,000,000 8,000 k
$150,000 6,000 k $100,000 4,000 k
8,000 k
$950,000 $900,000
6,000 k
$850,000
4,000 k
$800,000 2,000 k 0k
2,000 k
$750,000
NBER Recessions
Real GDP per worker (left axis)
Employment (right axis)
NBER Recessions
66
Real GDP per worker (left axis)
2016
2015
2014
2013
2012
2011
2010
2009
2008
2007
2006
2005
2004
2003
2002
2001
2000
0k
1999
$700,000
1997
$0
1998
$50,000
Employment (right axis)
TTU: Wholesale trade
TTU: Retail trade
$250,000
12,000 k 10,000 k
$200,000
$250,000
22,000 k 20,000 k
$200,000
8,000 k $150,000
18,000 k $150,000
6,000 k $100,000
16,000 k $100,000
4,000 k $50,000
2,000 k
$0
14,000 k $50,000
0k
NBER Recessions
Real GDP per worker (left axis)
12,000 k
$0
Employment (right axis)
10,000 k
NBER Recessions
Real GDP per worker (left axis)
TTU: Transportation and warehousing $250,000
$200,000
Employment (right axis)
Other Industries 12,000 k $250,000
12,000 k
10,000 k
10,000 k
$200,000
8,000 k
$150,000
8,000 k
$150,000 6,000 k
$100,000
6,000 k $100,000
4,000 k $50,000
2,000 k
$0
4,000 k $50,000
0k
NBER Recessions
Total Earnings GDP per worker
2,000 k
$0
Employment (right axis)
0k
NBER Recessions
Real GDP per worker (left axis)
Employment (right axis)
◦ Publishing Industries (except Internet): NAICS 511 $42.94 | $33.64 | $1,094 | 37.0 hours ◦ Data Processing, Hosting, and Related Services: NAICS 518 $41.02 | $32.77 | — | 37.8 hours ◦ Other Information Services: NAICS 519 $40.76 | $33.78 | — | 33.6 hours ◦ Broadcasting (except Internet): NAICS 515 $35.41 | $28.26 | $1,017 | 34.5 hours ◦ Telecommunications: NAICS 517 $32.90 | $28.41 | $1,182 | 38.3 hours ◦ Motion Picture and Sound Recording Industries: NAICS 512 $31.91 | $23.52 | $1,085 | 30.4 hours
• Financial Activities
$32.74 | $26.36 | $977 | 37.3 hours
. Finance and Insurance: NAICS 52
— | — | $1,039 | —
Employment: −.46 mil workers (2007–11) +.47 mil (2011–17) ◦ Securities, Commodity Contracts, and Other Financial Investments and Related Activities: NAICS 523
67
Figure 22: Employment and Real GDP per Worker in Manufacturing and Information 3-digit Minor Industries Information: 3-digit Minor (more than 1 million)
Durable Manufacturing: 3-digit Minor (more than 1 million) 2,500
2,500
2,000
2,000
Employment (Thousand)
Employment (Thousand)
2001 1,500
1,000
500
1,500
1997
2008
1,000
500
0 0
100,000
200,000
300,000
400,000
0
500,000
0
100,000
Real GDP (Millions of chained 2009 dollars)
200,000
300,000
400,000
500,000
Real GDP (Millions of chained 2009 dollars)
Fabricated metal products
Publishing industries, except internet (includes software)
Machinery
Broadcasting and telecommunications
Computer and electronic products Motor vehicles, bodies and trailers, and transportation equipment
Durable Manufacturing: 3-digit Minor (less than 1 million)
Information: 3-digit Minor (less than 1 million) 1,000
Employment
Employment
1,000
500
2001
500
1997
0 0
50,000
100,000
150,000
Real GDP
0
0
50,000
100,000
Real GDP
Wood products
Motion picture and sound recording industries
Nonmetallic mineral products Primary metals
Data processing, internet publishing, and other information services
Electrical equipment, appliances, and components
Furniture and related products Miscellaneous manufacturing
68
150,000
Figure 23: Robust Occupation Hierarchy in Average Wage by 22 Major Occupations $60
Average Hourly Wage
$50 $40 $30 $20 $10 $0 2000
2002
2007
2009
2016
Year (Bottom Line) Food Preparation and Serving Related Occupations Building and Grounds Cleaning and Maintenance Occupations Healthcare Support Occupations Office and Administrative Support Occupations Sales and Related Occupations Community and Social Services Occupations Construction and Extraction Occupations Arts, Design, Entertainment, Sports, and Media Occupations Business and Financial Operations Occupations Architecture and Engineering Occupations Legal Occupations
Farming, Fishing, and Forestry Occupations Personal Care and Service Occupations Transportation and Material Moving Occupations Production Occupations Protective Service Occupations Installation, Maintenance, and Repair Occupations Education, Training, and Library Occupations Life, Physical, and Social Science Occupations Healthcare Practitioners and Technical Occupations Computer and Mathematical Occupations Management Occupations (Top Line)
$49.95 | $40.24 | — | 37.4 hours ◦ Insurance Carriers and Related Activities: NAICS 524 $34.30 | $29.11 | $977 | 38.2 hours ◦ Credit Intermediation and Related Activities: NAICS 522 $30.18 | $22.77 | — | 38.1 hours ◦ Monetary Authorities - Central Bank: NAICS 521 —|—|—|— ◦ Funds, Trusts, and Other Financial Vehicles: NAICS 525 —|—|—|— . Real Estate and Rental and Leasing: NAICS 53
— | — | $827 | —
Employment: −.25 mil workers (2007–11) +.26 mil (2011–17) ◦ Real Estate: NAICS 531 $25.83 | $21.12 | — | 33.9 hours ◦ Rental and Leasing Services: NAICS 532 $24.30 | $19.89 | — | 35.2 hours ◦ Lessors of Nonfinancial Intangible Assets (except Copyrighted Works): NAICS 533 —|—|—|—
69
Figure 24: Wage Distribution by Major Occupations Wage Distribution by Occupation in 2000 $80 $70
90th percentile 75th percentile
Hourly Wage
$60 $50
50th percentile 25th percentile 10th percentile
$40 $30 $20 $10 $0
Wage Distribution by Occupation in 2016 $80 $70
90th percentile 75th percentile
Hourly Wage
$60 $50
50th percentile 25th percentile 10th percentile
$40 $30 $20 $10 $0
• Professional and Business Services
$31.57 | $25.92 | $992 | 36.0 hours
70
. Professional, Scientific, and Technical Services: NAICS 54 Employment: −0.42 mil workers (2008–10) +1.67 mil (2011–17) ◦ Professional, Scientific, and Technical Services: NAICS 541 $40.04 | $33.91 | $1,273 | 36.8 hours . Management of Companies and Enterprises: NAICS 55 Employment: −.05 mil (2008–10) +0.40 mil (2010–17) ◦ Management of Companies and Enterprises: NAICS 551 $39.11 | $27.76 | — | 38.6 hours . Administrative and Support and Waste Management and Remediation Services: NAICS 56
$20.17 | $17.84 | $613 | 33.9 hours
Employment: −1.50 mil (2008–09) +2.00 mil (2009–17) ◦ Waste Management and Remediation Services: NAICS 562 $25.67 | $22.37 | — | 40.7 hours ◦ Administrative and Support Services: NAICS 561 $19.85 | $17.60 | — | 33.5 hours
2. Tier 2a (40 mil workers, 29% of total employment ) • Federal, State, and Local Government: NAICS 99
$28.26 | — | — | —
• Education and Health Services= Educational Services: NAICS 61 + Health Care and Social Assistance: NAICS 62
$26.08 | $22.88 | $817 | 32.9 hours
3. Tier 2b (19 mil workers, 14% of total employment) • Construction
$28.55 | $26.37 | $822 | 38.7 hours
. Construction: NAICS 23 Employment: −2.30 mil workers (2007–11) +1.44 mil (2011–17) 63% of decline in employment during the Great Recession has recovered ◦ Construction of Buildings: NAICS 236 $30.65 | $25.80 | — | 37.4 hours ◦ Heavy and Civil Engineering Construction: NAICS 237 $30.22 | $28.14 | — | 42.0 hours ◦ Specialty Trade Contractors: NAICS 238 $27.57 | $26.06 | — | 37.7 hours • Manufacturing: NAICS 31-33
$26.39 | $20.70 | $857 | 40.7 hours
Employment: −2.70 mil workers (2007–10) +0.93 mil (2010–17) 35% of decline in employment during the Great Recession has recovered
71
4. Tier 3 (49 mil workers, 35% of total employment, average wage below $20 ) • Trade, Transportation, and Utilities: Wholesale Trade: NAICS 42 + Retail Trade: NAICS 44-45 + Transportation and Warehousing: NAICS 48-49 + Utilities: NAICS 22
$22.64 |
$19.22 | — | 34.3 hours • Other Services (except Public Administration): NAICS 81
$23.50 | $19.73 | $686 | 31.9
hours • Leisure and Hospitality: Arts, Entertainment, and Recreation: NAICS 71 + Accommodation and Food Services: NAICS 72
E
$15.32 | $13.24 | $528 | 26.0 hours
Trickle Down details
Manufacturing and Leisure and Hospitality industries are a good contrast. Employment size in manufacturing has declined in the most two recessions, while leisure and hospitality industry is growing overall. Figure 2 shows that the net hiring in manufacturing was negative while leisure and hospitality industry shows little changes. Manufacturing industry laid off more than 400 thousands workers in the 2008 recession, while leisure and hospitality industry does not particularly layoffs workers in the Great recession. Job openings declined during a recession as quits declined. Manufacturing sector do not open much vacancies during a recovery, so the decline in employment is associated with shortage in labor demand. Figure 5 compares the persistency in unemployment for all industries by normalizing the unemployment rate at March 2009 into zero. For all of the industries, we can see the lower average wage the sector unemployed workers worked before, the more persistent unemployment during a recovery, even though the employment fluctuations and layoffs were different by sectors.
72
Figure 25: Manufacturing (Tier 3) and Leisure and Hospitality (Tier 4): JOLTS Jobless Recovery v.s. Recovery with Jobs Employees in Manufacturing Industry 20,000 k
15,000 k
10,000 k
5,000 k
1995
1997
1999
2001
2003
2005
2007
2009
2011
2013
2015
1997
1999
2001
2003
2005
2007
2009
2011
2013
2015
2017
1993
1995
1991
1993
1989
1987
1985
1983
1981
1979
1977
1975
1973
1971
1969
1967
1965
1963
1961
1959
1957
1955
1953
1951
1949
1947
1945
1943
1941
1939
0k
Employees in Leisure and Hospitality Industry 20,000 k
15,000 k
10,000 k
5,000 k
2017
1991
1989
1987
1985
1983
1981
1979
1977
1975
1973
1971
1969
1967
1965
1963
1961
1959
1957
1955
1953
1951
1949
1947
1945
1943
1941
1939
0k
Net Hiring in Manufacturing Industry 500 k
3
400 k 2.5
300 k 200 k
2
100 k 0k
1.5 2000
2002
2004
2006
2008
2010
2012
2014
2016
-100 k 1
-200 k -300 k
0.5
-400 k -500 k
0
Net Hiring in Leisure and Hospitality Industry 500 k
2
400 k
1.8
300 k
1.6
200 k
1.4
100 k
1.2
0k
1
2000
2002
2004
2006
2008
2010
2012
2014
2016
-100 k
0.8
-200 k
0.6
-300 k
0.4
-400 k
0.2
-500 k
0
73
Figure 26: Manufacturing (Tier 3) and Leisure and Hospitality (Tier 4): JOLTS Layoffs without Job Openings v.s. No Layoffs but with Job Openings Layoffs and Discharges in Manufacturing Industry 500 k
400 k
300 k
200 k
100 k
0k
2000
2002
2004
2006
2008
2010
2012
2014
2016
2012
2014
2016
2012
2014
2016
2012
2014
2016
Layoffs and Discharges in Leisure and Hospitality Industry 500 k
400 k
300 k
200 k
100 k
0k 2000
2002
2004
2006
2008
2010
Job Openings in Manufacturing Industry 1,000 k 900 k 800 k 700 k 600 k 500 k 400 k 300 k 200 k 100 k 0k
2000
2002
2004
2006
2008
2010
Job Openings in Leisure and Hospitality Industry 1,000 k 900 k 800 k 700 k 600 k 500 k 400 k 300 k 200 k 100 k 0k 2000
2002
2004
2006
2008
2010
When we compare the unemployment level or rate, unemployed workers from the jobless sector (manufacturing) exits faster than the unemployed from lower-paying but actively hiring 74 industry (leisure and hospitality).
Figure 27: Manufacturing (Tier 3) and Leisure and Hospitality (Tier 4): JOLTS Fast Exit from Unemployment v.s. Persistent Unemployment Unemployed from Manufacturing Industry 2,500 k
2,000 k
1,500 k
1,000 k
500 k
0k 2000
2002
2004
2006
2008
2010
2012
2014
2016
Unemployed from Leisure and Hospitality Industry 2,500 k
2,000 k
1,500 k
1,000 k
500 k
0k 2000
2002
2004
2006
2008
2010
2012
2014
2016
Unemployment rate from Manufacturing and Unemployment rate from Leisure and Hospitality 16%
14%
12%
10%
8%
6%
4%
2%
0%
2000
2002 NBER Recessions
2004
2006
2008
2010
Unemployment rate from Leisure and Hospitality
75
2012
2014
2016
Unemployment rate from Manufacturing
Figure 28: Manufacturing (Tier 3) and Leisure and Hospitality (Tier 4): JOLTS Fast Exit from Unemployment v.s. Persistent Unemployment
76
F
Great Recession by Sectors Figure 29: Great Recession by Sectors
Main Shock (2008 Q4) Sectoral and Supply Shock
Great Recession Hierarchy of Industries
Tier 1 (21%) $31-37 1 Injury
Tier 2 (29%) $26-28 2 Injuries
Tier 3
Information Services Financial Activities
Year
Loss in Profits // Contribution to BC
2007-09
17% loss (- $13 bil) - 1% of GDP
2006-08
177% loss (- $243 bil) - 2.3% of GDP
Professional and Business Services
Jobless
100% more (+120 k)
30% less (-100 k)
Partially Jobless
30% more (+120 k)
31% less (-300 k)
Unemp
Fast
Unemployment Trickle-
Education and Health Services
Expansion
$21-27 8 Injuries
Manufacturing
2007-09
Tier 4
Trade, Transportation and Utilities
2007-08
$15-23 13 Injuries
Emp
30% less (-250 k)
2007-11
(35%)
Fewer Hiring
Recovery (2010-)
33% less (-30 k)
Govenment
Construction
(14%)
Additional Layoffs
Aftershock (2009) Aggregate, Demand
54% loss (- $30 bil) - 1% of GDP
60% loss (- $127 bil) - 1.9 % of GDP 25% loss (- $55 bil) - 3.6% of GDP
60% more (+200 k) 175% more (+280 k) 20% more (+ 100 k)
Leisure and Hospitality
10% less (-50 k)
Partially Jobless
25% less (-100 k)
Jobless
Stagnant
Fast
31% less (-400 k)
Unemployment Trickle-
27% less (-300 k)
Expansion
Stagnant
∗ Injury: Average number of sickness caused by work, injuries or fatality per year for an employee ∗ Loss in profit: percentage loss in profit per previous year profit (dollar amount of loss) ∗ Contribution to BC: sectoral output loss as percentage of contribution to aggregate output ∗ Additional layoffs: Spike in layoffs and discharges at 2008 comparing to 2003–2007, percentage of additional layoffs to previous layoffs (number of people) ∗ Fewer hiring: Decline in hiring at 2009–2010 comparing to 2004–2008, percentage of declined hiring to previous level (number of people) ∗ Jobless means that the employment level declined permanently after recession. Partially jobless means that the employment level have recovered but it takes 5–7 years, so we cannot tell whether the employment is recovered or economic growth has increased the employment.
77
Figure 30: Contributions to Percent Change in Real GDP by Private Industries (2005–2017) from U.S. Bureau of Economic Analysis, Industry Economic Accounts
78
Figure 31: Corporate Profits after Tax (1998–2017) from U.S. Bureau of Economic Analysis, National Economic Accounts
79
G
Outward shift in Beveridge Curve Figure 32: Outward Shift in Beveridge Curve (2000–2017): JOLTS
United States Beveridge Curve 4.0%
Nov 2016 3.5%
Vacancy Rate
3.0%
Dec 2000
2.5%
Nov 2007
Apr 2010
2.0%
Jun 2003 1.5%
1.0% 3.5%
4.0%
4.5%
5.0%
5.5%
6.0%
6.5%
7.0%
7.5%
8.0%
8.5%
9.0%
9.5%
10.0%
Unemployment Rate Dec 2000 - Jun 2003
Jul 2003 - Nov 2007
Dec 2007 - Apr 2010
80
May 2010 - Nov 2016
10.5%
H
Regression
H.1
Regression
The unemployment level from a industry k in time t evolves from the unemployment level in previous period by subtracting the outflow from unemployment and adding the inflow to unemployment. Uk,t = Uk,t−1 − Ok,t + Ik,t U is the unemployment level, O is the outflow from unemployment, I is the inflow to unemployment, k denotes the industry and t refers a year. The outflow from unemployment for workers who had worked in industry k is deduced in following equation. Ok,t = Uk,t−1 − Uk,t + Ik,t Unemployment level is observable in data, however, inflow to unemployment is not perfectly measurable. I use separation variables such as discharges and layoffs, quits, and other separation for regressions instead of inflow. I add control variables including aggregate unemployment level, aggregate job openings level, net hiring level by industry, to capture aggregate and industrial labor market tightness. Unemployment trickle down hypothesis predicts that the outflow rate after controlling tightness is decreasing in average wage in the industry. Ok,t = β0 + β1 Wk + β2 Hk,t + β3
k−1 X j=1
Hk,t + β4
K X
Hk,t + β5
X
j=k+1
Uk,t + β6
X
k
Vk,t + β7 Dt + k,t
(10)
k
W is industrial average wage rate, H is net hiring, D is discouraged and marginally attached workers in the not-in-the-labor-force and is a regression error. If β1 is significantly negative, then unemployment exit is negatively associated with average wage in industry. β2 captures how hiring in the same industry helps the unemployment exits (home advantage), β3 measures how hiring in higher-paying industries enhance the unemployment exits, and β4 refers how hiring in lower-paying industries increases job findings. Alternatively, I regress unemployment exit level to hiring in the most adjacent industries. Ok,t = β0 + β1 Wk + β2 Hk,t + β3 Hk+1,t + β4 Hk−1,t + β5
X k
H.2
Worker Transitions
Where Do Workers from Jobless Sector Find Their Next Jobs?
81
Uk,t + β6
X k
Vk,t + β7 Dt + k,t
(11)
H.3
Unemployment exit rate Uk (t + 1) = Uk (t) + Ek Uk − Uk Ek − Uk E−k + N Uk − Uk N
Uk Ek + Uk E−k = Uk (t) − Uk (t + 1) + Ek Uk + N Uk − Uk N Job finding transition for unemployed workers whose previous job is in industry k is the change in unemployment from industry k plus newly unemployed from k and net inflow from not-in-the-labor force. I assume that the net inflow from not-in-the-labor-force to unemployment is zero. Newly unemployed worker is not precisely measured, but I use proxy variable of discharges and layoffs. JFk (≡ Uk Ek + Uk E−k ) ≈ Uk (t) + Dk − Uk (t + 1)
H.4
Installation cost
Installation shadow cost of automation when the job position is occupied by a worker of type x is following. h
OJ (x, y, z)
(1 − β) p(x, y, z) − cJ (x, y) − ρU (x)
=
i
+ (βρ + δ)V (y) (1 − e−ρτ )
(12)
ρ+δ
Installation shadow cost of automation when the job position is empty is following. OV (y, z)
(13)
=
e−ρτ p(g, y, z) − cJ (g, y) − r + κV (y) J(g, y)
=
− OJ (x, y, z)
ρ+κ
(14) h
where OJ (x, y, z)
(1 − β) p(x, y, z) −
cJ (x, y)
− ρU (x)
=
i
+ (βρ + δ)V (y) (1 −
e−ρτ )
ρ+δ
e−ρτ p(g, y, z) − cJ (g, y) − r + κV (y) V (g, y)
=
ρ+κ
− OV (y, z) (15)
h
where OV (y, z)
(1 − β) p(x, y, z) −
cJ (x, y)
=
− ρU (x) ρ+δ
Opportunity cost of automation is followings.
82
i
+ (βρ + δ)V (y) (1 −
e−ρτ )
I
A Matching and Search Model
I use a matching and search model to demonstrate that a sudden and enduring decline in a particular class of employment causes a bumping chain of reallocations in the labor market. Labor income distribution in recessions is first order stochastically dominated by one of non-recession periods. Specifically, this paper extends Shimer and Smith (2000)’s model by adding automation that is a labor substitutable technology and time cost of capital adjustment. This model describes several aspects of technological job destruction we observed. First, the model gives a rationale why middle-wage jobs are more likely to adopt automation technology even if all tasks are feasible to be done by machines. Machines should be good enough and cheap enough to replace existing workers: high jobs are matched with workers because of a high quality and low jobs are matched with workers due to an inexpensive cost. Second, it provides a hypothesis why a recession accelerates the substitution of machines for existing employees. A shadow cost of retooling is low during a recession. Third, it explains why over-qualified workers are also laid off despite a high production, and find their next jobs in the upper lung. Because of an increasing outside options to worker’s type, the surplus of a match with an over-qualified (or under-qualified) worker is marginally positive. Lastly, it demonstrates the trickle down of unemployed workers and the pickier reservation level for low-type firms. When middle-wage jobs disappear through massive separations, the unemployed workers due to an industrial shock lower their reservation level and find their next jobs in a lower-paying industry. As an influx of the higher type of the counterparty is expected, the firms below the jobless sector elevate their standards for hiring, which some researchers call an upskilling effect. The bottom unemployed workers, therefore, have lower chances of getting hired until the congestion caused by the trickle down from the upper class is relieved. It results in a persistent low-wage unemployment of which some researchers claim to be a scarring effect. The model raises a possibility that the many atypical patterns in the labor market after the Great Recession are slices of a single comprehensive phenomenon from different angles. It suggests that technological unemployment and subsequent re-sorting process can be crucial to understand the declining labor share of income, negative skewness in earnings distribution, higher skill requirement for hiring, a shift in the Beveridge curve, and longer duration of bottom unemployment. In this section, I use a matching and search model to analyze labor reallocation initiated by technological job destruction. This paper use an extension of Shimer and Smith (2000) model with automation technology and time cost for capital adjustment. Firstly, the model gives a rationale why middle-wage jobs are more likely to adopt automation even if all tasks are feasible to be done by machines. Industrial robots are good enough and cheap enough to replace the middle-wage workers. High wage workers are better than the machines, whereas low wage workers are less costly than the machines. Secondly, this model provides a hypothesis why a recession accelerates the substitution of machines for existing employees. When there is time cost for capital adjustment, firms cannot produce in old way while substituting machines for workers. Because the recession is the time the shadow cost of retooling is low, more existing employee-employer matches are destructed. Thirdly, the model explains why overqualified workers are also laid off despite a high production. The higher wage of over-qualified workers
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is not worth for the job position, and the lower productivity of under-qualified workers is not attractive for the firm. The worst-matched workers are laid off and replaced by machines. Lastly, the model demonstrates the trickle down of unemployed workers and the pickier reservation level for low-type firms. I show that disappearing middle jobs causes trickle-down unemployment, which is a bumping chain in allocation of workers to jobs by stepping down a vertical occupation ladder. When middle jobs disappear abruptly but permanently, middle unemployed workers find their next jobs in the one-step lower paying occupation. They crowd out worst workers in the one-step lower lung so that bumped workers move to two-step lower paying occupation. The bumping chain is repeated from the jobless class to the bottom class. Even though middle jobs are disappearing, it is the bottom workers who lose their jobs and labor income. The wage distribution become more skewed negatively rather than hollowing out the middle. I need to mention that the quality of labor demand side is ranked by the labor productivity of a job position rather than a firm’s productivity or profitability itself. In real world, not every industry has the same labor share, therefore, the rank of productivity is not monotone to one of the labor productivity. For example, real estate and leasing industry has particularly low employment level comparing to the output production, and the rank of wages are middle despite the highest rank of production per worker. For simplicity, the contribution of labor to production is assumed to be identical across industry, but the result is identical with a particular order of jobs. In this model, labor productivity of a firm’s job opening is positively monotone to the firm’s productivity. However, what fundamentally determines the quality of job is its labor productivity. If learning process or on-the-job search is added, then the wage is not solely determined by labor productivity. However, the efficient wage to prevent worker’s quitting does not alter the extensive margin—job creation or destruction. The current version of model results the polar case of vertical sorting. If we allow worker’s skill set is a vector instead of a scalar, then even weak vertical sorting can be generated. In such extension, Becker’s sorting model and Roy’s occupation choice model will share a larger intersection. The theory part of this paper claims that a sudden and enduring decline in a particular class of employment causes a chain of reallocation in the labor market that induces unemployed workers in the jobless class or below to step down a job hierarchy, which I refer to as trickle-down unemployment. I use Pissarides’ (1985) search model by adding two-sided heterogeneity to analyze acceptance sets in the search equilibrium addressed by Shimer and Smith (2000). This approach enables me to analyze how disappearing jobs in a certain class relocate unemployed workers over time. Mortensen and Pissarides’ (1994) model has an idiosyncratic shock with identical productivity for new job openings. Productivity shock makes bottom matches dissolve rather than middle matches in a recession, and only the quantity of vacancy matters instead of the quality of vacancy in the subsequent recovery. Lise and Robin’s (2017) model is the closest to the current model as it has two-sided heterogeneity for workers and firms; it also has on-the-job search and a free entry condition. If there is an influx of middle workers in the job market in their model, the free entry condition makes firms open bottom vacancies as a jump variable. What we see in data is that the number of bottom vacancies does not jump upward, but the bottom
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vacancies become pickier so that it causes an outward shift in the Beveridge curve. Shimer and Smith (2000) focus on the core sorting allocation in a search equilibrium with the constant job finding rate.29 This model has an endogenous job finding rate, and the purpose of this study is to analyze reallocation patterns to disappearing jobs over time. Comparative statics can be done using Shimer and Smith’s algorithm, but dynamic adjustments may occur some new issues, such as algorithm path dependence (non-uniqueness) and irrational beliefs of agents. I add two-sided heterogeneity to Pissarides’ (1985) indirect search model to show why firms adopt automation to replace middle-wage workers during a recession. Two assumptions are the most essential. Firstly, an exogenous technology growth and price processes make automatic machines gets better— regarding a quality of task that it can replace the human labor—and cheaper. Secondly, firms need to spend a time to adjust capital (or production technology) instead of paying monetary costs. To replace some workers with machines, a firm needs to stop current production line, install new machines, do test runs, and educate workers who will operate the new machines. While retooling production facilities and retraining workers, the firm should give up producing goods in an original way for a certain time. The cost of adapting automation includes not only the cost of purchasing it but also a shadow cost that fluctuates over business cycles. Under the two assumptions I made above, firms have a bang-bang equilibrium. The best time of adapting automation during an expansionary period is the farthest point of time due to the continuous advent of better and cheaper machines. Whereas, the best time of retooling facilities during a recession is the closest point of time because the opportunity cost of capital adjustment is low enough. This is the reason why jobs replaced during a recession rather than other time. Employees will be laid off if and only if a machine is good enough and cheap enough to replace them. Replaced worker’s ability (or skills) should be lower than the productivity of machine, and the worker’s reservation wage must be higher than the cost of automation. Even though all tasks can be programmed ex-ante, it is natural that ex-post replaced workers are mostly middle-wage workers. High-wage workers are not replaced by machine, because the technology is not good enough to substitute them. On the other hand, low-wage workers have no incentive to be substituted by advanced technology, as hiring human labor is cheaper than using machines.
I.1
Setup
Time is continuous with discount rate ρ and agents live forever. Workers are heterogeneous in general ability of x with density H(x). Job positions (or tasks) are also heterogeneous in general productivity of y with density I(y). Productivity is not an optimal choice. Once a firm creates a job position, the labor augmented productivity is drawn randomly from distribution I0 (y). Firms pay fixed costs B > 0 29
Log supermodularity is the necessary condition for positive assortative matching, which is perfect one-to-one
matching with the same percentile of the counterparty without a single exception. However, this model does not strictly require a positive assortative matching as the core, so the log supermodularity assumption can be relaxed to supurmodularity.
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to create a job position, otherwise firms repeatedly draw and discard the productivity until they get the maximum realization. The number of workers nw is exogenous, whereas the number of job positions nj is endogenously determined by a free entry condition. Matched jobs are separated by Poisson rate of δ. A worker’s non-working benefit is b(x). A flow cost for a vacant job position is c > 0. The total factor productivity process z is ergodic, thus, agents cannot predict business cycles. The recession is the time when total factor productivity is lower than one. Production flow is denoted as zp(x, y) for a match with a worker of type x and a job position of type y in current state of z. Unemployment level is nu with distribution of unemployed workers Fu . In the same manner, vacancy level is nv with density of vacant job positions Fv . Acceptance sets are denoted as A(x, y) that indicate if searching agents are willing to form a match bilaterally when a worker x meets a firm with job position y. Only can unmatched agents search and successfully locate a random counter party with a matching function of M (nv , nu ). A feasibility condition for matching function is M (nu , nv ) ≤ min{nu , nv }. From a vacant firm’s perspective, the worker arrival rate is λF (nu , nv ) ≡ M (nu , nv )/nv . From an unemployed worker’s perspective, the job arrival rate is λW (nu , nv ) ≡ M (nu , nv )/nu .
I.2
Values and Surplus
The values of a matched job position, a vacant job position, an employed worker, and an unemployed worker are J(x, y), V (y), W (x, y) and U (x), respectively. ρ J(x, y)
=
z p(x, y) − w(x, y) + δ ( V (y) − J(x, y) )
ρ V (y)
=
−c + λF
Ex|y [J(x, y)] − V (y)
(16) ρ W (x, y)
=
w(x, y) + δ ( Ut () − W (x, y) )
ρ U (x)
=
b(x) + λW
Ey|x [W (x, y)] − U (x)
J(x, y) is the value of a job with productivity y that matched with worker whose ability is x. V (y) is the value of a unmatched job of type y. W (x, y) is the value of an employee whose type is x working at a firm with productivity y. U (x) is the value of an unemployed worker of type x. Only unemployed workers and firms with vacant job positions search in the job market. The flow cost of maintaining vacancy is constant for any job positions, which implies that the value of vacant job is increasing in productivity V 0 (y) > 0. The total surplus of a match between worker of type x and firm of type y is defined as following. S(x, y)
=
J(x, y) − V (y) + W (x, y) − U (y)
(17)
Because this paper analyzes comparative statics, the generalized Nash bargaining wage is the most simple without loss of generality when we only consider equilibrium wages.30
wN (x, y) 30
=
arg max [W (x, y) − U (x)]β [J(x, y) − V (y)]1−β w
(18)
Hall’s (2005) acyclical equilibrium wage is an alternative wage, but it gives the same results unless we analyze
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The generalized Nash bargaining satisfies two conditions.31 W (x, y) − U (x)
=
β S(x, y)
J(x, y) − V (x)
=
(1 − β) S(x, y)
After some algebra, the convenient expression for the generalized Nash bargaining wage is derived as following.32 wN (x, y)
β ( z p(x, y) − ρV (y) ) + (1 − β) ρU (x)
=
(19)
Now, we plug in Nash bargaining wage equation (19) into the value functions in equations (16). (ρ + δ) J(x, y)
=
(1 − β) (z p(x, y) − ρU (x)) + (βρ + δ)V (y)
(ρ + λF ) V (y)
=
−c + λF Ex|y [J(x, y)]
(ρ + δ) W (x, y)
=
β (z p(x, y) − ρV (y)) + ((1 − β)ρ + δ)U (x)
(ρ + λW ) U (x)
=
b(x) + λW Ey|x [W (x, y)]
(20)
dynamics. A rigid equilibrium wage is denoted as wR , which stays constant unless Pareto improvement by wage renegotiation is possible. Whenever employer-employee match negotiate the wage including the first wage, the wage is determined by generalized Nash Bargaining.
w˙ R t (x, y)
=
R I{[Jt (x, y) − Vt (y)][Wt (x, y) − Ut (x)] ≤ 0} wN t (x, y) − w t (x, y)
(3.a)
The second alternative equilibrium rigid wage is the wage of which adjustment is minimal so that the contract simply prevents negative surplus share for either party as long as the total match surplus is positive. M M w˙ M t (x, y) = I{Jt (x, y) ≤ Vt (y)} z p(x, y) − ρVt (y) − w t (x, y) + I{Wt (x, y) ≤ Ut (x)]} ρ Ut (x) − w t (x, y)
(3.b) 31
Plug in the generalized Nash bargaining wage into the equations (16). Multiply time discount rate ρ to the
equation (17) and substitutes four values. ρS(x, y)
=
z p(x, y) + c − b(x) − λF (1 − β)Ex|y [S(x, y)] − λW βEy|x [S(x, y)]
The surplus is a function of parameters and matching rate and expected gains when agents find an alternative counterparty after separation. A stationary acceptance set is used to calculate the conditional expectation terms. 32 To derive a wage as a function of outside options, we need two expression for a fraction of surplus. Firstly, we subtract ρV from the first line in equations (16) and replace J − V as a bargaining share of surplus. ρ(1 − β)S(x, y)
=
p(x, y, z) − cJ (x, y) − wN (x, y) − δ(1 − β)S(x, y) − ρV (y)
(5.a)
Secondly, we plug two values of matched agents J and W from equations (16) into the surplus equation (17), then multiply ρ(1 − β) for both hand sides. ρ(1 − β)S(x, y)
=
(1 − β) p(x, y, z) − cJ (x, y) − δS(x, y) − ρV (y) − ρU (x)
(5.b)
Equating the right hand sides of (5.a) and (5.b), the generalized Nash bargaining wage is solved as equation (19).
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The value of a filled job, and an employed worker are easily calculated as we know the outside values. The formula for value of an unfilled vacancy, and an unemployed worker are derived as following. ρ V (y)
=
(ρ + δ) (−c) + λF (1 − β) Ex|y [ z p(x, y) − ρU (x) ] ρ + δ + λF (1 − β) (21)
ρ U (x)
=
(ρ + δ) b(x) +
λW
β Ey|x [ z p(x, y) − ρV (y) ] ρ + δ + λW β
The value of a searching agent is the weighted average between net benefit when they do not form a match and expected net production when they form a match given the counter party’s outside option.
I.3
Stationary Equilibrium
I use Shimer and Smith’s (2000) definition of steady-state search equilibrium with two-sided heterogeneity. As the algorithm for finding the equilibrium is the same, I simply explain the notations in this paper. V (y) and U (x) are the unmatched values, Fu (x) and Fv (y) are the density for searching agents, and A(x, y) is a match indicator function that represents acceptance sets that is binary decision who is willing to be matched with whom bilaterally. Firstly, unmatched values solve the following equations given acceptance sets and distribution of vacancies and unemployed workers. −(ρ + δ) c + (1 − β)λF A(x, y) [ z p(x, y) − ρU (x) ] dFu (x) ρ (ρ + δ + (1 − β)λF ) R
V (y)
=
(22) U (x)
=
(ρ + δ) b(x) + βλW
R
A(x, y) [ z p(x, y) − ρV (y) ] dFv (y) ρ (ρ + δ + βλW )
Secondly, the acceptance set satisfies the optimality condition as following. A(x, y) = I{ (ρ + δ) S(x, y) ≥ 0 } = I { z p(x, y) − ρ V (y) − ρ U (x) ≥ 0 }
(23)
Thirdly, density functions satisfy the steady-state condition for distribution of searching agent given acceptance sets. δ(h(x) − fu (x)) = λW fu (x)
Z
A(x, y)fv (y)dy
(24)
The stationary equilibrium is a set of { V (y), U (x), Fu (x), Fv (y), A(x, y) } for any x and y that satisfies equations (22)–(24).
I.4
Free entry condition
Free entry condition in this model does not imply zero value of vacant job position. Instead, the value of empty job position is non-negative and increasing in its productivity: V (y) ≥ 0 and V 0 (y) > 0. There are two reasons why I do not impose the condition in this paper. When firms can freely choose the level of productivity, the reason why a firm ever choose low productivity is the lower vacancy
88
maintaining cost. A specification of recruiting cost maps to the distribution of the job openings, under the free entry condition, cV (p) 7→ Fv (p). Even using the free entry condition, the initial distribution of job positions is still arbitrary. Secondly, if the free entry condition holds, then the firm’s pickiness (or reservation threshold) gets very simple. What matters for the vacant firm is whether the worker who it encounters can jointly produce more than the worker’s unemployment benefit. The firm’s reservation decision is about viability whether the joint net product is positive or not. On the other hand, if the productivity of job position is a random draw instead of what a firm can choose, then the firm strategically rejects to hire a mediocre worker who can marginally produce more than his unemployment benefit when he works in the position. Since a higher-productive job opening is more valuable asset to the firm, V (y) ≥ 0 and
dV (y) dy
> 0, the firm that intends to fill up the high productive position prefers to
search longer instead of hiring a marginally qualified but not excellent worker. The firm’s reservation decision in this paper is whether the surplus is positive or not with positive outside options. When firms can choose any productivity type of y, then free entry condition implies zero value of vacancy, Vt (p) = 0 for any y. There are two reasons why I do not impose the condition in this paper. When firms can freely choose the level of productivity, the reason why a firm ever choose low productivity is the lower vacancy maintaining cost. A specification of recruiting cost maps to the distribution of the job openings, under the free entry condition, cV (y) 7→ Fv (y). Even using the free entry condition, the initial distribution of job positions is still arbitrary. Secondly, if the free entry condition holds, then the firm’s pickiness (or reservation threshold) gets very simple. What matters for the vacant firm is whether the worker who it encounters can jointly produce more than the worker’s unemployment benefit. The firm’s reservation decision is about viability whether the joint net product is positive or not. On the other hand, if the productivity of job position is a random draw instead of what a firm can choose, then the firm strategically rejects to hire a mediocre worker who can marginally produce more than his unemployment benefit when he works in the position. Since a higher-productive job opening is more valuable asset to the firm, V (y) ≥ 0 and
dV (y) dy
> 0, the firm that intends to fill up the high productive
position prefers to search longer instead of hiring a marginally qualified but not excellent worker. The firm’s reservation decision in this paper is whether the surplus is positive or not with positive outside options.
I.5
Automation Technology
I extend the baseline search model to have automation technology. Firms now choose to use either a human labor or an automatic machine to perform a task. As firm’s productive job position is a scarce asset, the automation technology substitutes human labor. If the job is currently done by a worker of type x, then the firm’s share of surplus is the same with
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the previous section. J(x, y)
=
p(x, y, z) − cJ (x, y) − wN (x, y) + δV (y) ρ+δ
(1 − β) p(x, y, z) − cJ (x, y) − ρU (x) =
(25) + (βρ + δ)V (y)
ρ+δ
The robot’s ability is g, it’s flow maintenance cost is r, and the risk of the machine completely broken down (or perfect deterioration) is κ. The installation of robots requires a fixed time of τ , and the firm cannot produce during the retooling period. If a firm replace an existing worker of type x by a robot, then the shadow cost is denoted as OJ (x, y, z). It counts the forgone benefits during the time period of τ with that worker would have produced in an old way. The value of producing with automatic machine instead of an incumbent worker is denoted as J(g, y).
J(r, y)
=
e−ρτ Ez p(r, y, z) − cJ (r, y) − g(r) + κV (y)
(26)
ρ+κ
The firm optimally choose whether it replaces an existing worker by a robot or not. The value of an occupied job position by a worker of type x is denoted as K(x, y). K(x, y)
=
max
{labor,robot}
{J(x, y), J(r, y)}
(27)
Firms replace existing worker of type x with an equilibrium wage of w(x, y) by a robot of ability r with a flow cost of g(r) if it is optimal to do so. J(x, y) < J(r, y)
⇔
ρ+κ p(x, y, z) − cJ (x, y) − w(x, y) + δV (y) < e−ρτ Ez p(r, y, z) − cJ (r, y) − g(r) + κV (y) ρ+δ
(28)
In the special case of κ = δ, p(x, y, z) = zp(x, y), and z is constant for any time, the automation adopted if following inequality holds.
zp(x, y) − cJ (x, y) − w(x, y) < e−ρτ zp(r, y) − cJ (r, y) − g(r)
(29)
If a job position of type y is currently not occupied, then the firm choose if it is going to search a worker or purchase a robot to fill up the position. The value of a vacancy of type y if the firm installs automatic machine is V (g, y).
V (r, y)
=
e−ρτ Ez p(r, y, z) − cJ (r, y) − g(r) + κV (y)
(30)
ρ+κ
The value of empty job position is denoted as K(y).
K(y)
=
max
{labor,robot}
90
{V (y), V (r, y)}
(31)
J
A Sorting Model
J.1
Setup
Time is discrete with a discount rate ρ. The population is given by N . Workers are different in general ability x that follows an exogenous density function of H(x). Jobs are heterogeneous in productivity y. There are K occupations indexed by k ∈ {0, 1, · · · , K}. For simplicity, jobs are assumed to be identical within an occupation but heterogeneous across occupations. The productivity in occupation k is denoted as yk , and the index of occupation are assigned by an ascending order of its productivity, y0 < y1 < · · · < yK . Occupation 0 implies the not-in-the-labor force or home production preferably. Anyone can be out-of-the marker (or work at home) of which productivity is zero, y0 = 0. Productive jobs are scarce so that the total number of jobs with positive productivity is smaller than the population, PK
k=1 γk
< N . The number of jobs for each occupations are exogenously given as a vector of γ =
(N, γ1 , γ2 , · · · γK ). Production function is p(x, y) that depends on both the worker’s ability and the job’s productivity. The specification can be any super-modular function so that the core equilibrium allocation is a Positive Assortative Matching (PAM). Production is distributed between a worker and a firm in terms of wages and profits, respectively. Wage is the over production after giving the firm a fixed profit that depends on occupation, therefore, it is increasing in worker’s ability,
∂wk (x) ∂x
> 0.
wk (x) = p(x, yk ) − Πk
(32)
As Groes, Kircher, and Manovskii (2015) explained, stationary competitive equilibrium makes entrepreneurs’ profits and worker cutoffs as constant over time. All employees who select occupation k prefer to work in occupation k instead of k-1, which gives incentive compatibility condition for occupation k. wk−1 (x) ≤ wk (x)
⇔
p(x, yk−1 ) − Πk−1 ≤ p(x, yk ) − Πk
(33)
The equality in equation (33) holds for a worker with the lowest ability in occupation k, and it is denoted as Bk . Bk = argx p(x, yk−1 ) − Πk−1 = p(x, yk ) − Πk
(34)
Workers whose ability in [Bk , Bk+1 ) would prefer to work in occupation k. The occupational labor market clears if the number of workers who select occupation k and the number of jobs in the occupation are the same. H(Bk+1 ) − H(Bk ) = γk
for k ∈ {1, 2, · · · K}
(35)
As we aggregate the market clearing conditions across occupations, the worker cutoffs can be calculated by ascending order, for k ∈ {1, 2, · · · K}. K X
γk = N − H(Bk )
i=k
Given workers occupational choices as a vector B = (B1 , · · · , Bk ), a vector of firms profits Π = (Π1 , · · · , ΠK ) is derived by applying equation (34).
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