## 6. Modeling the Change in the Labor Share: Robustness Checks III

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### Introduction and overall patterns
- Aggregate and historical patterns:
  - Since the early 2000s, the share of U.S. national income that accrues to labor has fallen by 3.5 percentage points.
  - Historically the aggregate labor share hovered near 56 percent of GDP and about 64 percent of corporate sector output.
- Cross-sectional breadth:
  - State-level decline in the labor share between 2001 and 2014 ranged from over 8 percentage points (Nebraska, Oregon, Oklahoma) to 0.2 percentage points (New Hampshire, Maine).
  - Median industry declines across states largest in information technology, manufacturing, transportation, mining, and agriculture; very small in real estate and accommodation and food services; positive in health, education, and other services.
- Distributional link:
  - Negative correlation between the Gini coefficient and the labor share.
  - Declining labor share increases overall income inequality because capital income is more concentrated at the top.

### Concepts and measurement of drivers
- Drivers studied:
  - Technological progress (routinization), globalization/international factors (offshorability, import competition, imported intermediate inputs), and labor market institutions (unionization).
- Routinization (technology):
  - Constructed from O*NET variables including “degree of automation”, “importance of repeating same tasks”, “structured versus unstructured work”, “pace determined by speed of equipment”, “spend time making repetitive motions”.
  - Composite routinization score normalized to mean zero and cross-occupation standard deviation of unity.
  - Industry/state index RTI_ist = sum_o (routinization_o * employment share w_oist) from CPS; baseline assumes occupation scores constant across states/industries/time.
- Offshorability:
  - Built from O*NET non-offshorability subcomponents (face-to-face contact and on-site job variables); score normalized and multiplied by negative one so index increases in offshorability.
  - Constructed analogously to routinization using employment weights.
- Imported intermediates:
  - Intensity = imported inputs relative to output from U.S. input-output tables for 206 NAICS industries, aggregated to 17 NAICS 2-digit industries and imputed to states by industry output shares.
- Import competition:
  - Industry competition measure aggregates imports relative to commodity production and is imputed to states by output shares.
- Unionization:
  - Measured as percentage of workers who are union members or covered by a union from CPS.
  - Since early 2000s: number of private sector employed workers who are union members dropped by 19 percent; fraction covered by collective bargaining agreements dropped by 2.4 percentage points to 7.3 percent.

### Key data patterns (industry medians across states)
- Initial (2001) exposures:
  - Routinization highest in mining; manufacturing; transportation and warehousing; accommodation and food services; utilities. Lowest in educational services; real estate, rental, and leasing; wholesale trade; professional and business services.
  - Offshorability highest in finance and insurance; professional and business services; information. Lowest in agriculture; construction; mining; transportation and warehousing.
- Changes 2001–2014:
  - Foreign inputs intensity: manufacturing highest increase, followed by agriculture, other services, and information; utilities largest drop, followed by mining and real estate.
  - Import competition: median-state increases largest in wholesale trade and agriculture; broadly constant in other services, accommodation and food services, healthcare, utilities, and construction; declined in mining.
  - Union density declined in virtually all industries, largest in information, manufacturing, and transportation and warehousing.

### Shift-share decomposition (2001–2014)
- Decomposition: total change = Within component + Between component + Residual.
- Result: 90 percent of the aggregate decline is driven by a fall in the labor share within industries/states (Within component).

### Econometric specification and principal findings
- Dependent variable: change in labor share for industry i and state s over 2001–2014.
- Regressors: levels in 2001 of routinization and offshorability; changes 2001–2014 in import competition, foreign input intensity, and unionization.
- Baseline significance and signs (specification (8) and alternates):
  - Initial Routinization: consistently negative and highly significant. Examples: -6.5578*** (0.7753), -6.9353*** (0.7792), -6.7081*** (0.7440), -6.7648*** (0.7268).
  - Unionization: positive and highly significant. Examples: 0.3525*** (0.0554), 0.3442*** (0.0560), 0.3765*** (0.0559).
  - Import Competition: negative and highly significant. Examples: -2.5927*** (0.5481), -2.8816*** (0.5487).
  - Foreign Input Intensity: negative and highly significant. Examples: -18.3826*** (5.2227), -21.0283*** (5.3520).
  - Initial Offshorability: statistically insignificant with large standard errors. Examples: 0.2834 (0.6499), 0.4692 (0.6297), 0.3071 (0.6435).
- Correlations reported:
  - Offshorability and routinization: – 0.38.
  - Import competition and foreign input usage: 0.16.
- Model fit examples: R-squared values include 0.1894, 0.2576, 0.2955, 0.3067 across specifications.

### Decomposition of the within labor share decline (2001–2014)
- Within component total ≈ 3 percentage points of the aggregate decline.
- Contributions (specification (9) of Table 3; ranges across models also reported):
  - Initial routinization: about 51 percent of the within decline ≈ 1.52 percentage points; alternative ranges reported 44 to 57 percent (1.3 to 1.7 percentage points across Table 4–6 models).
  - Foreign input usage (imported intermediates): 29 percent of the within decline; contributions reported as 0.6 to 0.9 percentage points across robustness models.
  - Import competition: 19 percent of the within decline; contributions reported as 0.5–0.6 percentage points.
  - Unionization: roughly the same magnitude as import competition (implied near 19 percent; contributions reported as 0.5–0.6 percentage points).
- International factors summary ranges:
  - Offshoring of intermediate products explains 21–33 percent of the decline across empirical models.
  - Competition from imports explains 16–21 percent of the decline across models.
- Joint contributions:
  - Across specifications, technology explains 44 to 57 percent of the within decline.
  - Global/international factors (import competition and foreign inputs) jointly explain between 41 to 51 percent.
  - Unionization ranks third quantitatively after technology and combined international factors.

### Robustness checks (models and core outcomes)
- Models overview:
  - Model 1: baseline (specification 8 of Table 3).
  - Model 2: alternative routinization/offshorability with time-varying occupation scores for 2001.
  - Model 3: adds initial capital-labor ratio (log).
  - Model 4: adds labor market deregulation index.
  - Model 5: deregulation index excluding right-to-work.
  - Model 6: combines models 2–4.
  - Model 7: variant of model 6 with alternative deregulation index.
- Robustness outcomes:
  - Initial routinization, unionization, import competition, and foreign input intensity retain expected signs and high statistical significance across specifications; magnitudes broadly similar to baseline.
  - Offshorability remains statistically insignificant in virtually all models and alternative measures.
  - Technology (routinization) retains explanatory power using alternative measures.
  - Labor market deregulation indexes do not exert a statistically significant impact on the labor share.
  - Initial capital-labor ratio enters negative and highly statistically significant, implying high substitutability between capital and labor.
- Selected robustness coefficients (examples from Table 4):
  - Initial Routinization: (1) -6.5578*** (0.7753); (2) -5.2586*** (0.8384); (5) -8.7963*** (0.8677).
  - Unionization: (1) 0.3442*** (0.0560); (6) 0.2596*** (0.0495).
  - Import Competition: (1) -2.6189*** (0.5495); (6) -2.6623*** (0.5067).
  - Foreign Input Intensity: (1) -18.4250*** (5.2287); (6) -15.6339*** (4.3837).
  - Initial Capital-Labor Ratio: (5) -0.0087*** (0.0025); (6) -0.0080*** (0.0017).
  - Observations: 599 in all models.
  - R-squared examples: (1) 0.3067; (2) 0.3342; (6) 0.3161.

### Conditioning on human capital and demographics
- Models augment baseline with education and experience measures (Tables 5 and 6).
- Main results:
  - Baseline drivers retain significance; offshorability remains imprecisely estimated.
  - Changes in labor share are positively related to changes in human capital/skills.
    - Example: specification 7 suggests industries with larger increases in average education and experience experienced less decline in labor share.
  - Alternative routinization/offshorability measures do not change core conclusions; routinization impact slightly higher, foreign input intensity slightly lower.
  - Quantitative education implication: specification 5 implies completely offsetting structural drag from routinization by education would require an increase in average schooling equivalent to about 2.5 times that observed since the early 2000s.
- Selected coefficients (Table 5 examples):
  - Initial Routinization: (1) -6.5578*** (0.7753); (7) -6.0929*** (0.7755).
  - Percent of Labor with College Degree: (6) 11.0280** (4.6339); (7) 14.1402** (5.6314).
  - Average Years of Schooling: (5) 2.8202*** (0.8224); (7) 2.2645*** (0.8422).
  - Observations: 599 in all models.
  - R-squared examples: (1) 0.3067; (5) 0.3236; (7) 0.3313.
- Table 6 (alternative routinization/offshorability) examples:
  - Initial Routinization_Alternative: (1) -8.7963*** (0.8677).
  - Foreign Input Intensity: (1) -13.3519** (5.1958).
  - Percent of Labor with College Degree: (6) 10.7825** (4.4668).
  - Observations: 599; R-squared (1) 0.3342; (5) 0.3415.

### Interpretation and links to literature
- Dominant role of technological progress (routinization) aligns with IMF 2017 and firm-level evidence in Autor et al. 2017.
- International factors (import competition and imported intermediates) play a significant but smaller role relative to technology when considered jointly.
- Unionization decline matters but quantitatively smaller relative to technology and combined international factors.
- Insignificance of offshorability index aligns with literature on polarization where offshorability often lacks significance once routinization is included.
- Findings consistent with hypothesis that technological progress may facilitate concentration of production in large “superstar” firms with higher profits and lower labor shares.

### Policy implications and research agenda
- Motivation:
  - Secular decline in the labor share since the early 2000s is strongly negatively correlated with inequality, which can weigh on investments in human and physical capital and hold back economic growth.
- Policy directions:
  - Encourage systems for continuous retooling and skill upgrading to enhance resilience of employment and productivity over time.
  - Invest in education and training programs outside traditional channels to prepare workers for technological progress and globalization challenges.
- Open research questions before policy scaling:
  - Why does growing skills premia not sufficiently encourage more education accumulation?
  - Is the issue availability/type of education (secondary vs tertiary) or barriers to borrowing to smooth education costs (implications for student loans policy or future tax supplements to repay education costs)?
  - How much more schooling could the U.S. population absorb and what would be the cost? Is the problem more quantity of schooling or quality of schooling?
  - What are the causes and consequences of de-unionization? Could de-unionization be related to globalization and external competition, or to other factors?
- Recommended research agenda:
  - Parallel development of research on effects of de-unionization and continued analysis of secular changes in the U.S. labor share.

*Source: 6. Modeling the Change in the Labor Share: Robustness Checks III (excerpt from IMF Working Paper wp17167).*

### References ________________________________________________________________24

### wp17167 - References ________________________________________________________________24

### Figures
- 1. Labor Share: Overall and Corporate Sector _____________________________________4
- 2. Labor Share by State: Change 2001–2001 ______________________________________4
- 3. Labor Share by Industry: Median Change Across States ___________________________4
- 4. U.S. Labor Share and Income Inequality: 1967–2015 _____________________________4
- 5. Labor Share Drivers by Industry: Median Across States __________________________12
- 6. Labor Share Decline: Shift-Share, 2001–14 ____________________________________13
- 7. Within Labor Share Decline: Contributions–Baseline ____________________________16
- 8. Within Labor Share Decline: Contributions I ___________________________________18
- 9. Within Labor Share Decline: Contributions II __________________________________21
- 10. Within Labor Share Decline: Contributions III  ________________________________21

### Tables
- 1. NAICS Industry Codes _____________________________________________________5
- 2. Modeling the Change in Routinization and Offshorability, 2001–14 _________________15
- 3. Modeling the Change in the Labor Share ______________________________________15
- 4. Modeling the Change in the Labor Share: Robustness Checks I ____________________18
- 5. Modeling the Change in the Labor Share: Robustness Checks II  ___________________19

*wp17167 - References ________________________________________________________________24*

### 6. Modeling the Change in the Labor Share: Robustness Checks III ___________________20

### 6. Modeling the Change in the Labor Share: Robustness Checks III

### Introduction and overall patterns
- Since the early 2000s, the share of U.S. national income that accrues to labor has fallen by 3.5 percentage points.
- Historically the aggregate labor share hovered near 56 percent of GDP and about 64 percent of corporate sector output.
- The decline is broad based across states and industries:
  - State-level decline in the labor share between 2001 and 2014 ranged from over 8 percentage points (Nebraska, Oregon, Oklahoma) to 0.2 percentage points (New Hampshire, Maine).
  - Median industry declines across states were largest in more tradable sectors: information technology, manufacturing, transportation, mining, and agriculture; very small in real estate and accommodation and food services; positive in health, education, and other services.
- There is a negative correlation between the Gini coefficient and the labor share (Figure 4).
- Declining labor share increases overall income inequality because capital income is more concentrated at the top of the distribution.

### Concepts and measurement of drivers
- The paper focuses on three leading drivers: technological progress (routinization), globalization/international factors (offshorability, import competition, imported intermediate inputs), and labor market institutions (unionization).
- Routinization (technology)
  - Constructed from O*NET variables: “degree of automation”; “importance of repeating same tasks”; “structured versus unstructured work”; “pace determined by speed of equipment”; “spend time making repetitive motions”.
  - Composite routinization score is normalized to mean zero and cross-occupation standard deviation of unity.
  - Occupations most routinizable: tire builders; telephone operators; postal service mail sorters, processors, and processing machine operators; reservation and transportation ticket agents and travel clerks; textile winding/twisting operators.
  - Occupations least routinizable: teachers; therapists; clergy; speech language pathologists; door-to-door sales workers, news and street vendors; directors of religious activities and education.
  - Industry/state index RTI_ist = sum over occupations of occupation routinization score times employment share (w_oist) from CPS. Scores assumed constant across states/industries/time in baseline; robustness checks allow time variation.
- Offshorability (international potential)
  - Built from O*NET non-offshorability subcomponents: face-to-face contact variables and on-site job variables (e.g., “face-to-face discussions”; “inspecting equipment, structures, or material”; “operating vehicles”).
  - Composite non-offshorability score normalized, multiplied by negative one so index is increasing in offshorability.
  - Most offshorable occupations: proofreaders and copy markers; mathematical science occupations; brokerage clerks; operational research analysts; interviewers (except eligibility and loan); financial analysts; actuaries; telemarketers.
  - Least offshorable occupations: emergency medical technicians and paramedics; elevator installers and repairers; firefighters; manufactured building and mobile home installers; electrical power-line installers and repairers.
  - Industry/state offshorability constructed analogously to routinization using employment weights.
- Imported intermediates (foreign input usage)
  - Intensity of foreign input usage for industry i: imported inputs relative to output, computed from U.S. input-output tables for 206 NAICS industries, aggregated into 17 NAICS 2-digit industries, and imputed to states by industry output shares.
- Import competition
  - For each industry, competition measure uses imports of commodities relative to commodity production: formula aggregates imports of commodity j (M_j) relative to gross outputs Y_ji and Y_j. Aggregated from 206 industries to 17 NAICS 2-digit industries and imputed to states by output shares.
- Unionization (institutions)
  - Measured as percentage of workers who are union members or covered by a union from CPS.
  - Since early 2000s: number of private sector employed workers who are union members dropped by 19 percent; fraction covered by collective bargaining agreements dropped by 2.4 percentage points to 7.3 percent (stated as “At 7.3 percent now”).

### Key data patterns (by industry, median across states)
- Initial routinization (2001): highest median exposure in mining; manufacturing; transportation and warehousing; accommodation and food services; utilities. Lowest in educational services; real estate, rental, and leasing; wholesale trade; professional and business services.
- Initial offshorability (2001): highest median exposure in finance and insurance; professional and business services; information. Lowest in agriculture; construction; mining; transportation and warehousing.
- Change 2001-2014 in intensity of foreign inputs: manufacturing saw the highest increase, followed by agriculture, other services, and information; utilities saw the largest drop, followed by mining and real estate.
- Change 2001-2014 in import competition: median-state increases largest in wholesale trade and agriculture; broadly constant in other services, accommodation and food services, healthcare, utilities, and construction; declined in mining.
- Change 2001-2014 in union density: unionization declined in virtually all industries, largest impacts in information, manufacturing, and transportation and warehousing.

### Shift-share decomposition (2001-2014)
- Decomposition formula: total change in aggregate labor share over 2001-2014 = Within component + Between component + Residual (with GDP shares and labor shares defined by industry i and state j).
- Result: 90 percent of the aggregate decline is driven by a fall in the labor share within industries/states (Within Industry/State component).

### Econometric analysis: specification and main regression results
- Dependent variable: change in labor share for industry i and state s over 2001-2014.
- Explanatory variables:
  - Levels in 2001 of routinization and offshorability indexes (to mitigate endogeneity from subsequent automation/offshoring).
  - Changes over 2001-2014 in import competition, intensity of foreign input usage, and unionization.
- Baseline regression highlights (Table 3; specification (8) includes all variables):
  - Coefficients of initial routinization intensity and changes in import competition, foreign input intensity of usage, and unionization have the expected signs and are statistically significant at the one percent level.
  - Initial offshorability coefficient is statistically insignificant and does not have the expected sign in baseline specifications.
  - Correlation between offshorability and routinization across industries/states: – 0.38.
  - Correlation between import competition and foreign input usage: 0.16.
- Selected coefficient values reported in the source (all entries with standard errors and significance):
  - Initial Routinization: -6.5578*** (standard error 0.7753) appears in specification (8); alternate entries include -6.9353*** (0.7792), -6.7081*** (0.7440), -6.5883*** (0.7973), -6.9874*** (0.7226), -6.4922*** (0.7427), -6.7707*** (0.7732), -6.3571*** (0.7948), -6.7648*** (0.7268).
  - Unionization: 0.3525*** (standard error 0.0554) in specification (8); alternate entries include 0.3758*** (0.0571), 0.3707*** (0.0578), 0.3839*** (0.0552), 0.3405*** (0.0569), 0.3765*** (0.0559), 0.3354*** (0.0576), 0.3442*** (0.0560).
  - Import Competition: -2.5927*** (0.5481) and alternate -2.8816*** (0.5487), -2.9231*** (0.5506), -2.6189*** (0.5495).
  - Foreign Input Intensity: -18.3826*** (5.2227) and alternate -21.0283*** (5.3520), -21.0746*** (5.3613), -18.4250*** (5.2287).
  - Initial Offshorability entries shown with large standard errors: 0.2834 (0.6499), 0.4692 (0.6297), 0.3071 (0.6435), 0.4789 (0.6269) — coefficients generally not significant.
- Model fit samples shown: example R-squared values include 0.1894, 0.2576, 0.2571, 0.2955, 0.2786, 0.2949, 0.2783, 0.3067, 0.3069 across specifications.

### Decomposition of the within labor share decline (2001-2014)
- Using specification (9) of Table 3 (retaining statistically significant variables), contributions to the within decline (3 percentage points within drop) are:
  - Initial routinization: about 51 percent of the within decline, equivalent to 1.52 percentage points out of the 3 percentage points within drop.
  - Foreign input usage (imported intermediates): 29 percent of the within decline.
  - Import competition: 19 percent of the within decline.
  - Unionization contributes roughly the same as import competition (implied near 19 percent).
- Earlier in the text: routinization intensity is reported as explaining 44 to 57 percent of the within decline since 2001 depending on empirical specification.
- International factors summary (from text): offshoring of intermediate products explains 21-33 percent and competition from imports facing domestic industry’s output and sales explains 16-21 percent of the decline (these ranges are the minimum and maximum contributions across empirical models).

### Interpretation and links to literature
- Dominant role of technological progress (routinization) is consistent with IMF 2017 and firm-level evidence in Autor et al. 2017.
- International factors (import competition and imported intermediate usage) also play a significant role, though smaller than technology when considered jointly.
- Unionization decline matters but appears quantitatively smaller relative to technology and combined international factors.
- Findings are consistent with Autor et al. 2017 hypothesis that technological progress may facilitate concentration of production in large “superstar” firms with higher profits and lower labor shares.
- Offshorability index insignificance aligns with literature on polarization (Autor and Dorn 2013; Goos, Manning, and Salomons 2011; Michaels, Natraj, and Van Reenen 2014) where offshorability often lacks significance once routinization is included.

### Robustness checks (overview)
- A battery of robustness checks were performed; key checks described include:
  - Model 1: baseline reference model (specification 8 of Table 3).
  - Model 2: replaces routinization and offshorability measures constructed with time-invariant occupation scores by alternatives where occupation scores are constructed for 2001 using the same criteria for 2014 (relaxing time-invariance).
  - Model 3: adds initial capital-labor ratio (in logarithm) to control for cross-industry differences in capital intensity.
- The paper reports that the key messages—dominant role of routinization, significant role of foreign input usage and import competition, and smaller role for unionization—continue to hold across robustness checks.

*Source: 6. Modeling the Change in the Labor Share: Robustness Checks III, excerpt from IMF Working Paper wp17167.*

### Appendix for details on the construction of this variable and others discussed below).

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_Source: https://www.imf.org/-/media/files/publications/wp/2017/wp17167.pdf_