Internet Appendix to Labor Mobility: Implications for Asset. Pricing. I. Derivation of Firm Value

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1 Internet Appendix to Labor Mobility: Implications for Asset Pricing This appendix provides proofs, an extension of the model, a discussion of the role of labor mobility in a search model, more details about the data sets used, and additional results. I. Derivation of Firm Value I omit time subscripts in what follows. Assume that there exists a traded asset that pays a continuous stream of dividends identical to the operating profits of the industry. The discounted value of a portfolio of a traded asset that continually reinvests its dividends in the asset is a martingale: 0 = ΛΠ dt + E[d(ΛV (Π ))]. (IA.1) Let V = Av(x). Applying Ito s Lemma to equation (IA.1) and simplifying leads to 0 = (1 α)x αδ 1 αδ + c0 v(x) + c 1 xv (x) + c 2 x 2 v (x), (IA.2) Citation format: Donangelo, Andres, Internet Appendix to Labor Mobility: Implications for Asset Pricing, Journal of Finance [DOI STRING]. Please note: Wiley-Blackwell is not responsible for the content or functionality of any supporting information supplied by the authors. Any queries (other than missing material) should be directed to the authors of the article. 1

2 where c 0 = r ησ A, (IA.3a) c 1 = (σ A σ G )(σ A σ G η), and (IA.3b) c 2 = (σ A σ G ) 2. (IA.3c) Equation (IA.2) has a known solution given by V = Av(x) = which simplifies to equation (15). Π αδ((c 2 c 1 )+(c 1 2c 2 )αδ)/(1 αδ) 2 c 0, II. Proof of Lemma 1 I omit time subscripts in what follows. Below, I show that, for sufficiently small σ, the assumption that the concentration of occupations increases with industry specialization, that is, dγ j d j < 0, implies that the average dispersion of occupations in the industry is increasing in labor mobility, that is, d(e[γ i]) 1 dδ > 0. From dγ j d j < 0 and from the mean value theorem for integration, we have that E[γ Γ i ] < 0, since 1 > Γ i = j 0 γ jd j/ j > γ > 0, where γ γ j j= j. From the assumption [ ] [ ] dγ j d j < 0 and the fact that d j dz = x dγ > 0, we have d j < 0, and therefore E dγ dz = E dγ d j d j dz < 0. δ 1 αδ From the definition of Γ i, we have de[γ i ] dδ dγ ] = E[ i (IA.4a) dδ [ 1 d j ] = E j dδ (γ Γ i ) (IA.4b) [ ] 1 = E δ (γ Γ α i ) + (1 αδ) 2 z(γ Γ i ) (IA.4c) = 1 δ E[γ Γ α i ] + (1 αδ) 2 E[z(γ Γ i )] (IA.4d) ( ) ( 1 = δ ασ2 ασ (1 αδ) 3 E[γ Γ 2 ) [ dγ ] i ] + (1 αδ) 2 E. (IA.4e) dz 2

3 The second equality uses the fact that the industry is small relative to the economy, so that dγ j dδ = 0, and the last equality follows from the application of Stein s Lemma. Therefore, for sufficiently ( ) small σ 2, such that 1 δ ασ2 0, we have 1 (1 αδ) 3 (E[Γ i ]) 1 δ = 1 E[Γ i ] E[Γ i ] 2 > 0. (IA.5) δ III. Investments Under Labor Mobility Here I present a simple extension of the model where firms are allowed to make lumpy investments as in Carlson, Fisher, and Giammarino (2004). The setup of the model is identical to the one without investments, except for the differences discussed below. The firms technology is now explicitly defined over capital, Y t = A t L α t K α K t, (IA.6) where K denotes the amount of physical capital employed in production and 0 < α K < 1 is the output elasticity of capital. Each firm is endowed with a single growth option. Upon exercise and payment of an investment cost of f K, the growth option doubles the firm s assets in place (from K to 2K). Optimized operating profits (Πt ) are given by α K δ Πt 1 αδ = (1 α)x t Kt, (IA.7) where X t A t x αδ 1 αδ t. Note that, similar to the case without investments, the asterisk reflects that operating profits are optimized for labor. I omit the asterisk in what follows to save notation. 3

4 Before investing, shareholders maximize firm value by deciding when to invest, ( [ T Λ s Λ s V (X t ) = max E t Π s (K)ds + Π s (2K)ds Λ ]) T f K T t Λ t T Λ t Λ t (IA.8) where T is the time of exercise of the growth option. Applying Ito s Lemma to equation (IA.8) and simplifying leads to 0 = X + rv (X) + (µ ησρ)xv (X) + σ2 2 X 2 V (X), (IA.9) subject to: (i) transversality conditions lim V b(x) = 0 X 0 lim V a(x) = 0, X 0 (IA.10a) (IA.10b) (ii) value-matching condition V b (X T ) = V a (X T ), and (IA.11) (iii) smooth-pasting condition V b (X) X = V a(x) X=XT X, X=XT (IA.12) where µ and σ are the drift and volatility of dx X, and V a and V b are the value of the firm before and 4

5 after investment. The solution is given by V t = α K δ Π t K 1 αδ r+βη 2 µ + α K δ Π t (2K) 1 αδ r+βη 2 µ 2 1 β 2 f KX β 2 t β 2 (r+βη2 µ) f K 1 α K 1 αδ β ( 2 α ) K 2 1 αδ 1 (1 α)(β 2 1) 1 β 2 if t < T, if t T, (IA.13) where β 2 is the positive root of the fundamental quadratic equation associated with the ODE in equation (IA.9) (see Dixit and Pindyck (1994) for details), and β is given in equation (16) of the published paper. Figure IA.1 illustrates the effect of endogenous investments in the model. Labor mobility affects investment decisions in two ways. The first is through scalability of cash flows. Industries with high labor mobility can grow faster without greatly affecting hourly wages. This is illustrated in Panels A, B, and C, which show that firm value increases in LM. The intuition is that investment positively affects the marginal product of labor and thus attracts mobile workers, who in turn increase the marginal product of capital and further increase output. Panel D shows that firms with more mobile labor invest sooner, that is, for lower-threshold operating profit levels. The second way is through firm risk. All else equal, firms with high LM have higher levels of cost of capital. This is illustrated in Panel E, which plots total firm beta as a function of LM. Panel F shows a nonmonotonic relation between the beta of the growth option and LM. This non-monotonic relation is driven by the fact that LM increases the risk of future assets in place while at the same time lowers the exercise threshold. 5

6 Panel A: Total Firm Value Labor Mobility HdL Labor Mobility HdL Labor Mobility HdL Beta of Growth Option Beta HTotalL Panel E: Firm Beta Labor Mobility HdL 1.0 Panel D: Exercise Threshold for Growth Option ad Panel C: Value of Growth Option Value of Growth Option Value of Assets in Place 15 Exercise Threshold HA x 1-a d L Value HTotalL 20 Panel B: Value of Assets in Place Labor Mobility HdL 1.0 Panel F: Beta of Growth Option Labor Mobility HdL 1.0 Figure IA.1. Solution of model with investment. This figure plots the solution of the model with investment. Parameter values used in the plots are TFP A = 1, relative productivity x = 1, market price of risk η = 0.2, risk-free rate r = 0.1, output elasticity of labor α = 0.5, output elasticity of capital αk = 0.25, drift of TFP growth µa = 0.05, loading of TFP growth on idiosyncratic shock σεa = 0, loading of TFP growth on systematic shock σλa = 0.3, drift of wage growth µg = 0, loading of wage growth on idiosyncratic shock συg = 0, loading of wage growth on systematic shock σλg = 0, and unit investment cost f = 1. 6

7 IV. Discussion of The Role of Labor Mobility in a Search Model Here I briefly discuss the role of labor mobility for wage dynamics in the Diamond-Mortensen- Pissarides (DMP) framework. 2 I start by discussing wage dynamics in a baseline search model with no on-the-job search (i.e., without labor mobility). I then compare the baseline case to the case with on-the-job search. I use the search model recently employed in asset pricing by Kuehn, Petrosky-Nadeau, and Zhang (2012) (KPZ) as a baseline search model without on-the-job search. The equilibrium wage equation in KPZ is given by w NM t = (1 β)z + β(px t + pcθ t ), (IA.14) where β is a worker s bargaining power (i.e., labor s weight in the Nash sharing rule), z is a worker s returns when unemployed (e.g., unemployment insurance), px t is labor productivity, pc is vacant job cost per unit of time (i.e., search cost for the firm), and θ t is number of vacant jobs over the number of job-seeking individuals (i.e., labor market tightness from the firm s point of view). 3 The superscript NM stands for No Mobility, since there is no on-the-job search and therefore no direct firm-to-firm labor flows in the KPZ model. All separations in the KPZ model are solely triggered by exogenous shocks. As a result, workers don t have a credible exit threat. Moreover, there is no interfirm mobility: only unemployed workers can search for jobs so that all labor flows are transitions between unemployment and employment. 4 In this sense, equation (IA.14) represents wages of very immobile workers. 5 I next briefly discuss the role of labor mobility in a more general DMP framework that includes on-the-job search and direct interfirm labor flows. Mortensen (1994) introduces an extension of the baseline DMP model in which workers are able to voluntarily leave their employers. In what follows, I refer to the version discussed in Pissarides (2000) with costless on-the-job search. 6 A 7

8 strictly positive cost simply implies that more employed workers optimally stop searching and effectively become immobile. Moreover, the procyclicality of the wages of workers actively engaging in on-the-job search (i.e., mobile ) is decreasing in σ. See Pissarides (2000) for details. In this extension, employed workers are able to search for better outside opportunities and switch jobs when successfully matched to a new firm. On-the-job searching is observable by the firm. When an employed worker does not search for jobs, wages are given by equation (IA.14). The wage equation for a mobile worker that conducts on-the-job search is given by 7 w M t = (1 β)z + βpx t, (IA.15) where the superscript M indicates the case with on-the-job search and mobility of workers across firms. Note that workers in this model only differ from those in the baseline model in their ability to search and directly move to different firms. Equations (IA.14) and (IA.15) show that wages of immobile workers that cannot search for other jobs while employed (w NM ) are affected by labor market tightness while those of mobile workers that actively search for jobs (w M ) are not. Wages for mobile workers (w M ) are smoother than those of immobile workers (w NM ), which is the key assumption of the labor mobility mechanism discussed in the paper. 8

9 V. Details on the BLS/OES Survey Methodology (Excerpts retrieved May 25, 2012 from ques) Although the OES survey methodology is designed to create detailed cross-sectional employment and wage estimates for the U.S., States, metropolitan and nonmetropolitan areas, across industry and by industry, it is less useful for comparisons of two or more points in time. Challenges in using OES data as a time series include changes in the occupational, industrial, and geographical classification systems, changes in the way data are collected, changes in the survey reference period, and changes in mean wage estimation methodology, as well as permanent features of the methodology. Permanent features of OES methodology: The OES methodology that allows such detailed area and industry estimates also makes it difficult to use OES data for comparisons across short time periods. In order to produce estimates for a given reference period, employment and wages are collected from establishments in six semiannual panels for three consecutive years. Every six months, a new panel of data is added, and the oldest panel is dropped, resulting in a moving average staffing pattern. The three years of employment data are benchmarked to represent the total employment for the reference period. The wages of the older data are adjusted by the Employment Cost Index. This methodology assumes that industry staffing patterns change slowly and that detailed occupational wage rates in an area change at the same rate as the national change in the ECI wage component for the occupational group. Changes in occupational classification: The OES survey used its own occupational classification system through The 1999 OES survey data provide estimates for most of the nonresidual occupations in the 2000 Standard Occupational Classification (SOC) system. The OES data provides estimates for all occupations in the 2000 SOC. The May 2010 data provides estimates for most occupations in the 2010 SOC (for more on the 2010 occupations, see below). Because of these changes, it may be difficult to compare some 9

10 occupations even if they are found in both classification systems. For example, both the old OES system and the 2000 SOC include the occupation computer programmers. However, estimates for this occupation may not be comparable over time because the 2000 SOC has several computer-related occupations that were not included in the older classification system. Workers in newly classified occupations, such as systems software engineers and applications software engineers, may have been reported as computer programmers in the past. Therefore, even occupations that appear the same in the two systems may show employment shifts due to the addition or deletion of related occupations. Changes in industrial classification: In 2002, the OES survey switched from the Standard Industrial Classification (SIC) system to the North American Industry Classification System (NAICS). As a result, there were changes in many industry definitions. Even definitions that appear similar between the two industry classifications may have differences because of the way auxiliary establishments are treated. For example, under SIC the industry grocery stores included their retail establishments, warehouses, transportation facilities, and administrative headquarters. Under NAICS, the four establishment types would be reported in separate industries. Only the retail establishments would be included in the NAICS industry for grocery stores. The change in industrial classification also resulted in changes to the occupations listed on the survey form for a given industry. In 2008, the OES survey switched to the 2007 NAICS classification system from the 2002 NAICS. The most significant revisions are in the Information Sector, particularly within the Telecommunications area. Beginning in 2010, Tennessee Valley Authority (TVA) data is included in the Federal Government estimates. 10

11 VI. Specific Vocational Preparation Levels I use Specific Vocational Preparation (SVP) levels, obtained from the Dictionary of Occupational Titles (DOT) (U.S. Department of Labor (1971, 1991)), as a proxy for occupation-specific preparation. The following description of SVP is from Appendix C of the Dictionary of Occupational Titles (U.S. Department of Labor (1991)): Specific Vocational Preparation is defined as the amount of lapsed time required by a typical worker to learn the techniques, acquire the information, and develop the facility needed for average performance in a specific job-worker situation. This training may be acquired in a school, work, military, institutional, or vocational environment. It does not include the orientation time required of a fully qualified worker to become accustomed to the special conditions of any new job. Specific vocational training includes: vocational education, apprenticeship training, in-plant training, on-the-job training, and essential experience in other jobs. Specific vocational training includes training given in any of the following circumstances: (i) vocational education (high school, commercial or shop training, technical school, art school, and that part of college training which is organized around a specific vocational objective), (ii) apprenticeship training (for apprenticeable jobs only), (iii) in-plant training (organized classroom study provided by an employer), (iv) on-the-job training (serving as learner or trainee on the job under the instruction of a qualified worker), and (v) essential experience in other jobs (serving in less responsible jobs, which lead to the higher-grade job, or serving in other jobs which qualify). The following is an explanation of the various levels of specific vocational preparation: 1. Short demonstration only 2. Anything beyond short demonstration up to and including 1 month 3. Over 1 month up to and including 3 months 11

12 4. Over 3 months up to and including 6 months 5. Over 6 months up to and including 1 year 6. Over 1 year up to and including 2 years 7. Over 2 years up to and including 4 years 8. Over 4 years up to and including 10 years 9. Over 10 years Note: The levels of this scale are mutually exclusive and do not overlap. 12

13 VII. Industry Definitions Used in the KLEMS Data Set 13

14 Table IA.I Industry Definitions from the KLEMS Data Set from the Multifactor Productivity Program, Bureau of Labor Statistics, Used in the Measure of Operating Leverage 14 Industry Title NAICS Codes Industry Title NAICS Codes Forestry, Fishing, and Related Activities Transit and Ground Passenger Transportation 485 Oil and Gas Extraction 211 Pipeline Transportation 486 Mining, except Oil and Gas 212 Other Transportation and Support Activities 487,488,492 Support Activities for Mining 213 Warehousing and Storage 493 Utilities 22 Publishing Industries 511,516 Construction 23 Motion Picture and Sound Recording Industries 512 Food and Beverage and Tobacco Products 311,312 Broadcasting and Telecommunications 515,517 Textile Mills and Textile Product Mills 313,314 Information and Data Processing Services 518,519 Apparel and Leather and Applied Products 315,316 Federal Reserve Banks, Credit Intermediation, and Related Act. 521,522 Paper Products 322 Securities, Commodity Contracts, and Investments 523 Printing and Related Support Activities 323 Insurance Carriers and Related Activities 524 Petroleum and Coal Products 324 Funds, Trusts, and Other Financial Vehicles 525 Chemical Products 325 Real Estate 531 Plastics and Rubber Products 326 Rental and Leasing Services and Lessors of Intangible Assets 532,533 Wood Products 321 Legal Services 5411 Nonmetallic Mineral Products 327 Computer Systems Design and Related Services 5415 Primary Metal Products 331 Miscellaneous Professional, Scientific, and Technical Services , Fabricated Metal Products 332 Management of Companies and Enterprises 55 Machinery 333 Administrative and Support Services 561 Computer and Electronic Products 334 Waste Management and Remediation Services 562 Electrical Equipment, Appliances, and Components 335 Educational Services 61 Transportation Equipment 336 Ambulatory Health Care Services 621 Furniture and Related Products 337 Hospitals and Nursing and Residential Care Facilities 622,623 Miscellaneous Manufacturing 339 Social Assistance 624 Wholesale Trade 42 Performing Arts, Spectator Sports, Museums, and Related Act. 711,712 Retail Trade 44,45 Amusements, Gambling, and Recreation Industries 713 Air Transportation 481 Accommodation 721 Rail Transportation 482 Food Services and Drinking Places 722 Water Transportation 483 Other Services, except Government 81 Truck Transportation 484

15 VIII. LM Measure and Ex-Post Mobility This section presents evidence that supports the validity of the occupation-level measure of concentration, CONC. This measure, which is the fundamental building block of the industrylevel measure LM, is designed to capture workers inflexibility to move across industries. We should therefore expect to observe relatively less significant flows of workers in high-conc, that is, low-mobility, occupations in response to industry shocks than of workers in low-conc, that is, high-mobility, occupations. I test this prediction using the following panel data regressions: OIEG i, j,t = λ 0,i, j,t + λ 1 TFPG i,t + λ 2 TFPG i,t CONC j,t + λ 3 CONC j,t + λ k control k, j,t + ε i, j,t, k>3 (IA.16) where λ 0,i, j,t denotes industry, occupation, and year fixed effects, OIEG i, j,t is the percentage growth in employment in the occupation-industry cluster (emp i, j ) from years t 1 to t, from the OES/BLS data set, TFPG i,t is the percentage growth of total factor productivity that proxies for industry shocks, from the Capital, Labor, Energy, Materials, and Services (KLEMS) data set provided by BLS, and {control k, j,t } k>3 is a vector of occupation-level controls, from the OES/BLS data set. Education and Wages are dummy variables for occupations with above-median levels of the minimum required years of formal education and above-median wages in that year, respectively. 8 As discussed in the paper and in this appendix, the OES/BLS data set on employment per occupation and industry is not ideal for time-series analyses. In particular, a number of occupations have employment oscillating around zero over the sample period, leading to extreme percentage changes that are unlikely to reflect true employment flows. To minimize the influence of outliers, OIEG is Winsorized at the 5% level (that is, the bottom and top 2.5% of the distribution) each year. Table IA.II reports the regression results. The table reports a negative sign on the coefficient λ 2 in regression (IA.16). This result is consistent with the hypothesis that high-conc (i.e., lowmobility) workers respond less to industry shocks than low-conc workers. Models III to V of 15

16 the table show that this result is robust to controlling for alternative occupation characteristics that could also affect workers responsiveness to shocks. 16

17 Table IA.II Panel Data Regressions of Employment Growth per Occupation-Industry Group on Industry TFP Growth The table shows estimates and standard errors of panel data regressions of employment growth per occupation-industry cluster on lagged industry total factor productivity growth (TFPG), interindustry occupation concentration (Concentration), and occupation-level controls. Education is a dummy for occupations with high levels of specific preparation, from survey-based measures from the Occupational Information Network (O*Net). Wage is a dummy for occupation-industry clusters with high wages relative to average wages in the economy. All employment and wage data are from the Bureau of Labor Statistics. Standard errors are clustered by occupation. Significance levels are denoted by * = 10% level, ** = 5% level, and *** = 1% level. The sample covers the period 1990 to I II III IV V TFPG (2.62) (3.66) (5.37) (3.85) (4.66) TFPG x Concentration (21.84) (22.48) (22.55) (23.28) Concentration (15.79) (15.83) (15.90) (15.95) TFPG x Education (4.82) (4.84) Education (1.20) (1.20) TFPG x Wage (6.68) (6.59) Wage (0.30) (0.30) Fixed Effects Year Y Y Y Y Y Occupation Y Y Y Y Y Industry Y Y Y Y Y Adj. R 2 (%) Observations 165, , , , ,812 17

18 IX. LM and Job Turnover This section discusses the relation between labor mobility and voluntary turnover. Turnover, voluntary or otherwise, is generally defined as the ex-post rate at which workers enter and exit firms. Turnover has three main components: flows of workers in and out of employment, flows of workers across firms in the same industry, and flows of workers across firms in different industries. When defined as in this paper, labor mobility is only related to the third component of turnover. Although related, labor mobility and interindustry labor flows are fundamentally different: whereas labor mobility captures the ex-ante flexibility of workers to move, interindustry labor flows are the ex-post movement enabled by this flexibility. Although outside the scope of my model, it is not unreasonable to expect that a greater fraction of separations in mobile industries should be worker initiated (quits) and not firm initiated (other separations). 9 To investigate this conjecture, I use the Job Openings and Labor Turnover Survey (JOLTS/BLS) data set. The data set has some limitations for this type of analysis, which I list below: 1. The JOLTS/BLS data set does not track the origin/destination (i.e., unemployment or employment inside or outside the industry) of hires/separations in the industry. 2. The JOLTS/BLS is very coarse and only covers broad sectors. In particular, there are only 16 unique nongovernment sectors available (vs. around 290 industries used in the paper). 3. The JOLTS/BLS only covers a relatively short sample period (2000 to 2011). Table IA.III shows that separation and hire rates are not significantly related to LM. This is not surprising given that 1) interindustry flows are just one of the three main turnover components (as discussed above) and 2) turnover is affected by ex-post shocks to firms and/or industries. In line with the prediction, the table also shows that quit rates are positively related to LM, although separation rates and hire rates are not significantly related. 18

19 Table IA.III Panel Data Regressions of Measures of Job Turnover on Labor Mobility The table reports estimates of panel data regressions with year fixed effects of measures of job turnover on lagged labor mobility and lagged industry-average characteristics. Quit Rate, Hire Rate, and Separation Rate are from JOLTS/BLS. Standard errors are clustered by industry. Significance levels are denoted by * = 10% level, ** = 5% level, and *** = 1% level. The sample covers the period 2001 to Quit Rate t Separation Rate t Hire Rate t I II III I II III I II III Mobility t (0.07) (0.13) (0.16) (0.32) (0.16) (0.30) Union t (0.09) (0.11) (0.31) (0.30) (0.30) (0.30) Lab. Int. t (0.02) (0.03) (0.19) (0.19) (0.19) (0.20) Education t (0.03) (0.02) (0.08) (0.07) (0.08) (0.08) Leverage t (0.19) (0.22) (0.73) (0.75) (0.71) (0.73) Year Eff. Y Y Y Y Y Y Y Y Y Adj. R 2 (%) Obs

20 X. Additional Results Table IA.IV presents returns of portfolios of firms sorted on the measure of operating leverage. The high operating leverage portfolio experienced higher asset returns than the low operating leverage portfolio during the sample period. The statistical and economic significance of the returns of the operating leverage portfolio H-L are lower than those of the LM portfolio H-L. This result might seem counterintuitive at first, given that the model suggests that LM indirectly affects returns through its effect on operating leverage. A possible reason for this finding is that the operating leverage measure is based on KLEMS/BLS data that have a coarser industry partition than that of the BLS/OES data used to construct the LM measure (59 industries in the KLEMS data set vs. 290 in the OES data set). Another possible explanation is that the estimate of TFP used in the operating leverage measure is noisier than that of the distribution of workers across occupations and industries used in the LM measure. Table IA.V reports asset pricing tests of the unconditional versions of the Fama and French (1993) three-factor model and Carhart (1997) four-factor model using five portfolios of stocks sorted on labor mobility. Regressions in the test are corrected for nonsynchronous trading following the methodology described in Lewellen and Nagel (2006). Returns are at a monthly frequency. The table shows that these models are not able to explain the higher returns of the high-lm portfolio. Table IA.VI investigates the relation between LM and conditional ex-post risk factor betas with the following panel data regressions: β f,t,t+5 = λ 0,t + λ 1 LM f,t 1 + λ k control k, f,t 1 + ε f,t, k>2 (IA.17) where λ 0,t denotes year fixed effects, {control k, f,t } k [3,8] are firm-level controls, and β f,t,t+5 are conditional betas defined as the slopes of 60-month rolling regressions of excess stock returns 20

21 between years t and t +5 on returns of the risk factor mimicking portfolio. Panel A of Table IA.VI reports that λ 1 > 0, consistent with the model s predictions. The table provides evidence that LM and conditional CAPM betas are positively related, and that this relation is not explained by other firm characteristics. Panel B of Table IA.VI documents the relation between unconditional risk factor betas and LM from the following panel data regressions: (β f,t,t+5 ) p = λ 0 + λ 1 LM f,p + λ k (control k, f,p ) + ε f, k>2 (IA.18) where (β f,t,t+5 ) p is the time-series mean of the conditional beta β f,t,t+5 over the period p, LM f,p is the time-series mean of LM for firm f in period p, and (control k, f,p ) is the time-series mean of the characteristic k over period p. Table IA.VII repeats the exercise in Table IX of the main text for portfolios sorted on market capitalization, that is, size. The table shows that the unconditional CAPM fails to price valueweighted stocks, while the conditional CAPM does not. Both versions of the model fail to price equally weighted portfolios during this period. Table IA.VIII reports asset pricing tests of a two factor model on portfolios of stocks sorted on LM. The factors are the excess returns of the market portfolio and the spread of the H-L LM portfolio. The modest statistical significance on the LM betas of portfolios 2 and 4 might be interpreted as evidence for a weak factor structure for these portfolios. This result is consistent with the mechanism of labor mobility as a source of a labor-induced form of operating leverage. Table IA.IX extends the results reported in Table IA.VIII for portfolios sorted on different characteristics that generate cross-sectional differences in returns. The characteristics are the O-score from Ohlson (1980), distress measure from Campbell, Hilscher, and Szilagyi (2008), organization capital from Esifeldt and Papanikolaou (2013), accruals from Dechow and Ge (2006) and Hirshleifer et al. (2004), short-term stock returns from Jegadeesh and Titman (1993), unexpected earn- 21

22 ings from Chen, Novy-Marx, and Zhang (2010), net stock issues from Fama and French (2008), book-to-market ratios, and market capitalization. Table IA.X provides results of portfolio sorts for two alternative measures of LM. The first alternative measure is based on the underlying idea of this paper: what drives the LM spread is the risk of losing workers in bad times. The measure is defined as the average elasticity of employment to negative industry shocks of workers in the industry. This measure leads to results that are very similar to other results reported in the paper. The second alternative measure is the average wage level in the industry. This measure is based on the documented fact that employment in high-wage industries is more elastic and procyclical than that of low-wage industries (Vroman (1977) and McLaughlin and Bils (2001)). This measure does not proxy for LM directly, but instead predicts which industries will face outflows of labor in bad times. Wages generate a significant difference in cross-sectional returns for equally weighted adjusted returns, but not for other portfolios. A possible reason for the low significance is that wage data are only available after 1997 at a finer industry partition. Table IA.XI reports one- and nine-year transition matrices of industries across LM quintile portfolios (nine years is the longest period for this analysis, given that industry codes changed in 2002 from SIC to NAICS). The estimated probabilities of a quintile change in one and nine years is around 12% and 39%, respectively. These estimates possibly underestimate the probability of a transition given the survey methodology employed by BLS discussed above. Although the measure of LM is not very persistent, as reported in Table IA.XI, Tables IA.XII and IA.XIII report a positive effect of LM on the extended the sample from 1965 to 2011, when the measure for 1990 is repeated for 1965 to Table IA.XII shows results for panel data regressions and Table IA.XIII for portfolio sorts. Note that the analysis with panel data regressions uses all available data, while portfolio sorts only use 40% of the sample (firms from the two extreme LM quintile portfolios), which could explain the greater significance of the former. 22

23 Table IA.XIV shows that the results of Table VIII are robust to controlling for the measure of organizational capital, constructed as in Esifeldt and Papanikolaou (2013). Tables IA.XV and IA.XVI provide a breakdown of the composition of labor expenses across portfolios sorted on LM and OC. 23

24 Table IA.IV Cross-Section of Returns of Stocks Sorted on Operating Leverage The table reports post-ranking mean realized excess monthly stock returns over one-month Treasury bill rates, and adjusted monthly returns of portfolios of stocks sorted on operating leverage. Operating leverage is defined as the slope of a time-series regression of payments to a unit of capital growth on TFP growth, using data from the KLEMS data set from the Multifactor Productivity Program of the Bureau of Labor Statistics. Excess are returns minus the one-month Treasury bill and Unlevered are estimated as excess stock returns times one minus the lagged leverage ratio (measured using the book value of debt and market value of equity). Raw are unadjusted excess returns and Adj are returns adjusted for size, book-to-market, and momentum, according to the methodology in Daniel et al. (1997). H-L is the zero investment portfolio long stocks of industries with high operating leverage (H) and short stocks of industries with low operating leverage (L). Newey-West standard errors are estimated with one lag. Significance levels are denoted by * = 10% level, ** = 5% level, and *** = 1% level. The sample covers the period 1989 to Value Weighted Equally Weighted Excess Unlevered Excess Unlevered Portfolio Raw Adj. Raw Adj. Raw Adj. Raw Adj. L H H-L (0.22) (0.18) (0.19) (0.15) (0.14) (0.12) (0.12) (0.09) 24

25 Table IA.V Standard Asset Pricing Tests of Portfolios Sorted on Labor Mobility (VW Portfolios) Portfolios Sorted on Labor Mobility L H H L FF 3-factor Alpha (%) (0.11) (0.16) (0.12) (0.13) (0.15) (0.19) MKT Beta (0.03) (0.05) (0.03) (0.03) (0.04) (0.05) SMB Beta (0.06) (0.06) (0.06) (0.05) (0.07) (0.08) HML Beta (0.05) (0.07) (0.06) (0.06) (0.09) (0.10) R 2 (%) GRS F 3.21 p-val (%) 0.79 Cahart Alpha (%) (0.11) (0.17) (0.12) (0.14) (0.15) (0.19) MKT Beta (0.04) (0.04) (0.03) (0.04) (0.04) (0.05) SMB Beta (0.05) (0.06) (0.07) (0.04) (0.07) (0.08) HML Beta (0.05) (0.07) (0.05) (0.06) (0.09) (0.10) UMD Beta (0.03) (0.07) (0.06) (0.03) (0.05) (0.06) R 2 (%) GRS F 3.38 p-val (%)

26 Table IA.V Standard Asset Pricing Tests of Portfolios Sorted on Labor Mobility (EW Portfolios) Portfolios Sorted on Labor Mobility L H H L FF 3-factor Alpha (%) (0.14) (0.18) (0.19) (0.13) (0.16) (0.18) MKT Beta (0.05) (0.05) (0.05) (0.05) (0.04) (0.04) SMB Beta (0.08) (0.08) (0.11) (0.07) (0.11) (0.06) HML Beta (0.07) (0.10) (0.09) (0.06) (0.09) (0.09) R 2 (%) GRS F 4.93 p-val (%) 0.02 Cahart Alpha (%) (0.14) (0.19) (0.17) (0.13) (0.16) (0.17) MKT Beta (0.04) (0.05) (0.04) (0.04) (0.04) (0.03) SMB Beta (0.06) (0.07) (0.08) (0.08) (0.10) (0.06) HML Beta (0.06) (0.09) (0.07) (0.05) (0.09) (0.08) UMD Beta (0.05) (0.09) (0.05) (0.04) (0.04) (0.05) R 2 (%) GRS F 4.85 p-val (%)

27 Table IA.VI Panel Data Regressions of Risk Factor Betas on Labor Mobility and Controls The table shows estimates and standard errors of panel data regressions with year fixed effects of risk factor betas on lagged LM and firm controls. MKT, SMB, HML, and UMD are the market, size, value, and momentum risk factors described in Fama and French (1993) and Carhart (1997). The dependent variables in Panel A are ex-post conditional betas defined as the slopes of 60- month rolling regressions. The dependent variables in Panel B are time-series averages over the full sample period. Standard errors are clustered by industry. Significance levels are denoted by * = 10% level, ** = 5% level, and *** = 1% level. The samples cover the period 1991 to Dep. Var. MKT SMB HML UMD Panel A: Conditional Betas Mobility (0.11) (0.12) (0.14) (0.15) (0.14) (0.15) (0.09) (0.09) Log Size (0.06) (0.07) (0.07) (0.05) Log B/M (0.12) (0.14) (0.14) (0.09) Year Eff. Y Y Y Y Y Y Y Y Adj. R 2 (%) Obs. 38,563 38,563 38,563 38,563 38,563 38,563 38,563 38,563 Panel B: Unconditional Betas Mobility (0.04) (0.04) (0.05) (0.09) (0.04) (0.04) (0.02) (0.02) Log Size (0.02) (0.03) (0.02) (0.01) Log B/M (0.04) (0.06) (0.04) (0.02) Time Eff. Y Y Y Y Y Y Y Y Adj. R 2 (%) Obs. 9,053 9,053 9,053 9,053 9,053 9,053 9,053 9,053 27

28 Table IA.VII Asset Pricing Tests (Sorts on Size) This table reports asset pricing tests of the CAPM using five portfolios of stocks sorted on market capitalization. The table reports the intercept (monthly alpha) of time-series regressions of excess portfolio returns on the excess market returns. Newey-West standard errors are estimated with one lag. Significance levels are denoted by * = 10% level, ** = 5% level, and *** = 1% level. The sample covers the period 1991 to Value-Weighted Portfolios Equally-Weighted Portfolios L H H-L L H H-L E[R] r f (%) (0.50) (0.48) (0.45) (0.40) (0.29) (0.37) (0.51) (0.48) (0.45) (0.41) (0.34) (0.35) Panel A: Unconditional CAPM Alpha (%) (0.30) (0.26) (0.22) (0.18) (0.06) (0.31) (0.33) (0.26) (0.23) (0.18) (0.10) (0.32) MKT Beta (0.09) (0.08) (0.07) (0.05) (0.02) (0.09) (0.10) (0.08) (0.07) (0.05) (0.03) (0.10) R 2 (%) Panel B: Conditional CAPM Avg. Alpha (%) (0.45) (0.35) (0.39) (0.36) (0.06) (0.44) (0.46) (0.36) (0.38) (0.36) (0.20) (0.37) Avg. MKT Beta (0.16) (0.14) (0.12) (0.11) (0.03) (0.17) (0.16) (0.14) (0.12) (0.11) (0.06) (0.16) Avg. R 2 (%)

29 Table IA.VIII Additional Asset Pricing Tests of Portfolios Sorted on Labor Mobility Portfolios Sorted on Labor Mobility L H H L MKT + LM Alpha (%) (0.10) (0.17) (0.13) (0.15) (0.12) (0.09) MKT Beta (0.03) (0.06) (0.04) (0.04) (0.04) (0.03) LM Beta (0.04) (0.08) (0.07) (0.05) (0.07) (0.05) R 2 (%) GRS F 1.57 p-val (%)

30 Table IA.IX Asset Pricing Tests with Labor Mobility 30 Portfolios Sorted on O-Score from Ohlson (1980) L H H L E[R] r f (%) (0.34) (0.32) (0.31) (0.31) (0.28) (0.29) (0.29) (0.32) (0.30) (0.41) (0.28) Obs CAPM Alpha (%) (0.16) (0.11) (0.10) (0.12) (0.09) (0.13) (0.14) (0.15) (0.16) (0.17) (0.28) MKT Beta (0.05) (0.02) (0.04) (0.04) (0.03) (0.04) (0.05) (0.06) (0.04) (0.05) (0.08) R 2 (%) GRS F 1.08 p-val (%) MKT + LM Alpha (%) (0.13) (0.11) (0.11) (0.12) (0.09) (0.13) (0.13) (0.15) (0.15) (0.20) (0.27) MKT Beta (0.04) (0.03) (0.04) (0.04) (0.03) (0.04) (0.04) (0.05) (0.03) (0.04) (0.07) LM Beta (0.04) (0.04) (0.04) (0.04) (0.04) (0.08) (0.03) (0.04) (0.07) (0.06) (0.07) R 2 (%) GRS F 0.99 p-val (%) 44.95

31 Table IA.IX Asset Pricing Tests with Labor Mobility (cont.) 31 Portfolios Sorted on Distress Measure from Campbell, Hilscher, and Szilagyi (2008) L H H L E[R] r f (%) (0.32) (0.27) (0.27) (0.29) (0.36) (0.39) (0.44) (0.54) (0.64) (0.78) (0.62) Obs CAPM Alpha (%) (0.16) (0.09) (0.08) (0.10) (0.14) (0.15) (0.20) (0.29) (0.35) (0.46) (0.49) MKT Beta (0.06) (0.03) (0.03) (0.03) (0.06) (0.05) (0.08) (0.10) (0.10) (0.12) (0.15) R 2 (%) GRS F 0.92 p-val (%) MKT + LM Alpha (%) (0.15) (0.10) (0.09) (0.11) (0.14) (0.15) (0.21) (0.30) (0.37) (0.49) (0.54) MKT Beta (0.05) (0.03) (0.03) (0.03) (0.06) (0.05) (0.08) (0.10) (0.10) (0.12) (0.14) LM Beta (0.08) (0.03) (0.04) (0.05) (0.05) (0.07) (0.10) (0.10) (0.22) (0.30) (0.28) R 2 (%) GRS F 0.68 p-val (%) 74.13

32 Table IA.IX Asset Pricing Tests with Labor Mobility (cont.) 32 Portfolios Sorted on Organization Capital from Eisfeldt and Papanikolaou (2013) L H H L E[R] r f (%) (0.40) (0.31) (0.33) (0.35) (0.31) (0.31) (0.27) (0.28) (0.28) (0.32) (0.27) Obs CAPM Alpha (%) (0.16) (0.11) (0.12) (0.15) (0.13) (0.12) (0.12) (0.14) (0.16) (0.18) (0.27) MKT Beta (0.05) (0.03) (0.05) (0.06) (0.04) (0.03) (0.04) (0.05) (0.05) (0.06) (0.07) R 2 (%) GRS F 1.71 p-val (%) 7.79 MKT + LM Alpha (%) (0.15) (0.11) (0.12) (0.15) (0.12) (0.11) (0.12) (0.13) (0.16) (0.18) (0.26) MKT Beta (0.04) (0.03) (0.05) (0.06) (0.04) (0.03) (0.04) (0.05) (0.06) (0.06) (0.07) LM Beta (0.06) (0.04) (0.06) (0.05) (0.04) (0.05) (0.05) (0.08) (0.09) (0.06) (0.11) R 2 (%) GRS F 1.31 p-val (%) 22.29

33 Table IA.IX Asset Pricing Tests with Labor Mobility (cont.) 33 Portfolios Sorted on Total Accruals from Dechow and Ge (2006) L H H L E[R] r f (%) (0.58) (0.38) (0.32) (0.28) (0.27) (0.27) (0.32) (0.31) (0.39) (0.44) (0.34) Obs CAPM Alpha (%) (0.32) (0.21) (0.12) (0.11) (0.10) (0.08) (0.11) (0.10) (0.16) (0.23) (0.35) MKT Beta (0.11) (0.06) (0.04) (0.03) (0.03) (0.03) (0.03) (0.03) (0.05) (0.08) (0.13) R 2 (%) GRS F 1.63 p-val (%) 9.72 MKT + LM Alpha (%) (0.29) (0.22) (0.13) (0.11) (0.09) (0.09) (0.10) (0.11) (0.15) (0.22) (0.33) MKT Beta (0.11) (0.06) (0.04) (0.03) (0.03) (0.04) (0.03) (0.03) (0.04) (0.08) (0.12) LM Beta (0.20) (0.07) (0.04) (0.03) (0.04) (0.05) (0.04) (0.05) (0.06) (0.12) (0.14) R 2 (%) GRS F 2.39 p-val (%) 1.02

34 Table IA.IX Asset Pricing Tests with Labor Mobility (cont.) 34 Portfolios Sorted on Accruals from Hirshleifer et al. (2004) L H H L E[R] r f (%) (0.49) (0.41) (0.32) (0.25) (0.29) (0.30) (0.29) (0.32) (0.37) (0.42) (0.30) Obs CAPM Alpha (%) (0.25) (0.17) (0.12) (0.10) (0.08) (0.11) (0.12) (0.13) (0.17) (0.25) (0.31) MKT Beta (0.07) (0.04) (0.04) (0.03) (0.03) (0.02) (0.04) (0.04) (0.05) (0.09) (0.09) R 2 (%) GRS F 2.50 p-val (%) 0.71 MKT + LM Alpha (%) (0.24) (0.15) (0.11) (0.09) (0.08) (0.11) (0.11) (0.14) (0.15) (0.24) (0.30) MKT Beta (0.07) (0.04) (0.04) (0.03) (0.03) (0.03) (0.04) (0.04) (0.05) (0.08) (0.09) LM Beta (0.12) (0.08) (0.06) (0.05) (0.04) (0.06) (0.05) (0.05) (0.06) (0.09) (0.10) R 2 (%) GRS F 2.89 p-val (%) 0.20

35 Table IA.IX Asset Pricing Tests with Labor Mobility (cont.) 35 Portfolios Sorted on Short-Term Stock Returns from Jegadeesh and Titman (1993) L H H L E[R] r f (%) (0.56) (0.42) (0.38) (0.36) (0.35) (0.29) (0.26) (0.30) (0.37) (0.47) (0.49) Obs CAPM Alpha (%) (0.33) (0.25) (0.21) (0.17) (0.14) (0.10) (0.12) (0.15) (0.19) (0.26) (0.47) MKT Beta (0.10) (0.07) (0.06) (0.06) (0.04) (0.03) (0.04) (0.04) (0.07) (0.09) (0.18) R 2 (%) GRS F 1.44 p-val (%) MKT + LM Alpha (%) (0.38) (0.28) (0.22) (0.18) (0.14) (0.11) (0.11) (0.15) (0.19) (0.25) (0.52) MKT Beta (0.09) (0.07) (0.06) (0.06) (0.04) (0.03) (0.04) (0.04) (0.07) (0.08) (0.15) LM Beta (0.16) (0.09) (0.08) (0.07) (0.06) (0.05) (0.06) (0.03) (0.08) (0.15) (0.24) R 2 (%) GRS F 1.49 p-val (%) 14.21

36 Table IA.IX Asset Pricing Tests with Labor Mobility (cont.) 36 Portfolios Sorted on Unexpected Earnings from Chen, Novy-Marx, and Zhang (2010) L H H L E[R] r f (%) (0.44) (0.39) (0.41) (0.30) (0.28) (0.27) (0.34) (0.32) (0.37) (0.40) (0.29) Obs CAPM Alpha (%) (0.25) (0.19) (0.14) (0.11) (0.09) (0.09) (0.12) (0.13) (0.18) (0.26) (0.29) MKT Beta (0.07) (0.05) (0.06) (0.03) (0.02) (0.03) (0.04) (0.04) (0.05) (0.06) (0.10) R 2 (%) GRS F 2.67 p-val (%) 0.41 MKT + LM Alpha (%) (0.30) (0.21) (0.14) (0.11) (0.10) (0.09) (0.12) (0.14) (0.18) (0.27) (0.32) MKT Beta (0.07) (0.04) (0.04) (0.03) (0.02) (0.04) (0.04) (0.04) (0.05) (0.06) (0.09) LM Beta (0.13) (0.07) (0.06) (0.04) (0.04) (0.05) (0.06) (0.05) (0.05) (0.09) (0.15) R 2 (%) GRS F 2.25 p-val (%) 1.60

37 Table IA.IX Asset Pricing Tests with Labor Mobility (cont.) 37 Portfolios Sorted on Net Stock Issues from Fama and French (2008) L H H L E[R] r f (%) (0.29) (0.24) (0.26) (0.30) (0.33) (0.35) (0.38) (0.43) (0.39) (0.36) (0.21) Obs CAPM Alpha (%) (0.13) (0.12) (0.11) (0.11) (0.12) (0.15) (0.16) (0.21) (0.17) (0.14) (0.21) MKT Beta (0.04) (0.04) (0.04) (0.03) (0.04) (0.03) (0.05) (0.07) (0.05) (0.04) (0.06) R 2 (%) GRS F 3.44 p-val (%) 0.03 MKT + LM Alpha (%) (0.13) (0.12) (0.11) (0.11) (0.13) (0.13) (0.15) (0.21) (0.17) (0.14) (0.20) MKT Beta (0.04) (0.04) (0.04) (0.03) (0.04) (0.03) (0.04) (0.07) (0.05) (0.04) (0.06) LM Beta (0.07) (0.05) (0.06) (0.05) (0.04) (0.07) (0.07) (0.12) (0.07) (0.05) (0.09) R 2 (%) GRS F 2.93 p-val (%) 0.17