Labor Similarity and Industry Classification
Mitsubishi UFJ Trust Investment Technology Institute Co., Ltd. (MTEC)1

1. Introduction
General industry classifications are defined by the type of product (output or service).
Industry classification can be viewed as a tool for analyzing the competitive environment of acompany or industry. Specifically, it can be used to identify the competitors of a company orindustry, establish competitive advantages, and determine the growth prospects of theindustry. When competitors are identified based on the drivers (labor, capital, andtechnology) in the production of a product, the competitive relationship is not necessarily
product-centric but may encompass indirect and potential competitive relationships. Would
information on such competitive relationships be immediately reflected in the market?
Liu and Wu [2022] identify competitors in terms of labor, one of the drivers of productcreation, and investigate economic links and market perceptions of these competitors.
Specifically, they define the similarity of labor demand across firms from job posting data andidentify the competitors. They report that this set of competitors does not overlap significantlywith industry classifications, and that information among competitors is not immediatelyreflected in stock prices.
In this report, we extend the 2010-2016 analysis period of Liu and Wu [2022] to early2023 and examine their results described above. Regarding the job posting data used in the1

The information contained in this report is provided "as is" and does not carry any

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Technology Institute Co., Ltd. shall bear no responsibility or liability for any actions taken
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the use of all or any part of this report. ©2023 Mitsubishi UFJ Trust Investment Technology
Institute Co., Ltd. All Rights Reserved.
1

analysis, they use job posting data from Burning Glass Technologies, whereas we use datafrom LinkUp. The full-year results with the extended period are generally consistent withprevious studies. As additional research, we conducted a sub-period analysis, and the return
predictability in labor similarity firms becomes statistically insignificant after 2016. However,when adjusting for common factors of industry classification representing product similarity,
the predictability is improved.
The rest of this paper is organized as follows. Section 2 provides an overview of the
Linkup job data used in the analysis of this report. Section 3 and 4 extend the analysis periodof Liu and Wu [2022] to the most recent period and tracks their main analysis. Section 5
provides a sub-period analysis. Section 6 summarizes.

2. Job Posting Data and Other Data
Job posting data comes from Link Up database. This database provides timely job data that
includes firm name, job title, location, creation date, and last check date. The firms we analyze
are firms that are included in the Russell 3000 Index and available in the Link Up data. Firms
included in the Russell 3000 Index are determined based on positions in the iShares Russell
3000 ETF from the FactSet Ownership database. The analysis period is from March 2010
through March 2023.
Figure 1 shows the number of firms and market value coverage in Russel 3000 at theend of the month. Job posting data of only about 400 firms are available in March 2010, but
the number of firms increases gradually, reaching 1,800 in March 2018 and fluctuatingaround the level since then. The coverage in market values is 60% in March 2010 and 90%

100%
90%
80%
70%
60%
50%
40%
30%
20%
10%
0%

ratio of market value

2000
1800
1600
1400
1200
1000
800
600
400
200
0

2010/3
2011/3
2012/3
2013/3
2014/3
2015/3
2016/32017/3
2018/3
2019/32020/32021/32022/32023/3

number of firmsin March 2018.

number of firms

ratio of market value

Figure1: The Number of Firms and Market Value Coverage in Russell 3000
2

Figure 2 indicates the means and medians of job postings per firm2. The means areabout ten times as large as the medians, the distribution has a heavy tail in the large values.
The number of records of job postings varies considerably from company to company.
The financial and market data in Section 3-5 are from FactSet Fundamentals and FactSet
Daily Prices. Factor model data in Sections 4 and 5 utilize French's data library:00

averagemedian102023/31002022/320

2021/330

200

2020/3300

2019/340

2018/3400

2017/350

2016/3500

2015/360

2014/370

600

2013/3700

2012/380

2011/3800

2010/3averagehttps://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html.

medianFigure2: The means and medians of Job Posting Data per Firm

3. Identifying Labor/Product Competitors
3.1. Labor Similarity and Industry Classification
To identify the competitors in terms of labor demand, the definition of labor similarity is given
below. First, Labor similarity is calculated by the following steps.
(1) Occupation weightfor firm , job

at time :Occupation weight is calculated as tf-idf which is familiar in text analysis:

where

=

(

(

)

0

log

is the number of job posting for firm , job

number of job posting on all firms for job
posting on firm2)

at time

,

>0
=0

,

at time ,at time ,

=∑

=∑ 1

is theis the number of job

is the total number of job posting. Job=∑ ∑As in Figure 1, the values represent end-of-month values.
3corresponds to the O*NET code3.
(2) Labor similarity

for firms ,at time :Labor similarity is measured as cosine similarity:
=‖
where

is a vector of

⋅

,

‖×

, ‖⋅‖ is the Euclidean distance.

We also define the discrete labor similarity by a threshold so that the edge density of labor
similarity network equals to that of industrial relationship network to compare the labor
similarity and the industrial classification.
Identification of product competitors utilize the 3-digit code (SIC3) and 4-digit code
(SIC4) of the Standard Industrial Classification. The industrial classification network showswhether two firms belong in the same industry. On the other hand, the labor similarity
networks shows whether two firms have high similarity.

3.2. Overlap between Labor/Product Competitors
Next, Figure 3 show the overlap ratio between the discrete labor similarity and industry
classification. The period is from March 2010 to March 2023. The average overlap rate isaround 20% for both SIC3 and SIC4, indicating that labor similarity captures thecompetitive relationships of firms differently from industry classification.
40%
35%

overlap ratio

30%
25%
20%
15%
10%
5%

SIC3

2023/32022/32021/32020/3

2019/3

2018/32017/3

2016/3

2015/3

2014/3

2013/3

2012/3

2011/3

2010/30%

SIC4

Figure3: Overlap Ratio between Discrete Labor Similarity and Industry Classification
3

LinkUp job posting data are associated with O*NET occupation codes. O*NET is acomprehensive database of occupations operated by the U.S. Department of Labor. This
database provides detailed information on approximately 1,000 different occupations.
44. Co-movement and Return Predictability in Labor Competitors
In the previous section, we show that labor competitors are different from productcompetitors. So how does the market perceive competitors based on labor demand? We
identify the co-movement and predictability of returns among labor competitors. The period
is from March 2010 to March 2023.

4.1. Labor Linked Return
Information of firms with similar labor demands is defined as Labor Linked Return (LLR).
Specifically, for a focal firm

at month ,
=

where

∑

is defined as follows:,∑is the labor similarity between firm

is stock return of firm

andat the end of month , andin month . Note that the focal firm return is not included in the

return calculation. Discrete Labor Linked Return (DLLR) can be calculated in the same way
by replacing LLR with DLLR. In addition, to identify the differences and impact of stock priceco-movements of firms with related products, Industry Linked Return (ILR) is defined as theweighted average return in the same industry. We use three-digit SIC (SIC3) and four-digit
SIC (SIC4) as the industry classification. ILR is different with general industry average returnin that it includes the focal firm return.

4.2. Regression Analysis
Returns of firms with related products co-move when common news occurs in the productmarkets. Similarly, those of firms with similar labor demands may also co-move. We confirm
this by the following Fama-Macbeth regressions (1):
=
=

1

+

,

,

+

∈{

,

,

,

(

, .

3),

(

4)},
(1)

Table 1 summarizes the statistical tests for β in the Fama-Macbeth regression. It shows thatall betas are significant. This suggests that the stock prices of the focal firms co-movecontemporaneously, responding not only to information from product competitors but also to
information from competitors with similar labor demands. This result also indicates that labor
similarity link information is different from industry link information.
5

Table 1: Return Co-movement in Labor Competitors
DLLR
LLR

mean

0.254

0.266

tvalue21.552 ***21.948 ***

mean

1.538

1.620

tvalue17.182 ***18.416 ***

ILR

mean

0.409

0.429

(SIC3)

tvalue42.583 ***40.634 ***

ILR

mean

(SIC4)

tvalue

***

0.367

0.384

41.230 ***37.592 ***Mean Num. of observations

1,074.2

1,270.6

996.6

1,170.6

Mean adj. R2

0.074

0.069

0.074

0.070

Statistical significance at 1%, 5%, 10% levels are expressed as *, **, *** respectively.

To further confirm whether these competitor returns predict the one-month-ahead
returns of the focal firm, we perform the Fama-Macbeth regression (2):
=

=

1

+

,
,

,

+

∈{

,

,

,

(

3),

.

(

4)},
(2)

Table 2 presents statistical tests ofin the Fama-Macbeth regression (2). DLLR issignificant for future returns. LLR is not significant for future returns, but it is close to thelevel of significance at the 10% level. Industry returns, on the other hand, are not significant.
This suggests that shocks to firms with related products are immediately reflected in stock
prices, while shocks to competitors with similar labor demand are not immediately reflectedin stock prices.
Table 2: Return Predictability in Labor Competitors
DLLR

mean

0.028

0.028

tvalue2.439 **

2.298 **

mean

LLR

tvalue

0.221

0.212

1.609

1.534

ILR

mean

-0.0040.000(SIC3)

tvalue-0.337-0.002

ILR

mean

0.003

0.007

(SIC4)

tvalue

0.229

0.598

Mean Num. of observations

1,062.6

1,257.9985.7

1,158.8

Mean adj. R2

0.008

0.012

0.008

0.012

Statistical significance at 1%, 5%, 10% levels are expressed as *, **, *** respectively.

6

4.3. Portfolio Analysis
This subsection examines economic significance through portfolio analysis. Table 3 shows thereturns of quintile portfolios and long-short portfolio returns. The long-short portfolios longthe first quintile (the highest LLR) portfolio and short positions the fifth quintile (the lowest
LLR) portfolio. The portfolios are held for one month and rebalanced. The long-shortportfolio returns of LLR and DLLR are significant, the mean returns of quintile portfolios
mostly decrease from the first quintile portfolio to the fifth quintile portfolio. On the other
hand, the long-short portfolio returns of ILRs are not significant, and the quintile mean
returns are not in the order expected in the sorting portfolio analysis.
Table 3: LLR/ILR Quintile Portfolio Returns and Long-short Portfolio Returns
quintilemeant value

1 12.79%

2.396 **

2 11.70%2.275 **

3 12.26%

2.262 **

4

9.00%

1.635

5

8.38%

1.386

quintile

DLLR

LLR

ILR(SIC3)ILR(SIC4)

1 12.25%

2.289 **

2 13.12%2.545 **

3 12.54%2.369 **

4 10.40%

1.822 *

5

1.028

6.29%

1 10.75%

2.151 **

2 12.62%

2.379 **

3 11.05%

2.088 **

4 12.37%

2.272 **

5 10.17%

1.649

1 11.85%

2.367 **

2 11.94%

2.287 **

3 11.30%

2.172 **

4 10.78%

1.973 *

5 10.79%

1.774 *

spreadmeant value

4.40% 1.917 *

5.96% 2.007 **0.58% 0.235

1.06% 0.422

Statistical significance at 1%, 5%, 10% levels are expressed as *, **, *** respectively.

Attributes of the quintile portfolios be checked. Table 4 summarizes nine attributeaverages. The definitions of the attributes are described in Appendix A. All attributes arenormalized in cross-section. The first and fifth quintiles by LLR have smaller size, higher
volatility, and lower ROE than other quintiles while all quintiles by ILR are only slightly
different in their size and their volatility and the first and fifth quintiles by ILR have higher
ROE compared to other quintiles. There is no strong similarity between the attributes of LLR
long-short portfolio and ILR long-short portfolio.
7

Table 4: Attributes of LLR Sorted Portfolios
quintile log MV BPR

DLLR

LLR

ILR(SIC3)ILR(SIC4)MOM

STDEV ROE

0.005 -0.017

0.128 -0.068

DE

ΔSALES PPEA

-0.1860.101

20.129 -0.040

0.040-0.0750.009

0.034 -0.003-0.022 -0.064

30.238 -0.049

0.029

0.010

-0.1350.077 -0.002-0.014 -0.092 -0.022

4

0.079

0.012

0.000

5

-0.2620.076 -0.054-0.0600.167 -0.087 -0.010

0.040-0.009 -0.043 -0.028
0.049

0.104

0.046

1

-0.2900.068 -0.040

0.153 -0.121 -0.054

0.045 -0.002

0.114

2

0.175 -0.066

0.048-0.072

0.067

0.024

-0.038 -0.013 -0.060

30.253 -0.087

0.033-0.124

0.096

0.053

-0.040 -0.012 -0.086

40.161 -0.037

0.017-0.076

0.065

0.036

-0.0230.021 -0.078

5-0.3000.123 -0.060

0.154 -0.111 -0.057

0.090

0.013

1

0.033

0.014

0.003

0.019

-0.0690.173 -0.177

2-0.007 -0.058

0.021-0.001 -0.039 -0.034

0.047 -0.110

0.131

3

-0.011 -0.040

0.013-0.013 -0.035 -0.040

0.053 -0.148

0.170

4

-0.0070.011 -0.005-0.037 -0.004 -0.002

0.020 -0.075

0.032

5

-0.0070.076 -0.031

0.059

0.029

0.024

-0.0210.170 -0.125

0.047

0.041

-0.0540.140 -0.134

0.048

0.009

0.006

0.054

0.018

RD

1

0.148

1

0.040 -0.013

0.003

0.028

2

-0.007 -0.051

0.026-0.008 -0.036 -0.033

0.037 -0.087

0.113

3

-0.011

0.006

0.001

-0.025 -0.033 -0.022

0.030 -0.140

0.105

4

-0.013

0.012

0.004

-0.034 -0.006

0.004

0.022 -0.069

0.034

5

-0.0090.049 -0.033

0.062

0.012

-0.0120.026

0.164 -0.097

Table 5 confirms the alpha and factor beta of the long-short portfolio using three factor
models (Fama-French 3-factor/5-factor model, Chart 4-factor model). ILR (SIC3, SIC4)
long-short portfolios are explained by the factor models, while LLR and DLLR long-shortportfolios have significant alphas that cannot be explained by the factor models.
Table 5: Alpha Test of LLR Long-short Portfolio Returns
DLLR

const
MKT
SMB
HML
WML
RMW
CMA

coef
t valuecoef

LLR

3factor4factor5factor3factor4factor5factor

0.00490.00460.00370.00650.00650.00522.581 **
-0.1187

2.4 **

1.947 *

-0.0977-0.09812.628 ***
-0.1362.604 **
-0.1365

2.081 **
-0.1127t value-2.682 ***-2.102 **-2.196 **-2.371 **-2.251 **-1.927 *coef-0.1019-0.0911-0.0231-0.1383-0.1385-0.0556t value-1.296-1.157-0.27-1.357-1.349-0.497coef

0.05

0.0726-0.0968

0.11230.1118-0.0418

t value

0.886

1.243

-1.254

1.534

1.467

-0.414coef

0.0828t value

1.445-0.0018-0.024coef

0.1233t value

1.19

0.943

coef

0.34720.3778t value

0.128

2.919 ***

2.426 **

Mean No. of observations

156

156

156

156

156

156

Mean adj. R2

0.059

0.066

0.107

0.057

0.05

0.086

8

ILR(SIC3)

const
MKT
SMB
HML
WML
RMW
CMA

coef

ILR(SIC4)

3factor4factor5factor3factor4factor5factor

0.00310.00280.00230.00330.00310.0025t value

1.606

1.452

1.195

coef

-0.2572-0.2395-0.2381.664 *
-0.2346

1.566

1.238

-0.224-0.2098t value-5.834 ***-5.166 ***-5.259 ***-5.107 ***-4.622 ***-4.472 ***coef-0.0559-0.0468-0.0286-0.0688-0.0634-0.0488t value-0.714-0.596-0.33-0.844-0.772-0.543coef-0.00120.0178-0.1032

0.03920.0505-0.0782t value-0.022

0.305

-1.32

0.669

0.83

-0.965coef

0.0698t value

1.22

0.04170.698

coef

0.0278t value

0.265

0.032

coef

0.25520.3045t value0.00352.118 **

2.437 **

Mean No. of observations

156

156

156

156

156

156

Mean adj. R2

0.2

0.202

0.214

0.162

0.16

0.185

Statistical significance at 1%, 5%, 10% levels are expressed as *, **, *** respectively.

At the end of this subsection, we show results consistent with investor limited attention
hypothesis, also argued in Liu and Wu [2022]. The hypothesis is that these links are not wellunderstood by investors, because of either their limited attention span or the complexity of
information processing. As a result, the stock prices of high-profile stocks may beundervalued and reflect abnormally high future returns. Most previous studies on economic
links claim this hypothesis (Moskowitz and Grinblatt [1999], Cohen and Frazzini [2008],
Lee et al. [2019]). Therefore, this hypothesis is more pronounced for firms that are more
likely to be overlooked by investors. Table 6 summarizes the long-short returns for small-cap
firms. Small-cap firms are defined as the bottom 1500 firms by market capitalization
employed in the Russell 3000 index and available from LinkUp.
Compared to Table 3, the long-short returns for small firms are higher than those for all
firms. The results suggest that information propagate across firms through the labor
similarity described above and that the price discovery process is more delayed for small
firms, which receive less investor attention than large firms.
Table 6: LLR Predictability in Small-cap Firms
DLLR
mean
t value

13.68%
3.062 ***

LLR
14.74%
3.142 ***ILR(SIC3)ILR(SIC4)

4.93%

4.58%

1.026

0.893

Statistical significance at 1%, 5%, 10% levels are expressed as *, **, *** respectively.

95. Additional Research
5.1. Sub-period Analysis
Liu and Wu [2022] showed that there is return predictability for DLLR and LLR using job
posting data through 2016. We confirm the return predictability of DLLR and LLR in two
periods, before and after 2016. The results are shown in Table 7. Before 2016, the returns of
DLLR and LLR long-short portfolios are significant as in Liu and Wu [2022], while after
2016 they are not significant.
Table 7: LLR Predictability in Sub-periods

2010-20162016-2023

DLLR

LLR

ILR(SIC3)ILR(SIC4)

mean

5.29%

5.65%

1.14%

1.90%

t value

2.225 **

2.084 **

0.370

0.644

mean

3.64%

6.23%

0.10%

0.35%

t value

0.969

1.241

0.027

0.089

Statistical significance at 1%, 5%, 10% levels are expressed as *, **, *** respectively.

5.2. LLR Industry Risk-adjusted Portfolio
The results of Table 2 show that the regression coefficients for DLLR are significant whenregressed simultaneously with ILR. In the post-2016 period, the impact of industry factors(ILR returns) may have affected the return spread for DLLR and LLR. Therefore, to reducethe impact of industry factors, we apply industry neutralization to LLR (and DLLR) and thenperform a sorted portfolio analysis. Specifically, we evaluate the quintile portfolios bysubtracting the LLR (and DLLR) average of the industry to which the firm belongs from the
LLR (and DLLR) of each firm.
Table 8 summarizes the details of the quintile portfolios and the industry-neutralized
long-short portfolios in SIC4. The quintile portfolio returns are almost the same as those
before neutralization. The long-short portfolio returns are smaller before industry
neutralization, but the t-values increase. Table 9 shows the factor analysis of the long-shortportfolio. The industry adjusted DLLR/LLR factor is significant for alpha even after
accounting for the factor model.4

4

The similar results are obtained when neutralizing by SIC3.
10

Table 8: Industry Neutralized DLLR/LLR Sorted Portfolio Returns
quintilemeant value

1 12.54%2.357 **

2 11.12%2.166 **

3 10.61%

1.944 *

4 11.89%2.275 **

5

9.55%

1.709 *

1 12.00%

2.218 **

2 12.22%2.389 **

3 11.48%2.056 **

4 12.03%2.260 **

5

1.640

quintile

DLLR

LLR

spread

8.85%

mean

t value

2.99% 2.469 **3.16% 2.910 ***Statistical significance at 1%, 5%, 10% levels are expressed as *, **, *** respectively.

Table 9: Alpha test for Industry Neutralized DLLR/LLR Portfolio Returns
DLLR

const
MKT
SMB
HML
WML
RMW
CMA

coef
t value

4factor5factor3factor4factor5factor

0.003

0.00290.00270.00270.00280.00282.923 ***

coef

LLR

3factor-0.0478

2.763 ***
-0.0383

2.56 **-0.0366

2.935 ***
0.00082.939 ***
-0.00122.895 ***
0.0016t value-2.005 **-1.529-1.4970.039-0.054

0.074

coef

-0.0293-0.0245-0.0207-0.0068-0.0078-0.0116t value-0.692-0.576-0.441-0.177-0.203-0.271

coef

0.023

0.0331-0.03080.05790.05570.06

t value

0.756

1.051

-0.7292.116 **

1.956 *

1.553

coef

0.0372t value

1.202-0.0081-0.289coef-0.0122t value-0.214-0.348coef

0.14070.0023t value-0.0182.158 **

0.039

Mean No. of observations

156

156

156

156

156

156

Mean adj. R2

0.021

0.024

0.038

0.01

0.004

-0.003

Statistical significance at 1%, 5%, 10% levels are expressed as *, **, *** respectively.

Table 10 shows the returns of industry-neutralized long-short portfolios over the two
periods. Compared to Table 7, the long-short portfolio returns for the pre-2016 period(2010/3-2016/3) remain significant due to industry neutralization. On the other hand, the tvalues for the long-short portfolio returns for the post-2016 period (2016/3-2023/3) improveover the pre-industry neutralization. In particular, the post-industry neutralization LLR is still11

significant at 10% after 2016. This suggests that inter-competitor information based on labordemand may not be fully reflected in stock prices for the post-2016 period.
Table 10: Industry Neutralized DLLR/LLR Portfolio Returns in Sub-Periods

2010-20162016-2023

DLLR

LLR

mean

3.72%

3.92%

t value

2.184 **

2.366 **

mean

2.37%

2.50%

t value

1.376

1.744 *

Statistical significance at 1%, 5%, 10% levels are expressed as *, **, *** respectively.

6. Summary
We extend the 2010-2016 analysis period of Liu and Wu [2022] to 2023 and examine
their main analysis results. Regarding the job posting data in the analysis, they use job postingdata from Burning Glass Technologies, whereas we use data from LinkUp. The full-year
results with the extended period are consistent with previous studies. As additional research,
we conducted a sub-period analysis, and the return predictability in labor similarity firms
becomes statistically insignificant after 2016. However, when we adjust for common factors
in industry classifications representing product similarity, the results show an improvementin predictive power over the industry-adjusted results.

References
Cohen, L., and A. Frazzini. 2008. “Economic links and predictable returns,” Journal of

Finance 63(4): 1977–2011.
Lee, L. M. C., S. T. Sun, R. Wang, and R. Zhang. 2019. “Technological links and predictable
returns,” Journal of Financial Economics 132(3): 76–96.
Liu, Y., and X. Wu. 2022. “Labor links, co-movement and predictable returns,” Preprint.
Moskowitz, T. J. and M. Grinblatt. 1999. “Do industries explain momentum?,” Journal of

Finance 54(4), 1249–1290.

12Appendix
A. Definitions of attributes

log MVThe logarithm of stock market capitalization

BPR

Book value of equity dividend by the market capitalization

MOM

The Cumulative 11-month return from month －11 to month －1

STDEV

The Standard deviation of monthly returns over the past 36 months

ROE

Return on Equity

DE

Debts to Equity Ratio

ΔSALES

Sales growth rate over a one-year

PPEA

PPE(Property, Plant, and Equipment) to AssetRD

R&D Expences to Asset13