Online Supplement to: Productivity and Wage Dispersion: Heterogeneity or Misallocation?∗ Jesper Bagger† Royal Holloway

Bent Jesper Christensen‡ Aarhus University

Dale T. Mortensen§ Northwestern University Aarhus University December 14, 2014

Abstract This supplement to our paper ”Productivity and Wage Dispersion: Heterogeneity or Misallocation?” contains (i) a detailed description of the construction of the analysis panel, (ii) detailed descriptions of variable definitions, and (iii) a full set of of estimations and associated decompositions performed on the four largest sub-industries within the Manufacturing industry.

1 1.1

Data Construction The FIDA Files

The firm ID used by Statistics Denmark in the employer data is different from that used for the employing firm in the employee data.1 We use the FIDA files to link the different firm ID definitions. Industry coverage in FIDA includes the industries subject to the accounting data survey. For each year, a FIDA file contains all last-week-of-November employment relationships, as well as a limited number of additional secondary jobs (not necessarily covering a last week of November). FIDA files are available for the required years 1995-2007, therefore allowing us to merge employer and employee data. To ensure that each worker in the employee data is assigned to one and only one firm in the employer data, we discard FIDA observations where the employing firm, defined in terms of the employee data firm ID, is linked to more than one ∗ Sadly, Dale T. Mortensen passed away on January 9, 2014. Dale worked until the end helping complete this paper. The authors gratefully acknowledge financial support from the Danish Social Science Research Council, the Cycles, Adjustment, and Policy research unit, CAP, and the Aarhus Institute of Advanced Studies, AIAS, Aarhus University. † Department of Economics, Royal Holloway, University of London, Egham, Surrey TW20 0EX, United Kingdom; E-mail: [email protected] ‡ Aarhus Institute of Advanced Studies, Aarhus University, Høegh Guldbergs Gade 6B, DK-8000 Aarhus C, Denmark; E-mail: [email protected] § Department of Economics, Northwestern University, 2001 Sheridan Road, Evanston, Illinois 60208, U.S.A. 1 The employer data firm ID is based on the Danish Central Business Registry, while the employee data firm ID is that used by the Danish Tax Authorities.

1

employer data firm ID in a given year (11 percent of the the FIDA observations are discarded). Also, we restrict our analysis to single-record employee-years.2

1.2

Matching Employer and Employee Data

We first merge employer data onto the FIDA panel using the (employer data) firm IDs. All except 276 firm-years (out of approximately 95,000) from the employer data are matched to the FIDA panel. Not every observation in FIDA is matched to an observation in the employer data, since this is survey based, whereas FIDA includes all firms (with economic activity) in the covered industries. The actual fraction matched is about 35 percent of all FIDA observations. We retain all observations in the FIDA panel. Next, we merge the FIDA panel with the IDA person files.3 All observations in the FIDA panel are matched with IDA person information. Since the IDA person files are population data sets, whereas FIDA only covers employed individuals (in selected industries), there are observations in the IDA person files that cannot be merged with FIDA (we merge around 50 percent of the IDA person file observations to FIDA). We retain the original FIDA panel observations. Merging the FIDA panel with the IDA job files results in 90 percent of all FIDA observations being matched with an observation from the IDA job files. Conversely, 67 percent of the observations in the IDA job files are matched with a FIDA observation. Still, we retain all the original FIDA observations. Finally, we match the FIDA file with the IDA establishment files. A slight complication arises here: FIDA provides a link between different firm IDs, but does not contain establishment (i.e. plant) IDs, whereas the unit of observation in the establishment file is the establishment. We circumvent this problem by aggregating the relevant information in the establishment files (industry codes and the size of the firm’s workforce in the last week of November) to the firm level before merging with FIDA. In so doing, we take the firm industry to be the industry of the firm’s largest establishment, and calculate firm size by adding up the number of employees in each of the firm’s establishments. Merging the firm level information thus constructed from the establishment files to FIDA results in 95 percent of all FIDA observations being matched to an IDA establishment. Conversely, we match 99 percent of all IDA firm observations to an observation in FIDA. In total, the resulting MEE panel contains 24,233,697 observations on 3,704,217 workers and 545,640 firms (some of which with accounting data information).

1.3

Selecting the Individual Level Panel

We impose the following selection rules: • First, we discard observations with missing or invalid industry information and restrict attention to the following industries (NACE codes and years in the sample in parentheses): 2

An employee-year in FIDA may contain several records if the employee has secondary employment relationships. Around 90 percent of all employee-years have only one record, around 10 percent have two, and very few have three or more. 3 Recall that IDA contains information on employees (an a bit of information on the employing establishment) and is made up of several files: Person files, job files and establishment files (see Section 3 in “Wage and Labor Productivity Dispersion: The Roles of Total Factor Productivity, Labor Quality, Capital Intensity, and Rent Sharing”).

2

Manufacturing (NACE rev. 1 section D, 1995-2007), Wholesale & Retail (NACE rev. 1 section G, 1999-2007), Transport, Storage & Communication (NACE rev. 1 section I, 1999-2007) and Real Estate, Renting & Business Activities (NACE rev. 1 section K, 1999-2007). About half of the observations are discarded in this step, and we are left with 11,686,096 observations. We also present results obtained from four sub-industries within Manufacturing. These are Food Products, Beverages & Tobacco (NACE rev. 1 section DA), Pulp, Paper, Paper Products, Publishing & Printing (NACE rev. 1 section DE), Basic Metals & Fabricated Metal Products (NACE rev. 1 section DJ), and Electrical & Optical Equipment (NACE rev. 1 section DL). • Second, we discard (relatively few) observations on workers aged below 18 and observations with invalid or missing education information. In this step we also define four occupation categories: Managers (consisting of ISCO-88 groups 1 and 2: Legislators, senior officials and managers and Professionals), Salaried workers (ISCO-88 group 3: Technicians and associated professionals), Skilled workers (ISCO-88 groups 4, 5, 6, 7 and 8: Clerks, Service workers and shop and market sales workers, Skilled agricultural and fishery workers, Craft and related trades workers, Plant and machine operators and assemblers) and Unskilled workers (ISCO-88 group 9: Elementary occupations). Workers with missing occupation data are assigned to an occupation group based on length of education. If they have 12 or more years of education they are assigned to the Skilled workers group, otherwise to the Unskilled workers group. • Third, we discard observations with missing or non-positive wages and trim the annual industry- and occupation-specific distributions of individual wages by removing the top and bottom 1%. We discard firm-years with missing or non-positive value added, hours, capital stock, energy cost, or wage bill.4 Furthermore, we discard all firm-years that report negative material costs.5 In this step, we also trim the annual industry-specific distributions of hourly value added (non-employment weighted) by removing the top and bottom 1%. Finally, we detrend all nominal variables (value added, the capital stock, material costs, energy costs, and wages) using the NACE rev. 1 section-specific implicit deflator in hourly value added.6 • Fourth, we retain only firm-years where at least two workers are employed in each of the four occupations. This takes the total number of observations to 6,107,986. The industry-specific number of observations are 3,327,480, 1,124,608, 757,150, and 898,748 for Manufacturing, Wholesale & Retail, Transport, Storage & Communication, and Real Estate, Renting & Business Activities, respectively. This selection criteria excludes small firms which lead to a large loss in the number of observations. Notice that the loss of information from the employer data is minimal due to that sampling scheme of the accounting data survey outlined in Table 1 in “Wage and Labor Productivity Dispersion: The Roles 4

That is, we retain firms with missing accounting data, as these observations carry information on workers’ individual wages that we utilize in the empirical analysis. 5 We do however retain firm-years where no material costs are reported. 6 We do not have firm- or industry level price data at our disposal. Hourly value added is computed using value added and number of full time equivalent employees, as reported in the employer data.

3

of Total Factor Productivity, Labor Quality, Capital Intensity, and Rent Sharing”. • Fifth, to ensure identification of the individual level log wage regression with workeroccupation and firm-year-occupation indicators, we select the largest group of “connected” workers and firm-years in each occupation and industry.7 Technically, the set of connected workers and firm-years is the maximal set of workers and firm-years for which the strong Hall property holds. Intuitively, a set of workers and firm-years is connected when the set contains all the workers who were ever linked to any of the firm-years in the group, and all the firms-years to which any of the workers were ever linked. In contrast, when a set of workers and firm-years is not connected to another set (within an occupation), no firm-year in the first set has ever been linked to a worker in the second set, nor has any worker in the first set ever been linked to a firm-year in the second set.8 The vast majority of workers and firm-years are connected in one large group in each of the occupations in each of the industries. We lose only 25,701, 49,791, 8,919, and 34,544 observations in Manufacturing, Wholesale & Retail, Transport, Storage & Communication, and Real Estate, Renting & Business Activities, respectively, taking the total number of observations in each industry to 3,301,779, 1,074,817, 748,231, respectively 864,204.

1.4

Selecting the Firm Level Panel

• First, we select only firm-years for which we have accounting data information (survey based and not available for all firm-years represented in the individual level panel). This reduces the industry specific sample sizes to 3,042,412, 962,352, 416,306, and 704,985 in Manufacturing, Wholesale & Retail, Transport, Storage & Communication, and Real Estate, Renting & Business Activities, respectively. • Second, we select only firm-years that are represented in all four occupations (this amounts to selecting firm-years that for each occupation belong to the largest group of connected workers and firm-years, such that each worker-occupation effect and firm-occupationtime effect is properly identified from the first step, see Section 4 in “Wage and Labor Productivity Dispersion: The Roles of Total Factor Productivity, Labor Quality, Capital Intensity, and Rent Sharing”), reducing sample sizes to 2,894,842, 782,223, 354,965, and 580,662 in Manufacturing, Wholesale & Retail, Transport, Storage & Communication, and Real Estate, Renting & Business Activities. • Third, we select only firm-years that are part of a sequence of at least three consecutive firm-years. This ensures that we can construct lagged differences at the firm level, which will play a key role in the identification of the structural parameters (again, we refer the reader to Section 4 in “Wage and Labor Productivity Dispersion: The Roles of 7

The identification of this type of two-way error component regression was studied by Abowd, Creecy, and Kramarz (2002) in the case where the error component consists of a worker-specific permanent effect and a firm-specific permanent effect. In the absence of time-varying observable covariates, their identification result carries over to our context, where the error component is made up of a worker-occupation effect and a firm-yearoccupation effect, with identification established within each occupation separately. 8 This description of the notion of connectedness is a slight paraphrasing of the description given in Abowd, Creecy, and Kramarz (2002, p. 3).

4

Total Factor Productivity, Labor Quality, Capital Intensity, and Rent Sharing” for details on identification and estimation). This last step reduces the industry specific sample sizes to 2,683,854, 979,521, 286,419, and 491,358 in Manufacturing, Wholesale & Retail, Transport, Storage & Communication, and Real Estate, Renting & Business Activities.

5

2

Details on Measurements

This appendix details the computations of value added and capital stock from the accounting data files. The accounting data consist of a series of annual surveys conducted by Statistics Denmark and available for the period 1995-2007. The surveys are intended to provide an accurate description of the Danish business community and serve as important inputs in the construction of national accounts. The surveys are subject to minor changes over the period 1995-2007. As a result, we also need to change the construction of value added. In graphical and other analysis not reported, we find evidence that these changes do not induce major breaks in the data.

2.1

Value Added

Value added is revenue net of cost of intermediate inputs. The changes in definition over the sample period affect the computation of both revenue and cost of material inputs. Below follows a list of the value added definitions we apply, and a short description of each of the variables entering the definitions. The formulas are applied by Statistics Denmark in the production of official statistics involving value added. 1995-1998:

For the initial four years, value added Y is defined as follows:

Y = (OM S + AU ER + ADR + DLG) − (KRH + KEN E + KLOE + U DHL + U ASI + OEEU + SEU D) where OM S is revenue, AU ER is work conducted at own expense and recorded under assets, ADR is other operating revenue, and DLG is ultimo inventory minus primo inventory. On the cost side, KRH is cost of intermediates, KEN E is cost of energy, KLOE is costs of subcontractors, U DHL is housing rents, U ASI is purchases of minor equipment, OEEU is other external costs, and SEU D is secondary costs. 1999-2001:

For the next three years, 1999-2001, Y is computed as follows:

Y = (OM S + AU ER + ADR + DLG + 0.0079 × T GT ) − (KRH + KEN E + KLOE + U DHL + U ASI + U DV B + U LOL + AN EU + SEU D), where T GT is total credits, U DV B is purchases of temporary employment agency services, U LOL is costs of long-term leasing, and AN EU is other external costs (net of secondary costs). 2002-2003:

In this period, the definition of value added changes to:

Y = (OM S + AU ER + ADR + DLG) − (KRH + KEN E + KLOE + U DHL + U ASI + U DV B + U LOL + AN EU + SEU D),

6

such that total credits TGT again drops out of the value added definition. 2004-2007:

From 2004, we apply the following value added definition:

Y = (OM S + AU ER + ADR + DLG) − (KV V + KRHE + KEN E + KLOE + U DHL + U ASI + U DV B + U LOL + AN EU + SEU D), where KV V is purchases of goods for resale, and KRHE is cost of intermediates.

2.2

Capital Stock

The accounting data allow us to measure a firm’s capital stock through the book value of material assets. As for value added, we follow Statistics Denmark’s official definition of the book value of material fixed assets, denoted K. Unlike for value added, the definition does not change over the sample period. It is given by K = AADI + GRBY + AT AM + F M AA, where AADI is operating equipment and other equipment and facilities, GRBY is buildings and sites, AT AM is technical equipment and machinery, and F M AA is pre-paid material fixed assets and material fixed assets under construction.

7

3

Results for Sub-Industries within Manufacturing

This appendix contains results obtained for the four largest sub-industries within Manufacturing: Food Products, Beverages & Tobacco (NACE rev. 1 section DA), Pulp, Paper, Paper Products, Publishing & Printing (NACE rev. 1 section DE), Basic Metals & Fabricated Metal Products (NACE rev. 1 section DJ), and Electrical & Optical Equipment (NACE rev. 1 section DL). It contains the same tables and figures of descriptive statistics and results as our main paper ”Wage and Labor Productivity Dispersion: The Roles of Total Factor Productivity, Labor Quality, Capital Intensity, and Rent Sharing”. We do not comment on the reported results. Table 1: Individual Level Panel—Number of Workers and Firms

Years Managers Average # workers Average # firms Salaried workers Average # workers Average # firms Skilled workers Average # workers Average # firms Unskilled workers Average # workers Average # firms

Food Products, Beverages & Tobacco

Pulp, Paper & Paper Products, Publishing & Printing

Basic Metals & Fabricated Metal Products

Electrical & Optical Equipment

1995-2007

1995-2007

1995-2007

1995-2007

2,455 110

3,991 107

1,190 103

4,715 159

5,265 120

3,032 111

2,301 121

4,940 165

33,753 133

10,552 132

14,463 178

17,095 182

6,030 110

2,252 74

1,553 60

4,517 128

Note: The reported average number of workers and firms are simple averages across annual cross sections of employed workers.

8

Figure 1: Log Labor Productivity and Log Wages—Employment Weighted Densities Pulp, Paper & Paper Products, Publishing & Printing 2.0

2.0

Food Products, Beverages & Tobacco

0.5

PDF 1.0

1.5

Log labor productivity Log wage

0.0

0.0

0.5

PDF 1.0

1.5

Log labor productivity Log wage

4.0

4.5

5.0 5.5 6.0 Log Danish Kroner

6.5

7.0

4.0

5.0 5.5 6.0 Log Danish Kroner

6.5

7.0

Electrical & Optical Equipment 2.0

2.0

Basic Metals & Fabricated Metal Products

4.5

0.5

PDF 1.0

1.5

Log labor productivity Log wage

0.0

0.0

0.5

PDF 1.0

1.5

Log labor productivity Log wage

4.0

4.5

5.0 5.5 6.0 Log Danish Kroner

6.5

7.0

4.0

4.5

5.0 5.5 6.0 Log Danish Kroner

6.5

7.0

Note: The plotted densities are simple averages of densities in annual cross sections of employed workers.

References Abowd, J. M., R. H. Creecy, and F. Kramarz (2002): “Computing Person and Firm Effects Using Linked Longitudinal Employer-Employee Data,” Discussion Paper TP-2002-06, U.S. Census Bureau, LEHD Program.

9

Figure 2: Regressions of Log Wages onto Log Labor Productivity—Employment Weighted

7.0

4.0

7.0

2.0 1.5 1.0 PDF 0.5

6.00 Log wage 5.50 5.75 5.25 5.00

7.0

Nonparametric (left axis) PDF (right axis)

0.0

2.0 0.5 0.0

5.00

5.25

1.0 PDF

Log wage 5.50 5.75

Nonparametric (left axis) PDF (right axis)

4.5 5.0 5.5 6.0 6.5 Log labor productivity

4.5 5.0 5.5 6.0 6.5 Log labor productivity

Electrical & Optical Equipment

1.5

6.00

Basic Metals & Fabricated Metal Products

4.0

2.0 0.5

1.0 PDF

1.5

Nonparametric (left axis) PDF (right axis)

0.0

6.00 Log wage 5.50 5.75 5.25 5.00

4.5 5.0 5.5 6.0 6.5 Log labor productivity

0.5 4.0

0.0

5.00

5.25

1.0 PDF

Log wage 5.50 5.75

Nonparametric (left axis) PDF (right axis)

2.0

Pulp, Paper & Paper Products, Publishing & Printing

1.5

6.00

Food Products, Beverages & Tobacco

4.0

4.5 5.0 5.5 6.0 6.5 Log labor productivity

7.0

Note: The plotted regression lines and densities are simple averages of regression lines and densities in annual cross sections of employed workers.

10

11

# # # # #

firms Managers (FTE) Salaried workers (FTE) Skilled workers (FTE) Unskilled workers (FTE)

71 29 63 422 71

1995-2007 46 66 45 128 35

1995-2007

Pulp, Paper & Paper Products, Publishing & Printing

39 14 31 156 32

1995-2007

Basic Metals & Fabricated Metal Products

83 44 46 160 47

1995-2007

Electrical & Optical Equipment

Note: The reported averages are simple averages across annual cross sections of firms. The firm level panel is constructed by aggregating individual level information from the individual level panel (see Table 1) to the firm level subject to selection criteria described in the main paper.

Average Average Average Average Average

Years

Food Products, Beverages & Tobacco

Table 2: Firm Level Panel—Number of Workers and Firms

Table 3: Average 90/10 Percentile Ratios and Correlation Coefficients Food Products, Beverages & Tobacco

Pulp, Paper & Paper Products, Publishing & Printing

Basic Metals & Fabricated Metal Products

Electrical & Optical Equipment

Average 90th to 10th Percentile Ratios Labor productivity Individual wage

1.84 1.90

1.96 2.51

1.73 1.89

2.43 2.16

Average Correlation Coefficients Labor productivity and wage

0.17

0.13

0.05

0.13

Note: The reported average percentile ratios and average correlation coefficients are simple averages of percentile ratios and correlation coefficients in annual cross sections of employed workers.

Figure 3: Occupation Specific Prices of Ability—Densities

200

400 600 Danish Kroner

0.000

0

Managers Salaried Skilled Unskilled

PDF 0.004 0.008

Managers Salaried Skilled Unskilled

PDF 0.004 0.008 0.000

Pulp, Paper & Paper Products, Publishing & Printing 0.012

0.012

Food Products, Beverages & Tobacco

800

0

200

400 600 Danish Kroner

800

Managers Salaried Skilled Unskilled

PDF 0.004 0.008 0.000

0.000

PDF 0.004 0.008

Managers Salaried Skilled Unskilled

0

400 600 Danish Kroner

Electrical & Optical Equipment 0.012

0.012

Basic Metals & Fabricated Metal Products

200

800

0

200

400 600 Danish Kroner

800

Note: The plotted densities are simple averages of densities in annual cross sections of firms included in the firm level panel.

12

Figure 4: Occupation Specific Ability Adjusted Labor Inputs—Densities

100 200 300 400 Ability adjusted labor input

0.000

0

Managers Salaried Skilled Unskilled

PDF 0.004 0.008

Managers Salaried Skilled Unskilled

PDF 0.004 0.008 0.000

Pulp, Paper & Paper Products, Publishing & Printing 0.012

0.012

Food Products, Beverages & Tobacco

500

0

100 200 300 400 Ability adjusted labor input

Managers Salaried Skilled Unskilled

PDF 0.004 0.008 0.000

0.000

PDF 0.004 0.008

Managers Salaried Skilled Unskilled

0

500

Electrical & Optical Equipment 0.012

0.012

Basic Metals & Fabricated Metal Products

100 200 300 400 Ability adjusted labor input

500

0

100 200 300 400 Ability adjusted labor input

500

Note: The plotted densities are simple averages of densities in annual cross sections of firms included in the firm level panel.

13

Table 4: Production Function Parameters—NLS and OLS Estimation Food Products, Beverages & Tobacco NLS αK αL γ1 γ2 γ3 γ4 

OLS

Pulp, Paper & Paper Products, Publishing & Printing

Basic Metals & Fabricated Metal Products

NLS

NLS

OLS

OLS

Electrical & Optical Equipment NLS

OLS

0.110

0.129

0.048

0.039

0.121

0.171

0.086

0.113

(0.033)

(0.036)

(0.344)

(0.026)

(0.021)

(0.027)

(0.018)

(0.019)

0.901

0.865

0.907

0.872

0.858

0.754

0.994

0.941

(0.040)

(0.043)

(0.044)

(0.045)

(0.036)

(0.051)

(0.029)

(0.032)

0.429

0.084

0.263

0.201

0.235

0.125

0.350

0.277

(0.078)

(0.048)

(0.041)

(0.035)

(0.106)

(0.046)

(0.043)

(0.037)

0.294

0.232

0.305

0.232

0.409

0.289

0.295

0.244

(0.056)

(0.040)

(0.058)

(0.055)

(0.071)

(0.067)

(0.041)

(0.035)

0.158

0.556

0.208

0.451

0.206

0.441

0.177

0.332

(0.021)

(0.048)

(0.031)

(0.048)

(0.035)

(0.078)

(0.025)

(0.040)

0.119

0.129

0.224

0.115

0.150

0.145

0.178

0.147

(0.016)

(0.018)

(0.039)

(0.031)

(0.025)

(0.021)

(0.017)

(0.017)

∞

1.000

∞

1.000

∞

1.000

9.628

1.000

(11.189)

# observations pCD pCRTS pCD∧CRTS

919 − 0.562 −

919 0.798

602 − 0.140 −

602 0.003

Note: The constant term is not reported.

14

502 − 0.529 −

502 0.081

1,076 0.442 0.001 0.001

1,076 0.028

Table 5: Production Function Parameters—GMM Estimation Food Products, Beverages & Tobacco (1) αK αL γ1 γ2 γ3 γ4 

(2)

Pulp, Paper & Paper Products, Publishing & Printing (1)

(2)

Basic Metals & Fabricated Metal Products (1)

(2)

# observations pJ pCD pCRTS pCD∧CRTS

(1)

(2)

0.010

0.183

0.184

0.021

0.116

0.118

0.102

0.193

(0.061)

(0.431)

(0.084)

(0.787)

(0.048)

(0.067)

(0.042)

(0.163)

1.028

0.817

0.685

0.979

0.853

0.882

0.991

0.807

(0.089)

(0.431)

(0.158)

(0.787)

(0.073)

(0.067)

(0.072)

(0.163)

0.688

0.011

0.166

0.071

0.000

0.072

0.219

0.431

(0.276)

(0.407)

(0.174)

(2.482)

(0.325)

(0.141)

(0.285)

(0.265)

0.215

0.371

0.537

0.140

0.578

0.184

0.522

0.194

(0.143)

(0.503)

(0.384)

(2.578)

(0.293)

(0.157)

(0.298)

(0.551)

0.097

0.538

0.235

0.325

0.250

0.399

0.216

0.091

(0.175)

(0.184)

(0.383)

(2.902)

(0.119)

(0.086)

(0.338)

(0.734)

0.000

0.080

0.062

0.464

0.172

0.346

0.044

0.284

(0.000)

(0.175)

(0.080)

(2.842)

(0.088)

(0.254)

(0.133)

(0.418)

∞

1.000

0.541

1.000

∞

1.000

9.384

1.000

(0.365)

η

Electrical & Optical Equipment

(172.89)

0.768

0.803

0.812

0.837

0.630

0.425

0.733

0.794

(0.034)

(0.035)

(0.039)

(0.143)

(0.052)

(0.362)

(0.027)

(0.052)

782 0.668 0.999 0.362 0.612

782

517 0.410 0.209 0.159 0.215

517

439 0.421 0.999 0.393 0.607

439

909 0.227 0.961 0.055 0.108

909

Note: Constant term not reported. Columns labeled (1) contain estimates obtained under CES labor aggregator and unrestricted returns to scale in capital and aggregated labor. Columns labeled (2) contain estimates obtained with a Cobb-Douglas labor aggregator and constant returns to scale in capital and aggregated labor. The reported standard errors are not corrected for the first step estimation of individual abilities.

15

Table 6: Ability Price Function Estimates Food Products, Beverages & Tobacco Managers Bargaining power β1 Outside option b1 Salaried workers Bargaining power β2 Outside option b2 Skilled workers Bargaining power β3 Outside option b3 Unskilled workers Bargaining power β4 Outside option b4

Pulp, Paper & Paper Products, Publishing & Printing

Basic Metals & Fabricated Metal Products

Electrical & Optical Equipment

0.503

0.317

0.309

0.201

[0.164,0.843]

[0.024,0.609]

[0.111,0.506]

[0.012,0.389]

379.0

[365.4,392.6]∗

214.4

280.7

190.6

[159.6,269.2]

[228.2,333.3]

[72.3,308.9]

0.098

0.161

0.279

0.350

[0.002,0.194]

[0.009,0.312]

[0.011,0.548]

[0.006,0.693]

141.9

180.6

120.3

121.1

[60.4,223.4]

[141.1,220.1]

[0.0,240.7]

[0.0,242.1]

0.189

0.221

0.244

0.462

[0.020,0.357]

[0.018,.424]

[0.008,0.480]

[0.012,0.912]

185.0

183.3

[184.3,185.7]

[172.1,194.4]

290.5

[192.3,388.7]∗

108.1 [27.4,188.7]

0.290

0.045

0.092

0.180

[0.002,0.578]

[0.008,0.083]

[0.027,0.157]

[0.006,0.355]

89.8

89.3

136.0

90.4

[0.0,179.7]

[27.7,151.0]

[81.2,190.9]

[0.0,180.8]

Note: The reported estimates are conditional on the production function parameter estimates reported in columns labeled (2) in Table 5. Numbers presented in square brackets are bounds obtained using reverse regression techniques.

Table 7: Employment Weighted Log Labor Productivity Variance Decomposition

h  i Y E V ar ln NJ(i,t),t |t J(i,t),t

Ability heterogeneity Occupational labor misallocation Aggregate factor misallocation

Food Products, Beverages & Tobacco

Pulp, Paper & Paper Products, Publishing & Printing

Basic Metals & Fabricated Metal Products

Electrical & Optical Equipment

0.063

0.057

.0.042

.108

19% 35% 46%

24% 3% 73%

8% −7% 99%

5% 25% 70%

Note: The decomposition is given by (27) in the main paper. J(i, t) = j if worker i is employed by firm j in period t. Results are based on the production function estimates reported in columns labeled (2) in Table 5.

16

Table 8: Log Wage Variance Decomposition Food Products, Beverages & Tobacco

Pulp, Paper & Paper Products, Publishing & Printing

Basic Metals & Fabricated Metal Products

Electrical & Optical Equipment

0.076

0.159

0.085

0.104

85% 15%

77% 23%

78% 22%

66% 34%

E [E [V ar (ln wit |h, t) |t]]

0.065

0.122

0.066

0.068

Worker ability Firm-level price of ability Residual

72% 10% 18%

86% 4% 10%

76% 9% 15%

72% 14% 14%

E [V ar (ln wit |t)] Within occupation Between occupation

Note: The decompositions are given by (28) and (29) in the main paper.

Table 9: Log Labor Productivity-Log Wage Covariance Decomposition Food Products, Beverages & Tobacco

Pulp, Paper & Paper Products, Publishing & Printing

Basic Metals & Fabricated Metal Products

Electrical & Optical Equipment

h  i Y E Cov ln NJ(i,t),t , ln wit |t

0.013

0.011

0.004

0.016

Ability heterogeneity Occupational labor misallocation Aggregate factor misallocation

−3% 23% 80%

30% −95% 165%

45% −24% 79%

15% 106% −21%

J(i,t),t

Note: The decomposition is given by (30) in the main paper. J(i, t) = j if worker i is employed by firm j in period t.

17

18

0.627 0.223 0.404 0.644 0.562 0.166 0.396 0.704 0.976 0.398 0.578 0.592 782

Salaried workers Gross ability flow Ability reallocation Ability churning Churning/Gross flow

Skilled workers Gross ability flow Ability reallocation Ability churning Churning/Gross flow

Unskilled workers Gross ability flow Ability reallocation Ability churning Churning/Gross flow

Number of firm-years

782

0.410 0.251 0.160 0.389

0.144 0.078 0.066 0.459

0.237 0.123 0.114 0.481

0.219 0.128 0.091 0.417

IN

782

0.565 0.219 0.346 0.612

0.418 0.112 0.306 0.732

0.390 0.144 0.246 0.631

0.466 0.201 0.265 0.568

EX

517

1.090 0.436 0.654 0.600

0.540 0.166 0.374 0.693

0.578 0.218 0.360 0.623

0.552 0.207 0.345 0.625

TO

517

0.349 0.225 0.125 0.357

0.124 0.068 0.056 0.453

0.176 0.112 0.063 0.361

0.129 0.088 0.042 0.323

IN

517

0.741 0.298 0.443 0.598

0.416 0.125 0.291 0.700

0.402 0.149 0.253 0.629

0.423 0.162 0.261 0.618

EX

Pulp, Paper & Paper Products, Publishing & Printing

439

0.866 0.371 0.495 0.572

0.508 0.152 0.356 0.701

0.528 0.206 0.322 0.610

0.592 0.238 0.354 0.598

TO

439

0.370 0.207 0.163 0.441

0.107 0.059 0.048 0.447

0.190 0.110 0.079 0.418

0.178 0.107 0.071 0.399

IN

439

0.496 0.224 0.272 0.547

0.400 0.121 0.279 0.698

0.339 0.139 0.200 0.589

0.414 0.189 0.225 0.543

EX

Basic Metals & Fabricated Metal Products

909

0.937 0.445 0.492 0.525

0.580 0.202 0.378 0.652

0.605 0.233 0.372 0.614

0.564 0.209 0.355 0.629

TO

909

0.444 0.288 0.156 0.351

0.185 0.097 0.088 0.474

0.250 0.143 0.107 0.428

0.162 0.092 0.070 0.434

IN

EX

909

0.493 0.226 0.267 0.541

0.395 0.144 0.251 0.636

0.356 0.144 0.212 0.595

0.402 0.162 0.240 0.597

Electrical & Optical Equipment

Note: Omitting superscripts T O, IN and EX for Total, Internal and External. Gross ability flow is the average gross ability flow rate E[LGF Rjht |h], Ability reallocation is the average ability reallocation rate E[LN RRjht |h], and Ability churning is the average ability churning rate E[LCF Rjht |h]. LGF Rjht , LN RRjht , and LCF Rjht are defined in the text. Churning/Gross flow is E[LCF Rjht |h]/E[LGF Rjht |h].

0.685 0.270 0.415 0.605

Managers Gross ability flow Ability reallocation Ability churning Churning/Gross flow

TO

Food Products, Beverages & Tobacco

Table 10: Annual Ability Flow Rates

Figure 5: Net Ability Flow Rates and Employer MPL Rank Pulp, Paper & Paper Products, Publishing & Printing

Managers Salaried workers Skilled workers Unskilled workers

0.00

0.25 0.50 0.75 Lagged MPL rank

1.00

Annual net ability flow rate −0.3 −0.1 0.1 0.3

Annual net ability flow rate −0.3 −0.1 0.1 0.3

Food Products, Beverages & Tobacco

Managers Salaried workers Skilled workers Unskilled workers

0.00

Managers Salaried workers Skilled workers Unskilled workers

0.00

0.25 0.50 0.75 Lagged MPL rank

1.00

Electrical & Optical Equipment

1.00

Note: The shaded areas are 95% confidence intervals.

19

Annual net ability flow rate −0.3 −0.1 0.1 0.3

Annual net ability flow rate −0.3 −0.1 0.1 0.3

Basic Metals & Fabricated Metal Products

0.25 0.50 0.75 Lagged MPL rank

Managers Salaried workers Skilled workers Unskilled workers

0.00

0.25 0.50 0.75 Lagged MPL rank

1.00

20

0.886 0.326 0.560

0.470 0.164 0.306

1.342 0.724 0.618

Salaried workers Transition: (Q, P ) = (25, 75) Transition: (Q, P ) = (25, 50) Transition: (Q, P ) = (50, 75)

Skilled workers Transition: (Q, P ) = (25, 75) Transition: (Q, P ) = (25, 50) Transition: (Q, P ) = (50, 75)

Unskilled workers Transition: (Q, P ) = (25, 75) Transition: (Q, P ) = (25, 50) Transition: (Q, P ) = (50, 75) 0.432 0.185 0.247

0.080 0.025 0.056

0.281 0.084 0.197

0.114 0.036 0.078

Rhw

1.048 0.407 0.641

0.733 0.380 0.353

0.657 0.325 0.332

0.494 0.203 0.290

RhM P L

0.248 0.073 0.174

0.154 0.069 0.085

0.115 0.049 0.066

0.062 0.022 0.040

Rhw

Pulp, Paper & Paper Products, Publishing & Printing

1.473 0.643 0.829

0.322 0.170 0.152

0.704 0.379 0.325

0.847 0.415 0.432

RhM P L

0.353 0.108 0.245

0.061 0.030 0.031

0.211 0.101 0.110

0.280 0.117 0.162

Rhw

Basic Metals & Fabricated Metal Products

1.300 0.397 0.903

0.706 0.244 0.462

0.636 0.305 0.331

0.893 0.438 0.455

RhM P L

0.489 0.109 0.380

0.206 0.060 0.146

0.387 0.174 .213

0.390 0.167 0.223

Rhw

Electrical & Optical Equipment

Note: RhM P L = RhM P L (Q, P ) is given by (31) in the main paper. Rhw = Rhw (Q, P ) is given by (32). Computations are based on the production function estimates reported in columns labeled (2) in Table 5, and in Table 6.

0.751 0.294 0.457

Managers Transition: (Q, P ) = (25, 75) Transition: (Q, P ) = (25, 50) Transition: (Q, P ) = (50, 75)

RhM P L

Food Products, Beverages & Tobacco

Table 11: Output and Wage Gains from Labor Reallocation