NIST Special Publication 1135

Characterization of the U.S. 

Construction Labor Supply

Stanley W. Gilbert

http://dx.doi.org/10.6028/NIST.SP.1135
NIST Special Publication 1135

Characterization of the U.S. 

Construction Labor Supply

Stanley W. Gilbert

Applied Economics Office

Engineering Laboratory

http://dx.doi.org/10.6028/NIST.SP.1135

December 2012

U.S. Department of Commerce 

Rebecca Blank, Acting Secretary

National Institute of Standards and Technology 

Patrick D. Gallagher, Under Secretary of Commerce for Standards and Technology and Director 
Certain commercial entities, equipment, or materials may be identified in this

document in order to describe an experimental procedure or concept adequately.

Such identification is not intended to imply recommendation or endorsement by the

National Institute of Standards and Technology, nor is it intended to imply that the

entities, materials, or equipment are necessarily the best available for the purpose. 

National Institute of Standards and Technology Special Publication 1135

Natl. Inst. Stand. Technol. Spec. Publ. 1135, 98 pages (December 2012) 

http://dx.doi.org/10.6028/NIST.SP.1135

CODEN: NSPUE2
iii

Abstract

This study characterizes the construction labor pool, and carries out preliminary work toward 

an estimation of the supply and demand for construction labor. Specifically, it evaluates the 

composition of the construction labor force by race, age, educational attainment, union 

membership and employer type, and how that composition is changing over time. It also 

identifies which industries are most closely related to construction, and estimates labor flows 

over time by race, place of birth, and age. Finally, the report makes a preliminary evaluation 

of how skills have changed in the construction labor force over time and how the skill level of 

the construction labor force changes with changing wages.

Keywords:

Construction; Labor Supply; Econometric Analysis; Labor Flows; Related Industries

v

Preface

This study was conducted by the Applied Economics Office in the Engineering Laboratory at 

the National Institute of Standards and Technology. The study characterizes several aspects of 

the construction labor supply. The intended audience is the National Institute of Standards 

and Technology, as well as other government agencies, private sector organizations concerned 

about the perceived decline in construction productivity, and standards development 

organizations that produce standards used by the construction industry.

Disclaimer

Certain trade names and company products are mentioned in the text in order to adequately 

specify the technical procedures and equipment used. In no case does such identification 

imply recommendation or endorsement by the National Institute of Standards and 

Technology, nor does it imply that the products are necessarily the best available for the 

purpose.

Cover Photography Credits

Cover photos, clockwise from the upper left are: Construction workers looking at blue print, 

provided courtesy of Microsoft; Construction cranes against sky, provided courtesy of Fotolia; 

City construction site, provided courtesy of Microsoft; and construction site, provided 

courtesy of Microsoft.

vii

Acknowledgements

The author wishes to thank all those who contributed so many excellent ideas and suggestions 

to this report. They include Dr. Robert Chapman, Chief of the Applied Economic Office (AEO) 

at the National Institute of Standards and Technology who provided support and many useful 

comments. Dr. David Butry, an AEO economist, provided many useful comments. Dr. James 

Filliben, of the Statistical Engineering Division at the National Institute of Standard and 

Technology provided comments that substantially improved the clarity and presentation of 

the results. Dr. Paul Goodrum of the University of Kentucky, College of Engineering reviewed 

an earlier version of this paper, and made several helpful suggestions. Ms. Carmen Pardo of 

the AEO assisted greatly in preparing the manuscript for review and publication. As always, 

any remaining flaws and errors are the responsibility of the author.

ix

Table of Contents

Abstract.....................................................................................................................................................iii

Preface........................................................................................................................................................ v

Acknowledgements ...............................................................................................................................vii

Table of Contents .................................................................................................................................... ix

List of Figures ........................................................................................................................................... x

List of Tables ...........................................................................................................................................xii

Executive Summary............................................................................................................................... xv

1. Introduction ...................................................................................................................................... 1

2. Relationship to Other Industries.................................................................................................... 5

2.1. Informal Theory and Methodology........................................................................................ 5

2.2. Results ......................................................................................................................................... 6

3. Characteristics of the Construction Labor Pool........................................................................... 9

3.1. Theory and Methodology ........................................................................................................ 9

3.2. Results ....................................................................................................................................... 13

3.2.1. Seasonality ........................................................................................................................ 16

3.2.2. Union Membership.......................................................................................................... 17

3.2.3. Employer Type ................................................................................................................. 19

3.2.4. Cohort Effects on Employer Type and Union Membership...................................... 21

3.2.5. Sex ...................................................................................................................................... 24

3.2.6. Age ..................................................................................................................................... 27

3.2.7. Race and Ethnicity ........................................................................................................... 31

3.2.8. Education .......................................................................................................................... 36

4. Labor Flows .................................................................................................................................... 39

4.1. Model and Methodology........................................................................................................ 39

4.2. White Men ................................................................................................................................ 42

4.3. Black Men ................................................................................................................................. 47

4.4. U.S. Born Hispanic Men ......................................................................................................... 52

4.5. Foreign Born Hispanic Men................................................................................................... 57

5. Discussion ....................................................................................................................................... 63

5.1. Skills .......................................................................................................................................... 63
x

5.2. Labor Supply and Wage......................................................................................................... 65

5.3. Future Directions..................................................................................................................... 68

6. References ....................................................................................................................................... 71

Appendices ............................................................................................................................................. 73

Appendix 1: Data ............................................................................................................................... 73

Appendix 2: Similarity Indices......................................................................................................... 76

List of Figures

Figure 1: Labor Productivity index for the US Construction industry and all non-farm 

industries................................................................................................................................................... 2

Figure 2: Interactions of the variables in the analysis....................................................................... 13

Figure 3: Proportion of men in construction in each categorical variable in 2010. ...................... 14

Figure 4: Main-Effects Plot of Unemployment v. Key variables analyzed in the paper. ............ 14

Figure 5: Cumulative Normalized Unemployment over the study period. ................................. 15

Figure 6: Average change in construction employment by month. ............................................... 16

Figure 7: Percent union membership in construction estimated from the CPS (data points) and 

calculated from regression (line). Blue regions represent recessions............................................ 18

Figure 8: Estimated and Calculated probability that a person in construction has a specified 

type of employer. ................................................................................................................................... 20

Figure 9: Changes in Employer type and Union membership with age for the 1960 cohort. .... 22

Figure 10: Changes in employer type and union membership with cohort at age 30................. 22

Figure 11: Monthly male and female participation in the construction industry. Left scale is 

male participation and right scale is female participation............................................................... 24

Figure 12: Percent women employed in construction by month. ................................................... 25

Figure 13: Monthly probability of being in construction given that a man is in a specified age 

category. .................................................................................................................................................. 28

Figure 14: Monthly probability of being in a given age group given that a man is working in 

construction. ........................................................................................................................................... 30
xi

Figure 15: Monthly Employment Probability by race and ethnicity. ............................................. 32

Figure 16: For each race/ethnicity, the fraction of men working in construction divided by the 

proportion of that race/ethnicity in the population, by month....................................................... 33

Figure 17: Monthly Conditional Probability by race and ethnicity................................................ 34

Figure 18: Proportion of men in construction who belong to each race/ethnicity, by region and 

time........................................................................................................................................................... 35

Figure 19: Monthly Employment Probability by level of education. ............................................. 37

Figure 20: Conditional Probability by educational level.................................................................. 38

Figure 21: Blue line is the number of White Men in construction in 1994, by age. Red line is the 

stable number of White men in construction assuming economic growth and unemployment 

continue at their average rates indefinitely........................................................................................ 42

Figure 22: Fit of estimates to data for White men in construction by age group.......................... 44

Figure 23: Net inflow to construction for White men, by age for selected years.......................... 45

Figure 24: Blue line is the number of Black Men in construction in 1994, by age. Red line is the 

stable number of Black men in construction assuming economic growth and unemployment 

continue at their average rates indefinitely........................................................................................ 47

Figure 25: Fit of estimates to data for Black men in construction by age group, by month. ...... 49

Figure 26: Net inflow to construction for Black men, by age for selected years........................... 50

Figure 27: Blue line is the number of US Born Hispanic Men in construction in 1994, by age. 

Red line is the stable number of US Born Hispanic men in construction assuming economic 

growth and unemployment continue at their average rates indefinitely...................................... 52

Figure 28: Fit of estimates to data for US Born Hispanic men in construction by age group..... 54

Figure 29: Net inflow to construction for U.S. born Hispanic men, by age for selected years... 55

Figure 30: Blue lines both represent the number of foreign-born Hispanic Men in construction 

in 1994, by age. Red line is the stable number in construction assuming economic growth and 

unemployment continue at their average rates indefinitely. Note that the solid blue line is 

plotted against the left axis, while the red line (and dashed blue line for scale) is plotted 

against the right axis.............................................................................................................................. 57
xii

Figure 31: Fit of estimates to data for foreign-born Hispanic men in construction by age group.

................................................................................................................................................................... 59

Figure 32: Net inflow to construction for foreign-born Hispanic men, by age for selected years.

................................................................................................................................................................... 60

Figure 33: Average years of education of men in construction by age, and normalized by the 

average years of education of men in the population at large. ....................................................... 64

Figure 34: Average normalized years of education for 30-year-old men in construction by year.

................................................................................................................................................................... 65

Figure 35: Interpolated Monthly GDP overlaid on reported Quarterly GDP............................... 75

List of Tables

Table 1: Select 2009 Statistics for construction. Values are in Billions of Dollars unless otherwise 

stated.......................................................................................................................................................... 1

Table 2: Top 12 industries in terms of similarity index with construction...................................... 7

Table 3: Top 10 industries in terms of inter-industry flows with construction. ............................. 8

Table 4: List of variables analyzed below and the number of levels for each variable. .............. 13

Table 5: Coefficients for the Conditional Probability estimate that a man employed in 

construction is a member of a union. .................................................................................................. 17

Table 6: Coefficients for the Conditional Probability that a man in construction has a specified 

type of employer. ................................................................................................................................... 19

Table 7: Marginal effects on the probability of working in the specified sector........................... 19

Table 8: Coefficients for the estimate of the Conditional Probability for employer type and 

union membership versus cohort and age......................................................................................... 21

Table 9: Coefficients for the estimate of Employment Probability by sex. .................................... 24

Table 10: Probability of being female given that a person is employed in construction............. 25

Table 11: Coefficients for the estimate of Employment Probability by age................................... 27

Table 12: Coefficients for the estimate of the Conditional Probability by age.............................. 29
xiii

Table 13: Marginal Effects on Conditional Probability by age group. ........................................... 29

Table 14: Coefficients for the estimate of Employment Probability by race/ethnicity................. 31

Table 15: Coefficients for the estimate of the Conditional Probability by race and ethnicity..... 33

Table 16: Marginal effects on Conditional Probability by race and ethnicity. .............................. 33

Table 17: Coefficients for the estimate of Employment Probability by level of education ......... 36

Table 18: Coefficients for the estimate of the Conditional Probability by educational level...... 37

Table 19: Marginal effects for Conditional Probability by educational level................................ 38

Table 20: Coefficients for net flows of White men into construction. ............................................ 43

Table 21: Net rate of inflow to construction by age and rate of economic growth. Colored cells 

indicate ages and circumstances where men are on net leaving construction. ............................ 45

Table 22: Impact of seasonality. Seasonal Coefficient is the absolute magnitude of the seasonal 

variation. Wald Test represents the probability that the seasonal variation is greater than zero. 

Percent change is calculated based on the highest estimated seasonal employment compared to 

the lowest estimated seasonal employment....................................................................................... 46

Table 23: Coefficients for net flows of Black men into construction............................................... 48

Table 24: Net rate of inflow to construction by age and rate of economic growth. Colored cells 

indicate ages and circumstances where men are on net leaving construction. ............................ 50

Table 25: Impact of seasonality. Seasonal Coefficient is the absolute magnitude of the seasonal 

variation. Wald Test represents the probability that the seasonal variation is greater than zero.

................................................................................................................................................................... 51

Table 26: Coefficients for net flows of US Born Hispanic men into construction......................... 53

Table 27: Net rate of inflow to construction by age and rate of economic growth. Colored cells 

indicate ages and circumstances where men are on net leaving construction. ............................ 55

Table 28: Impact of seasonality. Seasonal Coefficient is the absolute magnitude of the seasonal 

variation. Wald Test represents the probability that the seasonal variation is greater than zero.

................................................................................................................................................................... 56

Table 29: Coefficients for net flows of US Born Hispanic men into construction......................... 58
xiv

Table 30: Net rate of inflow to construction by age and rate of economic growth. Colored cells 

indicate ages and circumstances where men are on net leaving construction. ............................ 61

Table 31: Impact of seasonality. Seasonal Coefficient is the absolute magnitude of the seasonal 

variation. Wald Test represents the probability that the seasonal variation is greater than zero.

................................................................................................................................................................... 61

Table 32: Simultaneous estimation of construction wage and choice to work in construction for 

adult men. ............................................................................................................................................... 67
xv

Executive Summary

Construction is an engine of growth for the U.S. economy. Investment in plant and facilities, 

in the form of construction activity, provides the basis for the production of goods and the 

delivery of services. Investment in infrastructure promotes the smooth flow of goods and 

services and the movement of individuals. Investment in housing accommodates new 

households and allows existing households to expand or improve their housing. It is clear that 

construction activities affect nearly every aspect of the U.S. economy and that the industry is 

vital to the continued growth of the U.S. economy.

This study characterizes the construction labor supply, and in particular characterizes how it is 

changing over time. This is a preliminary step toward estimating the supply and demand for 

construction labor, which is itself part of an effort to understand changes in construction labor 

productivity.

It was not possible to characterize all variables that correlate with either construction labor 

supply or construction productivity due to limitations of both the data and time. The variables 

that were analyzed were chosen based on three main considerations. First, variables were 

selected based on data availability. Second, some variables were chosen because they have 

been previously identified as potentially being associated with the changes in construction 

productivity. Third, some variables are included because they may represent categories of 

workers that may respond differently to price signals in the construction labor market.

Four basic questions are answered in this study. First, the supply pool from which 

construction labor is drawn is identified. Second, composition of the work force is 

characterized, and how it changes over time. Third, net labor flows by age are estimated for 

several different groups within the construction labor force. Fourth, some specific issues 

related to skilled labor within the construction labor force are evaluated.

Data for this study are primarily taken from the Current Population Survey (CPS) from 1994 –

2010.

First, the supply pool from which construction labor is drawn is identified. In particular, the 

industries that are seen as approximate substitutes by construction workers, and those 

industries with relatively large labor flows between it and construction are identified. The 

main finding is that construction draws from a pool of industries that are low to medium 

skilled and not necessarily closely related to construction like retail trade and food-service. 

Closely related industries are usually either very small (in numbers of employees) or related to 

a specialty occupation within construction (like administrative and support services).

To evaluate the composition of the work force and how it changes over time, several 

characteristics are evaluated, including racial composition of the work force, which provides 

some insight into the extent to which there is an influx of unskilled foreign workers into the 
xvi

labor pool. In an effort to estimate skills and changing skill levels, the educational composition 

of the work force and changes in labor union membership are also evaluated. Finally, the age 

distribution of the workforce is evaluated.

The biggest change in the labor force is that Hispanics (probably dominated by the foreignborn) are growing rapidly. Union membership is declining. That means that the market for 

skilled trades is changing. The nature of those changes, however, cannot be determined from 

this data set. Lower skilled employees are the most susceptible to the business cycle. That 

includes non-union members, younger and less educated workers, and Hispanics.

Detailed findings include:

• The construction market is seasonal, with peak employment in the summer.

• About 10 % of the construction labor force is female.

• Union membership is declining at an average rate of about 2.5 % per year. Union 

membership is slightly countercyclical, which suggests that union members are slightly 

less susceptible to the business cycle1 than non-union members. However, it is possible 

that the difference in susceptibility to the business cycle is due to demographic 

characteristics (like age differences) rather than union membership.

• Over the long term, private employment and self-employment in construction are 

increasing as a proportion of total employment, while government employment in 

construction is decreasing. In fact, government employment in the construction sector 

is decreasing in absolute terms. The business cycle affects private employment more 

than the other sectors.

• As privately employed non-union members get older, many of them move into selfemployment. A similar process may be affecting privately employed union members as 

well. Publically employed union members are a small but constant fraction of 

construction workers, suggesting that such workers tend to stay put as they get older.

• The decline in union membership appears to be primarily due to younger cohorts 

choosing not to join unions rather than to existing members dropping out.

• More recent cohorts appear to be less likely to be self-employed. An estimated 30 % of 

people born in 1960 were likely to be self-employed at age 50, while only an estimated 

 1 The business cycle “refers to economy-wide fluctuations in production or economic activity over several months 

or years” (Business cycle. (2011, October 3). In Wikipedia, The Free Encyclopedia. Retrieved 13:25, October 4, 2011, 

from http://en.wikipedia.org/w/index.php?title=Business_cycle&oldid=453740220). The business cycle is to be 

distinguished from seasonality (which is also analyzed here). Seasonality is the regular fluctuation for different 

times of year, while the business cycle typically spans several years and includes recession and recovery.
xvii

20 % of those born in 1990 will be self-employed at age 50. However, the shift in selfemployment probability is a reflection of the changes in the racial and educational 

composition of the construction work-force. What is not clear is whether the changes in 

self-employment probability are caused by the demographic changes, or whether they 

are caused by other factors that correlate with the demographic changes.

• Susceptibility to the business cycle decreases with age. The oldest groups are nearly 

immune to the business cycle.

• Hispanic men are entering construction at an increasing rate compared to white or 

black men, while the likelihood of black men in construction is actually decreasing. 

Nevertheless, White men still make up about 75 % of the construction labor force.

• Hispanic men are more susceptible to the business cycle than black men, who in turn 

are more susceptible to the business cycle than white men.

• Initially, those with a high school education were the most likely to be in construction, 

with men without a high school education second most likely. However, the likelihood 

of a man without a high school education being in construction has increased at a faster 

rate than the likelihood for a man with a high school education.

• However, since the number of people with a high-school education greatly outnumbers 

those without one, the number of people in construction with a high school education 

still outnumbers those without one.

• The greater the level of education, the less susceptible a person is to the business cycle.

Labor flows were estimated to evaluate issues regarding the aging of the work force, the 

number of young people entering the industry, and shifts in the work force toward foreign 

immigrants. The basic questions answered here is who is entering the work force, who is 

leaving it, and when.

The bulk of entrants to the work force are younger than 25. In most years, young people 

entering the industry outnumber older people leaving it. So concerns about gentrification of 

the industry do not seem to be reflected in the data. Specific findings include:

• The bulk of the inflow of white men to construction over the long term occurs before the 

age of 21. In general, older worker are less susceptible to the business cycle than 

younger workers. Above the age of 55, the impact of the business cycle has no 

statistical effect on employment.

• The bulk of the inflow of black men to construction over the long term occurs before the 

age of 24. As usual, older worker are less susceptible to the business cycle than younger 
xviii

workers. Above the age of 55, the impact of the business cycle has no statistical effect 

on employment.

• The bulk of the inflow of US-born Hispanic men to construction over the long term 

occurs before the age of 25. As usual, older workers are less susceptible to the business

cycle than younger workers. Above the age of 55, the impact of the business cycle has 

no statistical effect on employment.

• The rate of inflow of foreign-born Hispanic men to construction is decreasing with age. 

However, inflow is still significant to the age of 55. The bulk of the inflow of foreignborn Hispanic men to construction over the long term occurs before the age of 34. 

Above the age of 55, the impact of the business cycle has no statistical effect on 

employment.

There is a perception that the construction industry has difficulty attracting and retaining 

skilled workers, and as a result faces a shortage of skilled workers. This problem is 

exacerbated by a 30-year decline in real construction wages relative to workers in other 

industries. This raises a number of economic questions that this report was intended, in part, 

to address.

In competitive markets, shortages are resolved by increases in price. That raises the question 

of why wages haven’t adjusted for the decline. If construction costs (including delay costs) 

have increased, why haven’t wages? To address this, two questions were evaluated: to what 

extent can a decline in skills be discerned in the data; and how does labor supply adjust to 

changes in wage?

• There is some support for the idea that there is a decline in skill level among the 

construction labor force. Average normalized years of education for men in 

construction at age 30 seems to decrease over time. Educational level also seems to be 

inversely related to the business cycle. However, since a formal model of education

was not specified, these observations cannot be statistically tested.

• Preliminary efforts to model supply and demand could not be statistically estimated. 

The most likely reason for the failure is that an omitted variable correlates with both 

wage and employment. The best candidate for such an omitted variable would be skill. 

If wages correlate with skill (as seems reasonable) and if low-skill people are the last 

hired and first fired, then the efforts to estimate supply and demand without taking into 

account skill will fail.

• When estimating labor supply directly from microeconomic data, the model finds that 

correlation between the construction wage and the choice to work in construction is 

negative. That implies that increases in construction wages are associated with people 

selecting out of construction. That suggests that the skill premium is higher in other 
xix

industries than in construction. So (all else equal) there are relatively few ‘highly 

skilled’ construction workers because such people can earn more in other industries—

presumably because they are more productive there.

There are a number of additional directions that would contribute to understanding the 

construction labor market.

• Characterization at the regional / local level.

This report characterized labor supply at the national scale for the most part. However, 

construction is primarily a local market and there will be aspects of the market that will 

be obscured by looking at it nationally. For example, racial makeup (and probably 

seasonality) clearly differs from region to region. So deepening the analysis to look at 

the data at a regional scale would likely improve our understanding of the market.

• Supply and demand need to be estimated. 

Estimating supply and demand functions for construction labor would help. That turns 

out to be surprisingly difficult due to the high correlation between wages and 

employment. During times of increasing employment, wages (presumably) increase, 

but the people hired are at the low end of the wage scale while the people at the high 

end of the wage scale are susceptible to poaching by other industries. Times of 

decreasing employment present the reverse situation. That makes it difficult to tease 

out the relationship between supply and wage holding all else constant. Completing 

the task of estimating supply and demand will help fill in some of the missing pieces of 

the picture of the construction labor market.

• Labor Unions

The perceived shortage in skilled labor is probably linked to the declines in union 

membership. So to understand what is going on, more information is needed on the 

place of unions in the market, why market share is declining (both from the supply side 

with people choosing whether to join and from the demand side of builders choosing 

whether to hire union labor), and what (if anything) is replacing unions in the 

marketplace. So to better understand the nature of skilled-labor shortages (or lack 

thereof) requires an understanding of the changing place of the trade unions in the 

market.

• Wage trends for skilled craft workers v. general construction labor

The CPS data used to generate this report is not detailed enough to distinguish skilled 

craft workers in construction from general laborers. It is possible that wages for general 

construction labor are declining while “shortages” for skilled craft workers are causing 
xx

their wages to increase. This could explain how there are “shortages” of skilled craft 

workers alongside declining construction wages. One way of assessing this possibility 

would be to look at the long-term trend of wages for craft workers versus general 

construction labor. Such data does not exist in the CPS, so other data sources would 

have to be found.

• Labor flows by educational level

Expanding the analysis of labor flows to address educational levels would provide 

additional insight into long-term changes in educational levels in people entering 

construction.

• Analysis by market segment

Eventually, this work needs to be done for different segments of the construction 

market. Housing is such a large portion of the market that the results above are likely 

dominated by that segment of the market. But other segments will likely be different.
1

1. Introduction

Construction is an engine of growth for the U.S. economy. Investment in plant and facilities, 

in the form of construction activity, provides the basis for the production of products and the 

delivery of services. Investment in infrastructure promotes the smooth flow of goods and 

services and the movement of individuals. Investment in housing accommodates new 

households and allows existing households to expand or improve their housing. It is clear that 

construction activities affect nearly every aspect of the U.S. economy and that the industry is 

vital to the continued growth of the U.S. economy.

The construction industry’s contribution to gross domestic product (GDP) and employment in 

2009 is shown in Table 1.

2 In 2009 construction was still in decline following the 2007 to 2009 

recession, and so the contribution of construction to GDP and employment was substantially 

below its long-term average.

Table 1: Select 2009 Statistics for construction. Values are in Billions of Dollars unless otherwise stated.

Statistic Value

(billions)

Value of Construction put in place 937.21

Residential 28 %

Commercial / Industrial 35 %

Manufacturing 8 %

Public Works 29 %

US GDP 14,119.04

Construction Value Added 537.46

Percent of GDP 3.8 %

Total US Employment (millions) 137.775

Construction Employment 9.702

Percent of Total Employment 7.0 %

In spite of its importance to the economy, construction seems to be undergoing a long-term 

decline in productivity3. To illustrate, Figure 1 shows the results of Teicholz4 for construction 

productivity growth over the last 40 years. He found that as measured by constant contract 

dollars of new construction work per field work hour, labor productivity in the construction 

industry has trended downward over the past 40 years at an average compound rate of -0.6 %

 2 Thomas, D., 2010. “Methodology for Calculating Construction Industry Supply Chain Statistics.” NIST Special 

Publication 1116. Gaithersburg, MD.

3 Not all researchers believe that construction productivity is in decline. For a discussion of the debate, see 

Huang, Allison, Robert Chapman and David Butry. (2009) “Metrics and Tools for Measuring Construction 

Productivity: Technical and Empirical Considerations.” NIST Special Publication 1101. Gaithersburg, MD.

4 From Teicholz, Paul. “Labor Productivity Declines in the Construction Industry: Causes and Remedies.” 

AECbytes Viewpoint. Issue 4. April 14, 2004.
2

per year. Reasons for the decline are debated, but some things that have been suggested as 

possible reasons include5 a shortage of skilled workers (and in particular skilled craft 

workers), an aging work force, the possibility that fewer young people are entering the 

industry, and the influx of unskilled labor from abroad.

Figure 1: Labor Productivity index for the US Construction industry and all non-farm industries.6

This study is intended as a preliminary step toward understanding the changes in construction 

labor productivity. Since many of the factors believed to influence the changes in construction 

productivity are related to changes in the construction labor supply, this study characterizes 

construction labor supply, and in particular characterizes how it is changing over time. What 

it does not do is characterize how these factors influence labor productivity. That is the subject 

of future research.

It was not possible to characterize all variables that correlate with either construction labor 

supply or construction productivity due to limitations of both the data and time. The variables 

that were analyzed were chosen based on three main considerations. First, variables were 

selected based on data availability. Construction sector is almost certainly a significant factor 

in both labor supply and construction productivity. However, the data set used here contains 

no information on the construction sector a worker is in. Second, some variables were chosen 

 5 Among other possible causes. For a more complete discussion of possible causes of the decline in productivity 

see Huang, Allison, Robert Chapman and David Butry. (2009) “Metrics and Tools for Measuring Construction 

Productivity: Technical and Empirical Considerations.” NIST Special Publication 1101.

6 Source: Teicholz, Paul. “Labor Productivity Declines in the Construction Industry: Causes and Remedies.” 

AECbytes Viewpoint. Issue 4. April 14, 2004.

0%

50%

100%

150%

200%

250%

196419661968197019721974197619781980198219841986198819901992199419961998200020022004

Percent building and nonbuilding output

Year

nonfarm business productivity construction productivity
3

because they have been previously identified as potentially being associated with the changes 

in construction productivity. Education and labor union membership are included because 

they are potentially associated with the perceived shortage of skilled craft workers. Third, 

some variables are included because they may represent categories of workers that may 

respond differently to price signals in the construction labor market. Race and sex are 

included in this category.

This report analyzes the entire labor force for the construction industry (including construction 

workers, skilled tradesmen, office staff, management, etc.). In particular, this report provides 

details on the methodology used to obtain the results, and a detailed discussion of what can be 

concluded from the data.

Data for this study are taken from the Current Population Survey (CPS) from 1994 to 2010. 

Variables used are listed in Appendix 1. The CPS is a monthly survey of about 60 000 

occupied households. The households represent a stratified random sample of households in 

the country. Each household is surveyed eight times in two blocks. A household is first 

surveyed for four consecutive months. The household is then out of the survey for the 

following eight months, followed by a second four-month period when it is surveyed. With 

this design, consecutive months have a 75 % overlap in the households in the survey, and 

surveys one year apart have a 50 % overlap in the households in the survey. A total of 18 

variables from the data set are included in the analysis. The dataset contains a total of about 

27 million records. Adult men employed in construction in the data set number about 800,000.

There are matching issues with the longitudinal aspect of the data. In particular, the months of

July 1995, March 2000, and March 2001 people in the survey cannot be matched with the 

surrounding months. However, this seems unlikely to bias the results where longitudinal 

elements are used.

A number of factors suggest that the data before the middle of 1995 may not be as reliable as 

the rest of the data. Reasons for such a conclusion are discussed in Appendix 1.

Definitions of industries used in the CPS changed between December 2002 and January 2003. 

That makes industry comparisons possibly problematic for the time periods 1994 to 2002 and 

2003 to 2010. Analysis of the data and definitions suggests that for construction data from the 

two periods is roughly comparable. However, for some other industries that is certainly not 

the case.

Supplemental data for quarterly GDP were obtained from the Bureau of Economic Analysis. 

Monthly data for Unemployment and Urban Consumer Price Index (CPI-U) were obtained 

from the Bureau of Labor Statistics. For purposes of this report, data was collected from 1993 

to 2010. Since the main data are monthly and GDP are published quarterly, it is necessary to 
4

interpolate the GDP data to monthly to effectively make use of it. Interpolation methods are 

discussed in Appendix 1.

Section 2 provides a measure of how closely related construction is to other industries, and 

how large the labor flows are between other industries and construction. Section 3 provides a 

detailed discussion of the characteristics of the construction labor pool. Section 4 evaluates the 

nature and magnitude of labor flows in and out of construction by worker characteristic. 

Section 5 concludes by discussing implications of the results, and suggesting directions for 

future research.
5

2. Relationship to Other Industries

In characterizing construction labor supply, it is helpful to identify the supply pool from 

which construction labor is drawn. In particular, it would be helpful to identify industries that 

are seen as approximate substitutes by construction workers. As an additional objective, 

identifying industries where cross-price elasticities might be significant is an important part of 

estimating supply and demand for construction labor.

2.1. Informal Theory and Methodology

One natural way to identify similar industries is to look at job changes. If two industries are 

seen as perfect substitutes by workers, then a person in one industry changing jobs will be 

relatively likely to move into the other industry. 7

Let J be the set of industries, and for any j ∈ J, | j | is the number of workers in that industry. 

Suppose K ⊂ J is a set of industries seen as perfect substitutes, and i, j ∈ K are two industries 

from that set. Consider a person in industry i who is changing jobs. That person will be 

equally likely to pick any available job from the set of all jobs available in the industries in K. 

If we assume that the number of jobs available is proportional to the number of people 

employed in each industry, then the probability (P) of persons in industry i who change jobs 

switching to industry j is:

P{j|i} = q

|j|

|K|

Where q = P{ K | i }, which is the probability of persons in industry i who change jobs 

switching to any industry found in set K. Rewriting, we get:

P{j|i}

|j| = q|K|

= P{i|i}

|i|

Where P{i|i} is the probability of persons in industry i who change jobs remaining in industry 

i. In general, we expect different industries to be imperfect substitutes. So, we expect:

P{j|i}

|j| ≤

P{i|i}

|i|

Where equality holds only in the case of perfect substitutes.8

 7 They would also need to be seen as perfect substitutes by employers as well. If they were not, then employers 

would be more likely to reject applicants from the other industry on the belief that their skills were not as good a 

match.

8 Strictly speaking this analysis applies only in a (relatively) static world where numbers of jobs in each industry 

are not changing relative to each other. If, for example, you have two moderately closely related industries (but 
6

That suggests a natural index of substitutability for construction jobs.

Define the index of substitutability as:

rij = |i|

|j|

P{j|i}

P{i|i}

Note that in general rij ≠ rji. In fact, they may be quite different since the assumption of perfect 

substitutability does not usually hold.

The index above has one major limitation. An industry may be a perfect substitute for 

construction from the perspective of the labor market, but if it is very small its impact on the 

construction labor market will be small as well. So it would be useful to develop a second 

index that estimates impact on the labor market. Here, a very simple index can give a useful 

idea.

fj = |i|P{j|i} + |j|P{i|j}

2|i|P{i|i}

This represents the gross flows between construction and the compared industry normalized 

by the construction-to-construction job flows.

All terms are readily estimated from the CPS data. Since industry definitions change between 

2002 and 2003, indexes are estimated solely for the period 2003 to 2010. Industry populations 

are the average population over the time period in question. 

2.2. Results

Full results are listed in Appendix 2. The calculated similarity indices for the top 12 industries 

from the 2003 – 2010 CPS are listed in Table 2.

 

still imperfect substitutes) one of which is rapidly growing while the other is rapidly declining, you could have P{j|i}

|j| > P{i|i}|i| even though they are imperfect substitutes. Where the above analysis fails is in the assumption that 

the number of jobs available is proportional to the number of people employed. In a growing industry the ratio 

of jobs available to people employed will be relatively high, while in declining industries jobs available will be 

relatively scarce.
7

Table 2: Top 12 industries in terms of similarity index with construction.

Industry rij

Wood products 17.04 %

Forestry, logging, fishing, hunting, and trapping 16.16 %

Petroleum and coal products manufacturing 15.45 %

Mining 15.12 %

Waste management and remediation services 14.85 %

Furniture and fixtures manufacturing 14.70 %

Nonmetallic mineral product manufacturing 14.24 %

Administrative and support services 13.80 %

Repair and maintenance 13.61 %

Agriculture 12.60 %

Utilities 10.57 %

Primary metals and fabricated metal products 10.11 %

Construction, like any industry, employs people from a number of different occupations. Top 

five occupations (as defined in the CPS) employed in construction are shown in a nearby table. 

It is worth noting that two of the occupations (Office and Administrative Support and 

Installation, Maintenance and Repair) match two of the industries on the similar industries list. 

That suggests that if the analysis were restricted to those occupations, the similarity indices for 

those industries would be much higher.

Calculated labor flow indices for the top 10 

industries are listed in Table 3. Complete results 

are listed in Appendix 2. Unsurprisingly, there is 

very little overlap with the industries in Table 2. 

Many of the most similar industries are very small, 

and so flows between them will be small. 

Meanwhile, retail trade, which does not appear in the top 12 similar industries, has the highest 

inter-industry flows because it is by far the largest industry (in terms of employment) in the 

survey.

The results (mainly from Table 3) suggest that construction draws from a pool of industries 

that are low to medium skilled and not necessarily closely related to construction. Some 

occupations within construction (like administrative and support services) likely draw from a 

more specialized pool. However the relatively low-skill industries like retail trade and foodservice make up a large portion of the industries that construction shares labor with.

Top 5 Occupations Employed in Construction

Construction and Extraction 66.48 %

Management 13.72 %

Office and Administrative Support 5.60 %

Installation, Maintenance and Repair 4.89 %

Transportation 2.67 %
8

Table 3: Top 10 industries in terms of inter-industry 

flows with construction.

Industry f

Retail trade 8.93 %

Administrative and support services 6.61 %

Transportation and warehousing 4.66 %

Food services and drinking places 4.52 %

Professional and technical services 3.24 %

Wholesale trade 3.09 %

Repair and maintenance 2.81 %

Educational services 2.52 %

Agriculture 2.25 %
9

3. Characteristics of the Construction Labor Pool

It is believed that the changing composition of the work force may be a factor in the decline in 

construction productivity. In this section the composition of the work force is characterized, 

and how it changes over time. The educational composition of the work force and changes in 

labor union membership would help understand the skill level of construction labor and how 

it is changing. The age distribution of the workforce is also estimated.

3.1. Theory and Methodology

In this section, two questions are evaluated. First, what is the probability that a member of a 

specified group will be working in construction? For example, about 12 % of Hispanic men 

worked in construction in 2010. Second, given that a person is in construction, what is the 

probability that he is a member of that predefined group? For example, of all the men 

working in construction in 2010, about 20 % of them are Hispanic.

Let I be the set of all people (or in most cases all men) in the labor market. Then let J = { Ej } be 

some partition of interest of the labor market—that is, for some i, j ∈ J, where i ≠ j, Ei ∩ Ej = ∅, 

and I = ⋃J Ej. The operator �Ej� represents the total number of people in member j of the 

partition. In the work that follows the labor market is partitioned on the basis of sex, race and 

ethnicity, educational level, age, employer type, and union membership.

Consider the market for construction. The market can be specified implicitly with the 

following set of supply and demand equations:

0 = D�C(C, P; X) = C − DC(P; X)

0 = Ŝ

C(C, P, L, w; Y) = C − SC(P, L, w; Y)

0 = D�L

j

(L,w, C, P; Y) = Lj − DL

j

(L,w, C, P; Y)

0 = Ŝ

L

j

(L,w; Z) = Lj − SL

j

(L,w; Z)

Where

DC Aggregate demand for construction

SC Aggregate supply of construction

DL

j Aggregate demand for construction labor from partition j

SL

j Aggregate supply of construction labor from partition j

C Total construction put in place

P Price of construction

L Vector of construction labor employed, where Lj is the total construction 

labor employed from partition j.

w Vector of construction wages, where wj is the construction wage for 

partition j.
10

X, Y, Z Exogenous factors, including among other things time, U.S. GDP (in X), 

prices of other factors (in Y), and unemployment rate (in Z).

Note that SC and the DL

j are in turn the joint solution to a production function for construction.

These implicit equations can be solved for the reduced-form equations of C, P, L, and w:

C∗ = C(X, Y, Z)

P∗ = P(X, Y, Z)

L∗ = L(X, Y, Z)

w∗ = w(X, Y, Z)

Of these functions, only L( X, Y, Z ) is estimated. As mentioned above, in this section 

L( X, Y, Z ) is estimated in two forms. First, Lj

�Ej� is estimated, then Lj

∑ Lj J

is estimated for each 

member of the respective partitions. For simplicity of exposition, the first value will be 

referred to below as the Employment Probability, while the second will be referred to as the 

Conditional Probability.

Exogenous factors included in the estimations9 are time, growth in U.S. GDP, and national 

unemployment.

If π(t) represents the Employment Probability at time t, then the change in probability over 

time is:

∆π = π �α∆t + β

ΔY

Y + γUΔt + o.t. �

Where ΔY

Y represents rate of economic growth, U represents current unemployment rate, α, β, 

and γ are parameters, and “o.t.” represents other terms that will sometimes appear (e.g., 

seasonality). Letting Δt → 0, we get:

1

π

dπ

dt = α + β

1

Y

dY

dt + γU + o.t.

Integrating gives:

π = π�0 exp �αt + β ln Y + γ � Udx

t

t0

+ o.t. �

This can be restated as rate of economic growth (instead of total economic activity):

 9 Except for the estimation of cohort effects, section 3.2.4.
11

π = π�0Y0

β exp �αt + β ln

Y

Y0

+ γ � Udx

t

t0

+ o.t. �

or 

π = π0 exp �αt + β ln(g + 1) + γ � Udx

t

t0

+ o.t. �

or

π = exp �ln π0 + αt + β ln(g + 1) + γ � Udx

t

t0

+ o.t. �

Where g is annualized growth in U.S. GDP. Taking into account the fact that monthly growth 

and unemployment are stated in annualized terms, this then becomes:

π = exp �ln π0 + αt +

1

12 β� ln(gi + 1)

t

i=t0

+

1

12 γ� Ui

t

i=t0

+ o.t. �

π = exp �ln π0 + αt + β̂ � ln(gi + 1)

t

i=t0

+ γ�� Ui

t

i=t0

+ o.t. �

The equation is normalized so that the parameter α represents average growth in the 

population over time. Specifically, if g̅= ∑ ln(gt+1)

T

and U� = ∑ Ut

T , then estimation becomes:

π = exp �ln π0 + α�t + β̂ �� ln(gi + 1)

t

i=t0

− g̅t� + γ� �� Ui

t

i=t0

− U�t� + o.t. �

Being in construction is a binary choice. As such the data are modeled using a binomial 

distribution. For any i ∈ I, xi = 1 if the individual is in construction, and xi = 0 if not. Then the 

likelihood function takes the form:

�(πi)xi(1 − πi)1−xi

i∈I

Where 

πi = exp �ln π0 + α�ti + β̂ �� ln(gi + 1)

ti

i=t0

− g̅ti� + γ� �� Ui

ti

i=t0

− U�ti� + o.t. �

For a particular partition of the population J = { Ej }, the likelihood function becomes:
12

���πi

j

�

xi

�1 − πi

j

�

1−xi

j∈J i∈Ej

Where 

πi

j = exp �ln πj

0 + α�jti + β̂

j �� ln(gi + 1)

ti

i=t0

− g̅ti� + γ�j �� Ui

ti

i=t0

− U�ti� + o.t. �

which is estimated using Maximum Likelihood Estimation.

The analysis is restricted to the adult (age 16 or older) non-institutionalized population. For all 

but the results on sex below (Section 3.2.5), the analysis is further restricted to the male 

population.

Estimates of the Conditional Probability are calculated using standard multinomial logit. 

Specifically, if pi

j is the probability that person i in construction is a member of group j, then:

pi

j = πi

j

∑ πi

k

k∈J

Where the πi

j are the same expressions as defined above (and no longer are interpreted as 

probabilities).

The expression is indeterminate without some normalization. The problem is solved by 

setting πi

j = 1 for some j ∈ J.

All statistical analysis was performed using Stata 11 (StataCorp., 2009).
13

3.2. Results

Table 4 contains the list of the ten variables evaluated in this section. Figure 2 shows how the 

variables interact in the analysis below. In addition, there is one analysis in which the 

interaction of union membership with employee type, age, and cohort is examined. In that 

case, the business cycle variables (on the right hand side of the figure) are not included.

Table 4: List of variables analyzed below and the number of levels for each variable.

Variable Number of levels

Union Membership 2

Employer type 4

Sex 2

Age 8

Race 3

Education 3

Year (by month)

Seasonality 12 (months)

Growth in GDP Continuous

Unemployment Continuous

Figure 2: Interactions of the variables in the analysis.

Figure 3 shows the proportion of men employed in construction in each category of the 

categorical variables (except for sex) in 2010.

Employees in the construction industry tend to be white male, high-school educated, nonunion, and employed in the private sector. Construction workers are almost all between the 

ages of 25 and 55.

• Union Membership

• Employer Type

• Sex

• Age

• Race

• Education

• Time 

• Seasonality

• Business Cycle 

o GDP

o Unemployment }X

{
14

Figure 3: Proportion of men in construction in each categorical variable in 2010.

Figure 4: Main-Effects Plot of Unemployment v. Key variables analyzed in the paper.10

 10 HRM represents calendar month. For Sex, the first point represents males while the second represents females 

in the sample. The Age categories represent the same categories as in Figure 3. For Race, the categories in order 

are White, Black, and Hispanic. The Education categories in order are “No High School”, High-School Education, 

and College. Union in order is Non-Union, Union, and unknown. Empl(oyer) categories in order are Unpaid, 

Self-Employed, Private, and Government.

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

Age Race Education Employer Union

Percent of men in construction

Union

Nonunion

Gov't

Self Private

No HS HS College

White

Black

Hispanic

16 - 19

20 - 24

25 - 34 35 - 44 45 - 54

55 - 64

> 64
15

Figure 4 is a Main-effects plot of unemployment versus key variables for people working in 

construction. Note that the unemployment term used in Figure 4 is the �∑ Ui

ti

i=t0 − U�ti� term 

from the regression above. As a comparison, Figure 5 shows the �∑ Ui

ti

i=t0 − U�ti� term plotted 

over the period of the study. If a group has low values in the plot, then the people who form 

that group tend to be in construction when the cumulative unemployment term is low. So, for 

groups that have low values in the plot, larger numbers are employed in construction later in 

the study period, and (secondarily) employment tends to correlate more strongly with the 

business cycle. Factors with large variations are those that distinguish between groups with 

large relative shifts in employment over time and those that have high vulnerability to the 

business cycle from those that have low vulnerability.

Based on this analysis, the sexes do not have large relative differences in employment over 

time, nor do they have large differences in vulnerability to the business cycle. Age and Race 

show large differences, with workers over 65 and Hispanics significantly more affected by the 

unemployment term. Results below suggest that the effect for age is probably primarily 

driven by changes over time, while the effects for Hispanics are due both to changes over time 

and vulnerability to the business cycle. The effects for education and unionization are likely 

due to a relative decline in the number of people without a high-school education and union 

members in construction over time. The impacts for Employer are probably primarily driven 

by vulnerability to the business cycle, with Self-Employed and Privately Employed people 

being more vulnerable to the business cycle than Government Employed people.

Figure 5: Cumulative Normalized Unemployment over the study period.

-120%

-100%

-80%

-60%

-40%

-20%

0%

20%

1994 1996 1998 2000 2002 2004 2006 2008 2010 2012

Cumulative Normalized Unemployment (%)

Year

Cumulative Normalized Unemployment
16

3.2.1. Seasonality

First, it is important to examine the effect of seasonality in construction employment. Monthly 

net change in construction employment is calculated and the results are averaged by month. 

These results are shown in Figure 6.

Figure 6: Average change in construction employment by month.

There is a clear seasonal effect on construction employment, with employment at its highest in 

summer. The June and September spikes are likely associated with the summer employment 

of students.

It seems likely that seasonal coefficients will vary significantly by region. The winter lull is 

probably strongest in the northeast where winter weather is most severe, while the seasonal 

effect is most likely weakest where winter weather is the mildest. It is possible that in areas 

where summers are the most severe (like the desert southwest) the seasonality could be 

reversed with employment at its highest in winter.

-300

-200

-100

0

100

200

300

400

Thousands of workers

Month
17

3.2.2. Union Membership

Results for the Conditional Probability regression for union membership are in Table 5. What 

is of interest are which variables are significant, and what is the magnitude and direction of 

the effect of each coefficient. The ‘Pr’ column gives the significance of a particular coefficient. 

Magnitude and direction of effects are discussed next.

Union membership is declining at an average rate of about 2.5 % per year. It goes from about 

22.5 % in 1994 to about 15.5 % in 2010. Union membership is slightly countercyclical as 

demonstrated by the negative coefficient on growth. This suggests that union members are 

slightly less susceptible to the business cycle than non-union members. However, it is possible 

that the difference here is due to covarying demographic characteristics (like age and race 

differences) rather than union membership. Highest to lowest growth rate makes a difference 

to union membership of about 2 %. Highest to lowest unemployment rate also makes a 

difference of about 2 % in union membership.

Estimated versus calculated union membership is shown in Figure 7. The data points 

represent the weighted11 percent of union members in the sample at each time, while the line is 

calculated from the results of the regression. In this figure and all subsequent figures, 

recessions are marked by a blue region. The vertical bars inserted in Figure 7, and in other 

figures throughout this report, designate periods of recession.

Table 5: Coefficients for the Conditional Probability estimate that a man employed in construction is a member of a union.

Var Coef. Std. Err. z Pr

years -0.02508 0.002238 -11.2 < 0.001

growth -0.08736 0.021251 -4.11 < 0.001

unemployment -0.12796 0.038993 -3.28 0.001

Jan -1.49016 0.023541 -63.3 < 0.001

Feb -1.44587 0.02281 -63.39 < 0.001

Mar -1.44993 0.023793 -60.94 < 0.001

Apr -1.49228 0.023703 -62.96 < 0.001

May -1.45917 0.023493 -62.11 < 0.001

Jun -1.46885 0.022804 -64.41 < 0.001

Jul -1.46903 0.022985 -63.91 < 0.001

Aug -1.4139 0.022931 -61.66 < 0.001

Sep -1.42104 0.022728 -62.52 < 0.001

Oct -1.41976 0.022903 -61.99 < 0.001

Nov -1.43575 0.023034 -62.33 < 0.001

Dec -1.42685 0.022661 -62.96 < 0.001

 11 Weights in this section and throughout the report are supplied by the Census Bureau as part of the CPS data set 

and represent their best estimate as to how many people in the general population each person in the sample 

represents.
18

Figure 7: Percent union membership in construction estimated from the CPS (data points) and calculated from regression 

(line). Blue regions represent recessions.

0%

5%

10%

15%

20%

25%

30%

Jan-94 Jan-96 Jan-98 Jan-00 Jan-02 Jan-04 Jan-06 Jan-08 Jan-10 Jan-12

Union Membership (% of workers in construction)

Year
19

3.2.3. Employer Type

Results for Conditional Probability by employer type are in Table 612. A likelihood ratio test 

demonstrates that the unemployment variables are jointly not significantly different from zero 

(χ2 = 2.77, df = 3, p = 0.4286).

Table 6: Coefficients for the Conditional Probability that a man in construction has a specified type 

of employer.

Coef. Std. Err. z Pr

Government

constant -2.12879 0.021522 -98.91 < 0.001

years -0.02672 0.003264 -8.19 < 0.001

growth -0.8741 0.098955 -8.83 < 0.001

unemployment -0.03937 0.187193 -0.21 0.833

Private (base outcome)

Self-Employed

constant -0.85149 0.011999 -70.96 < 0.001

years 0.004958 0.001645 3.01 0.003

growth -0.62204 0.050909 -12.22 < 0.001

unemployment 0.131137 0.093524 1.4 0.161

Unpaid

constant -5.59812 0.122181 -45.82 < 0.001

years -0.07399 0.021849 -3.39 0.001

growth -0.04714 0.589556 -0.08 0.936

unemployment -0.90791 1.196151 -0.76 0.448

Results are shown in Figure 8.

Interpretation of the coefficients in Table 6 is not straightforward. To help in interpreting the 

results marginal effects are shown in Table 7. Marginal effects represent the effect on the 

respective types of employment by a unit change in one of the regression variables. For 

example, a one-year increase in time decreases government share of construction employment 

by 0.14 %.

Table 7: Marginal effects on the probability of working in the specified sector.

Government Private Self Unpaid

Years -0.0014 0.0002 0.0014 -0.0001

Growth -0.0359 0.1435 -0.1079 0.0002

Unemployment -0.0038 -0.0211 0.0263 -0.0014

 12 As mentioned in the theory section, some normalization is required for the Conditional Probability estimation. 

In this case that is accomplished by setting all coefficients for people in Private employment to zero.
20

Figure 8: Estimated and Calculated probability that a person in construction has a specified type of employer.

Over the long term, private employment and self-employment are increasing as a proportion 

of total employment, while government employment is decreasing. In fact, government 

employment in the construction sector is decreasing in absolute terms (not shown here). 

According to the estimates, over the period of the study, government employment as a 

proportion of the construction industry has declined about 2 % while self-employment has 

increases by about the same amount.

The business cycle, as represented by the positive coefficient on growth and the negative 

coefficient on unemployment, affects private employment more than the other sectors. 

Highest to lowest growth rate makes a difference of about 7 % to the proportion of private 

employment with self-employment making up the majority of the difference. Highest to 

lowest unemployment rate makes a difference of about 1 % to the proportion of private 

employment with self-employment making up almost all the difference.

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

1994 1996 1998 2000 2002 2004 2006 2008 2010 2012

% of workers in construction

Year

Govt Priv Self Unpd
21

3.2.4. Cohort Effects on Employer Type and Union Membership

The Conditional Probability for combined employer and union membership are also 

evaluated. Here, though, the focus is on the effects of age and cohort on employer and union 

membership. Age is normalized as:

n_age = age − 45

40

Cohort is defined as Year – Age, and is normalized as:

n_cohort = cohort − 1960

50

In this case, the usual variables for time13 and business cycle are not included. Results are 

listed in Table 8.

Table 8: Coefficients for the estimate of the Conditional Probability 

for employer type and union membership versus cohort and age.

Coef. Std. error t value Pr

Government × Union

constant -1.53508 0.043891 -34.9746 < 0.001

n_cohort 0.07445 0.537959 0.1384 0.890

n_age -0.35404 0.445618 -0.7945 0.427

Government × Nonunion

constant -0.68792 0.021206 -32.4396 < 0.001

n_cohort -0.1212 0.196962 -0.6153 0.538

n_age 1.597478 0.157668 10.1319 < 0.001

Private × Union

constant 0.483497 0.020249 23.8775 < 0.001

n_cohort -0.93809 0.142498 -6.5831 < 0.001

n_age -0.70499 0.108587 -6.4924 < 0.001

Private × Nonunion

constant 1.795408 0.019098 94.0079 < 0.001

n_cohort 0.333857 0.109615 3.0457 0.002

n_age -0.80941 0.086114 -9.3992 < 0.001

Self-Employed

constant 1.164634 0.020868 55.8105 < 0.001

n_cohort -0.83631 0.124758 -6.7035 < 0.001

n_age 0.550928 0.095963 5.7411 < 0.001

The fitted estimates are shown in Figure 9 for the 1960 birth cohort. Results suggest that as 

privately employed non-union members get older, they move into self-employment. A similar 

process may be affecting privately employed union members as well. Publically employed 

 13 Time is not included explicitly. However, since time = age + cohort, it is included implicitly.
22

union members are a small but constant fraction of construction workers, suggesting that such 

workers tend to stay put as they get older.

Figure 9: Changes in Employer type and Union membership with age for the 1960 cohort.

Figure 10: Changes in employer type and union membership with cohort at age 30.

Figure 10 illustrates changes that correlate with cohort. More recent cohorts appear to be less 

likely to be self-employed. According to the estimates, 30 % of people born in 1960 were likely 

to be self-employed at age 50, while only an estimated 20 % of those born in 1990 will be selfemployed at age 50 (data not shown). Similarly, the decline in union membership appears to 

be due to younger cohorts choosing not to join rather than to existing members dropping out.

0%

10%

20%

30%

40%

50%

60%

70%

80%

10 20 30 40 50 60 70

% of workers in construction

age (years)

Govt-Union Govt-Non Pvt-Union Pvt-Non Self

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

1940 1950 1960 1970 1980 1990 2000

% of workers in construction

Year

Govt-Union Govt-Non Total Union Pvt-Non Self
23

The above regression was rerun while limiting the data to white men with a high-school 

education only (results not shown). In that regression, there was no significant change in selfemployment probability with cohort. Union membership, however, still declined with cohort. 

That implies that the shift in self-employment probability identified above is a reflection of the 

changes in the racial and educational composition of the construction work-force (discussed 

further below). What is not clear is whether the changes in self-employment probability are 

caused by the demographic changes, or by some other factor that correlates with the 

demographic changes.
24

3.2.5. Sex

Table 9 shows the results of the regression for Employment Probability by sex. Men greatly 

outnumber women in the construction industry. About 7 % of men are in the construction 

industry, while only about 0.7 % of women are. Results are shown in Figure 11.

Table 9: Coefficients for the estimate of Employment Probability by sex.

Coef. Std. Err. z Pr

Male

constant -2.6485 6.93E-05 -3.80E+04 < 0.001

male ×years 0.003404 8.90E-06 382.45 < 0.001

male × growth 0.163921 0.000089 1842.54 < 0.001

male × unemployment -0.09696 0.000154 -631.57 < 0.001

Female

constant -4.94406 0.00022 -2.30E+04 < 0.001

female ×years -0.00317 2.89E-05 -109.71 < 0.001

female × growth 0.141863 0.000284 498.98 < 0.001

female × unemployment -0.19933 0.000498 -400.5 < 0.001

Figure 11: Monthly male and female participation in the construction industry. Left scale 

is male participation and right scale is female participation.

A Wald test indicates that the likelihood that men are in the industry is increasing at a faster 

rate than that for women (χ2 = 5.43, df = 1, p = 0.0198). Over the study period men have 

increased by 0.4 % while women have increased by 0.04 %.

Women are more susceptible to the business cycle than men. Specifically, the impact of 

economic growth on female employment is indistinguishable from the impact on men (χ2 = 

1.01, df = 1, p = 0.3161), but the portion of the business cycle reflected in unemployment 

impacts women harder than men (χ2 = 8.25, df = 1, p = 0.0041). The difference is probably at 

least in part due to differences in the occupations they fill in the industry. The Construction 

0.6%

0.7%

0.8%

0.9%

1.0%

1.1%

6.0%

6.5%

7.0%

7.5%

8.0%

8.5%

9.0%

9.5%

10.0%

10.5%

11.0%

1994 1996 1998 2000 2002 2004 2006 2008 2010 2012

% of women

% of men

Year

Male Male

Female Female
25

labor occupation is dominated by men while the Office and Administrative Support 

occupations are dominated by women (results not shown). Highest to lowest growth rates 

reduce the participation of men in the construction industry by about 1.75 % (and women by 

one tenth of that). Highest to lowest unemployment rates increase the participation of men in 

the construction industry by about 0.8 %, while it increases women’s participation rate by 

about 1.7 %.

Likelihood of being female given that a worker is in construction is estimated in Table 10.

Table 10: Probability of being female given that a

person is employed in construction.

Coef. Std. Err. z Pr

constant -2.26426 -0.01565 144.64 < 0.001

years -0.00754 0.002227 -3.39 0.001

growth -0.08054 0.066655 -1.21 0.227

unemployment -0.3644 0.12511 -2.91 0.004

These results are graphed in Figure 12, which represents percent of construction workers who 

are women. Some 90 % of the people in the construction industry are male. Since the industry 

is so heavily male, for the remainder of this analysis we will restrict our attention to men.

Figure 12: Percent women employed in construction by month.

8.0%

8.5%

9.0%

9.5%

10.0%

10.5%

11.0%

11.5%

1994 1996 1998 2000 2002 2004 2006 2008 2010 2012

% of owrkers in construction

Year
26

Additional analysis (not shown) indicates that there are significant differences in female 

participation in the construction labor force based on education. As educational levels 

decrease, female participation in the construction labor force also decreases, from about 15 %

female for college educated workers down to less than 5 % female for workers without a highschool education.
27

3.2.6. Age

Results for Employment Probability by age are listed in Table 11, and shown in Figure 13.

Table 11: Coefficients for the estimate of Employment Probability 

by age.

Coef. Std. Err. z P>|z|

Men age 16 – 19

constant 0.02818

years -0.02591 0.005047 -5.13 < 0.001

growth 1.69962 0.142559 11.92 < 0.001

unemployment -0.06796 0.27607 -0.25 0.806

Men age 20 – 24

constant 0.07512

years -0.00486 0.002551 -1.91 0.057

growth 1.05623 0.074985 14.09 < 0.001

unemployment -0.57991 0.141961 -4.09 < 0.001

Men age 25 – 34

constant 0.09760

years 0.00807 0.00145 5.56 < 0.001

growth 0.48462 0.044117 10.98 < 0.001

unemployment -0.35592 0.082212 -4.33 < 0.001

Men age 35 – 44

constant 0.09876

years 0.00894 0.001396 6.4 < 0.001

growth 0.40514 0.042229 9.59 < 0.001

unemployment -0.16177 0.078807 -2.05 0.04

Men age 45 – 54

constant 0.07693

years 0.01961 0.001494 13.13 < 0.001

growth 0.34021 0.046911 7.25 < 0.001

unemployment -0.12399 0.083663 -1.48 0.138

Men age 55 – 64

constant 0.05730

years 0.01022 0.002155 4.74 < 0.001

growth 0.06954 0.068752 1.01 0.312

unemployment -0.16588 0.121645 -1.36 0.173

Men age 65 and over

constant 0.00916

years 0.02910 0.004642 6.27 < 0.001

growth -0.06576 0.145185 -0.45 0.651

unemployment -0.85774 0.258386 -3.32 0.001

Probability of being in construction increases with age up to about age 35, peaking at around 

10 % of men between 25 and 45. Then it decreases with age till retirement.
28

Figure 13: Monthly probability of being in construction given that a man is in a specified age category.

Percentage of men in construction is increasing over time for most age categories (the 

exceptions being men under the age of 25), with the rate of increase growing at an increasing 

rate with age. The magnitude of the change over time varies from about 0.5 % for men 65 and 

over to 1.75 % for men between 45 and 54.

Susceptibility to the business cycle decreases with age. The oldest groups are nearly immune 

to the business cycle as evidenced by the generally declining coefficients on growth and 

increasing coefficients on unemployment. Highest to lowest growth rate has essentially no 

effect on the participation rate of men 65 while it decreases the participation rate of men 

between 20 and 24 by more than 4 %. Similarly, highest to lowest unemployment rate has 

essentially no effect on the participation rate of men between 16 and 19, while it increases the 

participation rate of men between 20 and 24 by about than 1.75 %.

The effect of the broader unemployment rate is the least likely to be significant, but a 

Likelihood ratio test confirms that as a group they are significant (χ2 = 55.11, df = 7, p < 0.0001). 

All the effects over age are confirmed with Wald tests.

Estimates of Conditional Probabilities by age are listed in Table 12.

0%

2%

4%

6%

8%

10%

12%

14%

16%

18%

1994 1996 1998 2000 2002 2004 2006 2008 2010 2012

Probability of being in construction ( %)

Year

16 - 19 20 - 24 25 - 34 35 - 44 45 - 54 55 - 64 > 64

16 - 19 20 - 24 25 - 34 35 - 44 45 - 54 55 - 64 > 64
29

Table 12: Coefficients for the estimate of the Conditional Probability by age.

Coef. Std. Err. z P>|z|

Age: 16 - 19

constant -2.34345 0.033881 -69.17 < 0.001

years -0.01833 0.004771 -3.84 < 0.001

growth 1.288016 0.151714 8.49 < 0.001

unemployment 0.164418 0.270159 0.61 0.543

Age: 20 - 24

constant -1.27325 0.021077 -60.41 < 0.001

years -0.00009 0.002755 -0.03 0.974

growth 0.428302 0.090166 4.75 < 0.001

unemployment -0.58331 0.156767 -3.72 < 0.001

Age: 25 - 34

constant -0.09583 0.014602 -6.56 < 0.001

years 0.002653 0.001895 1.4 0.161

growth -0.27502 0.064563 -4.26 < 0.001

unemployment -0.0958 0.110396 -0.87 0.385

Age: 35 - 44 (base outcome)

Age: 45 - 54

constant -0.54408 0.015887 -34.25 < 0.001

years 0.036427 0.001921 18.96 < 0.001

growth -0.12569 0.066207 -1.9 0.058

unemployment -0.13302 0.110659 -1.2 0.229

Age: 55 - 64

constant -1.3054 0.020556 -63.51 < 0.001

years 0.047259 0.002355 20.07 < 0.001

growth -0.65225 0.083179 -7.84 < 0.001

unemployment -0.06925 0.135519 -0.51 0.609

Age: ≥ 65

constant -2.77963 0.038763 -71.71 < 0.001

years 0.044093 0.004313 10.22 < 0.001

growth -0.77255 0.150636 -5.13 < 0.001

unemployment -0.57292 0.244189 -2.35 0.019

Marginal effects are listed in Table 13.

Table 13: Marginal Effects on Conditional Probability by age group.

Age Group

16 – 19 20 – 24 25 – 34 35 – 44 45 – 54 55 – 64 ≥ 65

Years -0.00094 -0.00132 -0.00285 -0.00394 0.004972 0.003373 0.000715

Growth 0.040431 0.049635 -0.04271 0.029122 -0.00482 -0.05573 -0.01592

Unemployment 0.008372 -0.04285 0.006997 0.034671 -0.00205 0.005547 -0.01069

Proportion of men over 45 is increasing over time. As expected, younger men are more 

strongly affected by the business cycle.
30

Results are shown in Figure 14.

Figure 14: Monthly probability of being in a given age group given that a man is working in construction.

0%

5%

10%

15%

20%

25%

30%

35%

40%

1994 1996 1998 2000 2002 2004 2006 2008 2010 2012

Probability of working in construction (%)

Year

16 - 19 20 - 24 25 - 34 35 - 44 45 - 54 55 - 64 > 64

16 - 19 20 - 24 25 - 34 35 - 44 45 - 54 55 - 64 > 64
31

3.2.7. Race and Ethnicity

Coefficients for the estimate of the Employment Probability of the participation of Hispanics, 

Whites and Blacks in the construction industry are listed in Table 14. For the purposes of this 

report, people are considered Hispanic if they are reported to be Hispanic by the CPS, 

regardless of race. All other racial/ethnic categories were dropped since their populations 

were too small to produce significant results.

Table 14: Coefficients for the estimate of Employment Probability by race/ethnicity.

Coef. Std. Err. z P>|z|

Black -3.07451 0.00028 -1.10E+04 < 0.001

Black × years -0.01737 3.89E-05 -446.12 < 0.001

Black × growth 0.208439 0.000381 547.36 < 0.001

Black × unemployment -0.06554 0.000676 -96.92 < 0.001

Hispanic -2.64508 0.000187 -1.40E+04 < 0.001

Hispanic × years 0.034987 1.94E-05 1802.01 < 0.001

Hispanic × growth 0.33116 0.000195 1696.08 < 0.001

Hispanic × unemployment -0.15741 0.000313 -503.45 < 0.001

White -2.56821 7.86E-05 -3.30E+04 < 0.001

White × years -0.00249 1.06E-05 -234.54 < 0.001

White × growth 0.14538 0.000106 1378.27 < 0.001

White × unemployment -0.06485 0.000185 -350.31 < 0.001

Results are also shown in Figure 15.

Initially, White men were significantly more likely than Hispanic men to be in construction 

(χ2 = 14.81, df = 1, p = 0.0001), and Hispanic men were more likely than Black men to be in 

construction (χ2 = 286, df = 1, p < 0.0001).

However, the likelihood that Hispanic men are in construction has increased at a much higher 

rate than that of White (or Black) men (χ2 = 282, df = 1, p < 0.0001), while the likelihood of Black 

men in construction is actually decreasing. Hispanic participation rates in construction have 

increased more than 7 % over the study period, while the White participation rate decreased 

0.35 % and the Black participation rate decreased 1.35 %. At present, Hispanic men are more 

likely to be in construction than White (or Black) men (χ2 = 429, df = 1, p < 0.0001), with about 

12.5 % of Hispanic men in construction compared to 7.6 % of White men and 3.25 % of Black 

men.

Hispanic men are more susceptible to the business cycle than Black men, while Black and 

White men are about equally susceptible to the business cycle. A portion of the difference is 

likely due to differences in occupation within the industry (results not included here indicate 

that White men are more likely to be in management than the other groups).
32

Figure 15: Monthly Employment Probability by race and ethnicity.

Highest to lowest growth rate decreases the participation rate of White men by about 1.5 %, it 

decreases the participation rate of Black men by about 1.2 %, and it decreases the participation 

rate of Hispanic men by about 4.9 %. Similarly, highest to lowest unemployment rate 

increases the participation rate of White men by about 0.6 %, it increases the participation rate 

of Black men by about 0.3 %, and it increases the participation rate of Hispanic men by about 

2 %.

The same information in Figure 15 is presented in a different form in Figure 16. This 

represents the proportion of men from each race in construction, divided by the proportion of 

that race in the general population. So values above 1 represent groups that are preferentially 

concentrated in construction, while numbers less than one represent groups that preferentially 

avoid construction. As is apparent from the graph, there has been a major change in the 

employment of Hispanics over the last 20 years, with Hispanics now gravitating toward 

construction. Meanwhile Blacks gravitate away from it.

0%

2%

4%

6%

8%

10%

12%

14%

16%

18%

20%

1994 1996 1998 2000 2002 2004 2006 2008 2010 2012

Probability of working in construction (%)

Year

White Black Hisp

White Black Hisp
33

Figure 16: For each race/ethnicity, the fraction of men working in construction divided by the proportion of that 

race/ethnicity in the population, by month.

Estimates of the Conditional Probability by race and ethnicity are listed in Table 15.

Table 15: Coefficients for the estimate of the Conditional Probability 

by race and ethnicity

Coef. Std. Err. z P>|z|

Black

constant -2.77323 0.025509 -108.72 < 0.001

years -0.01279 0.003813 -3.35 0.001

growth 0.150975 0.113599 1.33 0.184

unemployment -0.11188 0.215452 -0.52 0.604

Hispanic

constant -2.46572 0.018306 -134.69 < 0.001

years 0.070575 0.002122 33.26 < 0.001

growth 0.880768 0.065718 13.4 < 0.001

unemployment -0.08542 0.115364 -0.74 0.459

White (base outcome)

Marginal effects are listed in Table 16. Results are displayed in Figure 17.

Table 16: Marginal effects on Conditional Probability by race and ethnicity.

White Black Hispanic

Years -0.0081 -0.0011 0.0092

Growth -0.1132 0.0004 0.1128

Unemployment 0.0146 -0.0044 -0.0102

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

1994 1996 1998 2000 2002 2004 2006 2008 2010 2012

Normalized Ratio in Construction

Year

Black

Hispanic

White
34

Unemployment is jointly indistinguishable from zero (χ2 = 0.75, df = 2, p = 0.6870). Proportion 

of Hispanic workers is increasing over time, mostly at the expense of White workers. The 

business cycle preferentially impacts Hispanic workers.

Figure 17: Monthly Conditional Probability by race and ethnicity.

As shown in Figure 18, there is strong regional variation in racial makeup, with the Northeast 

and Midwest still basically White, the West and increasingly the South becoming strongly 

Hispanic. The South started with about 10 % Black, but percentage of Black men in 

construction in the South has dropped dramatically. The West has always had relatively few

Black men in construction. The West and the Northeast are the only regions where the 

proportion of Black men is not declining.

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

1994 1996 1998 2000 2002 2004 2006 2008 2010 2012

% of men in construction

Year

White Black Hisp

White Black Hisp
35

Figure 18: Proportion of men in construction who belong to each race/ethnicity, by region and time.

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

1994199619982000200220042006200820102012

% of men in construciton

Year

Northeast

White

Black

Hisp

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

1994199619982000200220042006200820102012

Year

Midwest

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

1994199619982000200220042006200820102012

% of men in construction

Year

South

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

1994 1996 1998 2000 2002 2004 2006 2008 2010 2012

Year

West
36

3.2.8. Education

To analyze educational levels of men in construction, adult men are divided into three groups: 

those without a high-school education, those with a high-school degree but no college degree, 

and those with some kind of college degree (associates or higher). Results for the estimation of 

the Employment Probability by educational level are included in Table 17, and graphed in 

Figure 19.

Table 17: Coefficients for the estimate of Employment Probability by 

level of education

Coef. Std. Err. z P>|z|

No High School Education

constant 0.0626

years 0.0202 0.001675 12.04 < 0.001

growth 0.8075 0.050657 15.94 < 0.001

unemployment -0.1893 0.093932 -2.01 0.044

High School Education

constant 0.0909

years 0.0034 0.00092 3.74 < 0.001

growth 0.4446 0.028206 15.76 < 0.001

unemployment -0.2317 0.052099 -4.45 < 0.001

College Education

constant 0.0385

years 0.0127 0.001715 7.43 < 0.001

growth 0.1958 0.053616 3.65 < 0.001

unemployment -0.3348 0.096367 -3.47 0.001

Initially, those with a high school education were the most likely to be in construction, with 

men without a high school education second most likely. However, the likelihood of a man 

without a high school education being in construction has increased at a faster rate than the 

likelihood for a man with a high school education. Participation rates for men without a high 

school education in construction have increased about 3 % over the study period, while the 

participation rate of men with a high school education increased 0.3 % and the participation 

rate of men with a college education increased about 1 %.

The greater the level of education, the less susceptible a man is to the business cycle. Highest 

to lowest growth rate decreases the participation rate of men without a high school education 

by about 3 %, it decreases the participation rate of men with a high school education by about 

1.9 %, and it decreases the participation rate of men with some college education by about 

0.4 %. Note that the impact of the unemployment rate on each of the groups is jointly 

indistinguishable from zero according to the Wald test (χ2 = 1.28, df = 2, p = 0.527).
37

Figure 19: Monthly Employment Probability by level of education.

Estimates for the Conditional Probability by educational level are listed in Table 18.

Table 18: Coefficients for the estimate of the Conditional Probability 

by educational level.

Coef. Std. Err. z P>|z|

College

constant -1.43391 0.015342 -93.46 < 0.001

years 0.022239 0.002022 11 < 0.001

growth -0.23127 0.062776 -3.68 < 0.001

unemployment -0.16721 0.114125 -1.47 0.143

HS (base outcome)

NoHS

constant -1.43391 0.015342 -93.46 < 0.001

years 0.000723 0.00202 0.36 0.72

growth 0.480656 0.061145 7.86 < 0.001

unemployment 0.071576 0.113803 0.63 0.529

Marginal effects are listed in Table 19. Results are displayed in Figure 20.

0%

2%

4%

6%

8%

10%

12%

14%

1994 1996 1998 2000 2002 2004 2006 2008 2010 2012

% in construction

Year

NoHS HS College

NoHS HS College
38

Table 19: Marginal effects for Conditional Probability by educational level.

No HS HS College

Years -0.0007 -0.0025 0.0032

Growth 0.0860 -0.0354 -0.0506

Unemployment 0.0175 -0.0092 -0.0268

Unemployment is jointly indistinguishable from zero (χ2 = 3.16, df = 2, p = 0.2060). Proportion 

of college educated workers is increasing over time, mostly at the expense of high-school 

educated workers. The business cycle impacts most strongly those with no high-school 

education.

Figure 20: Conditional Probability by educational level.

0%

10%

20%

30%

40%

50%

60%

70%

1994 1996 1998 2000 2002 2004 2006 2008 2010 2012

% of men in construction

Year

NoHS HS College

NoHS HS College
39

4. Labor Flows

In order to further evaluate issues regarding the aging of the work force, the number of young 

people entering the industry, and shifts in the work force toward foreign immigrants, labor 

flows were estimated. The basic questions answered here is who is entering the work force, 

who is leaving it, and when.

4.1. Model and Methodology

As before, J represents useful partitions of the population of construction workers. Each 

member of the partition J is partitioned in turn by cohort. If H is the set of cohorts, then the 

final partition used here will be J̅= {J × H}. Then for any j ∈ J̅, Lt

j is the number of workers in 

group j in construction at time t, and nt

j is the number of workers in group j in construction at 

time t in the CPS sample.

In general, assume 

nt

j

~nb�rtμt

j

, σt

j

�

Where, “nb” represents the negative binomial distribution, rt is the sampling rate at time t, and 

μt

j = E�Ltj

�. The negative binomial distribution is used to allow for the possibility that there is 

over-dispersion in the selection of people into a particular partition.

The use of rt gives equal weight to each observation at a given time. The CPS contains detailed 

weighting information for each observation, and those weights sometimes differ significantly 

from individual to individual. The use of rt ignores that information. The principal reason for 

doing so here is because many of the groups used in the regression below contain zero 

individuals. Using individual-specific weights could end up giving those observations a 

disproportionately large weight. Therefore a month-specific average was used.

The value of μt

j is assumed to have the form:

μt

j = μt−1

j ∙ exp �αt

j

Δt + βt

j ΔY

Y + γt

j

UΔt + seasonal terms�

As before, this can be formulated as:

μt

j = exp �ln μt−1

j + � αj(τ)dτ + � βj(τ)d ln

Y

Y0

+ � γj(τ)U(τ)dτ + seasonal terms�

Νet inflows are assumed to vary by age, regardless of cohort. That is, for some j ∈ J, h ∈ H, and 

time t, a parameter αt

{j,h} can be expressed as a function fα( j, t – h ).
40

To simplify the analysis, it is assumed that relationships for net inflows are constant within 

age groups T defined as:

Age Group Ages

1 16 – 19

2 20 – 24

3 25 – 34

4 35 – 44

5 45 – 54

6 55 – 64

7 65 – 70

Define the following (overloaded) functions:

τj

(i): The time when group j enters age group i.

τj

(i,t) = max�min�τj(i) ,t�, 0�

Note that τj

(8) is defined as the time when group j turns 71. Then, since the regression 

variables are piece-wise constant, the relationship for μ becomes:

μt

j = exp �ln μ0

j + � αi�τj

(i + 1,t) − τj(i,t)�

I

+ � βi� ln(1 + gt) τj(i+1,t)

τj I (i,t)

+ � γi� Ut

τj(i+1,t)

τj I (i,t)

+ seasonal terms�

Here gt is economic growth in time period t.

For the sake of parsimony, seasonal employment is assumed to follow a sinusoidal pattern. 

That leads to the following parameterization.

μt

j = exp �ln μ0

j + � αi�τj

(i + 1,t) − τj(i,t)�

I

+ � βi� ln(1 + gt) τj(i+1,t)

τj I (i,t)

+ � γi� Ut

τj(i+1,t)

τj I (i,t)

+ θi

s sin 2πt + θic cos 2πt�

To simplify the analysis below, all people in the sample are assumed to be born on January 1 

of their cohort year. Since the CPS is a partially longitudinal dataset, and cohort is defined in 

the sample as Current Year – Age, that means that some people in the sample are assigned to 

two different cohorts at different times. Due to the nature of the data set, that will apply to 

about 1⁄4 of the people in the sample. While that introduces some additional dispersion into 

the results, the impact on the results is likely to be small.
41

This analysis implicitly assumes that net inflow/outflow rates are static (after accounting for 

the business cycle and seasonality). However, as will become clear from the results, that 

assumption is not true. In particular, during the study period, foreign-born Hispanics have 

entered construction in large numbers. These dynamic changes should be the subject of 

further study.
42

4.2. White Men

Figure 21 shows the number of White men in construction in 1994, by age.

Figure 21: Blue line is the number of White Men in construction in 1994, by age. Red line is the stable number of White

men in construction assuming economic growth and unemployment continue at their average rates indefinitely.

Table 20 contains the estimates of the coefficients for net inflows to construction by age group. 

A stable age distribution of White men in construction assuming economic growth and 

unemployment continue at their average rates indefinitely is also shown in Figure 21. Fit of 

the estimate to the data is shown in Figure 22.

0

20,000

40,000

60,000

80,000

100,000

120,000

140,000

160,000

180,000

200,000

10 20 30 40 50 60 70

Number of men in construction

Age
43

Table 20: Coefficients for net flows of White men into construction.

Var Coef. Std. Err. z P>|z|

Age 16 - 19: t 0.625661 0.012579 49.74 < 0.001

Age 16 - 19: growth 0.280391 0.069935 4.01 < 0.001

Age 16 - 19: unemployment 0.1152849 0.117699 0.98 0.327

Age 16 - 19: sin -0.1061827 0.020601 -5.15 < 0.001

Age 16 - 19: cos -0.294515 0.020652 -14.26 < 0.001

Age 20 - 24: t 0.0286478 0.004517 6.34 < 0.001

Age 20 - 24: growth 0.2942997 0.028535 10.31 < 0.001

Age 20 - 24: unemployment -0.0118243 0.049897 -0.24 0.813

Age 20 - 24: sin -0.0878365 0.01113 -7.89 < 0.001

Age 20 - 24: cos -0.0981155 0.01106 -8.87 < 0.001

Age 25 - 34: t 0.002898 0.002194 1.32 0.187

Age 25 - 34: growth 0.124388 0.017583 7.07 < 0.001

Age 25 - 34: unemployment -0.1096004 0.031504 -3.48 0.001

Age 25 - 34: sin -0.0487273 0.006955 -7.01 < 0.001

Age 25 - 34: cos -0.0314539 0.006915 -4.55 < 0.001

Age 35 - 44: t -0.0044467 0.001952 -2.28 0.023

Age 35 - 44: growth 0.07624 0.015831 4.82 < 0.001

Age 35 - 44: unemployment -0.0651126 0.02841 -2.29 0.022

Age 35 - 44: sin -0.0290964 0.006332 -4.59 < 0.001

Age 35 - 44: cos -0.0291836 0.0063 -4.63 < 0.001

Age 45 - 54: t -0.0131271 0.001999 -6.57 < 0.001

Age 45 - 54: growth 0.0871276 0.016806 5.18 < 0.001

Age 45 - 54: unemployment -0.0468046 0.028574 -1.64 0.101

Age 45 - 54: sin -0.0578177 0.006808 -8.49 < 0.001

Age 45 - 54: cos -0.0103273 0.006767 -1.53 0.127

Age 55 - 64: t -0.0723524 0.00283 -25.56 < 0.001

Age 55 - 64: growth -0.051779 0.023582 -2.2 0.028

Age 55 - 64: unemployment -0.0686209 0.038646 -1.78 0.076

Age 55 - 64: sin -0.0590978 0.009733 -6.07 < 0.001

Age 55 - 64: cos -0.0317859 0.00966 -3.29 0.001

Age > 64: t -0.1944142 0.008944 -21.74 < 0.001

Age > 64: growth 0.0001219 0.05949 0 0.998

Age > 64: unemployment -0.2762774 0.094223 -2.93 0.003

Age > 64: sin -0.1528037 0.023332 -6.55 < 0.001

Age > 64: cos -0.0395778 0.023005 -1.72 0.085

In general, as noted before, older worker are less susceptible to the business cycle than 

younger workers. Above the age of 55, the impact of the business cycle is not significantly 

different from zero.
44

Figure 22: Fit of estimates to data for White men in construction by age group.

Net inflow totals are shown in Figure 23. In the average year, 75 % of the White men who 

enter construction do so before the age of 21. Total net inflow across all age groups is positive 

in all but five years (data not shown).

0

500,000

1,000,000

1,500,000

2,000,000

2,500,000

1994 1996 1998 2000 2002 2004 2006 2008 2010 2012

Number of men in construction

Year

Age: 16 - 19

Age: 20 - 24

Age: 25 - 34

Age: 35 - 44

Age: 45 - 54

Age: 55 - 64

Age: 65 - 70

Age: 16 - 19

Age: 20 - 24

Age: 25 - 34

Age: 35 - 44

Age: 45 - 54

Age: 55 - 64

Age: 65 - 70
45

Figure 23: Net inflow to construction for White men, by age for selected years.

Net rate of inflow by age and rate of economic growth is shown in Table 21. Note that this 

underestimates the variation due to the business cycle, since it does not take into account the 

general unemployment rate. Inflow rates are very large for the 16 – 19 year old group because 

the initial number of white men in construction on turning 16 is so small.

Table 21: Net rate of inflow to construction by age and rate of economic growth. Colored cells indicate ages and 

circumstances where men are on net leaving construction.

Age

Deviation of Economic Growth from Average

-2 % -1 % 0 % 1 % 2 %

16 – 19 74.66 % 80.73 % 86.95 % 93.31 % 99.83 %

20 – 24 -4.18 % -0.68 % 2.91 % 6.59 % 10.36 %

25 – 35 -2.69 % -1.20 % 0.29 % 1.79 % 3.30 %

35 – 44 -2.27 % -1.35 % -0.44 % 0.47 % 1.38 %

45 – 54 -3.37 % -2.34 % -1.30 % -0.27 % 0.76 %

55 – 64 -5.80 % -6.40 % -6.98 % -7.55 % -8.12 %

65 – 70 -17.67 % -17.67 % -17.67 % -17.67 % -17.67 %

Impact of seasonality is shown in Table 22. As expected, the impact of seasonality decreases as 

workers get older, reaching a minimum at around age 40. Then seasonality increases slowly. 

The relatively large increase in seasonality for workers over the age of 65 probably reflects 

semi-retired workers returning to the work force when demand is high. The date when 

number of workers is highest is concentrated in late summer. Interestingly enough, date of 

peak employment is progressively later the older the worker gets. A Wald test on date of 

-30,000

-20,000

-10,000

0

10,000

20,000

30,000

40,000

50,000

60,000

70,000

15 20 25 30 35 40 45 50 55 60 65 70

Net Inflow - Number of workers

Age

1996 1999 2001

2007 2008 2010
46

maximum employment indicates that the dates are not all equal across age groups (χ2 = 7.80, 

df = 6, p = 0.01 %).

Table 22: Impact of seasonality. Seasonal Coefficient is the absolute magnitude of the seasonal variation. Wald Test 

represents the probability that the seasonal variation is greater than zero. Percent change is calculated based on the 

highest estimated seasonal employment compared to the lowest estimated seasonal employment.

Age

Seasonal 

Coefficient

% change: 

lowest to 

highest

Wald test

Max 

χ Date 2 df p

16 – 19 0.3131 87.04 % 56.23 1 < 0.01 % 20-Jul

20 – 24 0.1317 30.13 % 35.32 1 < 0.01 % 11-Aug

25 – 35 0.0580 12.30 % 17.44 1 < 0.01 % 27-Aug

35 – 44 0.0412 8.59 % 10.64 1 0.11 % 15-Aug

45 – 54 0.0587 12.46 % 18.64 1 < 0.01 % 19-Sep

55 – 64 0.0671 14.36 % 11.97 1 0.05 % 1-Sep

65 – 70 0.1578 37.12 % 11.58 1 0.07 % 15-Sep
47

4.3. Black Men

Figure 24 shows the number of Black men in construction in 1994, by age.

Figure 24: Blue line is the number of Black Men in construction in 1994, by age. Red line is the stable number of Black

men in construction assuming economic growth and unemployment continue at their average rates indefinitely.

Table 23 contains the estimates of the coefficients for net inflows to construction by age group. 

A stable age distribution of Black men in construction assuming economic growth and 

unemployment continue at their average rates indefinitely is shown in Figure 24. Fit of the 

estimate to the data is shown in Figure 25.

0

2,000

4,000

6,000

8,000

10,000

12,000

14,000

16,000

10 20 30 40 50 60 70

Number of men in construction

Age
48

Table 23: Coefficients for net flows of Black men into construction.

Var Coef. Std. Err. z P>|z|

Age 16 - 19: t 0.7353515 0.070693 10.4 < 0.001

Age 16 - 19: growth -0.0413578 0.393725 -0.11 0.916

Age 16 - 19: unemployment -0.4334484 0.65523 -0.66 0.508

Age 16 - 19: sin -0.0681683 0.10814 -0.63 0.528

Age 16 - 19: cos -0.3085816 0.108717 -2.84 0.005

Age 20 - 24: t 0.0742974 0.02003 3.71 < 0.001

Age 20 - 24: growth 0.1477798 0.126993 1.16 0.245

Age 20 - 24: unemployment -0.3426494 0.227113 -1.51 0.131

Age 20 - 24: sin -0.0020518 0.049001 -0.04 0.967

Age 20 - 24: cos -0.09982 0.048746 -2.05 0.041

Age 25 - 34: t 0.0088826 0.008981 0.99 0.323

Age 25 - 34: growth 0.2169711 0.070975 3.06 0.002

Age 25 - 34: unemployment -0.1671427 0.129634 -1.29 0.197

Age 25 - 34: sin -0.0396778 0.027576 -1.44 0.15

Age 25 - 34: cos 0.0286096 0.027433 1.04 0.297

Age 35 - 44: t -0.0198847 0.007726 -2.57 0.01

Age 35 - 44: growth 0.2005771 0.061379 3.27 0.001

Age 35 - 44: unemployment -0.175498 0.112466 -1.56 0.119

Age 35 - 44: sin -0.0870369 0.023908 -3.64 < 0.001

Age 35 - 44: cos -0.0732338 0.023798 -3.08 0.002

Age 45 - 54: t -0.0165047 0.007478 -2.21 0.027

Age 45 - 54: growth 0.1726808 0.063152 2.73 0.006

Age 45 - 54: unemployment 0.0378783 0.108248 0.35 0.726

Age 45 - 54: sin 0.0096741 0.025269 0.38 0.702

Age 45 - 54: cos -0.040474 0.025142 -1.61 0.107

Age 55 - 64: t -0.087921 0.011114 -7.91 < 0.001

Age 55 - 64: growth 0.178611 0.092684 1.93 0.054

Age 55 - 64: unemployment -0.0033049 0.153552 -0.02 0.983

Age 55 - 64: sin -0.1034498 0.036654 -2.82 0.005

Age 55 - 64: cos -0.0298301 0.03639 -0.82 0.412

Age > 64: t -0.2452788 0.037595 -6.52 < 0.001

Age > 64: growth -0.1290224 0.242949 -0.53 0.595

Age > 64: unemployment -0.534806 0.389604 -1.37 0.17

Age > 64: sin -0.2398704 0.09528 -2.52 0.012

Age > 64: cos -0.0393219 0.093518 -0.42 0.674

As usual, older worker are less susceptible to the business cycle than younger workers. Above 

the age of 55, the impact of the business cycle is not significantly different from zero.
49

Figure 25: Fit of estimates to data for Black men in construction by age group, by month.

Net inflow totals are shown in Figure 26. In the average year, 75 % of the Black men who enter 

construction do so before the age of 24. Total net inflow across all age groups is positive in all 

but six years (data not shown).

0

50,000

100,000

150,000

200,000

250,000

1994 1996 1998 2000 2002 2004 2006 2008 2010 2012

Number of men in construction

Year

Age: 16 - 19

Age: 20 - 24

Age: 25 - 34

Age: 35 - 44

Age: 45 - 54

Age: 55 - 64

Age: 65 - 70

Age: 16 - 19

Age: 20 - 24

Age: 25 - 34

Age: 35 - 44

Age: 45 - 54

Age: 55 - 64

Age: 65 - 70
50

Figure 26: Net inflow to construction for Black men, by age for selected years.

Net rate of inflow by age and rate of economic growth is shown in Table 24. As before, this 

underestimates the variation due to the business cycle, since it does not take into account the 

general unemployment rate.

Table 24: Net rate of inflow to construction by age and rate of economic growth. Colored cells indicate ages and 

circumstances where men are on net leaving construction.

Age

Deviation of Economic Growth from Average

-2 % -1 % 0 % 1 % 2 %

16 – 19 110.72 % 109.66 % 108.62 % 107.59 % 106.58 %

20 – 24 3.92 % 5.81 % 7.71 % 9.63 % 11.56 %

25 – 35 -4.28 % -1.71 % 0.89 % 3.54 % 6.23 %

35 – 44 -6.62 % -4.31 % -1.97 % 0.41 % 2.82 %

45 – 54 -5.67 % -3.66 % -1.64 % 0.41 % 2.48 %

55 – 64 -12.30 % -10.37 % -8.42 % -6.44 % -4.45 %

65 – 70 -19.27 % -20.52 % -21.75 % -22.95 % -24.11 %

Impact of seasonality is shown in Table 25. As expected, the impact of seasonality decreases as 

workers get older, reaching a minimum at around age 50, then seasonality increases again. 

However, seasonality is not significantly different from zero for any age group except 35 to 44 

year-olds. The date when number of workers is highest is concentrated in summer. A Wald 

-3,000

-2,000

-1,000

0

1,000

2,000

3,000

4,000

15 20 25 30 35 40 45 50 55 60 65 70

Net Inflow - Number of workers

Age

1996 1999 2001

2007 2008 2010
51

test on date of maximum employment indicates that the dates are not significantly different 

across age groups (Χ2 = 5.88, df = 6, p = 43.69 %).

Table 25: Impact of seasonality. Seasonal Coefficient is the absolute magnitude of the seasonal variation. Wald Test 

represents the probability that the seasonal variation is greater than zero.

Age

Seasonal 

Coefficient

% change: 

lowest to 

highest

Wald test

Max 

χ Date 2 df p

16 – 19 0.3160 88.15 % 2.070 1 15.03 % 13-Jul

20 – 24 0.0998 22.10 % 1.050 1 30.58 % 1-Jul

25 – 35 0.0489 10.28 % 0.790 1 37.38 % 5-Nov

35 – 44 0.1137 25.55 % 5.700 1 1.70 % 20-Aug

45 – 54 0.0416 8.68 % 0.680 1 40.85 % 16-Jun

55 – 64 0.1077 24.03 % 2.170 1 14.07 % 13-Sep

65 – 70 0.2431 62.60 % 1.650 1 19.93 % 20-Sep
52

4.4. U.S. Born Hispanic Men

Figure 27 shows the number of U.S. born Hispanic men in construction in 1994, by age.

Figure 27: Blue line is the number of US Born Hispanic Men in construction in 1994, by age. Red line is the stable number 

of US Born Hispanic men in construction assuming economic growth and unemployment continue at their average rates 

indefinitely.

Table 26 contains the estimates of the coefficients for net inflows to construction by age group. 

A stable age distribution of U.S. born Hispanic men in construction assuming economic 

growth and unemployment continue at their average rates indefinitely is shown in Figure 27.

The “stable age distribution” is well above the 1994 age distribution because of the rapid influx 

of Hispanics into the construction industry. Fit of the estimate to the data is shown in Figure 

28.

0

5,000

10,000

15,000

20,000

25,000

30,000

35,000

40,000

10 20 30 40 50 60 70

Number of men in construction

Age
53

Table 26: Coefficients for net flows of US Born Hispanic men into construction.

Var Coef. Std. Err. z P>|z|

Age 16 - 19: t 0.701 0.0410 17.120 < 0.01 %

Age 16 - 19: growth 0.573 0.2194 2.610 0.90 %

Age 16 - 19: unemployment 0.201 0.3458 0.580 56.20 %

Age 16 - 19: sin 0.113 0.0665 1.700 8.90 %

Age 16 - 19: cos -0.078 0.0658 -1.190 23.50 %

Age 20 - 24: t 0.060 0.0133 4.530 < 0.01 %

Age 20 - 24: growth 0.227 0.0854 2.660 0.80 %

Age 20 - 24: unemployment -0.273 0.1429 -1.910 5.60 %

Age 20 - 24: sin -0.068 0.0330 -2.060 3.90 %

Age 20 - 24: cos -0.027 0.0328 -0.840 40.30 %

Age 25 - 34: t 0.025 0.0070 3.520 < 0.01 %

Age 25 - 34: growth 0.127 0.0580 2.190 2.90 %

Age 25 - 34: unemployment -0.272 0.0987 -2.760 0.60 %

Age 25 - 34: sin -0.021 0.0230 -0.900 37.00 %

Age 25 - 34: cos -0.025 0.0229 -1.110 26.90 %

Age 35 - 44: t -0.009 0.0077 -1.190 23.40 %

Age 35 - 44: growth 0.064 0.0634 1.020 30.90 %

Age 35 - 44: unemployment -0.230 0.1095 -2.100 3.60 %

Age 35 - 44: sin -0.004 0.0257 -0.140 88.70 %

Age 35 - 44: cos -0.073 0.0256 -2.850 0.40 %

Age 45 - 54: t -0.021 0.0096 -2.250 2.50 %

Age 45 - 54: growth 0.181 0.0808 2.230 2.50 %

Age 45 - 54: unemployment -0.152 0.1347 -1.130 25.80 %

Age 45 - 54: sin -0.088 0.0327 -2.690 0.70 %

Age 45 - 54: cos -0.005 0.0324 -0.140 88.60 %

Age 55 - 64: t -0.069 0.0157 -4.370 < 0.01 %

Age 55 - 64: growth 0.278 0.1313 2.120 3.40 %

Age 55 - 64: unemployment -0.039 0.2140 -0.180 85.70 %

Age 55 - 64: sin 0.042 0.0531 0.780 43.30 %

Age 55 - 64: cos 0.063 0.0528 1.190 23.50 %

Age > 64: t -0.153 0.0493 -3.110 0.20 %

Age > 64: growth -0.021 0.3359 -0.060 95.10 %

Age > 64: unemployment 0.105 0.5129 0.210 83.70 %

Age > 64: sin 0.045 0.1344 0.330 73.90 %

Age > 64: cos -0.171 0.1345 -1.270 20.30 %

As usual, older worker are less susceptible to the business cycle than younger workers. Above 

the age of 55, the impact of the business cycle is not significantly different from zero.
54

Figure 28: Fit of estimates to data for US Born Hispanic men in construction by age group.

Net inflow totals are shown in Figure 29. In the average year, 75 % of the U. S. born Hispanic 

men who enter construction do so before the age of 25. Total net inflow across all age groups 

is positive in all but three years (data not shown).

0

50,000

100,000

150,000

200,000

250,000

300,000

1994 1996 1998 2000 2002 2004 2006 2008 2010 2012

Number of men in construction

Year

Age: 16 - 19

Age: 20 - 24

Age: 25 - 34

Age: 35 - 44

Age: 45 - 54

Age: 55 - 64

Age: 65 - 70

Age: 16 - 19

Age: 20 - 24

Age: 25 - 34

Age: 35 - 44

Age: 45 - 54

Age: 55 - 64

Age: 65 - 70
55

Figure 29: Net inflow to construction for U.S. born Hispanic men, by age for selected years.

Net rate of inflow by age and rate of economic growth is shown in Table 27. As before, this 

underestimates the variation due to the business cycle, since it does not take into account the 

general unemployment rate. Here, susceptibility to the business cycle reaches a minimum at 

around 40 (and above 65).

Table 27: Net rate of inflow to construction by age and rate of economic growth. Colored cells indicate ages and 

circumstances where men are on net leaving construction.

Age

Deviation of Economic Growth from Average

-2 % -1 % 0 % 1 % 2 %

16 – 19 75.51 % 88.20 % 101.66 % 115.94 % 131.07 %

20 – 24 0.52 % 3.34 % 6.20 % 9.12 % 12.08 %

25 – 35 -0.59 % 0.96 % 2.51 % 4.08 % 5.65 %

35 – 44 -2.45 % -1.68 % -0.91 % -0.15 % 0.62 %

45 – 54 -6.32 % -4.23 % -2.12 % 0.01 % 2.17 %

55 – 64 -12.74 % -9.73 % -6.65 % -3.49 % -0.26 %

65 – 70 -13.76 % -13.98 % -14.19 % -14.40 % -14.61 %

Impact of seasonality is shown in Table 28. Seasonality is not significantly different from zero 

for U.S.-born Hispanic men. The date when number of workers is highest is concentrated in 

summer. A Wald test on date of maximum employment indicates that the dates are not 

significantly different across age groups (χ2 = 2.48, df = 6, p = 87.09 %).

-4,000

-2,000

0

2,000

4,000

6,000

8,000

10,000

15 20 25 30 35 40 45 50 55 60 65 70

Net Inflow - Number of workers

Age

1996 1999 2001

2007 2008 2010
56

Table 28: Impact of seasonality. Seasonal Coefficient is the absolute magnitude of the seasonal variation. Wald Test 

represents the probability that the seasonal variation is greater than zero.

Age

Seasonal 

Coefficient

% change: 

lowest to 

highest

Wald test

Max 

χ Date 2 df p

16 – 19 0.1375 31.66 % 1.170 1 28.04 % 5-May

20 – 24 0.0734 15.82 % 1.230 1 26.72 % 7-Sep

25 – 35 0.0327 6.75 % 0.500 1 47.84 % 9-Aug

35 – 44 0.0730 15.71 % 2.030 1 15.39 % 3-Jul

45 – 54 0.0879 19.21 % 1.810 1 17.85 % 26-Sep

55 – 64 0.0752 16.24 % 0.510 1 47.60 % 3-Feb

65 – 70 0.1769 42.46 % 0.430 1 51.19 % 15-Jun
57

4.5. Foreign Born Hispanic Men

Figure 30 shows the number of foreign-born Hispanic men in construction in 1994, by age.

Figure 30: Blue lines both represent the number of foreign-born Hispanic Men in construction in 1994, by age. Red line is 

the stable number in construction assuming economic growth and unemployment continue at their average rates 

indefinitely. Note that the solid blue line is plotted against the left axis, while the red line (and dashed blue line for scale) 

is plotted against the right axis.

Table 29 contains the estimates of the coefficients for net inflows to construction by age group. 

A stable age distribution of U.S. born Hispanic men in construction assuming economic 

growth and unemployment continue at their average rates indefinitely is shown in Figure 30.

Fit of the estimate to the data is shown in Figure 31.

0

60,000

120,000

180,000

240,000

300,000

360,000

420,000

480,000

0

2,000

4,000

6,000

8,000

10,000

12,000

14,000

16,000

10 20 30 40 50 60 70

Number of men in constructionNumber of men in construction

Age
58

Table 29: Coefficients for net flows of US Born Hispanic men into construction.

Var Coef. Std. Err. z P>|z|

Age 16 - 19: t 0.795 0.0336 23.670 < 0.01 %

Age 16 - 19: growth 0.808 0.1750 4.620 < 0.01 %

Age 16 - 19: unemployment 0.519 0.2934 1.770 7.70 %

Age 16 - 19: sin 0.285 0.0522 5.450 < 0.01 %

Age 16 - 19: cos -0.068 0.0513 -1.320 18.60 %

Age 20 - 24: t 0.174 0.0098 17.720 < 0.01 %

Age 20 - 24: growth 0.646 0.0627 10.310 < 0.01 %

Age 20 - 24: unemployment -0.343 0.1042 -3.290 0.10 %

Age 20 - 24: sin 0.055 0.0235 2.350 1.90 %

Age 20 - 24: cos -0.069 0.0233 -2.950 0.30 %

Age 25 - 34: t 0.089 0.0046 19.540 < 0.01 %

Age 25 - 34: growth 0.542 0.0390 13.900 < 0.01 %

Age 25 - 34: unemployment -0.013 0.0622 -0.210 83.30 %

Age 25 - 34: sin -0.026 0.0148 -1.790 7.30 %

Age 25 - 34: cos 0.004 0.0147 0.260 79.20 %

Age 35 - 44: t 0.041 0.0050 8.370 < 0.01 %

Age 35 - 44: growth 0.353 0.0425 8.310 < 0.01 %

Age 35 - 44: unemployment -0.072 0.0670 -1.070 28.50 %

Age 35 - 44: sin -0.037 0.0170 -2.170 3.00 %

Age 35 - 44: cos -0.004 0.0169 -0.210 83.00 %

Age 45 - 54: t 0.019 0.0071 2.730 0.60 %

Age 45 - 54: growth 0.346 0.0603 5.730 < 0.01 %

Age 45 - 54: unemployment -0.124 0.0927 -1.340 18.10 %

Age 45 - 54: sin -0.065 0.0244 -2.650 0.80 %

Age 45 - 54: cos -0.003 0.0242 -0.110 91.30 %

Age 55 - 64: t -0.064 0.0130 -4.930 < 0.01 %

Age 55 - 64: growth 0.175 0.1054 1.660 9.70 %

Age 55 - 64: unemployment -0.250 0.1653 -1.510 13.00 %

Age 55 - 64: sin -0.040 0.0435 -0.920 35.50 %

Age 55 - 64: cos -0.002 0.0432 -0.040 97.00 %

Age > 64: t -0.220 0.0477 -4.620 < 0.01 %

Age > 64: growth 0.130 0.3227 0.400 68.70 %

Age > 64: unemployment 0.307 0.4569 0.670 50.20 %

Age > 64: sin -0.171 0.1303 -1.310 19.00 %

Age > 64: cos 0.030 0.1278 0.240 81.30 %

The rate of inflow (the t coefficients in Table 29) of foreign-born Hispanic men to construction 

is decreasing with age. However, when the age distribution stabilizes (and assuming that the 

current estimated rates do not change) then the number of foreign-born Hispanic men entering 

construction will be more or less constant up to the age of 55. However, the assumption of 

stable rates is not likely to hold.
59

Figure 31: Fit of estimates to data for foreign-born Hispanic men in construction by age group.

It is clear that number of foreign-born Hispanic men in construction is sharply increasing. Net 

inflow / outflow by age is shown in Figure 32 for selected years. In the average year, 75 % of 

the foreign-born Hispanic men who enter construction do so before the age of 34. Total net 

inflow across all age groups is positive in all but three years (data not shown).

0

100,000

200,000

300,000

400,000

500,000

600,000

700,000

800,000

900,000

1,000,000

1994 1996 1998 2000 2002 2004 2006 2008 2010 2012

Number of men in construction

Year

Age: 16 - 19

Age: 20 - 24

Age: 25 - 34

Age: 35 - 44

Age: 45 - 54

Age: 55 - 64

Age: 65 - 70

Age: 16 - 19

Age: 20 - 24

Age: 25 - 34

Age: 35 - 44

Age: 45 - 54

Age: 55 - 64

Age: 65 - 70
60

Figure 32: Net inflow to construction for foreign-born Hispanic men, by age for selected years.

Net rate of inflow by age and rate of economic growth is shown in Table 30. As before, this 

underestimates the variation due to the business cycle, since it does not take into account the 

general unemployment rate. As usual, older workers are less susceptible to the business cycle 

than younger workers. Above the age of 55, the impact of the business cycle is not 

significantly different from zero. Note that it is not until rates of economic growth are much 

less than average that net inflows turn negative for most age groups.

Impact of seasonality is shown in Table 31. As expected, the impact of seasonality decreases as 

workers get older, reaching a minimum at around age 35. However, seasonality is not 

significantly different from zero for any age group except those under age 25. The date when 

number of workers is highest is concentrated in fall. A Wald test on date of maximum 

employment indicates that the dates are not significantly different across age groups (χ2 = 1.18, 

df = 6, p = 97.77 %).

-20,000

-15,000

-10,000

-5,000

0

5,000

10,000

15,000

20,000

25,000

15 20 25 30 35 40 45 50 55 60 65 70

Net Inflow - Number of workers

Age

1996 1999 2001 2007 2008 2010
61

Table 30: Net rate of inflow to construction by age and rate of economic growth. Colored cells indicate ages and 

circumstances where men are on net leaving construction.

Deviation from Mean Rate of economic growth

Age -4 % -3 % -2 % -1 % 0 % 1 % 2 %

16 - 19 49.02 % 64.76 % 81.98 % 100.80 % 121.34 % 143.74 % 168.16 %

20 - 24 -13.33 % -6.08 % 1.70 % 10.03 % 18.95 % 28.50 % 38.70 %

25 - 34 -16.14 % -10.29 % -4.10 % 2.44 % 9.36 % 16.67 % 24.39 %

35 - 44 -12.34 % -8.40 % -4.32 % -0.11 % 4.24 % 8.73 % 13.37 %

45 - 54 -13.93 % -10.15 % -6.25 % -2.22 % 1.94 % 6.24 % 10.67 %

55 - 64 -13.93 % -12.04 % -10.12 % -8.18 % -6.22 % -4.24 % -2.24 %

65 - 70 -24.72 % -23.49 % -22.26 % -21.01 % -19.76 % -18.51 % -17.24 %

Table 31: Impact of seasonality. Seasonal Coefficient is the absolute magnitude of the seasonal variation. Wald Test 

represents the probability that the seasonal variation is greater than zero.

Age

Seasonal 

Coefficient

% change: 

lowest to 

highest

Wald test

Max 

χ Date 2 df p

16 – 19 0.2925 79.51 % 8.140 1 0.43 % 13-Apr

20 – 24 0.0883 19.31 % 3.620 1 5.71 % 22-May

25 – 35 0.0268 5.50 % 0.820 1 36.49 % 8-Oct

35 – 44 0.0371 7.70 % 1.190 1 27.63 % 24-Sep

45 – 54 0.0647 13.82 % 1.760 1 18.49 % 27-Sep

55 – 64 0.0403 8.39 % 0.210 1 64.34 % 27-Sep

65 – 70 0.1735 41.50 % 0.440 1 50.69 % 9-Oct
62
63

5. Discussion

As discussed earlier, there is a perception that the construction industry has difficulty 

attracting and retaining skilled workers, and as a result faces a shortage of skilled workers. It 

appears that the workforce is aging, and that few young people are entering the industry. 

Training programs for skilled craft workers were traditionally funded and administered 

through unions, and open-shop training programs have tended to be rare14. But since unions 

have been in a long-term decline, it is not clear where new skilled craft workers will come 

from. The resulting difficulty staffing projects results in increased costs and schedule delays. 

This problem is exacerbated by a 30-year decline in real construction wages relative to workers 

in other industries.

This raises a number of economic questions that this report was intended, in part, to address. 

Basic factual questions about entry of young people into the industry and trends in union 

membership are addressed in the earlier sections. Questions about skills and wages require 

more careful analysis.

It is not clear what is meant by a shortage of skilled labor. The construction market and the 

construction labor market appear to be highly competitive. Unlike many other industries, the 

construction market is dominated by a large number of small firms. No one firm has a 

significant fraction of the market. But in competitive markets, shortages are resolved by 

increases in price. An increasing price reduces demand and attracts additional supply into the 

market, thus balancing the market. Huang et al. (2009) report that the “[d]ifficulty in staffing 

projects has resulted in increasing costs and schedule delays.” That raises the question of why 

wages haven’t adjusted for the decline. If construction costs (including delay costs) have 

increased, why haven’t wages?

To begin answering this question, two questions are addressed below. First, to what extent 

can a decline in skills be discerned in the data? Second, how does labor supply adjust to 

changes in wage?

5.1. Skills

Since the CPS data does not distinguish skilled craft workers from general construction 

laborers, and does not directly measure skill level, indirect means must be used to estimate the 

change in skill level of construction workers over time. One approach would be to assess 

trends in education levels among construction workers.

To determine whether the educational level of construction workers is changing over time, an 

index of educational level was constructed and graphed versus age for four different years: 

 14 See Huang, Allison, Robert Chapman and David Butry. “Metrics and Tools for Measuring Construction 

Productivity: Technical and Empirical Considerations.” NIST Special Publication 1101.
64

1996, 2000, 2006 and 2010. In order to ensure that people were not included multiple times in 

the sample, the sample was restricted to people in the outgoing rotation.

First, the average years completed in school versus age was graphed (Figure 33). The chart 

seems to indicate that among men aged 25 – 45, average educational level is decreasing over 

time. Figure 34 shows that average normalized years of education for men in construction at 

age 30 by year. Again, there seems to be a decrease in educational level over time. However, 

this chart suggests that the educational level may be inversely related to the business cycle.

Figure 33: Average years of education of men in construction by age, and normalized 

by the average years of education of men in the population at large.

0.80

0.82

0.84

0.86

0.88

0.90

0.92

0.94

0.96

0.98

1.00

20 25 30 35 40 45 50 55 60

Years of Education Index

Age

1996 2000 2006 2010
65

Figure 34: Average normalized years of education for 30-year-old men in construction 

by year.

Since a formal model of education has not been specified, statistical significance of the 

observations above cannot be tested. However, this preliminary result provides some support 

for the idea that there is a decline in skill level among the construction labor force.

5.2. Labor Supply and Wage

The issue of shortages of skilled labor immediately raises questions regarding the nature of 

supply and demand for construction labor. Preliminary efforts to model supply and demand 

failed. Specifically, coefficients on price for demand and supply were routinely of the wrong 

sign. The most likely reason for the failure is that an omitted variable correlates with both 

wage and employment.

The best candidate for such an omitted variable would be skill. If wages correlate with skill (as 

seems reasonable) and if low-skill people are the last hired and first fired, then the efforts to 

estimate supply and demand without taking into account skill will fail. It seems reasonable to 

assume that skill will correlate with age, education, and years in service. There is no 

convenient proxy for years in service15. Age and education, though, do correlate with wage. 

However, even after accounting for them the problems with the demand and supply 

estimations remain.

One way of dealing with this would be to estimate labor supply directly from microeconomic 

data. As a preliminary approach to doing this, wage and the decision to work in construction 

 15 One possible proxy would be a simple binary variable identifying whether a person had the same employer 

upon leaving the survey as when they entered it 16 months earlier (thanks to Dave Butry who suggested it).

0.84

0.85

0.86

0.87

0.88

0.89

0.9

0.91

0.92

0.93

1994 1996 1998 2000 2002 2004 2006 2008 2010 2012

Years of Education Index

Year
66

for adult men in the CPS were simultaneously estimated. Since the decision to work in 

construction will be correlated with wage, there will be a selection effect that needs to be 

accounted for. The basic approach is set forth in Greene, 2000 and Heckman, 1979.

Assume construction wages for any individual are specified as:

wit = xit ∙ βw + ξt + εit

where

wit = Construction wage for worker i at time t.

xit = Set of factors that influence the wage received

βw = Regression parameters associated with wage

ξt = fixed-effect variables for average wage at time t

εit = random variable

The construction wage is only known for people working in construction. If the choice to 

work in construction were uncorrelated with construction wage, then a simple regression of 

wage versus regressors would suffice. However, construction wage is a factor in the decision 

whether to work in construction, so the censoring implicit in the decision to work in 

construction will bias the regression results. To account for this, a model of employment 

choice is also specified.

A latent-variable approach is used where:

yit = uit ∙ βc + ηit

and worker i works in construction at time t if and only if yit ≥ 0. Variables are:

yit = Latent variable reflecting whether worker i works in construction at time t.

uit = Set of factors that influence the choice to work in construction

βc = Regression parameters associated with the choice to work in construction

ηit = random variable

Finally, the two error terms are assumed to be jointly normally distributed as:

�

ε

η� ~N �0,�

σ2 σρ

σρ 1 ��

Note that since the only information we have on y is whether it is greater than or lesser than 

zero, the initial regression is indeterminiate. By specifying the variance of η as 1, we remove 

the indeterminacy.

The joint regression is solved by Maximum Likelihood Estimation.
67

Variables assumed to influence wage include age, age2

, race/ethnicity, and education. The 

choice to work in construction is assumed to be influenced by the construction wage, so all the 

regressors included in the wage equation are included in the choice equation. In addition, 

choice to work in construction is assumed to be influenced by marital status and whether there 

are children living at home.

Race/ethnicity, education, marital status, and children are all specified as dummy variables. 

For race/ethnicity, dummies are included for Black, Native-born Hispanic (Native), and 

Foreign-born Hispanic (Foreign). White is the omitted category. For education, dummy

variables are included for people with less than a high-school education (NoHS) and for 

people with a college degree (College). The omitted category is people with only a high-school 

diploma. Marital status (married) is coded for people who are currently married. The Child 

dummy (childs) is coded if there are children living at home.

Results are shown in Table 32. In the original regression, a fixed-effects variable for each 

quarter was included, so the parameters represent deviations from the average wage for a 

given quarter.

Table 32: Simultaneous estimation of construction wage and choice to work in construction for adult men.

Coef. Std. Err. z P>|z|

wage

age 38.12563 0.627959 60.71 < 0.001

age2 -0.37647 0.007785 -48.36 < 0.001

Black -179.542 5.283046 -33.98 < 0.001

Foreign -161.467 3.752785 -43.03 < 0.001

Native -72.5199 5.235203 -13.85 < 0.001

College 205.8818 3.097947 66.46 < 0.001

NoHS -140.119 3.091723 -45.32 < 0.001

construction

age 0.088357 0.002131 41.47 < 0.001

age2 -0.00112 2.55E-05 -43.87 < 0.001

married 0.210331 0.011291 18.63 < 0.001

childs 0.039352 0.014221 2.77 0.006

Black -0.25957 0.019085 -13.6 < 0.001

Foreign -0.03516 0.015884 -2.21 0.027

Native -0.10151 0.021117 -4.81 < 0.001

College -0.04251 0.013081 -3.25 0.001

NoHS -0.10035 0.012251 -8.19 < 0.001

rho -0.14258 0.013198

sigma 386.0331 0.824089
68

Most variables are pretty much what one would expect with one important exception. In the 

estimation rho is the correlation between the wage and the choice to work in construction 

otherwise unaccounted for in the model. In this model rho is negative. That implies that 

increases in construction wages are associated with people selecting out of construction.

As a general rule one would expect people to gravitate to the higher wage occupation. So if 

higher construction wages are associated with people selecting out of construction, then higher 

(potential) construction wages must generally be associated with higher wages in other 

industries as well. If it is assumed that workers are paid their marginal productivity (i.e.,

higher wage workers are more productive), then the results imply (all else equal) that workers 

who are more skilled at construction are also more skilled at other jobs as well. That is 

unsurprising, but the negative correlation between wage and choice of construction implies 

something stronger: the skill premium is higher in other industries than in construction. So 

(again, all else equal) there are relatively few ‘highly skilled’ construction workers because 

such people can earn more in other industries—presumably because they are more productive 

there.

This suggests that part of the decline in numbers of skilled craft workers may be attributable to 

macroeconomic factors. It is well known that the premium to college education has increased 

since the 1970’s (see for example Gottschalk, 1997). This increase in the college premium is 

partially attributable to a decline in wages for people with only a high-school education. This 

suggests that the decline in skilled craft workers may be driven by a larger decline in demand 

for low-skilled labor generally. Since construction seems to gain less in productivity terms 

from skill and ability than other industries, the growing skills premium in the modern 

economy induces people with relatively high skill and ability to seek employment elsewhere.

5.3. Future Directions

There are a number of additional directions that would contribute to understanding the 

construction labor market.

• Characterization at the regional / local level.

This report characterized labor supply at the national scale for the most part. However, 

construction is primarily a local market and there will be aspects of the market that will 

be obscured by looking at it nationally. For example, racial makeup (and probably 

seasonality) clearly differs from region to region. So deepening the analysis to look at 

the data at a regional scale would likely improve our understanding of the market.

• Estimation of supply and demand.

Estimating supply and demand functions for construction labor would help. That turns 

out to be surprisingly difficult due to the high correlation between wages and 
69

employment. During times of increasing employment, wages (presumably) increase, 

but the people hired are at the low end of the wage scale while the people at the high 

end of the wage scale are susceptible to poaching by other industries. Times of 

decreasing employment present the reverse situation. That makes it difficult to tease 

out the relationship between supply and wage holding all else constant. Completing 

the task of estimating supply and demand will help fill in some of the missing pieces of 

the picture of the construction labor market.

• Labor Unions

Some of the concern about productivity in construction centers on a perceived shortage 

of skilled labor. That seems to be linked to the decline in union membership. So to 

understand what is going on with this, an understanding is needed of the place of 

unions in the market, why market share is declining (both from the supply side with 

people choosing whether to join and from the demand side of builders choosing 

whether to hire union labor), and what (if anything) is replacing unions in the 

marketplace. So to better understand the nature of skilled-labor shortages (or lack 

thereof) requires an understanding of the changing place of the trade unions in the 

market.

• Wage trends for skilled craft workers versus general construction labor

The data above, derived from the CPS, is not detailed enough to distinguish skilled craft 

workers in construction from general laborers. It is possible that average wages are 

declining while wages for skilled craft workers are increasing. This would explain the 

conundrum of “shortages” of skilled craft workers alongside declining construction 

wages. One way of assessing this possibility would be to look at the long-term trend of 

wages for craft workers versus general construction labor. Such data does not exist in 

the CPS, so other data sources would have to be found for such information.

• Labor flows by educational level

Expanding the analysis of labor flows to address educational levels would provide 

additional insight into long-term changes in educational levels in people entering 

construction.

• Analysis by market segment

Eventually, this work needs to be done for different segments of the construction 

market. Housing is such a large portion of the market that the results above are likely 

dominated by that segment of the market. But other segments will likely be different.
70
71

6. References

Gottschalk, P. (1997, Spring). Inequality, Income Growth, and Mobility: The Basic Facts. The 

Journal of Economic Perspectives, 11(2), 21-40.

Greene, W. (2000). Econometric Analysis (4th ed.). Upper Saddle River, NJ: Prentice Hall.

Heckman, J. (1979). Sample Selection Bias as a Specification Error. Econometrica, 47(1), 153-161.

Huang, A., Chapman, R., & Butry, D. (2009). Metrics and Tools for Measuring Construction 

Productivity: Technical and Empirical Considerations. Gaithersburg, MD: National Institute 

of Standards and Technology.

StataCorp. (2009). Stata Statistical Software: Release 11. College Station, TX.

Teicholz, P. (2004, 14 April). Labor Productivity Declines in the Construction Industry: Causes 

and Remedies. AECbytes Viewpoint(4).

Thomas, D. (2010). Methodology for Calculating Construction Industry Supply Chain Statistics.

Gaithersburg, MD.: National Institute of Standards and Technology.
72
73

Appendices

Appendix 1: Data

Below is a table of variables used from the Current Population Survey

Variable Period Description

HRHHID 1994-2010 Household ID

HRHHID2 2004-2010 Part 2 of the Household ID Number (= the next 3 variables concatenated)

HRSAMPLE 1994-2004 Sample Number

HRSERSUF 1994-2004 Serial suffix

HUHHNUM 1994-2004 Household Number (replacement households)

OCCURNUM 1994-2010 Person Number in Household ( = PULINENO)

HRMIS 1994-2010 Month in Sample (1 – 8)

HRMONTH 1994-2010 Month

HRYEAR 1994-1998 2-Digit Year

HRYEAR4 1998-2010 4-Digit Year

GEREG 1994-2010 Region (1 – Northeast, 2 – Midwest, 3 – South, 4 – West)

PESEX 1994-2010 1 – Male

PRTAGE 1994-2010 Age as of the end of the survey week

PERACE 1994-2002 Race (see table in Codebook) (This is recoded in 1997)

PTDTRACE 2003-2010 Detailed Race (see table in Codebook)

PRHSPNON 1994-2002 Hispanic Status

PEHSPNON 2003-2010 Hispanic Status

PRCITSHP 1994-2010 Citizenship Status (1-3 – Native, 4 – Naturalized, 5 – Non Citizen)

PEEDUCA 1994-2010 Educational Levels (see Codebook for definitions)

PEMLR 1994-2010 Labor Force Status (see table in Codebook)

PEHRUSL1 1994-2010 Usual hours worked at job 1 (-4: hours vary)

PEHRACT1 1994-2010 Actual hours worked at job 1 last week.

PEERNHRY 1994-2010 Indicator for Hourly Employee. Only sampled when HRMIS ∈ { 4, 8}

PEERNLAB 1994-2010 Indicator for Labor Union Member. Only sampled when HRMIS ∈ { 4, 8}

PEIO1COW 1994-2010 Class of Worker (1st job) (Gov’t; Private; Self-Employed; unpaid)

PRDTIND1 1994-2010 Detailed Industry, Job 1. Definitions changed at the end of 2002. 

PRDTOCC1 1994-2010 Detailed Occupation, Job 1. Definitions changed at the end of 2002.

PUIODP1 1994-2010 Same Employer (1: Yes, 2: No, < 0: No Answer)

PTERNWA 1994-2010 Weekly Earnings (to the penny)

PWORWGT 1998-2010 Outgoing Rotation Weight

PWLGWGT 1994-2010 Longitudinal Weight

PWSSWGT 1994-2010 “Six-Step” Weight

The CPS independently asks people what industry they work in and whether they have 

changed jobs in the previous month. That sets up a quality check of the data. Specifically, 

there should be very few people who have changed industries without changing jobs. 

However, before the middle of 1995 approximately 15,500 people per month are listed as 

changing industries without changing jobs. That suggests that the data before the middle of 

1995 may not be as reliable as the rest of the data.

Time Period Average Max Total

Jan ’94 – Jun ‘95 15,561 30,501 278,293

Jul ’95 - 201016 252 632 45,399

 16 Excluding the end of 2002 when industry definitions changed.
74

Other results give a similar impression.

Data for quarterly GDP were obtained from the Bureau of Economic Analysis. Monthly data 

for Unemployment and Urban Consumer Price Index (CPI-U) were obtained from the Bureau 

of Labor Statistics. This reported used data for 1993 – 2010.

Since the main data are monthly and GDP are published quarterly, a method was needed to 

interpolate the GDP data to monthly to effectively make use of it. To interpolate the data two 

assumptions were made:

1. Reported quarterly growth is the geometric mean of the interpolated monthly growth 

rates for the months making up the calendar quarter. That is (for example), the 

geometric mean of growth for April, May and June 2007 equals the reported growth for 

the second quarter 2007.

2. Log of monthly growth is linearly interpolated between the log growth rates of the 

central months in each quarter. That is (for example), March 2007 and April 2007 

growth are linearly interpolated between Feb 2007 and May 2007.

If t represents months, gt represents the published growth rate for a calendar quarter (where 

the published growth rate is arbitrarily assigned to the central month in the quarter), and g̃t

represents interpolated monthly growth rate, then assumption 1 above is specified as:

1

3 ln(1 + g�t−1) +

1

3 ln(1 + g�t) +

1

3 ln(1 + g�t+1) = ln(1 + gt)

For the last month in a calendar quarter, assumption 2 is specified as:

2

3 ln(1 + g�t−1) − ln(1 + g�t) +

1

3 ln(1 + g�t+2) = 0

And similarly for the first month in a calendar quarter.

That produces a set of simultaneous equations, with two more unknowns than equations. By 

specifying that Jan 1993 and Dec 2010 are linear extensions of the subsequent (previous) series 

of months, there is a fully specified set of linear equations. Note that GDP is reported as 

annualized growth rates, and the equations listed above preserve that convention for the 

interpolated monthly growth rates. A graph of the interpolated monthly GDP figures overlaid 

on the reported quarterly GDP figures is shown in Figure 35.
75

Figure 35: Interpolated Monthly GDP overlaid on reported Quarterly GDP.

-10

-8

-6

-4

-2

0

2

4

6

8

10

1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012

Annualized Percent Growth in GDP

Year
76

Appendix 2: Similarity Indices

Industry rij f

Agriculture 12.60 % 2.25 %

Forestry, logging, fishing, hunting, and trapping 16.16 % 0.34 %

Mining 15.12 % 0.91 %

Construction 100.00 % 100.00 %

Nonmetallic mineral product manufacturing 14.24 % 0.74 %

Primary metals and fabricated metal products 10.11 % 2.23 %

Machinery manufacturing 7.08 % 0.92 %

Computer and electronic product manufacturing 3.24 % 0.38 %

Electrical equipment, appliance manufacturing 3.18 % 0.21 %

Transportation equipment manufacturing 4.30 % 1.43 %

Wood products 17.04 % 0.71 %

Furniture and fixtures manufacturing 14.70 % 0.86 %

Miscellaneous and not specified manufacturing 4.73 % 0.59 %

Food manufacturing 5.84 % 0.97 %

Beverage and tobacco products 4.44 % 0.18 %

Textile, apparel, and leather manufacturing 3.22 % 0.30 %

Paper and printing 3.83 % 0.49 %

Petroleum and coal products manufacturing 15.45 % 0.32 %

Chemical manufacturing 5.25 % 0.64 %

Plastics and rubber products 3.89 % 0.55 %

Wholesale trade 6.65 % 3.09 %

Retail trade 5.02 % 8.93 %

Transportation and warehousing 6.60 % 4.66 %

Utilities 10.57 % 1.60 %

Publishing industries (except internet) 0.97 % 0.17 %

Motion picture and sound recording industries 6.18 % 0.19 %

Broadcasting (except internet) 9.65 % 0.57 %

Internet publishing and broadcasting 0.00 % 0.00 %

Telecommunications 2.22 % 0.45 %

Internet service providers and data processing services 3.41 % 0.07 %

Other information services 0.00 % 0.01 %

Finance 1.38 % 0.83 %

Insurance 1.87 % 0.51 %

Real estate 7.02 % 1.82 %

Rental and leasing services 6.13 % 0.30 %

Professional and technical services 4.00 % 3.24 %

Management of companies and enterprises 0.34 % 0.00 %

Administrative and support services 13.80 % 6.61 %

Waste management and remediation services 14.85 % 0.65 %

Educational services 1.84 % 2.52 %

Hospitals 1.15 % 0.89 %

Health care services, except hospitals 1.27 % 1.15 %

Social assistance 0.99 % 0.37 %

Arts, entertainment, and recreation 6.02 % 1.50 %

Accommodation 4.72 % 0.66 %

Food services and drinking places 5.87 % 4.52 %

Repair and maintenance 13.61 % 2.81 %

Personal and laundry services 4.03 % 0.76 %

Membership associations and organizations 3.03 % 0.60 %

Private households 5.22 % 0.35 %

Public administration 2.82 % 2.05 %