Skill Prices over the Business Cycle Evgenia.pdf · Email: [email protected]. 1. increases in education and experience premia in the 1970s, 1980s and 1990s were extensively analyzed

Skill Prices over the Business Cycle∗

Gonzalo Castex and Evgenia Dechter†

January 2013

Abstract

We examine cyclical behavior of aggregate skill prices and find that the price of school-

ing is weakly procyclical and price of experience is countercyclical. Distinguishing between

technology and neutral productivity shocks, shows that both generate the countercycli-

cal pattern of experience premium whereas procyclicality of schooling premium is driven

by technological innovations. Changing demographics and compositional effects do not

explain the cyclical patterns. To explain these findings, we extend the capital-skill com-

plementarity framework to incorporate education, experience and vintage capital. Em-

ploying predictions of human capital and match quality theories, the model generates

cyclical patterns of skill prices observed in the data.

JEL Classification: E24, J24, J31

Keywords: Returns to education, Returns to experience, Skill prices, Wage structure

1 Introduction

A considerable amount of research is dedicated to study the cyclicality of real wages. More

recent studies, following Stockman (1983) and Bils (1985), show that real wages are pro-

cyclical. The cyclicality of wage differentials has received less attention. On the other hand,∗We would like to thank Mark Bils, Richard Blundell, Denise Doiron, Jesus Fernandez-Villaverde, Michael

Keane, Bob Miller, James Morley, Valentyn Pancheko, Sergio Rebelo, Robert Shimer, Guillaume Vanden-broucke, as well as seminar participants at UNSW, University of Santiago, Central Bank of Chile for commentsand suggestions. We also thank Cristian Munoz for excellent research assistance.†Gonzalo Castex, Central Bank of Chile. Email: [email protected]. Evgenia Dechter, School of Eco-

nomics, University of New South Wales. Email: [email protected].

1

increases in education and experience premia in the 1970s, 1980s and 1990s were extensively

analyzed in the context of technological change and shifts in demand and supply of skills.

Numerous studies document these developments, analyze their causes and implications. Katz

and Autor (1999) provide an extensive review of this wage structure literature. In the con-

text of business cycles, Reder (1955) was the first to formally examine the cyclicality of wage

differentials; his findings suggest that the aggregate skill premium was countercyclical in the

1930s and 1940s. More recently, Keane and Prasad (1993), Young (2003), Lindquist (2004)

and Castro and Coen-Pirani (2008) show that the aggregate skill premium is acyclical or

weakly procyclical, primarily focusing on the education premium.

This study evaluates how schooling and experience premia co-move with the business

cycle. To analyze the cyclicality, we build on the wage structure literature and control for

potential channels that could shift the supply and demand for skills. For example, Katz

and Revenga (1989), Katz and Murphy (1992) and Murphy and Welch (1992) explain the

increases in returns to skills between the 1970s and early 1990s, focusing on skill-biased tech-

nological change and the associated shifts in demand for skilled labor, globalization pressures

and shrinking relative demand for less skilled, declines in unionization and in real mini-

mum wage that primarily affected lower skilled workers. In the real business cycle context,

Krusell, Ohanian, Rios-Rull and Violante (2000) (hereafter KORV), Lindquist (2004), Cas-

tro and Coen-Pirani (2008), in the capital-skill complementarity framework, also identify the

technological change as the main driving force behind the increase in schooling premium and

show that an increase in the relative supply of schooling has a negative effect.1

Less attention is addressed to the post-1990th developments in skill prices. Between the

late 1990s and 2000s there was a slowdown in the increase of schooling premium whereas the

experience premium has declined.2 Jeong, Kim and Manovskii (2012) examine the develop-

ments in wage structure for the entire 1970s - 2000s period. They argue that changes in age

composition of the labor force can explain the rising experience differentials in the 1970s and

1Greenwood, Hercowitz and Krusell (2000) suggest that technological change is the source of about 30%of output fluctuations, thus the co-movement of skill prices with the technological change captures some ofthe prices’cyclicality.

2Figure 2 summarizes these empirical findings.

2

1980s as well as the decline that began in the second half of the 1990s. Some studies also

argue that there is a relationship between the age distribution and the magnitude of cyclical

output volatility; see, for example, Jaimovich and Siu (2009) and Lugauer (2012). We control

for the changing age distribution and for other changing demographics in our analysis.

The estimations are performed in two steps. First, using data from the 1962 - 2010 March

Current Population Surveys (CPS), we estimate the prices of schooling and work experience,

using the Mincer (1974) earnings equation for every year in the sample. Next, we examine the

correlations between the estimates of skill premia and business cycle measures: real output per

capita and unemployment rate. At this stage we also test whether the technological change

and compositional changes in the distributions of observed and unobserved characteristics

can explain the developments in skill prices.3

Simple correlations show that the price of schooling is weakly procyclical and the price

of experience is countercyclical. Further analysis distinguishes between investment-specific

and neutral (or other) productivity shocks. In these specifications, the former is measured by

technological change and the latter by output or unemployment fluctuations. We find that

experience premium is negatively correlated with both types of shocks whereas schooling

premium is positively correlated with technological change and negatively with the neutral

shocks. Thus, both types of shocks generate the countercyclical pattern of experience pre-

mium whereas the weak procyclicality of schooling premium is driven by technological inno-

vations. Changing demographics, although important, do not explain the cyclical patterns of

skill prices. Average education and experience of the work force are negatively correlated with

the education and experience premia, respectively. Decreasing unionization rate is negatively

associated with education and experience premia.

Studies that analyze the cyclicality of wages emphasize the importance of changing work-

ers’quality distribution over the business cycle. Stockman (1983), Bils (1985) and others show

that the distribution of unobservable workers’characteristics changes over the business cycle,

and argue that these compositional changes can generate a countercyclical trend in wages.

3To construct a measure of technological change we follow Cummins and Violante (2002).

3

Keane and Prasad (1993) argue that it is also important to control for individual fixed ef-

fects when evaluating the cyclicality of returns to skills. We find that changes in unobserved

characteristics of the workforce do not explain the cyclical patterns of skill premia.

The weak procyclicality of schooling premium is in line with findings in previous studies.

Keane and Prasad (1993), Young (2003) and Castro and Coen-Pirani (2008) estimate that

the aggregate schooling premium is acyclical. Ziliak, Wilson and Stone (1999) find it to be

weakly procyclical. Lindquist (2004) argues that the weak procyclicality of the schooling

premium is in line with predictions of capital-skill complementarity theory. Lindquist also

shows that investment-specific technological improvements increase the schooling premium

whereas neutral productivity shocks decrease the schooling premium.

The existing literature does not address the cyclicality of experience premium, and to

the best of our knowledge, there is no single theoretical framework that reconciles the weakly

procyclical education premium and the countercyclical experience premium. Countercyclical

experience premium emerges in frameworks that incorporate job match quality or on-the-job

human capital accumulation. Literature on match quality predicts that older workers are

more likely to benefit from a better quality job match and, therefore, hold better contracts

when unemployment is relatively high. Human capital theory predicts that more experienced

workers are more likely to have a higher human capital stock, which might be costly to acquire;

therefore, they are less likely to lose their jobs in a recession. Both theories predict that firms

are more likely to retain workers who have more job experience during recessions and that

firms will offer contracts with smoother wage profiles to more experienced workers.

To explain the empirical findings, we propose an extension to the capital-skill comple-

mentarity model, as in KORV, to incorporate education and experience in a vintage capital

framework. We employ predictions of human capital and match quality theories to make

assumptions about complementarity between experience of labor and vintage of capital. Hu-

man capital and match quality theories predict that more experienced workers have more

stable wage profiles and are less susceptible to job transitions, in our framework this implies

a higher complementarity of vintage capital with experienced labor than with inexperienced

4

labor. KORV estimates that schooling is complementary with capital equipment and tech-

nological innovations. We show that given these complementarity assumptions, our model

generates cyclical patterns of skill prices observed in the data.

The remainder of this paper is organized as follows. Section 2 describes and summarizes

the data. Section 3 discusses empirical methods and reports results. Here we also examine

the magnitudes of potential composition biases and discuss the practical relevance of our

findings. Section 4 outlines the theoretical framework to explain the cyclical variation of

schooling and experience premia. Section 5 concludes the paper.

2 Data

To examine the developments in wage structure, we use data from the March Consumer

Population Surveys (CPS) for 1962 through 2010. The raw sample contains approximately

5.5 million observations, 50,000 to 160,000 observations per year. The subsample used here

includes white males between 18 to 62 years old, who work full time, not self-employed, not

in the armed forces and not enrolled in school. The sample is also restricted to individuals

who were employed for at least 50 weeks in the calendar year prior to the March CPS year.

This restriction is imposed due to data collection methods. Prior to 1975 several variables are

reported in intervals. Weeks worked last year are reported in 6 categories, (the intervals are 1-

13, 14-26, 27-39, 40-47, 48-49 and 50+), to minimize potential measurement errors we choose

individuals with 50 to 52 weeks worked. Our subsample contains 1.1 million observations,

9,000 to 30,000 observations per year, as reported in column (2) of Table 8. Any further

selection criteria is explicitly noted.

Main variables of interest are real hourly wage, education and work experience. March

CPS data contain a wide range of information on labor market outcomes. Some questions

in March CPS refer to usual last year activity and some to labor market activity during the

previous week. Weeks worked and income from wages and salaries refer to last year. There

are two variables that report hours worked, usual hours worked per week refer to last year

but available only for 1976 - 2010, and hours worked last week which are available for the

5

entire period.4 We construct a measure of hours worked per week last year for the entire

sample period based on how they project on hours worked last week, for the available years.

Hourly wage rates are calculated using the last year annual income, divided by 52 and by

the projected hours worked per week. Because the income, weeks and hours data refer to

last year, the actual period covered is 1961 through 2009. Wage rates are expressed in 1999

prices, deflated using the Consumer Price Index.

To construct the schooling variable, we use individual information on highest grade

completed and transform it into years of schooling. Schooling information is not available

in 1962; therefore, this year is excluded from the analysis. The March CPS does not allow

constructing actual work experience, therefore, we apply the standard practice to calculate

the potential work experience: age minus years of education minus 6.5

To measure the business cycle, we use real GDP per capita and the unemployment rate

for 25 to 54-year-old individuals.6 To measure demographic transitions, we employ the CPS

data to calculate the mean experience and the mean education levels of white males between

18 to 62 years old in the labor force.

To obtain a measure of technological change, we follow methodology that was proposed

in Cummins and Violante (2002). The speed of technical change for each capital good in

the equipment and software category (E&S) can be measured as the difference between the

growth rate of constant-quality nondurable consumption and the growth rate of the good’s

quality-adjusted price. Price indexes are from the National Income and Product Accounts

(NIPA).7

4An intervaled measure of usual hours worked per week last year is also available. We do not use thisvariable to minimize potential biases associated with measurement errors.

5Using the potential work experience instead of actual work experience is also the main reason to restrictour sample to males only. There were significant changes in fertility and female labor force participationduring the last five decades.

6GDP data was downloaded from The Conference Board, Total Economy Database,http://www.conference-board.org/data/economydatabase/#Real_GDP. Unemployment data was obtainedfrom the Bureau of Labor Statistics (BLS) database, http://www.bls.gov/cps/data.htm.

7We retrieve data from Tables 1.1.4 and 5.3.4. of the NIPA series to obtain price indexes for nondurableconsumption and equipment and structures (E&S), respectively. For further discussion on construction ofindexes see Cummins and Violante (2002).

6

2.1 Summary Statistics

There were many important changes in the labor market over the last 50 years. We summarize

the developments in detrended real GDP per capita, unemployment rate, potential experience,

education, unionization rate and technological change. These series are depicted in Figure 1,

Table 1 reports correlations between the key variables. Unemployment rates vary significantly

during the 1961– 2009 period and strongly negatively correlated with the detrended GDP.

Mean experience data show the importance of the baby boom cohorts’entry into the labor

market. The average level of schooling is increasing throughout the 1961 - 2009 period and

unionization rate is falling. Figure 1 also reports the three aggregate technological change

measures, the indexes show a substantial decline in technical growth in the 2000s.

3 Econometric Analysis

To examine how labor market rewards productive attributes we use Mincer (1974) wage

equation. The terms "price of experience" and "price of education" refer to the effects of

experience and education on log wage rate. We perform the analysis in two steps. First, for

each year in the sample, using OLS or quantile regression estimation routines, we estimate the

prices of education and experience, controlling for various personal characteristics. Second,

we evaluate the determinants and cyclical variability of skill prices.

For first stage estimations, consider a year t cross-sectional regression of log real wage

rates of individual i on labor market experience, education and other personal characteristics,

logwit = β1tExperienceit + β2tExperience2it + β3tSchoolingit +Xitγt + εt, (1)

where Xit includes a constant, marital status and metro status, εt summarizes the mea-

surement error in the data. Some specifications include spousal schooling level and spousal

ranking in the schooling distribution to proxy for unobserved skills, employing the positive

assortative matching theory, (see for example Lam, 1988). We estimate this equation for

1961 - 2009 using the OLS. Alternatively, to control for compositional changes, we estimate

7

(1) for the 75th percentile using the quantile regresion technique, assuming that those at

higher quantiles are less affected by compositional changes associated with the business cy-

cle, (see for example Lindquist, 2004). Prices of education and experience are defined as

follows, PSCHOOLt = β̂3t and PEXPt = β̂1t + 2β̂2tExperiencet, where Experiencet is the

mean experience level of the workers in the sample in year t.8

The second stage estimations analyze the cyclicality of skill prices,

PEXPt = η1Yt + η2Zt + υt, (2)

PSCHOOLt = µ1Yt + µ2Zt + ωt, (3)

where Yt is a business cycle measure in year t, Zt is a set of control variables and υt, ωt are

uncorrelated measurement errors. For the second stage estimations, throughout the paper,

we report Newey-West robust standard errors with two lags to adjust for serial correlation in

residuals.

Most estimations of (2) and (3) include the technological change index and therefore dis-

tinguish between investment-specific and neutral (or other) productivity shocks. For example,

Greenwood, Hercowitz and Krusell (2000) argue that technological change is the source of

about 30% of output fluctuations. Thus, when controling for the technological change, out-

put or unemployment reflect productivity changes not associated with investment-specific

technology innovations. Further discussion on differential effects of the two types of shocks

is provided in Section 4.

Skill prices, PSCHOOLt and PEXPt , are depicted in Figure 2. We also report series of

prices obtained using the actual number of weeks and hours worked (instead of interval and

projected values, respectively), these estimates are available for the 1975 - 2009 period. The

price of experience is increasing in the 1960s through 1980s but it declines in later years. The

price of schooling is increasing throughout the entire period, but the growth rate is changing

over time and it is higher in the 1980s - 1990s period. Cross-correlations between skill prices,

8The estimates of price of experience for the 75th percentile is obtained using a relevant measure ofExperiencet.

8

business cycle measures and key aggregate indicators are reported in Table 1. Correlations

between the price of schooling and business cycle measures are positive but not statistically

significant. The average price of experience is positively correlated with unemployment and

negatively with detrended output. The countercyclical relationships with lagged business

cycle measures are stronger. Lindquist (2004) makes a similar observation when estimating

the cyclical variability of education premium, arguing that this outcome is consistent with

the capital-skill complementarity theory. In estimations of equations (2) and (3) we use

lagged business cycle measures and report outcomes obtained using contemporaneous values

for comparison.9

Patterns summarized in Figure 2 and Table 1 do not control for important demographic

and economic developments that occurred over the 1961 - 2009 period. Several important

trends are documented in Figure 1: technological progress, increase in average schooling,

decline in unionization, and U-shaped average experience.10 One approach to control for

some of these developments is to construct detrended series of skill prices, depicted in Fig-

ure 3. The correlations between unemployment and skill prices in Figure 3 are 0.60 for

experience and -0.48 for education. Detrended series of wage rates obtained using standard

measures of weeks and hours worked are available for 1975 - 2009 period and show similar

patterns. Results in Figures 2 and 3 suggest that experience premium is countercyclical and

education premium is procyclical. In the regression analysis, alternatively to using the time

trend, we estimate equations (2) and (3) controlling for changing demographics and techno-

logical change, (distinguishing between shocks driven by technological innovations and other

productivity shocks).

Tables 2 and 3 report the results. Columns (1) and (5) report results controlling for the

time trend only. In these specifications, the price of experience is countercylical, 1% increase

in unemployment rate is associated with a 0.16% increase in the experience premium.11 The

9Tables A1 and A2 report estimation results using contemporaneous business cycle measures. Similarcyclical patterns for skill prices emerge.

10See for example Autor, Katz, and Krueger (1998), Bound and Johnson (1992), Mincer (1991), amongmany others, for further discussion on how these changes could affect the skill prices.

11Average price of experience is 1.3%, thus a 1% increase in unemployment rate is associated with 13%increase in experience premium.

9

schooling premium is weakly procyclical. The remaining columns in Tables 2 and 3 report

results when adding control variables.12

The price of experience is countercyclical in all specifications but the magnitude of rela-

tionship is lower when adding more controls. Similarly to Jeong, Kim and Manovskii (2012)

we find a strong negative relationship between the price of experience and supply of experi-

ence, however the changing supply is not suffi cient to explain the countercyclical pattern.13

Unionization rate is negatively correlated with the experience premium, consistent with find-

ings in earlier literature. For example, DiNardo, Fortin, and Lemieux (1996), Freeman and

Katz (1996) and Lee (1999), discuss how the decline in unionization has changed the wage

setting norms and affected skill prices. Specifications in columns (2) - (4) and (6) - (8) include

the inverse quality adjusted relative price of equipment to control for technological change.

The results suggest that there is a negative relationship between the price of experience and

both neutral and investment-specific productivity improvements.

Columns (1) and (5) in Table 3 suggest that education premium is procyclical. Other

studies, Ziliak, Wilson and Stone (1999) and Lindquist (2004) find it to be weakly procyclical

while Keane and Prasad (1993), Young (2003) and Castro and Coen-Pirani (2008) estimate it

to be acyclical. Including the technological change measure in columns (2) - (4) and (6) - (8)

allows to distinguish between investment-specific productivity and neutral shocks. Results

show that investment-specific technological improvements increase the schooling premium

whereas neutral productivity improvements decrease the schooling premium, in line with

Lindquist (2004), who shows a similar outcome using the capital-skill complemetarity frame-

work. The relationship between unionization and the price of schooling is negative and in line

with other studies. The average education level has a negative association with education

premium, we interpret this result a negative supply effect, as for example discussed in Katz

12The estimates are robust in specifications that use contemporaneous business cycle measures, reportedin Tables A1 and A2.

13This negative relationship can be partially induced by using the average experience to construct experiencepremium. Table A3 reports estimation results using experience premium for a representative worker with 20years of experience, the average potential experience of the labor force calculated over the entire period. Theresults are quite similar to those reported in Table 2, implying that the outcome is not driven by constructionof experience premium.

10

and Murphy (1992).14

3.1 Composition effects

Using equations (2) and (3) allows to include controls for changing demographics, but does

not control for changing distributions of unobserved characteristics. Stockman (1983), Bils

(1985) and others show that cyclical changes in the work force composition may induce

a countercyclical bias in the aggregate wage. Aggregate measures of real wages tend to

give more weight to low-skill workers during expansions than during recessions because less-

productive workers are more vulnerable to layoffs in recessions than more productive workers.

Keane and Prasad (1993) find a weak countercyclical bias in experience and schooling wage

differentials.

We use three approaches to evaluate the importance of changing unobserved character-

istics of workers. First, we employ the positive assortative matching theory and estimate

equation (1) controlling for spousal schooling and spousal ranking in the schooling distrib-

ution to proxy for unobserved skills (see for example Lam, 1988). The second stage results

are reported in Tables 4 and 5 and are very similar to those in Tables 2 and 3, the price

of experience is strongly countercyclical and the price of schooling is positively correlated

with technological change but negatively with with neutral productivity improvements. Sec-

ond, we measure skill prices at the 75th percentile of the wage distribution, assuming that

employment is less sensitive to business cycle fluctuations for workers at the high end of

wage distribution. Results are reported in Tables 6 and 7, the cyclicality patterns are very

similar to those obtained using the OLS method in the first stage.15 Third, we compare

estimation outcomes obtained for nearby quantiles (45th, 50th and 55th), assuming that if

there was a shift in the unobserved skills distribution, an individual would not move too far

from the original location. We estimate equation (1) for the 45th, 50th and 55th quantiles

14To examine the robustness of estimates, we estimate equation (2) by education level and equation (3)by experience level. Tables A5 and A6 report the results and show that the cyclical patterns hold for eachsubgroup.

15Appendix Table A.4 reports results for the 75th percentile for price of experience constructed usingaverage experience for the entire period instead of annual averages, the cyclicality patterns are very similar.

11

for t = 1961, ..., 2009, then we test whether βq451t = βq501t = β

q551t , β

q452t = β

q502t = β

q552t and

βq453t = βq503t = β

q553t . For most years t-tests fail to reject the null at the 5% significance level.

Table 8 summarizes the results. There are 5 years for which β1t’s are statistically different,

1 year for β2t’s and 9 years for β3t’s. The probability that the coeffi cients are different is not

correlated with the unemployment rate, we conclude that the effects of composition changes

on estimated skill premia are relatively small.

3.2 Discussion

We find that the price of experience is countercyclical and the price of schooling is positively

related with investment-specific technological improvements and negatively with neutral pro-

ductivity shocks. Schooling and experience measure different types of human capital. Classi-

cal human capital theory suggests that wages reflect the full marginal product from general

training but respond partially to specific human capital (Becker, 1962; Oi, 1962). Therefore,

the costs of specific training are shared between workers and firms while employees bear all

the costs of investment in general human capital.16 To incorporate job match quality and

to distinguish between general and specific human capital in the empirical analysis, equation

(1) can be rewritten as follows,

logwit = λ1tSchoolingit + λ2tTijt + λ3tExpit + θi + ηijt + ξit, (4)

where wit is wage of person i at time t. Tijt is tenure on current job j and measures the

stock of specific human capital. The term Expit is the total work experience, that increases

regardless of the firm at which the worker is employed, while tenure (Tijt) only increases for

job stayers. Thus, Schoolingit and Expit may (partially) reflect the stock of general human

capital. There are three error terms, person specific (θi), match or firm specific (ηijt), and

an idiosyncratic term (ξit). The model is written as linear for expositional purposes. The

literature suggests that Tijt likely positively correlated with ηijt, see for example Altonji

and Shakotko (1987) and Topel (1991). Following the classical human capital theory and

16See for example Hashimoto (1981), Acemoglu and Pischke (1999) and Loewenstein and Spletzer (1999).

12

assuming costly on-the-job training, the larger the ηijt the less likely a firm is to dismiss

a worker. Workers with better matches also tend to have higher tenure since they are less

likely to receive a better outside offer. We would also generally expect ηijt and Tijt to be

positively correlated with experience (Expit), because workers who have been longer in the

labor market would have had more chances to get a better match draw and spend longer on

that job. We do not estimate the extended model as in Equation (4) and do not incorporate

specific human capital measures due to data limitations. In our simplified framework, the

estimated price of experience sums up the returns to tenure and match quality.

It is well established in the literature that the likelihood of job separation is nega-

tively correlated with tenure, see for example Parsons (1972), Mincer and Jovanovic (1981),

Abraham and Farber (1987). Table 9 reports the employment-to-employment, employment-

to-unemployment and job-to-job transitions by work experience, higher work experience is

associated with higher job stability. Another stream of literature, following Bils (1985), shows

that wages of newly hired workers are more procyclical than the wages of workers who stay in

their jobs. Hagedorn and Manovskii (2010) analyze the cyclicality of match-quality and find

it to be procyclical. Thus, there is a cyclical relationship between costly specific job training,

separation probability and match quality. Less experienced workers are more likely to lose

jobs when unemployment is high and accept job offers with a lower match quality. When

unemployment is low, these workers are more likely to move to jobs with a higher match

quality. Such mechanism generates a countercyclical price of experience.

Lindquist (2004) shows that the procyclicality of schooling premium is in line with pre-

dictions of capital-skill complementarity theory, in which the demand for skills is procyclical

and leads to a procyclical trend in the price of schooling. In the following section we offer

a stylized model that incorporates predictions of human capital and match quality theories

into the capital-skill complementarity framework. We show that such model can generate a

countercyclical price of experience and (weakly) procyclical price of schooling.

13

4 A Stylized Model

This section proposes a theoretical framework to explain the cyclical variation of schooling

and experience premia. We extend the capital-skill complementarity model as in KORV,

incorporating education and experience in a vintage capital framework. Our assumptions

about complementarity between different types of labor and capital are based on predictions

of human capital and match-quality theories.

The production process requires four types of labor inputs and three types of capital.

The four types of workers are non-educated inexperienced (Ut), non-educated experienced

(UXt), educated inexperienced (Et) and educated experienced (EXt). The capital inputs are

capital structures (kst), new capital equipment (kent), and vintage capital equipment (keot).

The stock of capital evolves in the standard way, incorporating the possibility that some

fraction of new capital equipment becomes vintage capital equipment.17

The production function is Cobb-Douglas in capital structures and a combination of CES

functions of the remaining factors of production:

G(Ωt) = kαst

[βF γU + (1− β) (τF

σE + (1− τ)F σEX)

γσ

] 1−αγ

(5)

where FU ={λ1U

θt + (1− λ1)UXθt

} 1θ ; FE = {λ2kηnet + (1− λ2)E

ηt }

1η and

FEX = {λ3kµoet + (1− λ3)EXµt }

1µ . The parameters α, β, τ , λ1, λ2, λ3 ∈ (0, 1) govern income

shares and θ, γ, σ, η, µ ∈ (−∞, 1) govern elasticities of substitution.

Equation (5) simplifies into KORV production function if there is no difference in degrees

of substitution within each production factor FU , FE and FEX , i.e., if θ = 1, and σ = η = µ.

On the other hand, σ > η and σ > µ imply that the substitution within FE and FEX is

higher than between the components of FE and FEX . For simplicity of the analysis we assume

one type of unskilled workers by setting θ = 1.

Assuming perfectly competitive factor markets, taking derivatives of equation (5) with

respect to labor inputs (U , E and EX), yields the skill prices (WE , WEX and WU ). Experi-

17A detailed description of the model is provided in Appendix A.

14

ence premium(WEXWE

)and education premium

(WEWU

)are defined as follows,

WEXWE

= κ1[λ3( keoEX )

µ+(1−λ3)]

σ−µµ

[λ2( kenE )η+(1−λ2)]

σ−ηη

(EXE

)σ−1(6)

WEWU

= κ2

[τ(λ2(kneE

)η+ (1− λ2)

)ση

+ (1− τ)(λ3(keoEX

)µ+ (1− λ3)

)σµ (EX

E

)σ] γ−σσ×[λ2(kneE

)η+ (1− λ2)

]σ−ηη (E

U

)γ−1 (7)where κ1 =

(1−τ)(1−λ3)τ(1−λ2) and κ2 =

(1−β)τ(1−λ2)β .

4.1 Qualitative analysis

To analyze the cyclical properties of skill prices we make assumptions about the elasticity of

substitution parameters. We assume that σ > η and σ > µ, i.e. a higher complementarity

between new equipment and educated labor or between vintage equipment and experienced

labor than between new equipment and experienced labor or vintage equipment and inex-

perienced labor. Human capital and match quality theories predict that more experienced

workers have more stable wage profiles and are less susceptible to job transitions. As dis-

cussed in Section 3.2, this occurs because more experienced workers accumulate job/match

specific human capital which increases productivity, in our framework this implies higher

complementarity between experience and vintage capital, i.e., σ > µ. KORV estimates that

education is complementary with capital equipment, Lindquist (2004) shows that education

premium comoves with investment-specific innovations, i.e., σ > η.

Education and experience premia in (6) and (7), are functions of keoEX ,kneE and

EXE ,

EU .

Taking derivatives of skills premia with respect to capital-skill ratios we obtain:

∂(WEXWE

)∂( keoEX )

> 0 if σ > µ; and∂(WEXWE

)∂( kneE )

< 0 if σ > η (8)

∂(WEWU

)∂( kneE )

> 0 if γ > σ and σ > η; and∂(WEWU

)∂( keoEX )

> 0 if γ > σ (9)

15

Changes in keoEX andkneE drive capital—skill complementarity effects. In (8), if σ > µ and

σ > η, a rise in keoEX or decline inkneE increase the experience premium. In (9), a rise in

kneE

has a positive effect on schooling premium if γ > σ and σ > η. Where γ > σ implies higher

comlementarity between composites of FE and composites of FEX , than between those and

unskilled labor. If γ > σ, we also obtain a positive relationship between keoEX and the price of

schooling. The ratios EXE andEU in equations (8) and (9) drive relative supply effects. A rise

in EXE reduces the experience premium and a rise inEU reduces the education premium.

To analyze the cyclicality of skill premia in the model we examine how keoEX andkneE move

over the business cycle. To measure the new capital equipment, kne, we use investment in

capital equipment and software over two years, to construct old capital equipment, keo, we use

undepreciated stock of capital equipment and software minus investment in two preceeding

years (using 1 or 2 preceeding years yield similar cyclical patterns). To construct EX we

use total hours worked by individuals with more than 15 years of education and with more

than 30 years of work experience, to construct E we use total hours worked by those with

more than 15 years of education and less than 10 years of experience.18 The correlation

between the unemployment rate and keoEX is 0.3278, between the unemployment rate andkenEX

is -0.3736. Correlation between the total capital stock (without substracting two preceeding

years of investment) is 0.2116.19

We conclude that keoEX is countercyclical whereaskneE is procyclical. Thus, controlling for

relative supply effects, equation (8) predicts a countercyclical experience premium. There is

an ambiguity about the cyclicality of education premium in equation (9) since both capital-

skill ratios have a positive effect. If the effect of kneE is stronger than the effect ofkeoEX , we

obtain a procyclical education premium.

Model predictions are consistent with empirical results reported in Section 3. We find

that experience premium is negatively correlated with neutral productivity shock, i.e. with

18Calculations are performed using data for 1975-2010. Data on capital equipment and software stockand investment are from Bureau of Economic Analysis, Table 4.1 and Table 2.7, respectively. Data on hoursworked is obtained from the CPS sample described in Section 2. Unemployment rate is for 25 to 54-year-oldindividuals, obtained from the Bureau of Labor Statistics (BLS) database, http://www.bls.gov/cps/data.htm.

19We find that keo and ken have similar cycliclal patterns as keoEX andkenEX, respectively.

16

output, or positively with unemployment rate, and negatively with technological change.

Education premium, in specifications that control for technological change, is negatively

correlated with neutral shock but positively with investment-specific technology innovations.

In the model, technological innovations have a direct effect on investment,(kenEX

), whereas

investment has a negative effect on experience premium and positive effect on education

premium. Effects of neutral, or other shocks, are summarized by the relationship between

the skill prices and vintage capital equipment, keoEX . This relationship is positive for both skill

prices, whereas keoEX is negatively correlated with output, (or positively with unemployment).

Relative supply effects in empirical estimations are given by average experience and average

education of the workforce and behave in line with the model predictions. Thus, our stylized

model can explain the cyclical patterns of skill prices observed in the data.

5 Conclusion

Using data from the 1962 - 2010 March Current Population Surveys, we analyze the cyclical

variability of skill prices. We control for a set of channels that may affect the prices directly

or that may shift the relative demand and supply of skills. These channels are extensively

studied in the wage structure literature. The dominant explanations focus on skill-biased

technological change and associated shifts in demand for skilled labor, decline in unioniza-

tion and changing age distribution. In the real business cycles context, in the capital-skill

complementarity framework, the technological change and relative supply of schooling are

also identified as main driving forces behind the developments in schooling premium.

Our results show that the price of schooling is weakly procyclical and the price of expe-

rience is countercyclical. In specifications that distinguish between investment-specific and

neutral (or other) shocks, we find that experience premium is negatively associated with both

types of shocks whereas schooling premium is positively correlated with technological change

(that measures the investment-specific shock) and negatively with the neutral shocks. Thus,

both types of shocks generate the countercyclical pattern of experience premium whereas the

weak procyclicality of schooling premium is driven by technological innovations. Changing

17

demographics and cyclical changes in the workforce composition, although important, do not

explain the cyclical patterns of skill prices.

To our knowledge, there is no single theoretical framework that reconciles the weakly

procyclical education premium and countercyclical experience premium. In the capital-skill

complementarity theory, the demand for skills is procyclical and yields procyclical returns to

schooling but cannot explain the countercyclical experience premium. The countercyclical

experience premium emerges in frameworks that incorporate job match quality or on-the-job

human capital accumulation. The former predicts that older workers are more likely to have

a higher match quality and therefore hold better contracts when unemployment is relatively

high. The latter predicts that more experienced workers are more likely to have higher human

capital, which might be costly to acquire, and, therefore, less likely to lose jobs in recessions.

Both theories predict that firms are more likely to retain workers with higher job experience

and offer them contracts with smoother wage profiles.

To interpret the empirical findings, we incorporate the key outcomes of human capi-

tal and match quality theories into the capital-skill compementarity framework developed

in KORV. Previous studies that use the KORV framework focus on the role of capital-skill

complementarity in the increase and cyclicality of the schooling premium, (see for example

Lindquist, 2004). Our simple model builds on the KORV framework and explains develop-

ments in both schooling and experiece premia. We incorporate three types of labor: un-

skilled, skilled inexperienced and skilled experienced, and three types of capital: structures,

new equipment and vintage equipement. The complementarity between skill and capital

varies with work experience and vinatage of capital, we show that if more experienced work-

ers have higher comlementarity with vintage capital, as human capital and match quality

theories predict, the model generates a procyclical schooling premium and a countercyclical

experience premium.

18

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22

23

45

67

unem

ploy

men

t

-2-1

01

2

1960 1970 1980 1990 2000 2010

detrended GDP unemployment

0.0

2.0

4.0

6.0

8.1

0.2

.4.6

d(PC

inde

x)

1960 1970 1980 1990 2000 2010

PC Violante-Cummins E&S

1111

.512

12.5

1313

.5m

ean

scho

olin

g

1960 1970 1980 1990 2000 2010

1819

2021

22m

ean

expe

rienc

e

1960 1970 1980 1990 2000 2010

.1.1

5.2

.25

.3co

llege

%

1960 1970 1980 1990 2000 2010

.1.1

5.2

.25

unio

n %

1960 1970 1980 1990 2000 2010

Summary Statistics

.008

.01

.012

.014

.016

.018

23

45

67

unem

ploy

men

t

1960 1970 1980 1990 2000 2010

unempl (t-1) price of exp (actual hours)price of exp (predicted hours)

Price of experience

.06

.07

.08

.09

.1.1

1

23

45

67

unem

ploy

men

t

1960 1970 1980 1990 2000 2010

unempl (t-1) price of school (actual hours)price of school (predicted hours)

Price of schooling

Edication and experience premia

23

-.00

50

.005

23

45

67

unem

ploy

men

t

1960 1970 1980 1990 2000 2010

unempl (t-1) price of exp (actual hours)price of exp (predicted hours)

Detrended price of experience

-.01

5-.

01-.

005

0.0

05.0

1

23

45

67

unem

ploy

men

t

1960 1970 1980 1990 2000 2010

unempl (t-1) price of school (actual hours)price of school (predicted hours)

Detrended price of schooling

Detrended education and experience premia

24

price of exp.

price of educ.

detrend. output

detrend. output (t-1)

unempl. rate

unempl. rate (t-1)

average exp.

average educ.

tech. change

(1) (2) (3) (4) (5) (6) (7) (8) (9)detrend. output -0.5797 0.1454

(0.0000) (0.3239)

detrend. output (t-1) -0.7696 0.1282 0.8048(0.0000) (0.3853) (0.0000)

unemployment 0.5072 0.0908 -0.8121 -0.5827(0.0002) (0.5393) (0.0000) (0.0000)

unemployment (t-1) 0.7300 0.0649 -0.6320 -0.8024 0.7464(0.0000) (0.6614) (0.0000) (0.0000) (0.0000)

average experience -0.9507 -0.3506 0.5051 0.6328 -0.4727 -0.6101(0.0000) (0.0146) (0.0003) (0.0000) (0.0007) (0.0000)

average education 0.5520 0.8641 -0.1693 -0.1643 0.3643 0.3330 -0.7028(0.0000) (0.0000) (0.2499) (0.2645) (0.0109) (0.0208) (0.0000)

tech. change 0.1467 0.9703 0.2116 0.2267 0.0896 0.0284 -0.3071 0.8723(0.3197) (0.0000) (0.1488) (0.1212) (0.5447) (0.8480) (0.0337) (0.0000)

union rate -0.4506 -0.9419 0.0227 0.0437 -0.2685 -0.2598 0.5834 -0.9619 -0.9354(0.0013) (0.0000) (0.8781) (0.7679) (0.0650) (0.0745) (0.0000) (0.0000) (0.0000)

Table 1: Correlations between skill prices, business cycle measures and aggregate indicators

Note: Price of schooling refers to the parameter β3t in Equation (1), price of experience referes to (β1t+2β2tAvg. exp), the parameters are estimated using 1962-2010 (excl. 1963) CPS, N=48. Output is the real GDP per capita and unemployment is the unemployment rate for 25 to 54 years old individuals. Average experience and education refer to employed averages. Technological change is constructed using Cummins and Violante (2002) methodology for equipment and software (E&S) category. Standard errors in parentheses.

25

(1) (2) (3) (4) (5) (6) (7) (8)

output -0.0033 -0.0023 -0.0014 -0.0015 (0.0003) (0.0004) (0.0002) (0.0003)

unemployment 0.0016 0.0010 0.0005 0.0006 (0.0002) (0.0002) (0.0001) (0.0002)

tech. change -0.0025 -0.0003 -0.0027 -0.0035 0.0000 -0.0034 (0.0008) (0.0004) (0.0006) (0.0006) (0.0005) (0.0006)

avg. experience -0.0026 -0.0026 (0.0002) (0.0002)

avg. education -0.0053 -0.0028 (0.0013) (0.0011)

unionization rate -0.0820 -0.0958 (0.0270) (0.0299)

time trend 0.0015 0.0014 0.0009 0.0008 0.0000 0.0005 0.0001 0.0002 (0.0001) (0.0001) (0.0002) (0.0002) (0.0000) (0.0001) (0.0001) (0.0002)

cons -2.9023 -2.6920 -1.5699 -1.4918 -0.0829 -0.9861 -0.0829 -0.2851 (0.2518) (0.2192) (0.3416) (0.3548) (0.0712) (0.1571) (0.2037) (0.3025)

(1) (2) (3) (4) (5) (6) (7) (8)output 0.0015 -0.0035 -0.0046 -0.0018

(0.0014) (0.0013) (0.0019) (0.0014) unemployment -0.0013 0.0004 0.0002 -0.0006

(0.0006) (0.0006) (0.0007) (0.0007) tech. change 0.0122 0.0094 0.0117 0.0091 0.0106 0.0093

(0.0028) (0.0021) (0.0024) (0.0025) (0.0023) (0.0021) avg. experience -0.0024 -0.0027

(0.0015) (0.0016) avg. education -0.0198 -0.0083

(0.0093) (0.0096) unionization rate -0.1740 -0.2402

(0.0820) (0.0755) time trend 0.0006 0.0011 0.0029 -0.0001 0.0013 0.0001 0.0002 -0.0008

(0.0006) (0.0004) (0.0012) (0.0007) (0.0001) (0.0003) (0.0007) (0.0004) cons -1.2003 -2.2395 -5.5006 0.3053 -2.4554 -0.1041 -0.2100 1.6543

(1.2311) (0.8695) (2.3534) (1.3969) (0.1673) (0.6229) (1.2359) (0.8045)

Note: Price of schooling refers to the parameter β3t in Equation (1), price of experience referes to (β1t+2β2tAvg. exp), the parameters are estimated using 1962-2010 (excl. 1963) CPS, N=48. Output is the real GDP per capita and unemployment is the unemployment rate for 25 to 54 years old individuals. Average experience and education refer to employed averages. Technological change is constructed using Cummins and Violante (2002) methodology for equipment and software (E&S). Newey-West standard errors (lag 2) in parentheses.

Table 2: Price of experience over the business cycle, OLS

Table 3: Price of schooling over the business cycle, OLS

26

(1) (2) (3) (4) (5) (6) (7) (8)

output -0.0030 -0.0023 -0.0013 -0.0016 (0.0003) (0.0004) (0.0002) (0.0002)

unemployment 0.0014 0.0008 0.0004 0.0004 (0.0002) (0.0002) (0.0001) (0.0002)

tech. change -0.0018 0.0005 -0.0020 -0.0030 0.0009 -0.0029 (0.0007) (0.0003) (0.0006) (0.0006) (0.0006) (0.0006)

avg. experience -0.0023 -0.0023 (0.0002) (0.0002)

avg. education -0.0034 -0.0008 (0.0012) (0.0011)


time trend 0.0013 0.0013 0.0006 0.0007 0.0000 0.0004 -0.0001 0.0001 (0.0001) (0.0001) (0.0002) (0.0002) (0.0000) (0.0001) (0.0001) (0.0002)

cons -2.6201 -2.4689 -1.1335 -1.3860 -0.0521 -0.8311 0.3155 -0.1357 (0.2202) (0.2162) (0.3226) (0.3071) (0.0715) (0.1494) (0.2131) (0.3135)

(1) (2) (3) (4) (5) (6) (7) (8)output 0.0021 -0.0024 -0.0020 -0.0010

(0.0013) (0.0012) (0.0017) (0.0011) unemployment -0.0014 0.0002 -0.0001 -0.0005

(0.0005) (0.0005) (0.0006) (0.0005) tech. change 0.0110 0.0119 0.0106 0.0088 0.0124 0.0090

(0.0021) (0.0024) (0.0018) (0.0018) (0.0021) (0.0017) avg. experience -0.0008 -0.0009

(0.0016) (0.0016) avg. education -0.0010 0.0045


(0.0657) (0.0580) time trend 0.0004 0.0008 0.0006 -0.0002 0.0013 0.0001 -0.0006 -0.0006

(0.0005) (0.0004) (0.0012) (0.0006) (0.0001) (0.0002) (0.0007) (0.0003) cons -0.6635 -1.6007 -1.1109 0.4028 -2.4506 -0.1719 1.2458 1.1698

(1.0834) (0.7716) (2.2502) (1.1304) (0.1527) (0.4727) (1.1687) (0.6955)


Table 5: Price of schooling over the business cycle, OLS (with spousal schooling controls)

Table 4: Price of experience over the business cycle, OLS (with spousal schooling controls)

27

(1) (2) (3) (4) (5) (6) (7) (8)

output -0.0038 -0.0035 -0.0020 -0.0019 (0.0005) (0.0007) (0.0006) (0.0007)

unemployment 0.0017 0.0011 0.0004 0.0003 (0.0003) (0.0004) (0.0003) (0.0004)

tech. change -0.0008 0.0026 -0.0013 -0.0030 0.0032 -0.0028 (0.0016) (0.0010) (0.0011) (0.0014) (0.0013) (0.0009)

avg. experience -0.0036 -0.0037 (0.0007) (0.0007)

avg. education -0.0059 -0.0015 (0.0036) (0.0042)


time trend 0.0017 0.0017 0.0008 0.0005 0.0001 0.0005 -0.0004 -0.0002 (0.0002) (0.0002) (0.0004) (0.0003) (0.0001) (0.0002) (0.0003) (0.0002)

cons -3.4034 -3.3323 -1.3612 -1.0121 -0.1378 -0.9059 0.8891 0.5196 (0.3893) (0.3850) (0.7068) (0.5907) (0.1004) (0.3544) (0.6035) (0.3351)

(1) (2) (3) (4) (5) (6) (7) (8)output 0.0004 -0.0039 -0.0047 -0.0023

(0.0013) (0.0014) (0.0018) (0.0015) unemployment -0.0008 0.0005 0.0002 -0.0005

(0.0006) (0.0006) (0.0008) (0.0008) tech. change 0.0108 0.0089 0.0103 0.0073 0.0101 0.0075

(0.0028) (0.0027) (0.0024) (0.0025) (0.0029) (0.0020) avg. experience -0.0016 -0.0019

(0.0021) (0.0021) avg. education -0.0132 -0.0015


(0.0985) (0.0867) time trend 0.0011 0.0015 0.0027 0.0004 0.0013 0.0003 0.0000 -0.0005

(0.0006) (0.0004) (0.0012) (0.0008) (0.0001) (0.0003) (0.0009) (0.0004) cons -2.1007 -3.0150 -5.1658 -0.6607 -2.4768 -0.5899 0.1776 1.1373

(1.1460) (0.8601) (2.2618) (1.5280) (0.1536) (0.6179) (1.5749) (0.8404)


Table 6: Price of experience over the business cycle, 75th quantile regression

Table 7: Price of schooling over the business cycle, 75th quantile regression

28

q=45% q=50% q=55% q=45% q=50% q=55%1961 8921 0.0595 0.0602 0.0614 0.0168 0.0177 0.01821963 9923 0.0580 0.0578 0.0592 0.0171 0.0178 0.01761964 9925 0.0603 0.0604 0.0611 0.0188 0.0194 0.01951965 20963 0.0650 0.0651 0.0644 0.0191 0.0190 0.01951966 13593 0.0616 0.0611 0.0627 0.0180 0.0184 0.01861967 21034 0.0653 0.0656 0.0666 0.0163 0.0164 0.01721968 21344 0.0619 0.0623 0.0623 0.0165 0.0165 0.01671969 20290 0.0634 0.0639 0.0651 0.0162 0.0166 0.01711970 19617 0.0626 0.0631 0.0645 0.0171 0.0175 0.01801971 18912 0.0641 0.0649 0.0654 0.0202 0.0205 0.02071972 19145 0.0612 0.0627 0.0632 0.0218 0.0215 0.02151973 19083 0.0621 0.0632 0.0625 0.0232 0.0233 0.02381974 18255 0.0599 0.0596 0.0606 0.0221 0.0225 0.02331975 18120 0.0658 0.0665 0.0677 0.0245 0.0243 0.02441976 21717 0.0648 0.0659 0.0659 0.0267 0.0268 0.02671977 21640 0.0666 0.0661 0.0656 0.0270 0.0275 0.02681978 21936 0.0669 0.0666 0.0673 0.0266 0.0268 0.02671979 25908 0.0636 0.0637 0.0629 0.0258 0.0262 0.02601980 25472 0.0673 0.0675 0.0676 0.0280 0.0283 0.02831981 22474 0.0672 0.0677 0.0692 0.0271 0.0276 0.02751982 21498 0.0751 0.0755 0.0751 0.0290 0.0286 0.02811983 21683 0.0794 0.0797 0.0790 0.0287 0.0282 0.02831984 22912 0.0796 0.0810 0.0814 0.0304 0.0301 0.03001985 22702 0.0856 0.0854 0.0852 0.0278 0.0285 0.02891986 22498 0.0871 0.0867 0.0872 0.0296 0.0294 0.02971987 23027 0.0847 0.0851 0.0844 0.0276 0.0283 0.02841988 21827 0.0864 0.0867 0.0881 0.0276 0.0279 0.02831989 24129 0.0916 0.0919 0.0915 0.0261 0.0260 0.02671990 23506 0.0908 0.0896 0.0911 0.0257 0.0263 0.02701991 22552 0.0942 0.0940 0.0946 0.0255 0.0260 0.02671992 22136 0.0980 0.0978 0.0976 0.0264 0.0262 0.02671993 21576 0.1010 0.1013 0.1006 0.0274 0.0279 0.02791994 21822 0.0996 0.0984 0.0990 0.0275 0.0280 0.02801995 20059 0.0990 0.0980 0.0988 0.0261 0.0275 0.02781996 20451 0.1030 0.1032 0.1033 0.0254 0.0254 0.02651997 20378 0.1004 0.1017 0.1024 0.0238 0.0241 0.02431998 21198 0.1028 0.1036 0.1035 0.0228 0.0232 0.02371999 21471 0.1046 0.1050 0.1046 0.0236 0.0238 0.02392000 33587 0.1004 0.1010 0.1014 0.0228 0.0227 0.02282001 32810 0.1031 0.1042 0.1051 0.0217 0.0223 0.02262002 31906 0.1045 0.1051 0.1060 0.0226 0.0233 0.02362003 31118 0.1042 0.1052 0.1063 0.0237 0.0241 0.02412004 30677 0.1042 0.1047 0.1059 0.0228 0.0233 0.02352005 31026 0.1043 0.1053 0.1062 0.0244 0.0245 0.02452006 30910 0.1047 0.1063 0.1081 0.0247 0.0251 0.02562007 30352 0.1040 0.1054 0.1063 0.0229 0.0227 0.02342008 29138 0.1053 0.1065 0.1079 0.0211 0.0215 0.02182009 27251 0.1085 0.1093 0.1109 0.0206 0.0206 0.0204

Note: Price of schooling refers to the parameter β3t in Equation (1), price of experience referes to (β1t+2β2tAvg. exp), the parameters are estimated using 1962-2009 (excl. 1963) CPS. Controls include a constant, marital status and metro status. All reported coefficients are significant at the 5% level.

Table 8: Skill prices, 1961 - 2009, by quantile

Year Obs Price of schooling Price of experience

29

(1) (2) (3) (4) (5) (6) (7) (8)

output -0.0024 -0.0006 -0.0008 -0.0002 (0.0005) (0.0007) (0.0003) (0.0004)

unemployment 0.0010 0.0002 0.0003 0.0000 (0.0004) (0.0004) (0.0001) (0.0002)

tech. change -0.0043 0.0004 -0.0039 -0.0047 0.0002 -0.0041 (0.0012) (0.0006) (0.0007) (0.0009) (0.0007) (0.0005)

avg. experience -0.0031 -0.0029 (0.0003) (0.0003)

avg. education -0.0048 -0.0034 (0.0022) (0.0018)


time trend 0.0011 0.0009 0.0005 0.0002 0.0000 0.0007 0.0001 0.0002 (0.0003) (0.0002) (0.0003) (0.0002) (0.0000) (0.0001) (0.0002) (0.0001)

cons -2.1181 -1.7482 -0.8046 -0.4410 -0.0848 -1.3186 -0.0606 -0.3162 (0.4963) (0.4284) (0.5035) (0.4705) (0.0840) (0.2166) (0.3068) (0.2677)

(1) (2) (3) (4) (5) (6) (7) (8)output 0.0024 -0.0020 -0.0034 -0.0012

(0.0012) (0.0016) (0.0016) (0.0012) unemployment -0.0016 -0.0003 -0.0001 -0.0006

(0.0006) (0.0005) (0.0005) (0.0006) tech. change 0.0108 0.0120 0.0114 0.0079 0.0105 0.0092

(0.0029) (0.0026) (0.0024) (0.0022) (0.0023) (0.0019) avg. experience -0.0043 -0.0026

(0.0015) (0.0016) avg. education -0.0210 -0.0074


(0.0737) (0.0729) time trend 0.0002 0.0007 0.0021 -0.0004 0.0013 0.0002 0.0002 -0.0007

(0.0006) (0.0005) (0.0009) (0.0005) (0.0001) (0.0003) (0.0007) (0.0004) cons -0.4066 -1.3447 -3.6976 0.9636 -2.4837 -0.4127 -0.1526 1.5122

(1.0930) (0.9984) (1.6979) (1.0789) (0.1617) (0.5548) (1.2179) (0.7957)


Table A1: Price of experience over the business cycle, OLS, contomporeneous business cycle measures

Table A2: Price of schooling over the business cycle, OLS, contomporeneous business cycle measures

30

(1) (2) (3) (4) (5) (6) (7) (8)

output -0.0020 -0.0016 -0.0014 -0.0011 (0.0002) (0.0002) (0.0002) (0.0002)

unemployment 0.0010 0.0007 0.0005 0.0005 (0.0001) (0.0001) (0.0001) (0.0001)

tech. change -0.0011 -0.0005 -0.0012 -0.0017 -0.0001 -0.0017 (0.0004) (0.0004) (0.0003) (0.0004) (0.0005) (0.0004)

avg. experience -0.0016 -0.0015 (0.0002) (0.0002)

avg. education -0.0054 -0.0029 (0.0013) (0.0011)


time trend 0.0009 0.0009 0.0009 0.0005 0.0000 0.0002 0.0001 0.0000 (0.0001) (0.0001) (0.0002) (0.0001) (0.0000) (0.0001) (0.0001) (0.0001)

cons -1.7725 -1.6819 -1.6517 -0.9288 -0.0185 -0.4656 -0.1709 -0.0258 (0.1635) (0.1498) (0.3488) (0.2108) (0.0391) (0.0995) (0.2096) (0.1650)

(1) (2) (3) (4) (5) (6) (7) (8)output -0.0023 -0.0019 -0.0015 -0.0012

(0.0002) (0.0003) (0.0003) (0.0002) unemployment 0.0011 0.0007 0.0005 0.0004

(0.0001) (0.0002) (0.0001) (0.0001) tech. change -0.0010 -0.0002 -0.0012 -0.0019 0.0002 -0.0018

(0.0007) (0.0005) (0.0004) (0.0006) (0.0007) (0.0004) avg. experience -0.0017 -0.0017

(0.0002) (0.0003) avg. education -0.0052 -0.0023


(0.0170) (0.0182) time trend 0.0010 0.0010 0.0009 0.0005 0.0000 0.0003 0.0000 0.0000

(0.0001) (0.0001) (0.0002) (0.0001) (0.0000) (0.0001) (0.0002) (0.0001) cons -1.9666 -1.8816 -1.6897 -0.9046 -0.0154 -0.5094 -0.0125 0.0797

(0.1651) (0.1503) (0.3911) (0.2488) (0.0441) (0.1484) (0.2769) (0.1606)

Table A3: Price of experience at 20 years of experience over the business cycle, OLS

Note: Price of schooling refers to the parameter β3t in Equation (1), price of experience referes to (β1t+2β2t*20), the parameters are estimated using 1962-2010 (excl. 1963) CPS, N=48. Output is the real GDP per capita and unemployment is the unemployment rate for 25 to 54 years old individuals. Average experience and education refer to employed averages. Technological change is constructed using Cummins and Violante (2002) methodology for equipment and software (E&S). Newey-West standard errors (lag 2) in parentheses.

Table A4: Price of experience at 20 years of experience over the business cycle, 75th quantile regression

31

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12)output -0.0025 -0.0014 -0.0013 -0.0031 -0.0017 -0.0014 -0.0040 -0.0009 -0.0013 -0.0035 -0.0006 -0.0014

(0.0003) (0.0004) (0.0004) (0.0003) (0.0004) (0.0005) (0.0005) (0.0006) (0.0004) (0.0006) (0.0007) (0.0006)

tech. change 0.0011 -0.0010 0.0008 -0.0016 -0.0027 -0.0053 -0.0033 -0.0053(0.0009) (0.0007) (0.0009) (0.0008) (0.0009) (0.0010) (0.0012) (0.0011)

avg. experience -0.0025 -0.0030 -0.0023 -0.0013(0.0004) (0.0004) (0.0006) (0.0007)

avg. education -0.0057 -0.0076 -0.0029 -0.0001(0.0023) (0.0023) (0.0036) (0.0039)

unionization rate -0.0932 -0.1243 -0.0640 0.0027(0.0272) (0.0303) (0.0325) (0.0375)

time trend 0.0012 0.0008 0.0005 0.0014 0.0009 0.0004 0.0017 0.0008 0.0010 0.0014 0.0005 0.0012(0.0001) (0.0003) (0.0002) (0.0001) (0.0003) (0.0002) (0.0002) (0.0004) (0.0002) (0.0003) (0.0004) (0.0003)

cons -2.4512 -1.5451 -1.0253 -2.6915 -1.7042 -0.7709 -3.3023 -1.3979 -1.9339 -2.7015 -0.9176 -2.2933(0.2746) (0.6047) (0.3705) (0.2837) (0.5555) (0.4576) (0.4451) (0.7084) (0.4391) (0.5637) (0.7651) (0.6307)

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12)output 0.0015 -0.0070 -0.0020 0.0032 -0.0056 -0.0020 0.0024 -0.0031 -0.0006 0.0010 -0.0021 -0.0014

(0.0023) (0.0035) (0.0024) (0.0019) (0.0028) (0.0020) (0.0009) (0.0015) (0.0010) (0.0009) (0.0010) (0.0014)

tech. change 0.0150 0.0169 0.0105 0.0157 0.0041 0.0087 0.0077 0.0075(0.0037) (0.0038) (0.0033) (0.0030) (0.0021) (0.0018) (0.0022) (0.0023)

avg. experience -0.0045 0.0009 -0.0009 -0.0030(0.0031) (0.0021) (0.0011) (0.0014)

avg. education -0.0302 -0.0132 -0.0186 -0.0138(0.0173) (0.0125) (0.0073) (0.0094)

unionization rate -0.3903 -0.1345 -0.0543 -0.0684(0.1549) (0.1169) (0.0628) (0.0631)

time trend 0.0007 0.0038 -0.0014 0.0001 0.0032 -0.0002 0.0002 0.0030 0.0002 0.0004 0.0014 0.0003(0.0010) (0.0022) (0.0012) (0.0009) (0.0018) (0.0011) (0.0004) (0.0011) (0.0005) (0.0004) (0.0009) (0.0006)

cons -1.2440 -6.9375 2.9294 -0.1016 -6.2118 0.4965 -0.3833 -5.6236 -0.3408 -0.7954 -2.4183 -0.4519(2.0569) (4.2112) (2.4567) (1.6907) (3.3890) (2.2207) (0.8794) (2.0743) (0.9607) (0.8417) (1.6147) (1.2073)

Table A5: Price of experience over the business cycle, OLS, by experience level

0

A Model description, wage premia and busines cycle

Consider an economy with mass one of skilled and unskilled infinitely lived agents, where skills

can be either education or experience. A non-educated worker can be either experienced or

non-experienced, similarly, an educated worker can be either experienced or non-experienced.

Let U , UX, E and EX denote the agent-types measures respectively. Agents are born at

time zero and endowed with the skill type and one unit of time they allocate between leisure

and labor.

There are three types of capital: capital structures, kst; vintage capital equipment, keot;

and new capital equipment, kent. The stock of capital evolves in the standard way, but

incorporating the possibility that some fraction of new capital equipment becomes vintage

capital equipment. Firms make investment decisions on new capital equipment and capital

structures each period. The laws of motion for capital are as follows,

Capital structures:

kst+1 = (1− δs)kst + Ist. (10)

Capital equipment:

kent+1 = ν(1− δen)kent + Iet,

keot+1 = (1− δeo)keot + (1− ν)(1− δen)kent,(11)

We allow for different depreciation rates. Note that a fraction (1 − ν) of new capital

equipment becomes vintage capital equipment each period.

The production process requires four types of labor inputs and three types of capital:

non-educated workers with no experience (Ut), non-educated workers with experience (UXt),

educated and non-experienced workers (Et), and educated and experienced workers (EXt),

capital structures (kst), new capital equipment (kent), and vintage capital equipment (keot).

The capital skill complementarity model incorporates two sectors with two types of final

goods, consumption (ct) and capital structures (Ist), and capital equipment (Iet). The output

33

in each sector is given by:

ct + Ist = AtG(kst, keot, kent, Ut, UXt, Et, EXt) (12)

Iet = AtqtG(kst, keot, kent, Ut, UXt, Et, EXt) (13)

Consumption is denoted by ct, investment in new structures given by Ist, and investment

in the equipment sector by Iet. Inputs of the same factor in each sector are different, we avoid

using superscript indicators to easy notation.

Aggregate technology is neutral to both sectors, At; and there is a specific technology

factor for the capital equipment sector, denoted by qt. For notation simplicity, we define the

set of production factors as Ωt ≡ {kst, keot, kent, Ut, UXt, Et, EXt}.

The production function G is assumed to be homogeneous of degree one and similar in

both sectors. Assuming perfect competition, aggregate output of the economy is given by:

Yt = ct + Ist +Ietqt

= AtG(kst, keot, kent, Ut, UXt, Et, EXt) = AtG(Ωt)

The production function is Cobb-Douglas in capital structures and a combination of CES

functions of the remaining factor of production:

G(Ωt) = kαst

[βF γU + (1− β) (τF


γσ

] 1−αγ

where the factor FU is defined as composites of non-educated labor with different experience

levels (FU ={λ1U


} 1θ ); FE is a composite of production factors for new

capital equipment with educated workers (FE = {λ2kηnet + (1− λ2)Eηt }

1η ); and the term FEX

is a composite of production factors for vintage capital equipment with experienced workers

( FEX = {λ3kµoet + (1− λ3)EXµt }

1µ ).

The parameters α, β, τ , λ1, λ2, λ3 ∈ (0, 1) govern income share and θ, γ, σ, η, µ ∈

(−∞, 1) govern the elasticity of substitution. For simplicity we assume θ = 1.

We derive skill premia and obtain wage ratios as described in equations (6) and (7).

34

A.1 Cyclicality Analysis

Following the procedure described in section 4.1, we analyze how skill premia comove with

capital-skill labor ratio. Equations (14) and (15) shows the cyclicality of experience premium.

∂(WEXWE

)∂( keoEX )

= κ1(σ − µ)λ3[λ3( keoEX )

µ+(1−λ3)]

σ−2µµ

[λ2( kenE )η+(1−λ2)]

σ−ηη

(EXE

)σ−1 ( keoEX

)µ−1(14)

∂(WEXWE

)∂( kneE )

= −κ1(σ − η)λ2[λ3( keoEX )

µ+(1−λ3)]

σ−µµ

[λ2( kenE )η+(1−λ2)]

ση

(EXE

)σ−1 (knrE

)η−1(15)

The cyclicality pattern of educational premium is described as follows:

∂(WEWU

)∂( kneE )

= κ2(γ − σ)τλ2(λ2(kneE

)η+ (1− λ2)

) 2(σ−η)η (kne

E

)η−1 (EU

)γ−1×[τ(λ2(kneE

)η+ (1− λ2)

)ση


)µ+ (1− λ3)

)σµ (EX

E

)σ] γ−2σσ+κ2(σ − η)λ2

[λ2(kneE

)η+ (1− λ2)

]σ−2ηη (E

U

)γ−1 (kneE

)η−1×[τ(λ2(kneE

)η+ (1− λ2)

)ση


)µ+ (1− λ3)

)σµ (EX

E

)σ] γ−σσ

(16)

∂(WEWU

)∂( keoEX )

= κ2(γ − σ)(1− τ)λ3[λ2(kneE

)η+ (1− λ2)

]σ−ηη (E

U

)γ−1 (EXE

)σ ( keoEX

)µ−1×[τ(λ2(kneE

)η+ (1− λ2)

)ση


)µ+ (1− λ3)

)σµ (EX

E

)σ] γ−2σσ×(λ3(keoEX

)µ+ (1− λ3)

)σ−µµ

(17)

Interpretations of the cyclical patterns of experience and educational premia are provided

in Section 4.1

A.2 Full Model: Differentiating between U and UX

In this section we make an extension of our model incorporating non-educated workers with

different experience levels. Results in terms of skill premia and cyclicality do not change.

35

A.2.1 Wages and Skill Premia

Considering the expended model, output is defined as:

G(Ωt) = Atkαst

[βF γU + (1− β) (τF


γσ

] 1−αγ

Where

FU ={λ1U


} 1θ

FE = {λ2kηnet + (1− λ2)Eηt }

1η

FEX = {λ3kµoet + (1− λ3)EXµt }

1µ

We derive skill premia for experience and education: first experience premium for edu-

cated and uneducated workers, then education premium for unexperienced and experienced

workers.

WEXWE

= κ̃1[λ3( keoEX )

µ+(1−λ3)]

σ−µµ

[λ2( kenE )η+(1−λ2)]

σ−ηη

(EXE

)σ−1(18)

WUXWU

= κ̃2(UXU

)θ−1(19)

WEWU

= κ̃3

[τ(λ2(kneE

)η+ (1− λ2)

)ση


)µ+ (1− λ3)

)σµ (EX

E

)σ] γ−σσ× [λ2(

kneE )

η+(1−λ2)]

σ−ηη[

λ1( UUX )θ+(1−λ1)

] γ−θθ

(Eγ−1

Uθ−1UXγ−θ

) (20)

WEXWUX

= κ̃4

[τ(λ2(kneE

)η+ (1− λ2)

)ση ( E

EX

)σ+ (1− τ)

(λ3(keoEX

)µ+ (1− λ3)

)σµ

] γ−σσ

× [λ3(keoEX )

µ+(1−λ3)]

σ−µµ[

λ1( UUX )θ+(1−λ1)

] γ−θθ

(EXUX

)γ−1(21)

Where κ̃i is a positive constant.

36

A.2.2 Cyclicality analysis of the full model

We analyze how wage premium, previously derived, fluctuates on a business cycle frequency.

∂(WEXWE

)∂( keoEX )

= κ̃1(σ − µ)λ3[λ3( keoEX )

µ+(1−λ3)]

σ−2µµ

[λ2( kenE )η+(1−λ2)]

σ−ηη

(EXE

)σ−1 ( keoEX

)µ−1(22)

Since the vintage-capital to experienced-labor ratio is coutercyclical, if σ > µ we obtain

a countercyclical return to experience for educated workers. This is in line with a higher

complementarity between vintage capital equipment and educated-experienced workers than

with non-experienced ones.

The experience premium for educated workers when there is a fluctuation in the new-

capital to unexperienced-labor ratio, is as follow:

∂(WEXWE

)∂( kneE )

= κ̃1(η − σ)λ2[λ3( keoEX )

µ+(1−λ3)]

σ−µµ

[λ2( kenE )η+(1−λ2)]

ση

(EXE

)σ−1 (kenE

)η−1 (23)Since the new capital to unexperience labor is procyclical, if σ > η we obtain a counter-

cyclical return to experience. This result is in line with our complementarity assumptions.

Now we analyze the educational premium for non-experienced workers, when there is a

change in the capital-labor ratio as a consequence of economic fluctuations. We consider first

fluctuations on the ratio of new capital equipment to educated and unexperienced workers.

∂(WEWU

)∂( kenE )

= κ̃3τλ2(γ − σ)[τ(λ2(kneE

)η+ (1− λ2)

)ση


)µ+ (1− λ3)

)σµ (EX

E

)σ] γ−2σσ× [λ2(

kneE )

η+(1−λ2)]

2(σ−ηη )[λ1( UUX )

θ+(1−λ1)

] γ−θθ

Eγ−1

Uθ−1UXγ−θ

(kneE

)η−1+κ̃3 (σ − η)

[τ(λ2(kneE

)η+ (1− λ2)

)ση


)µ+ (1− λ3)

)σµ (EX

E

)σ] γ−σσ×λ2

[λ2( kneE )η+(1−λ2)]

σ−2ηη[

λ1( UUX )θ+(1−λ1)

] γ−θθ

Eγ−1

Uθ−1UXγ−θ

(kneE

)η−1(24)

As(kneE

)is countercyclical, the education premium for unexperienced workers is pro-

37

cyclical if σ > γ and σ > η, which confirms our complementarity assumptions between new

capital equipment and unexperienced and educated workers.

When analyzing the ratio of vintage capital equipment to experienced and educated

workers, the educational premium for unexperienced workers is as follow:

∂(WEWU

)∂( keoEX )

= κ̃3(γ − σ)[τ(λ2(kneE

)η+ (1− λ2)

)ση


)µ+ (1− λ3)

)σµ (EX

E

)σ] γ−2σσ×(1− τ)λ3

[λ2( kneE )η+(1−λ2)]

σ−ηη[

λ1( UUX )θ+(1−λ1)

] γ−θθ

(λ3(keoEX

)µ+ (1− λ3)

)σµ Eγ−1

Uθ−1UXγ−θ

(keoEX

)µ−1(25)

If σ > γ we obtain procyclical educational premium fon unexperienced workers.

Now we show the cyclical pattern of educational premium for experienced workers,(WEXUX

), analyzing first the ratio of new capital equipment to unexperienced and educated

workers.

∂(WEXWUX

)∂( kneE )

= κ̃4(γ − σ)λ2τ[τ(λ2(kneE

)η+ (1− λ2)

)ση ( E

EX

)σ+ (1− τ)

(λ3(keoEX

)µ+ (1− λ3)

)σµ

] γ−2σσ

× [λ3(keoEX )

µ+(1−λ3)]

σ−µµ[

λ1( UUX )θ+(1−λ1)

] γ−θθ

(EXUX

)γ−1 (λ2(kneE

)η+ (1− λ2)

)σ−ηη ( E

EX

)σ (kneE

)η−1(26)

To obtain the procyclical pattern in education premium for experienced workers we need

σ > γ. The wage ratio also fluctuates with changes in the ratio of vintage capital equipment

38

to educated-experienced workers:

∂(WEXWUX

)∂( keoEX )

= κ̃4(γ − σ)[τ(λ2(kneE

)η+ (1− λ2)

)ση ( E

EX

)σ+ (1− τ)

(λ3(keoEX

)µ+ (1− λ3)

)σµ

] γ−2σσ

×λ2(1− τ)λ3[λ3( keoEX )

µ+(1−λ3)]

2(σ−µµ )[λ1( UUX )

θ+(1−λ1)

] γ−θθ

(EXUX

)γ−1 ( keoEX

)µ−1+κ̃4(σ − µ)

[τ(λ2(kneE

)η+ (1− λ2)

)ση ( E

EX

)σ+ (1− τ)

(λ3(keoEX

)µ+ (1− λ3)

)σµ

] γ−σσ

×λ3[λ3( keoEX )

µ+(1−λ3)]

σ−2µµ[

λ1( UUX )θ+(1−λ1)

] γ−θθ

(keoEX

)µ−1 (EXUX

)γ−1(27)

To obtain the procyclicality of the wage premium, we need σ > γ and σ < µ.

We have shown that if the complementarity between new capital equipment and non-

experienced educated workers is higher than complementarity with any other type of labor

force; and the complementarity between new capital equipment with educated workers with

no experience is higher than the complementarity when considering any other type of skills,

the model proposed generates the procyclical return to education and the countercyclical

return to experience we observe in the data.

39

new_tables_structure.pdftable1tables2-7Table8app.tables1-4tables_educ_cell_tables.pdfbyeduc

Documents

Skill Prices over the Business Cycle Evgenia.pdf · Email: [email protected]. 1. increases in education and experience premia in the 1970s, 1980s and 1990s were extensively analyzed