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In the presence of human capital investment, the link between wages and prices is broken. Wages reflect the product of the price of a unit of human capital or “skill” and the quantity of human capital supplied: wit = ptEit, where wit denotes the wage of individual i in

“utilized” skill by individualiin periodt, and pt denotes the price paid per unit of human

capital in the labour market. In a Becker (1964) or Ben-Porath (1967) framework, utilized skill is given by Eit = hit(1−nit), where hit denotes the skill level of individual i, andnit

denotes the fraction of time at work allocated to producing skills. In practice, only the total payment to human capital is observed, therefore the price and utilized skill cannot be separately identified. Implicit identifying assumptions made in the literature are either that the price of human capital is constant over time or that the quantity of human capital (conditional on some observable characteristics such as education, experience and gender) is constant over time. Studies which assume constant human capital levels over time within education-experience-gender groups include Katz and Murphy (1992), Card and Lemieux (2001) and Autor et al. (2008).13 _{Some of the few exceptions which allow for changes}

in skill levels over time within groups are Heckman et al. (1998), Huggett et al. (2011), Carneiro and Lee (2011), and Bowlus and Robinson (2012).

The human capital model used here is based on the extended Ben-Porath model used in Heckman et al. (1998) and Kuruscu (2006). In Heckman et al. (1998), the Ben-Porath model is modified to allow for heterogeneity in human capital levels or skills. Skill groups are associated with different education groups and each skill group is subject to different

skill prices. Workers of all ages (within an education group) are assumed to have the same type of human capital, and therefore, they are subject to the same price. Heckman et al. (1998) use the implication of the Ben-Porath model for constant utilized skill levels towards the end of working life to develop a strategy for the identification of price changes. At older ages, when there is no longer any skill investment (nit = 0), changes in wages

are generated only by changes in prices. Therefore, wage changes for older workers can be used to identify price changes. The implicit assumption here is perfect substitutability

13_{Some of the studies which make the assumption of constant prices over time include Ben-Porath (1967),}

between young and old workers.14 _{In particular, for individuals who are in the “flat spot”}

region of their life-cycle efficiency units profile:

Mean�lnEi,a,t�= Mean�lnEi,a+1,t+1�⇒ Mean�lnwi,a+1,t+1�−Mean�lnwi,a,t�=lnpt+1−lnpt

(3.7) The choice of theflat spot age intervals is important. Heckman et al. (1998) note that there could be differences in endowments, ability and human capital production function across

different cohorts, which could make it difficult to identify the appropriate age interval dur-

ing which skill levels are constant, however they ignore these effects. Bowlus and Robinson

(2012) build on Heckman et al. (1998) by allowing for cohort effects in the form of selec-

tion effects and technological improvements in human capital production functions. They

use cross section data for college graduates to sign the bias that is introduced by cohort effects, and identify the appropriateflat spot region in the age-utilized skill profile as the

region where the bias from cohort effects is removed.15

Another paper which uses the flat spot approach is Huggett et al. (2011). They study the sources of variation in lifetime earnings, wealth and utility in the U.S. using a model where human capital is subject to idiosyncratic shocks in each time period. They estimate this shock process using changes in wage moments for older males.

Both Bowlus and Robinson (2012) and Heckman et al. (1998)find that accounting for the distinction between prices and wages is important for understanding the evolution of wages, since prices and wages can move differently. Heckman et al. (1998) simulate the

effects of a skill-biased technological change andfind that wages and prices move in oppo-

site directions in the earlier stages of the transition while the increase in the college-high

14_{This assumption is relaxed in Card and Lemieux (2001). Theyfind strong substitutability by age. How-}

ever, they do not account for the fact that human capital investment levels may vary by age and over time. They implicitly assume thatnitisfixed.

15_{For a more detailed explanation on the framework for choosing theflat spots, see Bowlus and Robinson}

school wage differential is greater than the increase in relative skill prices in later stages

due to rational investment behaviour.16 _{In the light of the evidence given by Heckman et al.}

(1998), Bowlus and Robinson (2012), and the second chapter, it is important that we make a careful distinction between wages and prices. Failure to account for changes in human capital levels over time (even within education-experience-gender groups) when estimat- ing the canonical model may produce misleading results. The next section estimates price series at the regional level and describes the movements in prices and relative prices of college-high school labour across different regions.