Analysing wage differentials when workers maximize the return to human capital investment

ABSTRACT

The analysis of the determinants of differences in wages across workers has traditionally relied on the estimation of average earnings functions. In this article, we propose a new theoretical model where it is the workers who decide the amount they wish to invest in human capital, taking into account the costs of acquiring those skills, for the purpose of maximizing earnings. In this model, both human capital and marginal productivity are likely to be influenced by the individual’s (unobserved) characteristics such as ability or motivation, potentially giving rise to endogeneity problems. In this context, the empirical implementation of our theoretical model allows us, under certain assumptions, to obtain consistent estimates even under the assumption of endogeneity. We present an empirical application to the education sector using data from the Spanish Structure of Earnings Survey 2010. Our results show that females and workers in the private education sector face more difficulties in achieving their maximum potential wage.

KEYWORDS:

• Economics
• distance functions
• endogeneity
• earnings functions
• stochastic frontier analysis

JEL CODES:

• C51
• J24
• J31

Acknowledgements

The authors acknowledge financial support from the project ECO2013-43925-R (Ministry of Economy and Competitiveness) and the projects and the projects FC-15-GRUPIN14-064 ‘Oviedo Efficiency Group’ FC-15-GRUPIN14-048 (both within the European Regional Development Fund (FEDER) and Principality of Asturias, Science, Technology and Innovation Plan [2013–2017]).

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

¹ See, for instance, Kumbhakar and Lovell (2000c) for a survey on frontiers.

² For a review, see Card (1999), Psacharopoulos and Patrinos (2004c) or Heckman, Humphries and Veramendi (2016b).

³ An alternative strategy to estimate the returns to schooling in the absence of instruments relies on identification via conditional second moments (Farré, Klein, and Vella 2013b).

⁴ This idea stems from the seminal paper of Georgescu-Roegen’s (1951b), based on the maximization of the return to the outlay (return to the dollar), and that has been recently applied to firms’ behaviour by Kumbhakar (2011c).

⁵ In the empirical model, we will represent P_NC as a vector of firm and occupational category dummy variables that would pick up the working conditions within each firm.

⁶ The IDF is dual of the cost function. For details and empirical applications, see for example, Färe and Primont (1995b) or Baños-Pino, Fernández-Blanco and Rodríguez-Álvarez (2002).

⁷ See Kumbhakar (2011c) and Kumbhakar, Asche and Tveteras (2013c) for details.

⁸ H(1) in inputs implies ${\alpha }_s+{\alpha }_e=1;{\alpha }_{ss}+{\alpha }_{se}=0;{\alpha }_{es}+{\alpha }_{ee}=0;{\alpha }_{sy}+{\alpha }_{ey}=0$.

⁹ These restrictions make returns to scale unity (CRS), which is not an assumption but an implication of maximizing returns to the outlay.

¹⁰ We have transformed the school level variable to obtain years of formal education by assigning to each education level, the minimum number of years officially required to obtain that level.

¹¹ Note that in our model, earnings are E = MP × P_NC, that is, MP = E/P_NC. Then, ln MP = ln E − ln P_NC. If P_NC is considered to be constant for each firm and category, then P_NC will only affect the constant term (in particular the firm and category dummy variables) and we will be able to use E as a proxy of MP without biasing results.

¹² The data set does not provide information on individuals’ experience in the labour market; so, we have computed potential experience as age minus years of schooling minus 6, as is standard in labour economics.

¹³ The proportion of females in the Spanish SES is below 43%.

¹⁴ The value of this test was 116.85, higher than the critical value of the chi-square distribution for 1 degree of freedom at the usual levels of significance.

¹⁵ Let us recall that increases in the variance of u represent increases in the distance to the frontier (and vice versa).

¹⁶ We must remark that our analysis focuses on the education sector and the results obtained cannot be extrapolated to other sectors without taking the risk of incurring self-selection problem.

¹⁷ Similar results about the existence of sticky floors in the labour market, using different methodologies, have been revealed in other countries, see for instance Booth, Francesconi and Frank (2003) or Christofides, Polycarpou and Vrachimis (2013b).

Additional information

Funding

The authors acknowledge financial support from the project ECO2013-43925-R (Ministry of Economy and Competitiveness) and the projects FC-15-GRUPIN14-064 and “Oviedo Efficiency Group” FC-15-GRUPIN14-048 (both within the European Regional Development Fund (FEDER) and Principality of Asturias, Science, Technology and Innovation Plan [2013–2017]).