A failure of the market for college education and on-the-job human capital

Abstract

This paper shows that a competitive labor market fails to provide first-best incentives to invest in general human capital and this has distributive consequences: college students and firms underinvest in human capital, and this is more pronounced for high-skill students with low-income parents. Long-term contracts, together with privately provided wage-contingent loans, cannot restore efficiency and eliminate the distributive consequences of this labor market failure. Government student loans together with firm subsidies to human capital investments fully solve the market failure.

Introduction

Human capital is a fundamental determinant of economic performance (growth and inequality). Most individuals spend large amounts of time and money during their early years in order to acquire general human capital through formal education. Credit market imperfections play a crucial role in education decisions, since human capital or labor cannot be pledged as collateral. In fact, conditional on ability, college attendance is strongly increasing in family income and wealth, and, since the mid-1990s, more and more students around the world exhaust government student loan programs and turn to private lenders for additional credit (see, for instance Chapman (2006) and Lochner & Monge-Naranjo (2016)). Post-school training is also key to augmenting and adapting human capital acquired earlier in life to technical and structural changes, in order to decrease unemployment risk, increase wages, and improve career prospects. Firms invest considerable resources in training: Heckman, Lochner, & Taber (1998) estimate that over half of lifetime human capital is obtained through post-school investment, including training within firms. Estimates from Europe typically document that 80 to 90 percent of the training is general in nature, whereas U.S. based studies provide estimates of general training in the vicinity of 60 to 70 percent of all training spells (Barron, Berger, Black, 1999, Booth, Bryan, 2002, Loewenstein, Spletzer, 1997, Loewenstein, Spletzer, 1998, see, for instance,).

Since Becker (1964), economists have argued that, in a competitive labor market, workers capture the full return to their general human capital and, therefore, undertake the efficient investment–provided that they do not face credit constraints. Because workers get the full return to general skills, firms are fully held-up and thereby they do not invest in general human capital. Balmaceda (2005) shows that, when wages are determined by bargaining with outside options instead of inside options, and workers acquire specific skills that are neither complements nor substitutes with general skills, workers underinvest in general skills and firms invest in general skills despite the fact that the market pays workers a wage that fully rewards their productivity. In his setting, when outside options are modeled as inside options, Becker (1964)’s predictions hold. Thus, (Becker, 1964) result hinges on the particular assumption that bargaining with the incumbent firm and employment on the spot market are not mutually exclusive, establishing that rents are independent of general skills.

This paper studies human capital investments by both firms and college students when the labor market is competitive and students face credit constraints. Despite it being perfectly competitive, the labor market fails to provide incentives for first-best investments. This implies that investments are inefficiently low and this has distributive consequences: human capital underinvestment is most severe among high-ability low-income students. Long-term contracts that optimally set a downward rigid wage floor, together with privately provided income-contingent loans (ICLs), partially alleviate the inefficiency and distributive consequences of the market failure uncovered here. This calls for government interventions that take place in the form of merit-based firm subsidies and government student loans (GSL).

Section 3 proposes a model with pre- and post-school complementary investment in general human capital in a competitive labor market with endogenous separations due to match-specific shocks.² The model comprises three periods: in the first period, college students acquire human capital through college education; in the second period, each young worker-firm pair negotiates a long-term contract that specifies the first-period wage and a downward rigid wage floor applicable when the worker becomes old. Then, firms decide how much to invest in the general skills of young workers. At the end of this period, a match-specific shock is realized. Finally, in the last period, each firm-old worker pair renegotiates the contract terms if they so chose, the firm decides whether to fire the worker or not, and the old worker simultaneously decides whether to stay or quit. Wages are determined by Rubinstein (1982) alternating offers bargaining game with outside options, and the restriction that the wage cannot be lower than the wage floor established in the long-term contract. Workers are initially endowed with personal/family wealth that determines, together with credit protection laws and the inalienability of human capital, their access to private and government student loans. Private loans are subject to moral hazard, while government loans have an exogenous upper limit and can only be spent on educational expenses.

Given that contract terms can be renegotiated when the worker becomes old, the firm anticipates that it is going to be held-up with positive probability and thereby chooses an inefficiently low level of investment. The firm’s investment rises with the young worker’s amount of human capital, since college and post-college human capital are complements, and the former decreases the probability of the worker leaving the incumbent firm. When workers are young, firms and workers negotiate a wage for the current and next period. Because firms compete for young workers in a Bertrand-like fashion, the first-period wage must be such that total career wages are equal to total career productivity minus the firm’s investment costs. This implies that competition allows the student to receive the full return to their investment in general human capital. In equilibrium, the firm sets a positive wage floor, since this maximizes total career wages. This stems from the fact that the firm underinvests in general human capital, and a wage floor allows the firm to get a full marginal return to human capital with positive probability, which provides the firm with stronger incentives to invest in general skills. Thus, setting downward rigid wages is welfare-increasing, despite the fact that the labor market is competitive. This result is interesting in its own right, since it is contrary to existing economic theory, which suggests that price regulations in competitive markets are always welfare-decreasing.

In spite of the fact that students anticipate that they will get the full return to their investment in formal education, in the unique sub-game perfect equilibrium, they underinvest in general human capital since they anticipate the firm will underinvest and investments are complements. This underinvestment is exacerbated when students are credit-constrained, and this not only harms an individual’s lifetime accumulation of general human capital since less college education is undertaken, but also reduces the amount of investment to be received from future employers. Thus, workers are faced with lower expected total career productivity and wages. High-skill low-wealth students are the ones most harmed by this market failure.

Because competitive labor markets fail to provide first-best incentives to invest in general human capital, and this affects students with different initial skills and wealth differently, a government intervention is required. In Section 6, we show that the first-best efficient investment profile can be implemented by providing firms with subsidies and by GSLs. A firm’s subsidy that pays a share of the investment costs, and is made contingent on initial skills, implements the first-best investment profile. Alternatively, the subsidy can be made contingent in the firm’s investment in human capital, which facilitates its implementation. We also show that fully enforceable GSLs with positive upper limits that may or may not be contingent on students’ means is required. Hence, subsidies to human capital, together with private and publicly-provided loans for credit-constrained students, create a virtuous cycle; subsidies and GSL increase human capital investments, which results in better access to private loans, which in turn, increase investments in human capital even further.

In the next section, we provide a literature review. In Section 3, the model is presented. In the following section, the determination of old-.workers’ wage is studied, and the difference between treating outside offers as outside versus inside options is discussed. Also the cooperative benchmark is presented. In Section 5, the sub-game perfect equilibrium is derived. In the following section, Section 6, we derive the firm’s human-capital subsidies and the GSL’s limit that implements the first-best efficient investment in human capital, and discuss the empirical evidence regarding subsidies and student loans. In the last section, we present concluding remarks.