Economics Letters 223 (2023) 110985 Contents lists available at ScienceDirect Economics Letters journal homepage: www.elsevier.com/locate/ecolet Education choices and job market characteristics✩ ∗ Qianshuo Liu a,b,c , Inés Macho-Stadler a,c , a Universitat Autònoma de Barcelona, Spain b IAE-CSIC, Spain c BSE, Spain article info a b s t r a c t Article history: We propose a simple three-stage model where heterogeneous schools compete via tuition fees, Received 26 September 2022 individuals with the ex-ante unknown ability make their education choices to (eventually) get a Received in revised form 27 November 2022 diploma and reveal their ability, and finally the job market determines the assignment of workers Accepted 4 January 2023 to firms and the equilibrium wages. In equilibrium, wages in the labor market and schools’ fees and Available online 6 January 2023 individuals’ school choices are strongly related. We also analyze the effects of the existence of a public JEL classification: school or a subsidy on social welfare. I26 © 2023 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND C78 license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Keywords: Education choices Skills Job market 1. Introduction schooling choices. MacLeod and Urquiola (2019) consider two identical schools and study the school choice when each firm Education decisions determine the workers’ characteristics in recruits from only one school or schools face capacity constraints. the labor market and the economy’s output. Also, future wages Boleslavsky and Cotton (2015) consider one firm and two schools influence the schools’ competition and the individuals’ education of a given capacity, competing through investment and grading choices. systems. Hatfield et al. (2014) show how the labor market’s We propose a three-stage model. First, two schools differing in design and frictions affect incentives for human capital acquisi- terms of how demanding they are, compete for students through tion. We complement the literature by considering heterogeneous their tuition fees. Then individuals with ex-ante unknown ability schools competing via tuition fees and the relationship between select which school to attend, if any. Finally, a one-to-one labor schools’ competition and job market outcomes. market matching between firms and workers occurs. The equi- librium wages (hence, the gains from education) are a function 2. Model of the workers’ and the firms’ productivity. Among our results, we highlight that subsidizing high-deman- We consider three sets of (risk-neutral) players: individuals, ding schools is especially helpful when the workers’ ability is very schools, and firms. valuable and the dispersion of skills in the population is large. There is a continuous of individuals of size one. They have the Introducing a public school can also increase welfare. same ex-ante ability to perform a specialized task if they obtain We contribute to the literature that relates education decisions a diploma. It is public knowledge that ex-post a proportion α and job market conditions. Flinn and Mullins (2015) study the has an ability k > 0 in the specialized task, and the remaining effects of minimum wages and college costs in a search and individuals have ability 0. Hence, an individual’s ex-ante expected matching model where heterogeneous individuals make ex-ante ability is α k. Individuals can pay for education, or there is a perfect credit market. ✩ We thank David Pérez-Castrillo and an anonymous reviewer for their Two schools train and provide the diploma to perform the helpful comments, and MINECO and Feder, Spain (PID2021-122403NB-I00), the specialized task. The schools’ type is public information; they Generalitat de Catalunya, Spain (2017SGR-711), and the Severo Ochoa, Spain have no capacity constraints and bear no costs. An individual (CEX2019-000915-S) programmes for their financial support. ∗ Corresponding author. graduates at the high-demanding school SH if (and only if) he E-mail addresses: qianshuo.liu.qs@gmail.com (Q. Liu), ines.macho@uab.cat has ability k. Hence, the ability of SH ’s graduates is kh = k. An (I. Macho-Stadler). individual always graduates at the low-demanding school SL , with https://doi.org/10.1016/j.econlet.2023.110985 0165-1765/© 2023 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by- nc-nd/4.0/). Q. Liu and I. Macho-Stadler Economics Letters 223 (2023) 110985 the expected ability ke = α k. We denote type k∅ an individual EU(SH ) = αwh + (1 − α )β − FH . The individual selects the school without a degree. solving Max{U(∅), U(SL ), EU(SH )}. There is a continuum of firms. Firm i is characterized by its Stage 1: Schools choose FH and FL productivity γi , uniformly distributed in [0, 1]. We assume that Anticipating the effect on the individuals’ choice, the revenue- there is a mas-point of firms with γi = 0, so that the population maximizing schools set their fees simultaneously and non-coope- of firms is ‘‘larger’’ than that of individuals.1 ratively. Proposition 1 states, in particular, that all individuals Each firm needs one worker. A contract between firm i and attend school at equilibrium. worker j specifies the wage wij . Individuals without a degree can only perform routine tasks. Their output in firm i is Ri∅ = β . Proposition 1. In equilibrium, The outcome of a graduated worker of ability kj , with j = h, e, (i) schools’ fees: FH = 32 α (1 − α )k, FL = 13 α (1 − α )k, is Rij = β + γi kj .2 (ii) demands for schools: QH = 23 , QL = 31 , Decisions are made in three stages. First, schools SH and SL (iii) wages: w∅ = β , we = β + 23 α (1 − α )k, wh = β + (1 − α )k. compete in fees, FH and FL . Second, individuals decide their ed- ucation, given (FH , FL ). We denote QH (resp., QL ) the amount of Corollary 1. In equilibrium, individuals attending school SH (resp., SL ), and Q∅ the amount (i) schools’ total revenue: R = 59 α (1 − α )k, not attending any school. The school selection and the education (ii) individuals’ total surplus: U = β + 31 α (1 − α )k, outcome are public information. In the third stage, individuals (workers) and firms match in (iii) firms’ total profit: Π = 18 1 α (8α + 1)k, the labor market. We formalize it as a one-to-one assignment (iv) total welfare: W = β + 18 1 α (17 − 8α )k. game with transferable utility. The equilibrium determines the Education fulfills two roles in our model. First, graduating from matching between firms and workers and wages. any school allows performing the specialized task. Second, school SH reveals an individual’s productivity on this task. The market 3. Equilibrium decisions compensates this second role with higher expected salaries to students attending SH : αwh + (1 − α )w∅ > we . It also explains We solve by backward induction. that FH > FL . As expected, a higher k leads to higher wages, fees, and par- Stage 3: Labor market ticipants’ surplus. The influence of α is more complex. A higher We denote workers by their productivity kj , with j = h, e, ∅. α reflects a better pool of individuals. However, the population If the distribution of the individuals in schools at T = 2 is heterogeneity depends on α : it increases until α = 1/2 and then (QH , QL , Q∅ ), with QH + QL + Q∅ = 1, then there are α QH decreases. This explains the non-monotonicity of the equilibrium kh -workers, QL ke -workers, and Q∅ + (1 − α )QH k∅ workers. fees (FH , FL ) (and schools’ revenue) in α . For α = 0 and α = The total surplus generated by the partnership (i, j) coincides 1, schools have similar education systems; competition leads to with the outcome Rij . Given the complementary between firms’ FH = FL = 0. The maximum schools’ differentiation occurs at and workers’ productivity, the equilibrium matching is positive α = 12 , where fees are maximum. assortative. This implies two cut-offs, γe and γh , with 0 ≤ γe ≤ The individuals’ surplus is increasing (resp., decreasing) for γh ≤ 1, such that (a) firms in [γh , 1] match with the kh -workers, α < 21 (resp., α > 12 ). An increase in α makes kh -workers more (b) firms in [γe , γh ] hire ke -workers, (c) firms in (0, γe ] hire abundant and decreases wh . In contrast, we first increases and k∅ -workers, and (d) firms with γ = 0 are unmatched. The then decreases in α . Indeed, for low α , ke -individuals are less equilibrium cut-offs are γe = Q∅ + (1 − α )QH and γh = 1 − α QH . productive but also rarer, so the firm γe is more productive and In equilibrium, workers with the same productivity get the pays them more. For large α , ke -workers are more abundant and same wage. To explain the wages, suppose that the three types productive, but γe is smaller, which induces a lower wage. Still, of workers are in the market. First, the competition of firms with firms’ and total welfare increase with α . γi = 0 to hire k∅ -workers leads to w∅ = β . Second, the marginal 4. Improving the market outcome firm γe pays a ke -worker a salary that leaves it indifferent to hiring a k∅ -worker: we = β + γe α k. Finally, kh -workers obtain the most We have assumed that there are two schools. However, the firm γh is ready to pay for them (the alternative is a ke -worker): social welfare is maximum when all individuals attend school SH . wh = β + γh k − (γh − γe )α k. A similar argument leads to the Nevertheless, if SH is the only school, it can use its monopoly equilibrium wages for all possible configurations: power. Proposition 2 states its choice and total welfare under monopoly. Lemma 1. Given (α QH , QL , Q∅ + (1 − α )QH ): (1) If QH > 0 and QL > 0: w∅ = β , we = β + γe α k, Proposition 2. Under monopoly: wh = β + γh k − (γh − γe )α k. (a) For α ≥ 12 : FH = α2k , QH = 21α . Total welfare is WHT = β + 3k . (2) If QH > 0 and QL = 0: w∅ = β , wh = β + γh k. 8 (b) For α ≤ 21 : FH = α (1 − α )k, QH = 1. Total welfare is (3) If QH = 0, QL > 0, and Q∅ > 0: w∅ = β , we = β + γe α k. α (2−α )k WHT = β + . (4) If QH = 0, QL = 1 or Q∅ = 0: we = β . 2 Corollary 2. Total welfare is higher when √ SH is the only school in Stage 2: Individual’s education decision An individual’s utility is the difference between his expected the market (i.e., WHT ≥ W T ) iff α ≤ 17−16 73 ≈ 0.53. salary and the school’s fee: U(∅) = β , U(SL ) = we − FL , and When SH is a monopoly and the proportion of high-ability students is low (α ≤ 12 ), then their identification is essential for 1 This assumption is made only for convenience. It allows us to identify the the top firms. Thus, all the students attend SH . This is the first- salary of the lowest-ability workers straightforwardly. best. A social planner also benefits from preventing the entrance 2 The main characteristic of this production function is that there is comple- of SL if α is not too high. Otherwise, a monopoly SH sets too high mentarity between firms’ productivity and workers’ ability. Any function that a fee; consequently, too few individuals attend, and welfare is exhibits this complementary leads to similar results. lower. 2 Q. Liu and I. Macho-Stadler Economics Letters 223 (2023) 110985 Subsidizing the cost of attending SH can also improve welfare Under definition (b), if SH is public and FH = 0, then the with two schools. Consider a subsidy of δ to school SH for each social optimum is also reached. However, if school SL is public α (1−α )k student attending.3 Proposition 3 states the equilibrium, where λ and FL = 0, then SH sets FH = 2 , leading to QH = 12 and denotes the shadow cost of the public funds. QL = 2 . Total welfare is β + 8 α (7 − 3α )k, which is lower than 1 1 in the two-private school case because the public school attracts Proposition 3. In equilibrium with two schools and a subsidy δ too many students. per student to SH : (i) schools’ fees: FH (δ ) = 32 (α (1 − α )k − δ ), FL (δ ) = 13 (α (1 − 5. Final comments α )k − δ ), (ii) demands: QH (δ ) = 23 + 3α (11−α )k δ , QL (δ ) = 13 − 3α (11−α )k δ , Our model opens the door to many potential extensions. (iii) cost of the subsidy: C (δ ) = δ + 3α(11−α)k δ 2 , 2 3 We find it particularly enriching to consider differences in the schools’ cost structure and capacity or the abilities they teach to ) welfare: W (δ ) = β + 18 (α (17 − 8α )k + 2δ T 1 (iv) total students. These and other extensions can shed further light on 1 − α(1−α )k δ 2 − λC (δ ). the implications of the labor market characteristics on a country’s school system. A subsidy δ leads to a decrease of 23 δ in FH and only 13 δ for FL . Hence, demand QH is higher, which is the policy’s objective. Of Data availability course, the planner’s cost C (δ ) increases with δ . When λ = 0, total welfare W T (δ ) increases in δ until δ = No data was used for the research described in the article. α (1 − α )k, where all students attend SH . When λ > 0, the optimal subsidy is an interior solution. Appendix A. Supplementary data Corollary 3. The optimal subsidy δ when λ > 0 is (i) increasing in Supplementary material related to this article can be found k, and (ii) increasing (decreasing) in α for α < 1/2 (resp., α > 1/2). online at https://doi.org/10.1016/j.econlet.2023.110985. Corollary 3 suggests that subsidizing high-demanding schools is especially helpful in economies where graduates’ ability is References crucial for firms (a high k) and the dispersion of individuals’ skills Boleslavsky, R., Cotton, C., 2015. Grading standards and education quality. Am. is large. Econ. J.-Microecon. 7 (2), 248–279. Finally, consider that one of the two schools is public and the Flinn, C., Mullins, J., 2015. Labor market search and schooling investment. Int. other private. A public school can be defined by: (a) it sets its Econ. Rev. 56 (2), 359–398. fee to maximize total welfare; (b) it is free. Under definition (a), Hatfield, J.W., Kojima, F., Kominers, S.D., 2014. Investment incentives in labor market matching. Am. Econ. Rev. 104 (5), 436–441. the social optimum (QH = 1, QL = 0) is reached. If school SH is MacLeod, W.B., Urquiola, M., 2019. Is education consumption or investment? public, it sets FH = 0, and all individuals attend SH . If SL is public, Implications for school competition. Annu. Rev. Econ. 11, 563–589. then the Nash equilibrium is FL = FH = α (1 − α )k, which implies QH = 1, QL = 0. 3 This policy is equivalent to giving a subsidy of δ to each student attending SH . 3