Social returns to education in Italian local labor markets

Abstract

The paper estimates social returns to education in the Italian local labor markets. It shows that there is an important correlation between local human capital and average wages after controlling for individual characteristics. Estimated social returns to education range from 2 to 3%, whereas the private returns amount roughly to 6–7%. To find some support about causality running from local human capital to wages, the paper performs a number of robustness checks. It shows that: the estimated social returns are unlikely to be driven by spatially correlated omitted variables; they survive to the introduction of individual- and territorial-level variables; they are not due to imperfect substitutability across workers or spatial sorting; they are robust to IV techniques that deal with both local human capital and individual human capital endogeneity.

Appendix theoretical background

In what follows, we sketch a simple model that generates a Mincerian wage-equation “augmented” with a local human capital term. The framework is similar to those in Rauch (1993) and Acemoglu and Angrist (2000). As in Moretti (2004), each area j (with j = 1,... ,J) is treated as a competitive economy that produces a single output y traded on the global market at a price equal to one. We assume a constant-returns-to-scale Cobb-Douglas technology that employs capital, K, and effective units of labor, L. The typical firm operating in area j has the following production function:

$$ y=A(\hbox{HC}_j )\cdot K^{1-\alpha}\cdot L^\alpha $$

(2)

with 0 < α < 1. The term A(HC _j ), a function of local human capital HC _j , captures the effects of human capital spillovers on productivity in area j, and we assume that dA(HC _j )/dHC _j  ≥  0. Thus, A(HC _j ) measures the productivity advantage enjoyed by a firm operating in area j. Effective units of labor are defined as $L=\sum\nolimits_{i=1}^N{s(h_i)}$, with s′(h _i ) > 0: the firm hires N workers, and each worker i supplies s units of effective labor. The effectiveness s of worker i is increasing in his individual education, h _i . The additive form chosen for L implies perfect substitutability among differently educated workers (see Rauch 1993; for a discussion of this issue, see Ciccone and Peri 2006). In each area j, the competitive price of a unit of effective labor is denoted by ω _j . Capital is rented on the global market at rate r.

Given the local level of human capital HC _j , each competitive firm in area j maximizes profit, π = y − r· K − ω _j · L, by choosing (K,L). The first-order conditions for this maximum problem are:

$$ \frac{\partial \pi}{\partial K}=(1-\alpha)\cdot A(\hbox{HC}_j)\cdot K^{-\alpha} \cdot L^\alpha -r=0 $$

(3)

$$ \frac{\partial \pi}{\partial L}=\alpha \cdot A(\hbox{HC}_j)\cdot K^{1-\alpha} \cdot L^{\alpha -1}-\omega _j=0 $$

(4)

By using (2), expressions (3) and (4) can be manipulated into K = (1 − α)y/r and L = α y/ω _j , respectively. By substituting these expressions for (K,L) back into the production function (2), we obtain the equilibrium value of ω _j , the local price of an effective unit of labor:

$$ \omega_j =\mu\cdot \left[A(\hbox{HC}_j)\right]^{1/\alpha} $$

(5)

where μ≡ [α((1 − α)/r)^(1-α)/α]. Notice that dω _j /dHC _j  ≥  0: a higher level of local human capital will raise the price of an effective unit of labor in the area considered. Moreover, by substituting the equilibrium expressions for (K,L) into the profit expression π, it can be immediately verified that each firm will make zero profit in equilibrium. As a consequence, firms have no incentive to move across areas.

The wage received by individual i in area j, denoted by w _ij , is simply equal to ω _j  ×  s(h _i ). Thus, taking logs:

$$ \log w_{ij}=\log \mu+\log s(h_i)+\frac{1}{\alpha}\log A(\hbox{HC}_j) $$

(6)

Similarly to Moretti (2004, p. 178), we suppose that the logs of effective labor s and the production externality A(HC _j ) are linear functions of individual education and local human capital, respectively. Thus, it holds that:

$$ \log s(h_i)=\phi+\beta \cdot h_i,\quad \beta > 0 $$

(7)

and

$$ \log A(\hbox{HC}_j)=\theta+\gamma\cdot \hbox{HC}_,\quad \gamma\geq 0 $$

(8)

By substituting (7) and (8) into expression (6), we finally obtain a Mincerian wage-equation augmented with a local human capital term:

$$ \log w_{ij}=\kappa+\beta\cdot h_i+\eta\cdot \hbox{HC}_j $$

(9)

where the constant κ is equal to (logμ + ϕ  + θ/α), and η≡ γ/α. Equation (9) thus justifies the empirical model provided in expression (1) in the text. As in Rauch (1993), Acemoglu and Angrist (2000) and Moretti (2004), if local human capital generates positive spillovers on productivity, it will hold that η > 0. By contrast, when η = 0, the model collapses back into the standard Mincerian equation, where wage differences only depend on individual education (here, we obviously abstract from worker’s “experience”). This simple model also abstracts from the fact that, when firms in different areas pay different wages, workers will have an incentive to migrate, unless there are compensating differences in the levels of local amenities, or in the price of housing across areas. Such “general equilibrium” issues are considered in Roback (1982) and discussed in Moretti (2003).

Appendix: description of variables