The Contribution of Educated Workers to Firms’ Efficiency Gains: The Key Role of Proximity to the ‘Local’ Frontier

Abstract

Vandenbussche et al. (J Econ Growth 11(2):97–127, 2006) and Aghion et al. (in: Romer, Wolfers (eds) Brookings papers on economic activity: conference draft, Brookings, Washington, 2009) show that when economies operate close to the technological frontier, their ability to generate efficiency gains rests on the contribution of workers with advanced forms of education (i.e. tertiary). The contribution of this empirical paper is to revisit and improve the analysis of that assumption, in the context of firms located in advanced economics, assuming that what holds for OECD countries or US states should also be observed also at a more disaggregated level. To that end, we analyse a rich panel of Belgian firm-level data, covering the 2008–14 period. In the first step, we estimate each firm’s proximity to frontier using stochastic frontier methods. Step 2 consists in regressing each firm’s efficiency growth rate on (1) the share of workers by education attainment (2) its (initial) distance/proximity to the frontier and (3) (the main variable of interest) the interaction between (1) and (2), whose sign provides a direct test of the Vandenbussche/Aghion assumption. The main result of the paper supports the idea that the closer the firms are to what amounts to a local frontier; the more educated workers—in particular those with a master’s degree—matter for efficiency gains. The paper also shows that many of them are currently employed in firms that are distant from the efficiency frontier. Reallocating them would have a positive impact on overall efficiency.

Appendix: The ACF-GMM Estimator

Considering a stylised version our Stage 2 model Eq. (7),

$$ y_{it} = X_{it} \lambda + \, \varepsilon_{it} $$

(8)

with

$$ \begin{aligned} y_{it} &\equiv \widehat{ptf}_{it} - \widehat{ptf}_{it - \it1} \\ X_{it} &= [{pft_{it - \it1}} , \, SEC_{it - \it1} ; \, BACH_{it - \it1} ;MAST_{it - \it1} ; \, SEC_{it - \it1} {pft_{it - \it1}} ; BACH_{it - \it1} {pft_{it - \it1}} MAST_{it - \it1} {pft_{it - \it1}}] \\ \lambda &\equiv \, \left[ {\alpha ,\beta ,\gamma_{1} ,\gamma_{2} ,\gamma_{3} ,\eta_{1} ,\eta_{2} ,\eta_{3,} \theta } \right] \\ \end{aligned} $$

the logic of the ACF-GMM estimator is to consider that the error term comprise ε_it a time-varying unobserved terms (partially known or anticipated by the management of the firm) ω_it that is potentially correlated with the other regressors. It might for instance correspond to a (positive/negative) efficiency development influencing their educational mix.

$$ \varepsilon_{it} = \, \omega_{it} + \sigma_{it} $$

(9)

Key with ACF it to assume that firms’ (observable) demand for intermediate inputs (int_it) is a function of ω_it as well as labour inputs (here the shares of workers by educational attainement):

$$ int_{it} = f_{t} \left( {\omega_{it} ,X_{it} } \right) $$

(10)

ACF further assume that this function f_t is monotonic in ω_it and its other determinants, meaning that it can be inverted to deliver an expression of ω_it as a function of int_it, X_it and introduced into the model

$$ y_{it} = X_{it} \lambda + f_{t}^{ - 1} (int_{it} ,X_{it} ) + \sigma_{it} $$

(11)

The ACF algorithm consists of two steps. In step one, outcome variable (here efficiency growth) is regressed on a composite term Φ_it that comprises a constant, and 3rd order polynomial expansion in i int_it, X_it., approximating $f_{t}^{ - 1} (int_{it} ,X_{it} )$

$$ y_{it} = \varPhi_{it} (int_{it} ,X_{it} ) + \sigma_{it} $$

(12)

At that point λ is clearly not identified yet. The first-step regression delivers an unbiased estimate of the composite term Φ ^hat; _it i.e. outcome net of the purely random term σ_it. This is done at step 2. Key is the idea that one can generate implied values for ω_it using first-stage estimates Φ ^hat _it and candidate values for the vector of coefficients λ

$$ \omega_{it} = \varPhi_{it}^{hat} {-} \, X_{it} \lambda^{\$ } $$

(13)

ACF assume further that the evolution of ω_it follows a first-order Markov process

$$ \omega_{it} = E\left[ {\omega_{{\left. {it} \right|}} \omega_{it - 1} } \right] - \xi_{it} $$

(14)

That assumption simply amounts to saying that the realization of ω_it depends on some function g(.) (known by the firm) of t − 1 realisation and an (unknown) innovation term ξ_it.

$$ \omega_{it} = \, g\left( {\omega_{it - 1} } \right) +\xi_{it} $$

(15)

By regressing non-parametrically (implied) ω_it on (implied) ω_it-1, ω_it-2, one gets residuals that correspond to the (implied) ξ_it that can form a sample analogue to the orthogonality (or moment) conditions identifying λ ≡ [α,β,γ₁,γ₂,γ₃,η₁,η₂,η₃,θ].

$$ {\rm E}\left[ {\xi_{{\left. {it} \right|}} X_{it} } \right] = 0 $$

(16)

with the possibility, for some of the variables forming X_it to resort to lagged values, under that assumption that these are less likely to be uncorrelated with the innovation terms ξ_it. We followed this recommendation for the variables containing education share, meaning that our moment conditions are

$$ {\rm E}\left[ {\xi_{{\left. {it} \right|}} SEC_{it - 2} ,SEC_{it - 3} \ldots } \right] = 0 $$

(17)

$$ {\rm E}\left[ {\xi_{{\left. {it} \right|}} BACH_{it - 2} ,BACH_{it - 3} \ldots } \right] = 0 $$

(18)

$$ {\rm E}\left[ {\xi_{{\left. {it} \right|}} MAST_{it - 2} ,MAST_{it - 3} \ldots } \right] = 0 $$

(19)

$$ {\rm E}[\xi_{{\left. {it} \right|}} SEC_{it - 2} ,SEC_{it - 3} \ldots ] = 0 $$

(20)

$$ {\rm E}[\xi_{{\left. {it} \right|}} BACH_{it - 2} ,BACH_{it - 3} \ldots ] = 0 $$

(21)

$$ {\rm E}[\xi_{{\left. {it} \right|}} MAST_{it - 2} ,MAST_{it - 3} \ldots ] = 0 $$

(22)