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In each case, a benchmark equation is run containing all the controls plus union density (and the minimum wage).
In order to determine whether marginal wage costs of different educational groups are in line with corresponding output elasticities, we re-estimated our benchmark equation using as dependent variable the value added-wage cost gap.
These include controlling for sectoral shifts/deindustrialization, skill-biased technical change, social preferences in favor of greater inequality, the role of the finance sector, rising levels of formal schooling, and even the endogeneity of the union variable.19 In each case, the union argument proved robust, actually increasing in absolute magnitude vis-à-vis the benchmark equation.
Our benchmark equation is the following: e_{j} = alpha_{0} + alpha_{1} S2_{j} + alpha_{2} S3_{j} + alpha_{3} M_{Nj} + alpha_{4} M_{Ej} + alpha_{5} M_{Wj} + alpha_{6} Z_{j} + v_{j} ; (1 where e j is either employees' average years of schooling in establishment j or, alternatively, the fraction of college-educated employees.
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We also re-estimated our benchmark equations separately for firms operating respectively in the industry and services.
Another difference compared to the benchmark equations is that instead of using hours worked in the preceding year as a proxy for actual hours, we here assume full-time employment.
The point estimates of the wage semi-elasticity with respect to the net replacement rate are in all cases except one lower than in the benchmark equations: when controls are included the estimates are in the range of 0.16 0.32.
Our benchmark wage equation is based on the usual Mincerian equation where the log of employee i's hourly wage in establishment j, w ij, is a function of his individual characteristics.
8In the benchmark wage equations in Section 4.1, we instead used average wage growth.
Several benchmark elliptic equations are solved numerically with the inclusion of multiple grid-levels in two-dimensional domains at an optimal computational cost within the LB framework.
The algorithm is illustrated by an application to a benchmark stochastic differential equation model, and numerical experiments are carried out to demonstrate the effectiveness of the construction.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com