Estimating effort function with semiparametric model (Q1979105)

The effort function \(e(w)\) describes the dependence between the effort of a worker and his wages (\(w\)). The aim of the paper is to estimate \(e(w)\) of a representative worker by data on the Finish industry in 1991. From a model of firm's production function the author derives a semiparametric model for \(e(w)\) estimation: \[ \ln L_i=x_i^T\beta +g(w_i)+\varepsilon_i, \] where \(L_i\) is the number of hired persons, \(w_i\) is the wages rate, \(x_i\) are regressors which depend on the wage rate, firm output and the conditions of it's functioning (type of industry), \(g(w)=C\ln(e(w))\), and \(\beta\) is the vector of unknown parameters. The author estimates \(g(w)\) for this model using smoothing splines which minimize the penalized sum of squares. The hypothesis \(g(w)=0\) is tested by the Hong and White \(M\)-test [\textit{Y. Hong} and \textit{H. White}, Econometrica 63, No. 5, 1133-1159 (1995; see the preceding entry, Zbl 0941.62125)]) and by the Hastie and Tibshirani \(F\)-test [\textit{T.J. Hastie} and \textit{R.J. Tibshirani}, Generalized additive models. (1991; Zbl 0747.62061)]. A bootstrap technique is used to derive approximate distributions of the test statistics.