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In this paper, we derive a micro model of employment demand with hysteresis whereby firms can adjust along an intensive (employment) and an extensive (hours of work) margin. A mechanism of aggregation over heterogeneous firms is used to generate the corresponding aggregate dynamics. Longitudinal micro monthly data on a representative sample of Portuguese manufacturing firms are used in the empirical analysis. Our results indicate that signs of hysteresis found at the micro level do not vanish completely by aggregation and that hysteresis is magnified by the existence of an additional margin of adjustment (the hours adjustment margin).

Consider a nonlinear operator equation x − K(x) = f , where K is a Urysohn integral operator with a smooth kernel. Using the orthogonal projection onto a space of discontinuous piecewise polynomials of degree ≤ r, previous authors have established an order r + 1 convergence for the Galerkin solution and 2r + 2 for the iterated Galerkin solution. Equivalent results have also been established for the interpolatory projection at Gauss points. In this paper, a modified projection method is shown to have convergence of order 3r + 3 and one step of iteration is shown to improve the order of convergence to 4r + 4. The size of the system of equations that must be solved, in implementing this method, remains the same as for the Galerkin method. 2010 AMS Mathematics subject classification. Primary 45L10, 65J15, 65R20. Keywords and phrases. Urysohn integral operator, Galerkin method, collocation at Gauss points.