In this paper we extend a job search-matching model with firm-specific investments in training developed by Mortensen (1998) to allow for different offer arrival rates in employment and unemployment. The model by Mortensen changes the original wage posting model (Burdett and Mortensen, 1998) in two aspects. First, it provides a link between the wage posting framework and the search-matching framework (eg. Pissarides, 1990). Second, it improves the correspondence between the theoretical characterization of the endogeneously derived earnings density and the empirically observed earnings density. We subsequently estimate the model on Danish labour market data using a structural non-parametric estimation procedure. We find that the model provides a good characterization of some empirical features of the labour market.