We demonstrate that non-monotone behaviour of the right tail of earnings density may lead to the fact that nonparametric estimation of the Bontemps et al. (2000) equilibrium search model with employer heterogeneity does not yield consistent estimates. We propose an easy way of checking whether the Bontemps et al. (2000) estimation procedure can be applied and review the robustness of the alternative strategy once the Bontemps et al. (2000) procedure is inapplicable.