"Unobserved heterogeneity is an important factor to take into account when making inference based on micro-data. In linear panel data models it is well known how to control for permanent unobserved heterogeneity in a robust way, i.e. without assuming any parametric distribution of the heterogeneity on the population. In contrast the problem is much more difficult in nonlinear models. A significant part of the research on microeconometrics in the recent years has been about dealing with this issue and many solutions have been proposed. A first objective of this proposal is to study how well the bias correction methods recently proposed work for other specific nonlinear models and data set of interest in applied econometrics. This will provide practitioners with reliable evidence about whether the methods work for the case they are interested in and which method is better among the many that have been proposed. Unobserved heterogeneity in dynamic discrete choice models is usually only allowed through a specific constant individual term, as in linear panel data models. However, in nonlinear cases that assumption implies further strong restrictions in the model and previous explorations seems to indicate that we should allow for more heterogeneity. A second objective of this proposal is to analyze identification of a dynamic discrete choice panel model where not only the intercept but also the slope is heterogeneous. This will include to (i) see how much restrictions we have to impose on the distribution to point identify the model (or its parameters of interest) from a cross-section of a fixed periods; and (ii) study further the non-identified situations of that model by looking for partial identification. The interest on this is to know how much heterogeneity can be identify from a given data set, the minimum restrictions we have imposed to get point estimates of the parameters of interests, and what we still can learn if we do not imposed all those restrictions."