Final Report Summary - NONLINEAR PANEL (Nonlinear Panel Data Models: Heterogeneity, Identification and Estimation)
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. In particular, the estimation of a dynamic ordered probit with fixed effects has been considered, with an application to self-assessed health status. The well-known estimation problem of this kind of models when T is not very large is especially severe in our model because it contains two fixed effects: one in the linear index equation and one in the cut points. These two fixed effects, instead of only one as usually done, are implied by the potential existence of heterogeneity in both unobserved health status and reporting behaviour.
The contributions here are twofold. Firstly this contributes to the recent literature on bias correction in nonlinear panel data models by applying and studying the finite sample properties of two of the existing proposals to the ordered probit case. The most direct and easily applicable correction to our model is not the best one and still has important biases in our sample sizes. Secondly, this contributes to the literature that studies the determinants of self-assessed health measures by applying the previous analysis on estimation methods to the British household panel survey. This provides practitioners with more 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, that scheme to allow for heterogeneity in micro behaviour has two drawbacks: it does not fit the data and it rules out interesting economic models.
A second objective of this proposal is to analyse identification of a dynamic discrete choice panel model where not only the intercept, but also the slope is heterogeneous. This will include to see how much restrictions we have to impose on the distribution to point identify the model from a cross-section of a fixed periods. In this work, we have considered the time homogeneous first order Markov (HFOM) model that allows for maximal heterogeneity. That is, the modelling of the heterogeneity does not impose anything on the data (except the HFOM assumption for each agent) and it allows for any theory model (that gives a HFOM process for an individual observable variable). Maximal' means that the joint distribution of initial values and the transition probabilities is unrestricted.
We establish necessary and sufficient conditions for the point identification of our heterogeneity structure and show how it depends on the length of the panel. A feasible ML estimation procedure is developed. Tests for a variety of subsidiary hypotheses such as the assumption that marginal dynamic effects are homogeneous are developed. We apply our techniques to a long panel of Danish workers who are very homogeneous in terms of observables. We show that individual unemployment dynamics are very heterogeneous, even for such a homogeneous group. We also show that the impact of cyclical variables on individual unemployment probabilities differs widely across workers. Some workers have unemployment dynamics that are independent of the cycle whereas others are highly sensitive to macro shocks.
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. In particular, the estimation of a dynamic ordered probit with fixed effects has been considered, with an application to self-assessed health status. The well-known estimation problem of this kind of models when T is not very large is especially severe in our model because it contains two fixed effects: one in the linear index equation and one in the cut points. These two fixed effects, instead of only one as usually done, are implied by the potential existence of heterogeneity in both unobserved health status and reporting behaviour.
The contributions here are twofold. Firstly this contributes to the recent literature on bias correction in nonlinear panel data models by applying and studying the finite sample properties of two of the existing proposals to the ordered probit case. The most direct and easily applicable correction to our model is not the best one and still has important biases in our sample sizes. Secondly, this contributes to the literature that studies the determinants of self-assessed health measures by applying the previous analysis on estimation methods to the British household panel survey. This provides practitioners with more 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, that scheme to allow for heterogeneity in micro behaviour has two drawbacks: it does not fit the data and it rules out interesting economic models.
A second objective of this proposal is to analyse identification of a dynamic discrete choice panel model where not only the intercept, but also the slope is heterogeneous. This will include to see how much restrictions we have to impose on the distribution to point identify the model from a cross-section of a fixed periods. In this work, we have considered the time homogeneous first order Markov (HFOM) model that allows for maximal heterogeneity. That is, the modelling of the heterogeneity does not impose anything on the data (except the HFOM assumption for each agent) and it allows for any theory model (that gives a HFOM process for an individual observable variable). Maximal' means that the joint distribution of initial values and the transition probabilities is unrestricted.
We establish necessary and sufficient conditions for the point identification of our heterogeneity structure and show how it depends on the length of the panel. A feasible ML estimation procedure is developed. Tests for a variety of subsidiary hypotheses such as the assumption that marginal dynamic effects are homogeneous are developed. We apply our techniques to a long panel of Danish workers who are very homogeneous in terms of observables. We show that individual unemployment dynamics are very heterogeneous, even for such a homogeneous group. We also show that the impact of cyclical variables on individual unemployment probabilities differs widely across workers. Some workers have unemployment dynamics that are independent of the cycle whereas others are highly sensitive to macro shocks.