Correcting the bias in the estimation of a dynamic ordered probit with fixed effects of self-assessed health status

This paper considers the estimation of a dynamic ordered probit with fixed effects, with an application to self-assessed health status. The estimation of nonlinear panel data models with fixed effects by MLE is known to be biased when T is not very large. The problem is specially severe in our model because of the dynamics and because it contains two fixed effects: one in the linear index equation, interpreted as unobserved health status, and another one in the cut points, interpreted as heterogeneity in reporting behavior. The contributions of this paper are twofold. Firstly this paper 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, we contribute to the literature that study the determinants of Self-Assesed Health measures by applying the previous analysis on estimation methods to the British Household Panel Survey

Dynamic binary outcome models with maximal heterogeneity

Most econometric schemes to allow for heterogeneity in micro behaviour have two drawbacks: they do not fit the data and they rule out interesting economic models. In this paper we consider 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

Correcting the bias in the estimation of a dynamic ordered probit with fixed effects of self-assessed health status

This paper considers the estimation of a dynamic ordered probit with fixed effects, with an application to self-assessed health status. The estimation of nonlinear panel data models with fixed effects by MLE is known to be biased when T is not very large. The problem is specially severe in our model because of the dynamics and because it contains two fixed effects: one in the linear index equation, interpreted as unobserved health status, and another one in the cut points, interpreted as heterogeneity in reporting behavior. The contributions of this paper are twofold. Firstly this paper 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, we contribute to the literature that study the determinants of Self-Assesed Health measures by applying the previous analysis on estimation methods to the British Household Panel Survey.Dynamic ordered probit, Self-assessed health, Reporting bias, Panel data, Unobserved heterogeneity, Incidental parameters, Bias correction

Dynamic binary outcome models with maximal heterogeneity

Most econometric schemes to allow for heterogeneity in micro behaviour have two drawbacks: they do not fit the data and they rule out interesting economic models. In this paper we consider 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.Discrete choice, Markov processes, Nonparametric identification, Unemployment dynamics

The identification of a mixture of first order binary Markov Chains

Let S be the number of components in a finite discrete mixing distribution. We prove that the number of waves of panel being greater than or equal to 2S is a sufficient condition for global identification of a dynamic binary choice model in which all the parameters are heterogeneous. This model results in a mixture of S binary first order Markov ChainsDiscrete choice, Markov processes, Global identification

Dynamic Binary Outcome Models with Maximal Heterogeneity

Most econometric schemes to allow for heterogeneity in micro behaviour have two drawbacks: they do not fit the data and they rule out interesting economic models. In this paper we consider 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.discrete choice; Markov processes; nonparametric identification; unemployment dynamics

State dependence and heterogeneity in health using a bias corrected fixed effects estimator

This paper considers the estimation of a dynamic ordered probit of self-assessed health status with two fixed effects: one in the linear index equation and one in the cut points. The two fixed effects allow us to robustly control for heterogeneity in unobserved health status and in reporting behaviour, even though we can not separate both sources of heterogeneity. The contributions of this paper are twofold. First it contributes to the literature that studies the determinants and dynamics of Self-Assessed Health measures. Second, this paper contributes to the recent literature on bias correction in nonlinear panel data models with fixed effects by applying and studying the finite sample properties of two of the existing proposals to our model. The most direct and easily applicable correction to our model is not the best one, and has important biases in our sample sizesDynamic ordered probit, Fixed effects, Self-assessed health, Reporting bias, Panel data, Unobserved heterogeneity, Incidental parameters, Bias correction

State Dependence and Heterogeneity in Health Using a Bias Corrected Fixed Effects Estimator

This paper considers the estimation of a dynamic ordered probit of self-assessed health status with two fixed effects: one in the linear index equation and one in the cut points. The two fixed effects allow us to robustly control for heterogeneity in unobserved health status and in reporting behaviour, even though we can not separate both sources of heterogeneity. The contributions of this paper are twofold. First it contributes to the literature that studies the determinants and dynamics of Self-Assessed Health measures. Second, this paper contributes to the recent literature on bias correction in nonlinear panel data models with fixed effects by applying and studying the finite sample properties of two of the existing proposals to our model. The most direct and easily applicable correction to our model is not the best one, and has important biases in our sample sizes.Dynamic ordered probit, fixed effects, self-assessed health, reporting bias, panel data, unobserved heterogeneity, incidental parameters, bias correction

Modified Gravity at Astrophysical Scales

Using a perturbative approach we solve stellar structure equations for low-density (solar-type) stars whose interior is described with a polytropic equation of state in scenarios involving a subset of modified gravity theories. Rather than focusing on particular theories, we consider a model-independent approach in which deviations from General Relativity are effectively described by a single parameter $\xi$. We find that for length scales below those set by stellar General Relativistic radii the modifications introduced by modified gravity can affect the computed values of masses and radii. As a consequence, the stellar luminosity is also affected. We discuss possible further implications for higher density stars and observability of the effects before described.Comment: 12 pages, 7figures, matches published versio

Dynamic binary outcome models with maximal heterogeneity

Most econometric schemes to allow for heterogeneity in micro behavior have two drawbacks: they do not fit the data and they rule out interesting economic models. In this paper we consider the time homogeneous first order Markov (HFOM) model that allows for maximal heterogeneity. That is, the modeling 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 generic local point identification of our heterogeneity structure that are very easy to check, and we show how it depends on the length of the panel. 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. (C) 2013 Elsevier B.V. All rights reserved.The second author gratefully acknowledges that this research was supported by a Marie Curie International Outgoing Fellowship within the 7th European Community Framework Programme, by grants ECO2012-31358, ECO2009-11165 and SEJ2006-05710 from the Spanish Minister of Education, MCINN (Consolider- Ingenio2010), Conse- jería de Educación de la Comunidad de Madrid (Excelecon project)Publicad