Abstract
The economic researcher is sometimes confronted with panel datasets that come from a population made of a finite number of subpopulations. Within each subpopulation the individuals may also be heterogenous according to some unobserved characteristics. A good understanding of the behavior of the observed individuals may then require the ability to identify the groups to which they belong and to study their behavior across groups and within groups. This may not be a complicated exercise when a group indicator variable is available in the dataset. However, such a variable may not be included in the dataset; and as a result, the econometrician is forced to work with the marginal distribution of the observed response variable, which takes the form of a mixture distribution.One can model a given response variable with a variety of mixture distributions. In this paper, I present several related mixture models. The most flexible one is an extension of the model by Kim et al. (2008) to the panel data setting.I have reviewed the estimation of some of these models by the Expectation-Maximization (EM) algorithm. The intent is to exploit the nice convergence properties of this algorithm when it is difficult to find good starting values for a Newton-type algorithm. I have also discussed how to compare these models and ultimately identify the one that provides the best fit to the data set under investigation. As an application I examine the investment behavior of U.S. manufacturing firms.
Highlights
To model the heterogeneity of economic agents I present a series of panel data mixture models of increasing degree of flexibility and complexity and show how they can be used to handle at least two types of heterogeneity: heterogeneity with respect to group membership, and heterogeneity with respect to within group differences in individual characteristics
Heterogeneity is an important problem faced by the statistician or the econometrician trying to infer the behavior of economic agents from available data sets
Hidden Markov Model with Time Varying Transition Matrix, endogeneity and random effects (M9) For a panel data set, a natural extension of the previous model is obtained by adding random effects in the components using the specifications in Eqs. (30) - (32)
Summary
To model the heterogeneity of economic agents I present a series of panel data mixture models of increasing degree of flexibility and complexity and show how they can be used to handle at least two types of heterogeneity: heterogeneity with respect to group membership, and heterogeneity with respect to within group differences in individual characteristics. 3. Substitute E wit|yit; θ 0 in the complete-data log-likelihood Hidden Markov Model with Time Varying Transition Matrix and Random Effects (M7) Even though the groups are homogeneous with respect to the financial characteristics used to form them, there are still some unobserved characteristics with respect to which the firms within a given group can be considered to be heterogeneous.
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