DDCM: Dynamic Discrete Choice Models – Modelling and specification of dynamics in discrete choice models

• Applicant: Professor Dr. Dietmar Bauer
• Subject Area: Statistics and Econometrics
• Term: since 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 545500151

Discrete choice models are used in many different disciplines. Often, they are applied in panel data sets, where individuals repeatedly make choices. Consequently, often there are dynamics at work, whereby future choices are influenced by experiences from past choices, preferences of deciders evolve over time. At the same time, preferences are inhomogeneous in the population. Including both dynamics as well as inhomogeneities into models is complicated. Different disciplines, therefore, have developed various ways to reduce model complexity. In many cases, these are very specific for the application. In other cases, the most widely applied models contain assumptions that are hard to defend, like the possibility to observe states summarizing the time dependence of preferences. In this project we extend the methods for the specification and estimation of dynamic discrete choice models combining two approaches: On the one hand the usage of composite marginal likelihood (CML) based on pairs of choices provides an easier to work with criterion function. On the other hand so called subspace methods provide simple and hence easily adaptable ways to estimate linear dynamic models. In both cases the extended methods will create possibilities that are not accessible using conventional likelihood methods. Here, ease of application is achieved by using the CML framework instead of the classical likelihood setting, as the CML only requires the computation of probabilities of pairs of choices, while the likelihood includes joint treatment of all choices by a decider. Another advantage of the pairwise CML setting is that comparing different groupings of the pairs allows to detect multiple patterns of heterogeneity as well as temporal correlations: Comparing pairs of early choices to pairs of late choices, for example, can used in order to detect structural breaks. Examining only pairs of observations with a given time lag allows the extraction of autocovariances of the error terms at the lag considered. In the project we will investigate, how these estimated autocovariances, subsequently, can be used as input to so called subspace methods, which are used to specify and estimate linear dynamic state space models. The subspace methods will be extended in the project to cater the panel case and take the noise in the measurement of the autocovariances into account. These initial estimates then can be used in more general CML maximization procedures, where for the pairwise CML functions we will examine optimal choice of power weights for the various pairs. Additionally, we will investigate usage of the Mundlak device to incorporate and differentiate fixed and random effects to encode inhomogeneities. After the completion of the project an R package for detecting temporal dynamics and inhomogeneities, specification of the appropriate functional form and optimal estimation within the pairwise CML framework will be available.

• DFG Programme: Research Grants