Continuous panel models with time dependent parameters

It is shown how the likelihood function can be computed in this general linear setting by using a Kaiman filter algorithm. The estimation method is tested in a simulation study using a bivariate growth model and applied to the Brownian bridge.

Panel data are modeled as dynamic structural equations in continuous time t (stochastic differential equations). The continuously moving latent state vector y(t) is mapped to an observable discrete time series (or panel) zni = zn (t i,) with the help of a measurement equation including errors of measurement (continuous‐discrete state space model).

Therefore the approach is able to handle data with irregularly observed waves, missing values and arbitrarily interpolated exogenous influences (control variables). In order to model development and growth models, the system parameter matrices are assumed to be time dependent.

Key words:

• Panel data
• stochastic differential equations
• continuous‐discrete state space model
• time dependent parameters
• Kaiman filter
• growth models