Dynamic modeling with structural equations and stochastic differential equations: Applications with the German Socio-economic Panel

The paper discusses an application of linear dynamic models to multi-wave longitudinal data. Starting from three-wave and four-wave simplex models using standard structural equations, linear dynamic state space models with stochastic differential equations are presented. The main differences between longitudinal structural equations (static view) and stochastic differential equations (dynamic view) are emphasized. Substantively, the models prove the relation, stability and change of two concepts in a period of 10 years: National Identity and Intention to stay in Germany. Data from a sample of migrant workers in Germany included in the German Socio-economic Panel (GSOEP) are used for the analyses. Results and further developments of dynamic models are discussed in the final section.