ABSTRACT
In a social science context, the simple deterministic equation must be extended by a random initial condition and stochastic equation errors that model neglected variables and misspecifications in the functional form of the differential equation. In economics, many variables are cumulated or averaged over a certain period of time. Mathematically speaking, differential equations are the continuous time analog of time series models, that is, the state vector is a function of the real parameter (time) and the desired time function is implicitly given in terms of time derivatives. Models with time-varying matrices are of empirical interest, because fluctuating exogenous variables may influence a time invariant system or the system itself changes its dynamics over time. The differential equation method was applied to clinical data that were collected in a psychiatric hospital at arbitrary time points. The data set contains many behavioral, socioeconomic, and medical variables.
