This paper proposes a dynamic Markov model for the estimation of binary state-to-state transition probabilities from a sequence of independent cross-sectional samples. It discusses parameter estimation and inference using maximum likelihood (ML) methodology. The model is illustrated by the application of a three-wave panel study on pupils' interest in learning physics. These data encompass more information than what is used to estimate the model, but this surplus information allows us to assess the accuracy and the precision of the transition estimates. Bootstrap and Bayesian simulations are used to evaluate the accuracy and the precision of the ML estimates. To mimic genuine cross-sectional data, samples of independent observations randomly drawn from the panel are also analyzed.
Repeated cross-sectional data contain information on independent cross-sections of individual units at two or more points in time. Estimation of dynamic models with such data is made difficult by the general lack of information on lagged dependent and independent variables and the consequent unobservability of the intertemporal covariances needed to identify and estimate dynamic models. It is demonstrated here that the parameters of such models, both linear and nonlinear, both with and without fixed individual effects, are identified and can be consistently estimated with the imposition of certain restrictions. The paper includes an examination of the identification and estimation with repeated cross-sectional data of dynamic discrete dependent variable models, which can be parameterized in terms of transition rates between the different cross-sections.
Berzelius failed to make use of Faraday's electrochemical laws in his laborious determination of equivalent weights.