Dynamic cause – Effect models and their switching trends - Selected problems (mathematical economics approach)

The paper consists of two parts devoted to the cause-effect dynamic models. In each part of the deterministic properties of the dynamic version of the model are presented. Thus, each of the considered dynamic models can be presented in the form of an equivalent for it the switching trend. Switches in this trend were exogenous variables of the dynamic model expressed in terms of the respective functions. This approach allowed:first, clearly define short-term and long-uncorrected (Part I) and corrected (Part II) interaction effects of exogenous variables on the endogenous variable in a dynamic model; second, to simulate the behavior of the endogenous variable model for complex dynamic changes of exogenous variables and present graphs switching trend with its boundary levels; third, check the equivalence considered causal dynamic model of the trend defined correctness of the switching and impact effects of exogenous variables on the endogenous variable.For each version of the model a dynamic random effects impact on the formation of endogenous variable described by the trend of switching was assumed. It allowed to check the properties of estimates of causal dynamical model based on data generated by the trend in terms of stochastic switching.Generally, the first part of the paper is devoted to the dynamic models in which the exogenous variables are no time delays, which corresponds roughly to a certain concept of partial adjustment model (PAM). The second part of the paper focuses on dynamic models in which each of the exogenous variables, accompanied by the same variable with one-period time delay. Thus, this corresponds to the concept of error correction models (ECM). In both parts of the paper the problem of deterministic seasonality quarterly trends generated using switching was considered. Recursive set of equations was formulated so that on the basis of structural parameters of variables occurring in the zero-ones-in the dynamic model can clearly determine the effects of seasonal variations indicative of the level of endogenous variable switching trend, which is the level determined by exogenous factors model in a given period. In conclusion, the second part of the paper presents the results of the procedure specifications and estimates of cause-effect dynamic model describing the evolution of the level of wages in Poland. The model was estimated on the basis of statistical data for the period from 1 quarter of 1996 to the 4th quarter of 2013