Non-standard method of discretization on the example of Haavelmo Growth Cycle model

In the theory of economics most models describing economic growth make use of differential equations. The examples are Solow's and Haavelmo's models. However, when they are used by econometricians many questions arise. Firstly, economic data are presented in discrete form, which implies the use of difference equations. Secondly, the mode transition from continuous form to the discrete one in order to estimate its parameters is still controversial. It has been observed for sometime that standard (classical) discretization methods of differential equations often produce difference equations that do not share their dynamics (for example produce chaotic behavior). The essence of above-mentioned problems and proposal of solving them will be presented on the basis of Haavelmo model.