Time Varying Parameters with Random Components: The Orange Juice Industry

The assumption of nonstochastic parameters has long been recognized as restrictive to the solution of many marketing problems and to economic modeling in general. Parameter variation historically has been treated with the use of nonstochastic adjustments through interaction variables and the use of proxy dummy and trend variables. Though these empirical techniques in many cases give reasonable results, they presuppose that the researcher can specify the nature of the parameter change. In fact, it may not be obvious that random parameters are part of the estimation problem. Furthermore, specification of structural shifts in parameters is usually difficult. Comparison of parameter changes through techniques such as grouping of data and using various F-tests is most often dependent on the criteria for grouping (Maddala, p. 390–404). Also, the procedure fails to identify the dynamic path of adjustments that must have occurred when various F-tests indicate that parameters have changed. Other approaches to determining structural shifts in parameters may require elaborate search procedures. To limit the extent to which the search is required, restrictive assumptions about many of the parameters are sometimes made (Simon).