Several topics related to dummy variables are discussed in the literature that are rather advanced, including (1) random, or varying, parameters models, (2) switching regression models, and (3) disequilibrium models.
In the regression models considered in this text it is assumed that the parameters, the p's, are unknown but fixed entities. The random coefficient models—and there are several versions of them—assume the p's can be random too. A major reference work in this area is by Swamy.21
In the dummy variable model using both differential intercepts and slopes, it is implicitly assumed that we know the point of break. Thus, in our savings-income example for 1970-1995, we divided the period into
21P. A.V.B. Swamy, Statistical Inference in Random Coefficient Regression Models, SpringerVerlag, Berlin, 1971.
CHAPTER NINE: DUMMY VARIABLE REGRESSION MODELS 323
1970-1981 and 1982-1995, the pre- and postrecession periods, under the belief that the recession in 1982 changed the relation between savings and income. Sometimes it is not easy to pinpoint when the break took place. The technique of switching regression models (SRM) is developed for such situations. SRM treats the breakpoint as a random variable and through an iterative process determines when the break might have actually taken place. The seminal work in this area is by Goldfeld and Quandt.22
Special estimation techniques are required to deal with what are known as disequilibrium situations, that is, situations where markets do not clear (i.e., demand is not equal to supply). The classic example is that of demand for and supply of a commodity. The demand for a commodity is a function of its price and other variables, and the supply of the commodity is a function of its price and other variables, some of which are different from those entering the demand function. Now the quantity actually bought and sold of the commodity may not necessarily be equal to the one obtained by equating the demand to supply, thus leading to disequilibrium. For a thorough discussion of disequilibrium models, the reader may refer to Quandt.23
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