The Introduction of Constraints in Lancaster's Qualitative Comparative Statics Algorithm - Gillen, William J.; Guccione, Antonio (Quarterly Journal of Economics, 1990)
The qualitative restrictions available on the individual coefficients of a model are frequently insufficient to sign its multipliers. To eliminate this lack of determinacy, additional relations among coefficients must be incorporated into the analysis. In 1966 Lancaster proposed an algorithm for qualitative comparative statics with the very useful property . . that certain types of information, not qualitative in the strict sense, can be incorporated directly and quite simply into the system [1966, p. 281]. The same procedure was later adopted by Ritschard for the analysis of large-sized policy models [1983, p. 1164]. However, Burns and Formuzis have argued that the results obtained in the presence of constraints, are dependent on the order in which the original equations of the model were written [1970, p. 697]. To eliminate this difficulty, they suggested altering the order of the equations by trial and error, a procedure that is inefficient and will not work in many instances. The purpose of this note is to systematize the introduction of constraints. After a brief restatement of Lancaster's method, an algorithm is presented that provides information on the nature of the constraints needed to produce unambiguous solutions. Alternatively, if the analyst has an intuitive notion of the signs of the multipliers, the procedure can be used to indicate the form of constraints that will produce them. Basically, the method proposed generates sign patterns (including zeros) of additional equations that will yield any given solution consistent with the initial specification of the model. These additional equations are linear combinations of those in the given system. In fact, they constitute the minimum number of such combinations that can yield a determinate solution. It may be difficult, especially in large models, to reconcile the available a priori information with the sign patterns implied by the algorithm. In such cases, to supply the analyst with additional sets