For the full use of the theoretical development to derive three alternative specifications of the direct, inverse, and mixed demand systems, the following empirical procedure is proposed to address three issues of the identification, functional form, and comparisons among three specifications: (i) the graphical causal methods of the PC and GES algorithms are applied to obtain an empirical guidance for the specification choice among three demand specifications; (ii) the inferred specifications are estimated with the generalized functional forms, which extend the synthetic approach based on the differential functional form framework; and the statistical tests of synthetic coefficients are used to choose the best parameterizations among the Rotterdam, LA/AIDS, CBS, NBR, and generalized functional forms within each of the three specification; (iii) the estimated results of the chosen parameterization are interpreted and compared based on the identified relationships among three demand specifications; Finally, the overall results of three alternative specifications are evaluated based on the model selection frameworks. The validity of the procedure is illustrated by using retail checkout scanner data of soft drinks consumptions.


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