An alternative nesting link from the general NLPS to the restrictive LES demand functional forms is through the Restricted Non-Linear Preference System (RNLPS).
For this family of models, price flexibility is successively reduced by the increasingly restrictive constraints on the [Gamma] parameters as we move from NLPS to RNLPS to LES.
The estimated NLPS system, and all its nested models, satisfy most, but not all, of the regularity conditions required by utility theory.
Altogether, we have analysed ten models: NLPS, DCS-RNLPS, DT-RNLPS, DS-RNLPS and the nested submodels derived for the first two: RNLPS, LPS, LES, NS-RNLPS, DCS-LES and NS-LES.
2 The Estimation Results for NLPS, LPS, RNLPS and LES(14)
Besides the uncertainty of having attained NIL estimates, the data do not seem fine enough to allow the estimation of models as complex as NLPS.
From the values of the LR tests, shown in Table 1, it appears that all the models nested by both the NLPS and the DCS-RNLPS must be rejected.
3) The RNLPS non-linearity allows sufficient flexibility in the underlying demand system to make it successful in most empirical applications [see Chatterjee, Michelini and Ray (1994), and references therein] but, at the same time, the RNLPS has a simpler parameterisation than the NLPS form, and therefore is usually easier to estimate.