An alternative semiparametric estimate of the base-independence equivalence scale: an application to US consumer expenditure survey data

Abstract

This study proposes a semiparametric estimate and a test for base-independence equivalence scale. Our semiparametric approach is based on nondensity weighted loss function in contrast to Pendakur's (1999) density weighted loss function. Simulation results indicate that our specification tends to produce a smaller bias in estimating the equivalence scale and thus a more reliable test for base-independence hypothesis. We also provide an application using US Consumer Expenditure Survey data.

Notes

¹ As a practical measure, the parameter reflecting the composition of households can be described, for example, N ^α where N is the number of family and 0 ≤ α ≤ 1. Antolin et al . (1999) considered the model when α = 2/3 Atkinson (1998) allocated the fixed values 1, 0.7 and 0.5 for the first adult, an additional adult and a child, respectively.

² In Pendakur's (1999) application, the monotone property of the equivalence scale did not appear in the fully parametric specification.

³ When the regressors in one sample are differently distributed from those in the other, , that is, θ has the slower convergence rate.

⁴ Pendakur (1999) did not examine the size of test using boostrap resampling.

⁵ While Pendakur in his article used a grid search over the wide span of parameters to minimize, we use the Newton–Rapson algorithm without boundary restrictions.

⁶ With Canadian Family Expenditure Survey data, Pendakur's (1999) semiparametric tests do not reject the shape-invariance hypothesis in most comparison pairs.

⁷ Fry et al . (2000) proposed the modified methodology where the observed budget share is zero in the log-ratio Engel curves.