Direct estimation of equivalence scales and more evidence on independence of base
利用收入满意度数据直接估计家庭等价尺度，检验了等价尺度与收入无关的假设，发现不同家庭类型的规模经济随收入变化模式不同。
We explore a direct approach to estimating household equivalence scales from income satisfaction data. Our method differs from previous approaches to using satisfaction data for this purpose in that it can be used to directly fit and evaluate closed-form and non-parametric equivalence scales of any desired form. Its flexibility makes it easy to consider specific aspects such as income dependence or more specific information on household composition (such as whether household members live in a partner relationship). We estimate and evaluate a number of scales used in the literature. If the equivalence scale is assumed to be independent of income and to depend only on household size, we do not reject the validity of the widely used square-root scale at conventional significance levels. We also test GESE and GAESE restrictions (Donaldson and Pendakur, 2003, 2006) and investigate in detail to what extent household economies of scale depend on income. Our results suggest that the income dependence differs fundamentally across household types (rising economies of scale for ‘family’ households, falling economies of scale for multi-adult households without children and no income dependence for other households).