再看看RW的文章:
Most nonlinear price schedules take the form of multi-part tariffs. Since Gabor (1955),
economists have realized that multi-part tariffs imply that the consumer faces a nonlinear (i.e. a
kinked) budget constraint. The demand behaviour of a utility-maximizing consumer thus depends
not on the average price, nor any single marginal price, but on the entire price schedule. The
standard econometric approach to demand analysis in this setting, which traces to Hall (1973), is
to “linearize” the budget constraint. This amounts to using the plane tangent to the consumer’s
nonlinear budget constraint at the optimal consumption bundle as its linear approximation. By
doing so, one can express demand under nonlinear pricing in terms of the ordinary demand
function of classical consumer theory, which assumes a linear budget constraint.
To be specific, let x(p, y) be the ordinary demand function that indicates the consumer’s
desired quantity facing a constant (marginal and average) price p and income y. Suppose, however, that the consumer faces an increasing price schedule s(p) of the form depicted in Figure 1.
Here the consumer pays a low price p1 for each unit up to the quantity xˉ, and a higher price p2
thereafter. Then the optimal consumption level x∗ satisfies
From an econometric perspective, equation (3) is a nonlinear censored regression model in
which the censoring occurs in the interior of the distribution of outcomes rather than the
tails. Such models are generally estimated by maximum likelihood methods, using the discrete
structure in (3) to derive the change-of-variables from an (assumed) marginal distribution of
ε to the distribution of x∗. Burtless and Hausman (1978), with later extensions by Hausman
(1985), Moffitt (1986), and others, develop likelihood functions for models with this structure.
Unfortunately, maximum likelihood estimation quickly becomes computationally intractable
when the consumption outcomes from a mixed discrete/continuous model are aggregated over
time. This problem renders likelihood methods infeasible for our application.9 Consequently, we
pursue a moment-based approach to estimation.
这样的段落由很多,几乎就是原文翻译,就算借鉴模型也不至于全文翻译吧。。。


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