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Measuring Compliance
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which method is best.73 Though the technical differences between the two
methods are many, their relative advantageousness can be assessed with
reference to two central methodological characteristics:
i. The econometric approach is parametric so the shape of the frontier has to
be specified from the very beginning. This could make the model vulnerable
to functional form misspecification, which means that the model might not
be accounting for some important nonlinearity in the relationship between
variables. The mathematical approach, on the other hand, is non-parametric
so has the advantage that no assumption has to be made as to the shape of
the frontier.
ii. The econometric approach is stochastic, which allows for the model to distinguish between the effects of inefficiency and the effects of random noise.
The mathematical approach, however, is deterministic and provides only
a general measure of inefficiency, which is likely to hide within it random
noise, and hence risk being either under or overestimated.
Deciding when one method should be chosen over the other comes
down to an assessment of appropriateness to the individual dataset and the
research question(s) being asked. Presently, the primary objective is to determine the level of welfare basket attainment expected of each duty-bearer
in order to reveal whether this level is in fact being met within and across
countries. The data involved will be, by nature, highly heterogeneous, of
widely differing quality, and will therefore likely carry noise. As such, the
certain advantages of a model that allows for real non-compliance to be
distinguished from random noise must outweigh the potential limitations
posed by a risk of form misspecification. In this case, proceeding along an
econometric path would be most prudent.
With this strategy and a description of maximum available resources in
hand, both the level of social welfare attainment to which individuals have
a right and an estimate of how well duty-bearers are doing with respect to
what they owe can be estimated through a basic production function of the
following simple form:74
γit = α +Χ lit β + zli γ +νit–ui
where i = 1, . . . N and t = 1, . . . T. N is the duty-bearer, T is the year,
yit denotes the output (welfare basket attainment), X’it is the set of inputs
(maximum available resources), and z’I captures time invariant heterogeneity across and within countries (population density and favorability of the
73. See, e.g., id. at 112–14.
74. Dennis Aigner, C.A. Knox Lovell, & Peter Schmidt, Formulation and Estimation of Stochastic Frontier Production Function Models, 6 J. Econometrics 21 (1977); Wim Meeusen
& Julien van den Broeck, Efficiency Estimation from Cobb-Douglas Production Functions
with Composed Error, 18 Int’l Econ. Rev. 435 (1977).