Parametric and nonparametric income distribution estimators in CGE micro-simulation modeling

We consider the issue of income distribution modeling in the context of poverty analysis based on computable general equilibriummicro-simulationmodels. Speciffically, we study the situation where a poverty index of the FGT class is used to measure the impact of a given policy on the level of poverty in a population, which usually implies computing the chosen index in the pre and post simulation samples. Because FGT indexes are functions of the unknown distribution of income in the population, an estimator must be used. The empirical distribution function (EDF) is by far the most commonly used estimator in practice. It is, however, not the only available consistent estimator and there may be situations in which a different estimator would be able to provide more accurate results. For example, one shortcoming of the EDF is that it is discontinuous, which implies that, for any poverty line z, there is a neighborhood around z within which a given FGT index is constant. Even though this neighborhood becomes arbitrarily small as the sample size increases, this may cause some problems in moderately sized samples. An alternative that solves this problem is to use a smooth estimator of the population income distribution. Broadly speaking, two types of such estimators are available: parametric and nonparametric ones. In the first case, one has to chose a particular parametric form for the distribution function and estimate its parameters. The main drawback of this approach is the difficulty associated with the selection of the functional form, which must be done so as to balance infinite sample bias and variance. Oftentimes, this can be done using statistical tests and information criteria. The nonparametric approach sidesteps this functional form issue by using kernel density estimators that only impose mild restrictions on the distribution function. This is obviously an important advantage, but its cost is that the accuracy of these estimators typically depends to a large extent on the bandwidth used in the kernel function. Another advantage of the nonparametric kernel approach is that is nests the EDF as a special case. Boccanfuso, Decaluwé and Savard (2008) studied the use of parametric disribution estimators and found that they work quite well in some empirical applications. We propose to extend their work in two ways. First, we consider a larger set of parametric functions, including the 5 parameter generalized beta distribution and some of its special cases. We also consider likelihood ratio tests and information criteria as a way to chose the best fitting parametric estimator. Second, we use non-parametric kernel estimators and study their accuracy under different bandwidth selection schemes. Lastly, we provide Monte Carlo comparisons of the accuracy of these methods with the widely used EDF. See above See above