Nonparametric Policy Analysis

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Abstract
This article considers the problem of predicting the mean effect of a change in the distribution of certain policy-related variables on a dependent variable (Y). This is conventionally done using a parametric model. If, however, the conditional expectation of Y, given policy and nonpolicy variables X, is unaltered by the policy intervention, and if the support of X after the policy intervention lies within the support of X before the intervention, then this analysis can be performed nonparametrically. The proposed nonparametric estimator is developed for the model Yj = g(Xj ) + A′dj + uj where g(·) is a continuous unknown function of the continuous variables X, dj is an m-vector of dummy variables, A is an m-vector of unknown parameters representing fixed cell-specific effects, and uj is an error term with E(uj | xj, dj ) = 0. The estimand is B = Eg(Xj *) – Eg(Xj ), where X and X* (respectively) denote the values of X before and after the policy intervention. A nonparametric estimator Bn is proposed. The estimator is the sample average of the difference between the kernel regression estimates of E(Y | Xj *, dj ) and E(Y | Xj, dj ). To estimate these conditional expectations, A is first estimated using the residuals from nonparametric regressions of Y and d on X. The consistency and asymptotic normality of Bn are studied. The estimator, along with two estimators of its variance, is examined in a Monte Carlo experiment. In this experiment, the cost of using the nonparametric estimator, relative to the efficient parametric estimator, is found to be modest in terms of increased root mean squared error. When the dimension of X is large and the sample size is small, however, the nonparametric estimator can exhibit substantial bias.

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