arXiv subjects

Hidehiko Ichimura

Publications and source records attributed to Hidehiko Ichimura.

5 recordsLinked to original sources

arXiv2021

The Influence Function of Semiparametric Estimators

Many useful parameters depend on nonparametric first steps. Examples include games, dynamic discrete choice, average exact consumer surplus, and treatment effects. Often estimators of these parameters are asymptotically equivalent to a sample average of an object referred to as the influence function. The influence function is useful in local policy analysis, in evaluating local sensitivity of estimators, constructing debiased machine learning estimators, in efficiency comparisons, and in formulating primitive regularity conditions for asymptotic normality, We show that the influence function is a Gateaux derivative with respect to a smooth deviation evaluated at a point mass. This result generalizes the classic Von Mises (1947) and Hampel (1974) calculation to estimators that depend on smooth nonparametric first steps. We give explicit influence functions for first steps that satisfy exogenous or endogenous orthogonality conditions. We use these results to generalize the omitted variable bias formula for regression to policy analysis for and sensitivity to structural changes. We apply this analysis and find no sensitivity to endogeneity of average equivalent variation estimates in a gasoline demand application.

stat.ME↗

arXiv2020

Locally Robust Semiparametric Estimation

Many economic and causal parameters depend on nonparametric or high dimensional first steps. We give a general construction of locally robust/orthogonal moment functions for GMM, where moment conditions have zero derivative with respect to first steps. We show that orthogonal moment functions can be constructed by adding to identifying moments the nonparametric influence function for the effect of the first step on identifying moments. Orthogonal moments reduce model selection and regularization bias, as is very important in many applications, especially for machine learning first steps. We give debiased machine learning estimators of functionals of high dimensional conditional quantiles and of dynamic discrete choice parameters with high dimensional state variables. We show that adding to identifying moments the nonparametric influence function provides a general construction of orthogonal moments, including regularity conditions, and show that the nonparametric influence function is robust to additional unknown functions on which it depends. We give a general approach to estimating the unknown functions in the nonparametric influence function and use it to automatically debias estimators of functionals of high dimensional conditional location learners. We give a variety of new doubly robust moment equations and characterize double robustness. We give general and simple regularity conditions and apply these for asymptotic inference on functionals of high dimensional regression quantiles and dynamic discrete choice parameters with high dimensional state variables.

math.ST↗

arXiv2018

Quantifying Health Shocks Over the Life Cycle

We first show (1) the importance of investigating health expenditure process using the order two Markov chain model, rather than the standard order one model, which is widely used in the literature. Markov chain of order two is the minimal framework that is capable of distinguishing those who experience a certain health expenditure level for the first time from those who have been experiencing that or other levels for some time. In addition, using the model we show (2) that the probability of encountering a health shock first de- creases until around age 10, and then increases with age, particularly, after age 40, (3) that health shock distributions among different age groups do not differ until their percentiles reach the median range, but that above the median the health shock distributions of older age groups gradually start to first-order dominate those of younger groups, and (4) that the persistency of health shocks also shows a U-shape in relation to age.

econ.EM↗

arXiv2015

Optimal Bandwidth Selection for the Fuzzy Regression Discontinuity Estimator

A new bandwidth selection method for the fuzzy regression discontinuity estimator is proposed. The method chooses two bandwidths simultaneously, one for each side of the cut-off point by using a criterion based on the estimated asymptotic mean square error taking into account a second-order bias term. A simulation study demonstrates the usefulness of the proposed method.

stat.ME↗

arXiv2015

Simultaneous Selection of Optimal Bandwidths for the Sharp Regression Discontinuity Estimator

A new bandwidth selection rule that uses different bandwidths for the local linear regression estimators on the left and the right of the cut-off point is proposed for the sharp regression discontinuity estimator of the mean program impact at the cut-off point. The asymptotic mean squared error of the estimator using the proposed bandwidth selection rule is shown to be smaller than other bandwidth selection rules proposed in the literature. An extensive simulation study shows that the proposed method's performances for the sample sizes 500, 2000, and 5000 closely match the theoretical predictions.

stat.ME↗