arXiv subjects

Ahnaf Rafi

Publications and source records attributed to Ahnaf Rafi.

5 recordsLinked to original sources

arXiv2026

Gaussian approximation for maximum score and non-smooth M-estimators with multiway dependence

The maximum score estimator of Manski (1975) provides an elegant approach to estimate slope coefficient in binary choice models without requiring parametric assumptions on the error distribution. However, under i.i.d. sampling, it admits a non-Gaussian limiting distribution and exhibits cube-root asymptotics, which complicates statistical inference. We show that, under multiway dependence, the maximum score estimator attains asymptotic normality at a parametric rate. We obtain this surprising result through the development of a general M-estimation theory that accommodates non-smooth objective functions under multiway dependence. We further propose and establish the validity of a bootstrap procedure for inference.

econ.EM↗

arXiv2024

Regression Discontinuity Design with Spillovers

This paper studies regression discontinuity designs (RDD) when linear-in-means spillovers occur between units that are close in their running variable. We show that the RDD estimand depends on the ratio of two terms: (1) the radius over which spillovers occur and (2) the choice of bandwidth used for the local linear regression. RDD estimates direct treatment effect when radius is of larger order than the bandwidth and total treatment effect when radius is of smaller order than the bandwidth. When the two are of similar order, the RDD estimand need not have a causal interpretation. To recover direct and spillover effects in the intermediate regime, we propose to incorporate estimated spillover terms into local linear regression. Our estimator is consistent and asymptotically normal and we provide bias-aware confidence intervals for direct treatment effects and spillovers. In the setting of Gonzalez (2021), we detect endogenous spillovers in voter fraud during the 2009 Afghan Presidential election. We also clarify when the donut-hole design addresses spillovers in RDD.

econ.EM↗

arXiv2023

Efficient Semiparametric Estimation of Average Treatment Effects Under Covariate Adaptive Randomization

Experiments that use covariate adaptive randomization (CAR) are commonplace in applied economics and other fields. In such experiments, the experimenter first stratifies the sample according to observed baseline covariates and then assigns treatment randomly within these strata so as to achieve balance according to pre-specified stratum-specific target assignment proportions. In this paper, we compute the semiparametric efficiency bound for estimating the average treatment effect (ATE) in such experiments with binary treatments allowing for the class of CAR procedures considered in Bugni, Canay, and Shaikh (2018, 2019). This is a broad class of procedures and is motivated by those used in practice. The stratum-specific target proportions play the role of the propensity score conditional on all baseline covariates (and not just the strata) in these experiments. Thus, the efficiency bound is a special case of the bound in Hahn (1998), but conditional on all baseline covariates. Additionally, this efficiency bound is shown to be achievable under the same conditions as those used to derive the bound by using a cross-fitted Nadaraya-Watson kernel estimator to form nonparametric regression adjustments.

econ.EM↗

arXiv2023

Bootstrap based asymptotic refinements for high-dimensional nonlinear models

We consider penalized extremum estimation of a high-dimensional, possibly nonlinear model that is sparse in the sense that most of its parameters are zero but some are not. We use the SCAD penalty function, which provides model selection consistent and oracle efficient estimates under suitable conditions. However, asymptotic approximations based on the oracle model can be inaccurate with the sample sizes found in many applications. This paper gives conditions under which the bootstrap, based on estimates obtained through SCAD penalization with thresholding, provides asymptotic refinements of size \(O \left( n^{- 2} \right)\) for the error in the rejection (coverage) probability of a symmetric hypothesis test (confidence interval) and \(O \left( n^{- 1} \right)\) for the error in the rejection (coverage) probability of a one-sided or equal tailed test (confidence interval). The results of Monte Carlo experiments show that the bootstrap can provide large reductions in errors in rejection and coverage probabilities. The bootstrap is consistent, though it does not necessarily provide asymptotic refinements, even if some parameters are close but not equal to zero. Random-coefficients logit and probit models and nonlinear moment models are examples of models to which the procedure applies.

econ.EM↗

arXiv2022

On the Performance of the Neyman Allocation with Small Pilots

The Neyman Allocation is used in many papers on experimental design, which typically assume that researchers have access to large pilot studies. This may be unrealistic. To understand the properties of the Neyman Allocation with small pilots, we study its behavior in an asymptotic framework that takes pilot size to be fixed even as the size of the main wave tends to infinity. Our analysis shows that the Neyman Allocation can lead to estimates of the ATE with higher asymptotic variance than with (non-adaptive) balanced randomization. In particular, this happens when the outcome variable is relatively homoskedastic with respect to treatment status or when it exhibits high kurtosis. We provide a series of empirical examples showing that such situations can arise in practice. Our results suggest that researchers with small pilots should not use the Neyman Allocation if they believe that outcomes are homoskedastic or heavy-tailed. Finally, we examine some potential methods for improving the finite sample performance of the FNA via simulations.

econ.EM↗