Abstract: Many causal estimands, such as average treatment effects under unconfoundedness, can be written as continuous linear functionals of an unknown regression function. We study a weighting estimator that sets weights by a minimax procedure: solving an optimization problem that trades off worst‑case conditional bias against variance. Despite its growing use, general root‑n theory for this method has been limited. This paper fills that gap. Under regularity conditions, we show that the minimax linear estimator is root‑n consistent and asymptotically normal, and we derive its asymptotic variance. These results justify ignoring worst‑case bias when forming large‑sample confidence intervals and make inference less sensitive to the scaling of the function class. With a mild variance condition, the estimator attains the semiparametric efficiency bound, so an augmentation step commonly used in the literature is not needed to achieve first‑order optimality. Evidence from simulations and three empirical applications, including job‑training and minimum‑wage policies, points to a simple rule: in designs satisfying our regularity conditions, standard‑error confidence intervals suffice; otherwise, bias‑aware intervals remain important.

Abstract: We consider a two-step estimation procedure to estimate the panel sample selection models with interactive effects. In the first step, we follow the Robinson (1988) procedure to remove the sample selection factors. In the second step, we control the interactive effects. When the cross-section dimension N is large, we propose to use the Pesaran (2006) common correlated effects approach, and when the time series dimension T is large and N is finite we propose to follow the Hsiao, Shi, and Zhou (2022) transformed estimation procedure to eliminate the interactive effects. We show that the resulting estimators are consistent and asymptotically normally distributed. A limited Monte Carlo study is conducted, showing our methods appear to work well in a finite sample. An empirical illustration on female wage rate determination shows that an extra year of work experience could raise the expected log wage rate by 0.1507 under our maintained hypothesis, while neglecting sample selection or interactive effects could lead to seriously biased estimates.

Abstract: This paper develops a method for causal inference under the framework of high-dimensional generalized linear models with binary outcomes and general link functions. Recognizing the potential bias associated with regularized regression techniques like Lasso, we augment the regression plug‑in estimator with a novel weighting adjustment for debiasing. Our method frames an optimization problem aimed at controlling the bias and variance, suitable for both sparse and dense contrasts of the outcome model parameters. Unlike traditional methods that rely on the inverse of estimated propensity scores, our method computes debiasing weights directly from an optimization problem, leveraging structural assumptions of the outcome model. We provide a root-n consistent and asymptotically normally distributed estimator. Simulation results demonstrate the superior performance of our approach in comparison to alternatives such as inverse propensity score estimators and double machine learning estimators in finite samples. An empirical application demonstrates the practical implementation of our method.

Abstract: We consider panel interactive effects models when regressors are endogenous with instruments that could be correlated with the interactive effects (e.g., Nakamura and Steinsson (2014)). We propose a transformed generalized method of moment estimator (TGMM) and show that it is asymptotically normally distributed. It does not requite both (N, T) to go to infinity. All it requires is either N or T to go to infinity to achieve consistency and asymptotic normality. Neither do we need to worry about the asymptotic bias issue whether the idiosyncratic error terms are weakly cross-sectional or time dependent commonly associated with principal component approach to estimate factor structure. Monte Carlo studies show that the TGMM performs well in terms of bias, root mean of square error and size of the tests with finite sample.

Abstract: Generating counterfactuals through treating a variable as a function of its own past values or treating a variable as a function of other units, typically being referred to as horizontal or vertical regression, respectively, is widely used in the panel measurement of treatment effects. However, their inferences are often based on different assumptions for the data generating process. We consider unifying the underlying assumptions of the two approaches by a factor approach and compare their respective predictive power in terms of the sample configuration of the cross-section dimension N and the time dimension T.