Most Difference-in-Difference (DD)

Most Difference-in-Difference (DD)

SummaryWe revisit the classic semi-parametric problem of inference on a low-dimensional parameter θ 0 in the presence of high-dimensional nuisance parameters η 0 . We depart from the classical setting by allowing for η 0 to be so high-dimensional that the traditional assumptions (e.g. Donsker properties) that limit complexity of the parameter space for this object break down. To estimate η 0 , we consider the use of statistical or machine learning (ML) methods, which are particularly well suited to estimation in modern, very high-dimensional cases. ML methods perform well by employing regularization to reduce variance and trading off regularization bias with overfitting in practice. However, both regularization bias and overfitting in estimating η 0 cause a heavy bias in estimators of θ 0 that are obtained by naively plugging ML estimators of η 0 into estimating equations for θ 0 . This bias results in the naive estimator failing to be N −1/2 consistent, where N is the sample size. We show that the impact of regularization bias and overfitting on estimation of the parameter of interest θ 0 can be removed by using two simple, yet critical, ingredients: (1) using Neyman-orthogonal moments/scores that have reduced sensitivity with respect to nuisance parameters to estimate θ 0 ; (2) making use of cross-fitting, which provides an efficient form of data-splitting. We call the resulting set of methods double or debiased ML (DML). We verify that DML delivers point estimators that concentrate in an N −1/2 -neighbourhood of the true parameter values and are approximately unbiased and normally distributed, which allows construction of valid confidence statements. The generic statistical theory of DML is elementary and simultaneously relies on only weak theoretical requirements, which will admit the use of a broad array of modern ML methods for estimating the nuisance parameters, such as random forests, lasso, ridge, deep neural nets, boosted trees, and various hybrids and ensembles of these methods. We illustrate the general theory by applying it to provide theoretical properties of the following: DML applied to learn the main regression parameter in a partially linear regression model; DML applied to learn the coefficient on an endogenous variable in a partially linear instrumental variables model; DML applied to learn the average treatment effect and the average treatment effect on the treated under unconfoundedness; DML applied

This paper uses political reservations for women in India to study the impact of women's leadership on policy decisions. Since the mid-1990's, one third of Village Council head positions in India have been randomly reserved for a woman: In these councils only women could be elected to the position of head. Village Councils are responsible for the provision of many local public goods in rural areas. Using a dataset we collected on 265 Village Councils in West Bengal and Rajasthan, we compare the type of public goods provided in reserved and unreserved Village Councils. We show that the reservation of a council seat affects the types of public goods provided. Specifically, leaders invest more in infrastructure that is directly relevant to the needs of their own genders. Copyright The Econometric Society 2004.

Women empowerment and economic development are closely related: in one direction, development alone can play a major role in driving down inequality between men and women; in the other direction, empowering women may benefit development. Does this imply that pushing just one of these two levers would set a virtuous circle in motion? This paper reviews the literature on both sides of the empowerment—development nexus, and argues that the interrelationships are probably too weak to be self-sustaining, and that continuous policy commitment to equality for its own sake may be needed to bring about equality between men and women. (JEL I14, I24, I32, I38, J13, J16, O15)