patent premium我的资源Regression and matching

1. Causes of different estimates by regression and matching method1）Misspecification of model ( assumptions of linearity and constant treatment effect in regression)Two methods estimate the ATT effect under different assumptions. Regression model estimates the average treatment effect assuming that the treatment effect is constant across subpopulation defined by the covariate values (Engelhardt, H., et al., 2009, p.217). Therefore, when the treatment effect is a non-constant function of the covariates, the regression model and the matching approach can achieve different estimates of the treatment effect even if each method produces unbiased estimates.Another big difference is that regression controls for those characteristics in a linear fashion. Matching allows researchers and policymakers to avoid often arbitrary assumptions about the functional form. Again, if model is not well specified, the estimates can be inconsistent (Engelhardt, H., et al., 2009, p.216).2）Data is imbalanced when using regression.When data in the treated and control groups have different multivariate distributions of the covariates, the fitted regression involves extrapolations (Engelhardt, H., et al., 2009, p.216). (后面截图的slides详细说明了该问题，可以使用matching来改进regression的结果)3) Missing confounders and other factors.Both the regression and matching approaches produce consistent estimates of the treatment effect only when we have controlled for all confounding covariates (Engelhardt, H., et al., 2009, p.217) (这一点我们能否改善？现在把能想到的covariates都已经加进来了).2. Possible solution: Run regression on matched dataset.“Its not matching or regression, its matching and regression. Matching is a way to discard some data so that the regression model can fit better.” (Andrew, 2014)我们存在的问题不是treatment的main effect结果不一致，而是moderating effect不一致，没有查到这方面的讨论。因为用matching的方法做moderating effect的文章本身就不多，文章里也没有出现matching结果与regression结果的对比。我建议再尝试一下先将数据进行matching，然后再跑回归的方法（这也是一种常用的处理方法），如果结果能支持的话这样既解决了counterfactual的问题，解释调节效应也比较规范。可参考下列资料：Source: Stuart, E, 2011Rubin (2001) argues that If any of these conditions is not satisfied, the differences between the distributions of covariates in the two groups must be regarded as substantial, and regression adjustment will be unreliable and cannot be trusted.3. References:Andew. (2014) /2014/06/22/matching-regression-matching-regression/.Engelhardt, H., et al. (2009). Causal Analysis in Population Studies: Concepts, Methods, Applications, Springer Netherlands.Rubin, D. B. (2001). Using propensity scores to help design observational studies: application to the tobacco litigation. Health Services and Outcomes Research Methodology, 2(3), 169-188.Stuart, E. (20