Instrumental variable models allow us to identify a causal function between covariates X and a response Y, even in the presence of unobserved confounding. Most of the existing estimators assume that the error term in the response Y and the hidden confounders are uncorrelated with the instruments Z. This is often motivated by a graphical separation, an argument that also justifies independence. Posing an independence condition, however, leads to strictly stronger identifiability results. We connect to existing literature in econometrics and provide a practical method for exploiting independence that can be combined with any gradient-based learning procedure. We see that even in identifiable settings, taking into account higher moments may yield better finite sample results. Furthermore, we exploit the independence for distribution generalization. We prove that the proposed estimator is invariant to distributional shifts on the instruments and worst-case optimal whenever these shifts are sufficiently strong. These results hold even in the under-identified case where the instruments are not sufficiently rich to identify the causal function.
翻译:乐器变量模型允许我们确定共变 X 和响应 Y 之间的因果函数, 即使存在未观察到的混乱。 多数现有估计者认为, 响应Y 和隐藏的混淆器中的错误词与乐器 Z 并不相干。 这通常是由图形分解驱动的, 这也是独立的理由。 但是, 假设独立条件会导致严格的可识别性结果。 我们连接到计量经济学的现有文献, 并提供一种实用的方法来利用独立, 并且可以与任何基于梯度的学习程序相结合。 我们发现, 即使在可识别的环境下, 考虑到更高时刻, 我们利用分布的特性可能会产生更好的有限抽样结果。 此外, 我们利用了分布的特性。 我们证明, 拟议的估计符无法在仪器上分配变化, 最坏的情况是, 只要这些变化足够强大, 最坏的情况也会存在。 这些结果甚至存在于未查明的案例中, 因为仪器不够丰富, 无法识别因果关系。