dimensionality reduction when causal inference is the goal

过去十年产生的大量数据对计量经济学来说是福也是祸。有充分的证据表明，90%的可用数据仅在过去两年中产生，因此允许比以前更丰富的回归量、工具和控制范围。相反，“大p小n”范式对传统计量经济学提出了许多挑战。在最基本的层面上，当普通最小二乘估计量pn不再是唯一的。一个更有趣的问题是当p很大时回归量之间的伪共线性，这反过来又增加了错误模型选择的可能性。作为一个潜在的博士研究课题，我对研究在稀疏性假设下估计的高维数据的计量经济模型的性质很感兴趣。虽然已经存在大量关于在数据丰富的环境中进行预测的文献，但我的兴趣主要集中在为因果推理建立模型。在这个早期阶段，我有兴趣扩展Chernozhukov等人（2017）开发的建模程序；他们的方法对我来说特别有趣，因为即使在错误的模型选择下，也可以一致地估计因果参数。作为起点，我注意到Cho和Fryzlewicz提出的通过倾斜的变量选择似乎特别适合这种方法。我也有兴趣将这种方法扩展到时间和空间相关的数据，但我注意到Chernozhukov等人（2018）已经取得了重大进展。

The vast quantities of data generated in the last decade presents a blessing and a curse for econometrics. It is well documented that 90% of all available data was generated in the last two years alone, thus allowing for a far richer spectrum of regressors, instruments, and controls than previously possible. Conversely, the 'large p small n' paradigm poses numerous challenges for conventional econometrics. At the most fundamental level, when pn the ordinary least squares estimator ceases to be unique. A more interesting problem is posed by spurious collinearity among regressors when p is large, which in turn increases the likelihood of erroneous model selection . As a potential topic for doctoral studies, I am interested in investigating the properties of econometric models for highly dimensional data estimated under sparsity assumptions. While a large body of literature already exists on forecasting in data-rich environments, my interests center specifically around building models for causal inference. At this early stage, I am interested in extending the modelling procedure developed by Chernozhukov et al. (2017); their approach is particularly interesting to me, as causal parameters can be consistently estimated even under erroneous model selection. As a starting point, I note that variable selection via tilting, as proposed by Cho and Fryzlewicz seems particularly amenable to the approach. I would also be interested in extending the approach to data that is correlated in time and space, however I note that significant progress has already been made by Chernozhukov, et al. (2018).