High-Dimensional Methods and Inference on Structural and Treatment Effects

using scanner datasets that record transaction-level data for households across a wide range of products, or text data where counts of words in documents may be wide range of products, or text data where counts of words in documents may be used as variables. In both of these latter examples, there may be thousands or tens used as variables. In both of these latter examples, there may be thousands or tens of thousands of available variables per observation. of thousands of available variables per observation. Second, even when the number of available variables is relatively small, Second, even when the number of available variables is relatively small, researchers rarely know the exact functional form with which the small number of researchers rarely know the exact functional form with which the small number of variables enters the model of interest. Researchers are thus faced with a large set variables enters the model of interest. Researchers are thus faced with a large set of potential variables formed by different ways of interacting and transforming the of potential variables formed by different ways of interacting and transforming the underlying variables. underlying variables.