Why Subsample-Based Proxies Should Not Be Used As Dependent Variables

Researchers often use non-linear distributional properties of accounting variables (e.g., standard deviation of demand conditional on managers’ information) to measure economic constructs like demand uncertainty. To model these distributional properties conditional on explanatory variables X, researchers typically compute subsample-based proxies (e.g., standard deviation of demand over a five-year rolling window) and regress them on X. However, we show that this standard approach can cause severe biases through non-linear transformations of noisy proxies. We develop alternative methods that address these biases by directly modeling the distributional property of Y conditional on the value of X for each observation. Simulations confirm that our methods perform well even when the standard method is severely biased. Our methods are transparent, robust, and can be implemented in a few lines of code, for which we provide examples. The use of our methods changes major prior findings