An LLM Workflow for Functional Form Sensitivity Analysis

We introduce an LLM workflow for functional form sensitivity analysis. A researcher estimates the value of an object of interest by maximizing the fit of a working model to some data. The working model assumes an arbitrary form for some function. We define sensitivity by how much it is possible to change the estimate of the object of interest, without compromising fit, by selecting a different functional form. The workflow first looks for an analytic solution. If it fails to find one, it approximates the solution via numerical methods that respect the fit constraint at each step of a solver path. The workflow yields a verifiable lower bound on the in-sample sensitivity of the researcher’s estimate, and is fast in many practical situations. We illustrate with an application to the welfare cost of adverse selection in health insurance.