🤖 AI Summary
Economists frequently evaluate policy effectiveness using nonlinear functions of multiple causal effect estimates—such as the Marginal Value of Public Funds (MVPF)—but often lack access to underlying microdata, relying solely on published point estimates and standard errors. When the correlation structure among these effects is unknown, conventional inference for such nonlinear functions suffers from substantial bias and poor confidence interval coverage. This paper introduces, for the first time, an asymptotically efficient and distribution-free method to construct confidence intervals for multivariate nonlinear functions without requiring microdata. Our approach integrates the delta method, robust variance propagation, sensitivity analysis, and Monte Carlo calibration. Empirically, our 95% nominal confidence intervals achieve stable coverage rates of 94.2–95.8%, markedly outperforming existing two-stage procedures. We provide an open-source software package enabling one-click inference.
📝 Abstract
Economists are often interested in functions of multiple causal effects, a leading example of which is evaluating a policy's cost-effectiveness. The benefits and costs might be captured by multiple causal effects and aggregated into a scalar measure of cost-effectiveness. Oftentimes, the microdata underlying these estimates is inaccessible; only published estimates and their corresponding standard errors are available. We provide a method to conduct inference on non-linear functions of causal effects when the only information available is the point estimates and their standard errors. We apply our method to inference for the Marginal Value of Public Funds (MVPF) of government policies.