@TechReport{iza:izadps:dp18454,
            	author={Millimet, Daniel L. and Paloyo, Alfredo R.},
            	title={On the (Mis)Use of Composite Indices: with Applications in Political Economy},
            	year={2026},
	month={Mar},
            	institution={Institute of Labor Economics (IZA)},
            	address={Bonn},
            	type={IZA Discussion Paper},
            	number={18454},
            	url={https://www.iza.org/index.php/publications/dp18454},
	abstract={Empirical researchers often replace latent constructs with composite indices, treating this as a neutral data-processing step. We prove this is a consequential identification choice. Our (near) impossibility theorem demonstrates that no linear index can guarantee consistent estimates of all parameters in multiple regressions. We show that proxy indices induce residual confounding, while popular weighting schemes introduce nonclassical measurement error with method-dependent biases. Using simulations and 2024 U.S. election data, we reveal that substantive conclusions are often artifacts of the chosen index. We argue that measurement models require the same formal scrutiny as other identification strategies.},
	keywords={latent variables;composite indices;measurement models;errors-in-variables;proxy variables;political economy;community health},
            }