We study inference via heteroskedasticity in linear models commonly used for macroeconomic policy analysis, where covariate endogeneity must often be addressed with limited time and data. Our framework nests standard heteroskedasticity-based approaches, allows for new non-nested restrictions, and does not require ex-ante regime labelling. We propose an easily implementable weak-identification-robust test and derive sufficient conditions for its validity. Simulation results show good size and power properties in a wide range of settings. Empirical applications to the fuel-price passthrough in Sierra Leone, the effect of remittances on consumption in the Philippines, and exchange-rate passthroughs in many countries illustrate the versatility and scalability of our approach.