Applied economists are often interested in studying trends in important economic indicators, such as inequality or poverty, but comparisons over time can be made impossible by changes in data collection methodology. We describe an easily implemented procedure, based on inverse probability weighting, that allows to recover comparability of estimated parameters identified implicitly by a moment condition. The validity of the procedure requires the existence of a set of auxiliary variables whose reports are not affected by the different survey design, and whose relation with the main variable of interest is stable over time. We analyze the asymptotic properties of the estimator taking into account the presence of clustering, stratification and sampling weights which characterize most household surveys. The main empirical motivation of the paper is provided by a recent controversy on the extent of poverty reduction in India in the 1990s. Due to important changes in the expenditure questionnaire adopted for data collection in the 1999-2000 round of the Indian National Sample Survey, the resulting poverty numbers are likely to understate poverty relative to the previous rounds. We use previous waves of the same survey to provide evidence supporting the plausibility of the identifying assumptions and conclude that most, but not all, of the very large reduction in poverty implied by the official figures appears to be real, and not a statistical artifact.