Calculating Comparable Statistics From Incomparable Surveys, With an Application to Poverty in India

Abstract

Applied economists are often interested in studying trends in economic indicators such as inequality or poverty; however, 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 recovery of 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 relationship with the main variable of interest is stable over time. We analyze the asymptotic properties of the estimator when data belong to a stratified and clustered survey. The main empirical motivation of the article is provided by a recent controversy regarding the extent of poverty reduction in India in the 1990s. Due to changes in the expenditure questionnaire adopted for data collection in the 1999–2000 round of the Indian National Sample Survey, poverty is likely to be understated relative to 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, not a statistical artifact.