Are Two Cheap, Noisy Measures Better than One Expensive, Accurate One?

Executive Summary 1. Survey responses are always subject to measurement error. In general surveys (and especially longitudinal surveys), there are severe constraints on the time that can be spent eliciting a less noisy response for any target variable. In this paper we consider when it may be better to consider multiple noisy measures of the target measure rather than improving the reliability of a single measure. 2. The Kotlarski result states that if the measurement errors in two measures of the same target variable are mutually independent and independent of the true value then we can recover the entire distribution of the quantity of interest, up to location. 3. We consider designing surveys to deliver measurement error with desirable properties. This shifts the emphasis from reliability (the signal to noise ratio for any given measure) to the joint properties of the multiple measures. 4. To illustrate our ideas, we consider a concrete example: the measurement of consumption inequality. A small simulation study suggests that the approach we propose has promise. The next step in this research agenda is experiments in survey data collection.