The Information Content and Statistical Properties of Diffusion Indexes

Abstract

We study diffusion indexes constructed from qualitative surveys to provide real-time assessments of various aspects of economic activity. In particular, we highlight the role of diffusion indexes as estimates of change in a quasi-extensive margin, and characterize their distribution, focusing on the uncertainty implied by both sampling and the polarization of participants' responses. Because qualitative tendency surveys generally cover multiple questions around a topic, a key aspect of this uncertainty concerns the coincidence of responses, or the degree to which polarization co-moves, across individual questions. We illustrate these results using microdata on individual responses underlying different composite indexes published by the Michigan Survey of Consumers. We find a secular rise in consumer uncertainty starting around 2000, following a decade-long decline, and higher agreement among respondents in prior periods. In 2014, six years after the Great Recession, uncertainty arising from the polarization of responses in the Michigan Survey stood at its highest level, coinciding with the weakest recovery in U.S. postwar history. The formulas we derive allow for simple computations of approximate confidence intervals, thus affording a more complete real-time assessment of economic conditions using qualitative surveys.