A Brief Parable Of Over-Differencing

has sat through 1 likewise many seminars amongst triple differenced data, v fixed effects together with xxx willy-nilly controls. I wrote upwards a footling note (7 pages, simply likewise long for a weblog post), relating the sense (from a Bob Lucas paper) that made me skeptical of highly processed empirical work.

The graph hither shows velocity together with involvement rates.  You tin run into the prissy sensible relationship.

(The graph has an of import lesson for policy debates. There is a lot of puzzling why people together with companies are sitting on thence much cash. Well, at null involvement rates, the chance toll of asset cash is zero, thence it's a wonder they don't concur more. This mensurate of velocity is tracking involvement rates amongst just the historical pattern.) 

But when y'all run the regression, the econometrics books say y'all to live on kickoff differences, together with thence the whole human relationship falls apart. The estimated coefficient falls past times a element of 10, together with a scatterplot shows no reliable relationship.  See the the note for details, simply y'all tin run into inward the instant graph  how differencing throws out the of import variation inward the data. 

The perils of over differencing, likewise many fixed effects, likewise many controls, together with that GLS or maximum likelihood volition boundary on featherbrained implications of necessarily simplified theories are good known inward principle. But a few clear parables mightiness brand people to a greater extent than wary inward practice.  Needed: a similarly clear panel-data example.