So @nirupama_rao and I are finally in print. We look at why alcohol taxes are often "overshifted" so that $1 of tax leads to >$1 of price increase. Originally we thought PTR > 1 was an artifact of limited data from some weird tax increases in the 90's (Alaska?) ... 1/9
https://twitter.com/AEAjournals/status/1322157853914861569
But when we ran the usual 2WFE regression we got PT >1 and for some products closer to 3 [oops!].The typical explanation for overshifting in the literature is "something something market power", but it turns out you need some very strange demand curves to get PTR=3 2/9 
If cost shocks are smoothly transmitted into prices then PTR should be constant across products, but it is much higher for products whose prices change. In fact when you plot those PTR against tax changes they seem to suggest price changes are almost exactly $1 or $2 3/9
When you dig even further into the data around 80% of prices end in .99 (some chains use .97 or .49). And price changes are in whole dollar increments around 2/3 of the time. Even when taxes increase, many products don't change price at all. 4/9
Applying the PTR estimated from the linear model from one tax increase to another (or hypothetical) tax increase has basically no external validity. When price changes are discrete, as a bonus we'll also get tax incidence and welfare measures completely wrong 5/9
But we already know how to fix these kinds of problems. Instead we estimate an ordered logit with an (orthogonal) polynomial in the tax change. The key is to constrain predictions to discrete values as well (ie: treat this as a classification problem). 6/9
The linear model substantially overstates the efficiency costs of small taxes (DWL/tax dollar), but understates the costs of large tax increases (that trigger lots of $1 or $2 price changes). The ordered logit produces a series of U-shapes (rather than a straight line). 7/9
The linear (constant PTR) model nearly always overstates the burden of taxes on consumers (particularly for small taxes where firms take lower margins rather than adjust prices). Again we see U-shapes: raise taxes just to the point where firms begin to increase prices. 8/9
Takeway? Plugging a proposed tax increase into an average PTR estimate -> bad idea. If your counterfactuals depend on discreteness of outcomes --> smooth predictions from linear models are NOT just as good. If you get a weird PTR estimate-> look at your data! 9/9
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