Bias aware confidence interval for density estimation [JMP ]
This paper proposes a novel inference procedure for the value of probability density function (pdf) at a point. The procedure takes square root of histogram and smooths them with local polynomial regression. An advantage of working with square root of histogram is that the transformation makes them asymptotically homoskedastic, therefore, the method does not require pre-estimation of variance. Maximum bias is characterized by taking a stand on the smoothness of underlying density. Using these two ingredients, I construct a confidence interval (CI) for density at a point, which is valid asymptotically, uniformly over the smoothness class that the researcher imposed. I also show that the length of CI shrinks at an optimal rate. I show via simulations that the procedure achieves correct coverage in settings where existing procedures either undercover, or else are too conservative in terms of CI length. I apply my method for detecting manipulation in regression discontinuity design (RDD), by testing for discontinuity in the density of running variable. I illustrate the methodology in two applications, in the RDD setup, for testing manipulation in popular elections for the House of Representatives, and more generally, for measuring co-ordination among House members during roll call votes.
with Sneha Agrawal and Melinda Suveg
In this paper, we study a new channel to explain firms' price setting behavior. We propose that uncertainty about factor prices has a positive effect on markups. We show theoretically that firms with higher shares of inputs with volatile prices set higher markups. We use the Bartik shift-share approach to empirically test whether firms which use more oil relative to other inputs set higher markups when oil prices are more volatile. Our estimates imply that a one standard deviation increase in oil price volatility leads to a 0.38 percent increase in the markup of firms with average oil exposure.