Inference on Manipulation in the Density and Volatility Effect on the Markup

Abstract

The dissertation consists of two broad topics - in the first two chapters, I study the inference on probability density function (pdf), which helps to detect and quantify the amount of manipulation in various economic settings; and in the third chapter, I study the firm’s response of volatility in the factor prices, on the profit margin. Chapter 1 proposes a novel inference procedure for the value of the pdf at a point. The procedure takes square root of a histogram (rootogram) and smooths it with local polynomial regression. The key innovation in working with the rootogram is that they are asymptotically homoskedastic (i.e. with constant variance). Therefore, any requirement to estimate the variance is precluded. At the same time, smoothness class of the underlying density is pre-specified, which characterizes the maximum bias asymptotically. Using these two ingredients - variance and maximum bias, I construct a “bias aware confidence interval” for the density at a point, which is valid asymptotically, uniformly over the specified smoothness class. Chapter 2 studies large sample properties of the notching estimator. The notching estimator quantifies manipulation in the pdf and is useful for estimating parameters like the elasticity of income on the tax rate. Traditionally, notching parameter is estimated by regressing a polynomial on the histogram and the standard error is calculated by the residual bootstrap. Two contributions are made: first, I show that the currently used residual bootstrap procedure is not suitable. Instead, Iderive asymptotic distribution of the regression-based estimator. Second, I propose a novel, maximum likelihood based notching estimator. Maximum likelihood is theoretically known to be the most efficient estimator. The gains are substantial for the notching parameter - in the illustrated empirical application, the proposed estimator is five times more efficient. Changing topic, chapter 3, co-authored with Sneha Agrawal and Melinda Suveg, studies a new channel to explain firms’ price setting behavior. We theoretically show that uncertainty about factor prices has a positive effect on markups. Empirically, using Swedish data, we show that firms which use more oil relative to other inputs, set higher markups when oil prices are more volatile.