Joel Horowitz | Searcharxiv

arXiv2019

Estimation of a Heterogeneous Demand Function with Berkson Errors

Berkson errors are commonplace in empirical microeconomics. In consumer demand this form of measurement error occurs when the price an individual pays is measured by the (weighted) average price paid by individuals in a specified group (e.g., a county), rather than the true transaction price. We show the importance of such measurement errors for the estimation of demand in a setting with nonseparable unobserved heterogeneity. We develop a consistent estimator using external information on the true distribution of prices. Examining the demand for gasoline in the U.S., we document substantial within-market price variability, and show that there are significant spatial differences in the magnitude of Berkson errors across regions of the U.S. Accounting for Berkson errors is found to be quantitatively important for estimating price effects and for welfare calculations. Imposing the Slutsky shape constraint greatly reduces the sensitivity to Berkson errors.

econ.EM↗

arXiv2013

A simple bootstrap method for constructing nonparametric confidence bands for functions

Standard approaches to constructing nonparametric confidence bands for functions are frustrated by the impact of bias, which generally is not estimated consistently when using the bootstrap and conventionally smoothed function estimators. To overcome this problem it is common practice to either undersmooth, so as to reduce the impact of bias, or oversmooth, and thereby introduce an explicit or implicit bias estimator. However, these approaches, and others based on nonstandard smoothing methods, complicate the process of inference, for example, by requiring the choice of new, unconventional smoothing parameters and, in the case of undersmoothing, producing relatively wide bands. In this paper we suggest a new approach, which exploits to our advantage one of the difficulties that, in the past, has prevented an attractive solution to the problem - the fact that the standard bootstrap bias estimator suffers from relatively high-frequency stochastic error. The high frequency, together with a technique based on quantiles, can be exploited to dampen down the stochastic error term, leading to relatively narrow, simple-to-construct confidence bands.

math.ST↗