“Estimation of the Truncated Density Function at Its Unknown Truncation Point with Application to Estimation of the Entry Cost in First-Price Auctions” by Pai XU
University of British Columbia
Economic models that study individuals' behavior under uncertainty sometimes predict that the distribution that represents each individual's decision is truncated, reflecting a threshold for her to switch from one choice to another. For example, we observe a bid of an individual in an auction only if she anticipates a value of the object exceeding the cost from her participation. This causes the distribution of the bids to be truncated at the threshold for participation. The feature of the distribution in a neighborhood of the threshold is often of interest to economists, for whom the location of the threshold is typically unknown as well. In this paper, we propose using the nearest neighbor estimation technique to estimate truncated univariate probability density functions (pdf) at their unknown truncation points. The parameter of interest is, in practice, often a smooth function of the unknown pdf at the truncation point and some other attributes of the distribution. We also consider an approach in which such a parameter is estimated by first estimating the pdf at the truncation point and some other relevant attributes of the distribution, and then plugging the estimated values into the smooth function. We study the large sample properties of the plug-in estimator to establish sets of conditions sufficient for its consistency and asymptotic normality. We also conduct Monte Carlo simulations to assess the finite sample behavior of the proposed estimator. Finally, we apply the proposed method to estimate the cost of participation in the Michigan Highway Procurement Auctions. Our study rejects the null hypothesis of zero participation costs. Based on our estimation result, we infer how the optimal auction outcomes can be realized by using the regular policy tools. We demonstrate the improvement that the Michigan government could have made on payments if the optimal auctions had been employed. We also explain how the proposed method may be applied in other empirical researches.