Set-Asides and Subsidies in Auctions

American Economic Journal: Microeconomics 2013, 5(1): 1–27
Set-Asides and Subsidies in Auctions
Susan Athey, Dominic Coey, Jonathan Levin

Set-asides and subsidies are used extensively in government procurement and resource sales. We analyze these policies in an empirical model of US Forest Service timber auctions.

The model fits the data well both within the sample of unrestricted sales used for estimation, and when we predict (out-of-sample) outcomes for small business set-asides. Our estimates suggest that restricting entry substantially reduces efficiency and revenue, although it increases small business participation.

An alternative policy of subsidizing small bidders would increase revenue and small bidder profit, with little efficiency cost. We explain these findings by connecting to the theory of optimal auction design. (JEL D44, H57, L73, Q23)

Another publication from the same category: Machine Learning and Data Science

IEEE Computing Conference 2018, London, UK

Regularization of the Kernel Matrix via Covariance Matrix Shrinkage Estimation

The kernel trick concept, formulated as an inner product in a feature space, facilitates powerful extensions to many well-known algorithms. While the kernel matrix involves inner products in the feature space, the sample covariance matrix of the data requires outer products. Therefore, their spectral properties are tightly connected. This allows us to examine the kernel matrix through the sample covariance matrix in the feature space and vice versa. The use of kernels often involves a large number of features, compared to the number of observations. In this scenario, the sample covariance matrix is not well-conditioned nor is it necessarily invertible, mandating a solution to the problem of estimating high-dimensional covariance matrices under small sample size conditions. We tackle this problem through the use of a shrinkage estimator that offers a compromise between the sample covariance matrix and a well-conditioned matrix (also known as the "target") with the aim of minimizing the mean-squared error (MSE). We propose a distribution-free kernel matrix regularization approach that is tuned directly from the kernel matrix, avoiding the need to address the feature space explicitly. Numerical simulations demonstrate that the proposed regularization is effective in classification tasks.