Set-Asides and Subsidies in Auctions

Set-asides and subsidies are used extensively in government procurement and natural resource sales. We analyze these policies in an empirical model of U.S. Forest Service timber auctions. The model fits the data well both within the sample of unrestricted sales where we estimate the model, and when we predict (out of sample) bidder entry and prices for small business set-asides. Our estimates suggest that restricting entry to small businesses substantially reduces efficiency and revenue, although it does increase small business participation. An alternative policy of subsidizing small bidders would increase revenue and small bidder profit, while eliminating almost all of the efficiency loss of set-asides, and only slightly decreasing the profit of larger firms. We explain these findings by connecting to the theory of optimal auction design.set-asides, subsidies, natural resources, timber, auctions

Empirical Bayesian Selection for Value Maximization

We study the common problem of selecting the best $m$ units from a set of $n$ in the asymptotic regime $m / n \to \alpha \in (0, 1)$, where noisy, heteroskedastic measurements of the units' true values are available and the decision-maker wishes to maximize the average true value of the units selected. Given a parametric prior distribution, the empirical Bayesian decision rule incurs $\mathcal{O}_p(n^{-1})$ regret relative to the Bayesian oracle that knows the true prior. More generally, if the error in the estimated prior is of order $\mathcal{O}_p(r_n)$, regret is $\mathcal{O}_p(r_n^2)$. In this sense selecting the best units is easier than estimating their values. We show this regret bound is sharp, by giving an example in which it is attained. Using priors calibrated from a dataset of over four thousand internet experiments, we find that empirical Bayes methods perform well in practice for detecting the best treatments given only a modest number of experiments

Set-Asides and Subsidies in Auctions

Set-asides and subsidies are used extensively in government procurement and natural resource sales. We analyze these policies in an empirical model of U.S. Forest Service timber auctions. The model fits the data well both within the sample of unrestricted sales where we estimate the model, and when we predict (out of sample) bidder entry and prices for small business set-asides. Our estimates suggest that restricting entry to small businesses substantially reduces efficiency and revenue, although it does increase small business participation. An alternative policy of subsidizing small bidders would increase revenue and small bidder profit, while eliminating almost all of the efficiency loss of set-asides, and only slightly decreasing the profit of larger firms. We explain these findings by connecting to the theory of optimal auction design.