- 2016 This paper is concerned with economic analysis of first-price sealed-bid auctions with risk averse bidders. The identification is based on exogenous variations in the number of bidders across auctions. We present a shape constrained estimator of the bidding function, which satisfies the theoretical properties of passing through origin, positivity and monotonicity. The underlying utility function and bidder value distribution are readily obtained from the estimated bidding function. Monte Carlo simulations demonstrate good performance of the proposed estimator.