This paper is about the economic theory of biodiversity preservation. A cost-effectiveness methodology is constructed, which results in a ranking criterion sufficiently operational to be useful in suggesting what to look at when determining actual conservation priorities. The formula is firmly rooted in a mathematically rigorous optimization framework, so that its theoretical underpinnings are clear. The underlying model, called the 'Noah's Ark Problem, ' is intended to be a kind of canonical form that hones down to its analytical essence the problem of best preserving diversity under a limited budget constraint.

The least-absolute-deviations (LAD) estimator for a median-regression model does not satisfy the standard conditions for obtaining asymptotic refinements through use of the bootstrap because the LAD objective function is not smooth. This paper overcomes this problem by smoothing the objective function. The smoothed estimator is asymptotically equivalent to the standard LAD estimator. With bootstrap critical values, the rejection probabilities of symmetrical t and X 2 tests based on the smoothed estimator are correct through O(n -γ ) under the null hypothesis, where γ<1 but can be arbitrarily close to 1. In contrast, first-order asymptotic approximations make errors of size O(n -γ ). These results also hold for symmetrical t and X 2 tests for censored median regression models.

The method of simulated scores (MSS) is presented for estimating limited dependent variables models (LDV) with flexible correlation structure in the unobservables. We propose simulators that are continuous in the unknown parameter vectors, and hence standard optimization methods can be used to compute the MSS estimators that employ these simulators. The first continuous method relies on a recursive conditioning of the multivariate normal density through a Cholesky triangularization of its variance-covariance matrix. The second method combines results about the conditionals of the multivariate normal distribution with Gibbs resampling techniques. We establish consistency and asymptotic normality of the MSS estimators and derive suitable rates at which the number of simulations must rise if biased simulators are used.

anonymous referees for comments and Tel–Aviv University for its hospitality during part of the work on this paper. Dekel thanks the NSF and Lipman thanks SSHRCC for financial support for this research. Dekel and Lipman particularly thank Phil Reny for a series of discussions which led to this project. This paper was formerly titled “Possibility Correspondences Preclude Unawareness.” 2