Cowles Foundation for Research in Economics

We study how privacy regulation affects menu pricing by a monopolist platform that collects and monetizes personal data. Consumers differ in privacy valuation and sophistication: naive users ignore privacy losses, while sophisticated users internalize them. The platform designs prices and data collection options to screen users. Without regulation, privacy allocations are distorted and naive users are exploited. Regulation through privacy-protecting defaults can create a market for information by inducing payments for data; hard caps on data collection protect naive users but may restrict efficient data trade.

We propose a new formulation of the maximum score estimator that uses compositions of rectified linear unit (ReLU) functions, instead of indicator functions as in Manski (1975, 1985), to encode the sign alignment restrictions. Since the ReLU function is Lipschitz, our new ReLU-based maximum score criterion function is substantially easier to optimize using standard gradient-based optimization pacakges. We also show that our ReLU-based maximum score (RMS) estimator can be generalized to an umbrella framework defined by multi-index single-crossing (MISC) conditions, while the original maximum score estimator cannot be applied. We establish the n −s/(2s+1) convergence rate and asymptotic normality for the RMS estimator under order-s Holder smoothness. In addition, we propose an alternative estimator using a further reformulation of RMS as a special layer in a deep neural network (DNN) architecture, which allows the estimation procedure to be implemented via state-of-the-art software and hardware for DNN.

This paper outlines an economic model that provides a framework for organising the growing literature on the performance of physicians and judges. The primary task of these professionals is to make decisions based on the information provided by their clients. The paper discusses professional decisions in terms of what Kahneman (2011) calls fast and slow decisions, known as System 1 and System 2 in cognitive science. Slow decisions correspond to the economist’s model of rational choice, while System 1 (fast) decisions are high‑speed, intuitive choices guided by training and human capital. This distinction is used to provide a model of decision‑making under uncertainty based on Bewley (2011)’s theory of Knightian uncertainty to show that human values are an essential input to optimal choice. This, in turn, provides conditions under which artificial intelligence (AI) tools can assist professional decision‑making, while pointing to cases where such tools need to explicitly incorporate human values in order to make better decisions.

We study how privacy regulation affects menu pricing by a monopolist platform that collects and monetizes personal data. Consumers differ in privacy valuation and sophistication: naive users ignore privacy losses, while sophisticated users internalize them. The platform designs prices and data collection options to screen users. Without regulation, privacy allocations are distorted and naive users are exploited. Regulation through privacy-protecting defaults can create a market for information by inducing payments for data; hard caps on data collection protect naive users but may restrict efficient data trade.

This paper develops probability pricing, extending cash flow pricing to quantify the willingness-to-pay for changes in probabilities. We show that the value of any marginal change in probabilities can be expressed as a standard asset-pricing formula with hypothetical cash flows derived from changes in the survival function. This equivalence between probability and cash flow valuation allows us to construct hedging strategies and systematically decompose individual and aggregate willingness-to-pay. Four applications examine the valuation of changes in the distribution of aggregate consumption, the efficiency effects of varying performance precision in principal-agent problems, and the welfare implications of public and private information.

This paper proposes a novel framework for the global optimization of a continuous function in a bounded rectangular domain. Specifically, we show that: (1) global optimization is equivalent to optimal strategy formation in a two-armed decision problem with known distributions, based on the Strategic Law of Large Numbers we establish; and (2) a sign-based strategy based on the solution of a parabolic PDE is asymptotically optimal. Motivated by this result, we propose a class of Strategic Monte Carlo Optimization (SMCO) algorithms, which uses a simple strategy that makes coordinate-wise two-armed decisions based on the signs of the partial gradient (or practically the first difference) of the objective function, without the need of solving PDEs. While this simple strategy is not generally optimal, it is sufficient for our SMCO algorithm to converge to a local optimizer from a single starting point, and to a global optimizer under a growing set of starting points. Numerical studies demonstrate the suitability of our SMCO algorithms for global optimization well beyond the theoretical guarantees established herein. For a wide range of test functions with challenging landscapes (multi-modal, non-differentiable and discontinuous), our SMCO algorithms perform robustly well, even in high-dimensional (d = 200 ∼ 1000) settings. In fact, our algorithms outperform many state-of-the-art global optimizers, as well as local algorithms augmented with the same set of starting points as ours.

For a long time, the majority of economists doing empirical work relied on choice data, while
data based on answers to hypothetical questions, stated preferences or measures of subjective
beliefs were met with some skepticism. Although this has changed recently, much work needs
to be done. In this paper, we emphasize the identifying content of new economic measures. In
the first part of the paper, we discuss where the literature on measures in economics stands at
the moment. We first consider how the design and use of new measures can help identify causal
links and structural parameters under weaker assumptions than those required by approaches
based exclusively on choice data. We then discuss how the availability of new measures can
allow the study of richer models of human behavior that incorporate a wide set of factors. In
the second part of the paper, we illustrate these issues with an application to the study of risk
sharing and of deviations from perfect risk sharing.

This paper proposes a novel framework for the global optimization of a continuous function in a bounded rectangular domain. Specifically, we show that: (1) global optimization is equivalent to optimal strategy formation in a two-armed decision problem with known distributions, based on the Strategic Law of Large Numbers we establish; and (2) a sign-based strategy based on the solution of a parabolic PDE is asymptotically optimal. Motivated by this result, we propose a class of Strategic Monte Carlo Optimization (SMCO) algorithms, which uses a simple strategy that makes coordinate-wise two-armed decisions based on the signs of the partial gradient (or practically the first difference) of the objective function, without the need of solving PDEs. While this simple strategy is not generally optimal, it is sufficient for our SMCO algorithm to converge to a local optimizer from a single starting point, and to a global optimizer under a growing set of starting points. Numerical studies demonstrate the suitability of our SMCO algorithms for global optimization well beyond the theoretical guarantees established herein. For a wide range of test functions with challenging landscapes (multi-modal, non-differentiable and discontinuous), our SMCO algorithms perform robustly well, even in high-dimensional (d = 200 ∼ 1000) settings. In fact, our algorithms outperform many state-of-the-art global optimizers, as well as local algorithms augmented with the same set of starting points as ours.