Linear Regression from Strategic Data Sources

Linear regression is a fundamental building block of statistical data analysis. It amounts to estimating the parameters of a linear model that maps input features to corresponding outputs. In the classical setting where the precision of each data point is fixed, the famous Aitken/Gauss-Markov theorem in statistics states that generalized least squares (GLS) is a so-called "Best Linear Unbiased Estimator" (BLUE). In modern data science, however, one often faces strategic data sources, namely, individuals who incur a cost for providing high-precision data. In this paper, we study a setting in which features are public but individuals choose the precision of the outputs they reveal to an analyst. We assume that the analyst performs linear regression on this dataset, and individuals benefit from the outcome of this estimation. We model this scenario as a game where individuals minimize a cost comprising two components: (a) an (agent-specific) disclosure cost for providing high-precision data; and (b) a (global) estimation cost representing the inaccuracy in the linear model estimate. In this game, the linear model estimate is a public good that benefits all individuals. We establish that this game has a unique non-trivial Nash equilibrium. We study the efficiency of this equilibrium and we prove tight bounds on the price of stability for a large class of disclosure and estimation costs. Finally, we study the estimator accuracy achieved at equilibrium. We show that, in general, Aitken's theorem does not hold under strategic data sources, though it does hold if individuals have identical disclosure costs (up to a multiplicative factor). When individuals have non-identical costs, we derive a bound on the improvement of the equilibrium estimation cost that can be achieved by deviating from GLS, under mild assumptions on the disclosure cost functions.Comment: This version (v3) extends the results on the sub-optimality of GLS (Section 6) and improves writing in multiple places compared to v2. Compared to the initial version v1, it also fixes an error in Theorem 6 (now Theorem 5), and extended many of the result

The Groucho Effect of Uncertain Standards

Consumers are rarely sure of the exact standard that product labels and other certificates of quality represent. We show that any such uncertainty creates a “Groucho effect” in which seeing that a product has a label leads consumers to infer that the standard for the label itself is not very demanding. Label adoption is therefore always less likely to be an equilibrium than without uncertainty over the standard, and if it is an equilibrium it is always less informative than without such uncertainty. The Groucho effect leads to an information externality so better firms are reluctant to adopt labels if worse firms adopt them. Applying the model to eco-labels, we find that industry groups, governments, and NGOs can increase label adoption by publicizing labeling criteria, by encouraging consumers to expect label adoption when there are multiple equilibria, and by setting high standards that are less likely to be devalued by low quality firms.Eco-labels, disclosure, certification, persuasion, standards

Effects of carbon reduction labels: Evidence from scanner data

We investigate the effects of carbon reduction labels using a detailed scanner data set. Using a difference-in-differences estimation strategy, we find that having a carbon label has no impact on detergent prices or demand. We also investigate possible heterogeneous effects of carbon labels using the synthetic control method. We find no evidence to indicate that the prices for the counterfactual detergents without the label would have been any different from the prices of the carbon-labeled detergents. We investigate the reasons for these results and conclude that the specific design of the carbon label is responsible for its lack of success

Updating beliefs with imperfect signals: experimental evidence

This article analyses belief updating when agents receive a signal that restricts the number of possible states of the world. We create an experiment on individual choice under uncertainty. In this experiment, the subject observes an urn, containing yellow and blue balls, whose composition is partially revealed. The subject has to assess the composition of the urn and form an initial belief. Then, he receives a signal that restricts the set of the possible urns from which the initial observed sample is drawn. Once again, he has to estimate the composition of the urn. Our results show that, on the whole, this type of signal increases the frequency of correct assessment. However, differences appear between validating and invalidating signals (i.e. signals that either confirm or disprove the initial belief). The later significantly increase the probability to make a correct assessment whereas validating signals reduce the frequency of correct estimations. We find evidences of lack of persistence in choice under uncertainty. The literature shows that people may persist with their choice even when they are wrong. We show that they may also change even if they are right.Beliefs; Imperfect Information; Experiment

Agreeing on efficient emissions reduction

We propose a simple mechanism providing incentives to reduce harmful emissions to their efficient level without infracting upon productive efficiency. The mechanism employs a contest creating incentives among participating nations to simultaneously exert efficient productive and efficient abatement efforts. Participation in the most stylised form of the scheme is voluntary and individually rational; all rules are mutually agreeable and are unanimously adopted if proposed. The scheme balances its budget and requires no principal. In a perhaps more realistic stochastic output version which could potentially inform policy decisions, we show that the transfers required by the efficient mechanism create a mutual insurance motive which may serve as effective rationale for the (gradual) formation of International Environmental Agreements

Agreeing on Efficient Emissions Reduction

We propose a simple mechanism providing incentives to reduce harmful emissions to their efficient level without infracting upon productive efficiency. The mechanism employs a contest creating incentives among participating nations to simultaneously exert efficient productive and efficient abatement efforts. Participation in the most stylised form of the scheme is voluntary and individually rational; all rules are mutually agreeable and are unanimously adopted if proposed. The scheme balances its budget and requires no principal. In a perhaps more realistic stochastic output version which could potentially inform policy decisions, we show that the transfers required by the efficient mechanism create a mutual insurance motive which may serve as effective rationale for the (gradual) formation of International Environmental Agreements