We propose a method for estimating static games of incomplete information. A static game is a generalization of a discrete choice model, such as a multinomial logit or probit, which allows the actions of a group of agents to be interdependent. Unlike most earlier work, the method we propose is semiparametric and does not require the covariates to lie in a discrete set. While the estimator we propose is quite flexible, we demonstrate that in most cases it can be easily implemented using standard statistical packages such as STATA. We also propose an algorithm for simulating the model which finds all equilibria to the game. As an application of our estimator, we study recommendations for high technology stocks between 1998-2003.We find that strategic motives, typically ignored in the empirical literature, appear to be an important consideration in the recommendations submitted by equity analysts.
The main goal of this paper is to develop a theory of inference of player valuations from observed data in the generalized second price auction without relying on the Nash equilibrium assumption. Existing work in Economics on inferring agent values from data relies on the assumption that all participant strategies are best responses of the observed play of other players, i.e. they constitute a Nash equilibrium. In this paper, we show how to perform inference relying on a weaker assumption instead: assuming that players are using some form of no-regret learning. Learning outcomes emerged in recent years as an attractive alternative to Nash equilibrium in analyzing game outcomes, modeling players who haven't reached a stable equilibrium, but rather use algorithmic learning, aiming to learn the best way to play from previous observations. In this paper we show how to infer values of players who use algorithmic learning strategies. Such inference is an important first step before we move to testing any learning theoretic behavioral model on auction data. We apply our techniques to a dataset from Microsoft's sponsored search ad auction system.
Measurement errors in economic data are pervasive and nontrivial in size. The presence of measurement errors causes biased and inconsistent parameter estimates and leads to erroneous conclusions to various degrees in economic analysis. While linear errors-in-variables models are usually handled with well-known instrumental variable methods, this article provides an overview of recent research papers that derive estimation methods that provide consistent estimates for nonlinear models with measurement errors. We review models with both classical and nonclassical measurement errors, and with misclassification of discrete variables. For each of the methods surveyed, we describe the key ideas for identification and estimation, and discuss its application whenever it is currently available. (JEL C20, C26, C50)
We survey and apply several techniques from the statistical and computer science literature to the problem of demand estimation. To improve out-of-sample prediction accuracy, we propose a method of combining the underlying models via linear regression. Our method is robust to a large number of regressors; scales easily to very large data sets; combines model selection and estimation; and can flexibly approximate arbitrary non-linear functions. We illustrate our method using a standard scanner panel data set and find that our estimates are considerably more accurate in out-of-sample predictions of demand than some commonly used alternatives.
The promise of data science is that if data from a system can be recorded and understood then this understanding can potentially be utilized to improve the system. Behavioral and economic data, however, is different from scientific data in that it is subjective to the system. Behavior changes when the system changes, and to predict behavior for any given system change or to optimize over system changes, the behavioral model that generates the data must be inferred from the data. The ease with which this inference can be performed generally also depends on the system. Trivially, a system that ignores behavior does not admit any inference of a behavior generating model that can be used to predict behavior in a system that is responsive to behavior. To realize the promise of data science in economic systems, a theory for the design of such systems must also incorporate the desired inference properties.Consider as an example the revenue-maximizing auctioneer. If the auctioneer has knowledge of the distribution of bidder values then she can run the first-price auction with a reserve price that is tuned to the distribution. Under some mild distributional assumptions, with the appropriate reserve price the first-price auction is revenue optimal [Myerson 1981]. Notice that the historical bid data for the first-price auction with a reserve price will in most cases not have bids for bidders whose values are below the reserve. Therefore, there is no data analysis that the auctioneer can perform that will enable properties of the distribution of bidder values below the reserve price to be inferred. It could be, nonetheless, that over time the population of potential bidders evolves and the optimal reserve price lowers. This change could go completely unnoticed in the auctioneer's data. The two main tools for optimizing revenue in an auction are reserve prices (as above) and ironing. Both of these tools cause pooling behavior (i.e., bidders with distinct values take the same action) and economic inference cannot thereafter differentiate these pooled bidders. In order to maintain the distributional knowledge necessary to be able to run a good auction in the long term, the auctioneer must sacrifice the short-term revenue by running a non-revenue-optimal auction.We consider the following auction and bidding model. The auction design space is given by a position auction environment and either first-price or all-pay semantics. There are n agents and n positions and each position has a corresponding service probability. We restrict attention to a class of rank-based auctions wherein the auctioneer A full version of this abstract can be found at http://arxiv.org/abs/1404.5971.
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