Econometric Methods for Structural Models

Harvard University, Cambridge MA

Investigators

Abstract

This proposal contains projects that develop statistical econometric methods for certain economic models of interest. The econometric issues considered include estimation in dynamic auctions, optimal estimation of procurement auction and job search models, and estimation of certain kinds of economic shifts or breaks. A substantial empirical project on daily auctions in the deregulated electric utility market in England and Wales applies some of the econometric tools. Our estimates are used to determine profitability and examine the incentives to invest in new capacity. Our model and estimates could also be used to consider outcomes associated with alternative auction designs or to analyze possible collusion among suppliers in this market For the empirical project on multi-unit electricity auctions, we have obtained a license to use the actual software used by the auctioneer to determine price and quantity outcomes (given bids), and we are also obtaining the three most recent years of data. With software and data in hand, we use an equilibrium model of firm supplier behavior to estimate start-up and fixed costs for each generator. These costs will then be used to examine profits and investment incentives. We will also incorporate a cost of capital approach to maintenance and availability decisions. The estimation method to be used in the empirical electricity auction project is developed in detail due to its more general applicability in a variety of auction settings. Similar in spirit to an Euler equation approach, our econometric method uses the first order conditions as the basis for moments of estimation. This approach avoids the computational difficulty associated with numerically solving for optimal bidding strategies. The technique extends the approach of Berry and Pakes (2000), which was designed for estimation of oligopolistic models, to work in dynamic auctions. A key challenge to a first order condition approach in auctions is the inherent discontinuity in the firm profit function. This discontinuity leads to a nondifferentiability that makes approximation of the first order condition difficult. We overcome this difficulty with a semiparametric smoothing technique and obtain parameter estimates at a nonparametric rate. Next, we consider parameter-dependent support models which include certain auction models as well as production frontier models, and some search models. While estimation in these models has been studied broadly, we examine what estimators are most efficient. We use LeCam's theory of statistical experiments to show that the maximum likelihood estimators are not asymptotically efficient in such nonregular models, while Bayes' estimators are. In another project, efficient estimation in structural break models is studied. Again a limit of experiments approach will be used to explore efficiency and other issues in traditional unknown change point models. Another project considers estimation of breaks in a nonparametric regression curve model. Such estimates are useful in certain regression discontinuity settings.