We document the numerical challenges we experienced estimating random-coefficient demand models as in Berry, Levinsohn, and Pakes (1995) using two well-known data sets and a thorough optimization design. The optimization algorithms often converge at points where the first-and second-order optimality conditions fail. There are also cases of convergence at local optima. On convergence, the variation in the values of the parameter estimates translates into variation in the models' economic predictions. Price elasticities and changes in consumer and producer welfare following hypothetical merger exercises vary at least by a factor of 2 and up to a factor of 5.

, the participants of the Spring 2014 Harvard seminar in Environmental Economics and Policy, and the 2014 NBER Environmental and Energy Economics Summer Institute for very helpful comments and suggestions. The views expressed herein are those of the authors and do not necessarily reflect the views of the National Bureau of Economic Research. NBER working papers are circulated for discussion and comment purposes. They have not been peerreviewed or been subject to the review by the NBER Board of Directors that accompanies official NBER publications.

and the 2008 NBER Winter IO meeting. Metaxoglou acknowledges financial support from Bates White, LLC. We are also grateful to Bates White, LLC for making their computing resources available. All remaining errors are ours. The views expressed herein are those of the author(s) and do not necessarily reflect the views of the National Bureau of Economic Research. NBER working papers are circulated for discussion and comment purposes. They have not been peerreviewed or been subject to the review by the NBER Board of Directors that accompanies official NBER publications.

We introduce a state-space representation for vector autoregressive moving-average models that enables maximum likelihood estimation using the EM algorithm. We obtain closed-form expressions for both the E- and M-steps; the former requires the Kalman filter and a fixed-interval smoother, and the latter requires least squares-type regression. We show via simulations that our algorithm converges reliably to the maximum, whereas gradient-based methods often fail because of the highly nonlinear nature of the likelihood function. Moreover, our algorithm converges in a smaller number of function evaluations than commonly used direct-search routines. Overall, our approach achieves its largest performance gains when applied to models of high dimension. We illustrate our technique by estimating a high-dimensional vector moving-average model for an efficiency test of California's wholesale electricity market. Copyright 2007 The Authors Journal compilation 2007 Blackwell Publishing Ltd.

Financial support of a SSHRC Insight Development Grant is gratefully acknowledged. Metaxoglou completed parts of this project while visiting CEEPR at MIT and he thanks the Center for their hospitality. We thank Patrick Higgins for providing us with an updated investment deflator series. We thank Nadav Ben Zeev, Garth Heutel, Lutz Killian, Aaron Smith, Jim Stock, and seminar participants at the Bank of Canada, for comments. The usual disclaimer applies. The views expressed herein are those of the authors and do not necessarily reflect the views of the National Bureau of Economic Research. NBER working papers are circulated for discussion and comment purposes. They have not been peer-reviewed or been subject to the review by the NBER Board of Directors that accompanies official NBER publications.