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Estimating Loss Function Parameters


  • Elliott, Graham
  • Komunjer, Ivana
  • Timmermann, Allan G


In situations where a sequence of forecasts is observed, a common strategy is to examine ‘rationality’ conditional on a given loss function. We examine this from a different perspective - supposing that we have a family of loss functions indexed by unknown shape parameters, then given the forecasts can we back out the loss function parameters consistent with the forecasts being rational even when we do not observe the underlying forecasting model? We establish identification of the parameters of a general class of loss functions that nest popular loss functions as special cases and provide estimation methods and asymptotic distributional results for these parameters. The methods are applied in an empirical analysis of IMF and OECD forecasts of budget deficits for the G7 countries. We find that allowing for asymmetric loss can significantly change the outcome of empirical tests of forecast rationality.

Suggested Citation

  • Elliott, Graham & Komunjer, Ivana & Timmermann, Allan G, 2003. "Estimating Loss Function Parameters," CEPR Discussion Papers 3821, C.E.P.R. Discussion Papers.
  • Handle: RePEc:cpr:ceprdp:3821

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    Cited by:

    1. Martin Skitmore & Franco K. T. Cheung, 2007. "Explorations in specifying construction price forecast loss functions," Construction Management and Economics, Taylor & Francis Journals, vol. 25(5), pages 449-465.
    2. Graham Elliott & Ivana Komunjer & Allan Timmermann, 2008. "Biases in Macroeconomic Forecasts: Irrationality or Asymmetric Loss?," Journal of the European Economic Association, MIT Press, vol. 6(1), pages 122-157, March.
    3. Stan Hurn & Ralf Becker, 2009. "Testing for Nonlinearity in Mean in the Presence of Heteroskedasticity," Economic Analysis and Policy, Elsevier, vol. 39(2), pages 311-326, September.
    4. Tom Engsted & Niels Haldrup & Boriss Siliverstovs, 2004. "Long-run forecasting in multicointegrated systems," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 23(5), pages 315-335.
    5. Basu, Sudipta & Markov, Stanimir, 2004. "Loss function assumptions in rational expectations tests on financial analysts' earnings forecasts," Journal of Accounting and Economics, Elsevier, vol. 38(1), pages 171-203, December.
    6. Yang Yang & Tae-Hwy Lee, 2004. "Bagging Binary Predictors for Time Series," Econometric Society 2004 Far Eastern Meetings 512, Econometric Society.
    7. Lee, Tae-Hwy & Yang, Yang, 2006. "Bagging binary and quantile predictors for time series," Journal of Econometrics, Elsevier, vol. 135(1-2), pages 465-497.
    8. Patton, Andrew J & Timmermann, Allan G, 2003. "Properties of Optimal Forecasts," CEPR Discussion Papers 4037, C.E.P.R. Discussion Papers.
    9. Adrian Pagan & Hashem Pesaran, 2007. "Econometric Analysis of Structural Systems with Permanent and Transitory Shocks. Working paper #7," NCER Working Paper Series 7, National Centre for Econometric Research.
    10. Alexander, Marcus & Christakis, Nicholas A., 2008. "Bias and asymmetric loss in expert forecasts: A study of physician prognostic behavior with respect to patient survival," Journal of Health Economics, Elsevier, vol. 27(4), pages 1095-1108, July.

    More about this item


    asymmetric loss; imf; macroeconomic forecasting; oecd;

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • E00 - Macroeconomics and Monetary Economics - - General - - - General

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