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Curved Exponential Models in Econometrics

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  • van Garderen, Kees Jan

Abstract

Curved exponential models have the property that the dimension of the minimal sufficient statistic is larger than the number of parameters in the model. Many econometric models share this feature. The first part of the paper shows that, in fact, econometric models with this property are necessarily curved exponential. A method for constructing an explicit set of minimal sufficient statistics, based on partial scores and likelihood ratios, is given. The difference in dimension between parameterand statistic and the curvature of these models have important consequences for inference. It is not the purpose of this paper to contribute significantly to the theory of curved exponential models, other than to show that the theory applies to many econometric models and to highlight some multivariate aspects. Using the methods developed in the first part, we show that demand systems, the single structural equation model, the seemingly unrelated regressions, and autoregressive models are all curved exponential models.

Suggested Citation

  • van Garderen, Kees Jan, 1997. "Curved Exponential Models in Econometrics," Econometric Theory, Cambridge University Press, vol. 13(6), pages 771-790, December.
    • Handle: RePEc:cup:etheor:v:13:y:1997:i:06:p:771-790_00
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    Cited by:

    1. van Garderen, Kees Jan, 2001. "Optimal prediction in loglinear models," Journal of Econometrics, Elsevier, vol. 104(1), pages 119-140, August.
    2. Alexandre Belloni & Victor Chernozhukov, 2014. "Posterior inference in curved exponential families under increasing dimensions," Econometrics Journal, Royal Economic Society, vol. 17(2), pages 75-100, June.
    3. Sancetta, A. & Nikanrova, A., 2005. "Forecasting and Prequential Validation for Time Varying Meta-Elliptical Distributions with a Study of Commodity Futures Prices," Cambridge Working Papers in Economics 0516, Faculty of Economics, University of Cambridge.
    4. Vassilios Bazinas & Bent Nielsen, 2022. "Causal Transmission in Reduced-Form Models," Econometrics, MDPI, vol. 10(2), pages 1-25, March.
    5. Sancetta, Alessio, 2009. "Nearest neighbor conditional estimation for Harris recurrent Markov chains," Journal of Multivariate Analysis, Elsevier, vol. 100(10), pages 2224-2236, November.
    6. Christis Katsouris, 2023. "Optimal Estimation Methodologies for Panel Data Regression Models," Papers 2311.03471, arXiv.org, revised Nov 2023.
    7. Kees Jan van Garderen & Noud van Giersbergen, 2020. "A Nearly Similar Powerful Test for Mediation," Papers 2012.11342, arXiv.org, revised Jan 2022.

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