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Expectations, Learning Gains, and Forecast Errors: Assessing Nonlinearities with a Functional Coefficient Approach

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  • Fabio Milani

Abstract

This paper investigates potential nonlinearities in the gain function, which, under adaptive learning, regulates the updating of agents' beliefs in response to recent forecast errors. I use data on professional survey forecasts to estimate nonparametric functional-coefficient regression models. The estimation results reveal nonlinearities in the relationships between expectations and forecast errors, which are indicative of nonlinear gain functions. Gains increase when forecast errors are historically large, and respond asymmetrically to past overpredictions and underpredictions. The findings suggest incorporating nonlinearities in the modeling of learning gains, instead of relying on the constant-gain assumption.

Suggested Citation

  • Fabio Milani, 2025. "Expectations, Learning Gains, and Forecast Errors: Assessing Nonlinearities with a Functional Coefficient Approach," CESifo Working Paper Series 12124, CESifo.
    • Handle: RePEc:ces:ceswps:_12124
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    References listed on IDEAS

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    1. Slobodyan, Sergey & Wouters, Raf, 2012. "Learning in an estimated medium-scale DSGE model," Journal of Economic Dynamics and Control, Elsevier, vol. 36(1), pages 26-46.
    2. Milani, Fabio, 2017. "Sentiment and the U.S. business cycle," Journal of Economic Dynamics and Control, Elsevier, vol. 82(C), pages 289-311.
    3. George William Evans, 2001. "Expectations in Macroeconomics Adaptive versus Eductive Learning," Revue économique, Presses de Sciences-Po, vol. 52(3), pages 573-582.
    4. Sergey Slobodyan & Raf Wouters, 2012. "Learning in a Medium-Scale DSGE Model with Expectations Based on Small Forecasting Models," American Economic Journal: Macroeconomics, American Economic Association, vol. 4(2), pages 65-101, April.
    5. Albert Marcet & Juan P. Nicolini, 2003. "Recurrent Hyperinflations and Learning," American Economic Review, American Economic Association, vol. 93(5), pages 1476-1498, December.
    6. Fabio Milani, 2011. "Expectation Shocks and Learning as Drivers of the Business Cycle," Economic Journal, Royal Economic Society, vol. 121(552), pages 379-401, May.
    7. Leland E. Farmer & Emi Nakamura & Jón Steinsson, 2024. "Learning about the Long Run," Journal of Political Economy, University of Chicago Press, vol. 132(10), pages 3334-3377.
    8. Cai, Zongwu & Fan, Jianqing & Yao, Qiwei, 2000. "Functional-coefficient regression models for nonlinear time series," LSE Research Online Documents on Economics 6314, London School of Economics and Political Science, LSE Library.
    9. Gáti, Laura, 2023. "Monetary policy & anchored expectations—An endogenous gain learning model," Journal of Monetary Economics, Elsevier, vol. 140(S), pages 37-47.
    10. Milani, Fabio, 2007. "Expectations, learning and macroeconomic persistence," Journal of Monetary Economics, Elsevier, vol. 54(7), pages 2065-2082, October.
    11. Milani, Fabio, 2014. "Learning and time-varying macroeconomic volatility," Journal of Economic Dynamics and Control, Elsevier, vol. 47(C), pages 94-114.
    12. Patton, Andrew J. & Timmermann, Allan, 2010. "Why do forecasters disagree? Lessons from the term structure of cross-sectional dispersion," Journal of Monetary Economics, Elsevier, vol. 57(7), pages 803-820, October.
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    Keywords

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    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • E31 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Price Level; Inflation; Deflation
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles
    • E70 - Macroeconomics and Monetary Economics - - Macro-Based Behavioral Economics - - - General

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