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The vector error correction index model: representation, estimation and identification

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  • Gianluca Cubadda
  • Marco Mazzali

Abstract

SummaryThis paper extends the multivariate index autoregressive model to the case of cointegrated time series of order (1,1). In this new modelling, namely the vector error-correction index model (VECIM), the first differences of series are driven by some linear combinations of the variables, namely the indexes. When the indexes are significantly fewer than the variables, the VECIM achieves a substantial dimension reduction with reference to the vector error correction model. We show that the VECIM allows one to decompose the reduced-form errors into sets of common and uncommon shocks, and that the former can be further decomposed into permanent and transitory shocks. Moreover, we offer a switching algorithm for optimal estimation of the VECIM. Finally, we document the practical value of the proposed approach by both simulations and an empirical application, where we search for the shocks that drive the aggregate fluctuations at different frequency bands in the US.

Suggested Citation

  • Gianluca Cubadda & Marco Mazzali, 2024. "The vector error correction index model: representation, estimation and identification," The Econometrics Journal, Royal Economic Society, vol. 27(1), pages 126-150.
    • Handle: RePEc:oup:emjrnl:v:27:y:2024:i:1:p:126-150.
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    File URL: http://hdl.handle.net/10.1093/ectj/utad023
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    Cited by:

    1. Alain Hecq & Ivan Ricardo & Ines Wilms, 2024. "Reduced-Rank Matrix Autoregressive Models: A Medium $N$ Approach," Papers 2407.07973, arXiv.org.
    2. Cubadda, Gianluca & Grassi, Stefano & Guardabascio, Barbara, 2025. "The time-varying Multivariate Autoregressive Index model," International Journal of Forecasting, Elsevier, vol. 41(1), pages 175-190.
    3. Razan Alghannam & Abeer Alharbi, 2026. "Assessing the impact of government healthcare expenditure and life expectancy on economic growth in Saudi Arabia: an econometric time-series study (2000–2023)," Health Economics Review, Springer, vol. 16(1), pages 1-15, December.
    4. Gianluca Cubadda, 2025. "VAR Models with an Index Structure: A Survey with New Results," Econometrics, MDPI, vol. 13(4), pages 1-17, October.
    5. Hecq, Alain & Ricardo, Ivan & Wilms, Ines, 2025. "Detecting cointegrating relations in non-stationary matrix-valued time series," Economics Letters, Elsevier, vol. 248(C).

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