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ANOVA-HDFE: Fast Variance Decomposition with High-Dimensional Fixed Effects and an Application to Trade Flows

Author

Listed:
  • Hanna L. Adam
  • Mario Larch
  • Michael Nower

Abstract

Performing an analysis of variance (ANOVA) on a large dataset spanning many dimensions becomes computationally challenging or even infeasible. We develop a new, fast procedure, ANOVA-HDFE, which uses sequential linear regressions and builds on recent advances in regression analysis with high-dimensional fixed effects (HDFE). It accommodates both balanced and unbalanced settings with many categorical and continuous covariates, while also allowing for high-dimensional fixed effects. Applying ANOVA-HDFE to bilateral trade flows, we find that 60% of the variation is at the country or country-time level. Moreover, a substantial proportion of the pair-specific variation remains unexplained by standard trade cost proxy variables.

Suggested Citation

  • Hanna L. Adam & Mario Larch & Michael Nower, 2025. "ANOVA-HDFE: Fast Variance Decomposition with High-Dimensional Fixed Effects and an Application to Trade Flows," CESifo Working Paper Series 12055, CESifo.
    • Handle: RePEc:ces:ceswps:_12055
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    References listed on IDEAS

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    1. Paulo Guimarães & Pedro Portugal, 2010. "A simple feasible procedure to fit models with high-dimensional fixed effects," Stata Journal, StataCorp LLC, vol. 10(4), pages 628-649, December.
    2. Redding, Stephen J. & Weinstein, David E., 2024. "Accounting for trade patterns," Journal of International Economics, Elsevier, vol. 150(C).
    3. Torres, Sónia & Portugal, Pedro & Addison, John T. & Guimarães, Paulo, 2018. "The sources of wage variation and the direction of assortative matching: Evidence from a three-way high-dimensional fixed effects regression model," Labour Economics, Elsevier, vol. 54(C), pages 47-60.
    4. Egger, Peter & Nigai, Sergey, 2015. "Structural Gravity with Dummies Only," CEPR Discussion Papers 10427, C.E.P.R. Discussion Papers.
    5. Mittag, Nikolas, 2019. "A simple method to estimate large fixed effects models applied to wage determinants," Labour Economics, Elsevier, vol. 61(C).
    Full references (including those not matched with items on IDEAS)

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    Keywords

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    JEL classification:

    • F14 - International Economics - - Trade - - - Empirical Studies of Trade
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models
    • C55 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Large Data Sets: Modeling and Analysis
    • F16 - International Economics - - Trade - - - Trade and Labor Market Interactions

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