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

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  • 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. Mittag, Nikolas, 2019. "A simple method to estimate large fixed effects models applied to wage determinants," Labour Economics, Elsevier, vol. 61(C).
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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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