Stanisław Marek Sergiusz Halkiewicz, Andrzej Kałuża
arXiv 7 Dec 2025 · Econometrics
arXiv:2512.06946 · PDF · Extracted main text
This article develops a significance test for the Difference-in-Differences (DiD) estimator based on doubly randomised inference, in which both the treatment and time indicators are permuted to generate an empirical null distribution of the DiD coefficient. Unlike classical $t$-tests or single-margin permutation procedures, the proposed method exploits a substantially enlarged randomization space. We formally characterise this expansion and show that dual randomization increases the number of admissible relabelings by a factor of $\binom{n}{n_T}$, yielding an exponentially richer permutation universe. This combinatorial gain implies a denser and more stable approximation of the null distribution, a result further justified through an information-theoretic (entropy) interpretation. The validity and finite-sample behaviour of the test are examined using multiple empirical datasets commonly analysed in applied economics, including the Indonesian school construction program (INPRES), brand search data, minimum wage reforms, and municipality-level refugee inflows in Greece. Across all settings, doubly randomised inference performs comparably to standard approaches while offering superior small-sample stability and sharper critical regions due to the enlarged permutation space. The proposed procedure therefore provides a robust, nonparametric alternative for assessing the statistical significance of DiD estimates, particularly in designs with limited group sizes or irregular assignment structures.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Imbens, Guido W. and Rubin, Donald B (2015) Causal Inference for Statistics, Social, and Biomedical Sciences: An Introduction | 0.874 | 6 | 2 | 100% |
| 2 | MacKinnon, James G. and Webb, Matthew D (2020) Randomization inference for difference-in-differences with few treated clusters | 0.843 | 3 | 3 | 100% |
| 3 | Fisher, Ronald A (1935) The Design of Experiments | 0.811 | 4 | 2 | 100% |
| 4 | Neyman, Jerzy (1990) On the Application of Probability Theory to Agricultural Experiments. Essay on Principles | 0.737 | 3 | 2 | 100% |
| 5 | Rosenbaum, Paul R (2002) Observational Studies | 0.644 | 4 | 1 | 100% |
| 6 | Cameron, A. Colin and Trivedi, Pravin K (2005) Microeconometrics: Methods and Applications | 0.644 | 2 | 2 | 100% |
| 7 | Conley, Timothy G. and Taber, Christopher R (2011) Inference with "Difference in Differences" with a Small Number of Policy Changes | 0.644 | 2 | 2 | 100% |
| 8 | Ferman, Bruno and Pinto, Cristine (2019) Inference in Differences-in-Differences with Few Treated Groups and Heteroskedasticity | 0.644 | 2 | 2 | 100% |
| 9 | Halkiewicz, Stanisław M. S (2023) Modele Difference-in-Differences w ewaluacji wpływu zdarzeń ekonomicznych na poprawę edukacji self | 0.644 | 2 | 2 | 100% |
| 10 | Stanisław M. S. Halkiewicz (2024) Ocena możliwości aplikacyjnych modeli Difference-in-Differences w badaniu efektywności komunikacji marketingowej self | 0.644 | 2 | 2 | 100% |
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