References
==========

This library implements methods from the following scholarly works.

Difference-in-Differences
-------------------------

- **Ashenfelter, O., & Card, D. (1985).** "Using the Longitudinal Structure of Earnings to Estimate the Effect of Training Programs." *The Review of Economics and Statistics*, 67(4), 648-660. https://doi.org/10.2307/1924810

- **Card, D., & Krueger, A. B. (1994).** "Minimum Wages and Employment: A Case Study of the Fast-Food Industry in New Jersey and Pennsylvania." *The American Economic Review*, 84(4), 772-793. https://www.jstor.org/stable/2118030

- **Angrist, J. D., & Pischke, J.-S. (2009).** *Mostly Harmless Econometrics: An Empiricist's Companion*. Princeton University Press. Chapter 5: Differences-in-Differences.

Two-Way Fixed Effects
---------------------

- **Wooldridge, J. M. (2010).** *Econometric Analysis of Cross Section and Panel Data* (2nd ed.). MIT Press.

- **Imai, K., & Kim, I. S. (2021).** "On the Use of Two-Way Fixed Effects Regression Models for Causal Inference with Panel Data." *Political Analysis*, 29(3), 405-415. https://doi.org/10.1017/pan.2020.33

Wooldridge ETWFE
----------------

- **Wooldridge, J. M. (2025).** "Two-Way Fixed Effects, the Two-Way Mundlak Regression, and Difference-in-Differences Estimators." *Empirical Economics*, 69(5), 2545-2587. (Published version of NBER Working Paper 29154.)

  Primary source for the saturated OLS ETWFE design implemented in our ``WooldridgeDiD`` class.

- **Wooldridge, J. M. (2023).** "Simple Approaches to Nonlinear Difference-in-Differences with Panel Data." *The Econometrics Journal*, 26(3), C31-C66. https://doi.org/10.1093/ectj/utad016

  Secondary source for the logit/Poisson QMLE (ASF-based ATT) extensions in ``WooldridgeDiD``.

Robust Standard Errors
----------------------

- **White, H. (1980).** "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity." *Econometrica*, 48(4), 817-838. https://doi.org/10.2307/1912934

- **MacKinnon, J. G., & White, H. (1985).** "Some Heteroskedasticity-Consistent Covariance Matrix Estimators with Improved Finite Sample Properties." *Journal of Econometrics*, 29(3), 305-325. https://doi.org/10.1016/0304-4076(85)90158-7

- **Cameron, A. C., Gelbach, J. B., & Miller, D. L. (2011).** "Robust Inference With Multiway Clustering." *Journal of Business & Economic Statistics*, 29(2), 238-249. https://doi.org/10.1198/jbes.2010.07136

Wild Cluster Bootstrap
----------------------

- **Wu, C. F. J. (1986).** "Jackknife, Bootstrap and Other Resampling Methods in Regression Analysis." *The Annals of Statistics*, 14(4), 1261-1295. https://doi.org/10.1214/aos/1176350142

  Source of the ``sqrt(n_h/(n_h-1))`` Bessel small-sample correction applied to within-stratum bootstrap multipliers in :func:`diff_diff.bootstrap_utils.apply_stratum_centering`.

- **Liu, R. Y. (1988).** "Bootstrap Procedures Under Some Non-I.I.D. Models." *The Annals of Statistics*, 16(4), 1696-1708. https://doi.org/10.1214/aos/1176351062

- **Cameron, A. C., Gelbach, J. B., & Miller, D. L. (2008).** "Bootstrap-Based Improvements for Inference with Clustered Errors." *The Review of Economics and Statistics*, 90(3), 414-427. https://doi.org/10.1162/rest.90.3.414

- **Davidson, R., & Flachaire, E. (2008).** "The Wild Bootstrap, Tamed at Last." *Journal of Econometrics*, 146(1), 162-169. https://doi.org/10.1016/j.jeconom.2008.08.003

  Wild bootstrap for heteroskedastic regression. Cited as an ingredient — the within-cluster mean-zero requirement on the multipliers (the canonical ``η_g`` centering that makes the wild bootstrap recover heteroskedasticity-robust inference) is the analog applied within each stratum in :func:`diff_diff.bootstrap_utils.apply_stratum_centering`. The paper does NOT cover stratified-survey designs directly; the stratification extension is the library synthesis (see REGISTRY § "Note (Stute stratified survey-bootstrap calibration)").

- **Kreiss, J.-P., & Lahiri, S. N. (2012).** "Bootstrap Methods for Time Series." In *Time Series Analysis: Methods and Applications* (Vol. 30, pp. 3-26). Elsevier. https://doi.org/10.1016/B978-0-444-53858-1.00001-6

  Bootstrap methods for time series. Cited as a methodological touchstone for the family of block-bootstrap / within-block centering arguments that underpins the wild-cluster-bootstrap extension to stratified PSU sampling. The exact composition (within-stratum demean + ``sqrt(n_h/(n_h-1))`` Bessel rescale on PSU multipliers applied before the per-obs broadcast in a wild-residual refit-in-loop bootstrap for a nonlinear empirical-process functional like the Stute CvM) is NOT in any single paper — it is a library synthesis of these ingredients.

- **Webb, M. D. (2014).** "Reworking Wild Bootstrap Based Inference for Clustered Errors." Queen's Economics Department Working Paper No. 1315. https://www.econ.queensu.ca/sites/econ.queensu.ca/files/qed_wp_1315.pdf

- **MacKinnon, J. G., & Webb, M. D. (2018).** "The Wild Bootstrap for Few (Treated) Clusters." *The Econometrics Journal*, 21(2), 114-135. https://doi.org/10.1111/ectj.12107

- **Djogbenou, A. A., MacKinnon, J. G., & Nielsen, M. Ø. (2019).** "Asymptotic Theory and Wild Bootstrap Inference with Clustered Errors." *Journal of Econometrics*, 212(2), 393-412. https://doi.org/10.1016/j.jeconom.2019.04.035

  Theorem 2 establishes empirical-process consistency of the cluster wild bootstrap for nonlinear smooth-functional consumers of per-obs residuals — the theoretical anchor for the stratified Stute CvM survey-bootstrap in :func:`diff_diff.had_pretests.stute_test` / :func:`stute_joint_pretest` (Phase 4.5 C strata extension).

- **Hlávka, Z., & Hušková, M. (2020).** "Multivariate Tests of Independence and the Wild Bootstrap." *Computational Statistics & Data Analysis*, 152, 107048. https://doi.org/10.1016/j.csda.2020.107048

  Vector-valued wild bootstrap consistency for empirical-process functionals (§3 condition on shared per-replicate multipliers preserving cross-component dependence). The theoretical anchor for the multi-horizon joint Stute survey-bootstrap in :func:`diff_diff.had_pretests.stute_joint_pretest` (the same ``psu_mults[b, :]`` row is shared across horizons within each replicate, preserving cross-horizon empirical-process dependence).

Nonparametric Bias-Corrected Inference
--------------------------------------

- **Calonico, S., Cattaneo, M. D., & Titiunik, R. (2014).** "Robust Nonparametric Confidence Intervals for Regression-Discontinuity Designs." *Econometrica*, 82(6), 2295-2326. https://doi.org/10.3982/ECTA11757

  Source of the bias-combined design matrix used by the in-house ``lprobust`` port that backs ``HeterogeneousAdoptionDiD`` Phase 1c (continuous-dose paths) for the bias-corrected weighted-robust SE.

- **Calonico, S., Cattaneo, M. D., & Farrell, M. H. (2018).** "On the Effect of Bias Estimation on Coverage Accuracy in Nonparametric Inference." *Journal of the American Statistical Association*, 113(522), 767-779. https://doi.org/10.1080/01621459.2017.1285776

- **Calonico, S., Cattaneo, M. D., & Farrell, M. H. (2019).** "nprobust: Nonparametric Kernel-Based Estimation and Robust Bias-Corrected Inference." *Journal of Statistical Software*, 91(8), 1-33. https://doi.org/10.18637/jss.v091.i08

  CCF (2018, 2019) is the underlying ``nprobust`` machinery (MSE-optimal bandwidth selection and robust bias-corrected CIs) that ``HeterogeneousAdoptionDiD`` ports in-house for the continuous-dose paths.

Survey-Design Inference (Taylor-Series Linearization)
-----------------------------------------------------

- **Binder, D. A. (1983).** "On the Variances of Asymptotically Normal Estimators from Complex Surveys." *International Statistical Review*, 51(3), 279-292. https://doi.org/10.2307/1402588

  Foundational TSL (Taylor-Series Linearization) variance derivation used across diff-diff's survey-aware estimators (``compute_survey_if_variance`` and the per-estimator influence-function compositions, including the dCDH and HeterogeneousAdoptionDiD ``survey_design=`` paths).

- **Gerber, I. (2026).** "Design-Based Variance Estimation for Modern Heterogeneity-Robust Difference-in-Differences Estimators." *arXiv:2605.04124* (stat.ME). https://arxiv.org/abs/2605.04124

  Proposition 1 shows that the influence-function representations of 15 modern DiD estimators (including TwoStageDiD, explicitly derived in the Appendix) satisfy Binder's (1983) smoothness conditions, so standard stratified-cluster Taylor linearization produces design-consistent SEs. SpilloverDiD's Wave E.1 survey-design integration composes this result with the Wave D Gardner GMM first-stage uncertainty correction; see ``docs/methodology/REGISTRY.md`` SpilloverDiD section "Variance (Wave E.1)".

Placebo Tests and DiD Diagnostics
---------------------------------

- **Bertrand, M., Duflo, E., & Mullainathan, S. (2004).** "How Much Should We Trust Differences-in-Differences Estimates?" *The Quarterly Journal of Economics*, 119(1), 249-275. https://doi.org/10.1162/003355304772839588

Synthetic Control Method
------------------------

- **Abadie, A., & Gardeazabal, J. (2003).** "The Economic Costs of Conflict: A Case Study of the Basque Country." *The American Economic Review*, 93(1), 113-132. https://doi.org/10.1257/000282803321455188

- **Abadie, A., Diamond, A., & Hainmueller, J. (2010).** "Synthetic Control Methods for Comparative Case Studies: Estimating the Effect of California's Tobacco Control Program." *Journal of the American Statistical Association*, 105(490), 493-505. https://doi.org/10.1198/jasa.2009.ap08746

- **Abadie, A., Diamond, A., & Hainmueller, J. (2015).** "Comparative Politics and the Synthetic Control Method." *American Journal of Political Science*, 59(2), 495-510. https://doi.org/10.1111/ajps.12116

Synthetic Difference-in-Differences
-----------------------------------

- **Arkhangelsky, D., Athey, S., Hirshberg, D. A., Imbens, G. W., & Wager, S. (2021).** "Synthetic Difference-in-Differences." *American Economic Review*, 111(12), 4088-4118. https://doi.org/10.1257/aer.20190159

Triply Robust Panel (TROP)
--------------------------

- **Athey, S., Imbens, G. W., Qu, Z., & Viviano, D. (2025).** "Triply Robust Panel Estimators." *Working Paper*. https://arxiv.org/abs/2508.21536

  This paper introduces the TROP estimator which combines three robustness components:

  - **Factor model adjustment**: Low-rank factor structure via SVD removes unobserved confounders
  - **Unit weights**: Synthetic control style weighting for optimal comparison
  - **Time weights**: SDID style time weighting for informative pre-periods

  TROP is particularly useful when there are unobserved time-varying confounders with a factor structure that affect different units differently over time.

Triple Difference (DDD)
-----------------------

- **Ortiz-Villavicencio, M., & Sant'Anna, P. H. C. (2025).** "Better Understanding Triple Differences Estimators." *Working Paper*. https://arxiv.org/abs/2505.09942

  This paper shows that common DDD implementations (taking the difference between two DiDs, or applying three-way fixed effects regressions) are generally invalid when identification requires conditioning on covariates. The ``TripleDifference`` class implements their regression adjustment, inverse probability weighting, and doubly robust estimators.

- **Gruber, J. (1994).** "The Incidence of Mandated Maternity Benefits." *American Economic Review*, 84(3), 622-641. https://www.jstor.org/stable/2118071

  Classic paper introducing the Triple Difference design for policy evaluation.

- **Olden, A., & Møen, J. (2022).** "The Triple Difference Estimator." *The Econometrics Journal*, 25(3), 531-553. https://doi.org/10.1093/ectj/utac010

Parallel Trends and Pre-Trend Testing
-------------------------------------

- **Roth, J. (2022).** "Pretest with Caution: Event-Study Estimates after Testing for Parallel Trends." *American Economic Review: Insights*, 4(3), 305-322. https://doi.org/10.1257/aeri.20210236

- **Lakens, D. (2017).** "Equivalence Tests: A Practical Primer for t Tests, Correlations, and Meta-Analyses." *Social Psychological and Personality Science*, 8(4), 355-362. https://doi.org/10.1177/1948550617697177

Honest DiD / Sensitivity Analysis
---------------------------------

The ``HonestDiD`` module implements sensitivity analysis methods for relaxing the parallel trends assumption.

- **Rambachan, A., & Roth, J. (2023).** "A More Credible Approach to Parallel Trends." *The Review of Economic Studies*, 90(5), 2555-2591. https://doi.org/10.1093/restud/rdad018

  This paper introduces the "Honest DiD" framework implemented in our ``HonestDiD`` class:

  - **Relative Magnitudes (ΔRM)**: Bounds post-treatment violations by a multiple of observed pre-treatment violations
  - **Smoothness (ΔSD)**: Bounds on second differences of trend violations, allowing for linear extrapolation of pre-trends
  - **Breakdown Analysis**: Finding the smallest violation magnitude that would overturn conclusions
  - **Robust Confidence Intervals**: Valid inference under partial identification

- **Roth, J., & Sant'Anna, P. H. C. (2023).** "When Is Parallel Trends Sensitive to Functional Form?" *Econometrica*, 91(2), 737-747. https://doi.org/10.3982/ECTA19402

  Discusses functional form sensitivity in parallel trends assumptions, relevant to understanding when smoothness restrictions are appropriate.

Multi-Period and Staggered Adoption
-----------------------------------

- **Borusyak, K., Jaravel, X., & Spiess, J. (2024).** "Revisiting Event-Study Designs: Robust and Efficient Estimation." *Review of Economic Studies*, 91(6), 3253-3285. https://doi.org/10.1093/restud/rdae007

  This paper introduces the imputation estimator implemented in our ``ImputationDiD`` class:

  - **Efficient imputation**: OLS on untreated observations, impute counterfactuals, aggregate
  - **Conservative variance**: Theorem 3 clustered variance estimator with auxiliary model
  - **Pre-trend test**: Independent of treatment effect estimation (Proposition 9)
  - **Efficiency gains**: ~50% shorter CIs than Callaway-Sant'Anna under homogeneous effects

- **Callaway, B., & Sant'Anna, P. H. C. (2021).** "Difference-in-Differences with Multiple Time Periods." *Journal of Econometrics*, 225(2), 200-230. https://doi.org/10.1016/j.jeconom.2020.12.001

- **Sant'Anna, P. H. C., & Zhao, J. (2020).** "Doubly Robust Difference-in-Differences Estimators." *Journal of Econometrics*, 219(1), 101-122. https://doi.org/10.1016/j.jeconom.2020.06.003

- **Sun, L., & Abraham, S. (2021).** "Estimating Dynamic Treatment Effects in Event Studies with Heterogeneous Treatment Effects." *Journal of Econometrics*, 225(2), 175-199. https://doi.org/10.1016/j.jeconom.2020.09.006

- **Gardner, J. (2022).** "Two-stage differences in differences." *arXiv preprint arXiv:2207.05943*. https://arxiv.org/abs/2207.05943

- **Butts, K., & Gardner, J. (2022).** "did2s: Two-Stage Difference-in-Differences." *The R Journal*, 14(1), 162-173. https://doi.org/10.32614/RJ-2022-048

- **Butts, K. (2023).** "Difference-in-Differences with Spatial Spillovers." *arXiv:2105.03737v3* (originally posted 2021). https://arxiv.org/abs/2105.03737

  Identifies the ring-indicator estimator implemented in our ``SpilloverDiD`` class. Section 2-3 covers non-staggered timing (Equations 5/6/8); Section 5 covers staggered timing via two-stage Gardner (Table 2). Section 3.1 (page 13) recommends Conley spatial-HAC for inference with cutoff = ``d_bar``. Section 4 Table 1 Panel A (TVA agriculture) is the empirical anchor for tutorial ``docs/tutorials/23_spillover_tva.ipynb`` (~40% understatement direction).

- **Kline, P., & Moretti, E. (2014).** "Local Economic Development, Agglomeration Economies, and the Big Push: 100 Years of Evidence from the Tennessee Valley Authority." *The Quarterly Journal of Economics*, 129(1), 275-331. https://doi.org/10.1093/qje/qjt034

  Original Tennessee Valley Authority application that Butts (2021) §4 revisits to illustrate spillover bias in the canonical place-based-intervention DiD. Cited as the motivating real-world example in ``docs/tutorials/23_spillover_tva.ipynb``.

- **Conley, T. G. (1999).** "GMM Estimation with Cross Sectional Dependence." *Journal of Econometrics*, 92(1), 1-45. https://doi.org/10.1016/S0304-4076(98)00084-0

  Primary source for the Conley spatial-HAC variance estimator. Equations 5-9 derive the spatial-kernel cross-product meat. Our ``diff_diff/conley.py`` implements the practitioner specializations (Bartlett / uniform kernels with haversine / euclidean metrics) cited in our ``SpilloverDiD`` Wave A/D Conley path and composed with Binder TSL + Gardner GMM in Wave E.2 (``_compute_stratified_conley_meat`` at ``diff_diff/two_stage.py``).

- **de Chaisemartin, C., & D'Haultfœuille, X. (2020).** "Two-Way Fixed Effects Estimators with Heterogeneous Treatment Effects." *American Economic Review*, 110(9), 2964-2996. https://doi.org/10.1257/aer.20181169

- **de Chaisemartin, C., & D'Haultfœuille, X. (2022, revised July 2023).** "Difference-in-Differences Estimators of Intertemporal Treatment Effects." *NBER Working Paper* 29873. https://www.nber.org/papers/w29873

  Dynamic companion to the 2020 paper. Web Appendix Section 3.7.3 contains the cohort-recentered plug-in variance formula implemented in our ``ChaisemartinDHaultfoeuille`` class.

- **Goodman-Bacon, A. (2021).** "Difference-in-Differences with Variation in Treatment Timing." *Journal of Econometrics*, 225(2), 254-277. https://doi.org/10.1016/j.jeconom.2021.03.014

- **Newey, W. K., & West, K. D. (1987).** "A Simple, Positive Semi-Definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix." *Econometrica*, 55(3), 703-708. https://doi.org/10.2307/1913610

  Primary source for the Bartlett serial-HAC kernel weights `1 - |t-s|/(L+1)` used in time-series and panel HAC variance estimators. Our ``diff_diff/conley.py`` panel-block path at L949-965 hardcodes this kernel for the within-unit serial component (mirrors R ``conleyreg::time_dist``); SpilloverDiD's Wave E.2 follow-up composes the same kernel weights with Binder/Gerber TSL + Wave D Gardner GMM correction for the panel-block survey case (``_compute_stratified_serial_bartlett_meat`` at ``diff_diff/two_stage.py``; see REGISTRY section "Variance (Wave E.2 follow-up)").

- **Lumley, T. (2010).** *Complex Surveys: A Guide to Analysis Using R.* Hoboken, NJ: John Wiley & Sons. https://doi.org/10.1002/9780470580066

  Authoritative reference for the R ``survey`` package. §2.5 "Domains and subpopulations" documents the ``svyrecvar(subset(design, mask))`` zero-pad convention: subpopulation analyses preserve the full survey design (strata / PSU / FPC) and treat out-of-domain observations as zero-score padding rows rather than physically subsetting the design. SpilloverDiD's Wave E.3 adopts this convention at the ``_compute_gmm_corrected_meat`` boundary, matching the existing in-library precedents at ``diff_diff/imputation.py:2175-2183`` (PreTrendsImputation lead regression) and ``diff_diff/prep.py:1401-1432`` (DCDH cell variance); see REGISTRY section "Variance (Wave E.3)".

- **Wing, C., Freedman, S. M., & Hollingsworth, A. (2024).** "Stacked Difference-in-Differences." *NBER Working Paper* 32054. https://www.nber.org/papers/w32054

- **Chen, X., Sant'Anna, P. H. C., & Xie, H. (2025).** "Efficient Difference-in-Differences and Event Study Estimators." *Working Paper*.

  Primary source for the optimal-weighting / PT-All / PT-Post efficient DiD implemented in our ``EfficientDiD`` class.

- **Baker, A., Callaway, B., Cunningham, S., Goodman-Bacon, A., & Sant'Anna, P. H. C. (2025).** "Difference-in-Differences Designs: A Practitioner's Guide." *arXiv preprint* arXiv:2503.13323. https://arxiv.org/abs/2503.13323

  Source for the 8-step practitioner workflow surfaced via ``diff_diff.get_llm_guide("practitioner")`` and the README ``## Practitioner Workflow`` section. See ``docs/methodology/REGISTRY.md`` for the diff-diff renumbering and per-step deviations.

Continuous Treatment DiD
------------------------

- **Callaway, B., Goodman-Bacon, A., & Sant'Anna, P. H. C. (2024).** "Difference-in-Differences with a Continuous Treatment." *NBER Working Paper* 32117. https://www.nber.org/papers/w32117

  Primary source for ATT(d), ACRT, dose-response curves, and B-spline flexibility implemented in our ``ContinuousDiD`` class.

Heterogeneous Adoption (No-Untreated Designs)
---------------------------------------------

- **de Chaisemartin, C., Ciccia, D., D'Haultfœuille, X., & Knau, F. (2026).** "Difference-in-Differences Estimators When No Unit Remains Untreated." *arXiv preprint* arXiv:2405.04465v6. https://arxiv.org/abs/2405.04465

  Primary source for the Weighted Average Slope (WAS) estimator and its multi-period event-study extension implemented in our ``HeterogeneousAdoptionDiD`` class. Targets panels where no unit remains untreated at the post period and treatment dose ``D_{g,2}`` is nonnegative, using local-linear regression at the dose support boundary - both Design 1' (the QUG case with ``d̲ = 0``) and Design 1 (no QUG with ``d̲ > 0``) are supported.

Power Analysis
--------------

- **Bloom, H. S. (1995).** "Minimum Detectable Effects: A Simple Way to Report the Statistical Power of Experimental Designs." *Evaluation Review*, 19(5), 547-556. https://doi.org/10.1177/0193841X9501900504

- **Burlig, F., Preonas, L., & Woerman, M. (2020).** "Panel Data and Experimental Design." *Journal of Development Economics*, 144, 102458. https://doi.org/10.1016/j.jdeveco.2020.102458

  Essential reference for power analysis in panel DiD designs. Discusses how serial correlation (ICC) affects power and provides formulas for panel data settings.

- **Djimeu, E. W., & Houndolo, D.-G. (2016).** "Power Calculation for Causal Inference in Social Science: Sample Size and Minimum Detectable Effect Determination." *Journal of Development Effectiveness*, 8(4), 508-527. https://doi.org/10.1080/19439342.2016.1244555

General Causal Inference
------------------------

- **Imbens, G. W., & Rubin, D. B. (2015).** *Causal Inference for Statistics, Social, and Biomedical Sciences: An Introduction*. Cambridge University Press.

- **Cunningham, S. (2021).** *Causal Inference: The Mixtape*. Yale University Press. https://mixtape.scunning.com/
