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fix(docs): repair UTF-8 characters and MathJax inline rendering in tables
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‎_config.yml‎

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mathjax:
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source: https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/latest.js?config=TeX-AMS_CHTML
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config: 'MathJax.Hub.Config({ TeX: { equationNumbers: { autoNumber: "AMS" } } })'
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config: 'MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }, TeX: { equationNumbers: { autoNumber: "AMS" } } })'

‎docs/01_stata.md‎

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| [csdid](https://friosavila.github.io/playingwithstata/main_csdid.html) | `ssc install csdid, replace` | Fernando Rios-Avila; Pedro H.C. Sant'Anna; Brantly Callaway | [Callaway & Sant'Anna (2020)](https://www.sciencedirect.com/science/article/abs/pii/S0304407620303948) |
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| [csdid2](https://github.com/friosavila/stpackages/tree/main/csdid2) | [Instructions](https://github.com/friosavila/stpackages/tree/main/csdid2) | Fernando Rios-Avila | [Callaway & Sant'Anna (2020)](https://www.sciencedirect.com/science/article/abs/pii/S0304407620303948) |
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| [did2s](https://github.com/kylebutts/did2s_stata) | `ssc install did2s, replace` | Kyle Butts | [Gardner (2022)](https://arxiv.org/abs/2207.05943) |
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| [did_multiplegt](https://github.com/chaisemartinPackages) | `ssc install did_multiplegt, replace` | Clément de Chaisemartin; Xavier D'Haultfoeuille | [de Chaisemartin & D'Haultfoeuille (2020)](https://www.aeaweb.org/articles?id=10.1257/aer.20181169); [de Chaisemartin & D'Haultfoeuille (2021)](https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3751060) |
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| [did_multiplegt_dyn](https://github.com/chaisemartinPackages) | `ssc install did_multiplegt_dyn, replace` | Clément de Chaisemartin; Diego Ciccia; Xavier D'Haultfoeuille; Felix Knau; Mélitine Malézieux; Doulo Sow | [de Chaisemartin & D'Haultfoeuille (2024a)](https://doi.org/10.1162/rest_a_01414); [de Chaisemartin et al. (2024c)](https://drive.google.com/file/d/1NGgScujLCCS4RrwdN-PC1SnVigfBa32h/view) |
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| [did_multiplegt](https://github.com/chaisemartinPackages) | `ssc install did_multiplegt, replace` | Clément de Chaisemartin; Xavier D'Haultfoeuille | [de Chaisemartin & D'Haultfoeuille (2020)](https://www.aeaweb.org/articles?id=10.1257/aer.20181169); [de Chaisemartin & D'Haultfoeuille (2021)](https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3751060) |
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| [did_multiplegt_dyn](https://github.com/chaisemartinPackages) | `ssc install did_multiplegt_dyn, replace` | Clément de Chaisemartin; Diego Ciccia; Xavier D'Haultfoeuille; Felix Knau; Mélitine Malézieux; Doulo Sow | [de Chaisemartin & D'Haultfoeuille (2024a)](https://doi.org/10.1162/rest_a_01414); [de Chaisemartin et al. (2024c)](https://drive.google.com/file/d/1NGgScujLCCS4RrwdN-PC1SnVigfBa32h/view) |
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| [did_imputation](https://github.com/borusyak/did_imputation) | `ssc install did_imputation, replace` | Kirill Borusyak; Xavier Jaravel; Jann Spiess | [Borusyak, Jaravel, Spiess (2024)](https://academic.oup.com/restud/advance-article/doi/10.1093/restud/rdae007/7601390) |
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| [did_stepwise](https://github.com/nikoharm/did_stepwise) | [Instructions](https://github.com/nikoharm/did_stepwise) | Nikolaj Harmon | [Harmon (2024)](https://web.econ.ku.dk/nharmon/docs/harmon2022difference.pdf) |
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| [drdid](https://friosavila.github.io/playingwithstata/main_drdid.html) | `ssc install drdid, replace` | Fernando Rios-Avila; Pedro H.C. Sant'Anna; Asjad Naqvi | [Sant'Anna & Zhao (2020)](https://www.sciencedirect.com/science/article/abs/pii/S0304407620301901) |
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| xtdidregress | Stata 17+ | StataCorp | Canonical panel DiD (official Stata implementation) |
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| [honestdid](https://github.com/mcaceresb/stata-honestdid) | `ssc install honestdid, replace` | Mauricio Caceres Bravo; Jonathan Roth | [Rambachan & Roth (2023)](https://www.restud.com/a-more-credible-approach-to-parallel-trends/) |
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| [jwdid](https://friosavila.github.io/playingwithstata/main_jwdid.html) | `ssc install jwdid, replace` | Fernando Rios-Avila | [Nagengast, Rios-Avila, Yotov (2024)](https://ideas.repec.org/p/ris/drxlwp/2024_005.html), [Wooldridge notes](https://www.dropbox.com/sh/zj91darudf2fica/AADj_jaf5ZuS1muobgsnxS6Za?dl=0) |
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| [lpdid](https://github.com/danielegirardi/lpdid) | `ssc install lpdid, replace` | Alexander Busch; Daniele Girardi | [Dube, Girardi, JordÃ, Taylor (2023)](https://www.nber.org/papers/w31184) |
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| [multe](https://github.com/gphk-metrics/stata-multe) | [Instructions](https://github.com/gphk-metrics/stata-multe) | Mauricio Caceres Bravo; Paul Goldsmith-Pinkham | [Goldsmith-Pinkham, Hull, Kolesár (2024)](https://arxiv.org/abs/2106.05024) |
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| [lpdid](https://github.com/danielegirardi/lpdid) | `ssc install lpdid, replace` | Alexander Busch; Daniele Girardi | [Dube, Girardi, Jordá, Taylor (2023)](https://www.nber.org/papers/w31184) |
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| [multe](https://github.com/gphk-metrics/stata-multe) | [Instructions](https://github.com/gphk-metrics/stata-multe) | Mauricio Caceres Bravo; Paul Goldsmith-Pinkham | [Goldsmith-Pinkham, Hull, Kolesár (2024)](https://arxiv.org/abs/2106.05024) |
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| [pretrends](https://github.com/mcaceresb/stata-pretrends) | `ssc install pretrends, replace` | Mauricio Caceres Bravo; Jonathan Roth | [Roth (2022)](https://www.aeaweb.org/articles?id=10.1257/aeri.20210236) |
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| [robustate](https://sites.google.com/site/yuyasasaki/Home/stata/stata-command-robustate) | `ssc install robustate, replace` | Yuya Sasaki; Takuya Ura | [Sasaki & Ura (2021)](https://www.cambridge.org/core/journals/econometric-theory/article/abs/estimation-and-inference-for-moments-of-ratios-with-robustness-against-large-trimming-bias/6505FD01751EE01FEFFD34071C873FB6) |
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| [sdid](https://github.com/Daniel-Pailanir/sdid) | `ssc install sdid, replace` | Damian Clarke; Daniel Pailañir | [Arkhangelsky, Athey, Hirshberg, Imbens, Wager (2021)](https://www.aeaweb.org/articles?id=10.1257/aer.20190159) |
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| [sdid](https://github.com/Daniel-Pailanir/sdid) | `ssc install sdid, replace` | Damian Clarke; Daniel Pailañir | [Arkhangelsky, Athey, Hirshberg, Imbens, Wager (2021)](https://www.aeaweb.org/articles?id=10.1257/aer.20190159) |
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| [sdid_event](https://github.com/DiegoCiccia/sdid/tree/main/sdid_event) | [Instructions](https://github.com/DiegoCiccia/sdid/tree/main/sdid_event) | Diego Ciccia | [Ciccia (2024)](https://arxiv.org/abs/2407.09565) |
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| [stackedev](https://sites.google.com/view/joshbleiberg) | `ssc install stackedev, replace` | Joshua Bleiberg | [Cengiz, Dube, Lindner, Zipperer (2019)](https://academic.oup.com/qje/article/134/3/1405/5484905) |
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| [staggered_stata](https://github.com/jonathandroth/staggered#stata-implementation) | [Instructions](https://github.com/jonathandroth/staggered#stata-implementation) | Jonathan Roth | [Roth & Sant'Anna (2023)](https://www.journals.uchicago.edu/doi/abs/10.1086/726581) |
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| [twowayfeweights](https://github.com/chaisemartinPackages/twowayfeweights) | `ssc install twowayfeweights, replace` | Clément de Chaisemartin; Xavier D'Haultfoeuille; Antoine Deeb | [de Chaisemartin & D’Haultfoeuille (2020)](https://www.aeaweb.org/articles?id=10.1257/aer.20181169) |
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| [twowayfeweights](https://github.com/chaisemartinPackages/twowayfeweights) | `ssc install twowayfeweights, replace` | Clément de Chaisemartin; Xavier D'Haultfoeuille; Antoine Deeb | [de Chaisemartin & D'Haultfoeuille (2020)](https://www.aeaweb.org/articles?id=10.1257/aer.20181169) |
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| [wooldid](https://github.com/thegland/wooldid) | `ssc install wooldid, replace` | Thomas Hegland | [Wooldridge (2021)](https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3906345) |
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| [xtevent](https://github.com/JMSLab/xtevent) | `ssc install xtevent, replace` | Simon Freyaldenhoven; Christian Hansen; Jorge Perez Perez; Jesse M. Shapiro | [Freyaldenhoven, Hansen, Shapiro (2019)](https://www.aeaweb.org/articles?id=10.1257/aer.20180609) |
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| [yatchew_test](https://github.com/chaisemartinPackages/yatchew_test) | `ssc install yatchew_test, replace` | Clément de Chaisemartin; Diego Ciccia; Xavier D'Haultfoeuille; Felix Knau; Doulo Sow | [Yatchew (1997)](https://www.sciencedirect.com/science/article/pii/S0165176597002188?via%3Dihub); [de Chaisemartin and D'Haultfoeuille (2024b)](https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4284811) |
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| [yatchew_test](https://github.com/chaisemartinPackages/yatchew_test) | `ssc install yatchew_test, replace` | Clément de Chaisemartin; Diego Ciccia; Xavier D'Haultfoeuille; Felix Knau; Doulo Sow | [Yatchew (1997)](https://www.sciencedirect.com/science/article/pii/S0165176597002188?via%3Dihub); [de Chaisemartin and D'Haultfoeuille (2024b)](https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4284811) |
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‎docs/03_python.md‎

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| pysynthdid | [GitHub](https://github.com/MasaAsami/pysynthdid) | Masa Asami | Arkhangelsky et al. (2021) |
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| synthdid.py | [GitHub](https://github.com/d2cml-ai/synthdid.py) | d2cml-ai contributors | Arkhangelsky et al. (2021) |
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| diffindiff | [GitHub](https://github.com/geowieland/diffindiff_official) | Geo Wieland and contributors | Difference-in-differences workflows in Python |
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| LPDiD | [GitHub](https://github.com/pjlambert/LPDiD) | P. J. Lambert | Dube, Girardi, JordÃ, Taylor (2023) |
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| LPDiD | [GitHub](https://github.com/pjlambert/LPDiD) | P. J. Lambert | Dube, Girardi, Jordá, Taylor (2023) |
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‎docs/code_stata/06_01_twfe.md‎

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| | Treatment = 0 | Treatment = 1 | *Difference* |
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| ------------------ | -------------------- | ---------------------------------------- | -------------------- |
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| **Post = 0** | \(\beta_0\) | \(\beta_0 + \beta_1\) | \(\beta_1\) |
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| **Post = 1** | \(\beta_0 + \beta_2\) | \(\beta_0 + \beta_1 + \beta_2 + \beta_3\) | \(\beta_1 + \beta_3\) |
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| Difference | \(\beta_2\) | \(\beta_2 + \beta_3\) | \(\beta_3\) |
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| **Post = 0** | \\(\beta_0\\) | \\(\beta_0 + \beta_1\\) | \\(\beta_1\\) |
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| **Post = 1** | \\(\beta_0 + \beta_2\\) | \\(\beta_0 + \beta_1 + \beta_2 + \beta_3\\) | \\(\beta_1 + \beta_3\\) |
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| Difference | \\(\beta_2\\) | \\(\beta_2 + \beta_3\\) | \\(\beta_3\\) |
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---
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. Rather than writing one large table, it is easier to present results for \(C = 0\) (main group) and \(C = 1\) (comparison group). The difference between those two DDs is exactly \(\beta_7\).
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. Rather than writing one large table, it is easier to present results for \\(C = 0\\) (main group) and \\(C = 1\\) (comparison group). The difference between those two DDs is exactly \\(\beta_7\\).
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Main group (\(C = 0\)):
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Main group (\\(C = 0\\)):
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| | T = 0 | T = 1 | Difference |
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| --------------- | -------------------- | ---------------------------------------- | -------------------- |
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| **P = 0** | \(\beta_0\) | \(\beta_0 + \beta_3\) | \(\beta_3\) |
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| **P = 1** | \(\beta_0 + \beta_1\) | \(\beta_0 + \beta_1 + \beta_3 + \beta_4\) | \(\beta_3 + \beta_4\) |
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| Difference | \(\beta_1\) | \(\beta_1 + \beta_4\) | \(\beta_4\) |
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| **P = 0** | \\(\beta_0\\) | \\(\beta_0 + \beta_3\\) | \\(\beta_3\\) |
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| **P = 1** | \\(\beta_0 + \beta_1\\) | \\(\beta_0 + \beta_1 + \beta_3 + \beta_4\\) | \\(\beta_3 + \beta_4\\) |
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| Difference | \\(\beta_1\\) | \\(\beta_1 + \beta_4\\) | \\(\beta_4\\) |
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Comparison group (\(C = 1\)):
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Comparison group (\\(C = 1\\)):
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| | T = 0 | T = 1 | Difference |
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| --------------- | ---------------------------------------- | -------------------------------------------------------------------------------- | ---------------------------------------- |
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| **P = 0** | \(\beta_0 + \beta_2\) | \(\beta_0 + \beta_2 + \beta_3 + \beta_5\) | \(\beta_3 + \beta_5\) |
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| **P = 1** | \(\beta_0 + \beta_1 + \beta_2 + \beta_6\) | \(\beta_0 + \beta_1 + \beta_2 + \beta_3 + \beta_4 + \beta_5 + \beta_6 + \beta_7\) | \(\beta_3 + \beta_4 + \beta_5 + \beta_7\) |
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| Difference | \(\beta_1 + \beta_6\) | \(\beta_1 + \beta_4 + \beta_6 + \beta_7\) | \(\beta_4 + \beta_7\) |
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| **P = 0** | \\(\beta_0 + \beta_2\\) | \\(\beta_0 + \beta_2 + \beta_3 + \beta_5\\) | \\(\beta_3 + \beta_5\\) |
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| **P = 1** | \\(\beta_0 + \beta_1 + \beta_2 + \beta_6\\) | \\(\beta_0 + \beta_1 + \beta_2 + \beta_3 + \beta_4 + \beta_5 + \beta_6 + \beta_7\\) | \\(\beta_3 + \beta_4 + \beta_5 + \beta_7\\) |
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| Difference | \\(\beta_1 + \beta_6\\) | \\(\beta_1 + \beta_4 + \beta_6 + \beta_7\\) | \\(\beta_4 + \beta_7\\) |
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Let's take the difference between the two matrices or (C = 1) - (C = 0):
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| | T = 0 | T = 1 | Difference |
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| --------------- | -------------------- | ---------------------------------------- | -------------------- |
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| **P = 0** | \(\beta_2\) | \(\beta_2 + \beta_5\) | \(\beta_5\) |
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| **P = 1** | \(\beta_2 + \beta_6\) | \(\beta_2 + \beta_5 + \beta_6 + \beta_7\) | \(\beta_5 + \beta_7\) |
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| Difference | \(\beta_6\) | \(\beta_6 + \beta_7\) | \(\beta_7\) |
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| **P = 0** | \\(\beta_2\\) | \\(\beta_2 + \beta_5\\) | \\(\beta_5\\) |
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| **P = 1** | \\(\beta_2 + \beta_6\\) | \\(\beta_2 + \beta_5 + \beta_6 + \beta_7\\) | \\(\beta_5 + \beta_7\\) |
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| Difference | \\(\beta_6\\) | \\(\beta_6 + \beta_7\\) | \\(\beta_7\\) |
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This final table makes it clear that the DDD estimand is
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