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fix: correct goodman2021difference cite key to goodmanbacon2021difference
The references.bib entry has always been goodmanbacon2021difference, but four citations across three docs used a misspelled goodman2021difference that had never resolved. Fixes the resulting bibtex.key_not_found warnings flagged during the per-document bibliography revert build.
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docs/source/notebooks/panel-fixed-effects.ipynb

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"cell_type": "markdown",
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"source": "## Connection to Difference-in-Differences\n\nTwo-way fixed effects (TWFE) - with both unit and time fixed effects - is closely related to difference-in-differences (DiD).\n\nWith a simple 2x2 design (2 groups, 2 periods, binary treatment), TWFE produces **numerically identical** estimates to the classic DiD estimator. The model:\n\n$$Y_{it} = \\alpha_i + \\gamma_t + \\beta \\cdot D_{it} + \\epsilon_{it}$$\n\nwhere:\n- $\\alpha_i$ = unit fixed effects\n- $\\gamma_t$ = time fixed effects\n- $D_{it}$ = treatment indicator\n\nis a workhorse of applied causal inference. The coefficient $\\beta$ captures the treatment effect.\n\nWith more complex designs (staggered treatment adoption, heterogeneous effects), TWFE and simple DiD can diverge. Recent econometrics research {cite:p}`goodman2021difference,dechaisemartin2020twfe` has highlighted that TWFE can give misleading results when:\n\n1. **Treatment effects vary over time** (dynamic effects)\n2. **Treatment rolls out at different times** (staggered adoption)\n3. **Treatment effects differ across units** (heterogeneity)\n\nFor these cases, consider using CausalPy's `DifferenceInDifferences` class or newer estimators designed for staggered designs.\n\n:::{seealso}\nSee the [Difference-in-Differences notebook](difference-in-differences-pymc.ipynb) for more on DiD methods in CausalPy.\n:::\n"
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"source": "## Connection to Difference-in-Differences\n\nTwo-way fixed effects (TWFE) - with both unit and time fixed effects - is closely related to difference-in-differences (DiD).\n\nWith a simple 2x2 design (2 groups, 2 periods, binary treatment), TWFE produces **numerically identical** estimates to the classic DiD estimator. The model:\n\n$$Y_{it} = \\alpha_i + \\gamma_t + \\beta \\cdot D_{it} + \\epsilon_{it}$$\n\nwhere:\n- $\\alpha_i$ = unit fixed effects\n- $\\gamma_t$ = time fixed effects\n- $D_{it}$ = treatment indicator\n\nis a workhorse of applied causal inference. The coefficient $\\beta$ captures the treatment effect.\n\nWith more complex designs (staggered treatment adoption, heterogeneous effects), TWFE and simple DiD can diverge. Recent econometrics research {cite:p}`goodmanbacon2021difference,dechaisemartin2020twfe` has highlighted that TWFE can give misleading results when:\n\n1. **Treatment effects vary over time** (dynamic effects)\n2. **Treatment rolls out at different times** (staggered adoption)\n3. **Treatment effects differ across units** (heterogeneity)\n\nFor these cases, consider using CausalPy's `DifferenceInDifferences` class or newer estimators designed for staggered designs.\n\n:::{seealso}\nSee the [Difference-in-Differences notebook](difference-in-differences-pymc.ipynb) for more on DiD methods in CausalPy.\n:::\n"
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docs/source/notebooks/sensitivity_checks.md

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### {doc}`PreTreatmentPlaceboCheck <../api/generated/causalpy.checks.pre_treatment_placebo.PreTreatmentPlaceboCheck>`
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`PreTreatmentPlaceboCheck` examines pre-treatment event-study effects in staggered DiD. If negative event times are far from zero, the parallel trends story is harder to defend and the treatment effect may be biased {cite:p}`goodman2021difference,borusyak2024revisiting`.
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`PreTreatmentPlaceboCheck` examines pre-treatment event-study effects in staggered DiD. If negative event times are far from zero, the parallel trends story is harder to defend and the treatment effect may be biased {cite:p}`goodmanbacon2021difference,borusyak2024revisiting`.
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## Working with check results
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docs/source/notebooks/staggered-difference-in-differences-pymc.ipynb

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"$$Y_{it} = \\alpha_i + \\lambda_t + \\tau D_{it} + \\varepsilon_{it}$$\n",
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"can produce biased estimates in staggered settings {cite:p}`goodman2021difference` because:\n",
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"can produce biased estimates in staggered settings {cite:p}`goodmanbacon2021difference` because:\n",
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"1. Already-treated units serve as implicit controls for later-treated units\n",
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"**How it works.** The check extracts all event-time estimates with negative event-time values (pre-treatment periods) from `att_event_time_`. It computes the mean and maximum absolute pre-treatment ATT and applies a threshold-based test.\n",
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"**Interpreting the output.** If the mean pre-treatment ATT is close to zero, the check **passes**, providing evidence consistent with parallel trends. If it deviates, the check **fails**, suggesting that the counterfactual model may be mis-specified or that the groups were already diverging before treatment. Note that this is a necessary but not sufficient condition: passing the pre-treatment check does not guarantee that parallel trends would have held in the post-treatment period {cite:p}`goodman2021difference`."
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"**Interpreting the output.** If the mean pre-treatment ATT is close to zero, the check **passes**, providing evidence consistent with parallel trends. If it deviates, the check **fails**, suggesting that the counterfactual model may be mis-specified or that the groups were already diverging before treatment. Note that this is a necessary but not sufficient condition: passing the pre-treatment check does not guarantee that parallel trends would have held in the post-treatment period {cite:p}`goodmanbacon2021difference`."
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