results-analysis

name	results-analysis
description	This skill should be used when the user asks to "analyze empirical results", "generate results section", "interpret regression output", "create regression tables", "visualize DID results", "plot event study", "check pre-trends", "first stage F-statistic", "run robustness checks", "interpret causal estimates", or mentions connecting empirical analysis to social science paper writing. Covers DID, IV, RDD, and Synthetic Control designs.
tags	["Research","CausalInference","Statistics","Visualization","Econometrics"]
version	1.0.0

Results Analysis for Social Science Empirical Research

A systematic empirical results analysis workflow for political science and economics papers — from raw regression output to publication-ready tables, figures, and Results section text.

Core Features

1. Identification Assumption Checks — Pre-trend tests, first-stage F, McCrary density, MSPE ratios
2. Main Results Presentation — Regression tables with proper SE clustering, LaTeX output
3. Robustness Battery — Alternative specifications, placebo tests, subgroup analysis
4. Visualization — Event study plots, coefficient plots, RD plots, binned scatter
5. Results Section Writing — Social science journal structure (APSR/AJPS/AER/QJE)

When to Use

• Validate identification assumptions (pre-trends, exclusion restriction, continuity)
• Generate LaTeX regression tables ready for insertion
• Create event study / coefficient plots
• Conduct and report robustness checks
• Write or revise the Results / Empirical Findings section
• Interpret causal estimates in substantive terms

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Workflow

Data Loading → Identification Checks → Main Results → Robustness → Visualization → Writing → Quality Check

Step 1: Data and Output Loading

Common Input Formats:

• .dta — Stata dataset (load via pystata or pandas + pyreadstat)
• .csv — Panel / cross-sectional data
• Stata log (.smcl / .log) — Regression output to parse
• Python objects — Results from statsmodels, linearmodels, econml

Initial Data Checks:

• Sample dimensions: N units, T periods, total observations
• Panel structure: balanced vs. unbalanced, attrition pattern
• Missing values: which variables, which groups/periods
• Treatment/control proportions and overlap

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Step 2: Identification Assumption Checks

Always validate before reporting main results.

DID / Event Study

• Pre-trend test: plot event-study coefficients for periods t = −k to t = −1; all should be statistically indistinguishable from zero
• Parallel trends visual: plot raw outcome trends for treated and control groups pre-treatment
• Anticipation effects: inspect t = −1 and t = −2 coefficients
• Callaway-Sant'Anna / Sun-Abraham for staggered treatment: check for heterogeneity-robust estimates

Instrumental Variables

• First stage F-statistic: report Kleibergen-Paap (clustered) F, not Cragg-Donald; Stock-Yogo critical values
• Weak instrument: F > 10 as rule of thumb; F > 104.7 for 5% size distortion (Stock-Yogo)
• Exclusion restriction: theoretical argument + placebo outcome test
• Endogeneity test: Hausman test (if OLS and IV differ significantly, report both)

RDD

• Density continuity: McCrary (2008) test; plot histogram around cutoff
• Covariate balance: run RDD on pre-determined covariates (should be ≈ 0)
• Optimal bandwidth: IK (2012) or CCT (2014); report results across multiple bandwidths
• Donut-hole robustness: exclude observations very close to cutoff

Synthetic Control

• Pre-period fit: MSPE ratio (treated vs. donor pool); target < 2
• Placebo in-space: run SC for each donor unit; treated effect should be an outlier
• Placebo in-time: use an artificial earlier treatment date; effect should be near zero
• Leave-one-out: drop each donor and re-run; check stability

See references/identification-checklist.md for detailed protocols and code snippets.

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Step 3: Main Results

Regression Table Standards (social science journals):

Element	Requirement
Standard errors	Clustered at appropriate level (state, county, individual); heteroskedasticity-robust as minimum
Significance markers	†p<0.10, *p<0.05, **p<0.01, ***p<0.001 (or journal-specific)
Fixed effects rows	Include "Unit FE ✓", "Time FE ✓" rows at bottom
Sample info	N (observations), N_clusters if clustered
Model fit	R² (within R² for FE models), first-stage F for IV

Recommended Column Progression:

(1) OLS / Baseline
(2) Main specification (DID / IV / RDD)
(3) + Controls
(4) Alternative clustering
(5) Alternative fixed effects / specification

Effect Size Interpretation:

• Raw coefficient + percentage of outcome mean (e.g., "0.23 SD increase, or 14% of the sample mean")
• For log outcomes: elasticity ("a 10% increase in X → Y% change in outcome")
• For binary outcomes: marginal effects at the mean alongside LPM/logit

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Step 4: Robustness Checks

Standard Robustness Battery:

Check	Description
Alternative window/bandwidth	±50%, ±200% of main specification
Different control sets	No controls → parsimonious → saturated
Alternative outcome definitions	Different measurement, normalization
Alternative clustering level	One level up / down
Wild bootstrap	For small N_cluster (< 50)
Placebo treatment	Assign treatment to untreated units
Placebo outcome	Test on predetermined variable
Subgroup analysis	Key heterogeneity dimensions
Balanced panel	Restrict to always-observed units

Present robustness as a coefficient plot across specifications (point estimate + 95% CI per column), or a robustness table in the appendix.

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Step 5: Visualization

Event Study / Coefficient Plot:

• Point estimates + 95% CI for each event-time period
• Reference line at zero; vertical dashed line at treatment date
• Pre-period serves as visual identification test
• Use matplotlib + pandas or plotnine (ggplot2 equivalent)

Coefficient Plot (across specifications):

• One row per specification, all on same scale
• Ordered by model complexity or specification dimension

RD Plot:

• Binned scatter with local polynomial fit on each side of cutoff
• Confidence band around polynomial
• Raw scatter as background (lighter color)

Binned Scatter:

• For non-parametric relationship visualization
• Residualize on controls / FE before binning

Publication Standards:

• Vector format (PDF preferred for journals)
• Colorblind-safe palette (Okabe-Ito or similar)
• Font size ≥ 10pt
• Axis labels in plain English (not variable names like ln_gdppc)
• Caption must be self-contained

See references/visualization-guide.md for Python/Stata code templates.

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Step 6: Writing the Empirical Results Section

Social Science Results Structure:

## [N]. Empirical Results

### [N.1] Main Results
[Lead with headline number and substantive significance]
[Table X presents the main results. Column (1) shows... Column (2) adds...]
[Interpret magnitude: "a one-standard-deviation increase in X is associated with a Y-unit / Z% change in outcome"]

### [N.2] Identification Tests
[Pre-trend test: "Figure X plots event-study coefficients... none of the pre-treatment coefficients are statistically distinguishable from zero"]
[First stage: "The Kleibergen-Paap F-statistic is XX, exceeding the Stock-Yogo critical value"]

### [N.3] Robustness
[Brief summary: "These results are robust to..."; point to Appendix Table X]

### [N.4] Heterogeneity / Mechanisms
[Which subgroups show larger/smaller effects and why — connect to theory]

Writing Principles:

• Lead with substantive significance ("equivalent to 0.3 years of average wage growth"), not just stars
• Always interpret magnitudes in context
• Explicitly link identification evidence back to the causal claim
• Acknowledge limitations honestly; reviewers will raise them anyway

See references/results-writing-guide.md for journal-specific style guidance.

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Step 7: Quality Checklist

• Identification assumptions explicitly tested and reported
• Standard errors clustered at correct level (justified in text)
• Regression table includes N, FE indicators, clustering info
• Effect sizes interpreted in substantive terms (not just "significant")
• Pre-trend / first-stage F / density test results reported
• At least 3 robustness specifications
• Figures are vector format, colorblind-safe, self-contained captions
• Results section connects back to theoretical motivation

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Integration with Paper Writing

Causal analysis complete (Stata / Python)
    ↓
results-analysis: validate assumptions, generate tables/figures
    ↓
ml-paper-writing: integrate into full paper structure
    ↓
Complete Empirical Results section

This skill handles:

• Assumption validation and reporting
• Regression tables (LaTeX)
• Visualization (event study, coefficient plots, RD plots)
• Results section drafting

ml-paper-writing handles:

• Full paper structure (Introduction, Theory, Data, Conclusion)
• Citation formatting
• Journal submission requirements

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Reference Resources

• references/identification-checklist.md — DID/IV/RDD/SC assumption testing with code
• references/visualization-guide.md — Python + Stata code templates for coefficient plots, event studies
• references/results-writing-guide.md — Results section writing standards for APSR/AJPS/AER/QJE
• references/statistical-methods.md — Statistical tests reference (clustered SE, wild bootstrap, etc.)