Applied Micro Toolkit

After selecting a method, the econometric-reviewer agent can review the implementation and the identification-critic agent can evaluate the identification argument.

Method Selection Decision Tree

Start with the fundamental question: What source of variation identifies the causal effect?

Step 1: What is your source of variation?

Step 2: Refinements Within Method Families

Within DiD:

Is treatment timing staggered?
├── No → Classic 2x2 DiD (TWFE is fine)
└── Yes
    ├── Can treatment turn off (reversals)?
    │   ├── Yes → de Chaisemartin-D'Haultfoeuille (2020)
    │   └── No
    │       ├── Do you have never-treated units?
    │       │   ├── Yes → Callaway-Sant'Anna (2021) with never-treated controls
    │       │   └── No → Callaway-Sant'Anna with not-yet-treated controls
    │       │           or Sun-Abraham (2021)
    │       └── Are effects likely heterogeneous across cohorts?
    │           ├── Yes → Callaway-Sant'Anna or Sun-Abraham (NOT TWFE)
    │           └── No → TWFE is OK, but report Bacon decomposition

Within IV:

How many instruments for how many endogenous regressors?
├── Exactly identified (K instruments = K endogenous)
│   └── 2SLS (= IV = Wald estimator for single instrument)
├── Over-identified (K instruments > K endogenous)
│   ├── 2SLS (default)
│   ├── GMM (efficient, use if heteroskedasticity suspected)
│   └── LIML (less biased with weak instruments)
└── Under-identified (K instruments < K endogenous)
    └── Cannot identify all parameters — need more instruments or fewer endogenous regressors

Within RDD:

Does crossing the threshold guarantee treatment?
├── Yes → Sharp RDD
└── No → Fuzzy RDD
    └── Is the running variable continuous?
        ├── Yes → Standard rdrobust
        └── No (discrete / few mass points)
            └── Cattaneo-Idrobo-Titiunik (2019) discrete RD methods

Within Matching / Selection on Observables:

Is the selection-on-observables assumption plausible?
├── No → Need a different identification strategy
└── Yes
    ├── Do you need ATE or ATT?
    │   ├── ATE → IPW or AIPW
    │   └── ATT → Matching or IPW with ATT weights
    ├── Is the propensity score model well-specified?
    │   ├── Uncertain → Use AIPW (doubly robust)
    │   └── Confident → IPW or regression adjustment
    └── Many covariates or nonlinear confounding?
        ├── Yes → ML-based methods (causal forests, DML)
        └── No → Parametric PS model + AIPW

Standard Diagnostics by Method

Key diagnostics to run for each method family. For full reporting checklists and minimum standards, see references/reporting-standards.md.

For implementation details and diagnostic code by method, see the causal-inference skill.

Inference Frameworks

Clustering Decision Rule

1. Identify the level at which treatment is assigned → cluster at that level (minimum)
2. If there are within-cluster correlations beyond treatment (e.g., spatial), consider multi-way clustering
3. If the number of clusters is small (< 30–40), use wild cluster bootstrap (Cameron-Gelbach-Miller 2008)
4. If the number of clusters is very small (< 10), cluster-robust methods may not work at all — consider randomization inference or aggregate to the cluster level

Design-Based vs Model-Based Inference

Design-based is appropriate when the assignment mechanism is known (experiments, lotteries, cutoffs). Model-based when random sampling is reasonable. The standard in applied micro is hybrid: design-based identification + model-based inference. Doubly robust methods (AIPW) combine both.

Power Analysis

The key quantity is the Minimum Detectable Effect (MDE) — the smallest effect detectable with 80% power at alpha = 0.05.

Quick MDE formula (equal groups, two-sided test):

MDE = 2.8 × sigma / sqrt(N)

Required N = (2.8 × sigma / MDE)²

For IV designs, the effective MDE is inflated by the inverse of the first-stage coefficient: MDE_IV ≈ MDE_OLS / |pi|. A weak first stage (small pi) dramatically reduces power.

For DiD designs, effective power increases with more post-treatment periods and higher within-group correlation (absorbed by FEs). For RDD, use effective N (observations within bandwidth), not total N.

For cluster-randomized designs, the design effect (1 + (m-1) × ICC) inflates variance — with ICC = 0.05 and cluster size m = 50, you need 3.45x as many observations.

For full MDE formulas (DiD, IV, RDD, cluster-randomized), power simulation code, and MDE interpretation tables, see references/reporting-standards.md.

Research Design Checklist

Before Touching Data

• Research question: What causal parameter are you trying to estimate? Write it as a formal estimand.
• Identification strategy: What source of variation identifies the effect? Draw the DAG.
• Assumptions: List all identification assumptions explicitly. Which are testable?
• Threats: For each assumption, what is the most plausible violation? How would you detect it?
• Power: Given your expected sample size, what is the MDE? Is it policy-relevant?
• Pre-analysis plan: For prospective studies, register the plan before seeing outcomes.

During Analysis

• Data cleaning documented: Every sample restriction justified and recorded.
• Summary statistics: Know your data before running regressions.
• Main specification: Run the main spec first. Resist the urge to search for significance.
• Diagnostics: Run all standard diagnostics for your method (see table above).
• Robustness: Vary specification choices systematically.
• Magnitude interpretation: Can you explain the coefficient in plain language?

Before Submission

• All diagnostics reported: See method-specific standards in references/reporting-standards.md.
• Replication package: Code runs from raw data to all tables and figures.
• Seeds set: All random number generators seeded for reproducibility.
• Limitations discussed: What are the strongest objections? Address them in the paper.
• Literature positioned: Have you cited and compared to the 5 closest papers?

Common Pitfalls

Bad Controls

A "bad control" is a variable that is itself an outcome of treatment. Conditioning on it introduces selection bias.

Rule of thumb: If you cannot be sure a variable is determined before treatment, do not include it as a control. When in doubt, draw the DAG.

Staggered DiD with Heterogeneous Effects

Forbidden Regressions

Never plug a manual first-stage into an OLS second stage (SEs are wrong — use proper 2SLS). Never use a nonlinear first stage with linear second stage (not consistent — use control function). Never include generated regressors without bootstrapping the full two-step procedure.

Integration

For full minimum reporting standards (method-specific checklists for IV, DiD, RDD, SC, Matching) and complete power analysis code, see references/reporting-standards.md. For sensitivity analysis procedures (Oster bounds, Conley bounds, breakdown frontiers, specification curves), see references/sensitivity-analysis.md.

Agents:

• econometric-reviewer: Reviews identification strategy, standard errors, and diagnostic results
• identification-critic: Evaluates identification argument completeness and exclusion restrictions
• numerical-auditor: Designs power simulations for nonstandard study designs
• journal-referee: Reviews whether the empirical strategy meets journal standards

Cross-references:

• identification-proofs skill: Formalize an identification argument for the chosen method
• references/diagnostic-battery.md: Run the full diagnostic battery for the estimated specification
• references/sensitivity-analysis.md: Run sensitivity analysis (Oster bounds, specification curve, breakdown frontier)
• publication-output skill: Format regression tables and diagnostic output for publication