25.1-part-quasi-ex.Rmd

# (PART\*) B. QUASI-EXPERIMENTAL DESIGN {-}

Quasi-experimental methods bridge the gap between fully randomized experiments (covered in Part A) and purely observational analysis. When true randomization is infeasible, unethical, or too expensive, researchers exploit naturally occurring, plausibly exogenous variation in treatment assignment to approximate the credibility of an experiment.

## What makes a study "quasi-experimental"?

In a randomized controlled trial, random assignment guarantees (in expectation) that treated and control groups are comparable on both observed and unobserved characteristics. In a quasi-experiment, we substitute *design* for randomization. We focus on units just above and below an assignment cutoff, track shared trends across groups over time, construct weighted counterfactuals from untreated units, or use an outside source of variation that shifts treatment without affecting outcomes directly.

The price of giving up randomization is a set of identifying assumptions: continuity, parallel trends, independence, monotonicity, conditional ignorability. Each method in this part makes a different assumption, and each chapter spells out what that assumption means, when it is plausible, and how to probe it.

## Chapter roadmap and ordering

The chapters in this part are sequenced by *design credibility*, moving from the most credible identification strategies (those that most closely mimic randomization) to those that rely on stronger, harder-to-verify assumptions. Readers who proceed linearly will encounter increasingly demanding assumptions.

-   [Quasi-Experimental Methods](#sec-quasi-experimental) establishes the foundations: SUTVA, conditional ignorability, overlap, and the logic of natural experiments.
-   [Regression Discontinuity](#sec-regression-discontinuity) covers local randomization at a known cutoff. This is typically the most credible design when a sharp assignment rule exists.
-   [Temporal Discontinuity Designs](#sec-temporal-discontinuity-designs) covers Regression Discontinuity in Time and Interrupted Time Series. These are the sharp and segmented variants where the running variable is time.
-   [Synthetic Difference-in-Differences](#sec-synthetic-difference-in-differences) is introduced *before* standard DiD because SDID is typically the most robust panel-data estimator. It combines the reweighting logic of Synthetic Control with the differencing logic of DiD, and performs well whenever *either* method's assumptions hold. Readers unfamiliar with DiD or SC should skim those chapters first and return.
-   [Difference-in-Differences](#sec-difference-in-differences), together with its extensions on [staggered adoption](#sec-modern-estimators-for-staggered-adoption), [panel-match variants](#sec-panel-match-did-estimator-with-in-and-out-treatment-conditions), [non-linear DiD](#sec-nonlinear-did), and [modern concerns](#sec-modern-concerns-in-did), is the workhorse panel estimator. Parallel trends is the central assumption and must be defended with care.
-   [Changes-in-Changes](#sec-changes-in-changes) is a quantile-level extension of DiD. Use it when the policy effect is likely heterogeneous across the outcome distribution.
-   [Synthetic Control](#sec-synthetic-control) covers settings with one (or a few) treated units and a donor pool. It relies on the treated unit sitting inside the convex hull of donor pre-treatment characteristics.
-   [Event Studies](#sec-event-studies) is a visualization and estimation framework layered on top of DiD, RD, or IV. Event-study output is *descriptive* unless the surrounding design establishes a causal channel.
-   [Instrumental Variables](#sec-instrumental-variables), plus the [Decision-Maker IV / examiner design](#sec-examiner-design) and proxy variables. When treatment is endogenous, IV provides a way out, but only for a specific subpopulation (compliers) and only if the exclusion restriction holds.
-   [Matching Methods](#sec-matching-methods) relies on selection on observables. It rests on the weakest identification assumption of the part, since unconfoundedness is untestable, so matching is often best used as a preprocessing step before one of the methods above.

## Common themes

Across these chapters you will see the same conceptual moves repeated.

First, we rely on potential outcomes throughout. We write $Y_i(d)$ for the outcome of unit $i$ under treatment status $d \in \{0, 1\}$. Panel variants add a time subscript: $Y_{it}(d)$. Treatment is indicated by $D_i$ or $D_{it}$. Instruments and running variables are denoted $Z_i$ and $X_i$ where the context makes the role clear.

Second, each method rests on a single untestable assumption that does the heavy lifting: continuity, parallel trends, exclusion, or unconfoundedness. Pre-trend tests, placebo tests, and sensitivity analyses only *support* the assumption. They never prove it.

Third, the estimand is specific. RD estimates a LATE at the cutoff. DiD estimates an ATT on the treated. IV under monotonicity estimates a LATE for compliers. Matching can estimate ATT or ATE depending on how the match is set up. Be precise about what you are identifying.

Fourth, the threats are the same family in different clothing. Selection, anticipation, manipulation, heterogeneity, weak first stages, poor overlap. These recur across chapters under different names, and so do the remedies (robustness checks, honest bounds, sensitivity analyses).

## How to use this part

Readers new to causal inference should read the [foundations chapter](#sec-quasi-experimental) first, then proceed in order. If you hit SDID without DiD or SC background, skim the [Simple DiD](#sec-simple-difference-in-differences) section and [Synthetic Control](#sec-synthetic-control) first, then return.

Practitioners with a specific question can jump to the relevant chapter. Each chapter is designed to be self-contained, with assumptions and estimation strategy spelled out up front.

Reviewers or editors of quasi-experimental work should focus on the [modern concerns in DiD](#sec-modern-concerns-in-did) section and the threats-to-validity subsections throughout. These catalog the standard objections to each design.

A compact decision table is provided at the end of the [foundations chapter](#sec-quasi-experimental) to help match a given research setting to one of the methods introduced here.