Flood Risk and Home Values

Parallel Pre-Trends

The identifying assumption requires that treated and control zip codes would have followed parallel home value trajectories absent the LOMR. The raw trends below show treated zips are higher in levels (coastal proximity), but the year-over-year movements track closely. This is consistent with the parallel trends assumption that the zip and county×year fixed effects absorb.

Pre-Period Joint F-Test

A formal joint test of whether all pre-treatment coefficients (τ = −4, −3, −2) are simultaneously zero. Failure to reject supports the parallel trends assumption required for causal identification.

Treatment Timing Distribution

The staggered treatment design relies on variation in LOMR effective dates across zip codes. Treatment is spread across the full 2009–2022 window, with increasing frequency in later years as FEMA's mapping modernization program accelerated. This variation identifies the event-time coefficients.

Two-Way Fixed Effects DiD

A simple TWFE DiD with a binary post-treatment indicator estimates the average treatment effect. The coefficient is negative but imprecisely estimated, consistent with the event study showing effects that build gradually over time. A single-period pooled estimate averages early (near-zero) and late (large negative) effects, yielding a small, insignificant average.

Unweighted & Geographic Intensity

Unweighted specification: Dropping population weights yields same-direction but smaller and insignificant effects (τ=+4: −0.8% vs −2.8%), consistent with the effect being concentrated in larger, more liquid housing markets where Zillow coverage is strongest.

Geographic intensity: Replacing NFIP policy penetration with the LOMR polygon area / ZCTA area ratio as the intensity measure. Coefficients flip positive and are insignificant, suggesting that raw spatial overlap with reclassified zones is not sufficient; the effect operates through channels tied to insurance exposure and risk information rather than geographic footprint alone.

Urban Subsample (Density ≥ 1,000)

Restricting to zip codes with population density ≥ 1,000 per square mile reduces the sample by 44% (228,005 → 127,790 obs; 339 → 155 county clusters) but tests whether the effect concentrates in denser, more liquid housing markets. The binary event study coefficients are uniformly larger in the urban subsample: τ=+4 reaches −3.1% (vs −2.8% in the full sample), and τ=+3 gains a significance star (** vs *). The intensity specification is even sharper: τ=+1 roughly doubles (−1.69*** vs −0.81**) and τ=+2 gains two stars.

Parallel trends still hold (F(3, 154) = 1.72, p = 0.16) but with less margin than the full sample. The pattern is consistent with flood risk capitalization being strongest where housing is most liquid and Zillow coverage is most reliable.

Goodman-Bacon Decomposition

With staggered treatment timing, the TWFE estimator is a weighted average of all 2×2 DiD comparisons, including potentially problematic comparisons that use already-treated units as controls (Goodman-Bacon, 2021). The decomposition below shows the weight and estimate for each comparison type. The Bacon specification uses an annual balanced panel without controls or weights, yielding a positive overall estimate (+0.020) that differs from the main TWFE (−0.007). The event study's intensity specification reveals the heterogeneity that a single DiD number obscures.

Callaway & Sant'Anna Estimator

The heterogeneity-robust Callaway & Sant'Anna (2021) estimator computes group-time average treatment effects separately for each cohort and aggregates them without the problematic comparisons identified by Goodman-Bacon. The ATT estimates are positive (+0.2% to +1.5%), opposite in sign to the main TWFE, and pre-treatment ATTs are significantly positive, suggesting the C&S specification (annual, no controls, balanced panel) does not fully satisfy parallel trends. The discrepancy likely reflects the stripped-down specification required by the csdid package (no continuous controls, no weights, annual collapse).

Placebo Test: Unemployment as Outcome

Running the main event study specification with county unemployment as the outcome provides a placebo check: if the housing effect is specific to home values, unemployment should be unaffected. However, the pre-treatment interaction test rejects parallel trends (F(3, 338) = 7.22, p = 0.0001), and the τ=+4 bin is significantly negative. This result should be read as a warning sign, not supportive evidence. It implies that the processes generating LOMRs may correlate with local economic changes not fully absorbed by a linear unemployment control. The housing estimates remain the paper's primary results, but readers should note that the placebo does not cleanly rule out macro-level confounds.

Leave-One-Out by State

Each row shows the τ = +4 coefficient when a single state is excluded from the sample. The dashed blue line marks the full-sample estimate. Stability across exclusions indicates that no single state drives the result.

Alternative Clustering: County vs State

The baseline specification clusters standard errors at the county level (339 clusters). Clustering at the state level (22 clusters) accounts for broader spatial correlation in shocks, producing wider confidence intervals. The τ=+4 coefficient remains significant under state-level clustering (CI: [−0.055, −0.003]), but τ=+3 loses its borderline significance. Point estimates are unchanged; only the standard errors differ.

Identification & Design

Data & Proxy Quality