Datasets:
Identification Strategy
This document is the place where causal language is earned or refused. Nothing in
reports/ may carry tier quasi_experimental unless the corresponding argument
here is written, and the corresponding diagnostic is reported.
1. The estimand
Let $g$ index geographies and $t$ months. Let $E_g$ be predetermined exposure to low-coupon mortgages, measured at a pre-shock date $t_0$. Let $R_t$ be the national market mortgage rate. The target is the coefficient path
$\beta_k$ is the differential response of outcome $y$ in a high-exposure geography relative to a low-exposure geography, at date $k$, relative to reference date $k_0$.
What is not identified. The level effect of the national rate increase. $R_t$ is common to all geographies and is absorbed by $\gamma_t$. Any statement of the form "the rate increase reduced national transactions by X%" is not available from this design. Only cross-sectional differences in the response are.
Interpretation of $\beta_k$. Under the assumptions in §2, $\beta_k$ is the causal effect of an additional unit of predetermined lock-in exposure on the outcome, at date $k$, holding common national shocks fixed. It is a relative effect and it embeds general-equilibrium spillovers between geographies (a locked-in household in one metro who does not move also does not buy in another metro). Spillovers bias $\beta_k$ toward zero if high- and low-exposure markets are linked by migration.
2. Assumptions required, stated explicitly
A1 (Parallel trends in exposure). Absent the national rate increase, outcomes in high- and low-exposure geographies would have evolved in parallel, conditional on $\alpha_g$, $\gamma_t$, and $X_{gt}$.
Diagnostic: joint test that $\beta_k = 0$ for all $k < k_0$. Reported, with the
F/Wald statistic and p-value, in outputs/eventstudy/*.json under pretrend_test.
A pre-trend failure demotes the result to descriptive.
A2 (No anticipation). Geographies did not adjust before $t_0$ in anticipation of the rate increase. Plausible: the speed of the 2022 rate increase was widely unforecast, and exposure was built up by the 2020–21 refinance wave, whose motivation was the low rate then prevailing.
Diagnostic: leads in the event study; a placebo shock date in a low-rate-volatility period (2018-01, 2019-06).
A3 (Exposure is predetermined). $E_g$ is computed only from information
available at $t_0$. Enforced in code: the exposure builder takes a as_of date
and asserts that no input row has a date after it.
A4 (Shock–share exogeneity, for the shift-share variant). Predetermined is not exogenous. The shift-share form $E_g = \sum_k \omega_{gk}^{\text{pre}} \cdot s_k$ requires either (i) the shares $\omega_{gk}$ are conditionally uncorrelated with unobserved determinants of the outcome trend, or (ii) the shocks $s_k$ are as-good-as-random across coupon bins.
Neither is credible here without argument. The coupon distribution at $t_0$ is a function of when a geography's housing stock last turned over, which correlates with pandemic in-migration, price growth, and construction. The exposure is therefore not an instrument. We report:
- the concentration of exposure across coupon bins (Herfindahl of $\omega_{gk}$),
- the correlation of $E_g$ with pre-period covariates (a balance table),
- results with and without controls for pre-period price growth and refi intensity.
We do not use IV language. The design is a conditional difference-in-differences with a continuous, predetermined treatment. If a future version wants IV, the exclusion restriction must be stated here first: "$E_g$ affects post-2022 purchase originations only through the lock-in channel", and the obvious violation — that the same 2020–21 refinance wave also reflects a local demand boom that independently predicts 2023 outcomes — must be defended, not asserted.
A5 (SUTVA / limited spillovers). Treated above. Direction of bias: toward zero.
A6 (Measurement). $E_g$ is measured on the Freddie-acquired population, not all mortgages. If Freddie's share of a geography's mortgages varies systematically with the outcome, $E_g$ is measured with non-classical error. We report Freddie loan counts per geography as a coverage variable and test sensitivity to dropping low-coverage geographies.
3. Threats, one by one
3.1 Pandemic housing-demand reallocation
2020–21 saw large, geographically uneven demand shifts. Markets with the biggest price booms also had the most refinancing (equity + rate incentive), hence the lowest coupons at $t_0$, hence the highest $E_g$. Those same markets then mean-reverted in 2022–23 for reasons unrelated to lock-in.
Response: control for 2019-01→2021-12 log price growth; exclude top-decile boom markets as a robustness cell; report both.
3.2 Remote-work exposure
Teleworkable employment share drives both migration and construction, and correlates with the pandemic boom.
Response: optional adapter for a teleworkable-share control; heterogeneity split. Documented as an unresolved threat if the control is unavailable in the slice.
3.3 Differential refinancing booms
A market where nearly everyone refinanced in 2020–21 has both extreme exposure and an exhausted refinance pipeline, which mechanically depresses subsequent refi counts regardless of lock-in.
Response: refi-origination outcomes are reported but treated as mechanically contaminated; the headline outcome is purchase originations. Exclude top-decile refi-intensity markets as a robustness cell.
3.4 Local labour-market shocks
Response: state unemployment control (optional adapter); region × period fixed effects as a robustness cell.
3.5 Housing-supply constraints
Supply elasticity determines whether a demand shift shows up in prices or quantities. This is not a nuisance — it is part of the mechanism.
Response: predetermined supply-constraint proxy (historical permits per housing unit); interact with exposure rather than only controlling for it.
3.6 Composition change in the observed mortgage stock
The active stock shrinks and its composition drifts. Contemporaneous exposure is endogenous to the outcome (markets with more transactions churn their stock faster).
Response: exposure is fixed at $t_0$ and never recomputed. Contemporaneous exposure is reported only as a descriptive series.
3.7 National monetary-policy endogeneity
The Fed raised rates in response to macro conditions that also affect housing. Because the rate path is national, this is absorbed by $\gamma_t$. The residual concern is that the interaction of the national shock with exposure picks up the interaction of macro conditions with whatever else exposure proxies for.
Response: this is exactly A1/A4. Handled by the balance table and controls, and flagged as the deepest remaining threat.
3.8 Geography-specific mortgage-rate differences
PMMS is national. Local offered rates differ by tens of basis points.
Response: measurement error in the level of the gap, attenuating loan-level coefficients. Robustness: HMDA-reported interest rates (available 2018+) to build a local rate series; documented as future work if not in the slice.
3.9 Differential credit conditions
Tightening credit standards in 2022–23 varied locally and reduce originations independent of lock-in.
Response: HMDA denial rates as a control/placebo outcome.
4. Falsification tests
| Test | Prediction if lock-in is the mechanism | Prediction if confounded |
|---|---|---|
| Placebo shock date 2018-01 or 2019-06 | $\beta_k \approx 0$ (rate move too small) | non-zero, similar sign |
| Multifamily (5+) permits as outcome | Weak — multifamily demand is renter-driven, not lock-in-driven | similar magnitude to single-family |
| HMDA denial rate as outcome | $\approx 0$ | non-zero |
| Exposure among investor loans only | Weaker (investors are less locked-in behaviourally, and second-home/investment loans are a small share) | similar |
| Reverse the sign of the shock (2019 rate decline) | Opposite-signed | same sign |
Each writes a row to outputs/robustness/grid.parquet and a paragraph to
reports/failed_hypotheses.md if it fails.
5. Loan-level vs local-level: the firewall
The loan-level hazard results and the local-market results answer different
questions and carry different tiers. They are reported in separate files
(reports/loan_hazard_analysis.md vs reports/local_market_event_study.md) and
the synthesis in reports/technical_report.md must state the tier of each
sentence it combines.
The loan-level rate-gap coefficient is not a causal elasticity of mobility. It is the conditional association between a point-in-time rate gap and the probability that a loan's balance goes to zero, in a selected population, where the gap is mechanically a function of the note rate the borrower chose and the national rate path. A borrower with a 2.8% note rate in 2023 is different from a borrower with a 6.8% note rate in 2023 in cohort, credit, equity, and tenure. The age dummies, cohort controls, and covariates reduce but do not eliminate that.
6. Decision rule for causal language
A report sentence may use causal language ("reduced", "caused", "led to") only if all of the following hold for the underlying artifact:
evidence_tier == "quasi_experimental".pretrend_test.pvalue >= 0.10(or the failure is disclosed in the same paragraph).- At least one placebo specification is reported and does not itself produce a significant effect of the same sign.
- Clustered standard errors are reported, with the cluster count.
- The exposure definition and pre-shock date are stated in the sentence or its table.
Otherwise the sentence must read "is associated with" / "predicts" / "under the model".