YXYang XiaoResearch portfolio
Yang XiaoHousing & household finance
Research question

Does a cheap mortgage keep a loan in place?

When a new mortgage costs more than the one a homeowner already has, giving up the old loan becomes expensive. I study whether those loans are less likely to be paid off.

01 · Method

I compare monthly payoff rates across rate gaps, then estimate a complementary log-log hazard model with observed loan and local-market controls.

02 · Conclusion

Bigger rate gaps are associated with fewer mortgage exits.

The adjusted model reports a hazard ratio of 0.817 for a one-percentage-point larger gap. Unweighted sample shares show the broad ordering, but are not population exit probabilities.

Scope of the evidence. An association, not a causal estimate. Payoff and maturity are pooled; refinancing-related and sale-related payoff cannot be distinguished. Household moves are not observed. This is a selected Freddie Mac sample.

03 · Direct evidence

See what supports the finding.

Open interactive Space ↗

The adjusted association remains negative

Complementary log-log model · estimation sample, 2021–2023

The adjusted association remains negative

What this shows. A one-percentage-point larger rate gap is associated with an 18.3% lower conditional hazard in this model (1 − 0.817). This is a relative association, not an 18.3-point fall in monthly probability. No confidence interval is displayed; this is not a causal estimate.

View exact values & source
ModelRate-gap coefficientHazard ratioLoan-months
Complementary log-log-0.20180.8173808045

Source: RealEstate/reports/loan_hazard_analysis.md

Download figure (SVG)

The sample shows the broad rate-gap pattern

Unweighted estimation sample · 2021–2023

The sample shows the broad rate-gap pattern

What this shows. Each point is a rate-gap group, placed at its mean gap. The sample overrepresents loans that exit; these unweighted shares are not population monthly probabilities. The downward pattern has reversals and differs from the adjusted model above.

View exact values & source
Rate-gap groupMean gap (pp)Unweighted sample exit share (%)Loan-months
< −200 bp-2.326.909120158
−200 to −100-1.47.886654515
−100 to 0-0.485.918991436
0 to +1000.393.66650129
+100 to +2001.533.89370268
+200 to +3002.53.433498736
+300 to +4003.493.215518394
> +400 bp4.413.077208188

Source: RealEstate/reports/loan_hazard_analysis.md

Download figure (SVG)
Research notes

Design, sources & limitations

What I built

I built the registered-data pipeline: point-in-time rate gaps, loan-month survival models, local event studies, evidence-tiering, and a public synthetic reproduction path.

0.817hazard ratio per +1 pp gap
−0.2018adjusted rate-gap coefficient
6.909%unweighted exit share below −200 bp
3.077%unweighted exit share above +400 bp

Research question and relevance

Question: How does the gap between homeowners' existing mortgage rates and current market mortgage rates affect mortgage exits, housing-market activity, local prices, and new construction?

Mortgage lock-in may remove the same owner from both sides of the market: fewer existing homes may be listed, while repeat-buyer demand may also fall. The project therefore treats lock-in as a measurable state, not an effect, and does not assume the sign of the price response.

Vocabulary boundary: Freddie Mac Zero Balance Code 01 identifies a voluntary payoff or maturity. It does not distinguish a refinance from a sale-related payoff and is not a measure of moving. The loan-level outcome is always described as prepayment or mortgage exit.

Data and publication boundary

The registered analysis uses a 5% loan sample from Freddie Mac cohorts originating from 2013Q1 through 2022Q4, together with PMMS rates, FHFA house-price indexes, HMDA aggregations, Census building permits, BLS labor-market data, and documented geographic crosswalks.

MaterialPublic release treatment
Source, tests, configuration, documentationPublished on GitHub and mirrored in the Dataset.
Synthetic fixturesPublished with explicit SYNTHETIC labeling.
Registered Freddie Mac loan recordsNever redistributed.
Loan-granular derivatives and local cachesExcluded from every public package.
Aggregate reports and coefficientsPublished with evidence tiers, population statements, and source attribution.

Capabilities demonstrated

  1. Construct eight point-in-time lock-in measures without forward-looking rate alignment.
  2. Build mortgage-exit and competing-risk outcomes with explicit left truncation and censoring.
  3. Estimate survival summaries and discrete-time hazards at the loan-month level.
  4. Freeze pre-shock local coupon exposure and estimate state and metropolitan event studies.
  5. Automatically demote results when pre-trends or placebos fail.
  6. Keep model-dependent policy scenarios in a separate simulation tier and never call them forecasts.

Every result artifact is labeled descriptive, hazard_association, quasi_experimental, or simulation. A sentence that mixes these tiers is treated as a defect.

What the registered-data run supports

ResultEvidence tierInterpretation
Complementary log-log coefficient: -0.2018; hazard ratio: 0.817 per percentage pointHazard associationGreater lock-in is strongly associated with lower monthly prepayment hazard after observed controls. This is not a causal elasticity and not a mobility estimate.
Purchase-originations estimates are negative at state and MSA levelsDescriptivePre-trends fail at both geographic levels, so greater precision does not earn causal interpretation.
Single-family permit event studyQuasi-experimental candidatePre-trends pass, but the estimate is statistically indistinguishable from zero.
Policy scenariosSimulationUseful for comparing modeled orderings, not for forecasting magnitudes.

The honest headline is the ordering of evidence: the loan-level association is strong, while the market-level designs do not establish a causal effect on purchase activity, prices, or permits.

Reproduction and citation

Run make setup followed by make reproduce-sample for the public synthetic vertical slice. A registered-data run requires the user to obtain licensed Freddie Mac archives independently and place them in the documented local path; the project never bypasses registration or redistributes the files.

Cite the Observatory release, Dataset revision, project repository, and every original data provider used in a run.

Evidence boundary

  • Prepayment is not a home sale, refinance, or household move; the source does not separate those events.
  • The Freddie Mac population excludes major mortgage segments and all-cash transactions.
  • Predetermined exposure is not exogenous, and time effects absorb the common national rate shock.
  • The demand-versus-supply decomposition is framed but not identified without listings, transactions, or household mobility data.
  • Published scenario outputs rely on calibrated assumptions and are not forecasts.