The two shocks
What the rate shock did to the payment and to turnover, and what the migration shock did to prices.
Two event studies. The payment on the same home, quarter by quarter from 2019, split exactly into the part the price moved and the part the rate moved; the rate part overtook the price part in 2023Q3. Then the lock in: originations of 2019 to 2021 under four percent per hundred owner households, and what turnover did where owners had the most to lose, with the pre period placebo beside it. And the migration shock: price growth over 2019Q4 to 2021Q4 against the pandemic migration shock per hundred residents, with the placebo on 2016Q4 to 2018Q4 and three synthetic controls.
The rate shock
The rate part of the payment overtook the price part in 2023Q3. The rate shock froze turnover where owners had the most to lose: 0.06 fewer purchases per 100 owner households per point of lock in (interval -0.08 to -0.03), and the placebo on the years before the shock sits at 0.00 with an interval that includes zero.
The monthly payment on the median home from 2019Q1: the part from the price and the part from the rate
dollars per month
- price
- rate
real:hmda
The lock in
Each point of lock in: -0.056 purchases per hundred owners (-0.077 to -0.034); placebo +0.001 (-0.002 to +0.004); 388 metros, 86 state clusters. Plan dc55265cae0a0e21.
Turnover fell by 0.06 purchases per 100 owners per point of lock in; placebo 0.00
Change in purchase originations per 100 owner households, 2023 onward against 2018 and 2019, by originations under four percent per 100 owners
purchases per 100 owners, change
- metro
- slope
real:hmda
| Threshold | Coefficient | Low | High | Placebo | Note |
|---|---|---|---|---|---|
| 3.00% | -0.094 | -0.146 | -0.042 | +0.001 | |
| 3.50% | -0.067 | -0.096 | -0.038 | +0.001 | |
| 4.00% | -0.056 | -0.077 | -0.034 | +0.001 | chosen |
Source: HMDA loan level extract (real); model: lock_in; population: every metropolitan area with quarterly prices from 2019Q1 and loans in the base and test years (388 metros, 86 states); as of 2026-10-23.
The migration shock
+1.48% price growth over the window per person gained per hundred residents beyond the pre pandemic pace (+0.40% to +2.55%); placebo -0.78% (-1.35% to -0.20%); 385 metros, 85 state clusters. Plan b2cbe5f6a4559c90.
The metros that gained people were already lagging before the pandemic: the placebo on the years before it is -0.8% (interval -1.4% to -0.2%), so the headline of +1.5% price growth over the window per person gained per hundred residents beyond the pre pandemic pace is a lower bound on what the migration itself did.
Price growth 2019Q4 to 2021Q4 against the migration shock per hundred residents (over 2020 and 2021 less 2018 and 2019), with the placebo window beside it
Price growth against the migration shock
log price growth over the window
- metro
- slope
- placebo
Synthetic control for Panama City-Panama City Beach, FL
log index, last pre quarter = 0
- actual
- synthetic
real:popest+fhfa
| Window | Growth per person per 100 residents of shock | Low | High | p | Clusters |
|---|---|---|---|---|---|
| 2019Q4 to 2021Q4 | +1.48% | +0.40% | +2.55% | 0.007 | 85 |
| 2016Q4 to 2018Q4 (placebo) | -0.78% | -1.35% | -0.20% | 0.009 | 85 |
| 2019Q4 to 2021Q4 (level alone, no pre pandemic control) | +2.41% | +1.87% | +2.95% | 0.000 | 85 |
Source: population estimates beside the price index (real); model: migration; population: 385 metropolitan areas with migration over 2020 and 2021 and the index in both windows (85 states); as of 2026-10-23.
| Metro | Mean post gap | Peak gap | Peak quarter | Latest gap | Reversal since peak | Permutation p | Donors searched | Top weights |
|---|---|---|---|---|---|---|---|---|
| Panama City-Panama City Beach, FL | +0.7% | +9.4% | 2023Q2 | -2.0% | +11.3 pts | 0.829 | 192 | Boise City 0.31; Michigan City-La Porte 0.25; Monroe 0.18 |
| Amherst Town-Northampton, MA | -1.2% | +1.5% | 2024Q2 | +0.9% | +0.6 pts | 0.725 | 192 | Lebanon 0.27; Dover 0.18; Roanoke 0.14 |
| Fairbanks-College, AK | -4.7% | +0.5% | 2020Q3 | -6.0% | +6.5 pts | 0.254 | 192 | Hattiesburg 0.31; Victoria 0.30; Florence 0.20 |
Source: population estimates beside the price index (real); model: synthetic_control; population: 385 metropolitan areas with migration over 2020 and 2021 and the index in both windows (85 states); as of 2026-10-23.
Proven on the simulator first
The lock in difference in differences recovered the planted response with a mean bias of +0.0015 and interval coverage of 94% across conditions. The migration estimator's bias was 0.00% with no reverse causality, 0.00% with mild and -0.07% with strong, where the placebo flagged the condition 46% of the time: that is the limit this chapter admits in print.
What the housing economist would push back on
Lock in is measured from originations, so a metro where owners refinanced twice at the bottom counts each refinance; the measure is an intensity, not a count of owners, and the notebook keeps the version that counted refinances twice as a dead end. Turnover also fell because inventory fell, and a metro with little inventory sees fewer purchases whatever its owners hold; the placebo bounds the trend, it does not remove the mechanism.
Migration follows affordability: people move to the metros they can afford, and a metro that was already cheap for its incomes was already on a different price path. On the simulator the regression on the migration level alone carries that bias and the pre pandemic control removes most of it, but the simulator's households move for one reason with one lag, and the placebo flags the planted reverse causality only part of the time; that is the limit this chapter admits in print. The population estimates count domestic migration from July to June, so the migration years and the price window overlap by two quarters and not four. Remote work moved demand without moving many people, and that part is not in the migration series.