Mortgage Lock-In, Mobility, and Labor Reallocation

∗

Julia Fonseca

†

Lu Liu

‡

March 2023

Abstract

We study the impact of rising mortgage rates on mobility and labor reallocation.

Using individual-level credit record data and variation in the timing of mortgage orig-

ination, we show that a 1 p.p. decline in mortgage rate deltas (∆r), measured as the

diﬀerence between the mortgage rate locked in at purchase and the current market rate,

reduces moving rates by 0.68 p.p, or 9%. This eﬀect is economically meaningful and im-

plies that projected rate increases until 2033 will reduce moving by 25%. Moreover, we

show that this relationship is nonlinear: once ∆r is high enough, households’ alterna-

tive of reﬁnancing without moving becomes attractive enough that moving probabilities

no longer depend on ∆r. Lastly, we ﬁnd that mortgage lock-in attenuates household

responsiveness to shocks to employment opportunities, measured as MSA-level wage

growth and instrumented with a shift-share instrument. The responsiveness of moving

rates to wage growth is half as large for households who are more locked in (below-

median ∆r) than for those who are less locked in. We provide causal estimates of

mortgage lock-in eﬀects, highlighting unintended consequences of monetary tightening

with long-term ﬁxed-rate mortgages on mobility and labor markets.

Keywords: Mortgages, housing lock-in, mobility, labor reallocation, monetary tightening

JEL Codes: G21, G51, J62, R30, E58

∗

We thank John Campbell, Itamar Drechsler, Sasha Indarte, Greg Kaplan, Ben Keys, Adair Morse, David

Musto, Nick Roussanov and Heidi Thysen for helpful comments and discussions. Fonseca thanks Jialan Wang

for help in creating the Gies Consumer and Small Business Credit Panel and the Gies College of Business for

generously supporting this dataset. Peter Han and Yizhong Zhang provided excellent research assistance.

†

Gies College of Business, University of Illinois Urbana-Champaign. Email: [email protected]

‡

The Wharton School, University of Pennsylvania. Email: [email protected]enn.edu

1 Introduction

Mortgage loans in the United States allow borrowers to lock in interest rates for up to

30 years. After broadly declining for decades and hitting record lows at the end of 2020,

mortgage rates rose sharply in 2022 (Figure 1) and are projected to remain at higher levels.

For households who have locked in low mortgage rates, these rate increases add an implicit

ﬁnancial cost to the cost of moving, as moving requires prepayment of the current mortgage

and remortgaging at signiﬁcantly higher mortgage rates. For instance, a 1 percentage point

(p.p.) rise in rates increases the present value of future mortgage payments for the median

borrower by around 27,000 USD, and annual payments by around 1,900 USD.

This implicit ﬁnancial cost might have unintended consequences for household mobility and

labor reallocation. A widely-cited concern is that this ﬁnancial cost may “lock in” households,

reducing housing market transactions and labor mobility (Ferreira et al., 2010).

On the

other hand, if this ﬁnancial cost is small relative to the beneﬁt of moving, the real eﬀects on

mobility and labor reallocation may be relatively muted. In this paper, we provide causal

evidence of the eﬀect of mortgage lock-in on labor mobility. We do so by developing a

simple theoretical framework relating mortgage rates to households’ moving behavior and

using it to derive testable implications. We then take these predictions to the data using

individual-level credit record data and exploiting plausibly exogenous variation in the timing

of mortgage origination.

In our theoretical framework, we deﬁne the diﬀerence between the previously locked-in mort-

gage rate and current prevailing mortgage rate as the “mortgage rate delta” (∆r). A positive

delta implies that there is a ﬁnancial gain from remortgaging, while a negative delta implies

a ﬁnancial cost because the current mortgage rate is higher than the rate that was previously

locked in. Households make a choice between three options: staying put (not reﬁnancing

or moving); reﬁnancing; or moving and remortgaging at the current rate.

The net beneﬁt

of remortgaging depends on the mortgage rate delta and loan balance, which determine the

This calculation assumes a remaining term of 20 years, an initial loan balance of 260,000 USD, a discount

factor of 0.96, and a mortgage rate change from 4.5% (matching the median monthly mortgage payment of

around 1,300 USD) to 5.5%. This ignores the option value of reducing payments again once interest rates

decrease, which would lower the expected NPV.

For discussions of this concern in the media, see, for instance, Wall Street Journal, September 22, 2022,

Financial Times, January 12, 2023.

We refer to the process of obtaining a new mortgage priced at current mortgage rates more generally

as remortgaging, while we refer to prepayment and remortgaging of the existing loan more speciﬁcally as

reﬁnancing.

change in mortgage payments when remortgaging, and on a ﬁxed cost of remortgaging. The

net beneﬁt of moving (ignoring the cost of remortgaging) depends on a moving shock and a

ﬁxed cost of moving.

Mortgage lock-in occurs when the beneﬁt of remortgaging net of the remortgaging cost

is negative, leading some households to stay put even though the net beneﬁt of moving

is positive. As a result, we predict an asymmetric relationship between moving and ∆r.

As long as the beneﬁt of reﬁnancing is smaller than the cost, an increase in ∆r alleviates

mortgage lock-in. Because it is costly to remortgage, lock-in can occur when mortgage rate

deltas are positive, i.e. when current mortgage rates are lower than locked-in rates.

Once

the beneﬁt of reﬁnancing is greater than the cost, households’ reﬁnancing option becomes

attractive and provides an outside option to capture the beneﬁt from remortgaging without

the need to move. From that point onward, the relationship between ∆r and moving rates

ﬂattens, as moving only depends on fundamental moving shocks and the moving cost. Thus,

our framework predicts a kink in the relationship between moving rates and ∆r. Lastly, we

predict that ∆r attenuates household responsiveness to a given moving shock, such as an

increase in wage income that can be obtained by moving. In other words, some households

do not pursue higher-paid employment opportunities due to the ﬁnancial cost imposed by

mortgage lock-in.

To test these predictions, we employ a novel consumer credit panel dataset, the Gies Con-

sumer and small business Credit Panel (GCCP), which allows us to measure locked-in mort-

gage rates and moving for millions of borrowers from 2010 to 2018.

We measure households’

mortgage rate deltas as the diﬀerence between the mortgage rate that the household locked

in at the time of mortgage origination and the current mortgage rate. Our main empirical

challenge is that a simple OLS regression of moving rates on household-speciﬁc mortgage

rate deltas may be biased if, for instance, households choose to reduce their mortgage rate

by buying points when they are less likely to move (Stanton and Wallace, 1998). To over-

come this challenge, we use an instrumental variables (IV) research design and instrument

household-speciﬁc mortgage rate deltas with the aggregate mortgage rate delta determined

by current mortgage rates and average mortgage rates in the month of mortgage origination.

We thus isolate the variation in mortgage rate deltas coming solely from the timing of mort-

gage origination, and control for zip code ﬁxed eﬀects, county×year ﬁxed eﬀects, mortgage

This is in contrast to predictions of negative home equity lock-in where lock-in kicks in below home

equity levels of zero.

The next revision of the paper will use data available up to and including 2022.

and borrower controls, and a zip code house price index.

Our paper has three main sets of ﬁndings. First, our two-stage least squares estimate implies

that a 1 p.p. increase in mortgage rate deltas leads to a 0.68 p.p. increase in moving rates,

or 9% of the sample mean. This estimate suggests that the recent rise in mortgage rates will

have substantial eﬀects on future moving rates. In a back-of-the-envelope calculation, we

use forward rates to project mortgage rates until 2033 and ﬁnd that future mortgage rate

rises should lead to a 1.9 p.p. decline in moving by 2033, or 25% of the sample mean.

Second, we show that the eﬀect of ∆r is indeed nonlinear. Our framework predicts that,

once ∆r is higher than the cost of reﬁnancing, households’ alternative to reﬁnance without

moving becomes attractive enough that moving probabilities become unrelated to ∆r. We

provide graphical evidence consistent with these predictions through a binned scatter plot

of the relationship between moving rates and aggregate mortgage rate deltas, showing that

the relationship between ∆r and moving ﬂattens at a level of ∆r of around 1.8 p.p., broadly

consistent with recent estimates (Andersen et al., 2020; Fisher et al., 2021) and survey

measures (Keys et al., 2016) of reﬁnancing costs, given a median loan balance of around

152,000 USD.

Third, consistent with our theoretical prediction, we ﬁnd that low ∆r attenuates household

responsiveness to moving shocks such as higher-wage employment opportunities. We measure

the availability of higher-wage employment opportunities using MSA-level wage growth,

which we instrument using a shift-share instrument. We ﬁnd that the slope of the relationship

between local wage growth and moving rates is higher for borrowers with above-median

aggregate ∆r than for those with below-median aggregate ∆r. This implies that borrowers

who have locked in lower mortgage rates (and thus have lower mortgage rate deltas) move

at lower rates in response to higher local wages. We estimate that, for borrowers with

low aggregate mortgage delta, a one standard deviation increase in MSA-level wage growth

increases within-MSA moving by 0.51 p.p., which is not signiﬁcant at 5%. On the other

hand, within-MSA moving increases by 1.21 p.p. for borrowers with high mortgage delta,

and that estimate is signiﬁcant at 1%. This suggests that mortgage lock-in modulates the

geographical allocation of labor and leads to a mismatch between workers and jobs, as some

households forego higher-paid employment opportunities due to the ﬁnancial cost imposed

by mortgage lock-in.

The two key identifying assumptions behind our IV research design are that (1) aggregate

mortgage deltas are associated with household-speciﬁc mortgage deltas and (2) aggregate

mortgage deltas only aﬀect moving rates through their eﬀect on household-speciﬁc mortgage

deltas. The latter would be violated if, conditional on controls, the timing of mortgage orig-

ination is related to moving rates through channels other than its eﬀect on the aggregate

mortgage delta. For instance, one potential concern is that ﬁnancially sophisticated house-

holds are more likely to time their mortgage origination and may move at diﬀerent rates

than unsophisticated households. While the exclusion restriction is untestable, we conduct

a range of robustness checks that support a causal interpretation of our ﬁndings.

First, we directly address the issue of market timing by exploiting increasingly narrow sources

of variation in aggregate mortgage deltas. We show that our results are qualitatively iden-

tical and quantitatively larger when we include origination year, origination half-year, or

origination quarter-year ﬁxed eﬀects. In the most stringent of these speciﬁcations—with

origination quarter-year ﬁxed eﬀects—variation in aggregate mortgage deltas comes from

monthly variation in aggregate mortgage rates within the same quarter of mortgage origina-

tion. This speciﬁcation compares individuals who had a mortgage originated in, for instance,

January with those with a mortgage originated in February or March of that same year. We

also control for the timing of mortgage reﬁnancing by including ﬁxed eﬀects for the year in

which the household last reﬁnanced. Combining origination date and last reﬁnancing ﬁxed

eﬀects, we compare households with similar reﬁnancing and mortgage origination behavior,

further alleviating concerns that our results might be driven by market timing.

We provide further indirect evidence in support of a causal interpretation of our results

by conducting an event study. Using our theoretical framework, we generate dynamic pre-

dictions about the relationship between moving rates and average 30-year ﬁxed mortgage

rates and test those predictions in an event-study setting. Speciﬁcally, our framework pre-

dicts that moving rates of borrowers with suﬃciently high mortgage rate diﬀerentials should

not respond to declining mortgage rates, but should start decreasing once mortgage rates

increase. We document that this pattern holds in the data using the period of declining

mortgage rates in 2010–2012 and the sharp mortgage rate increase of mid-2013. Finally, our

results are also quantitatively similar when we measure the present value of future mortgage

payments in dollars rather than focusing on mortgage rate diﬀerentials.

We provide quantitative estimates of mortgage lock-in eﬀects and highlight unintended con-

sequences of monetary tightening in the presence of long-term ﬁxed-rate mortgages. Our

ﬁndings suggest that mortgage lock-in is likely to substantially impact housing and labor

markets going forward.

1.1 Related Literature

Our paper contributes to a broader literature of how housing markets aﬀect household mo-

bility (Ferreira et al., 2010, 2012). While earlier studies found mixed evidence of negative

home equity lock-in on labor mobility (e.g. Chan, 2001; Schulhofer-Wohl, 2012; Coulson

and Grieco, 2013), more recent work shows that negative home equity reduces mobility,

labor supply, wages, and job search intensity (Bernstein, 2021; Bernstein and Struyven,

2021; Gopalan et al., 2021; Brown and Matsa, 2020). Negative eﬀects on mobility have also

been documented due to property tax lock-in, caused by caps on property tax growth for

incumbent owners (Wasi and White, 2005). Another source of lock-in are down-payment

constraints (Stein, 1995; Genesove and Mayer, 1997; Andersen et al., 2022), and behavioral

eﬀects such as loss aversion and reference dependence (Genesove and Mayer, 2001; Engel-

hardt, 2003; Anenberg, 2011; Andersen et al., 2022), with evidence of households raising list

prices and spending a longer time on the market to avoid losses relative to their previous

purchase price.

Existing work by Quigley (1987) and Ferreira et al. (2010) shows that mortgage lock-in

reduces household mobility using Panel Study of Income Dynamics (PSID) and American

Housing Survey (AHS) data, respectively, in a broadly declining interest rate environment.

We build on these ﬁndings to make progress along a number of dimensions. Similar to more

recent work on home equity constraints (Bernstein, 2021; Bernstein and Struyven, 2021;

Gopalan et al., 2021), we employ micro-level household panel data and use an IV strategy

to allow for a causal interpretation. The granularity of our data allows us to document

asymmetric eﬀects of mortgage rate deltas on moving rates consistent with a simple model

of household moving and remortgaging. We further provide evidence that a reduction in

mortgage rate diﬀerentials reduces households’ moving rates in response to higher-wage

employment opportunities. We hence provide direct evidence that mortgage rate lock-in

reduces labor reallocation.

Our ﬁndings highlight a seeming trade-oﬀ between insurance provision and allocative eﬃ-

ciency.

Fixed-rate mortgages provide insurance against interest rate increases, but can cause

prolonged periods of mortgage lock-in when rates rise, especially in the US where the close

Our ﬁndings are consistent with other quasi-experimental settings where alleviating household liquidity

constraints improves moving and labor market matching (He and le Maire, 2021), and somewhat in contrast

to e.g. Demyanyk et al. (2017).

These distortionary eﬀects have been documented in studies on rent control, which can provide insurance

against rent price increases, but reduce allocative eﬃciency of housing (Glaeser and Luttmer, 2003; Favilukis

et al., 2023).

to 30-year average ﬁxation length is a relative outlier in international comparison (Badarinza

et al., 2016; Liu, 2022). Reduced mobility and a reduction in housing market turnover can

lead to a greater mismatch between employees and jobs and between households and houses

or locations. Understanding the unintended consequences of monetary tightening with ﬁxed-

rate mortgages should further help inform mortgage market design (Piskorski and Tchistyi,

2010; Campbell, 2012; Campbell et al., 2021; Guren et al., 2021; Liu, 2022). The paper

raises the importance of alternative housing market policies such as mortgage assumability

and portability, which provide a way to alleviate the distortionary eﬀects of mortgage lock-in

and are common in many other countries, but not widely available in the US (Quigley, 1987;

Lea, 2010; Berg et al., 2018; Madeira, 2021).

Our work further relates to monetary policy pass-through and the role of the mortgage

market (Scharfstein and Sunderam, 2016; Beraja et al., 2019; DeFusco and Mondragon,

2020; Di Maggio et al., 2020; Fuster et al., 2021; Agarwal et al., 2023), with an emphasis on

the eﬀects of monetary tightening, and the role of past mortgage rates (Berger et al., 2021;

Eichenbaum et al., 2022). More broadly, our paper also relates to studies of the eﬀect of

monetary policy on the allocation of labor across occupations, ﬁrms, and sectors (e.g. Faia

et al., 2021; Jasova et al., 2021; Guerrieri et al., 2021; Singh et al., 2022; Bergman et al.,

2022). We complement these works by focusing on how interest rates aﬀect mobility and the

geographical allocation of labor through the mortgage lock-in channel.

The remainder of the paper is structured as follows. Section 2 outlines the conceptual

framework using a simple model of household moving and reﬁnancing. Section 3 introduces

the data and empirical strategy. Section 4 presents the main results and section 5 provides

additional results and robustness checks. Section 6 concludes.

2 Theoretical Framework

2.1 A Simple Model of Household Moving and Remortgaging

Household Problem. Households live for two periods and are endowed with a house

and mortgage loan of size L. The mortgage interest rate r

is ﬁxed for both periods but

households have the option to prepay after period one and remortgage, to obtain interest rate

in period two. Households maximize their lifetime utility, which is linear in consumption.

For notational simplicity, there is no discounting. At the end of period one, households

face stochastic interest rate and moving shocks and, upon realization of these shocks, make

decision D ∈ {S, R, M}, which aﬀects outcomes in period two. Households choose between

three actions: staying put (D = S); reﬁnancing (D = R); or moving (D = M). A simplifying

assumption is that households move into a similarly sized house, such that L stays the same,

and there is no loan repayment in period two.

Moving requires households to pay a moving cost κ

, and to prepay the existing loan, and

take out a new loan at rate r

, at cost κ

. Reﬁnancing requires households only to pay the

cost to remortgage, κ

Households earn income Y

, pay mortgage payment M

, and consume C

in each period

t ∈ {1, 2}. The mortgage payment in period one is r

· L. The mortgage payment in period

two is:







· L, if D = S

· L, if D ∈ {R, M},

(1)

i.e. households are protected from interest rate changes in the second period, but they need

to remortgage in order to obtain the mortgage rate r

. Mortgage rates in period two are

stochastic and follow a random walk:

= r

+ ϵ, where ϵ ∼ i.i.d. N (0, σ

), (2)

In period two, households also face a stochastic moving opportunity in the form of a potential

shock to income η that they can realize if they move, and the realization of the shock is known

before decision D needs to be made. The moving shock is i.i.d. normally distributed with

mean 0 and standard deviation σ

. Denote Y the initial income level. Households obtain

= Y in period one. Income in period two is given by







Y, if D ∈ {S, R}

Y · (1 + η), if D = M, where η ∼ i.i.d. N (0, σ

(3)

Given the short time frame of two periods, there is no option value of waiting for the reﬁnancing and

moving decisions, but one can generalize the meaning of reﬁnancing and moving beneﬁts to incorporate a

notion of option value, e.g. using the framework by Agarwal et al. (2013). This framework would likely

result in scaling of household optimality conditions but would preserve model predictions qualitatively.

Households solve the following optimization problem:

max

U = C

+ C

s.t. budget constraint Λ (4)

where

Λ =











+ C

= 2Y − 2r

L, if D = S

+ C

= 2Y − (r

+ r

)L − κ

, if D = R

+ C

= (2 + η)Y − (r

+ r

)L − κ

− κ

, if D = M.

(5)

Household Decision Rules. Comparing total consumption (i.e., the sum of period one

and period two consumption) when reﬁnancing (D = R) and subtracting total consumption

when staying put (D = S) gives

− r

)L − κ

≡ ∆rL − κ

, (6)

i.e. the net beneﬁt of reﬁnancing can be represented as the mortgage rate delta (∆r) scaled

by the loan balance, less the cost of reﬁnancing. Using equation 2, equation 6 can be further

simpliﬁed to ϵL − κ

, which we will use further below.

Similarly, comparing the budget constraint when moving (D = M ) and subtracting the

budget constraint when staying put (D = S) gives

ηY + ∆rL − κ

− κ

, (7)

i.e. the net beneﬁt of moving and remortgaging is the sum of the moving beneﬁt (change in

income if moving) and beneﬁt from remortgaging, less the cost of remortgaging and moving.

We can deﬁne the following useful conditions: when

∆rL − κ

≥ 0, (8)

the household is a potential reﬁnancer, as the beneﬁt of remortgaging is greater or equal to

the cost of remortgaging; in other words, the option to reﬁnance is in the money. In a world

without moving concerns, household would ﬁnd it optimal to reﬁnance.

When

ηY − κ

≥ 0, (9)

the household is a potential mover, i.e. in a world where the household does not have a

mortgage, the household would move since the income beneﬁt from moving is greater or

equal to the cost of moving.

Solving the household’s optimization problem yields the following optimal household decision

rules:

∗

= S, iﬀ:

∆rL − κ

< 0 ∧ ηY + ∆rL − κ

− κ

< 0, (10)

∗

= R, iﬀ:

∆rL − κ

≥ 0 ∧ ηY − κ

< 0, (11)

∗

= M, iﬀ:

ηY − κ

≥ 0 ∧ ηY + ∆rL − κ

− κ

≥ 0. (12)

Household Groups. To build intuition for households’ decision rules, we can divide house-

holds into ﬁve diﬀerent (mutually exclusive, collectively exhaustive) groups, by splitting

them by their potential mover and potential reﬁnancer status.

Group 1 (Non-Marginal Stayers):

∆rL − κ

< 0 ∧ ηY − κ

< 0. (13)

These households are neither potential movers nor potential reﬁnancers, and clearly ﬁnd it

optimal to just stay put (D

∗

= S).

Group 2 (Reﬁnancers):

∆rL − κ

≥ 0 ∧ ηY − κ

< 0. (14)

These households are potential reﬁnancers, but not potential movers, meaning their net

beneﬁt of moving without remortgaging is negative. This implies that ηY +∆rL−κ

−κ

∆rL − κ

, such that households are better oﬀ exercising the reﬁnancing option, without

moving (thus D

∗

= R).

Group 3 (Non-Marginal Movers):

∆rL − κ

≥ 0 ∧ ηY − κ

≥ 0. (15)

These households are potential movers and potential reﬁnancers, and clearly ﬁnd it optimal

to move and remortgage (D

∗

= M).

What about households who are potential movers, but not potential reﬁnancers? Ideally,

these households would like to port their current mortgage when moving or assume an

existing mortgage, as they want to move, but not reﬁnance. In the absence of such mortgage

policies, their behavior depends on whether the net moving beneﬁt or net reﬁnancing cost

dominates, i.e. whether ηY + ∆rL − κ

− κ

⋛ 0. We can split this group of households

into the following two sub-groups.

Group 4 (Marginal Movers):

∆rL − κ

< 0 ∧ ηY − κ

≥ 0 ∧ ηY + ∆rL − κ

− κ

≥ 0 (16)

These households move marginally (D

∗

= M), as the net beneﬁt of moving and remortgaging

is positive (last condition above), even though households pay a net penalty to remortgage,

meaning the moving net beneﬁt is large enough to prevent mortgage lock-in.

Group 5 (Marginal Stayers):

∆rL − κ

< 0 ∧ ηY − κ

≥ 0 ∧ ηY + ∆rL − κ

− κ

< 0 (17)

These households do not move (D

∗

= S), as the net beneﬁt of moving and remortgaging is

negative. They are households with mortgage lock-in, in the sense that the ﬁnancial cost

of remortgaging marginally prevents them from moving despite the net beneﬁt of moving

without remortgaging being positive.

The decision rules of these household groups lead to the optimal decision rules to stay,

reﬁnance or move in equations 10 to 12.

Share of Stayers, Reﬁnancers and Movers. Recall that households i are heterogeneous

in moving shocks η

, with cumulative distribution function F (η

) and density f (η

), and

interest rate shocks ϵ

, with cumulative distribution function G(ϵ

) and density g(ϵ

) (we

were able to omit the i subscript until here). There is a unit mass of households. Denote

, with j ∈ {S, R, M }, the share of stayers, reﬁnancers and movers, respectively, such that

j∈{S,R,M }

= 1.

Using condition 9, we can deﬁne a cutoﬀ value η

∗

above which a household would be con-

sidered a potential mover:

∗

. (18)

Similarly, using condition 8, we can deﬁne a cutoﬀ value ϵ

∗

above which a household would

be considered a potential reﬁnancer:

∗

. (19)

Lastly, using condition 7, we can deﬁne a household-speciﬁc cut-oﬀ value η

∗∗

(for a given

value of ϵ

) above which the joint moving and remortgaging net beneﬁt is weakly positive:

∗∗

+ κ

− ϵ

. (20)

As a result, we obtain the fraction of stayers (D

∗

= S) following equation 10 as:

{(η

,ϵ

): η

<η

∗∗

∩ ϵ

<ϵ

∗

}

f(η

)g(ϵ

)dη

dϵ

, (21)

and the fraction of households who are reﬁnancers (D

∗

= R) as:

{(η

,ϵ

): η

<η

∗

∩ ϵ

≥ϵ

∗

}

f(η

)g(ϵ

)dη

dϵ

. (22)

To determine the fraction of movers (D

∗

= M ), we need to consider which of the two

conditions in equation 12 is binding, i.e. whether η

∗

or η

∗∗

is greater:

{(η

,ϵ

): η

≥max{η

∗

,η

∗∗

}}

f(η

)g(ϵ

)dη

dϵ

. (23)

2.2 Model Predictions and Simulation

We use the model to derive predictions regarding the comparative statics of moving. First,

we are interested in household moving decisions with respect to changes in their mortgage

rate delta, ∆r

= ϵ

Proposition 1 Moving is strictly increasing in ∆r

, up to a cutoﬀ value of ∆r

∗

. Above

the cutoﬀ value ∆r

∗

, moving is weakly increasing in ∆r

Proof of Proposition 1: An increase in ϵ

reduces the cutoﬀ value of η

∗∗

(equation 20),

which raises the fraction of movers λ

as long as η

∗∗

≥ η

∗

. η

∗∗

≥ η

∗

holds as long as

≥ ϵ

L, meaning as long as ∆r

≤

= ∆r

∗

. Once η

∗∗

< η

∗

and η

∗

becomes binding for

moving, moving only depends on moving fundamentals, i.e. households move if η

≥

= η

∗

regardless of further increases in ∆r

Observation on Reﬁnancers. For households who are not potential movers (ηY −κ

< 0),

an increase in ∆r increases the number of reﬁnancers (group 2), as non-marginal stayers

(group 1) turn into reﬁnancers.

Next, we are interested in how moving responds to a given moving shock η, when the degree

of lock-in as measured by ∆r

= ϵ

diﬀers.

Proposition 2 For any given interval [

η, ¯η] (¯η >

η) and [

ϵ, ¯ϵ] (¯ϵ >

ϵ), λ

{[

η, ¯η],[

ϵ, ¯ϵ]}

≤

{[

η, ¯η],[

ϵ+x, ¯ϵ+x]}

, where x < +∞.

To see this, consider the diﬀerence between households who are potential movers and who

actually move. The share of potential movers (PM) is:

P M

{(η

,ϵ

): η

≥η

∗

}

f(η

)g(ϵ

)dη

dϵ

. (24)

For any given interval [η, η + x] where x < +∞, λ

P M

≥ λ

, i.e. for any given interval of η,

there is a weakly positive share of households who are locked in (i.e. for whom ∆r

≤

∆r

∗

), such that the number of potential movers is weakly greater than the number of actual

movers. We also know that the share of households who are locked in is weakly decreasing

in ∆r

, such that the share of movers is weakly increasing in ∆r

This yields the following predictions.

Prediction 1: Non-Linear Relationship between Moving and ∆r

. The relationship

between moving and ∆r

is nonlinear: moving is increasing in ∆r

for marginal households

for whom an increase in ∆r

L − κ

relaxes the moving and remortgaging constraint. It is

ﬂat for households for whom ∆r

L ≥ κ

Prediction 2: Non-Linearity at ∆r

> 0. With a strictly positive cost of reﬁnancing

> 0, the increasing relationship between ∆r

and moving ﬂattens out at ∆r

> 0.

The moving conditions suggest that moving is only beneﬁcial if the net beneﬁt of moving

without remortgaging (η

Y − κ

) is positive. While ∆r

L − κ

< 0, households pay a net

penalty to remortgage. However, as soon as ∆r

L − κ

= 0, households have the outside

option to reﬁnance to capture the ﬁnancial beneﬁt of lower interest rates (meaning higher

mortgage rate deltas). That means that the probability of moving is increasing in ∆r

and hence ∆r

up to a point. Once ∆r

≥

= ∆r

∗

, moving only depends on whether

≥

= η

∗

. We should hence see a ﬂattening in the relationship between ∆r

and moving

for ∆r

≥

> 0, with costly reﬁnancing (κ

> 0).

Lastly, we expect a lower ∆r

to tighten the moving and remortgaging constraint for any

given level of the moving shock η

Prediction 3: Moving Rate w.r.t η

and ∆r

. A lower ∆r

(i.e. a greater degree of

lock-in) weakly reduces the probability of moving for any given level of the moving shock η

relative to a higher ∆r

Model Simulation. In the empirical analysis, we exploit variation in ∆r

. To map the

model to our empirical ﬁndings, we simulate predictions for household moving behavior

based on the model. To capture dimensions of household heterogeneity in the data, we

further assume heterogeneity in reﬁnancing (k

) and moving cost (k

), and calibrate the

income level and income shock (Y , σ

), initial interest rate level and shock (r

,σ

) to match

stylized features of the data, with further detail provided in Appendix Section B.

Figure B5 in the appendix illustrates Predictions 1 and 2, while Figure B6 illustrates Pre-

diction 3.

3 Data and Empirical Strategy

3.1 Data

Our main dataset is the Gies Consumer and small business Credit Panel (GCCP), a novel

panel dataset with credit record data on consumers and small businesses from Experian,

one of the three major national credit reporting agencies in the United States. The GCCP

consists of a one percent random sample of individuals with a credit report, which is linked

to alternative credit records from Experian’s alternative credit bureau, Clarity Services, and

to business credit records for individuals who own a business.

We use data on mainstream consumer credit records between 2010 and 2018 and, given

Figure B7 provides a simpliﬁed simulation with a greater range of positive wage shocks, which illustrates

that the moving gap between high and low ∆r

households widens, but once the wage shock η

is suﬃciently

large, the wage shock dominates and the share of locked-in households becomes very small, such that the

moving gap narrows again.

See Fonseca (2023) for a discussion of the link between mainstream and alternative credit records in the

GCCP and Fonseca and Wang (2022) on the link between consumer and business credit records.

our focus on the eﬀect of interest rates on mortgage rate lock-in, we restrict attention to

consumers with positive mortgage balances. These records include detailed credit attributes

and tradelines of each individual, including debt levels for all major forms of formal debt

such as mortgages, student loans, and credit cards. The data also includes individuals’ credit

scores and payment history, as well as bankruptcies and other public records. The GCCP

also has information on mortgage interest rates from Experian’s Estimated Interest Rate

Calculations (EIRC) enhancement, which provides interest rate estimates based on balance,

term, and payment information. In addition, the dataset includes basic demographics such

as zip code of residency, age, gender, marital status, and employment status. We deﬁne

moving at time t as having a diﬀerent zip code of residency at time t + 1 than at time t.

We supplement these data with county-level employment and wages from the Quarterly

Census of Employment and Wages (QCEW), average 30-year ﬁxed mortgage rates from the

Federal Reserve Bank of St. Louis, and a house price index at the zip code level from the

Federal Housing Finance Agency.

We report summary statistics for the ﬁnal sample in Table 1. The average mortgage loan

balance is 205,480 USD, the average remaining loan term is 21 years, and the average mort-

gage rate is 5.10%. The average ∆r is 1.04%, with the distribution shown in Appendix

Figure A1. Moreover, in Appendix Figure A2, we show average mortgage rates by quartile

of the distribution, as well as average 30-year ﬁxed mortgage rates.

3.2 Empirical Strategy

3.2.1 Baseline

Deﬁne household i’s mortgage rate delta at time t, ∆r

, as the diﬀerence between the

mortgage rate that the household locked in at purchase time p(i), r

ip(i)

, and the current

mortgage rate, r

∆r

= r

ip(i)

− r

(25)

Consider a model that relates household moving rates to mortgage rate deltas:

Note that, since we deﬁne moving as a forward-looking variable, our main dependent variable is not

deﬁned for the last year of available data, 2018. In future revisions, we will use data up to 2022.

I[moved]

= α + βX

+ γ∆r

+ ε

, (26)

where i is a household, t is the year of observation, X

is a vector of controls, and γ is the

causal eﬀect of mortgage rate lock-in on moving rates.

The key challenge that our empirical strategy seeks to overcome is that OLS estimates of

Equation (26) will be biased if moving rates are correlated with unobserved determinants of

mortgage rate deltas. One concern is that household choices and characteristics might be

related to both their propensity to move and their mortgage rate. For instance, households

may choose to purchase points in order to reduce their mortgage rate when they anticipate

that they are unlikely to move.

We estimate the eﬀect of mortgage rate lock-in on moving rates by instrumenting household-

speciﬁc mortgage rate deltas with the aggregate mortgage rate delta determined by current

(annual) mortgage rates and mortgage rates in the month of mortgage origination:

Aggregate ∆r

= r

p(i)

− r

, (27)

where r

p(i)

is the average 30-year ﬁxed mortgage rate in the month of household i’s home

purchase and r

is the average 30-year ﬁxed mortgage rate at time t. We thus isolate the

variation in mortgage rate lock-in coming solely from the timing of mortgage origination.

The ﬁrst stage of this instrumental variables (IV) research design takes the form:

∆r

= δ

z(i)

+ κ

c(i)t

+ γAggregate ∆r

+ βX

+ ε

, (28)

where δ

z(i)

are zip code ﬁxed eﬀects, κ

c(i)t

are county×year ﬁxed eﬀects, and X

includes

the log mortgage balance, mortgage payment, the fraction of the mortgage that has been

paid oﬀ, credit score, age, age squared, gender, and a zip code house price index. We double

cluster standard errors at the county and origination-month-year throughout.

We estimate the following second-stage equation using two-stage least squares:

I[moved]

= δ

z(i)

+ κ

c(i)t

+ γ

∆r

+ βX

+ ε

, (29)

where

∆r

represents predicted mortgage rate deltas from estimating the ﬁrst stage Equation

(28).

The two key identifying assumptions are that (1) aggregate mortgage deltas are associated

with household-speciﬁc mortgage deltas and (2) aggregate mortgage deltas only aﬀect moving

rates through their eﬀect on household-speciﬁc mortgage deltas. The ﬁrst assumption is

empirically testable. Our ﬁrst stage F-statistic exceeds 1,000, indicating a strong instrument.

The second assumption would be violated if, conditional on controls, the timing of mortgage

origination is related to moving rates through channels other than its eﬀect on the aggregate

mortgage delta. For instance, one concern is that ﬁnancially sophisticated households might

be more likely to time their mortgage origination and may have diﬀerent moving propensities

than unsophisticated households. While the exclusion restriction is untestable, we conduct

a range of robustness checks that support a causal interpretation of our ﬁndings.

First, we directly address the issue of market timing in Section 5.1 by exploiting increas-

ingly narrow sources of variation in aggregate mortgage deltas. We show that our results

are qualitatively identical and quantitatively larger when we include origination year, orig-

ination half-year, or origination quarter-year ﬁxed eﬀects. In the most stringent of these

speciﬁcations—with origination quarter-year ﬁxed eﬀects—variation in aggregate mortgage

deltas comes from monthly variation in aggregate mortgage rates within the same quar-

ter of the house purchase. For instance, this speciﬁcation compares individuals who had a

mortgage originated in, say, January with those with a mortgage originated in February or

March of that same year. Conditional on observables, it seems plausible that households

cannot perfectly time their mortgage origination or predict the current level of mortgage

rates within the span of a quarter.

Second, we also control for the timing of mortgage reﬁnancing by including ﬁxed eﬀects

for the year in which the household last reﬁnanced. By combining origination date and

last reﬁnancing ﬁxed eﬀects, we compare households with similar reﬁnancing and mortgage

origination behavior, further alleviating concerns that our results might be driven by market

timing.

Third, we provide indirect evidence in support of a causal interpretation of our results in

Section 5.2 by conducting an event study. Using our theoretical framework, we generate

dynamic predictions about the relationship between moving rates and average 30-year ﬁxed

mortgage rates and test those predictions in an event-study setting. Speciﬁcally, our frame-

work predicts that moving rates of borrowers with suﬃciently high mortgage rate diﬀerentials

should not respond to declining mortgage rates, but should start declining once mortgage

rates increase. We document that this pattern holds in the data using the period of declining

mortgage rates in 2010–2012 and the sharp mortgage rate increase of mid-2013.

3.2.2 Interaction With Employment Opportunities

Our theoretical framework suggests that mortgage rate lock-in also modulates households’

responsiveness to shocks to the monetary beneﬁt of moving, such as shocks to employment

opportunities. To generate shocks to employment opportunities, we instrument local wage

growth using a shift-share IV that interacts past industry-level wage shares with aggregate

industry-level wage growth.

Let w

ℓt

denote wage growth in area ℓ in year t. We can write:

ℓt

ℓk

ℓkt

= g

+ ˜g

ℓkt

where z

ℓk

is the wage share of industry k in area ℓ, and g

ℓkt

is the wage growth of industry k

in area ℓ in year t. The latter has two components: g

, the national wage growth of industry

k, and ˜g

ℓkt

, the idiosyncratic component of wage growth for industry k in area ℓ in year t.

We instrument w

ℓ

using a Bartik (1991) instrument:

ℓt

ℓk

The instrument exploits the fact that past local industry wage shares are pre-determined

and that industry-level wage growth at the national level is plausibly exogenous to local-area

wage growth.

For a household residing in county c, we deﬁne a local area ℓ as the MSA to which county c

belongs.

We construct industry wage shares z

ℓk

using data from 2007, three years prior to

the start of our sample.

We estimate the following second-stage regression using two-stage least squares:

I[moved within MSA]

= δ

l(i)

+ κ

+ γ bw

l(i)t

+ βX

+ ε

, (30)

where bw

l(i)t

represents ﬁtted values from the ﬁrst stage regression. In order to test whether

the responsiveness of moving to local wage growth varies with the degree of mortgage rate

lock-in, we estimate Equation (30) separately for borrowers with aggregate mortgage deltas

above or below the sample median.

4 Main Results

We begin by estimating the eﬀect of mortgage rate lock-in on moving rates. We then explore

how moving responds to shocks to employment opportunities and how that relationship

changes with the degree of mortgage lock-in.

4.1 Mortgage Rate Lock-In and Moving Rates

One of the key predictions of our framework is that mortgage rate deltas aﬀect moving

rates up to a point and, from that point onward, there is no relationship between the two

variables (Prediction 1). Our framework also predicts that the kink point happens in the

strictly positive region of ∆r (Prediction 2). We provide graphical evidence consistent with

these predictions through a binned scatter plot of the relationship between moving rates and

aggregate mortgage rate deltas, which we report in Figure 2. As our framework predicts,

there is a kink in the relationship between aggregate mortgage rate deltas and moving rates

in the strictly positive region of aggregate deltas. The kink point is at a level of around

1.8 p.p., broadly consistent with recent estimates (Andersen et al., 2020; Fisher et al., 2021)

and survey measures (Keys et al., 2016) of reﬁnancing cost, given a median loan balance of

around 152,000 USD.

Table 2 reports estimates of the eﬀect of mortgage rate diﬀerentials on moving rates. We

report the OLS estimate in column 1, which shows a positive correlation between household-

An alternative would be to construct the instrument by leaving out the eﬀect of county c, but this

adjustment has been found to be unimportant in the classic Bartik setting (Goldsmith-Pinkham et al., 2020;

Borusyak et al., 2022).

speciﬁc mortgage rate deltas and moving rates. In column 2, we report the ﬁrst-stage

estimate of Equation (28). We ﬁnd that a 1 p.p. increase in the aggregate mortgage rate

delta is associated with a 0.53 p.p. increase in the household-speciﬁc mortgage rate delta.

The ﬁrst stage F-statistic is above 1,000, suggesting that the aggregate mortgage rate delta

is a strong instrument. Column 3 reports the two-stage least squares estimate of Equation

(29). We estimate that a 1 p.p. increase in mortgage rate deltas leads to a 0.68 p.p. increase

in moving rates (or 9% of the sample mean). This eﬀect is higher than the OLS estimate of

column 1, suggesting that the latter is downward biased.

This estimate suggests that the recent rise in mortgage rates will have substantial eﬀects

on future moving rates. To quantify this eﬀect, we project future mortgage rates using

10-year treasury rates 1-, 2-, and 10 years forward and assuming a constant mortgage rate

spread between 30-year ﬁxed-rate mortgage rates relative to 10-year treasury spot rates.

Using projected rates, we then project the distribution of mortgage deltas using the 2018

distribution of locked-in mortgage rates and projected average mortgage rates, and plot the

actual and projected time-series of average mortgage deltas in Figure 3.

This back-of-the-

envelope calculation suggests that, between 2020 and 2033, the average household-speciﬁc

mortgage delta will decline by 2.8 p.p. Our estimates imply that this should lead to a 1.9

p.p. (0.68 × 2.8) decline in moving, or 25% of the sample mean.

4.2 Interaction With Employment Opportunities

Next, we test the third prediction of our model: that mortgage rate deltas attenuate the

sensitivity of moving rates to a moving shock. We explore how mortgage lock-in aﬀects labor

reallocation, by studying the response of moving rates to employment opportunities, and how

this response varies with the degree of mortgage rate lock-in. We start by illustrating our

main ﬁndings with a binned scatter plot of the relationship between within-MSA moving

rates and predicted MSA-level wage growth in Figure 4. Consistent with our theoretical

prediction, we ﬁnd that the slope of this relationship is higher for borrowers with above-

OLS estimates might be downward biased if, for example, ﬁnancially sophisticated borrowers are able

to lock in lower mortgage rates (leading to lower mortgage rate deltas) and are more likely to move than

unsophisticated borrowers.

We set the constant mortgage rate spread to 168 b.p. This equals the average spread between 30-year

ﬁxed-rate mortgage rates and 10-year treasury rates over the 1990–2022 period, which has remained broadly

stable.

Future revisions will use the 2022 mortgage rate distribution for this exercise.

This is against the backdrop of an already declining secular trend in interstate migration (Kaplan and

Schulhofer-Wohl, 2017).

median aggregate ∆r than for those with below-median aggregate ∆r. This implies that

borrowers who have locked in lower mortgage rates (and thus have lower mortgage rate

deltas) move at lower rates in response to higher local wages.

Table 3 reports estimates of Equation (30) separately for borrowers with below-median

(columns 1–3) and above-median aggregate mortgage rate delta (columns 4–6). Columns

1 and 3 report OLS estimates and show no signiﬁcant correlation between wage growth and

moving for borrowers with high or low aggregate ∆r. Columns 2 and 4 report ﬁrst-stage

estimates, with F-statistics of around 20 for both groups of borrowers. Columns 3 and 6

report estimates of Equation (30). For borrowers with low aggregate mortgage delta, a one

standard deviation increase in wage growth increases within-MSA moving by 0.51 p.p., which

is not signiﬁcant at 5% (column 3). On the other hand, within-MSA moving increases by

1.21 p.p. for borrowers with high mortgage delta, and that estimate is signiﬁcant at 1%.

In appendix Table A1, we show that these results are robust to excluding borrowers who are

past the kink point of the relationship mortgage rate deltas and moving rates. Speciﬁcally,

we re-run this analysis excluding from the high aggregate ∆r group those borrowers with

aggregate ∆r > 2%. If anything, we ﬁnd that the diﬀerence between borrowers who are

more vs. less locked in is even starker in this setting, with the responsiveness of moving

rates to wage growth being three times as large for households with high aggregate ∆r than

for those who with low aggregate ∆r (column 6 vs column 3).

These results imply that mortgage rate lock-in modulates borrowers’ response to employ-

ment opportunities, with borrowers who have locked in lower rates being less likely to move

in response to rising wages. This suggests that mortgage lock-in meaningfully aﬀects the

geographical allocation of labor, with some households foregoing higher-paid employment

opportunities due to the ﬁnancial cost imposed by lock-in.

5 Additional Results and Robustness

5.1 Robustness to Market Timing

In this section, we address the concern that the timing of mortgage origination might aﬀect

moving rates through channels other than its eﬀect on aggregate mortgage rate deltas. We

do so by using increasingly narrow sources of variation in origination timing by including

origination year, origination half-year, or origination quarter-year ﬁxed eﬀects in Equation

(29). In the most stringent of these speciﬁcations, with origination quarter-year ﬁxed eﬀects,

we compare individuals who had a mortgage origination in the same quarter of the same

year, exploiting only monthly variation in average 30-year ﬁxed mortgage rates within a quar-

ter. Conditional on observables, households plausibly cannot perfectly time their mortgage

origination or predict the current level of mortgage rates within the span of a quarter.

We supplement this analysis by also controlling for reﬁnancing behavior. We do so by includ-

ing ﬁxed eﬀects for the year in which the household last reﬁnanced. By combining origination

date and last reﬁnancing ﬁxed eﬀects, we compare households with similar reﬁnancing and

mortgage origination behavior, further alleviating concerns that our results might be driven

by market timing.

Appendix Table A2 reports the results of this exercise, with column 1 reporting our baseline

estimate. Across columns 2–5, we see that coeﬃcients become larger as we control for

origination timing and remain signiﬁcant at 1%, suggesting that our baseline estimate is

a conservative estimate of the eﬀect of mortgage lock-in. One interpretation of the fact

that coeﬃcients become larger is that, to the extent that omitted variables inﬂuence both

origination timing and moving rates, they introduce a downward bias in our estimates. This

would be the case if, for instance, ﬁnancially sophisticated households are more likely to time

the market to lock in lower rates (leading to lower aggregate mortgage rate deltas) and are

more likely to move than unsophisticated households.

5.2 Event Study

In order to further support a causal interpretation of our ﬁndings, we use our framework to

derive dynamic predictions of how borrowers should respond to changing mortgage rates and

test those predictions in an event-study setting. Speciﬁcally, our framework predicts that

moving rates of borrowers with suﬃciently high mortgage rate diﬀerentials—high enough

that they are in the region of ∆r where the relationship between ∆r and moving is ﬂat—

should not respond to declining mortgage rates. That is because declining mortgage rates

will further increase their mortgage rate deltas but, since those are already high enough that

there is no longer a relationship between mortgage rate deltas and moving, there should be

no moving response to declining rates.

On the other hand, once mortgage rates increase, mortgage rate deltas will decrease. This

will push at least some borrowers into the region where there is a positive relationship

between ∆r and moving rates. Thus, our model predicts that, once mortgage rates increase,

moving rates should decrease.

We test this prediction through an event study, exploiting the period of declining mortgage

rates in 2010–2012 and the sharp increase in rates in mid-2013 (Figure 1). We focus on the

group of borrowers who were past the kink point in mortgage rate deltas, after which there

is no relationship between moving rates and deltas, at the start of our sample period. To

alleviate the endogeneity concerns discussed in Section 3, we use aggregate mortgage rate

deltas—our instrumental variable—to select this group of consumers. Speciﬁcally, we restrict

attention to consumers with aggregate ∆r in 2010 greater or equal to 2 p.p., based on the

graphical evidence of Figure 2 suggesting that this is approximately equal to the kink point.

We estimate the following event-study speciﬁcation for this group of borrowers:

I[moved]

= δ

2017

τ=2010

I[t = τ] + βX

+ ϵ

, (31)

where δ

are zip code ﬁxed eﬀects and the vector of controls X

includes mortgage balance,

mortgage payment, the fraction of the mortgage that has been paid oﬀ, credit score, age,

age squared, gender, and a zip code house price index. Our coeﬃcients of interest are γ

which show the evolution of moving rates across years.

We report coeﬃcient estimates and 95% conﬁdence intervals of Equation (31) in Appendix

Figure A3, with 2013 as the omitted category. As our model predicts, we see no eﬀect of

declining mortgage rates between 2010 and 2012 in the moving rates of this group of bor-

rowers. But after the rate rise of mid-2013, moving rates start declining and are statistically

distinguishable from their 2013 baseline from 2015 to 2017.

5.3 Placebo Check: Reﬁnancing and Employment Opportunities

One potential concern with the analysis of Section 4.2 is that MSA-level wage growth, in-

strumented by our shift-share instrumental variable, could function as a shock to variables

other than moving rates, such as income levels. In this section, we provide further evidence

that (instrumented) local wage growth is a moving shock.

To do that, we analyze a related household decision for which our model generates starkly

diﬀerent predictions: the decision to reﬁnance. Our model predicts that reﬁnancing rates

should not increase with the monetary beneﬁt of moving. In fact, since moving provides

households with an alternative way to realize the same option value as reﬁnancing, our

framework predicts that the reﬁnancing rates of households with high mortgage rate deltas

decline with the magnitude of the wage growth shock. We illustrate this prediction in

Appendix Figure B8, which plots simulated reﬁnancing rates against the moving shock for

diﬀerent levels of mortgage deltas.

We test this prediction by estimating Equation (30) with a dummy for reﬁnancing as the

dependent variable. As in Section 4.2, we start with a binned scatter plot of the relation-

ship between reﬁnancing rates and predicted MSA-level wage growth in Appendix Figure

A4. As our model predicts, we see no relationship between reﬁnancing rates and predicted

wage growth for borrowers with below-median aggregate mortgage deltas and a negative

relationship for those above the median.

We report two-stage least squares estimates of Equation (30) with reﬁnancing as the depen-

dent variable in Appendix Table A3. Consistent with the graphical evidence discussed above,

we see that the two-stage least squares estimate of the eﬀect of wage growth on reﬁnancing

is indistinguishable from zero for borrowers with low aggregate ∆r (column 3) and negative

and signiﬁcant for those with high aggregate ∆r (column 6). This evidence is consistent

with our interpretation of instrumented MSA-level wage growth as a shock to within-MSA

moving rates.

5.4 Robustness to Present Value of Mortgage Payments

Next, we show that our results are robust to focusing on changes in the present value of

mortgage payments (∆PVM) rather than on interest rate diﬀerentials. This measure, which

we describe in detail in Appendix C, captures how changes in interest rates aﬀect the present

value of all mortgage payments and more closely maps to the dollar eﬀect of varying mortgage

rates.

We report estimates of Equation 29 with ∆PVM as the explanatory variable and ﬁnd results

that are consistent with our baseline ﬁndings, even in terms of magnitudes. We ﬁnd that a

$1,000 increase in ∆PVM leads to a 0.04 p.p. increase in moving (column 4). This implies

that a one standard deviation ($45, 897) increase in ∆PVM increases moving by 1.84 p.p.

($45, 897 × 0.04). Similarly, our baseline estimate suggests that a one standard deviation

(1.97 p.p.) increase in ∆r leads to a 1.34 p.p. increase in moving.

5.5 Housing Market Liquidity

We expect mortgage lock-in to aﬀect housing market turnover and hence liquidity in the

market, as a decrease in the mortgage rate delta raises the ﬁnancial cost of buying and selling

a house with a mortgage. We test whether mortgage lock-in aﬀects housing market liquidity

using data from Realtor.com Economic Research, which provides aggregated information

on the number of active listings, average listing price, and median days on the market for

all MLS-listed for-sale homes at monthly frequency.

We create county-by-year averages of

aggregate ∆r and merge them with county-level annual averages of the Realtor.com database.

We then regress variables relating to housing market liquidity on average aggregate ∆r and

include county and year ﬁxed eﬀects.

The regression results are presented in Table A5 in the Appendix. Controlling for county-

level ﬁxed eﬀects, the log number of active listings (Column 1) and median days on the

market (Column 5) are signiﬁcantly increasing in aggregate ∆r, while the log average listing

price is decreasing (Column 3). Controlling for both county and year ﬁxed eﬀects, only

the eﬀect on log number of active listings remains statistically signiﬁcant at the 10 percent

level (Column 2), suggesting that a 1 p.p. decrease in aggregate ∆r reduces the number of

listings by around 5%. The eﬀects are consistent with mortgage lock-in reducing housing

market liquidity in the form of fewer houses being listed for sale. There is limited evidence

that mortgage lock-in is mitigated by house prices fully adjusting and oﬀsetting changes in

mortgage rates.

6 Conclusion

This paper provides causal evidence of the eﬀect of mortgage lock-in on moving and la-

bor reallocation. We document three main ﬁndings. First, household moving rates decline

as mortgage rate deltas decrease, or as households incur a greater ﬁnancial cost when re-

mortgaging. We estimate that a 1 p.p. decline in ∆r leads to a 0.68 p.p. decrease in the

probability of moving. This eﬀect is economically meaningful and implies that projected

rate increases until 2033 will reduce moving by 25%. Second, we show that this eﬀect is

nonlinear: once ∆r is high enough so that the beneﬁt of reﬁnancing exceeds its cost, moving

probabilities become unrelated to ∆r. Third, we ﬁnd that low ∆r attenuates household

responsiveness to moving shocks in the form of higher-wage employment opportunities. Us-

ing a shift-share instrument for MSA-level wage growth, we show that the responsiveness

of within-MSA moving rates to wage growth is half as large for households who are more

locked in (below-median aggregate ∆r) than for those who are less locked in.

The ﬁndings highlight unintended consequences of monetary tightening with long-term ﬁxed-

rate mortgages, stressing the importance of alternative mortgage market policies. In most

countries other than the US, mortgage contracts have some degree of assumability (allowing

Accessible via https://www.realtor.com/research/data/.

buyers to assume an existing mortgage on the same property), or portability (allowing bor-

rowers to transfer their mortgage to a new property), such that households can move without

having to prepay their current loan (Lea, 2010). In the US, “due-on-sale” clauses typically

mandate that the balance of the mortgage loan is due and payable upon sale of the property

(Quigley, 1987). For assumability to alleviate widespread distortionary eﬀects, these policies

would likely need to be available to a broad range of households as a household’s moving de-

cision would depend on the mortgage associated with the next house being assumable, which

the household likely has limited control over.

And even with improvements in assumability

and portability, our ﬁndings suggest that costs associated with assuming and porting could

still generate mortgage lock-in eﬀects.

The predominant mortgage contract in the US, the 30-year ﬁxed-rate mortgage, provides

households with insurance against interest rate increases, but can cause prolonged periods

of mortgage lock-in when mortgage rates rise, emphasizing the role of mortgage market

design (Campbell, 2012; Piskorski and Seru, 2018). This also highlights the unique mortgage

composition of the US, with average interest rate ﬁxation length in most other countries not

exceeding 10 years (Badarinza et al., 2016; Liu, 2022). Moreover, a reduction in labor

reallocation may aﬀect productivity and inﬂationary pressures in the medium term, which

is relevant for monetary policy and labor market policies.

Mortgages insured by the FHA (and VA and USDA) are assumable, but only a subset of households is

eligible for FHA-insured loans (see the FHA Handbook 4000.1).

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Figure 1: Average 30-Year Fixed-Rate Mortgage Rates

Mortgage Rate (p.p)

01jan1990 01jan2000 01jan2010 01jan2020

This ﬁgure shows average monthly 30-year ﬁxed-rate mortgage rates from the Federal Reserve Bank of St.

Louis.

Figure 2: Moving Rates and Aggregate Mortgage Rate Deltas

7.5

8.5

Moving rate (p.p)

-1 0 1 2 3

Aggregate Δ r (p.p.)

This ﬁgure shows a binned scatter plot of the relationship between individual-level moving rates and aggregate

mortgage rate deltas. Variables are residualized from controls. Controls include mortgage balance, mortgage

payment, the fraction of the mortgage that has been paid oﬀ, credit score, age, age squared, gender, a zip

code house price index, and county× year ﬁxed eﬀects.

Figure 3: Actual and Projected Average Mortgage Deltas

-1.5

-1

-.5

1.5

Avg. Δr (p.p.)

2010 2015 2020 2025 2030 2035

Actual Projected

This ﬁgure shows actual and projected average mortgage diﬀerentials. We project the distribution of mort-

gage deltas using the 2018 mortgage rate distribution and aggregate 30-year ﬁxed-rate mortgage rates (2018-

2023) and projected mortgage rates (2024, 2025 and 2033). Projected mortgage rates are computed using

10-year treasury rates 1-, 2-, and 10-years forward, and assuming a constant mortgage rate spread between

30-year ﬁxed rate mortgage rates relative to 10-year treasury spot rates.

Figure 4: Moving Rates and Wage Growth by Degree of Mortgage Rate Lock-In

4.2

4.4

4.6

4.8

5.2

Within-MSA moving rate (p.p)

1.5 2 2.5 3 3.5

Predicted wage growth (p.p.)

Low Aggregate Δr High Aggregate Δr

This ﬁgure shows a binned scatter plot of the relationship between within-MSA moving rates and MSA-

level wage growth. Variables are residualized from controls. Controls include mortgage balance, mortgage

payment, the fraction of the mortgage that has been paid oﬀ, credit score, age, age squared, gender, a zip

code house price index, and county and year ﬁxed eﬀects. High and low aggregate ∆r refer to borrowers

who are above or below the sample median aggregate ∆r, respectively.

Table 1: Summary Statistics

Mean Med. St. Dev.

Moving Rate (p.p) 7.47 0.00 26.28

Within-MSA Moving Rate (p.p) 4.53 0.00 20.80

Reﬁnancing Rate (p.p) 6.12 0.00 23.96

∆ r (p.p.) 1.04 0.77 1.97

Aggregate ∆ r (p.p.) 1.07 1.03 1.06

Mortgage Rate (p.p.) 5.10 4.86 2.00

Average 30-Year Fixed Mortgage Rate (p.p.) 4.06 3.99 0.35

Mortgage Balance ($1,000) 205.48 151.85 213.97

Mortgage Payment ($1,000) 1.66 1.30 3.13

Remaining Mortgage Term (years) 21.02 24.00 8.00

Vantage Score 745.93 770.00 85.21

Income ($1,000) 69.87 61.00 33.26

Debt-to-Income Ratio (p.p) 23.57 22.00 12.05

Credit Card Utilization (p.p) 26.71 14.00 29.86

Female (p.p.) 48.62 0.00 49.98

Age (years) 49.52 49.00 12.94

Observations 3,924,788

Notes: This table shows descriptive statistics for our sample between 2010 and 2017. Credit

outcomes and demographics are from the Gies Consumer and small business Credit Panel. Av-

erage 30-year ﬁxed mortgage rates are from the Federal Reserve Bank of St. Louis.

Table 2: The Eﬀect of Mortgage Rate Deltas on Moving Rates

Dependent Variable: I[Moved] ∆r I[M oved]

OLS FS IV

(1) (2) (3)

∆ r 0.18*** 0.68***

(0.02) (0.07)

Aggregate ∆ r 0.53***

(0.01)

Zipcode FE Yes Yes Yes

County×Year FE Yes Yes Yes

Controls Yes Yes Yes

F-Stat 1,910.76

Observations 3,924,792 3,924,792 3,924,792

Notes: Column 1 reports OLS estimates of Equation (29). Column 2 re-

ports estimates of the ﬁrst-stage Equation (28). Column 3 reports two-

stage least squares estimates of Equation (29). Controls include mortgage

balance, mortgage payment, the fraction of the mortgage that has been

paid oﬀ, credit score, age, age squared, gender, and a zip code house price

index. Standard errors are double clustered at the county and origination-

month-year level. * p < 0.10, ** p < 0.05, *** p < 0.01.

Table 3: The Eﬀect of Wage Growth on Moving Rates by Degree of Lock-In

Dependent Variable: I[Moved]

Aggregate ∆r Group: Low High

OLS FS IV OLS FS IV

(1) (2) (3) (4) (5) (6)

Wage Growth 0.01 0.51* 0.01 1.20***

(0.02) (0.29) (0.01) (0.43)

Wage Growth IV 0.64*** 0.69***

(0.14) (0.16)

County FE Yes Yes Yes Yes Yes Yes

Year FE Yes Yes Yes Yes Yes Yes

Controls Yes Yes Yes Yes Yes Yes

F-Stat 20.64 18.82

P-value of (3) = (6) 0.13

Observations 1,898,764 1,898,764 1,898,764 1,895,616 1,895,616 1,895,616

Notes: Columns 1 and 3 report OLS estimates of the relationship between moving rates and MSA-level wage growth.

Columns 2 and 4 report ﬁrst-stage estimates of the Bartik wage growth IV. Columns 3 and 6 report two-stage least

squares estimates of Equation (30). High and low aggregate ∆r refer to borrowers who are above or below the sam-

ple median aggregate ∆r, respectively. Controls include mortgage balance, mortgage payment, the fraction of the

mortgage that has been paid oﬀ, credit score, age, age squared, gender, and a zip code house price index. Standard

errors are double clustered at the county and origination-month-year level. * p < 0.10, ** p < 0.05, *** p < 0.01.

Internet Appendix for

“Mortgage Lock-In, Mobility, and Labor Reallocation”

Julia Fonseca Lu Liu

A Additional Figures and Tables

Appendix Figure A1: Histogram of Mortgage Rate Deltas

.05

.15

.25

Density

-2 0 2 4 6 8

Δr (p.p.)

This ﬁgure shows a histogram of household-speciﬁc mortgage rate deltas (∆r), measured as the diﬀerence

between the mortgage rate that the household locked in at the time of mortgage origination and the current

average 30-year ﬁxed mortgage rate.

Appendix Figure A2: Average Mortgage Rates by Quartile

Avg. Mortgage Rates (p.p.)

2010 2012 2014 2016

30-Year Fixed Q1 Q2

Q3 Q4

This ﬁgure shows average mortgage rates by quartile of the mortgage rate distribution, as well as the

average 30-year ﬁxed rate. When computing average mortgage rates for a given year, we restrict attention

to mortgages originated that year with a 30-year term and a balance below the conforming loan limit.

Appendix Figure A3: Event Study

-1.5

-1

-.5

Moving rate (p.p)

2010 2011 2012 2013 2014 2015 2016 2017

This ﬁgure shows estimates and 95% conﬁdence intervals of Equation (31) for borrowers with aggregate

mortgage delta greater or equal to 2 p.p. in 2010. Controls include mortgage balance, mortgage payment,

the fraction of the mortgage that has been paid oﬀ, credit score, age, age squared, gender, a zip code house

price index, and zip code ﬁxed eﬀects. Standard errors are double clustered at the county and origination-

month-year level.

Appendix Figure A4: Placebo Check: Reﬁnancing Rates and Wage Growth

Reﬁnancing rate (p.p)

1.5 2 2.5 3 3.5

Predicted wage growth (p.p.)

Low Aggregate Δr High Aggregate Δr

This ﬁgure shows a binned scatter plot of the relationship between reﬁnancing rates and MSA-level wage

growth. Variables are residualized from controls. Controls include mortgage balance, mortgage payment,

the fraction of the mortgage that has been paid oﬀ, credit score, age, age squared, gender, a zip code house

price index, and county and year ﬁxed eﬀects. High and low aggregate ∆r refer to borrowers who are above

or below the sample median aggregate ∆r, respectively.

Appendix Table A1: The Eﬀect of Wage Growth on Moving Rates by Degree of Lock-In

Excluding Borrowers Past the Kink

Dependent Variable: I[Moved]

Aggregate ∆r Group: Low High

OLS FS IV OLS FS IV

(1) (2) (3) (4) (5) (6)

Wage Growth 0.01 0.51* 0.03* 1.53**

(0.02) (0.29) (0.02) (0.61)

Wage Growth IV 0.63*** 0.63***

(0.14) (0.17)

County FE Yes Yes Yes Yes Yes Yes

Year FE Yes Yes Yes Yes Yes Yes

Controls Yes Yes Yes Yes Yes Yes

F-Stat 20.10 14.38

P-value of (3) = (6) 0.08

Observations 1,898,764 1,898,764 1,898,764 1,107,551 1,107,551 1,107,551

Notes: Columns 1 and 3 report OLS estimates of the relationship between moving rates and MSA-level wage growth.

Columns 2 and 4 report ﬁrst-stage estimates of the Bartik wage growth IV. Columns 3 and 6 report two-stage least

squares estimates of Equation (30). High and low aggregate ∆r refer to borrowers who are above or below the sample

median aggregate ∆r, respectively. We exclude from the high aggregate ∆r group those borrowers with aggregate

∆r > 2%, which approximately corresponds to the kink point in the relationship between aggregate ∆r and moving

rates. Controls include mortgage balance, mortgage payment, the fraction of the mortgage that has been paid oﬀ,

credit score, age, age squared, gender, and a zip code house price index. Standard errors are double clustered at the

county and origination-month-year level. * p < 0.10, ** p < 0.05, *** p < 0.01.

Appendix Table A2: Robustness to Controlling for Timing

Dependent Variable: I[Moved]

(1) (2) (3) (4) (5)

∆ r 0.68*** 1.99*** 2.00*** 2.84*** 2.08***

(0.07) (0.15) (0.49) (0.69) (0.67)

Zipcode FE Yes Yes Yes Yes Yes

County×Year FE Yes Yes Yes Yes Yes

Origination Year FE No Yes No No No

Origination Half-Year FE No No Yes No No

Origination Quarter-Year FE No No No Yes Yes

Last Reﬁ FE No No No No Yes

Controls Yes Yes Yes Yes Yes

F-Stat 1,910.76 319.51 74.60 105.64 105.77

Observations 3,924,792 3,924,792 3,924,792 3,924,792 3,924,792

Notes: This table reports two-stage least squares estimates of Equation (29) with additional ﬁxed eﬀects, in-

dicated in the bottom rows. F-stat refers to the ﬁrst stage F-statistic. Controls include mortgage balance,

mortgage payment, the fraction of the mortgage that has been paid oﬀ, credit score, age, age squared, gender,

and a zip code house price index. Standard errors are double clustered at the county and origination-month-

year level. * p < 0.10, ** p < 0.05, *** p < 0.01.

Appendix Table A3: Placebo Check: The Eﬀect of Wage Growth on Reﬁnancing Rates

Dependent Variable: I[Refinanced]

Aggregate ∆r Group: Low High

OLS FS IV OLS FS IV

(1) (2) (3) (4) (5) (6)

Wage Growth 0.08** -0.45 0.09*** -1.59***

(0.04) (0.48) (0.03) (0.56)

Wage Growth IV 0.64*** 0.69***

(0.14) (0.16)

County FE Yes Yes Yes Yes Yes Yes

Year FE Yes Yes Yes Yes Yes Yes

Controls Yes Yes Yes Yes Yes Yes

F-Stat 20.64 18.82

P-value of (3) = (6) 0.12

Observations 1,898,764 1,898,764 1,898,764 1,895,616 1,895,616 1,895,616

Notes: Columns 1 and 3 report OLS estimates of the relationship between reﬁnancing rates and MSA-level wage

growth. Columns 2 and 4 report ﬁrst-stage estimates of the Bartik wage growth IV. Columns 3 and 6 report two-

stage least squares estimates of Equation (30) with reﬁnancing as the dependent variable. High and low aggregate

∆r refer to borrowers who are above or below the sample median aggregate ∆r, respectively. Controls include mort-

gage balance, mortgage payment, the fraction of the mortgage that has been paid oﬀ, credit score, age, age squared,

gender, and a zip code house price index. Standard errors are double clustered at the county and origination-month-

year level. * p < 0.10, ** p < 0.05, *** p < 0.01.

Appendix Table A4: Robustness to Present Value of Mortgage Payments

Dependent Variable: I[Moved]

OLS IV

(1) (2) (3) (4) (5) (6)

∆ PVM 0.01*** 0.01*** 0.01*** 0.04*** 0.06*** 0.06***

(0.00) (0.00) (0.00) (0.00) (0.01) (0.01)

Zipcode FE Yes Yes Yes Yes Yes Yes

County×Year FE Yes Yes Yes Yes Yes Yes

Origination Quarter-Year FE No Yes Yes No Yes Yes

Last Reﬁ FE No No Yes No No Yes

Controls Yes Yes Yes Yes Yes Yes

F-Stat 420.07 75.65 75.76

Observations 3,847,503 3,847,503 3,847,503 3,847,503 3,847,503 3,847,503

Notes: This table reports two-stage least squares estimates of Equation (29) with ∆ PVM as the independent variable. F-

stat refers to the ﬁrst stage F-statistic. Controls include mortgage balance, mortgage payment, the fraction of the mortgage

that has been paid oﬀ, credit score, age, age squared, gender, and a zip code house price index. Standard errors are double

clustered at the county and origination-month-year level. * p < 0.10, ** p < 0.05, *** p < 0.01.

Appendix Table A5: County-Level Mortgage Rate Delta and Housing Market Outcomes

Dependent Variable: Log(No. of Listings) Log(Listing Price) Log(Days on Market)

(1) (2) (3) (4) (5) (6)

Aggregate ∆ r 0.14*** 0.05* -0.07*** -0.00 0.05*** 0.02

(0.01) (0.03) (0.01) (0.03) (0.01) (0.03)

County FE Yes Yes Yes Yes Yes Yes

Year FE No Yes No Yes No Yes

Observations 6,056 6,056 6,058 6,058 6,058 6,058

Notes: Columns 1 and 2 report results for the log number of listings. Columns 3 and 4 report results for the

log average listing price. Columns 5 and 6 report results for the median number of days on the market. Robust

standard errors are reported in parentheses. * p < 0.10, ** p < 0.05, *** p < 0.01.

B Model Calibration and Simulation

We calibrate the model in described in Section 2 to match stylized features of the data, and

to obtain predictions for household moving behavior that we can map to our empirical ﬁndings.

The parameters used for the model calibration are shown in Table B6. Note that the simulation

primarily captures relative moving patterns with respect to ∆r, and does not target the moving

rate level across households.

In addition, we introduce a drift term c to the interest rate process, to match the ∆r distribution

in the data, which has more mass in the positive domain given a history of decreasing rates.

= c + r

+ ϵ, where ϵ ∼ i.i.d. N (0, σ

). (32)

Panel 1 shows the calibration of mortgage rates, which broadly match the distribution of ∆r, and

the median loan balance in the data. Since mortgage rates have been declining over most of the

sample period, the interest rate shock is shifted by c to match the mass of ∆r that is in the positive

domain, but the simulation could be done to cover any given range of ∆r. Panel 2 shows that

the standard deviation of the moving shock σ

is 0.05, while the starting level of income Y

100,000 USD. To allow for additional dimensions of household heterogeneity, we further assume

heterogeneity in reﬁnancing (k

) and moving cost (k

), which are i.i.d normally distributed with

mean and standard deviation µ

, σ

and µ

, σ

, respectively, shown in Panel 3.

For the

moving cost parameters, we do not have underlying information on the true distribution of moving

cost in the data. We set the mean to 10,000 USD and the standard deviation to 5,000 USD to

capture, together with the magnitude of the moving shock, that only a small fraction of households

would want to move in a given period, in line with the data. The calibration of these magnitudes

largely governs the level probability of moving across households, which we are not targeting. We

further set the mean of the reﬁnancing cost to 2,000 USD, and the standard deviation to 500 USD,

which (together with the loan size) determine the point from which the relationship between moving

rates and ∆r ﬂattens.

We truncate the cost distributions such that all costs are weakly positive. An alternative would be to

assume a log-normal distribution which does not materially aﬀect results.

Appendix Table B6: Model Calibration

Parameter Value Description

Panel 1: Mortgage Rates

4 Initial level of mortgage rate (p.p.)

c -2 Constant (shift of interest rate shock distribution) (p.p.)

1.5 S.d. of interest rate shock (p.p.)

L 150,000 Starting loan balance (USD)

Panel 2: Wages and Moving Shock

0.05 S.d. of moving shock

100,000 Starting income level (USD)

Panel 3: Moving and Reﬁnancing Cost

10,000 Mean moving cost (USD)

5,000 S.d. moving cost (USD)

2,000 Mean reﬁnancing cost (USD)

500 S.d. reﬁnancing cost (USD)

Notes: This table shows the calibration of parameters for the baseline simulation of the model (described in Sec-

tion 2).

Appendix Figure B5: Simulated Moving Rates and Mortgage Rate Deltas

-1 0 1 2 3 4 5

r (p.p.)

Moving rate (p.p.)

This ﬁgure shows an equal-sized binned scatter plot of the relationship between simulated moving rates and

mortgage rate deltas.

Appendix Figure B6: Simulated Moving Rates and Positive Wage Shocks by Degree of

Mortgage Rate Lock-In

0.0 2.0 4.0 6.0 8.0 10.0

Wage growth shock (p.p.)

Moving rate (p.p.)

High r

Low r

This ﬁgure shows an equal-sized binned scatter plot of the relationship between simulated moving rates and

positive wage growth shocks (over the range of the wage growth shock η ∈ [0, 10]%), for households with low

(below median) and high (above median) mortgage rate deltas.

Appendix Figure B7: Simulated Moving Rates and Positive Wage Shocks by Degree of

Mortgage Rate Lock-In (Large Wage Shocks)

0.0 5.0 10.0 15.0 20.0

Wage growth shock (p.p.)

100

Moving rate (p.p.)

High r

Low r

This ﬁgure shows an equal-sized binned scatter plot of the relationship between simulated moving rates

and positive wage growth shocks (over the full range of the wage growth shock in the positive domain),

for households with low (below median) and high (above median) mortgage rate deltas. In this simulation,

we reduce the mean of the moving cost µ

to 5,000 USD, with no heterogeneity in moving or reﬁnancing

cost (σ

= 0, σ

= 0), and increase the standard deviation of the moving shock σ

to 0.1, relative to the

baseline calibration speciﬁed in Table B6.

Appendix Figure B8: Simulated Reﬁnancing Rates and Wage Shocks by Degree of

Mortgage Rate Lock-In

0.0 2.0 4.0 6.0 8.0 10.0

Wage growth shock (p.p.)

100

Refinancing rate (p.p.)

High r

Low r

This ﬁgure shows an equal-sized binned scatter plot of the relationship between simulated reﬁnancing rates

and wage growth shocks.

C Present Value of Mortgage Payments

A fully-amortizing mortgage with original term to maturity T

(in years), annual mortgage rate r

and original loan size L

has a constant annual mortgage payment M (r

, L

, T

) of:

M(r

, L

, T

) =

1 − (1 + r

)

−T

· L

(33)

The discounted present value of all mortgage payments (“PVM”) between today and time T is:

P V M =

t=0

· M (r

, L

, T

) = (ρ + ρ

...ρ

) · M (r

, L

, T

) =

(1 − ρ

)

1 − ρ

M(r

, L

, T

), (34)

where ρ =

1+δ

and δ is the discount rate used for discounting. The diﬀerence in the net present

value of mortgage payments under the locked-in rate r

and the current market rate r

is:

∆P V M (r

, r

) ≡

(1 − ρ

)

1 − ρ

[M(r

, L

, T

) − M (r

, L

, T

)] . (35)

To measure ∆P V M (r

, r

) empirically, we start by using our observed measure of payments

M(r

, L

, T

), the locked-in interest rate r

, and the term T

to infer the original loan size L

using equation (33). Once we have a measure of L

, we use equation (33) to compute the counter-

factual loan payment under the current interest rate M (r

, L

, T

), measured as the average 30-year

ﬁxed prime rate in year t. With both the observed and the counterfactual payment, we compute

∆P V M (r

, r

) according to equation (35), setting the discount factor ρ to 0.96.

Our instrument for ∆P V M (r

, r

) is analogous to our baseline instrument for mortgage rate deltas

and exploits variation coming solely from the timing of mortgage origination. Speciﬁcally, we use

equation (33) to compute the counterfactual payment under the average 30-year ﬁxed prime rate

at the month of origination, M(r

p(0)

, L

, T

). We then deﬁne our instrument for ∆P V M (r

, r

) as:

Aggregate ∆P V M (r

p(0)

, r

) ≡

(1 − ρ

)

1 − ρ



M(r

p(0)

, L

, T

) − M (r

, L

, T

)



. (36)