Mortgage Prepayment and Path-Dependent Effects of Monetary
Policy
∗
David Berger
†
Konstantin Milbradt
‡
Fabrice Tourre
§
Joseph Vavra
¶
December 2018
Abstract
How much ability does the Fed have to stimulate the economy by cutting interest rates? We argue
that the presence of substantial debt in fixed-rate, prepayable mortgages means that the ability to
stimulate the economy by cutting interest rates depends not just on their current level but also on
their previous path. Using a household model of mortgage prepayment matched to detailed loan-
level evidence on the relationship between prepayment and rate incentives, we argue that recent
interest rate paths will generate substantial headwinds for future monetary stimulus.
Keywords: Monetary Policy, Path-Dependence, Refinancing, Mortgage Debt
JEL codes: E50, E21, G21
∗
We would like to thank Daojing Zhai, Ariza Gusti and Yang Zhang for excellent research assistance. We would also
like to thank our discussant Dan Greenwald as well as Erik Hurst, Andreas Fuster, Pascal Noel, Amir Sufi, Amit Seru, Sam
Hanson, Gadi Barlevy, Anil Kashyap, Arlene Wong, Greg Kaplan, Adi Sunderam and seminar participants at NYU, NBER
ME, Duke, Northwestern Housing and Macro Conference, the ECB, Arizona State, the Chicago Fed, Marquette, Copenhagen
Business School, EIEF, University of Munich, the Bank of Canada and the Philadelphia Fed. This research was supported by
the Institute for Global Markets and the Fama-Miller Center at the University of Chicago Booth School of Business, and the
Guthrie Center for Real Estate Research at Kellogg. Fabrice Tourre is also affiliated with the Danish Finance Institute and
kindly acknowledges its financial support.
†
Northwestern University and NBER; david.berger@northwestern.edu
‡
Northwestern University and NBER; milbradt@northwestern.edu
§
Copenhagen Business School; ft.fi@cbs.dk
¶
University of Chicago and NBER; joseph.vavra@chicagobooth.edu.
1 Introduction
How much room does the Federal Reserve have to stimulate the economy by lowering interest rates? At
the end of 2015, the Fed ended its extended period of zero interest rates, and it has steadily increased
rates since then. Higher interest rates leave more room for future cuts. However, in this paper we argue
that looking only at current rates provides an incomplete view of Fed stimulative power, and that it may
take an extended period of time with elevated rates before the Fed regains "ammunition" to stimulate
the economy.
In particular, we argue that the presence of vast amounts of US household debt in the form of fixed-
rate prepayable mortgages leads to path-dependent consequences of monetary policy and thus stimulus
power which depends on both current and past rates. For example, suppose that the current interest
rate is cut from 3% to 2%.
1
If rates were previously 3% for a long period of time, then many households
will have an incentive to refinance their mortgage debt, which can then lead to increases in spending.
In contrast, if rates were previously below 2% for a long period of time, then many households would
have already locked in a low rate and will have no incentive to refinance in response to today’s rate cut.
Figure 1: Outstanding vs. Current Market Mortgage Rates
2
4
6
8
10
1990m1 2000m1 2010m1 2020m1
Average Outstanding Mortgage Rate Current 30 Year FRM
The average outstanding mortgage rate is the average interest rate on all fixed-rate first mortgages calculated using BKFS
McDash Monthly Performance data. The current 30 year FRM is the monthly average of the Freddie Mac weekly PMMS
survey 30 year fixed rate mortgage average: https://fred.stlouisfed.org/series/MORTGAGE30US
Before describing our detailed analysis, we begin by illustrating the basic qualitative importance of
path-dependence using simple aggregate time-series relationships. In particular, the solid gray line in
Figure 1 shows the current 30-year fixed rate which can be obtained on new mortgages at a point in
time. The dashed black line shows the average outstanding rate on the stock of mortgages which were
originated in prior months. This figure shows that when the current rate (solid) is below the average
outstanding rate (dashed), the outstanding rate converges rapidly towards the current rate, but the
reverse is not true: when the current rate is high relative to the old locked in rate, few people refinance
and convergence is very slow. This asymmetry leads to a distinct stair-step pattern with the outstanding
1
For illustrative purposes here we make no explicit distinction between short rates and mortgage rates and do not specify
the extent to which Fed policy affects mortgage rates. We make these distinctions precise in our subsequent analysis which
endogenizes the link between short rates and mortgage rates and delivers pass-through consistent with empirical estimates.
1
rate only tracking the current rate when the former is above the latter, thus clearly demonstrating the
qualitative presence of path-dependence in the mortgage market.
To provide a more precise and systematic evaluation of this path-dependence channel, we begin with
a detailed empirical analysis using loan-level micro data, which we use to motivate a theoretical model
of mortgage prepayment featuring endogenous borrowing, lending, consumption and pass-through of
short-rates to long-rates. In both our model and in the data, the key feature driving the path-dependent
effects of monetary policy is this observation that mortgages with positive "rate gaps" (the difference
between the outstanding mortgage rate on a loan m
∗
and the current market rate m on similar mortgages)
are much more likely to refinance. Holding m constant, the past history of rates will affect m
∗
and thus
the response of prepayment rates to current rate changes.
While this is a simple observation, it delivers many insights for the consequences of monetary pol-
icy: 1) The strength of monetary stimulus has been substantially amplified by the secular decline in
mortgage rates over the last 30 years, and we should anticipate less effective monetary policy in a sta-
ble or increasing rate environment. This is because trend declines in mortgage rates encourage more
frequent refinancing, amplifying the strength of monetary policy. 2) For similar reasons, in a stochastic
but stationary rate environment, monetary policy is less effective after an extended period of low rates
like we observed in the aftermath of the Great Recession. This is because if past rates were low, many
households would have already locked in low rates, reducing current monetary policy ammunition. 3)
It takes a very long time for the Fed to reload its ammunition after raising rates, yet it uses any accu-
mulated ammunition rapidly when lowering rates. This is because households avoid prepaying when
current rates are high and rapidly refinance when current rates are low. The remainder of the paper
fleshes out these implications using a model of mortgage prepayment fit to a variety of detailed loan
and individual level micro data.
Using micro data from Black Knight Financial Services, CoreLogic and Equifax spanning the period
1992-2017, we begin by documenting the relationship between the distribution of loan-level rate incen-
tives and prepayment activity. Pooling across time, we calculate the overall distribution of rate gaps as
well as the fraction of loans which prepay for a given rate gap. Overall, we find that there is a strong
positive relationship between rate gaps and mortgage prepayment, even after controlling for a variety
of other loan characteristics, household fixed effects and time-varying household characteristics.
2
More-
over, and importantly for our theoretical analysis, we find a sharp step in prepayment probabilities at
exactly zero: loans with any positive rate incentive are significantly more likely to prepay than loans
without such an incentive. This suggests that the fraction of loans with positive rate gaps is a useful
summary statistic for the complicated distribution of rate gaps.
Turning to time-series evidence, we find this is the case: the fraction of loans with positive rate
gaps ( f rac > 0) in a given month both changes dramatically across time and strongly predicts the
fraction of loans prepaying in that month.
3
Importantly, we show that f rac > 0 is a stronger predictor
2
Most of our results focus on total prepayment since the distribution of rate gaps is determined by all prepayment and not
just refinancing. However, one would expect that f rac > 0 is particularly important for rate refinancing (as opposed to cash-
out refinancing or prepayment due to moving houses). While prepayment cannot be decomposed using data from individual
loans, from 2005-2017, we can link loans to households using Equifax CRISM data. This allows us to measure both which
loans prepay and associate a prepaying loan with the (potential) new loan which is originated and so distinguish prepayment
types. We find the sharpest effects of f rac > 0 for rate refinancing.
3
One might rightfully be concerned that f rac > 0 is endogenous and that this relationship may not be causal; however we
show that results are similar when instrumenting for f rac > 0 using lagged high-frequency monetary policy shocks.
2
of prepayment than any other threshold, such as the fraction of loans with at least a 50 basis point rate
gap or the fraction of loans with at least a 100 basis point rate gap. More surprisingly, we find that
f rac > 0 conveys almost all of the information contained in the entire shape of the gap distribution:
including fully non-parametric controls for the shape of the rate distribution at a point in time adds
little predictive power for prepayment after controlling for f rac > 0. When turning to the theoretical
implications of our empirical evidence, we rely on this result to substantially simplify our analysis.
While most of our empirical work focuses on aggregate prepayment activity, we really care about
households’ mortgage payments and spending behavior, not on prepayment per se. However, we find
that the behavior of average outstanding rates mirrors prepayment behavior: when f rac > 0 is large,
more loans prepay and the average outstanding rate drops more rapidly. Moreover, as predicted by
our theoretical analysis, we find that when f rac > 0 is large, there is greater pass-through of current
mortgage rate changes into the average outstanding mortgage rate. Finally, in order to explore impli-
cations for spending, we turn to regional analysis using local auto sales data from R.L. Polk. We find
that regions with greater f rac > 0 have 1) greater prepayment activity and 2) prepayment activity and
auto sales which are more responsive to interest rate changes (even after controlling for both region and
month fixed effects).
4
What do these strong empirical relationships between mortgage rate gaps and prepayment imply
for monetary policy? In order to explore this question, we turn to a theoretical model that can be
used to assess a variety of effects and counterfactuals which cannot be measured directly in our data.
In particular, we embed a simple model of mortgage prepayment into an incomplete markets model
with endogenous mortgage pricing. We intentionally focus on a simple model of prepayable mortgages
which includes only the minimal elements necessary to generate path-dependence. In particular, the
model features rate but not cash-out refinancing. This is mostly for simplicity, but rate refinancing is
also quantitatively important empirically: it represents a little over half of refinancing activity from
1992-2017 and is strongly associated with proxies for increased spending in our data.
5
Focusing on
rate refinancing isolates the most direct channel of path-dependence in monetary policy from a host
of other features of mortgage contracts and housing which are less essential for this result. Finally,
rate refinancing is especially policy relevant because the Fed can fairly directly affect incentives for rate
refinancing but has less direct control over cash out incentives via house prices.
We capture the "state-dependent" relationship between prepayment and rate gaps in a simple man-
ner by assuming that households follow a "Calvo-style" refinancing process: they can only refinance
at Poisson arrival times, and will do so if their old mortgage rate is above the current market rate.
6
This random process proxies for a variety of pecuniary and non-pecuniary costs of refinancing and it
generates a simple random "step-hazard" of prepayment in which mortgages with positive rate gaps are
prepaid at a constant but higher rate than mortgages with negative rate gaps. As we show formally, this
is the simplest model of infrequent refinancing which still allows for refinancing decisions that depend
4
Specifications with month fixed effects also help alleviate concerns about endogeneity of monetary policy.
5
Freddie Mac annual refinancing statistics on agency loans show that on average 52% of refinances from 1992-2017 involve
no balance increase. In our broader data, the rate-refi share is close to 60%. Cashout refinancing is a larger share during the
housing boom that is the focus of much previous analysis on equity extraction. However, we argue that the distinction between
rate and cash-out refinancing is not particularly important for the main forces we identify and that modeling cash-out would
complicate the analysis but would also result in path-dependence.
6
We also abstract from housing choice, equity extraction and default but later argue that including these forces would
amplify our conclusions.
3
on rate gaps, but our empirical results show that it nevertheless has good explanatory power for actual
prepayment.
7
This empirically realistic dependence of refinancing decisions on individual rate gaps is
then the crucial feature which generates aggregate path-dependence of monetary policy.
Importantly, in addition to delivering straightforward intuition, this simple form of state-dependence
buys us substantial analytical tractability and allows us to break our model into two blocks: a mortgage
refinancing component and a consumption-savings component. Our setup implies that household re-
financing decisions are orthogonal to consumption-savings decisions, which means that the mortgage
refinancing block of the model can be analyzed on its own and does not depend on households’ prefer-
ences, labor income characteristics, borrowing constraints or wealth. The mortgage block of the model
pins down the equilibrium mortgage interest rate given exogenous short term interest rates as well as all
mortgage related outcomes like prepayment and rate gaps. This allows us to explore the transmission of
conventional monetary policy into mortgage rates and resulting mortgage outcomes without specifying
the consumption block of the model.
However, we ultimately care about the transmission of monetary policy to spending rather than
mortgage market outcomes. The mortgage block of our model delivers a redistribution of disposable
income in response to changes in interest rates, which depends on the distribution of outstanding mort-
gage rates. When interest rates decline, wealthy net-lender households face lower returns on their net
wealth while poor net-borrower households free up money if they can refinance into a lower mortgage
rate. The consumption block of the model translates these disposable income shocks into consumption.
Since the consumption block is set up as an intentionally standard incomplete markets problem, the
transmission mechanism from this redistribution of disposable income is straightforward: the joint dis-
tribution of wealth and mortgage coupons directly determines the response of aggregate spending to
current rate shocks.
8
Rate histories affect current responses by altering this distribution. Our framework,
which integrates the simplest model of state-dependent refinancing into an off-the shelf incomplete mar-
kets model, then delivers substantial aggregate path-dependence.
9
What are these effects? First, our model delivers many implications for mortgage market outcomes.
These results can all be explained by the fact that under our step-hazard setup, f ra c > 0 is a sufficient-
statistic for the response of mortgage coupons to interest rate shocks. More specifically, using an appli-
cation of results in Caballero and Engel (2007) which characterizes impulse responses in models with
state-dependence, we show that the initial response of average mortgage coupons to a change in mort-
gage rates depends only on f ra c > 0 and not on any other features of the gap distribution. This result
is driven crucially by the fact that our model features a step-hazard with a single jump at zero, and
this is the formal sense in which our mortgage prepayment model is the simplest possible model with
state-dependence: all other models with state-dependent prepayment require additional information on
7
Enriching the model to include a fixed cost of refinancing would not change any of the basic economic forces or our
conclusions for path-dependence but would substantially complicate the model solution and analysis.
8
We do not endogenize labor income or the relationship between aggregate spending and output, which will depend on
the strength of nominal rigidities. Thus, our model shows that fixed-rate mortgages lead to equilibrium nominal spending
responses to monetary policy which are path-dependent, but does not translate these time-varying spending effects to aggre-
gate production. See Greenwald (2017) and Greenwald, Landvoigt and Van Nieuwerburgh (2018) for representative agent GE
models with production where mortgage rate driven spending effects translate to important real GDP effects.
9
We view this as an illustration that the prepayment channel can have important path-dependent effects in a standard
model which explicitly isolates this novel mechanism from other complicating but well-understood forces. However, a more
quantitatively precise policy evaluation would clearly require a refined analysis with richer consumption dynamics integrated
into a full-fledged DSGE setup, which we leave for future work.
4
