Conferência Anual do Banco Central 2026 - 14/05 (PT/EN)

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Brazil.
Economia International Finances.
Central Brazil.
Brazil.
Finch.
technology.
Brazil,
Gabrielle,
Professor
Harvard,
you
to good morning everyone. Uh it's a
great pleasure to introduce today's
distinguished speaker, Professor Gabriel
Kodorav Reich from Harvard University.
Professor Codorov Reich is a leading
microeconomist whose innovative research
has significantly advanced our
understanding of monetary policy,
financial markets, and real economy
shocks. Widely recognized for combining
rigorous empirical analysis with a
strong policy relevance, his work has
shaped modern economic thinking on
financial frictions, central bank
interventions, and labor market
dynamics. His influential research is
frequently published in leading academic
journals including the American economic
review, the quarterly journal of
economics and the journal of political
economy. In addition to his academic
achievements achievements, he brings
valuable policymaking experience to the
field having served as a senior
economist at the White House Council of
Economic Advisors and as economic an
economist at the Federal Reserve Bank of
New York. [clears throat] Today he will
present his timely research on
foundation microeconomic challenge the
measurement of housing in the consumer
price index. In this work, Professor
Kodorov Reich reassesses how housing
costs are captured in official inflation
statistics, providing new insights into
the measurement of housing costs and
their implications for interpreting
inflation dynamics. Please join me in
giving a warm welcome to Professor
Gabriel Kod Reich.
[applause]
Thank you Neilton for that very warm and
kind introduction and thank you to the
banko central Brazil for organizing such
a wonderful conference. I've learned so
much already and such a warm uh welcome
uh to Brazil.
I am uh not at a central bank so I don't
usually have a disclaimer but in this
conference everybody else has had a
disclaimer and the place where I work
Harvard has been as much in the news and
under eye as any central bank or IMF. So
let me say that these are not the views
of Harvard and some of these things I
might say may not be the views of my
co-authors uh either. Uh so with that
let me uh go in and tell you uh what
this work is is about.
So, I'm going to start by telling you
how in the United States we measure
shelter inflation. So, inflation of
people who are renting their home or
people are owning their home. Uh for
renters, it's pretty straightforward.
The Bureau of Labor Statistics, the
agency that compiles the consumer price
index, runs a survey of properties. Uh
they ask those properties every six
months, what rent are you charging
tenants? and they use that uh to produce
a growth rate of rental costs uh for
those uh properties.
That's the uh yellow gold uh line on the
top there. Uh in the yaxis, it's scaled
to be the average uh rent paid in the
first quarter of 1996 when this uh chart
begins and it goes up uh but pretty
smoothly thereafter.
For owners, uh, the BLSCPI does
something referred to as the rental
equivalence approach, which means for
owners, they think of somebody who owns
their home as if they rent it to
themselves,
and they measure the cost growth using
that same survey of renters, and they
just reweigh it a little to make the
properties of renters look more like the
properties of owners. So, put more
weight on single family housing, a
little bit less weight on multifamily
housing.
So almost by construction those two
lines are going to move uh very similar
together. Now in the CPI in the US this
is a big component. Total shelter is
about a third of the total basket. The
rental component is about 70%. The owner
occupied component is about 25%. So how
we do how we treat these costs is going
to matter to the total inflation that we
measure in the economy into which the
central bank is going to respond.
If you come from being a housing
economist or an macroeconomist who
thinks about durable goods, a more
natural price for owner occupiers would
be something like a user cost. So user
cost in a frictionless
environment where people can buy and
sell all the time would be the cost of
buying a property at the beginning of
the period. If there's a mortgage
associated with that property, it's
making the down payment at the beginning
of the period, making the mortgage
payment, doing any maintenance along uh
side during that uh ownership period,
and then selling that property back at
the end of the period and paying off the
mortgage.
To construct a user cost, one needs to
take into account the expectations at
which you're going to sell. Uh so we did
that for three different measures of
expectations.
uh the one let me see if this Yep. So
uh this measure using the average house
price growth over the full sample. So
nothing dynamic.
This measure here at the end and the
dots this comes from a survey of from
the New York Fed survey of consumer
expectations where they ask households
how much do you think house prices are
going to go up over the next year? And
we plug that into the user cost formula.
And this one that goes back comes from a
Beijian V that I'll talk a little bit
about much later in the talk, but where
we tried to use a statistical forecast
to come up with house price
expectations.
And the first thing you should see is
the owner's equivalent rent line. This
relatively smooth uh red dots looks
nothing like the user cost. They're very
different in levels. They have different
low frequency trends and they have very
different high frequency trends.
You can ask well is the user cost really
a an easy thing to capture? Maybe
there's some noise there. One useful
thing is to look at one particular
episode. So this is 2021 2022. What's
happening in 2021 2020 2022 2023 the
Federal Reserve is raising interest
rates. As it raises interest rates,
mortgage rates go from a little under 3%
to close to 7%. At the same time that
mortgage rates are going up,
expectations of house price growth are
coming down. And so both of them those
push up the user cost substantially. And
so there's this very sharp increase in
the user cost line at a time where the
owner's equivalent rent isn't doing
much.
So why does an agency like the BLS use
the owner's equivalent rent approach?
Under two basic assumptions, the user
cost should equal owner's equivalent
rent. Those assumptions are people are
perfectly indifferent between owning and
renting for the same dollar value and
there's no frictions to moving and so
there's no transaction costs associated
with ownership that one doesn't pay uh
with renting.
So that's the uh theoretical
foundation for the owner's equivalent
rent approach.
The empirical divergence of rents and
user costs tells us that those
assumptions must have uh some failure.
And
so what broadly we're going to do uh in
this uh project is relax those
assumptions and ask what is a good
measure of shelter inflation. when we
relax those assumptions.
I'm going to give you a little bit of
historical perspect international
perspective uh on this problem as well.
Uh here's some data for Brazil. Uh the
blue line is the rental component of the
consumer price index deflated by the
total CPI. In Brazil the rental weight
is about 3%. So deflating by the total
CPI is just effectively depating
deflating by the the overall change in
the price level. And let me express
gratitude to people at the Central Bank
of Brazil for helping me uh find uh
those data.
The red line is house prices coming from
a BIS index of house prices in Brazil.
Uh again deflated by the same overall
Brazil CPI.
So under the rental equivalence approach
if that is equivalent to the user cost
on some balanced growth path and I'll
make this more precise as I go through
rents and house prices should move
together the price rent ratio would be
stable and if the price rent ratio is
stable then you could see how rents
would be a good proxy for the cost of
owning. [snorts]
Uh this picture shows very clearly that
that price
than the CPI.
A couple of more examples. Canada has a
similar measurement for renters and for
owners, it does something like the user
cost without the expected house price
appreciation component. So the Canada
CPI uh measures the cost of the mortgage
interest, the replacement cost, the
depreciation
uh and maintenance and the repairs and
transaction costs but leaves out the
expected growth uh component.
The Euro area also similarly for renters
measures uh the cost growth of rent. The
Euro area does not include any owner
occupied housing uh in the consumer
price index. uh it has stated that it
intends to move towards the US approach
of rental equivalents.
Brazil likewise uh to the euro area
measures rent of renters directly and
does not include anything about owner
occupied housing.
If you are someone who works with data
across countries, uh this is an anomaly.
In most data construction, there is a
lot of conform conformity across
countries. There are reports put out.
The system of national accounts makes
recommendations. Countries adopt them.
uh sometimes with some lags on timelines
to implement but there's general
agreement about the right way that we
should measure economic activity and the
right way that we should measure prices
and costs
in this case the reason for this
divergence in practice is that those
official recommendations have not
coalesed on a single uh recommendation.
So this comes from uh the uh CPI manual
uh of concepts and methods that was
updated in 2020 and 2025. Uh this was
done under the opices of the IMF
together with essentially every
international organization uh that one
uh can think of. Uh here's what they
wrote about owner occupied housing. The
treatment of owner occupied housing
services costs and CPIs is arguably one
of the most difficult issues faced by
CPI compilers. Depending on the
proportion of the population that are
occupiers, alternative concepts can have
a significant impact on the CPI
affecting both weights and especially in
the short-term measured inflation. And
then the manual goes on to offer uh five
different approaches to measuring owner
occupied housing. uh the user cost
approach which is trying to measure a
user cost directly, the rental
equivalence approach which I just
described,
a maximum of the user cost and rental
equivalence, a payments approach that
just tries to measure what are people
actually paying uh when they are owning
a housing and an acquisition approach
which you can think of as treating
housing like other durable goods like
cars, like non-durable goods like
apples. you just measure the cost people
are paying when they buy a house.
And of course, there's a sixth, which is
just leave owner occupied housing out of
the basket entirely, which is the
current Euro area practice and the
current Brazil practice.
So the purpose of this paper and project
is to start from uh this uh very uh uh
heterogeneous set of recommendations and
see if we can go back to first
principles and understand why is the
treatment of owner occupied housing a
difficult measurement topic. And if we
relax those assumptions that break the
rental equivalence user cost approach,
what would be a theoretically grounded
measure of shelter inflation? And then
we'll try and implement that uh for the
United States and think about or see how
it differs uh from uh other measures. So
this is what I'm going to do uh for the
rest of uh my talk. Uh, I'm going to
start by relaxing that assumption that
people are perfectly indifferent between
owning and renting. So, people might
have some preference for owning because
they want to be able to customize their
residence or they want to be in a
particular neighborhood that is mostly
owner occupied housing or they don't
like having a landlord who can come
knock on the door and inspect the
property at will. I'm going to call that
preference little theta.
And I'm going to show that uh
heterogeneity in that little theta can
rationalize the divergence between rents
and user costs. And once we allow for
heterogeneity in that little theta, user
costs are unambiguously the right
measure of uh inflation growth for uh
owner occupiers.
Then I'll bring in the transaction costs
associated with buying and selling uh
housing.
That's going to take a little bit of a
conceptual leap because now what is a
per period price index when the costs of
owning depend on previous payments and
previous choices. And so we will define
a value function. So a total present
value of welfare for the household and
then annuitize that to get back to
inflation.
Then I'll tell you about a survey we
ran. Uh so to do this in practice, one
needs to know something about these
little thetas. How much do people prefer
owning versus renting? So we ran a
survey of households in the US and and
gathered some data on that. And I'll
tell you about that and show you uh what
we found.
uh and then we'll put this into a
quantitative calibrated model in which
we can try and speak quantitatively to
the question of what would inflation
look like and in shelter inflation in
particular uh if we had these our
preferred alternative definition of how
to measure uh inflation
and I'll show you how this matters uh
both for a one-time increase in the
mortgage rate and then a decomposition
of inflation going back to 2019. So
through the inflation surge and how that
would look different for the shelter
component and why it would look
different for the shelter component uh
using our measurement approach.
Okay,
let's go in.
So the static model of tenure choice is
simple enough that I can present the
whole model on one slide and if you've
had your coffee this morning uh you can
follow along.
So households uh are going to be indexed
by that little theta and they're either
going to own or they're going to rent
and these properties are xanti are
identical across households. So that
script h will be owners script h equals
zero uh are renters. If you rent,
you're gonna pay a rent of big r. And so
your utility from shelter, whatever your
theta is, is be minus r. You only get
the theta if you if you own. So for
renters, we're going to normalize the
non-punary utility from owning from
renting to be zero. So the utility
contribution is just they have to pay r
out of pocket.
For owners, uh, we're going to assume
this frictionless environment. So owners
are going to do the user cost thing.
They're going to make a down payment on
the house at the beginning of a period.
So L would be the loan to value of the
house of the mortgage. 1 minus L is the
down payment scaled by the house price
PH.
They're going to make a mortgage
payment. So, their mortgage is little L*
PH with an interest rate of I. They're
going to make some maintenance costs,
pay some property taxes, and then
they're going to sell the property back
at the end of the period. They're going
to get PT + 1H. They're going to have to
pay off their mortgage, and they're
going to discount those future proceeds
using the discount factor beta. And I'm
going to summarize all of that as a uh
scalar row row t uh that multiplies the
house price. And that's the user cost.
That's the cost of of owning.
If a household chooses to own, they're
also going to get this warm glow from
owning uh which is their theta. So
again, think of this as the utility they
get from being able to
change a bedroom, update a bathroom, not
have a landlord come around, be in a
neighborhood that they want to be in
that is mostly owner occupied housing.
That theta will come from some
distribution fub theta.
So their total net utility from shelter
if they own is they get their theta and
they have to pay the cost of owning
which is the user cost row time ph.
So immediately if that f theta
distribution is non- degenerate there's
going to be some cut off there's going
to be a theta star and that theta star
is going to be the theta of somebody
who's just indifferent between renting
and owning. So just indifferent means if
they rent they pay R and they have
utility minus R. If they own they get
theta star minus the user cost row PH.
And so that's going to immediately pin
down what the user cost is going to be
relative to rents and it's going to
scale by that theta star.
So the home ownership rate is then going
to just come from that distribution of
thetas. Everybody who has a theta above
theta star is going to own. Everybody
who has a theta below theta star is
going to uh rent. I made a little
picture uh of this uh to capture all the
economics I just described.
Uh so here's the cost of rent. We're
going to take rent as exogenous
pinned down by something in the
construction market.
That's the utility of somebody who
rents. The utility of somebody who owns
is their theta minus the cost of owning.
And so that's just going to scale one
for one with the theta. Where that
intersects the rent line is going to pin
down what theta star is. Anybody who has
a theta above theta star owns. Anybody
who has a theta below theta star is
going to rent.
So what I'm going to do next is
characterize welfare and hence a price
index. as things move around as the rent
moves around as things move around in
the user cost. And the way that this
little model is going to reconcile the
divergence between rents and the user
cost is this theta star is going to move
around. And by allowing that theta star
to move around, we can get movements in
rents relative to the user cost. So let
me do that.
So what I'm going to call a price index
here is what's sometimes referred to as
the economics approach to price indexes
or the kunis price index repro approach
which is to define
inflation the change in prices as the
change in utility when prices change.
Or if you're used to seeing this in a
broader expenditure minimization
problem, think of there being some
outside non-shelter good when costs
change in the shelter market that
changes how much can be spent on the
non-shelter good. And in order to
restore utility, you have to come up
with some transfer to the household to
offset the lower non-housing consumption
that they're going to be able to do. And
that transfer represents the price.
So the change in prices for somebody of
type theta is a change in the utility
they get under the prices that exist at
date t where prices include rents,
mortgage rates, loan to values, all
those things that go into the user cost
relative to the utility they would get
at T+1.
If we aggregate
and compute a total price change, it's
going to have the following elements.
There's going to be the change in rent.
Then there's going to be the additional
owner costs. So remember that the theta
star, that's the wedge between the user
cost and the rent.
So the additional owner costs at t+1 are
theta star t+1 times the total fraction
of the population that's owning the home
ownership rate at t+1 minus the theta
star the additional payments in the user
cost at date t times the fraction of the
population that's owning at date t.
And then we have this term that comes
because that warm glow utility component
is going to change if the home ownership
rate changes. And so this is the total
uh utility uh that people are getting
from owning through the theta term at
t+1 minus the total utility they're
getting from owning at date t.
Of course, what's moving around in the
background to move the home ownership
rate and rent would require saying
something about the supply side of this
model and how the cost of owning
relative to renting change with the home
ownership rate. And we can put that in.
But for doing preferences, welfare and
utility and price indexes, we don't need
to specify the supply side. We can just
take those prices as given and ask what
they do uh to household welfare. And
that's what this equation gives.
[snorts]
So let me do two uh special cases. Uh
one is suppose we had a degenerate
distribution of theta.
A degenerate distribution of theta if
there's an interior uh indifference
means the home ownership rate is not
going to change and these terms are all
going to cancel out and the change in
prices is just going to be given by the
change in rents. So we can rationalize a
rental equivalence approach through the
utility price index if
there's no heterogeneity in theta. But
of course that's the case where rents
and the user cost perfectly track each
other. And we saw at the beginning that
that's counter to reality.
A second example would be something
changes in the user cost. So suppose the
mortgage interest rate goes up
and let's suppose just to make this
clean uh that rents don't change
then the price change is going to have
two components.
If rents don't change under the rental
equivalence approach there would be no
inflation in shelter
under this utility first principles
approach. There's two components. One is
the change in the cost of owning for
owners. So again, theta star that's the
wedge between the user cost and rents.
So that change in the wedge times the
people who are owning at both T and T+1
is the additional cost to owning when
mortgage rates go up. And then there's
the second term which is an extensive
margin consumer surplus term. It's the
change in the ownership times the
average surplus that people were getting
when they owned that they're going to
lose when they go to rent. So that
average surplus is if you had a theta
above theta star you were getting some
surplus from owning and when you then
switch into renting because the cost of
owning has gone up you lose that surplus
and we have to value that surplus as
well. So those examples say in this uh
in this environment
the right approach to a price index
would be the user cost not rental uh
equivalence.
Now I'm going to go and add in uh
dynamics.
So dynamics are going to complicate
thinking about a price index in the
following uh sense.
In the first year of graduate school, we
teach price index theory. Actually, in
intermediate macroeconomics, sometimes I
teach price index theory. And we start
from a static expenditure minimization
problem.
Uh, a household has some amount of
income. They face some prices that's
going to give them some utility. And
then if the prices change, they're going
to change how much utility they get. And
the price index is going to be the
transfer required to to compensate them.
Dynamics mean the utility one gets and
more specifically the cost of obtaining
that utility depends not just on the
prices you face today but also the
prices you faced in the past. So I'll
put a little notation on on that
statement.
So the script HT is now going to be the
tenure history. So tenure means renting
or owning in the housing context. Uh for
somebody who last moved S periods ago.
So script H could be you owned you owned
you owned four periods ago you bought
five periods ago you were renting you
were renting and you were renting uh uh
before that
I'm going to call a bold variable the
whole history of prices
from the dawn of time to the end of the
world.
And obviously for the prices that are uh
after date t those are going to
incorporate expectations.
And those prices are going to include
the house price, the rent, the mortgage
rate, all of those elements that go into
the cost of of shelter.
And what dynamics mean is today's
shelter outlay, the amount of spending a
household's doing on shelter at date t,
which I'm going to call x, depends on
whether they were owning or renting last
period,
whether they're owning or renting today,
how long they've been in their current
residence, and that whole history of
prices. And so that's what it means to
have dynamics. It means that today's
outlay depends on
past decisions and past prices. And so a
concrete example of this would be if an
owner has a mortgage and they bought
their house 10 years ago, their mortgage
payment today, that's their outlay,
depends on what house prices were 10
years ago. and if it's a fixed rate
mortgage, what mortgage rates were 10
years ago. So that's the sense of of
dependence.
So the dynamic analog to the standard
expenditure minimization problem
is to not solve for what it would take
to fix
utility in a single period but what it
would take to fix the present value of
utility from today forward. And that
present value of utility from today
forward is what in macroeconomics we
call a value function. And I'm going to
call that big V.
And DVT
is going to be the change in the value
function when there's some change in
that price matrix, the bold W.
And so the game to understand what
changes in shelter prices, what changes
in the W are going to do to shelter
inflation is going to be to first
characterize what they do to the value
function.
what they do to V and then
bring that V down to a per period price
index that's comparable to changes in
the price of apples or oranges.
So let me add a little bit more notation
uh that's going to be relevant for when
we go to make this quantitative. So
capital theta,
that's this letter,
is going to be all of the exogenous
characteristics that a household has. So
that's going to include their little
theta that we've spent some time on
already, but also some households might
have uh uh expectations of moving more
quickly that might affect their tenure
choice. Uh they may have differences in
liquidity, ability to make a down
payment or buy the buy the house. So all
that's going to be the big uh capital
theta.
So the state variables, what a household
has when it enters at into date t, I'm
going to call that capital omega t. And
capital omega t is going to include the
household's assets, its non-housing
assets, whether it is owning or renting
as it comes into the period, how long
it's been since it changed, since it
moved,
and those exogenous preferences, the
capital theta.
And to make this uh
as tractable as possible, I'm going to
make two further assumptions. One is I'm
going to uh have households act like
they have perfect foresight over those
future prices.
And the second is I'm going to have them
have full insurance over the
idiosyncratic shocks. So idiosyncratic
shocks are their theta might change,
their ability to make a down payment or
buy a house might change and insurance
over those idiosyncratic shocks means
their non-housing consumption is not
going to depend on the realization of
those shocks.
So with those assumptions I can
characterize
uh several objects about the present
value of uh owning or renting a home and
being in a particular state uh as
follows.
So remember x was my notation for how
much are you spending today on shelter.
So, vx is the present value of spending
on shelter or the expected present value
of spending on shelter for a household.
That's going to depend on their state.
So, it's going to depend on their omega.
Beta, that's the financial discount
factor. So, that's like one over one
plus the interest rate. So, this is
expected discounted value of all those
future shelter payments the household is
going to make, whether it's owning or
renting.
That's vx of omega.
Then I'm going to introduce a
non-shelter good. I'll call that c.
And the present value of non-shelter
utility.
That's the discounted value using a
subjective discounter founder factor. So
that's what I'll call beta tilda of
their utility of the non-shelter good.
So U of C. And to put this back in
moneymetric terms or dollar terms, I'm
going to divide that present value of
utility by the marginal utility
consumption today.
And I can write that. So that's VC, the
value of non shelter consumption
as depending on two things. One is total
non-shelter assets. That's the a net of
all the spending that the household is
going to be doing on shelter. So a t
minus one minus vtx that's all of the uh
wealth the household has that can be uh
spent on non-housing uh consumption and
that's going to determine the
household's value of uh non-housing
consumption.
Then there's the theta component. So v
theta is the present value of all those
future thetas the household is going to
get from owning. But of course they only
get the theta in periods where they own.
So they only get the period theta if
that script ht plus j is equal to one.
And so the total welfare, the total
present value of utility from
non-housing consumption and from the
thetas, that's just V of omega. That's
going to be the VC, the utility from the
non-housing consumption plus the V
theta.
So now I'm going to take some
perturbations. So I'm going to suppose
that these prices change.
Prices change mean of course I'm doing
the bold W. Bold W was the whole history
of prices from the dawn of time to the
end of the world. But prices in the past
can't change. So when we have changes in
W, those are changes in today's prices
or expected future prices.
So dy of some object it's going to
depend on the individual's type omega
and those change in prices that's going
to be what does the uh household uh have
under the new set of prices minus what
they expected to have uh at date t.
So the first result uh that comes from
this framework
is the change in welfare the change in
the value function DV is going to have
two terms.
One term is the change in the present
value of spending on shelter. So if
shelter prices change, rents change,
house prices change, mortgage rates
change, or expectations of those
variables change, that's going to change
how much a household of type omega
expects to be spending on shelter. And
that's going to affect the welfare
because it's going to change how much
they can spend on noun shelter because
there's a budget constraint that has to
hold. So minus dvx is the first term of
this welfare change. And the second term
is this household is going to change
whether they expect to be owning or
renting in future periods. And so the
value of those thetas that they're going
to get in the future is going to change.
So there's a pecunary component minus
dvx and there's a non-computinary
component uh dv theta.
Our
second result
is going to be what does the impulse
response of inflation or of our shelter
price index uh look like when we have
one of these price changes.
And
to do this, we're going to have to do
something additional because the change
in the value function tells us how much
we have to compensate the household
today at date t to compensate for all
those prices changing today and possibly
in the future.
But a shelter inflation index or
inflation when we do changes in the
price of bananas,
we don't calculate inflation as the
change in the present value of all the
spending the household's going to do on
bananas. Inflation over bananas is how
much are you spending on bananas today?
So the analog that we're going to
propose in the durables dynamic case is
we're going to take the change in that
value function and we're going to ask
if the household's going to change its
present value of spending on non-housing
goods on the C's by DVX, how much does
it change its consumption on non-housing
goods today at date t?
[snorts]
And that object
I'm going to call uh MJ.
MJ is if
uh wealth changes today, if the assets
change or the value spending on shelter
changes today, how much does consumption
change J periods later? I'm going to
call that MJ. In the heterogeneous agent
uh literature they refer to these as
intertemporal marginal propensities to
consume. Marginal propensity consume
traditionally in the old Keynesian
tradition was if income changes today
how much do you change spending today
and temporal marginal propensity consume
is if income or wealth changes today how
much do you change spending? How much do
you change consumption at any future
date? And those intertemporal marginal
propensities to consumer or IMPC's are
going to characterize exactly when we
should count the change in spending on
shelter against the household's utility
and so when that price index should
change.
So that's the first term, the MJ times
the DVX.
The second term is the change in whether
the household is owning or renting at
future date T plus J.
And then of course we have to aggregate
all those over all the households. So
we're going to take an expectation at
date t over all the different types at
day t. So that's what the e subscript
omega notation is doing. So we're going
to do for each household for each omega
type how much are they changing their
consumption at each future date because
prices changed. Are they changing
whether they're owning or renting? And
so are they getting a different theta at
that future date? And then we take that
average across households. And for a
one-time change in prices, that tells us
what the price path on shelter should
be.
Then we want to do a price index. And a
price index means of course shelter
prices can change month by month or day
by day or quarter by quarter or year by
year or by whatever the unit of time is.
And so we prove a result that says uh
under some nice functional form
assumptions
uh in particular log utility over the
nonhousing consumption
the change in prices and I snuck in some
R bars here that's allowing for some
trend growth in rent but you feel should
feel free to ignore the R bars or just
set them all equal to one. The change in
prices is going to be the annuity value
of the change in spending on shelter
expenditure.
That's this first term
minus the change in the total utility
non-punary utility people are getting
from owning. So the present value or the
average of those thetas between t and t
minus one. And the intuition of this
result is with log utility consumption
is proportional to wealth.
as DVX changes because prices change.
That's like a change in the agent's
wealth or its ability to spend on
non-durable consumption. And so the
amount that that's going to change
consumption today is going to be the
annuity value of that change in in DVX.
And uh under this uh construction,
consumption is going to act like a
random walk. And so all we need to keep
track of is the uh uh new news about
house prices that arrive at date t. How
much does that change consumption?
That's what's going to go into the price
index.
If uh
you really like
uh to uh get into the depths of welfare
and price indexes or the heterogeneous
agents literature and you want to think
about incomplete markets rather than
this full insurance setup that kept the
seas fixed. Uh we have an appendix
extension of that in the paper. Uh the
short answer is instead of having uh
future consumptions running around, we
have future certainty equivalent
consumptions running around. And that's
the analog in an incomplete markets
world. But if you don't like to think
about those things, let the last uh
sentence I said just slip through uh and
uh we'll go forward.
All right. [snorts]
When did we start and how long should I
go? Or how much longer should I go?
If we start
>> I should talk for 15 minutes and then
we'll have a little time.
>> Whatever.
>> Okay. For like 15 minutes I think.
>> Yeah.
>> Okay. So I'll uh speed up then.
>> Thank you.
>> So uh we ran a survey to try and
understand what these thetas are. The
basic idea of the third survey uh was to
uh tell people
go back to when you bought your home or
when you moved into a rental and imagine
or think about the choice you were
making about whether to own or rent.
And when you make that choice uh you
have to consider
the punary costs of owning versus
renting and anything else. And then we
said, imagine,
we told them a lot about what those
costs are. Then we said, imagine 10
years later if you had rented or you had
owned, you would be spending exactly the
same amount on shelter. You'd have the
same wealth after 10 years. So we're
going to hold the pecuniary component
fixed.
10 years ago, you bought, you're
currently an owner. Would you still have
wanted to buy if you knew that the
pecuniary outlays the dollar cost would
be the same? And if people said yes, I
would still choose to buy. Then we asked
them to tell us how much more money
would you need in the rental scenario if
you had chosen to rent. Maybe because
the stock market did really well and so
the money you put into a down payment
could have gone into the market. How
much more money would you need that
would have make you choose to rent
rather than buy? And that's what we call
uh the the theta. So this is what it
looks like. Uh there's some
heterogeneity in those thetas.
uh that heterogeneity maps onto revealed
preference. So people who currently own
have higher
revealed have higher uh stated
willingness to pay to own than people
who rent.
And there's a life cycle element to it.
So people who are young tend to be
pretty indifferent between owning and
renting given the costs. As people move
into middle age, maybe the period where
they have children, where they care more
about having a house in the right
neighborhood with the right school, they
express a higher willingness to pay to
own. And then at some point, as people
reach the retirement age, uh they become
happy to move into a rental property
again.
So, I'm going to take those statistics
and some other things. I'm going to put
them into a uh model of owning versus
renting where we can compute uh these
price changes and welfare measures.
So, uh I have to put in some transaction
costs. So, there's going to be some
transaction costs of buying a new moving
into new rental property or selling a
home. Uh there's going to be some uh
non-shelter inflation. That's going to
matter because uh we're going to
calibrate this for the US where people
have fixed rate mortgages and so
non-shelter inflation is going to be
really good uh for homeowners who are
indebted.
Uh we're going to have a standard for
the US 30-year mortgage uh uh uh
contract and two additional types of
heterogeneity. Lambda type is going to
be how likely are you to have to move.
So I think of this as um people who are
currently in an internship or in college
or in graduate school. They tend not to
own in part because they know they're
going to have to move in a few years and
so they don't want to pay the
transaction cost of of owning relative
to renting. And Zeta is going to be do
you have uh uh the ability to buy a
house? Can you make the required down
payment if you're getting a mortgage?
Okay. Okay. And then there's going to be
some life cycle element uh to all of
this
and some things to smooth out the value
functions.
Okay, let me skip through the uh details
of seeing what those value functions
look like. Uh tell you briefly about how
we put numbers on that and then get to
some of the results.
So, we're going to uh model uh
households as being in one of uh 1 2 3 4
five age groups. That's going to match
the age information we have in the
survey. Uh we're going to calibrate the
theta. So, the theta goes up over the
life cycle, but periodically will fall.
And we think of the falling as when you
decide to downsize. [snorts] Uh we're
going to calibrate the zeta to match the
share of uh households who can't make a
minimum down payment.
We're going to externally calibrate a
bunch of things and then we're going to
jointly estimate a bunch of other
parameters uh to match mobility rates uh
of households across owning and renting
uh and to match uh those two moments I
just showed you from our survey, the
distribution of the thetas and the
average difference in the thetas between
uh those who own and those who rent and
uh the overall home ownership rate in
the US economy.
>> [snorts]
>> This is what this looks like. So this
just gives you a sense of the selection
that's then going to drive some of the
welfare results. [snorts]
So these guys on the left, the Z equals
1, these are the households that can't
make a down payment. So they're going to
be renting by construction. So a darker
color here means more of the population
of this group is renting and all these
households are renting because they
don't have the ability to uh buy a
house.
These are the households uh who can buy
a house and who don't expect to move
anytime soon. So for those households,
if their theta is at all positive,
they're going to want to uh they're
going to want to own.
These are the households who uh can buy
a house but for whatever life cycle
reasons are expecting to have to move
relatively soon. And they're going to
require a higher theta to be willing to
buy because owning if they're going to
have to move at some point is going to
require paying the transaction cost of
selling the house. And so they might
prefer to rent and forgo those
transaction costs even though all else
equal they would they would like to own.
All right. [snorts] So, we do two
applications. Um,
in the interest of time, why don't I
jump to the uh historical uh price index
um and and tell you how this matters if
we want to understand the inflation
surge in the US and its effect on um and
where it comes from and how it differs
depending on how we measure things.
So the exercise we're going to do is uh
suppose the US housing market starts in
steady state in 2019. I think that's not
a a bad assumption. Uh then we're going
to give everybody these forecasts of the
W's of rent growth, of price growth, of
mortgage rates, and of non-shelter
inflation. And we're going to draw these
uh from survey data from a Beijian V
over house prices and rents that we did
and uh from forecast coming from the
Cleveland Fed of uh non-chelter
inflation and the term structure of
Treasury rates which is going to tell us
something about forecast of future
mortgage rates.
There's one subtlety in computing this
sort of price index which is there may
be demand shocks that are not in our
model and in this period that
encompasses co those could be very
salient. COVID was a period uh where uh
many households wanted to move out of
the city center both for school district
reasons because the city center was
denser and thought to be more prone to
disease. And so that's a demand shock
that affects that sort of shifts the
distribution of those thetas. So we're
going to take those out of the price
index, but we're going to um feed in
some some wedges so that we're going to
match the home ownership rate. So by
construction, what I'm going to show you
is going to match time series of home
ownership rates, rents, house prices,
mortgage rates, and the expectations uh
that we've constructed over all those
objects.
So this is what we're we're actually
going to feed in. So what do the data
look like? Uh rents in the US go up
after the inflation surge. So in real
terms, real meaning relative to
non-shelter CPI, rents fall and then go
up. Uh house prices go up very quickly.
So those are real house prices. Uh the
mortgage rate goes up in the Fed rate
hiking cycle in 2022 and 2023. And of
course there's a surge in non-shelter uh
inflation.
So this is what uh this is what we get.
So for perspective, uh this line at the
bottom is the uh BLS official CPI for
shelter, okay? Which goes down again
relative to non-shelter CPI by 6% and
then comes back up.
This is our uh preferred uh measure.
This is the part that comes from that
pecuniary component. So not the thetas
but just the vx is moving around. So
think of that as the most important part
and then these bars decompose uh where
these changes are coming from. So the
fallen real rents is going to directly
contribute to changes in shelter CPI.
The non-shelter inflation is really good
for homeowners.
It erodess the value of their mortgages.
So non-shelter inflation from the
perspective of a CPI and shelter is
going to reduce uh that CPI and those
are the green bars. And the other one
I'll draw attention to is the nominal
mortgage rate. So the nominal mortgage
rate as we saw in the simple example is
irrelevant in the rental equivalence
approach. But a large increase in the
mortgage rate is going to have a large
increase on uh shelter CPI and that
comes through in this uh decomposition.
We did a couple of other exercises on
how to treat uh those changes in house
prices, changes in non-shelter
inflation. Uh there are arguments for
taking them in or out of the index. Um
and if you take them out, not
surprisingly, uh if we don't count the
non-shelter inflation contribution,
we're going to have a smaller uh decline
uh in inflation and but a similar rise.
But let me let me conclude to leave a
little bit of time uh for questions.
So where I started was there's divergent
practice all over the world and how to
understand shelter in the CPI and
shelter in the CPI can be really
important. It's a third of the basket in
the US. It's 3% of Nebraska and Brazil,
7% in the Euro area. So, we're doing
very different uh things. When we see
very different things, that calls for
doing some first principles analysis of
what we should be doing. And so, that's
what we tried to do uh in this paper.
Uh I leave that with two caveats. One is
for the statistical agencies. Uh
statistical agencies have to be able to
produce statistics that are transparent
to the public.
And we have acknowledgment or I will
acknowledge that calculating a value
function and smoothing it over time
might not be transparent to the public.
At the same time, try asking somebody
who owns their house whether they think
that the cost of owning is the cost of
renting the house to themsel. And you'll
find that people don't really understand
that concept either. So I think uh
there's a a a bar here that is not
incredibly high. Uh and last monetary
policy. So I just argued for measuring
shelter inflation in a way that would
incorporate changes in mortgage interest
rates. And that's a little bit awkward
for monetary policy because when you
increase interest rates, you increase
mortgage rates and that's going to
directly increase shelter inflation.
And uh the principle I would propose is
we should measure shelter inflation
properly so that we know what pain
households are feeling and we understand
that and then we should think about
what's the right target for monetary
policy and those two things might not be
the same and in fact in Canada they have
a target for monetary policy that
excludes those interest payment
components and I think that's a more
more coherent uh way forward than
pretending uh that these changes in
mortgage rates don't affect household
welfare. Why don't I stop there and I'm
happy to take questions if there's any
time.
[applause]
Thank you, professor. Uh was fantastic.
A lot of details.
Um so I wonder if we have questions from
the the crew.
We have one here in center. Thank you.
>> Uh, hi Lewis from the University of Ban.
That was a great uh keynote
[clears throat] speech and I really
enjoyed it. [snorts] I think the the
rest of people can say the same. Uh,
thanks for being here. Um, I just wanted
to ask you something. How do you
consider owners who have already well
they own the property so they don't
really have a mortgage and considering
that a lot of wealth or a non-trivial
share is inherited how do you
internalize that in your measure
thank you very much uh for the question
uh it's a great question uh to put a
little data on this my understanding
from looking at some data for Brazil is
a very high share of uh homes are owned
outright
without a mortgage. So in our life cycle
model, we're going to have some
households who have paid off their
mortgage. If they've owned for long
enough uh and they've paid down their
mortgage than they own outright. Uh
that's obviously a calibration question
and for the US that's going to be a
lower share of owners who own outright
than in in a country like uh Brazil.
conceptually uh how to account for this
um is hard to think about unless you
start from this sort of framework. And
so uh here if you own and you expect to
sell in the future um maybe because
you're going to downsize and and and
rent uh then you do have some expected
changes in VX and those are going to
change when house prices are going to
change and we're going to want to
capture that. If you own and expect to
pass the property down to your uh
children and and never sell, then you're
uh immune to changes in house prices and
those shouldn't uh matter in a price
index. Uh the decision we made in the
implementation here was to take a
dynastic view where households care
about the welfare of their offspring,
but we force them to sell when they die
and so people make new tenure decisions
uh when they come into the economy. But
I would consider that to be a detail
that I'd be very willing to litigate in
practice rather than a core principle of
the of the approach.
We have another one here.
Oh, thanks for the presentation. was
very interesting. U I would like to
submit to you another uh u variation for
consideration like regarding your last
topic there about separating the
monetary policy target from from the uh
theoretically sound uh inflation
measurement. Uh you consider that we
might want to exclude interest payments.
uh but uh how would you react if someone
told you perhaps we should exclude also
uh the capital uh uh gains uh especially
uh considering that like know if you for
instance like know start by u easing
policy cutting rates uh this should make
uh um house prices go up uh and this is
like know reducing your correct
measurement of uh housing uh inflation
and then the central bank should perhaps
cut even more. Uh but if it cuts even
more uh you start like know [snorts]
producing almost like a bubble out of
this. So how how what would you say?
[snorts]
So there's a question about what
changing interest rates will do to house
prices and rents. That's an empirical
question and the data show when the
central bank raises interest rates uh it
tends to choke off house price growth
and it also tends to choke off rent
growth. Then there's a question about
what we're measuring uh in the price
index and what are we measuring and what
the central bank is tracking. So I
didn't really spend much time on this
picture but I'll take the question to to
spend one more minute on this picture.
Um so there is a a view on price indexes
that they should not include capital
gains components and the index I put
forward includes them and it includes
them because it's a dynamic problem and
so it's sort of awkward to separate them
out. Um but the way we we did it was uh
we said suppose when a household buys a
house it signs a separate financial
contract that locks in the expected
capital gains at the time that it buys
and it also locks in a path of inflation
non-shelter inflation at the time of it
buys and any deviations from that we're
going to call a financial return rather
than part of the uh change in housing.
And so that's uh what um what we did in
the top line there that take out the
capital gains and the inflation. So if
that's so we can we can accommodate that
uh perspective. Um I think in terms of
the another way to put the the
separating the targeting is interest
rate changes
look a lot like cost push shocks in this
framework. they increase the cost of
owning. And um monetary policy has a
pretty strong tradition of wanting to
look through one-time price level
changes, which is what permanent changes
in interest rates are. And the case here
is actually stronger than say the tariff
case. In the tariff case, we worry about
those one-time price changes actually
taking a while to filter through the
economy because there are production
networks and there sticky prices. And so
a one-time change in the price level
actually generates some inflation and
some misallocation. And we don't have to
worry about any of that here. It's just
in the housing market, it increases
costs. And and so I think that's another
way of thinking about why uh there would
be a a theoretical grounds for for
excluding it.
Thank you. There's another one.
>> Thanks for this, Gib. I I had a small
question on the rental price
measurement. From my understanding in
your framework, it's basically coming
from a supply side of the model. So I I
was just wondering how the team is
thinking about the the distortions in
the housing supply side of things,
right? because I think people would
agree that in this lecture there's been
a lot of discussion about declining
construction productivity but at the
same time rental price growth does not
seem to exclusively reflect supply side
phenomena. So I was just wondering how's
the team thinking about that side that
also seems to have a little bit of a
demand flavor of choosing between rental
and ownership.
So, as you know, my co-author and
colleague Ed Glazer uh spends all of
this time thinking about the supply side
of uh housing. Uh in uh the impulse
responses, which I did not show uh in
the interest of time, but are in the
paper, uh we close the supply side with
um think of these as as like private
equity agents who can convert owner
occupied housing to rental housing. Or
you can just think of there being some
depreciation of housing and when you
build onto the stock you can build
rental or owner occupied and uh the cost
is going to depend on that mix of of
what you're building. So that's a way of
closing the model and then we can feed
in an interest rate shock and think
about general equilibrium on house
prices. to bring in rents, we would have
to then also have some construction
center of the rental market and how much
household formation is there and and and
all that, but we could do that. However,
when we're doing welfare from the
household's perspective,
a neat thing is you don't need to go to
general equilibrium. The household takes
prices as given. And when we do price
indexes and welfare, we want to know
what's happening to utility given those
prices. And so to think about what are
the deep shocks that are driving the
market. Sure, you need to close a thing
and and understand the supply side. But
to do this exercise of how to measure
inflation properly, we want to be able
to take all those prices as given and
then ask how is it affecting utility and
therefore how much do we have to
compensate households to keep them
whole.
Um hi uh thank you for your uh
presentation. Uh there's a growing
discussion in the US about whether uh
housing afford a affordability may be
related to institutional investors
entering the housing market uh such as
hedge funds buying family homes and um
do you believe this may be related to
the wedge between the user costs and
rent prices and uh how could your model
accommodate such market forces?
>> So that's a great question. is very
related to the question Adriano just
asked about what's going on in the
supply side.
So one way to think about again where
the supply side comes from is exactly
think about these institutional
investors and they can buy up single
family homes and then rent them out. And
when they do that uh they're going to
tend to increase rents and reduce the uh
u uh uh they're going to they're going
to change the price rent ratio uh in the
economy. Um, so we could uh we could
model that and we could model a change
in that uh 10-year supply curve
effectively. What's the how does the
price rent ratio vary uh with um changes
[snorts] in the home ownership rate.
Again, for doing the the welfare, we're
going to take those prices as given, but
uh as an exercise of this model is
potentially well suited to handle. And
how does that change household welfare?
It would be an interesting extension to
think about.
>> Okay. Well, thank you very much,
Professor Kodor. [laughter]
Uh like um very thorough the explanation
and the details and I'm just in the
meantime thinking how the would work in
Brazil. A lot of things behave a little
bit different here like people do not
tend to borrow back by by as we're
talking yesterday. But uh very very
interesting. Thank you. Thank you very
much. Thank you. [applause]
in French.
>> [applause]
>> But they don't matter.
to the point Check out. [music]
[music]