# Gentrification, Mobility, and Consumption

Giacomo De Giorgi111Giacomo De Giorgi acknowledges financial support from the
SNF grant $\\#100018\\_182243$. We thank Yujung Hwang, Pietro Campa, Davide
Pietrobon, Jaromir Nosal for providing feedback and support for this project.
(IEE-GSEM University of Geneva, BREAD, CEPR)
Enrico Moretti (UC Berkeley, CEPR, NBER)
Harrison Wheeler (University of Toronto)

###### Abstract

We study the effect of localized housing price hikes on renters’ mobility,
consumption, and credit outcomes. Consistent with a spatial equilibrium model,
we find that the consumption responses vary greatly for movers and stayers.
While movers increase their consumption, purchase homes, and cars, stayers are
relatively unaffected.

JEL: R23, D12
Keywords: Gentrification, Mobility, Consumption

##  1 Introduction

A growing empirical literature finds that changes in house prices have sizable
effects on homeowner consumption and standard of living. For example, [Mian et
al., 2013] and [Cerutti et al., 2017] find that the Marginal Propensity to
Consume (MPC) out of housing wealth is 5-7 cents on the dollar, suggesting a
significant wealth effect.222[Berger et al., 2018] provide a model that
explains the magnitude of the effects.

Much less is known about the effect of house price, and therefore rental cost,
increases on renters. Rent increases in the years leading up to the Great
Recession and more recent rent increases since the end of the Great Recession
have generated widespread policy concerns in many cities about gentrification
and renter displacement. For example, between January 2012 and 2018 the
average rent in US cities increased by more than 20%. In San Francisco,
Seattle, and Boston, rents have increased on average by 40%, 40% and 22%,
respectively, with even larger increases in some gentrifying
neighborhoods.333U.S. Bureau of Labor Statistics, Consumer Price Index for All
Urban Consumers: Rent of Primary Residence in U.S. City Average, retrieved
from FRED, Federal Reserve Bank of St. Louis, April 10, 2024. Rents in San
Francisco’s Mission district and in Seattle’s Pioneer Square area have
increased by more than 50% in the same period.444[Guerrieri et al., 2013]
investigate which neighborhoods gentrify. [Collinson et al., 2024] study the
effects of evictions on marginal tenants in Chicago and uncover limited
effects on employment outcomes. Yet, there is limited systematic empirical
evidence on the how rent increases affect incumbent renters consumption and
standard of living. [Desmond, 2012] provides a narrative account of the
effects of eviction on the lives of low income renters.

In this paper, we use a panel from Experian Credit Report Data on a 1% sample
—or 2.2 million individuals— of the US population, with credit data
longitudinally linked between 2004 and 2016 to analyze renters’ responses to
house prices shocks. We focus on non-housing consumption responses — overall
consumption, as measured by credit cards balances, home purchase, auto
purchase —and mobility responses. In our analysis, a renter is exposed to a
price shock if she lives in a zip code that experience a mean housing price
increase of 25, 30, 50 percent over the three previous years.

We find that, on average, the consumption effect of a price shock on renters
is not large. Renters who live in affected zip codes do not appear to change
their overall consumption levels compared to renters of similar age who live
in non-affected zip codes in the same CZ, nor do they seem to change the
probability of having a mortgage or owning a car. This is consistent with a
spatial equilibrium model in which rent shocks are offset by wage increases,
as would be in the case in which rents increase in some areas because of labor
demand shifts, and local rents fully adjust to higher local wages.

However, we uncover vastly different effects when we split the sample between
“movers”—defined as those who change address following the price shock—and
stayers. While stayers experience modest declines in consumption, movers
experience significant increase in consumption, purchase homes and cars. Most
of the movers appear to move to zip codes with lower housing prices. A higher
level of non housing consumption is consistent with lower expenditures on
housing.

Overall, we conclude that the standard of living of renters in areas that are
hit by house price increases do not decline significantly. If anything, they
improve for those who decide to move. While we have little to say about
welfare and utility changes, our finding suggest that popular concerns about
gentrification and renter displacement need to take into account endogenous
wage changes for those who stay and lower costs of living for those who move.

The reminder of the paper is organized as follows. Section 2 presents the data
used. Section 3 introduces a simple conceptual framework. Section 4 covers
some descriptive results, while in Section 5 we develop our empirical
analysis. Finally, Section 6 concludes.

##  2 Data

We use several data sources for our analysis, of which the main ones are: 1)
credit report data for a 1% panel ($\approx 2.2m$ individuals) of the US
population with credit score from 2004 to 2016; and, 2) house price data
series from the FHFA and other sources. Here, we describe the two sources of
data and their limitations.

###  2.1 Credit Data

The source of the credit report data is Experian. Selection into our sample
depends on having a valid credit score at a point in time (in 2010). Over 70%
of the US population has a credit report in 2010, with that share increasing
over age.

A credit report is generated any time an individual opens or initiates a
credit operation, e.g. applies for a credit card, a car loan, a mortgage, etc.
In general, any formal credit operation will generate a record in the report.
We draw our data on June 30th of every year, from 2004 to 2016, and at that
date we register all the closing balances transmitted by the financial
institution to Experian.555From Experian source: credit card lenders don’t
typically report at the end of the month. They report throughout the month in
cycles, every single day a portion of the portfolio. Experian takes the
snapshot at the end of the month so to take into account everything that has
been reported. For example, most credit card lenders report the statement
balance that was sent out on the consumers’ monthly invoice or statement.
Typically, for credit cards that means that even for those customers that pay
in full every month, the balance reported would be the full cycle expenditure.

An advantage relative to data like Mint.com is the fact that selection into
the sample does not depend on user sign-up. An important limitation of our
sample is that we miss those individuals who have no valid score in 2010,
these are individuals with no credit lines (sometimes referred to as unbanked)
or insufficient credit information – overall, accounting for no more than 20%
of the adult
population.666https://files.consumerfinance.gov/f/201505_cfpb_data-point-
credit-invisibles.pdf Both groups are likely to be over-represented among low-
income households. A second limitation is that we do not observe family or
household structures, as our data are drawn at the individual-level.

For each individual–year pair in the sample, we have information on
residential location at the level of zip code, year of birth, (imputed)
income, credit use, and delinquencies. Specifically, we have information on
all individual credit lines and balances: credit cards, mortgages, auto loans
and personal loans. Credit card balances are obtained by Experian from the
different credit card companies. In addition, we have information on
delinquencies, defaults, as measured by balances outstanding after 1, 2, 3, 4,
6 months, and chapter 7 and 13 status and foreclosures.

To have a sense of how our sample compares with the US population, Appendix
Figure A.1 plots the log size of our sample in each commuting zone against the
log number of households in the 2010 ACS. Two features are noteworthy. First,
there appears to be a tight link between our sample size and the corresponding
number of households in ACS. Second, the slope (standard error) is essentially
1 (0.006 or 0.007 if we weight by population), the Experian data somewhat
under-sample lower population/rural areas and over-sample larger cities.

Appendix Figure A.2 plots the log size of our sample in each zip code against
the log number of households in 2010 IRS data. The slope (standard deviation)
here is again very close to 1 (.013). The Figure also reveals significantly
more dispersion in zip codes that are small according to IRS data. In essence,
our sample tends to underrepresent zipcodes with fewer than 400 IRS returns,
but appears to be quite tight for any zipcode with more than 1800 returns.

Throughout the paper, we define as homeowners those who have a mortgage, and
as renters those without a mortgage. This definition is likely to contain
measurement error, since we miss ownership cases when a property is paid in
cash or the mortgage is fully repaid. However, we expect that the probability
of having fully repaid a mortgage is low in the age group that we are focusing
on: 25-55 years old. Similarly, cash purchases might be less relevant in the
prime age segment.777The share of houses sold in cash in the period of
interest appear to be within .03 and .12, U.S. Census Bureau and U.S.
Department of Housing and Urban Development, Houses Sold by Type of Financing,
Cash Purchase [HSTFC], retrieved from FRED, Federal Reserve Bank of St. Louis;
https://fred.stlouisfed.org/series/HSTFC, April 19, 2024. We have no
information on the break-down by age of the buyer.

Appendix Figure A.5 plots the probability of homeownership over the lifecycle
in our data and in the 2010 American Community Survey (ACS). The Figure
indicates that we are indeed underestimating ownership rates, especially at
younger ages. This is perhaps because those owners purchase their homes
through parental transfers. What is reassuring though is that by age 33 the
two lines are quite close, the differences are of 2/3pp, and the shapes are
very comparable.

Furthermore, Appendix Figure A.6 plots ownership rates in our data against
ownership rates in the 2010 ACS. We then estimate the slope (standard
deviation) of that relationship to be .46 (.065). Measurement error in
ownership status does not appear to have any obvious geographical component.

Income We have access to two measures of income: 1) An individual W2 based
measure, and 2) a more comprehensive measure Total Income which is based on W2
and other sources of income (e.g. investment, farming, and so on).888It is
important to note that the reason why those measure are available is because
of “market” need for detecting the ability to pay by potential borrowers to be
incorporated in the credit score and credit applications. Below is an extract
from the Experian document on the matter: …Final Federal rules implementing
the Credit CARD Act became effective on February 22, 2010, require that card
issuers consider a borrower’s ability to pay in lending decisions. This allows
use of empirically derived and statistically sound models Income Insight
released December 2009 New rules issued on March 18, 2011 Require card issuers
to consider borrower’s independent income, rather than household income New
rules become effective on October 1, 2011. Income Insight W2 released April
2011. Income Insight provides a comprehensive measurement of total income
offering a complete financial picture of a borrower for greater insight into
their ability to meet their obligations. Income Insight W2 estimates the wage
income of a consumer which is especially applicable for low to mid-range
income levels where income is comprised mostly from wages. Both measures are
top coded at 900,000USD, and are ultimately significantly highly correlated,
$.8332$.

Our measure of incomes are inputed and validated through third party data.
While the exact methodology of inputation is proprietary to Experian, we do
know the broad steps taken for producing such measures. In practice, all the
variables available in the credit report data and premier attributes (400
variables characterizing credit behavior) are used, while demographic
information is not used. Experian had access to a number of administrative
records on income either as W2 or as total incomes for the years 2005 to 2009,
then validated subsequent waves for a smaller sample. From that, they
constructed an imputation model. The model appears to perform relatively well
and is able to match fairly closely some moments of the income distribution
circulated by the IRS.

Like any imputation, these are likely to be measures of income with error. The
Appendix Figure A.3 shows average income, at the zip code level, versus IRS
derived ones. Appendix Figure A.4 plots the life cycle profiles of incomes
from Experian and the ACS. While, as expected given selection into the credit
market, the Experian imputed income appears higher than the ACS one, the shape
of the profiles are very comparable. To get a better sense of the
representativeness of our sample, Appendix Figure A.3 plots mean income in our
sample in each zip code against household income in the IRS data. The slope
here is .4 (.004), indicating that the Experian income tracks IRS income.

In our analysis, we focus on individuals aged 25 to 55 years old. Appendix
Figure A.4 indicates that mean income by age in our data track reasonably well
to mean income by age in the ACS, in the prime age range. While income in the
data is higher in each age group, income changes over the life cycle appear to
be consistent with ACS data.

Overall, despite the limitations of our data, the income distribution in our
data appears to match well with the income distribution from the ACS micro-
level data and its changes over the life cycle.

Consumption. We create measures of consumption using information on auto loans
balances, mortgage balances, and credit card balances. For auto loans and home
mortgages, we observe both loan origination and amount of the loan. Thus, we
can measure both the probability of buying a car and a home (the extensive
margin) as well as the amount spent on cars and homes (the intensive
margin).999While it is true that car loans and mortgages balances and payment
will reflect the terms of the loans, those are indeed the amounts paid by the
consumers at the end of the loan cycle, including the interest rate payments.
These measures of consumption are not perfect because they are based on loans.
Thus, we miss car and home purchases made in cash, and of course we miss the
component due to down payments.

To measure consumption of goods outside cars and real estate, we use
information on credit card balances. [Collinson et al., 2024] and [Diamond and
Moretti, 2021] take a similar approach. The idea is that for consumers who
regularly pay their credit card balance, their credit card balance, on June
30th, is a good measure of the value of goods purchased by credit card in a
representative month. The problem of course is that for consumers who do not
pay their full credit card balance regularly, the balances include not just
the value of goods purchased, but also interest payments (and other fees). In
our data, interest charges and fees are not separately identified. One, could
however argue that such fees are in fact the consumption of financial
services. The snapshot of data on card balances will in general give the end
of cycle balance of credit card, i.e. the amount spent in the latest cycle.

In our analysis of credit card purchases, we focus on credit card balances
conditional on the consumer not experiencing a large negative decline in her
credit score in the sample period and not defaulting on her credit card debt
by 2016, which is the end of the sample period. Negative declines in her
credit score are drops of 100 points in any year of the data. We also provide
a separate analysis where we focus on the probability of experiencing large
negative decline in credit score and the probability of default as outcomes.

The assumption is that consumers who do not experience large negative decline
in credit score and by the end of the sample period have never defaulted, tend
to pay their monthly balance regularly, or if they accumulate debt at some
point during the sample period, they tend to repay it in a timely fashion.
This assumption fails for consumers who accumulate debt in the absence of a
significant downward movement in their credit score and in the absence of
default. This type of measurement error seems unlikely to be widespread. A
large unpaid balance is likely to trigger a downward movement in credit score
and, in some cases, it may result in default. However, it is possible that
this measurement error is present in the last year of our data, since for some
consumers whose balances include significant interest charges in late 2016,
the credit score may not have adjusted because those charges are too recent to
trigger a credit score adjustment within 2016.

Under our assumption, credit card balances can be used to measure consumption
by credit card. Note however that even for consumers for whom this assumption
is valid, there might be measurement error in the exact timing of consumption.
For example, if a consumer accumulates debt in 2010, and repays it in 2012, we
would overestimate consumption in 2011 and underestimate in 2012.

Since this paper is about consumption, it is important to benchmark our
measure of consumption based on credit card balances against other known
measures of consumption. As a first benchmark, we compare our measure of
average household expenditure with the corresponding measure in the National
Income and Product Accounts (NIPA) and in the Consumer Expenditure Survey
(CEX). To make NIPA data comparable to our data and to CEX data, we remove
from NIPA receipts from sales of goods and services by nonprofit institutions
and net expenditure from retirement plans. This figure shows that our measure
of consumption expenditure appears to match NIPA aggregate consumption
closely, although not perfectly. By contrast, average consumption in the CEX
is only 71% and 75% relative to NIPA and our data, respectively. This is
consistent with the fact that CEX has high non-response among high income
households [Sabelhaus and Groen, 2000]. Even more importantly, the CEX
significantly underestimates consumption relative to NIPA [Attanasio and
Pistaferri, 2014], [Aguiar and Bils, 2015]. We also note that the average
savings rate in our data is not very different from that in NIPA at 5.5%.
Overall, our data appear to be more comprehensive than the CEX, at least in
comparison with aggregate expenditures in NIPA.

A separate issue is the fact that consumption expenditure can take many
different forms. In particular, consumers may pay using credit card, debit
card, ACH, cash and checks. This matters for us because our data provide
different amounts of information on the type of consumption based on the form
of payment. While we observe the sum of all expenditure by credit card, we do
not observe expenditures by other means. On average, 31% of expenditures in
2022 are by credit card. This share varies across income groups, but not very
much (2023 Federal Reserve Report).101010https://tinyurl.com/yc3n9bvh For
example, it is 20% for consumers with income between 25,000 and 50,000, 31%
for consumers with income between 75,000 and 100,000, and 37% for consumers
with income between 100,000 and 150,000. In our empirical analysis, we will
assume that this share is uncorrelated with exposure to price shocks. More
specifically, we assume that the share of expenditures paid by credit card by
a specific individual is not systematically associated with the rent paid by
that individual.

###  2.2 House Price Data

We measure house price shocks using data at the zip code level for years 1998
to 2016.

Appendix Figure A.8 and A.9 shows the national time series of price level.
More important for us, Figure 3 shows some examples of mean price changes at
the zip code level in 2007 for some selected cities.

There is a large variation within Commuting Zones (CZs). The geographical unit
of analysis is the zip code. We define as shocks to house prices those price
increases of 25 percent over the three previous years in 2007 and 2014 at the
zip code level (we also used 30 and 50 percent as thresholds). For 2007,
Figure 2 shows which zip codes are affected in seven selected CZ: Austin, New
York, Newark, Philadelphia, Chicago, Los Angeles and Seattle. The within CZ
distribution of shocks is not the same in all cities. Rather, it appears to be
specific to each city. For example, while shocks were concentrated near the
city center in some cities, they were more spread out in others.

Appendix Table A.1 shows means of the key variables in the areas that
experience a price shock and areas that do not. A comparison of “treatment”
and “control” zip codes suggests that home prices increases occurred in areas
with a younger population, lower credit score, and lower incomes. These
differences are not economically large, and are consistent with [Mian et al.,
2013] and [Albanesi et al., 2022].

Appendix Table A.2 compares average characteristics of movers and non-movers.
Not surprisingly, movers are younger, have lower scores have slightly lower
income and consumption and higher car loan balances.

Since we focus on renters, a more direct measure of rent shocks would be
changes in rents. We use house prices because unlike rents they are available
at the zip code level for the entire country. In principle, changes in rents
and house prices don’t need to be perfectly correlated. Variation in rents
reflects current housing demand and supply, while variation in house prices
also reflect expectations of future appreciation and depreciation, and credit
market conditions. To assess the relationship between rent changes and house
price changes in our sample period, we use ACS data at the MSA level.

Figure A.7 plots log house price changes on the x axis and log rent changes on
the y axis for the 300 MSAs from 2000 to 2010. The figure shows that cities
with an increase in house prices also experience increases in rents. The slope
is 0.43 (.03), indicating that empirically a 10% increase in house prices is
correlated with 4.3% increase in rents. This magnitude is useful in scaling
our empirical estimates below.

##  3 Framework

This section presents a simple spatial equilibrium model of the labor market
and housing market, which is useful for considering how shocks to cost of
housing may impact different individuals. We adopt the standard assumptions of
Rosen-Roback spatial equilibrium models, with specific functional form
assumptions similar to those in [Moretti, 2011]. For brevity, we focus on the
simplest version of the model with intuitive closed-form solutions ([Moretti,
2011], [Kline and Moretti, 2014]).

There are two cities, $a$ and $b$. Each city is a competitive economy,
producing a single output good $Y$ that is traded on the international market
at a fixed price normalized to 1. The production function in city $c$ is: $\ln
Y_{c}=A_{c}+(1-h)n_{c}$, where $A_{c}$ is city-specific log total factor
productivity (TFP); $n_{c}$ is the log of the share of employment in city $c$;
and $0<h<1$.

Indirect utility of worker $i$ in city $c$ is given by:

$v_{ic}=w_{c}-\beta r_{c}+x_{c}+e_{ic}$

where $w_{c}$ is the log of nominal wage, $r_{c}$ is the log of cost of
housing, $x_{c}$ is the log value of amenities, and $\beta$ measures the
importance of housing consumption in utility and equals the budget share spent
on housing. Since people do not spend their entire budget on housing, the
effect of a 1% increase in rent is smaller than the effect from a 1% decrease
in wage.

The random variable $e_{ic}$ is an idiosyncratic location preference, for
which a large draw of $e_{ic}$ means that worker $i$ particularly likes city
$c$ aside from real wages and amenities. We assume that worker $i$’s relative
preference for city $b$ over city $a$ ($e_{ib}-e_{ia}$) is distributed
uniformly $U[-s,s]$. The assumption of a uniform distribution is analytically
convenient, allowing us to derive closed-form expressions for the endogenous
variables in equilibrium. The comparative statics are unchanged in an extended
version of this model that assumes the $e_{ic}$’s are distributed according to
a type I Extreme Value distribution [Kline and Moretti, 2014].

Workers locate wherever utility is maximized. Worker $i$ chooses city $b$,
rather than city $a$, if and only if the strength of location preferences
exceeds any real wage premium and higher amenity value:
$e_{ib}-e_{ia}>(w_{a}-\beta r_{a})-(w_{b}-\beta r_{b})+(x_{a}-x_{b})$. In
equilibrium, there is a marginal worker who is indifferent between city $a$
and $b$.

The parameter $s$ governs the strength of idiosyncratic preferences for
location and, therefore, the degree of labor mobility and the city’s
elasticity of local labor supply. If $s$ is large, many workers will require
large differences in real wages or amenities to be compelled to move, and the
local labor supply curve is less elastic. If $s$ is small, most workers are
not particularly attached to one city and will be willing to move in response
to small differences in real wages or amenities, and cities face a more
elastic local labor supply curve. In the extreme case where $s$ is zero, there
are no idiosyncratic preferences for location and there is perfect labor
mobility. In this case, workers will arbitrage any differences in real wages
adjusted for amenities and local labor supply is infinitely elastic.

We characterize the elasticity of housing supply by assuming the log price of
housing is governed by: $r_{c}=k_{c}n_{c}$. This is a reduced-form
relationship between the log cost of housing and the log number of residents
in city $c$.111111The model assumes that housing is of constant quality, such
that housing supply costs increase only with the number of residents. Our
focus is on changes in real housing costs, holding quality fixed, and in the
empirical analysis we also present estimates that control for potential
changes in housing quality. The parameter $k_{c}$ reflects differences in the
elasticity of housing supply, which varies across cities due to differences in
geographic constraints and local regulations on land development [Glaeser and
Gryourko, 2005], [Glaeser et al., 2006, Gyourko, 2009, Saiz, 2010].

In cities where the geography and regulatory structure make it relatively easy
to build new housing, $k_{c}$ is relatively smaller. In the extreme case where
there are no constraints on building housing, $k_{c}$ is zero and the supply
curve is horizontal. In the extreme case where it is impossible to build new
housing, $k_{c}$ is infinite and the supply curve is vertical.121212For
simplicity, we are ignoring durability of the housing stock and the asymmetry
between positive and negative shocks uncovered by [Glaeser and Gryourko,
2005].

There are two types of residents. The first type receives a wage that is set
competitively on the labor market. Specifically, workers of this type are paid
their marginal product, and labor demand is derived from the usual first order
conditions.131313We abstract from labor supply decisions in the model and
assume that each worker supplies one unit of labor. The second type include
workers who receives a wage that is not fully determined on the labor market.
For simplicity, we will assume that workers of type 2 are paid a fixed wage.
For example, they may be on welfare or on social security. Or they could be
government employees, under the assumption that the government does not fully
and immediately adjust wages after every shock. (In practice, of course,
government do need to adjust wages to market conditions in the long run, but
adjustment may not be immediate and even in the long run may not be complete.)

We are interested in what happens when one of the two cities is hit by a
positve shock to local rents. For example, consider the case where two cities
are initially identical and TFP increases in city $b$ by an amount $\Delta$.
If $A_{b1}$ is initial TFP, the TFP gain is $A_{b2}-A_{b1}=\Delta$. TFP in
city $a$ does not change.

Increased productivity in city $b$ shifts the local labor demand curve to the
right, resulting in higher employment and higher nominal wages for type 1
workers. Higher employment leads to higher housing costs. Assuming an interior
solution, the changes in equilibrium of type 1 worker nominal wage and housing
rent in city $b$ are:

$\displaystyle
w_{b2}-w_{b1}=\frac{\beta(k_{a}+k_{b})+h+s}{\beta(k_{a}+k_{b})+2h+s}\Delta>0,$
(1) $\displaystyle r_{b2}-r_{b1}$ $\displaystyle=$
$\displaystyle\frac{k_{b}}{\beta(k_{a}+k_{b})+2h+s}\Delta>0.$ (2)

The magnitudes of these effects depend on the elasticities of labor supply and
housing supply. Nominal wages increase more when the elasticity of labor
supply is lower ($s$ is larger), and housing costs increase more when the
elasticity of housing supply in $b$ is lower ($k_{b}$ is larger). Type 2
worker wages are fixed by assumption, and therefore can’t adjust to the
shock.141414To obtain equations 1, and 2, we equate local labor demand to
local labor supply in each city and equate local housing demand to local
housing supply in each city. From the spatial equilibrium condition, the
(inverse of) the _local_ labor supply to city $b$ in period $t$ is:
$w_{bt}=w_{at}+\beta(r_{bt}-r_{at})+(x_{at}-x_{bt})+2s(N_{bt}-1)$, where
$N_{bt}$ is the share of employment in city $b$. Since $N_{bt}$ is in levels,
rather than logs, to obtain closed-form solutions in equations 1, and 2, we
use a linear approximation around $1/2$: $n_{bt}=\ln
N_{bt}\approx\ln(1/2)+2N_{bt}-1$, so that we can assign
$N_{bt}\approx(1/2)(n_{bt}-\ln(1/2)+1)$ in the above equation for the (inverse
of) the _local_ labor supply to city $b$ in period $t$. We approximate around
$1/2$ because of the assumption that the two cities are initially identical,
which implies that their employment share is initially $1/2$. We assume that
local housing demand is proportional to city population.

Following the shock, some workers move. First, as we mentioned, some type 1
workers move from city $a$ to city $b$, attracted by the stronger labor demand
in $b$. Second, some type 2 workers leave city $b$ due to the higher cost of
living and move to $a$, which is now more affordable. Since their wage is
fixed, city $a$ affords them a higher level of non housing consumption. This
process of mobility will continue until all workers have maximized their
utility.

Note that not all type $2$ workers abandon city $b$ to move to city $a$. Some
decide to stay in $b$ because they have strong attachment to city $b$. In the
model notation, the draw of $e_{ic}$ makes their preferences for $b$ relative
to $a$ particularly strong. There is nothing in this model stopping them from
relocating but these workers optimally choose $b$ over $a$ even if the cost of
living in $b$ is higher, and their salary is fix. Clearly they are worse off
after the TFP shock compared to before the shock, but even after the shock
they are better off in $b$ than in $a$, otherwise they would have moved.

Turning to consumption, the following expression describes the change of non-
housing consumption of type 1 workers in city $b$, defined as the increase in
nominal wage minus the budget-share weighted increase in housing cost:

$\displaystyle(w_{b2}-w_{b1})-\beta(r_{b2}-r_{b1})=\frac{\beta
k_{a}+h+s}{\beta(k_{a}+k_{b})+2h+s}\Delta>0.$ (3)

Equation 3 shows how the benefits from productivity growth are split between
workers and landowners, with the relative incidence depending on which of the
two factors (labor or land) is supplied more elastically at the local level.
Intuitively, inelastically supplied factors should bear more incidence. For a
given elasticity of housing supply, a lower local elasticity of labor supply
(larger $s$) implies that a larger fraction of the productivity shock in city
$b$ accrues to workers in city $b$ and that a smaller fraction accrues to
landowners in city $b$. When workers are less mobile, they capture more of the
economic gains from local productivity growth. In the extreme case, if labor
is completely immobile ($s=\infty$), then equation 3 becomes:
$(w_{b2}-w_{b1})-\beta(r_{b2}-r_{b1})=\Delta$. The real wage (or purchasing
power) in city $b$ then increases by the full amount of the productivity
shock, such that the benefit of the shock accrues entirely to workers in city
$b$. That is, when labor is a fixed factor, workers in the city directly
impacted by the TFP shock will capture the full economic gain generated by the
shock.

For a given elasticity of labor supply, a lower elasticity of housing supply
in city $b$ (larger $k_{b}$) implies that a larger fraction of the
productivity shock in city $b$ accrues to landowners in city $b$ and that a
smaller fraction accrues to workers in city $b$. When housing supply is more
inelastic, the quantity of housing increases less in city $b$ and housing
prices increase more following the local productivity shock. In the extreme
case, if housing supply in city $b$ is fixed ($k_{b}=\infty$), the entire
productivity increase is capitalized into land values in city $b$ and worker
purchasing power is unchanged.

Since their wage is fixed, the expression for the change of non-housing
consumption of type 2 workers who stay in city $b$ is:

$\displaystyle-\beta(\frac{k_{b}}{\beta(k_{a}+k_{b})+2h+s}\Delta)<0.$ (4)

By contrast, the change of non-housing consumption of type 2 workers who move
to city $a$ is positive, since their wage is unchanged and housing costs in
$a$ have declined due to the out-migration to city $b$.

Motivated by equations 3 and 4, the empirical analysis will explore what
happens to consumption of renters. We will first look at how the consumption
of renters who are in a zip code that is hit by a sharp price increase changes
in the years after the increase (compared to the consumption of renters who
are in a zip code that is not hit by a sharp price increase changes in the
years after the increase). We will then split the sample in two groups:
Renters who relocate following the shock and renters who stay in the original
zip code after the shock.

In the context of our setting, the former group—made by those who leave—should
include type 2 workers with weak preferences for their original location. We
expect them to move to areas that are cheaper and, as a consequence, to
experience an increase in their non-housing consumption. The latter group—made
of stayers—should include a combination of type 1 workers, whose wage adjusts
to the shock and inframarginal type 2 workers, with preferences so strong that
they are willing to remain in their original zip code despite the increase in
rents. The effects on the average consumption of this group depends on whether
the consumption increase experienced by type 1 workers who stay is larger or
smaller than the consumption decrease experienced by type 2 workers who stay.

Empirically, the exact type of each worker is unknown.

##  4 Descriptive Statistics

As mentioned above, our sample is drawn from the universe of individuals with
a valid credit score in 2010. We then trace this population backwards and
forward, at yearly frequency, to 2004 and 2016 respectively. This gives a
total of over 28 millions individual-year observations, and around 450 credit
variables including basic demographics such as date of birth, zip code of
residence, and two measures of income.

In the main text we use as definition of shock a sustained HPI cumulative
increase of 25% in the previous 3 years up to 2007 or 2014.

Figure 1 shows the areas with such a house price shock in terms of the shares
of zip codes treated within the specific CZ for both the 2007 and the 2014
shock. It is easy to notice that the 2007 shocks affect mostly California, New
York, and the sand States (Arizona, Nevada, Florida). While the 2014 shock
appears more concentrated in California, Nevada, and part of Florida. However,
we notice that there is substantial variation within CZs in Figure 2

Table A.1 and A.2 provide some basic description of the working sample of
renters in treated and control areas as well as for movers and stayers.

A few facts stand out in the comparison between individuals in treated and
control areas, at baseline: 1) treated areas comprise larger urban CZ; 2)
younger individuals (41.6 vs. 44.3 years old on average); 3) lower average
credit score (677 vs. 663); 4) about 5% lower (yearly) income (38,140 vs.
36,350 USD); 5) slightly lower consumption (credit card balance) (3,855 vs
3,839 USD monthly); 6) similar mobility profiles before the shock zipcode-to-
zipcode (0.13 vs. 0.16) or CZ-to-CZ (.05 vs. .05); 7) similar auto loan
origination (.09) and with larger payments (4,336 vs. 4,616 USD monthly); 8)
similar rate of Chapter 7 and Chapter 13 bankruptcy occurrences.

We next characterize movers and stayers in treated areas. As expected movers
are: 1) younger 39 vs 43 years of age; 2) have lower credit scores 647 vs.
674; 3) lower incomes 35,870 vs. 36,699 USD per year; 4) lower consumption; 5)
the share of movers prior to the shock is substantially larger at 0.28 vs. 0.1
zip-to-zip, and 0.1 to 0.02 for CZ-to-CZ. This last fact is consistent with
the theoretical framework, as movers are typically mobile people to start with
so their attachment to a given location is not very high. Finally, we observe
that movers have higher rates of auto loan origination (0.1 to 0.08) and
larger monthly car payments (5,101 vs. 4,140 USD).

##  5 Empirical Findings

###  5.1 Event Study

We proceed as in a standard event study, where the estimating equation is:

$y_{ict}=\alpha_{i}+\gamma_{t}+\sum_{j=-k,\neq-1}^{k}P_{i}\cdot
1(\tau=j)\cdot\beta_{j}+X_{it}^{\prime}\zeta+\epsilon_{ict}$ (5)

with $y$ as the outcome of interest, i.e. mobility, consumption, mortgage
origination, etc. for individual $i$, in CZ $c$, at time $t$. Because we have
two periods of housing price shocks, and an individual could appear in
neither, either, or both spells, $\alpha_{i}$ is an individual-spell fixed
effect, where the housing price spell is either 2004-2010 or 2011-2016. The
$\gamma_{t}$ are year fixed effects. $P_{i}$ is the event (price shock); and
$\epsilon$ is an error term. The $X_{it}$ are controls we include to assess
the robustness of our results to trends, e.g. commuting zone (at the time of
the shock) by time fixed effects.

We are here interested in the $\beta^{\prime}s$, which measure the effect of
the HPI shock on our measures of consumption expenditures. The set of
consumption expenditures, as dependent variables, comprises credit card
balances (what we label as, consumption), mortgage balances, auto loans and in
some cases mortgage originations, and auto loan originations.

In Table 1, we present the effects of the price shock for several measures of
consumption and in particular we find that for our main measure of consumption
(credit card balances), we have no pre-trends and that on average, for movers
and stayers, consumption increases by 3 to 5% in the 3 years following the
shock. Recall that we cannot look beyond the 3 years period given the
available data. We define the shocks as occurring in 2007 and 2014, so we only
have 3 years before and after for non-overlapping periods. At the same time we
see a fall in mortgage balances of about 2-6%, lower originations of about
0.16-0.28pp (notice the mean of origination is 0.0128, so these are non-
trivial magnitudes). We also find a slight increase in auto loan balances, but
no sizeable effects on originations. For this latter measure, however, it
appears that the no pre-trends assumption is violated.

###  5.2 Movers and Stayers

As described in Section 3, we believe that mobility is one of the main
channels through which we should analyze the effects on consumption for
renters. In these specifications, the dependent variable $y_{ict}$ is a dummy
equal to 1 if the relevant consumer has changed zip code or CZ between $t-1$
and $t$. Alternatively, $y_{ict}$ is a dummy equal to 1 if the relevant
consumer has changed CZ between $t-1$ and $t$ and the destination zip code or
CZ is 20% less expensive than the origin CZ in terms of mean house price.

What seems to happen is that people move, at least in the short-run to cheaper
zip codes and CZs (see Table 2). These results are not overly sharp as we see
some pre-trends and some lack of precision.

The testable prediction is that individuals who move (to a cheaper location)
will experience an increase in consumption due to lower housing costs, for a
given income. For stayers, the net effect on consumption will depend on the
income effects associated with the sharp increase in housing prices.

We investigate exactly that in Figures 4 and 5, the coefficients, for movers,
are in Tables 3 and 4. In Appendix Tables A.3 and A.4, we provide a robustness
check based on an adjusted propensity score method.

In the left panels of Figures 4 and 5 (the corresponding coefficients are in
Table 3) we study the impact on consumption for stayers and find that the
impact is rather limited if any at all.

In the right panels of Figures 4 and 5 (the corresponding coefficients are in
Table 4) we study the impact on (log)consumption, and consumption, for movers
and find that the impact is positive, large, and significant on impact and
fairly stable for the next 3 years. In terms of credit card consumption, we
see a pretty large increase for those who move, quantifiable in an increase on
impact of about 9.5% then rising to about 16.5% by the second year, and
remaining at a 12% in the third year after the shock (if we use consumption
levels, the effects are still sizeable and significant with magnitudes of
400-500 USD). Of course, mobility isn’t exogenous, and that’s what our
theoretical framework suggests.

In terms of mortgage behavior documented in Figures 6 and 7, we find a rather
striking differential effect for movers versus stayers (irrespective of
whether we use logs or levels). Essentially, people move to become homeowners.
The effects on mortgage originations are the largest on impact, which
presumably coincides with the time of moving. In terms of magnitudes, for
stayers we see a fall in mortgage balances (or log) of 5,000 to 17,000 USD in
the 3 years following the shock. These are falls of 20-100 log points. For
movers, the story is totally different, mortgage balances go up by 110 to 150
log points, or in levels by 30-35 thousand USD. Mortgage origination are the
essential part of the story with a fall of 2 percentage points for stayers and
a jump up on impact of 9 percentage points then down to about 2 percentage
points in the following years. The magnitudes on mortgage origination are very
large, as the average origination is around 1.4pp. This suggests that upon
moving, typically to a cheaper location, individuals open up new mortgages and
keep larger balances. Not only do movers buy properties, but they also seem to
buy cars (Figures 9, 10, and Table 4). The auto loan balance increases 13.4%
on impact, and by 13.3%, 21.6%, and 23.3% after 1, 2, and 3 years,
respectively. On auto loan origination, we see a similar pattern with movers
purchasing a new car on impact with a higher probability of 1.2 percentage
points over a base of 8.4pp.

In Appendix B, we confirm all the results running a more aggregate version of
the previous analysis, where we condense the analysis in a simple two-periods
differences-in-differences specification. That specification shows, in a
compact manner, the dynamics presented in this section. As expected, the
results are very much in line with those discussed above, if anything they are
more precisely estimated.

##  6 Conclusions

In this paper we investigate, under the lenses of a spatial equilibrium model,
the impact of sustained house prices increases, which we believe is part of
what is commonly termed “gentrification”, and how such increases impact
individual consumption. The narrative has often focused on homeowners and less
is known for renters, who of course are different in many respects, but also
because they generally do not see an increase in the value of their main
assets, given that they do not own properties. What we find is that renters’
consumption remains relatively flat after such a shock, but this masks very
important heterogeneity between those who stay and those who move. Stayers,
who probably benefit from the productivity increases which brought about the
price shock, are not particularly affected as they are insured from the shock
by capturing most of the productivity increases. Movers are rational, in the
sense that they move to cheaper places. They might be in occupations without
automatic productivity adjustments, and now they see an increase in their
consumption – a substantial one – and they become homeowners as well as buy
more and more expensive cars.

##  7 Bibliography

## References

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##  8 Figures

Map of 2007 HPI Shocks (Share of CZ’s ZIPs)

Map of 2014 HPI Shocks (Share of ZIPs affected by CZs)

Figure 1: Comparison of HPI Shocks in 2007 and 2014

Figure 2: Examples of within cities shocks at zip code level in 2007

Figure 3: Examples of within cities shocks at zip code level in 2007

Log Consumption - No Move

Log Consumption - Move ($t=0$)

Figure 4: Effects on Log Consumption

Consumption - No Move

Consumption - Move ($t=0$)

Figure 5: Effects on Consumption

Log Mortgage Balances - No Move

Log Mortgage Balances - Move ($t=0$)

Figure 6: Effects on Log Mortgage Balances

Mortgage Balances - No Move

Mortgage Balances - Move ($t=0$)

Figure 7: Effects on Mortgage Balances

Mortgage Origination - No Move

Mortgage Origination - Move ($t=0$)

Figure 8: Effects on Mortgage Origination

Log Auto Balances - No Move

Log Auto Balances - Move ($t=0$)

Figure 9: Effects on Log Auto Balances

No Move

Move ($t=0$)

Figure 10: Effects on Auto Loan Balances

No Move

Move ($t=0$)

Figure 11: Effects on Auto Loan Originations

##  9 Tables

| (1) | (2) | (3) | (4) | (5)
---|---|---|---|---|---
VARIABLES | Log Consumption | Log Mortgage Bal. | Mortgage Orig. | Log Auto Bal. | Auto Orig.
3 yrs until shock | 0.00555 | 0.0135** | -0.000468 | 0.0226 | -0.00887***
| (0.00857) | (0.00588) | (0.000361) | (0.0208) | (0.00256)
2 yrs until shock | -0.00391 | 0.00713 | 0.000284 | -0.0173 | -0.00469**
| (0.00728) | (0.00440) | (0.000181) | (0.0165) | (0.00195)
shock | 0.0207*** | -0.0192** | -0.00227*** | 0.0298* | 0.000928
| (0.00730) | (0.00818) | (0.000688) | (0.0161) | (0.00197)
1 yr since shock | 0.0393*** | -0.0477*** | -0.00158** | 0.0383* | -0.00403**
| (0.00799) | (0.0116) | (0.000742) | (0.0201) | (0.00196)
2 yrs since shock | 0.0519*** | -0.0625*** | -0.000401 | 0.0370 | -0.00588***
| (0.00874) | (0.0145) | (0.000736) | (0.0226) | (0.00195)
3 yrs since shock | 0.0317*** | -0.0510** | 0.00284** | -0.0410 | -0.0113***
| (0.0105) | (0.0226) | (0.00115) | (0.0289) | (0.00227)
Observations | 1,372,704 | 1,617,767 | 1,483,291 | 1,617,767 | 1,483,291
Shock | HPI | HPI | HPI | HPI | HPI
No. ID | 203272 | 219891 | 214125 | 219891 | 214125
Dep. Var Mean | 7.764 | .3133 | .01279 | 2.96 | .0825
Robust standard errors in parentheses
*** p$<$0.01, ** p$<$0.05, * p$<$0.1

Table 1: HPI Shock on Consumption

| (1) | (2) | (3) | (4) | (5)
---|---|---|---|---|---
VARIABLES | Move Zip | Move CZ | Move Zip (cheaper) | Move CZ (cheaper zip) | Move CZ (cheaper)
3 yrs until shock | 0.00887*** | -0.000613 | 0.0117*** | 0.00724*** | 0.00813***
| (0.00340) | (0.00182) | (0.00263) | (0.00130) | (0.00136)
2 yrs until shock | 0.00471** | -0.000932 | 0.00387** | 0.00156 | 0.00282***
| (0.00231) | (0.00138) | (0.00184) | (0.000977) | (0.00102)
shock | -0.000976 | -0.00243 | 0.0145*** | 0.0151*** | 0.0198***
| (0.00261) | (0.00151) | (0.00199) | (0.00111) | (0.00116)
1 yr since shock | -0.00500** | 0.000481 | 0.00685*** | 0.0125*** | 0.0162***
| (0.00234) | (0.00140) | (0.00194) | (0.00104) | (0.00108)
2 yrs since shock | 0.000120 | 0.00253* | 0.00722*** | 0.0110*** | 0.0142***
| (0.00228) | (0.00136) | (0.00197) | (0.00102) | (0.00104)
3 yrs since shock | 0.000325 | 0.00177 | 0.00617** | 0.00852*** | 0.0106***
| (0.00286) | (0.00169) | (0.00243) | (0.00124) | (0.00129)
Observations | 1,483,291 | 1,465,074 | 1,483,066 | 1,483,066 | 1,465,647
Shock | HPI | HPI | HPI | HPI | HPI
No. ID | 214125 | 211737 | 214114 | 214114 | 211842
Dep. Var Mean | .1407 | .04455 | .07097 | .02227 | .02297
Robust standard errors in parentheses
*** p$<$0.01, ** p$<$0.05, * p$<$0.1

Table 2: HPI Shock on Mobility

| (1) | (2) | (3) | (4) | (5)
---|---|---|---|---|---
VARIABLES | Log Consumption | Log Mortgage Bal. | Mortgage Orig. | Log Auto Bal. | Auto Orig.
3 yrs until shock | -0.0103 | -0.0273*** | -0.00431*** | 0.0395 | -0.00765***
| (0.0102) | (0.00385) | (0.000193) | (0.0243) | (0.00281)
2 yrs until shock | -0.0145* | -0.0147*** | -0.000522*** | 0.000692 | -0.00362
| (0.00878) | (0.00275) | (0.000109) | (0.0191) | (0.00226)
shock | 0.00452 | -0.253*** | -0.0209*** | 0.00776 | 0.000314
| (0.00849) | (0.00500) | (0.000433) | (0.0178) | (0.00224)
1 yr since shock | 0.00647 | -0.516*** | -0.0220*** | 0.000849 | -0.00549**
| (0.00969) | (0.00709) | (0.000448) | (0.0232) | (0.00230)
2 yrs since shock | 0.000925 | -0.738*** | -0.0198*** | -0.0157 | -0.00572**
| (0.0106) | (0.00862) | (0.000433) | (0.0270) | (0.00228)
3 yrs since shock | -0.0154 | -1.099*** | -0.0222*** | -0.0870** | -0.0106***
| (0.0131) | (0.0137) | (0.000733) | (0.0347) | (0.00267)
Observations | 1,186,616 | 1,397,989 | 1,289,000 | 1,397,989 | 1,289,000
Shock | HPI and no move | HPI and no move | HPI and no move | HPI and no move | HPI and no move
No. ID | 180216 | 195859 | 191055 | 195859 | 191055
Dep. Var Mean | 7.758 | .2343 | .009542 | 2.909 | .08061
Robust standard errors in parentheses
*** p$<$0.01, ** p$<$0.05, * p$<$0.1

Table 3: HPI Shock on Consumption Dynamics for Stayers

| (1) | (2) | (3) | (4) | (5)
---|---|---|---|---|---
VARIABLES | Log Consumption | Log Mortgage Bal. | Mortgage Orig. | Log Auto Bal. | Auto Orig.
3 yrs until shock | 0.0144 | 0.0819*** | 0.00298* | -0.0194 | -0.00953
| (0.0182) | (0.0217) | (0.00152) | (0.0448) | (0.00657)
2 yrs until shock | 0.00453 | 0.0308* | 0.000884 | -0.0300 | -0.00317
| (0.0152) | (0.0167) | (0.000650) | (0.0369) | (0.00419)
shock | 0.0943*** | 1.216*** | 0.0897*** | 0.133*** | 0.0117***
| (0.0152) | (0.0345) | (0.00275) | (0.0379) | (0.00402)
1 yr since shock | 0.144*** | 1.373*** | 0.0235*** | 0.216*** | 0.00104
| (0.0158) | (0.0366) | (0.00206) | (0.0389) | (0.00390)
2 yrs since shock | 0.164*** | 1.380*** | 0.0130*** | 0.233*** | -0.00295
| (0.0163) | (0.0401) | (0.00196) | (0.0429) | (0.00398)
3 yrs since shock | 0.121*** | 1.423*** | 0.0119*** | 0.134** | -0.00903**
| (0.0195) | (0.0502) | (0.00262) | (0.0523) | (0.00433)
Observations | 1,015,439 | 1,189,482 | 1,100,845 | 1,189,482 | 1,100,845
Shock | HPI and move | HPI and move | HPI and move | HPI and move | HPI and move
No. ID | 164462 | 178192 | 174070 | 178192 | 174070
Dep. Var Mean | 7.753 | .3641 | .01418 | 3.001 | .08391
Robust standard errors in parentheses
*** p$<$0.01, ** p$<$0.05, * p$<$0.1

Table 4: HPI Shock on Consumption Dynamics for Movers ($t=0$)

##  Appendix A Figures and Tables

###  A.1 Figures

Figure A.1: CZ Population (vs. Census) Figure A.2: ZIP Code Population (vs.
IRS returns)

Figure A.3: ZIP Code Income (vs. IRS) Figure A.4: Lifecycle Income (vs. ACS)

Figure A.5: Lifecycle Homeownership

Figure A.6: CZ Homeownership

Figure A.7: Rents and home values 2000-2010

Growth

Home Value

Figure A.8: 2007 Price Shock

Growth

Home Value

Figure A.9: 2014 Price Shock

###  A.2 Tables

| (1) | (2) | (3) | (4) | (5)
---|---|---|---|---|---
| Total | Control | Treated | Diff. | Diff. (w/ FE)
| mean | mean | mean | b | b
Age | 43.46 | 44.34 | 41.56 | 2.78∗∗∗ | 0.00∗∗∗
Credit Score | 673.01 | 677.48 | 663.40 | 14.08∗∗∗ | -0.49∗∗
Income | 37571.21 | 38139.71 | 36349.61 | 1790.10∗∗∗ | 256.91∗∗∗
Consumption | 3849.76 | 3854.81 | 3838.91 | 15.91 | 56.80∗∗∗
Move Zip | 0.14 | 0.13 | 0.16 | -0.04∗∗∗ | 0.00
Move CZ | 0.05 | 0.05 | 0.05 | -0.00∗ | -0.00
Auto Orig. | 0.09 | 0.09 | 0.09 | -0.01∗∗∗ | -0.00∗∗
Auto Bal. | 4424.75 | 4335.97 | 4615.64 | -279.67∗∗∗ | -40.70
Observations | 251573 | 171710 | 79863 | 251573 | 246801

Table A.1: Summary Statistics for $t=-1$: Treat vs. Control

| (1) | (2) | (3) | (4) | (5)
---|---|---|---|---|---
| Treated | No Move | Move (t=0) | Diff. | Diff. (w/ FE)
| mean | mean | mean | b | b
Age | 41.56 | 43.32 | 38.90 | 4.42∗∗∗ | 0.00∗∗∗
Credit Score | 663.40 | 674.06 | 647.49 | 26.57∗∗∗ | -2.34∗∗∗
Income | 36349.61 | 36698.63 | 35869.69 | 828.94∗∗∗ | 1701.70∗∗∗
Consumption | 3838.91 | 3878.88 | 3732.28 | 146.60∗∗ | 221.09∗∗∗
Move Zip | 0.16 | 0.10 | 0.28 | -0.18∗∗∗ | 0.17∗∗∗
Move CZ | 0.05 | 0.02 | 0.10 | -0.07∗∗∗ | 0.03∗∗∗
Auto Orig. | 0.09 | 0.08 | 0.10 | -0.02∗∗∗ | 0.00
Auto Bal. | 4615.64 | 4140.44 | 5100.99 | -960.55∗∗∗ | 174.16∗∗∗
Observations | 79863 | 46940 | 13825 | 60765 | 59693

Table A.2: Summary Statistics for $t=-1$: Move vs. No Move

| (1) | (2) | (3) | (4) | (5)
---|---|---|---|---|---
VARIABLES | Log Consumption | Log Mortgage Bal. | Mortgage Orig. | Log Auto Bal. | Auto Orig.
3 yrs until shock | -0.00701 | -0.0291*** | -0.00408*** | 0.0943** | 0.00412
| (0.0203) | (0.00881) | (0.000528) | (0.0465) | (0.00520)
2 yrs until shock | 0.00487 | -0.0141** | -0.000531* | 0.0286 | -0.00258
| (0.0167) | (0.00661) | (0.000295) | (0.0367) | (0.00460)
shock | -0.0279* | -0.265*** | -0.0219*** | -0.0484 | -0.000342
| (0.0169) | (0.0127) | (0.00113) | (0.0347) | (0.00464)
1 yr since shock | -0.0438** | -0.525*** | -0.0219*** | -0.105** | -0.00363
| (0.0197) | (0.0180) | (0.00124) | (0.0464) | (0.00456)
2 yrs since shock | -0.0499** | -0.777*** | -0.0219*** | -0.133** | 0.000159
| (0.0210) | (0.0238) | (0.00135) | (0.0549) | (0.00465)
3 yrs since shock | -0.0620** | -1.253*** | -0.0275*** | -0.0926 | 0.000965
| (0.0274) | (0.0403) | (0.00225) | (0.0772) | (0.00591)
Observations | 226,472 | 265,909 | 241,685 | 265,909 | 241,685
Shock | HPI and no move | HPI and no move | HPI and no move | HPI and no move | HPI and no move
No. ID | 38,844 | 41,913 | 41,830 | 41,913 | 41,830
Dep. Var Mean | 7.873 | .2042 | .008114 | 2.681 | .07067
Matching? | Yes | Yes | Yes | Yes | Yes
Robust standard errors in parentheses
*** p$<$0.01, ** p$<$0.05, * p$<$0.1

Table A.3: HPI Shock on Consumption Dynamics for Stayers - Propensity Score

| (1) | (2) | (3) | (4) | (5)
---|---|---|---|---|---
VARIABLES | Log Consumption | Log Mortgage Bal. | Mortgage Orig. | Log Auto Bal. | Auto Orig.
3 yrs until shock | 0.00509 | 0.0832** | 0.00629** | 0.101 | 0.00826
| (0.0367) | (0.0422) | (0.00251) | (0.0911) | (0.0114)
2 yrs until shock | 0.0424 | 0.0387 | 0.00141 | 0.0153 | -0.00623
| (0.0289) | (0.0317) | (0.00132) | (0.0735) | (0.00855)
shock | 0.105*** | 1.507*** | 0.121*** | 0.127 | 0.0190**
| (0.0323) | (0.0785) | (0.00689) | (0.0812) | (0.00860)
1 yr since shock | 0.0853*** | 1.720*** | 0.0254*** | 0.225*** | 0.0142*
| (0.0327) | (0.0820) | (0.00501) | (0.0853) | (0.00861)
2 yrs since shock | 0.0928*** | 1.748*** | 0.0103** | 0.252** | 0.00492
| (0.0331) | (0.0886) | (0.00470) | (0.100) | (0.00865)
3 yrs since shock | 0.0645 | 1.772*** | 0.00549 | 0.323** | 0.00176
| (0.0429) | (0.117) | (0.00700) | (0.130) | (0.0104)
Observations | 152,591 | 177,729 | 160,427 | 177,729 | 160,427
Shock | HPI and move | HPI and move | HPI and move | HPI and move | HPI and move
No. ID | 26,396 | 28,233 | 28,171 | 28,233 | 28,171
Dep. Var Mean | 7.891 | .4938 | .0186 | 2.934 | .07814
Matching? | Yes | Yes | Yes | Yes | Yes
Robust standard errors in parentheses
*** p$<$0.01, ** p$<$0.05, * p$<$0.1

Table A.4: HPI Shock on Consumption Dynamics for Movers ($t=0$) - Propensity
Score

##  Appendix B DID

We start off with the simplest specification, which is described below in
Equation 6

$y_{ict}=\alpha+\beta HPI_{ct}+bX_{ict}+\mu_{i}+\epsilon_{ict}$ (6)

| (1) | (2) | (3) | (4) | (5)
---|---|---|---|---|---
VARIABLES | Log Consumption | Log Mortgage Bal. | Mortgage Orig. | Log Auto Bal. | Auto Orig.
Post | 0.0354*** | -0.0500*** | -0.000961** | 0.0224 | -0.000875
| (0.00595) | (0.0107) | (0.000410) | (0.0168) | (0.00116)
Observations | 1,372,704 | 1,617,767 | 1,483,291 | 1,617,767 | 1,483,291
Shock | HPI | HPI | HPI | HPI | HPI
No. ID | 203272 | 219891 | 214125 | 219891 | 214125
Dep. Var Mean | 7.764 | .3133 | .01279 | 2.96 | .0825
Robust standard errors in parentheses
*** p$<$0.01, ** p$<$0.05, * p$<$0.1

Table A.5: DID: HPI Shock on Consumption

| (1) | (2) | (3) | (4) | (5)
---|---|---|---|---|---
VARIABLES | Log Consumption | Log Mortgage Bal. | Mortgage Orig. | Log Auto Bal. | Auto Orig.
Post | 0.00930 | -0.561*** | -0.0203*** | -0.0263 | -0.00185
| (0.00731) | (0.00664) | (0.000236) | (0.0203) | (0.00135)
Observations | 1,186,616 | 1,397,989 | 1,289,000 | 1,397,989 | 1,289,000
Shock | HPI and no move | HPI and no move | HPI and no move | HPI and no move | HPI and no move
No. ID | 180216 | 195859 | 191055 | 195859 | 191055
Dep. Var Mean | 7.758 | .2343 | .009542 | 2.909 | .08061
Robust standard errors in parentheses
*** p$<$0.01, ** p$<$0.05, * p$<$0.1

Table A.6: DID: HPI Shock on Consumption for Stayers

| (1) | (2) | (3) | (4) | (5)
---|---|---|---|---|---
VARIABLES | Log Consumption | Log Mortgage Bal. | Mortgage Orig. | Log Auto Bal. | Auto Orig.
Post | 0.124*** | 1.300*** | 0.0388*** | 0.197*** | 0.00392*
| (0.0109) | (0.0322) | (0.00115) | (0.0311) | (0.00222)
Observations | 1,015,439 | 1,189,482 | 1,100,845 | 1,189,482 | 1,100,845
Shock | HPI and move | HPI and move | HPI and move | HPI and move | HPI and move
No. ID | 164462 | 178192 | 174070 | 178192 | 174070
Dep. Var Mean | 7.753 | .3641 | .01418 | 3.001 | .08391
Robust standard errors in parentheses
*** p$<$0.01, ** p$<$0.05, * p$<$0.1

Table A.7: DID: HPI Shock on Consumption for Movers


# Effectiveness and Efficiency Trade-off in Selective Query Processing

Josiane Mothe  0000-0001-9273-2193 IRIT UMR5505 CNRS, INSPE, Univ. de Toulouse
ToulouseFranceF-31062<EMAIL_ADDRESS>and  Md Zia Ullah
0000-0002-4022-7344 SCEBE, Edinburgh Napier University  EdinburghUnited
KingdomEH10 5DT<EMAIL_ADDRESS>
(Feb. 2023)

###### Abstract.

Query processing in search engines can be optimized for use for all queries.
For this, system component parameters such as the weighting function or the
automatic query expansion model can be optimized or learned from past queries.
However, it may be more interesting to optimize the processing thread on a
query-by-query basis by adjusting the component parameters; this is what
selective query processing does. Selective query processing uses one of the
candidate processing threads chosen at query time. The choice is based on
query features. In this paper, we examine selective query processing in
different settings, both in terms of effectiveness and efficiency; this
includes selective query expansion and other forms of selective query
processing (e.g., when the term weighting function varies or when the
expansion model varies). We found that the best trade-off between
effectiveness and efficiency is obtained when using the best trained
processing thread and its query expansion counter part. This seems to be also
the most natural for a real-word engine since the two threads use the same
core engine (e.g., same term weighting function).

Information Systems, Information retrieval, Selective Query Expansion,
Effectiveness, Efficiency.

††journalyear: 2023††doi: XXXXXXX.XXXXXXX††ccs: Information systems
Information retrieval††ccs: Information systems Retrieval effectiveness††ccs:
Information systems Retrieval efficiency

##  1\. Introduction

In information retrieval, system effectiveness can be optimized by adjusting
many parameters and components the system consists of. For example,
participants to shared tasks such as TREC 111Text REtrivial Conference,
https://trec.nist.gov generally consider a system where the parameters of the
term weighting function and the ones of the query expansion model are
optimized for a given collection (Song and Croft, 1999; Ma et al., 2022).
Similarly, in real-world system, the component parameters can be optimized
based on past queries or users’ implicit feedback (Ai et al., 2018; Gao and
Shah, 2019).

Alternatively, the query processing thread can be adapted to each query. For
example, selective query expansion (SQE) uses one of two alternative query
processing threads: the original query or the automatically expanded query
(Amati et al., 2004; Cronen-Townsend et al., 2004; He and Ounis, 2007; Zhao
and Callan, 2012). Selective query processing (SQP) generalizes SQE to various
query processing threads. Here, the threads may use different term weighting
schemes or different query expansion models (He and Ounis, 2004; Xu et al.,
2016; Deveaud et al., 2018). SQP thus differs from selective search which aims
to improve the response time by limiting the part of the data the system is
searching from, like in shard selection, for example (Baeza-Yates et al.,
2009; Aly et al., 2013). In SQP, the optimization takes place in the
processing threads and retrieval component parameters.

For SQE, the decision on which thread should process the query is based on
some query features. Cronen-Townsend et al. (Cronen-Townsend et al., 2004) and
Amati et al. (Amati et al., 2004) estimated how much the results of the
expanded query strayed away from the sense of the original one to make the
decision. Xu et al. (Xu et al., 2009) improved SQE such that the system
chooses between more options and considered different query expansion
strategies according to the query type. They defined three types of queries:
ambiguous queries, queries about a specific entity, and broader queries, and
proposed different methods to treat each type. Queries are categorized in an
unsupervised way, based on Wikipedia page types. Kevyn Collins-Thompson
(Collins-Thompson, 2009) introduced a constraint optimization framework for
SQE by reducing the risk of query expansion. He et al. clustered the queries
according to query features such as their length or term ambiguity and then
associated the best processing thread to each cluster through a training phase
(He and Ounis, 2004). Deveaud et al. learned the best processing thread using
learning to rank principle, where threads are ranked for each query according
to their effectiveness (Deveaud et al., 2018). Mothe et al. (Mothe and Ullah,
2021) used a risk-based approach to decide which threads should be included in
the meta-system. The risk-reward trade-off function they defined adds a
configuration if it increases system effectiveness on some queries and at the
same time minimizes the risk of poor performance of that configuration if it
is chosen for other queries.

SQE/SQP mainly focuses on effectiveness but seldom mentions efficiency. We
believe that both are important criteria to consider. This paper thus examines
selective query processing in different settings, both in terms of
effectiveness and efficiency. We conduce intensive experiments using three
TREC adhoc collections (TREC78, GOV2, and WT10g) and three effectiveness
measures (AP, nDCG@10, and P@10). We compare the results to different
baselines, including fusion techniques and best trained. In our experiments,
candidate query processing threads vary in the weighting function used, the
query expansion model as well as the number of documents and terms used in the
query expansion. Candidate query processing threads are defined based on a
risk-based function (Mothe and Ullah, 2021). The selective model is trained
using a supervised approach that considers query features. For efficiency,
similar to Kulkarni and Callan (Kulkarni and Callan, 2015), we measure the
elapsed time for each processing steps: data generation (Gen), model training
(Train), and runtime processing (RT).

The contributions of this paper are three folds:

  * •

First, we analyze the selective query processing methods in terms of both
effectiveness and efficiency on three adhoc reference collections when two
query processing threads are used in different settings;

  * •

Second, we compare the performance to different baselines (BM25, learning to
rank, best trained, and CombSum) and show that selective query processing
outperforms all our baselines both in terms of effectiveness and efficiency;

  * •

Third, when comparing selective query processing methods, we found that the
best trade-off between effectiveness and efficiency is obtained when using the
best trained processing thread and its query expansion counterpart. This seems
to be also the most natural for a real-word engine since the two threads use
the same core engine (e.g., same term weighting function).

##  2\. Methodology

###  2.1. Query processing threads and grid of points

Processing threads can differ according to the term weighting schema, the type
of expansion model used, the number of documents and expansion terms used. A
query processing thread is a set ($W$,$Q$,$D$,$T$), where $W$ is the term
weighting function, $Q$ is the query expansion model, $D$ is the number of
documents for query expansion, and $T$ is the number of added terms in query
expansion. For $W$ and $Q$, we consider all the models implemented in
Terrier222http://terrier.org/docs/current/javadoc/org/terrier/matching/models/package-
summary.html. $D$ and $T$ can vary from 0 (no expansion) to a defined number.
We build all the possible comprehensive query processing threads using the
values as detailed in Table 1. This results in more than $20,000$ query
processing threads. We used all the query processing threads to perform batch
retrieval on the topics. The parameters of the query processing threads and
the estimated effectiveness measures produce a grid of points (Ferro and
Silvello, 2016).

Table 1. Parameters of the query processing threads Weighting model $W$
---
BB2, BM25, DFRee, DirichletLM, HiemstraLM,InB2, InL2, JsKLs,
PL2, DFI0, XSqrAM, DLH13, DLH, DPH, IFB2, TFIDF, InexpB2,
DFRBM25, LGD, LemurTFIDF, InexpC2
Query expansion model $Q$
None, KL, Bo1, Bo2, KLCorrect, Information, KLComplete
QE Hyperparameter and Values
# of Expansion document $D$: 0, 2, 5, 10, 20, 50, 100
# of Expansion terms $T$: 0, 2, 5, 10, 15, 20

###  2.2. Candidate threads

To select the candidate threads from the grid of points, we use the $E_{Risk}$
function as defined by Mothe and Ullah (Mothe and Ullah, 2021). Their function
aims at selecting $k$ candidate query processing threads. We re-implemented it
so that it can fit our purpose of selecting two threads, either for SQE or
SQP. The first candidate $C_{1}$: ($W_{1}$, $Q_{1}$, $D_{1}$, $T_{1}$) is the
thread that gets the highest effectiveness -considering the chosen measure- in
average over the training query set. It is used in both SQE ans SQP. The
second candidate $C_{2}$: ($W_{2}$, $Q_{2}$, $D_{2}$, $T_{2}$) may differ for
SQE and SQP.

For SQE, if $Q_{1}$ $=$ “None”, then the second candidate will correspond to
the same thread with query expansion. That is, $C_{2}$: ($W_{1}$, $Q_{2}$,
$D_{2}$, $T_{2}$). That is to say, the same weighting model $W_{1}$, but the
next best thread with query expansion will be selected. Reversely, if the best
thread includes query expansion ($Q_{1}$ $\neq$ “None”), the second query
processing thread will not use query expansion $C_{2}$: ($W_{1}$, None, 0, 0).

For SQP, given the first thread and grid of points, we select the second
thread by maximizing the overall gain for retrieval effectiveness, following
the $E_{Risk}$ function (Mothe and Ullah, 2021). We estimate risk, reward, and
gain for threads in grid of points and choose the one which obtains the
maximum gain. It is thus a greedy diversification technique that optimizes
effectiveness.

###  2.3. Candidate selection

Following in Deveaud et al. (Deveaud et al., 2018) or in Mothe and Ullah
(Mothe and Ullah, 2021), the query-thread association problem is cast as a
ranking problem where L2R algorithms (e.g., SVM-rank) are applied to decide
which of the two threads should be used by the meta-system (See 3.4).

##  3\. Experiments

###  3.1. Datasets

We report here results on three standard TREC collections, TREC78, GOV2, and
WT10g from the adhoc task. For TREC78, there are approximately 500K newspaper
articles. GOV2 collection includes 25 million web pages from .gov domain. The
WT10G collection is composed of approximately 1.6 million Web/Blog page
documents. The TREC test collections include a set of topics. The “standard”
format of a TREC topic statement comprises a topic ID, a title, a description,
and a narrative. We consider the topic title that contains two or three words,
on average as the query to process. There are 100 topics in TREC78 (merging
topics from TREC7 and TREC8), 150 in GOV2, and 100 in WT10g. The collections
provide qrels (i.e., judged documents) which are used in the evaluation
program trec_eval333http://trec.nist.gov/trec_eval/ to calculate the
effectiveness measures for adhoc metrics.

###  3.2. Evaluation protocol

We used two-fold cross-validation to ensure independent sets and keep enough
samples in both the training and test sets (Wong and Yang, 2017). We proceeded
as follows: half of the queries, let us call this query set $Q_{A}$, are used
for training, while the other half, $Q_{\overline{A}}$, is used for testing.
Then, reversely, $Q_{\overline{A}}$ is used for training, while $Q_{A}$ is
used for testing. We made three random draws to split the query set into
$Q_{A}$ and $Q_{\overline{A}}$. To prepare the folds for three trials, we
shuffled the query set using the R’s sample function (random seed=42) and
divided the query set into two subsets for each trial. We report the average
and standard deviation across three trials and the two test folds. Thus, each
mean and standard deviation is over a total of six measurements. The same
splits are used in whatever method needs training. We use a two-tailed paired
t-test with Bonferroni correction (p-value $<$ 0.05) for statistical
significance analysis.

###  3.3. Query processing thread selection.

To compare the combination methods, we consider the three settings (the two
first have been described in detail in Section 2.2) as follows:

  * •

In ERisk-SQE we take the first query processing thread selected by ERisk
function and its query expansion/non-expansion counterpart.

  * •

In ERisk-SQP we take the first two search threads selected by ERisk function.
The chosen threads may or may not have a query expansion component.

  * •

In Best-SQE, we take the best thread overall and its query expansion/non-
expansion counterpart. In each case, we have two query processing threads that
are then selected by SQE based on SVM-rank machine learning.

###  3.4. Features and labels for model training

Query features are required to train some models, specifically for
L2R-document and selective approaches. We opted for LETOR features that were
used for document ranking models (Qin et al., 2010). To extract the LETOR
features, we use the FAT component of Terrier IR (Macdonald et al., 2013). The
FAT component stores the posting lists of all the documents that make the
top-K retrieved set in memory. Different features are computed using these
posting lists. We calculate LETOR features directly from BM25 and aggregate
the query-document features as Chifu et al. successfully did for query
performance prediction (Chifu et al., 2018). Then, the query vector is labeled
by the effectiveness of the query processing thread applied to that query.

###  3.5. Evaluation metrics

We consider the effectiveness and efficiency-based evaluation metrics to
compare the combination methods. Effectiveness metrics: We considered the
Precision at the cut-off 10 documents (P@10), Average Precision (AP)
(Carterette and Voorhees, 2011; Sakai, 2007), normalized Discounted Cumulative
Gain at the cut-off 10 documents (nDCG@10) (Järvelin and Kekäläinen, 2017).
Efficiency metrics: Running a query processing thread requires several
processing steps, such as data pre-processing, batch retrieval, model
training, prediction, and eventually re-ranking. To estimate the efficiency of
a process, we measure the elapsed time (TTotal) when accomplishing each
underlying process.

$T_{Total}$: a total of elapsed time at accomplishing a process.

Kulkarni and Callan (Kulkarni and Callan, 2015) used a similar approach to
estimate the efficiency in selective search. We categorize the different
processes into three groups: data generation (Gen), model training (Train),
and main processing (Run-time (RT)). The Gen and Train groups are offline
processes and the main processing is a run-time process. In the Gen group, the
usual process involves query processing thread selection, batch retrieval,
feature extraction, etc. In the Train group, the process involves training the
machine learning model. The main processing includes feature extraction,
models’ prediction, retrieval process using different query processing
threads, result fusion (Data fusion), per-query retrieval, etc. The
combination methods we evaluate do not necessarily require all these
processes.

###  3.6. Baselines and compared methods

We consider the BM25, L2R-D SVMr, Best trained, and CombSum as baselines.

  * •

BM25 is obtained using Terrier BM25 with default parameters b=0.75 and k=1.2
(default hyperparameter values) (Robertson et al., 2009) on the entire set of
the queries;

  * •

L2R-D SVMr is the usual learning to rank (L2R) documents where the initial
ranking is obtained using BM25. The L2R is learned based on the SVM-rank.

  * •

Best trained is the best query processing thread among the grid of points, the
one that maximized the effectiveness measure considered: it is chosen for
$Q_{A}$ and applied to $Q_{\overline{B}}$, and vice versa.

  * •

CombSum: It implements data fusion as the combinations of system document
lists; we consider the CombSum (Fox and Shaw, 1994) on the two configurations
selected by $E_{Risk}$-SQE.

##  4\. Results and discussion

We evaluate the results on baselines, ERisk-SQE, ERisk-SQP, and Best-SQE (See
Tables 2, 3, and 4) for TREC78, GOV2, and WT10g, respectively. The first four
rows refer to the baseline models, BM25, L2R-Document (L2R-D SVMr), the Best
trained, and CombSum. Then, the next rows denote the ERisk-SQE, the SQP for
ERisk-SQP, and the Best-SQE. The SQP ranking function is learned using SVM-
rank technique. The left-side of the tables shows the effectiveness metrics
(AP, nDCG@10, and P@10) while the right-side reports the efficiency metrics in
terms of elapsed time when accomplishing a process (Gen, Train, and Run-time)
in milliseconds for each query in average.

Table 2. Effectiveness and efficiency for SQP on TREC78. $\vartriangle$ and ${\uparrow}$ indicate statistically significant improvement of SQP over baselines L2R documents and Best trained - paired t-test ($p<0.05$). Training was based on SVM-rank algorithm. Effectiveness is on the left side and efficiency on the right side for Generation (Gen), Training (Train), and Run-time phases. The mean and [standard deviation] for 3 trials are reported. |  | Effectiveness |  | Efficiency (ms)
---|---|---|---|---
| Methods | AP | nDCG@10 | P@10 |  | Gen | Train | RT
Baselines |  |  |  |  |
| BM25 | .211${}^{~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}}$ | .465${}^{~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}}$ | .448${}^{~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}}$ |  | - | - | 40.49
| L2R-D SVMr | .216 [.000]${}^{~{}~{}}$ | .478 [.001]${}^{~{}~{}}$ | .459 [.004]${}^{~{}~{}}$ |  | 3601 [9.5] | 25.1 [17] | 673 [14]
| Best trained | .240 [.003]${}^{~{}~{}}$ | .525 [.004]${}^{~{}~{}}$ | .486 [.007]${}^{~{}~{}}$ |  | - | 367 [5.8] | 425 [23]
| CombSUM |  .256△↑ [.003] | .496 [.006] | .467 [.010] |  | 1450 [3] | - | 1056 [50]
Selective query expansion and processing |  |  |  |  |
| ERisk-SQE | .248△↑ [.002] | .503 [.027] |  .503△↑ [.003] |  | 1535 [42] | .93 [.23] |  45 [1.5]
| ERisk-SQP | .247△↑ [.002] |  .530△ [.002] | .500△ [.005] |  | 1091 [27] | .67 [.11] |  46 [1.7]
| Best-SQE | .248△↑ [.002] | .499 [.028] |  .503△↑ [.003] |  | 1049 [23] | .78 [.08] |  46 [2.1]
Table 3. Effectiveness and efficiency for SQP on GOV2. The notations are the same as in Table 2. |  | Effectiveness |  | Efficiency (ms)
---|---|---|---|---
| Methods | AP | nDCG@10 | P@10 |  | Gen | Train | RT
Baselines |  |  |  |  |
| BM25 | .269${}^{~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}}$ | .458${}^{~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}}$ | .527${}^{~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}}$ |  | - | - | 294.67
| L2R-D SVMr | .279 [.000]${}^{~{}~{}}$ | .491 [.002]${}^{~{}~{}}$ | .567 [.003]${}^{~{}~{}}$ |  | 75842 [21] | 20 [.24] | 625 [4.5]
| Best trained | .351 [.005]${}^{~{}~{}}$ | .487 [.012]${}^{~{}~{}}$ | .590 [.010]${}^{~{}~{}}$ |  | - | 364 [1.9] | 9556 [662]
| CombSUM | .358△ [.003] | .553△↑ [.003] | .645△↑ [.001] |  | 1441 [.9] |  | 14700 [670]
Selective query expansion and processing |  |  |  |  |
| ERisk-SQE |  .362△↑ [.001] | .540△↑ [.004] |  .649△↑ [.004] |  | 1540 [50] | .55 [.07] | 3190 [1273]
| ERisk-SQP |  .363△↑ [.002] | .538△↑ [.006] |  .649△↑ [.003] |  | 1119 [46] | .65 [.16] |  2121 [24]
| Best-SQE |  .362△↑[.001] | .540△↑[.004] |  .649△↑[.004] |  | 968 [15] | .62 [.14] |  2090 [34]
Table 4. Effectiveness and efficiency for SQP on WT10g. The notations are the same as in Table 2. |  | Effectiveness |  | Efficiency (ms)
---|---|---|---|---
| Methods | AP | nDCG@10 | P@10 |  | Gen | Train | RT
Baselines |  |  |  |  |
| BM25 | .172${}^{~{}~{}}$${}^{~{}~{}}$ | .288${}^{~{}~{}}$${}^{~{}~{}}$ | .273${}^{~{}~{}}$${}^{~{}~{}}$ |  | - | - | 249.77
| L2R-D SVM | .192 [.002]${}^{~{}~{}}$ | .330 [.002]${}^{~{}~{}}$ | .310 [.005]${}^{~{}~{}}$ |  | 7144 [5] | 18 [.69] | 690 [1.0]
| Best trained | .224 [.006]${}^{~{}~{}}$ | .401 [.002]${}^{~{}~{}}$ | .396 [.012]${}^{~{}~{}}$ |  | - | 345 [23] | 1842 [278]
| CombSUM | .267△↑ [.004] | .437△↑ [.010] | .418△↑ [.006] |  | 1372 [23] |  | 3736 [270]
Selective query expansion and processing |  |  |  |  |
| ERisk-SQE | .242△↑${}^{~{}~{}}$ [.014] | .388△${}^{~{}~{}}$ [.028] | .376△${}^{~{}~{}}$ [.015] |  | 1574 [55] | .83 [.12] | 722 [244]
| ERisk-SQP |  .255△↑${}^{~{}~{}}$ [.009] |  .414△${}^{~{}~{}}$${}^{~{}~{}}$ [.010] |  .395△${}^{~{}~{}}$${}^{~{}~{}}$ [.005] |  | 1085 [19] | .73 [.09] |  329 [44]
| Best-SQE | .242△↑${}^{~{}~{}}$ [.014] | .400△${}^{~{}~{}}$ [.034] | .374△${}^{~{}~{}}$ [.025] |  | 1021 [43] | .69 [.08] |  325 [135]

First, we can observe that BM25 is consistently less effective than the other
non-combined approaches (See first row, Tables 2 to 4). Although this result
was expected, it is worth to check that simpler methods do not achieve better
results. Among baselines, the CombSum is the only one that does not need any
training (4th row). It achieves, however, better results than the baselines
that need training on GOV2 and WT10g collections in terms of effectiveness.
The CombSum is not efficient because it implies to run each query twice and
then to fuse the results. Among baselines, best-trained offers a good trade-
off.

Considering the selective query processing approaches, they are consistently
more effective than non-trained baselines across measures and collections
(statistically significant). Comparing the three settings, the SQP approach is
slightly more effective than the SQE approach on WT10G, however Best-SQE is
slightly more effective on the two other collections. Best-SQE is the most
efficient at run time; thus could be considered as the best option with regard
to effectiveness vs. efficiency trade-off. Meaning that the query expansion
part of a thread should be optimized rather than the other system components
such as the weighting function. This result somehow contradicts previous
results that show that the weighting model is a key factor (Ayter et al.,
2015; Ferro and Silvello, 2018). However, here a training step is used to
select the best processing thread that should be effective for many queries.
We are not considering the best component parameters for each query
individually, but rather the two best processing threads for a set of queries.

All SQE or SQP methods require training time. From the result, we can observe
that the SQP with SVM-rank ($E_{Risk}-SQP$) achieves significantly better
performance over the baselines in terms of both effectiveness and efficiency
metrics. These findings are consistent in both Tables 2 and 3. The reason is
that most of the time, a second processing thread that does not use query
expansion is more effective than a query expansion one.

##  5\. Conclusions

In this paper we aimed to compare selective query processing (SQP) settings
considering different threads. We found that all settings are more effective
than the baselines. Our results contradict the intuition that data fusion was
more effective although less efficient (CombSum baseline). We found that
selective approach is both more effective and efficient than data fusion.

With regard to the different selective query processing settings, the best
effectiveness vs. efficiency trade-off goes to the selective query processing
(SQP) where one thread is selected as the best over the set of queries and the
second as a query expansion counterpart.

Here we consider two query processing threads. But both data fusion and
selective query processing could handle more than two. In our future work, we
would like to investigate the combination of more than two query processing
threads.

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