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VOL. 9, NO. 14 • DECEMBER 2014­­

DALLASFED

Economic
Letter
Consumer Price Differences Persist
Among Eight Texas Cities
by Michele Ca’Zorzi, Alexander Chudik and Chi-Young Choi

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ABSTRACT: The differences
in what consumers pay for a
given product in eight Texas
cities increased considerably
in the 2000s—Dallas being
by far the most expensive
city in the sample. A strong
price adjustment mechanism,
however, ensures that the
relative price between any
two Texas locations tended
to rapidly revert to its mean
value.

W

hat an item costs in various
geographic locations has
attracted economists’ attention
for decades.
One theory—the law of one price—
states that the same good should cost
the same across different geographic
locations. Any departure from a common
price should be short-lived.
This theory is typically refuted
empirically when it comes to markets
for consumer goods and services; overwhelming evidence suggests that price
differences can persist for long periods.
Texas provides an interesting location to view how this price mechanism
works. Drawing on data for eight cities from 1985 to 2009 collected by the
American Chamber of Commerce
Researchers Association, it appears that
the degree of price dispersion among
metropolitan areas has increased over
time. Moreover, the magnitude of price
differences varies across the types of
goods or services, and Dallas is the most
expensive city in the sample.1
The dataset allows us also to investigate whether the “strong” or “weak” form
of the law of one price holds. The strong
version clearly fails for Texas cities, since
the prices of the same product differ
considerably; however, the weak version holds. It postulates that the relative
price—the price of a given good in one

city relative to the price of the same good
in another city—should revert to some
mean or normal level over time.
This mean level could differ from an
identical price because of structural factors, such as differences in the scarcity of
land or in income levels. It helps to justify why goods and especially services are
more expensive in some locations.
Analysis of the Texas city data suggests that relative prices for all the
product categories rapidly revert to their
mean. The speed of such convergence of
relative prices may be explained by the
nature of products (goods that are easily
traded and more homogenous converge
faster) and by geographic distance.

Consumer Price Data
Quarterly price data for Abilene,
Amarillo, Dallas, Houston, Lubbock,
Odessa, San Antonio and Waco cover 45
individual product categories in each
location from 1985 to 2009. Product categories encompass a range of goods and
services, including apartment rents, and
are generally narrowly defined, such as
“one dozen Grade A large eggs” or “adult
teeth cleaning.”
This dataset has been used in a number of academic publications.2 It allows
economists to study price dispersion
of relatively narrowly defined products
across different geographic locations.

Economic Letter
This would not be possible with the consumer price index data collected by the
Bureau of Labor Statistics, which publishes price indexes only. They are indicative of the price changes over time and
cannot be used to investigate the level or
dispersion of prices across cities.

Differences Increase Over Time
Price dispersion is clearly visible on
a daily basis—for example, among gas
stations. The incentive to buy from a location with cheaper prices should ensure
equalization of prices over time. However,
the search for a cheaper price is costly (in
terms of time and effort), while the products offered by different sellers/producers
are not exactly identical. These factors
could contribute to price differences persisting. It is therefore not surprising that
price dispersion can prevail within cities
as well as from city to city.
There are different ways of measuring price dispersion. The simplest is to
compute, for each product category and
time period, a Texas average price (given
by the simple average of the individual
prices in the eight cities).
Using the Texas average as a benchmark, we compute the price deviation
(in percent) for each city and each prod-

Chart

1

uct. A simple price dispersion measure
for each product is then obtained by
averaging the absolute value of such percentage price deviations across quarters
(Chart 1).
The smallest amount of dispersion—
about 3 percent on average—is observed
for gasoline (defined as one gallon of
regular unleaded gasoline, national
brand, including all taxes). This is to be
expected since gasoline is tradable and a
rather homogenous product category.
On the other hand, the largest price
differences of about 13 percent are for
the bowling category (defined as price
per line, Saturday evening nonleague
rate). The dispersion of prices is highly
product-specific and in many cases quite
large.
Instead of only looking at the price
differences for a given product category,
it is worth also investigating whether
price dispersion has changed over time.
To this end, Chart 2 shows, for every
quarter in the sample, the average of
absolute deviations of prices across all
products. The price dispersion was fairly
constant prior to the 2000s, where it
hovered around 7.5 percent, but it subsequently increased, reaching about 10
percent.

Dallas, Houston Most Expensive
Various factors can affect the distribution of prices across cities. The
Balassa–Samuelson hypothesis suggests
that price differences might persist if the
movement of labor is not fully flexible
across locations (and therefore wages
need not equalize across locations).3
Additionally, consumer product categories contain elements that are not tradable, such as local distribution costs.
As a result, locations with higher
income (wages) will have systematically
higher consumer prices. The differences
in the average prices of the goods and
services surveyed may therefore reflect
differences in income levels by city.
Idiosyncratic factors other than income
also could contribute to price differences. Some examples are market structure,
population density and city size.
Simple (equally weighted) averages
of price deviations of individual product
categories from the benchmark Texas
average are shown in Chart 3 for each of
the eight sample cities. Dallas is the most
expensive city, followed by Houston.
These are the two largest cities (with
highest incomes) in the sample; thus, the
findings appear intuitive. This chart also
divides the sample into two subperiods

Average Price Difference in Eight Texas Cities Varies by Product

Percent

16
14
12
10
8
6
4

0

Gasoline
McDonald’s
Movie
Canned peaches
Shortening
Sugar
Cheese
Coffee
Home price
Mortgage payment
Pizza
Detergent
Fried chicken
Beer
Tissue
Eggs
Milk
Wine
Steak
Telephone
Frozen corn
Canned peas
Whole chicken
Dry cleaning
Lettuce
Appliance repair
Auto maintenance
Potatoes
Man’s shirt
Toothpaste
Bananas
Doctor visit
Cornflakes
Dentist visit
Tennis balls
Canned tuna
Ground beef
Man’s haircut
Margarine
Bread
Soft drink
Beauty salon
Apartment rent
Newspaper
Bowling

2

NOTES: This chart shows average price dispersion (computed for 1985–2009) for individual product categories in the American Chamber of Commerce Researchers Association database for
eight Texas cities. Price dispersion is a simple average of the price deviations (in percent, absolute values) of individual cities from the Texas average.
SOURCES: American Chamber of Commerce Researchers Association; authors’ calculations.

2

Economic Letter • Federal Reserve Bank of Dallas • December 2014

Economic Letter
(1985–97 and 1998–2009). The price differences between Dallas and other cities
became more pronounced in the second
half of the sample, where the average
price of the 45 goods or services surveyed was about 8 percent more expensive in Dallas.4 Mainly tradable products
drive Dallas’ price increase relative to
other Texas cities in the second half of
the sample period.

Rapid Price Convergence

Chart

2

Price Dispersion Increases Over Time

Percent

11
Average price dispersion

10

Four-quarter moving average
9
8

Although price differences persist
across cities, relative prices of a given
product between two locations may fluctuate around a mean. This weak form of
the law of one price is also referred to as
a weak form of purchasing power parity—the idea that identical goods in two
countries with two currencies should
cost the same.
What interests economists most is not
whether a pricing rule holds but at what
speeds relative prices converge to their
means, following a shock. The speed of
convergence is usually measured by the
so-called half-life statistic, an estimate
of the time needed for 50 percent of the
deviations of relative prices from their
mean to dissipate in the absence of any
new economic shocks. Estimates of halflife statistics over the full sample are
shown in Chart 4.5
The speed is very fast—the half-life
statistics are less than one quarter in
most product categories and, in all but
one category, less than two quarters.
The speeds of convergence are generally
slower for products that are less tradable
in nature, such as various services.

7
6
Jan.
’85

Jan.
’87

Jan.
’89

Jan.
’91

Jan.
’93

Jan.
’95

Jan.
’97

Jan.
’99

Jan.
’01

Jan.
’03

Jan.
’05

Jan.
’07

Jan.
’09

Jan.
’11

NOTE: Price dispersion for a given good or service (across the 45 product categories) is defined as the average of the price
deviations (in percent) of individual cities from the Texas average.
SOURCES: American Chamber of Commerce Researchers Association; authors’ calculations.

Chart

3

Dallas Price Differences Increase Most in Recent Period

Price differences relative to Texas average (in percent)
10

First half of sample (1985–97)

8

Second half of sample (1998–2009)

6

Full sample (1985–2009)

4
2
0
–2
–4
–6

Abilene

Amarillo

Dallas

Houston

Lubbock

Odessa San Antonio Waco

NOTE: This chart shows average (across products and time) of price differences of individual products relative to the Texas
average.

Persistent Differences
Price differences across Texas cities may be large and persistent. There
is, however, evidence of an important
price adjustment mechanism: relative
consumer prices between different cities
in Texas rapidly revert to a mean difference. These findings are broadly in line
with the evidence on consumer prices in
the scholarly literature where a number
of different intranational datasets are
scrutinized.
Future research may attempt to
understand what is driving the higher
degree of price dispersion among Texas
cities in the 2000s.

SOURCES: American Chamber of Commerce Researchers Association; authors’ calculations.

Additionally, the marked increase
in Dallas prices relative to Houston in
the second half of the sample period
appears somewhat puzzling. This development is driven mainly by products
that are tradable and cannot be easily justified by differences in income,
population growth or other idiosyncratic
factors.
Ca’ Zorzi is a senior economist in the
international policy analysis division at
the European Central Bank, Chudik is a

senior research economist in the Research
Department at the Federal Reserve Bank of
Dallas and Choi is an associate professor
at the University of Texas at Arlington.

NOTES
The views expressed in this paper are those of
the authors and do not necessarily reflect those
of the Federal Reserve Bank of Dallas, the Federal
Reserve System, the European Central Bank or the
Eurosystem.
1
Specifically, the dataset comes from the American
Chamber of Commerce Researchers Association’s

Economic Letter • Federal Reserve Bank of Dallas • December 2014

3

Economic Letter

Chart

4

Speed of Convergence Is Fast, But Varies Across Products

Half-life statistics (quarters)
3

2.5
2
1.5

.5

Whole chicken
Beer
Potatoes
Bread
Lettuce
Cheese
Canned peas
Gasoline
Canned tuna
Soft drink
Sugar
Ground beef
Man’s shirt
Detergent
Coffee
Bananas
Milk
Steak
Margarine
Wine
Man’s haircut
Cornflakes
Tissue
Auto maintenance
Tennis balls
Shortening
Frozen corn
Eggs
Canned peaches
Toothpaste
Newspaper
Doctor visit
Bowling
McDonald’s
Pizza
Dry cleaning
Fried chicken
Dentist visit
Appliance repair
Beauty salon
Mortgage payment
Movie
Home price
Telephone
Apartment rent

1

NOTES: For each of the eight Texas cities, the speed of convergence is given by the half-life statistics of relative prices of the chosen city and an aggregate of the remaining cities. The half life is an
estimate of the time needed for 50 percent of the deviations of relative prices from their mean to dissipate absent a new shock.
SOURCES: American Chamber of Commerce Researchers Association; authors’ calculations.

retail price survey publication “Cost of Living Index.”
More detailed description of this dataset can be
found, for instance, in the following publications:
“Convergence to the Law of One Price Without Trade
Barriers or Currency Fluctuations,” by David C. Parsley and Shang-Jin Wei, Quarterly Journal of Economics,
vol. 111, no. 4, 1996, pp. 1211–36; “The Bigger
They Are, the Harder They Fall: Retail Price Differences Across U.S. Cities,” by Paul G.J. O’Connell
and Shang-Jin Wei, Journal of International Economics,
vol. 56, no. 1, 2002, pp. 21–53; and “Does Distance
Reflect More than Transport Costs?” by Chi-Young
Choi and Horag Choi, Economics Letters, vol. 125, no.
1, 2014, pp.82–86.
2

DALLASFED

The Balassa–Samuelson effect refers to an economic model that justifies the observation that consumer price levels in locations with higher income
are systematically higher. The Balassa–Samuelson
effect is attributed to two papers: “The Purchasing Power Parity Doctrine: a Reappraisal,” by Bela
Balassa, Journal of Political Economy, vol. 72, no. 6,
1964, pp. 584–96; and “Theoretical Notes on Trade
Problems,” by Paul A. Samuelson, Review of Economics and Statistics, vol. 46, no. 2, 1964, pp. 145–154.
4
Chart 3 does not weigh the price differences across
products by the share of the income expenditures of
households, and therefore it does not quantify the
3

Economic Letter

is published by the Federal Reserve Bank of Dallas. The
views expressed are those of the authors and should not
be attributed to the Federal Reserve Bank of Dallas or the
Federal Reserve System.
Articles may be reprinted on the condition that the
source is credited and a copy is provided to the Research
Department of the Federal Reserve Bank of Dallas.
Economic Letter is available on the Dallas Fed website,
www.dallasfed.org.

Federal Reserve Bank of Dallas
2200 N. Pearl St., Dallas, TX 75201

differences in the cost of living of households.
5
The speed of convergence estimated seems to be
fairly constant over time. Estimates of the half-life
statistics are very similar when splitting the full
sample into two subsamples (before and after second quarter 1997, the middle point). The aggregation
methodology for the remaining cities is explained in
more detail in “Spatial Considerations on the PPP
Debate,” by Michele Ca’ Zorzi and Alexander Chudik,
Federal Reserve Bank of Dallas, Globalization and
Monetary Policy Institute Working Paper no. 138,
January 2013.

Mine Yücel, Senior Vice President and Director of Research
Anthony Murphy, Executive Editor
Michael Weiss, Editor
Jennifer Afflerbach, Associate Editor
Ellah Piña, Graphic Designer