May 1, 2013

The following white paper contains an examination of the price sensitivity of postal 

customers of three market dominant Postal Service products: First-Class Mail, 

Standard Mail, and Periodicals.

The marketplace for traditional Postal Service products is increasingly competitive. In 

addition to the long term trend toward electronic media, Postal Service products face 

intense pressures brought about by the Great Recession. This paper explores an open 

question raised by these disruptive trends: Are Postal Service customers becoming 

more price sensitive? Though intuition may suggest that growing competition would 

have this effect, the answer to this question is best found by letting the data do the

talking.

Toward that end, this paper presents the results of an open-minded, rigorous empirical 

review of the demand for these postal products. Price sensitivity was analyzed with a 

battery of tests using both the Postal Service demand models and alternative models. 

The analysis was subjected to extensive peer review.

We were surprised to find that, no matter how we stressed the models or which models 

we used, the data told the same story: Demand for postal products is not becoming 

more price sensitive. In fact, a case can be made that these products are becoming less

price sensitive. This may be because customers most likely to leave the Postal Service 

for the Internet have already done so, leaving the remaining customers more loyal in the 

face of price increases. 

In the course of our analysis, we did uncover some technical problems with the Postal 

Service’s demand models. We recommend that the Postal Service make adjustments to 

its models as appropriate. These technical problems had no significant effect on our 

conclusions.

David C. Williams

Inspector General
Analysis of Postal Price 

Elasticities

May 1, 2013

Report Number: RARC-WP-13-008

WHITE PAPER
U.S. Postal Service Office of Inspector General May 1, 2013

i

Analysis of Postal Price Elasticities

This paper analyzes the effect of postal 

price increases on revenue and volume. 

Opponents of price increases assert that 

higher prices will drive customers away, 

reducing revenue and exacerbating the 

loss of volume to electronic alternatives. 

Proponents of price increases cite the long 

history of price increases that led to 

revenue increases prior to the 

implementation of a price cap in 2007. The 

resolution of this dispute lies in the data. 

Analysis of the demand for postal products 

shows that price increases will increase 

revenues. Recent events such as the Great 

Recession and the growth of use of the 

Internet do not change this conclusion. 

Economists use the concept of price 

elasticity to analyze the effect of price 

changes on revenue changes. When price 

increases lead to decreased revenue the 

demand for the product is said to be price 

elastic. When price increases cause 

revenues to increase demand is inelastic. 

Price elasticity is estimated using econometric models of product demand. The Postal 

Service has produced its econometric demand models for more than 30 years with 

periodic refinements to reflect changes in the economy and postal industry. Some argue 

that the models provide evidence of an upward trend in price elasticity and that the price 

elasticity of postal customers is “in flux” due to the increase of electronic alternatives 

and the disruptive effects of the Great Recession.1 In order to test these propositions, 

this paper examines the demand for three classes of market dominant postal services: 

 1 United States Postal Service, Plan to Profitability: 5 Year Business Plan, February 16, 2012, 

http://about.usps.com/news/national-releases/2012/pr12_0217profitability.pdf, p. 4, and Five Year Business Plan, 

April 16, 2013, http://about.usps.com/strategic-planning/fiveyearplan-04162013-final.pdf, p. 6.

EXECUTIVE SUMMARY

Highlights

The OIG asked Christensen Associates 

to review the Postal Service’s demand 

models for First-Class Mail, Standard 

Mail, and Periodicals.

Christensen Associates found that 

these postal products are price 

inelastic: raising their prices will 

increase postal revenues. Lowering 

them will decrease revenues.

There was no evidence that either the 

long-term trend toward using electronic 

alternatives to mail or the Great 

Recession has caused postal customers 

to become more price sensitive.

There were some technical problems 

with the Postal Service models. 

Correcting these problems did not 

change the findings; the demand for 

these postal products is still price 

inelastic. 
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ii

First-Class Mail®, Standard Mail®, and Periodicals. These classes account for the 

majority of mail volume, mail revenue, and contribution to institutional costs. 

The Office of Inspector General retained Lauritis R. Christensen Associates, an 

independent economic consulting firm, to conduct the analysis. Christensen Associates 

is well-known for its expertise in econometrics, productivity measurement, and 

regulatory industry policy analysis. The analysis is included as a technical appendix. 

Christensen Associates reviewed the demand models that the Postal Service filed with 

the Postal Regulatory Commission in 2011 and 2012. The Postal Service uses these 

models in financial forecasting, pricing, marketing, and planning processes. Christensen 

Associates also reviewed other econometric formulations of the demand for postal 

services. This econometric evaluation of Postal Service price elasticities uses both the 

Postal Service’s models as well as an alternative set of models.

Results of Analysis

 The demand for the postal products studied is price inelastic. Price increases will 

increase revenues. Decreases in postal prices, either through price cuts or 

widespread use of discounting, will reduce Postal Service revenues.

 A case can be made that the demand for postal products (with the possible 

exception of Standard Enhanced Carrier Route (ECR) mail) has actually become 

more price inelastic over time. Moreover, even the most price sensitive product 

examined in this report, Standard Mail ECR, is price inelastic.

 The Great Recession and the availability of electronic alternatives clearly 

decreased the demand for the postal services examined in this report, as 

evidenced by a drastic decline in volume over the past 7 years. However, neither 

the recession nor any other event since 2008 caused postal price elasticities to 

increase in any significant way. Postal price elasticities are not in flux. The 

demand for postal products remains price inelastic.

 Price elasticities generally are higher when competitive alternatives are more 

readily available. Since electronic alternatives to mail have become increasingly 

widespread in recent years, one might think that price elasticity estimates that 

use data from an earlier, less competitive era would understate the price 

elasticities of mailers today. Christensen Associates found, however, that 

including historical data (from the 1990s, for example) in the econometric 

demand analysis does not materially affect the estimates of price elasticities. 

 Christensen Associates found technical shortcomings in the Postal Service 

models. Because of this, Christensen Associates ran its analysis with both the 

Postal Service’s models and its preferred alternatives, error correction models. 

Correcting these technical problems resulted in only small changes to the price 

elasticity estimates and had no bearing on the major results described above. 
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Table of Contents

Introduction ..................................................................................................................... 1

What is a Demand Model?.............................................................................................. 2

Estimates of Price Elasticities over Time......................................................................... 4

Econometric Analysis and Results .................................................................................. 5

Business Implications...................................................................................................... 7

Appendix

Is Demand for Market Dominant Products of the U.S. Postal Service 

Becoming More Own Price Elastic? ................................................................................ 8
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Analysis of Postal Price Elasticities

Introduction

The adoption of Internet-based communications and the most severe economic 

downturn in eight decades have combined to reduce dramatically the demand for 

traditional postal services. Mail volume in the United States in 2012 was 160 billion 

pieces, 25 percent less than its peak of 213 billion pieces in 2006. The 2012 volume 

level is roughly the same as in the late 1980s despite a population increase of 80 million 

and an increase in delivery points of 37 million.2 To make matters even worse, the vast 

majority of the decline in volume came from the U.S. Postal Service’s most profitable 

products: First-Class Mail and Standard Mail.3 

There have been many disruptive events for postal customers during the last 7 years. 

The Internet has caused a revolution in communications away from hard copy to digital. 

A severe economic contraction has crippled economic growth and reduced consumer 

demand. Postal prices have increased. Economists use econometric methods to 

provide a rigorous analytical framework to separate out these kinds of effects. These 

econometric tools are designed to provide an objective basis for understanding what 

happened in the past and what is likely to happen to mail volume when these factors 

change in the future. This paper relies on these accepted analytical tools.

Economists measure the degree to which consumers respond to price changes and 

alter their demand for products or services with the concept of elasticity. The measure 

of price elasticity is critical to making business and public policy decisions. A product is 

considered to be price inelastic if a 1-percent increase in price brings about a less than 

1-percent decrease in volume. If a product is price inelastic, a price increase will 

increase gross revenue. If we can confidently conclude that the demand for a product is 

inelastic with respect to price, then price increases can be a powerful financial tool. 

When a product is price inelastic, cutting prices or discounting will be counterproductive, 

resulting in decreased revenue and profitability. 

One way to offset the adverse financial effects of a volume decline is to raise prices. 

Prior to the passage of the Postal Accountability and Enhancement Act (PAEA) in 2006, 

the Postal Service regularly raised prices to improve its finances. Price increases were 

pursued because mailer demand was regarded as price inelastic. Since the passage of 

the PAEA, price increases have been capped at the rate of inflation except for exigent 

circumstances. The Postal Service has been reluctant to pursue an exigent price 

increase. This reluctance is based at least partially on the assumption that the Internet 

 2 For population data, see U.S. Census data as posted at http://www.multpl.com/united-states-population/table. For 

delivery points, see U.S. Postal Service figures as posed at http://about.usps.com/who-we-are/postal-history/deliverypoints-since-1905.pdf. 3 Domestic First-Class Mail volume peaked at nearly 104 billion pieces in 2001. Today, there are only 69 billion 

pieces. Standard Mail volume peaked at nearly 104 billion pieces in 2007 and now stands at about 80 billion pieces.
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has increased competition, thereby making mailers more sensitive to price increases. 

Ultimately, the question of mailer response to price increases is an empirical one.

The Postal Service maintains a set of econometric demand models that estimate, 

among other things, mailers’ price elasticity of demand. This paper examines these 

models for three market dominant classes of mail: First-Class Mail, Standard Mail, and 

Periodicals.

4 Our examination focuses on several interrelated questions. Has the 

demand for these postal services experienced a structural change? In the presence of 

electronic alternatives and profound changes in the economy, are postal customers 

more price sensitive now than was previously thought? Are the Postal Service’s 

econometric demand models properly estimated and how, if at all, can they be 

improved? The U.S. Postal Service Office of Inspector General contracted with 

Lauritis R. Christensen Associates (Christensen Associates), an independent consulting 

firm with extensive postal and econometric expertise, to examine these questions. Their 

technical report is attached as an appendix.

What is a Demand Model?

Consumers of goods and services purchase products in such a way as to maximize 

their satisfaction (called utility by economists) subject to a budget constraint (usually 

income). Businesses purchase resources to maximize profits. For most goods, this 

means that as prices increase, the quantity demanded decreases. This relationship 

gives rise to the familiar downward-sloping demand curve. There are many other factors 

that are important in determining the demand for goods and services. These factors 

include prices of substitutes and complements, consumer income, population-related 

factors, and changes in consumer taste and technology. These factors generally cause 

a demand curve to shift up or down or change shape depending on the direction of their 

influence on consumers.5

The actual behavioral processes that underlie the demand for a good or service are

unobservable, but economists can use econometric tools to model and estimate them. 

These tools quantify the causal influence of each demand factor on the level of product 

demand. In general, when one estimates the demand for postal services, one applies 

some basic economic concepts of demand to specify mathematical models for 

estimation purposes. For postal services, these econometric models include the 

following demand factors:

 The real price of the postal product. This is the price of the postal product itself 

adjusted for inflation.6 It is also called the own price.

 4 According to the Postal Service’s 2012 Cost and Revenue Analysis Report, the products analyzed in this study 

constitute 97 percent of mail volume, 74 percent of revenue, and 81 percent of contribution to institutional costs. 

5 See Figure 3 in the Christensen Associates report in the appendix for an illustration. 6 Prices are adjusted for inflation to account for the erosion of the value of the dollar over time. In this way, prior years 

can be compared to recent years on an even footing.
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 The real price of substitutes for the postal product. A substitute can be another 

postal product or a product offered by a competitor. Prices of substitutes are 

referred to as cross prices.

 The real price of complements. A complement would be a good that is used 

hand-in-glove with postal products. Paper and printing are examples of 

complements of postal products. The prices of complements are also referred to 

as cross prices. 

 The real level of economic activity. The greater the level of economic activity, the 

greater is the demand for postal products. Real retail sales and employment are 

examples.

 Population. Higher population means more consumers and more demand for 

postal products. 

 Changes in consumer tastes and technology. Examples include the availability 

of electronic alternatives to mail, such as electronic bill payment.

 Seasonal effects, such as the pre-Christmas increase in catalogue mailing.

 Other factors and events such as elections, the decennial census, changes to the 

definition of a product, the anthrax attacks, and the like.

The specific drivers of the demand for each postal product, of course, differ. 

Nevertheless, demand for all postal products follows these same basic economic 

principles.

Most postal demand factors have a known direction of influence on demand, but the 

effects of technology and taste can be either positive or negative, often in subtle and 

surprising ways. In the 1970s, the expansion of the use of computers was famously 

predicted to bring about the paperless office.7 Using similar reasoning, a 1977 

commission on the future of the Postal Service predicted the decline of mail volume 

growth in the 1980s.8 Rather than become paperless, we experienced a boom in the 

use of paper in the office (and beyond). People were reluctant to give up paper, a 

medium that had been ubiquitous for hundreds of years. Laser printing made printing 

easy and convenient. Inexpensive computer technology made it easier to develop 

mailing lists that facilitated direct mail advertising campaigns. Instead of experiencing a 

 7 For the original article, see “The Office of the Future,” Business Week, June 30, 1975, 

http://www.businessweek.com/stories/1975-06-30/the-office-of-the-futurebusinessweek-business-news-stock-marketand-financial-advice. For an interesting discussion of why it turned out to be such a bad prediction, see Gordon Kelly, 

“The Paperless Office: Why It Never Happened,” Itproportal.com, March 9, 2012, 

http://www.itproportal.com/2012/03/09/paperless-office-why-it-never-happened. 8 Commission on Postal Service, Report on the Commission on Postal Service (Washington, DC: Government 

Printing Office, April 1977), p. 30.
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decline in mail volume in the 1980s, the Postal Service saw a sharp increase aided by 

the very computer technology that was supposed to cause the decline.9

 

Estimates of Price Elasticities over Time

The Postal Service has a long history of using econometric tools to estimate the 

demand for its products. Estimates of price elasticity for market dominant products are 

publically available. Table 1 in the Christensen Associates appendix lists these 

estimates over the last two-and-a-half decades. 

An elasticity estimate less than 1.0 indicates that demand for a product is price inelastic. 

Of the 133 values listed, only nine (less than seven percent) are above 1.0, indicating 

elastic demand. Moreover, all of the price elasticities from 2011 or 2012, the most 

recent years listed, are less than 1.0. Another interesting fact is that year-to-year 

fluctuations in the Postal Service’s price elasticities are not a recent phenomenon. The 

estimated price elasticity for Within County Periodicals, for example, follows a saw tooth 

pattern, declining in one year and increasing the next. Finally, there does not seem to 

be any discernible trend toward higher elasticity values in recent years. 

Somewhat ironically, the Postal Service’s econometrician takes issue with using this 

table to find evidence of trends in price elasticities. Each price elasticity listed comes 

from a demand model that estimates a single price elasticity applicable over the entire 

period included in the analysis, often more than 20 years in length. In the view of the 

Postal Service’s econometrician, the best estimates of today’s price elasticities are the 

most recent ones, because they include all currently available information.10

Additionally, changes in the elasticity from one set of models to the next generally 

reflect changes to the specification of the model, not changes in underlying mailer 

behavior. One such model change could be the use of a different economic activity 

measure, using retail sales instead of disposable income, for example. Using a different 

economic variable might be done because it allows the demand model to better fit 

historical data. Another reason for changing a demand driver is that the old driver may 

no longer be useful for forecasting purposes. Broadband adoption, for example, is an 

obvious choice to represent the expansion of the Internet, but broadband adoption 

stalled for several years at about two-thirds of American households. Basing a mail 

volume forecast on this data series would be nonsensical since we expect the Internet 

to have an increasing effect on mail demand for many years to come. Using different 

demand drivers in the models can change the estimates of all the elasticities, including 

its own price elasticity, even when the underlying mailer behavior has not changed. 

With a few exceptions, Table 1 in the appendix shows that the Postal Service has 

consistently found that the demand for market dominant products is price inelastic, 

 9 Of course, to some extent, these pessimistic prognosticators were right; they just missed on the timing of these 

events by 20 years or so. 

10 Thomas. E, Thress, “Response of Postal Service Witness Thress to Interrogatories of ABA-NAPM” in Postal 

Regulatory Commission, Transcript, Volume 6, Docket No. R2006-1, August 9, 2006, 

http://www.prc.gov/Docs/52/52241/Vol-6-R2006-1.pdf, pp. 1201-1203.
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sometimes extremely so.11 Traditional economic theory states that one determinant of 

price elasticity is intensity of competition: The more competition, the higher the price 

elasticity. Low postal price elasticities in recent years seem at odds with the emerging 

intense competition from the Internet and other electronic alternatives to mail. There is 

an alternative school of thought, however, that supports low or even declining price 

elasticities. Suppose the market consists of two classes of customers: the Traditionals 

and the Digitals. The Traditionals stick with an old technology through thick and thin 

because it meets their business and personal needs. The Digitals look to new 

alternatives and once they switch to that alternative they do not switch back. If 

Traditionals are less price elastic than Digitals, the movement of the Digitals to the new 

alternatives would cause the price elasticity for the users of the old technology to 

decline over time.12 In the case of the Postal Service, there are some Traditionals who 

prefer to use hard-copy mail as opposed to electronic alternatives, and Digitals who 

have already switched to e-mail, electronic bill payment, and other forms of digital 

communication. The postal customer base may now be made of Traditionals who are

unlikely to abandon their mail usage even in the face of a price increase. 

The Great Recession could also affect price elasticities. It could be the case that the 

disruptive effects of the Great Recession have fundamentally changed the demand for 

postal products. For example, recession-induced pressure to reduce costs may intensify 

mailers’ desire to move customers to electronic bill payment, and electronic bill and 

statement presentment.

A formal analysis of these phenomena would answer the technical question: Has a 

structural change in demand caused price elasticities to increase significantly in recent 

times? This sort of change would reveal itself in the data and can be tested easily. The 

Christensen Associates analysis performs these tests.

Econometric Analysis and Results

The econometric analysis followed two tracks. The first track used the Postal Service’s 

most recent demand models and subjected them to four separate analytical reviews. 

Because technical problems were discovered in the Postal Service’s models, an 

alternative set of models was developed. These alternative models were subjected to 

the same four analytical reviews. 

 11 The closer to zero, the more price inelastic a product is. 12 For a discussion of this phenomenon in the pharmaceutical industry, see U.S. Postal Service, Rebuttal Testimony 

of Thomas E. Thress, Transcript Volume 38, Docket R2006-1, pp.13023-24. Thress’s discussion, in turn, cites F.M. 

Scherer, Industrial Structure, Strategy and Public Policy (New York: Harper Collins, College Publishers, 1996), p. 377 

and Richard G. Frank and David S. Salkever, “Pricing, Patent Loss, and the Market for Pharmaceuticals,” Southern 

Economic Journal, October 1992, pp. 165-79, http://www.people.vcu.edu/~lrazzolini/GR1993.pdf. A recent study that 

applies a remarkably similar approach to postal markets is Frederique Feve, Jean-Pierre Florens, Frank Rodriquez, 

Soterios Soteri, and Leticia Veruete-McKay, “Evaluating Demand for Letter Price Elasticities and Technology Impacts 

in an Evolving Communications Market is Higher than Econometricians Think?” 2012. 

http://idei.fr/doc/conf/pos/papers_2012/soteri.pdf (used with permission of the authors). This study does find an 

upward trend in price elasticity, but that the price elasticity remains “near the magnitude” of Lpeople, who we are 

calling Traditionals. 
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The first review estimated the demand models using a shortened version of the dataset, 

starting with the oldest data. The models were re-estimated adding the next most recent 

data point. For example, the first iteration would use the first 60 data points. The second 

would use 61 data points, the first 60 plus the next most recent. This exercise was 

repeated until all data points were included.13 The price elasticity estimate from each 

iteration was graphed over time. The resulting graphs shows whether the price elasticity 

estimates have trended up or down over time. 

The second review essentially repeated the first analysis in reverse, starting with the 

most recent data, adding older data points one at a time.14 In this case, for example, the 

most recent 60 observations are used for the first estimation. The next estimation uses 

the most recent 61 observations, and so on. As before, the price elasticity from each 

iteration was graphed indicating whether the elasticities have exhibited a trend over 

time.

The third review sequentially estimated the demand equation over a subset of the 

available data, holding the size of the data subset constant. The first estimate was 

conducted with the oldest data. The equations were re-estimated by moving the dataset 

forward in time, one quarter at a time until only the most recent data were used.15 In this 

case, the first estimation would use the oldest 60 data points. The next estimation drops 

the oldest observation and adds the next most recent one, such that 60 data points are 

used in each iteration. The estimated price elasticity from each iteration was graphed 

over time. This analysis also depicts evidence of trends over time.

The fourth review involved a series of so-called dummy variable tests. These tests 

include a binary or dummy variable that allows the price elasticity to shift either up or 

down with recent events, like the Great Recession. If the estimated price elasticity 

increased or decreased, the dummy variable analysis measured the magnitude of the 

change and its statistical significance.

Both research tracks reached the following conclusions:

 The demand for First-Class Mail, Standard Mail, and Periodicals is price inelastic, 

and Christensen Associates’ estimates are generally in the same range 

estimated by the Postal Service’s 2012 models. A case can be made for the 

proposition that Standard Enhanced Carrier Route (ECR) Mail has a price 

elasticity of one.16

 With the possible exception of Standard ECR, Christensen Associates found no 

evidence that the demand for the market dominant products in this study has 

become more price elastic over time. In fact, one could reasonably conclude that 

some products have become less price elastic in recent years.

 13 In the Christensen Associates report, this is called the recursive coefficient analysis. 14 The Christensen Associates report refers to this as the reverse recursive coefficient analysis. 15 This is called the rolling coefficient analysis in the Christensen Associates report. 16 A price elasticity equal to one, also called a unitary price elasticity, means that raising ECR’s price would leave 

gross revenue unchanged. 
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 The Great Recession (or other recent events) does not seem to have had any 

discernible effect on price elasticities.

 Use of historic data from a time with fewer electronic alternatives in the Postal 

Service’s demand analyses does not lead to underestimates of price elasticities. 

As mentioned above, Christensen Associates found evidence of a technical problem 

often evident in time series analyses, in the Postal Service’s models. Christensen 

Associates used an alternative set of econometric models to remedy this problem. We 

recommend that the Postal Service review its regression diagnostics and consider using 

alternative modeling methods where appropriate. The use of alternative models did not 

change any of the above findings, but it did produce more defensible elasticity estimates 

and better measures of the variance of the estimates. 

Business Implications

One of the primary purposes of econometric demand models is to determine what 

factors cause (or do not cause) changes in mail volume. These models show that recent 

volume declines are the result of the effects of the Great Recession and the long-term 

trend away from printed communications. Price increases are not the cause of the 

Postal Service’s volume losses. Mailers are not more sensitive to price increases than 

in the past.

Based on the econometric evidence, raising the price level for First-Class Mail, 

Standard Mail, and Periodicals above the rate of inflation will increase the gross 

revenues of the Postal Service. However, it is important to note that each price elasticity 

estimate applies to an aggregate classification of mail. It may be the case that market 

segments within an aggregate classification examined in this report are price elastic. 

However, this implies that the remaining market segments within that classification are 

more inelastic than the overall econometric estimates.

Widespread discounting among these market dominant products that lowers price levels 

will reduce revenue. Such indiscriminant use of discounting, therefore, is a 

counterproductive pricing strategy. Mailers are unlikely to increase volume sufficiently to 

offset the reductions in price.
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Appendix
Laurits R. Christensen Associates, Inc.

800 University Bay Drive, Suite 400

Madison, WI 53705-2299

Voice 608.231.2266 Fax 608.231.2108

Is Demand for Market 

Dominant Products of the U.S. 

Postal Service Becoming More 

Own Price Elastic?

A. Thomas Bozzo

Kristen L. Capogrossi

B. Kelly Eakin

Mithuna Srinivasan

May 1, 2013
1

Table of Contents

I. INTRODUCTION AND EXECUTIVE SUMMARY ......................................................................................................4

I.B. SCOPE OF ANALYSIS..................................................................................................................................................6

II. PRICE ELASTICITY AND THE STRUCTURE OF POSTAL DEMANDS .........................................................................7

II.A. PRICE ELASTICITY ....................................................................................................................................................7

II.B. HOUSEHOLD AND BUSINESS DEMAND FOR POSTAL SERVICES...........................................................................................9

II.C. DETERMINANTS OF THE PRICE ELASTICITY OF DEMAND.................................................................................................10

II.D. THE DISTINCTION BETWEEN A CHANGE IN DEMAND AND A CHANGE IN THE ELASTICITY OF DEMAND.....................................10

III. ECONOMETRIC ESTIMATION METHODS FOR POSTAL SERVICE DEMANDS ...................................................... 12

III.A. POSTAL SERVICE BASELINE MODELS ........................................................................................................................12

III.B. NONSTATIONARITY AND ERROR CORRECTION MODELS................................................................................................15

III.C. MODIFIED USPS BASELINE DEMAND MODELS ..........................................................................................................19

III.D. ERROR CORRECTION MODELS ................................................................................................................................22

IV. TESTING STABILITY OF OWN PRICE ELASTICIITES ............................................................................................ 23

IV.A. ROLLING AND RECURSIVE COEFFICIENT ANALYSIS.......................................................................................................23

IV.B. RESULTS OF ROLLING AND RECURSIVE PARAMETER ANALYSIS .......................................................................................25

IV.C. DUMMY VARIABLE INTERACTION MODELS................................................................................................................39

V. CONCLUSIONS ................................................................................................................................................. 42

APPENDIX A: PRICE ELASTICITY AND THE ECONOMIC STRUCTURE OF POSTAL DEMANDS ................................... 43

A.1. PRICING AND THE IMPORTANCE OF THE ELASTICITY OF DEMAND ....................................................................................43

A.2. DETERMINANTS OF THE PRICE ELASTICITIES OF HOUSEHOLD DEMAND.............................................................................44

A.3. DETERMINANTS OF THE PRICE ELASTICITIES OF BUSINESS DEMAND.................................................................................46

A.4. ALL OTHER THINGS AREN’T THE SAME: HOW THE DEMAND AND THE ELASTICITY OF DEMAND FOR POSTAL SERVICES MIGHT—OR 

MIGHT NOT—BE CHANGING.........................................................................................................................................49

A.5. CONCLUSION .......................................................................................................................................................50

APPENDIX B: SUMMARY OF CRRI CONFERENCE PAPERS REVIEWED .................................................................... 51

B.1. TIME SERIES MODELS ............................................................................................................................................51

DISCRETE CHOICE MODEL OF CIGNO, PEARSALL, AND PATEL ................................................................................................52
2

List of Tables

Table 1. Own Price Elasticity History ............................................................................................ 14

Table 2. Results of Stationarity and Cointegtration Tests for Postal Service Demand Variables. 18

Table 3. Comparison of Long-Run Own Price Elasticities from USPS Demand Models and LRCA 

Modified Baseline Models, Full Sample Periods Ending Q4 FY2011 and Q4 FY2012................... 21

Table 4. Long-run Own Price Elasticities from Error Correction Models, Full Sample Periods 

Ending Q4 FY2011 and Q4 FY2012................................................................................................ 23

Table 5. Results from Dummy Variable Interaction Models ........................................................ 40
3

List of Figures

Figure 1: Relative Elasticity ............................................................................................................. 8

Figure 2: Perfectly Elastic Demand and Perfectly Inelastic Demand.............................................. 9

Figure 3: Demand Decreases and Impacts on Elasticity of Demand ............................................ 11

Figure 4a. Rolling and Recursive Analysis for Standard Regular, Modified Baseline ................... 26

Figure 4b. Rolling and Recursive Analysis for Standard Mail Regular, ECM Version 1................. 26

Figure 5a. Rolling and Recursive Analysis for Standard ECR, Modified Baseline ......................... 27

Figure 5b. Rolling and Recursive Analysis for Standard ECR, ECM Version 1............................... 28

Figure 6a. Rolling and Recursive Analysis for Standard Nonprofit, Modified Baseline................ 29

Figure 6b. Rolling and Recursive Analysis for Standard Nonprofit, ECM Version 1 ..................... 29

Figure 7a. Rolling and Recursive Analysis for Standard Nonprofit ECR, Modified Baseline......... 30

Figure 7b. Rolling and Recursive Analysis for Standard Nonprofit ECR, ECM Version 1.............. 31

Figure 8a. Rolling and Recursive Analysis for Periodicals, Modified Baseline.............................. 32

Figure 8b. Rolling and Recursive Analysis for Periodicals, ECM Version 1 ................................... 32

Figure 9a. Rolling and Recursive Analysis for Single Piece First-Class Mail, Modified Baseline... 33

Figure 9b. Rolling and Recursive Analysis for Single Piece First-Class Mail, ECM Version 1 ........ 34

Figure 10a. Rolling and Recursive Analysis for Workshared First-Class, Modified Baseline ........ 35

Figure 10b. Rolling and Recursive Analysis for Workshared First-Class, ECM Version 1 ............. 35

Figure 11a. Rolling and Recursive Analysis for Single Piece First-Class Cards, Modified 

Baseline......................................................................................................................................... 36

Figure 11b. Rolling and Recursive Analysis for Single Piece First-Class Cards, ECM Version 1 .... 37

Figure 12a. Rolling and Recursive Analysis for Workshared First-Class Cards, Modified 

Baseline......................................................................................................................................... 38

Figure 12b. Rolling and Recursive Analysis for Workshared First-Class Cards, ECM Version 1 ... 38
4

I. INTRODUCTION AND EXECUTIVE SUMMARY

The price elasticity of demand is a concept that measures customers’ response to price changes 

for a product. From a seller’s point of view, the price elasticity of demand is important 

information for determining pricing strategies. The own price elasticity of demand specifically 

measures the degree of response of a product’s volume (demand) to changes in the product 

price. Since demand curves are generally downward sloping in the product price, own price 

elasticities are almost always assumed to be negative, so price increases reduce quantity 

demanded, other things equal. For example, if a product’s own price demand elasticity is -0.2, 

then a one percent increase in the (real) price of the product would result in a 0.2 percent 

decline in volume. Own price elasticities less than unity in absolute value are termed “inelastic;” 

if the volume response is larger in percentage terms than the price change, then the elasticity is 

greater than 1 in absolute value and demand is “elastic.”1

Among other considerations, raising the price of an own price inelastic product will increase a 

firm’s revenues, net of expected volume losses. The Postal Service has estimated demand 

models for many years, which have found inelastic demands for most market dominant postal 

products. However, in the wake of large and persistent volume declines for key market 

dominant products such as First-Class Mail letters and Standard Mail flats, the Postal Service 

and other parties have claimed that postal demand may have become more own price elastic 

over time, potentially due to factors such as increased competition from electronic substitutes 

or increased price sensitivity of mailers seeking cost savings as a result of the Great Recession. 

These claims bear on a number of important pricing issues, including the utility of exigent rate 

increases, and the effects of rate rebalancing in which certain products within mail classes may 

face systematic increases in real price to meet regulatory cost coverage requirements.

While the Postal Service’s demand models incorporate features to account Internet diversion 

and cyclical economic effects, they do not directly provide for changes in own price elasticities 

of demand. The history of own price elasticities from the demand models provides some 

indication of the sensitivity of the results to the inclusion of data from more recent years. If 

adding data to the end of a demand model sample caused a large increase in the measured 

elasticity, it would be appropriate to conclude that demands were becoming more elastic over 

time. However, it is possible that the long sample periods and other model assumptions could 

attenuate changes in the elasticities, so the lack of longer-range trends in the elasticity histories 

is not dispositive of the question of whether own price elasticities are increasing or otherwise 

“in flux.” 

Our analysis addresses a primary question of interest, “Can the Postal Service’s demand models 

be used to test the proposition that the price elasticity of demand has changed as a result of 

the Internet or other recent events?” We review the theory of demand, including consumer 

demands for goods and services and firms’ demands for factors of production, to assess 

 1 In the discussion below, we mean “larger” own price elasticities to refer to elasticities that are larger in absolute 

value—that is, more own price elastic demands. 
5

whether recent changes to postal and communications markets necessarily imply increasing 

own price elasticities for the Postal Service’s market dominant products. Section II summarizes 

our review of demand issues, which is presented in Appendix A. We also reviewed the Postal 

Service’s econometric models of market dominant product demands, filed with the Postal 

Regulatory Commission in January 2012,2 and compared Postal Service methodology with that 

of recent papers on postal demand estimation presented at recent conferences sponsored by 

the Rutgers University Center for Research in Regulated Industries (CRRI).3 Our econometric 

analysis, which covers the First-Class Mail, Periodicals, and Standard Mail product groups from 

the Postal Service’s demand analysis, is presented in Sections III and IV. A summary of our 

review of the CRRI conference papers is provided in Appendix B.

Our main findings are:

• We find that the Postal Service’s demand models, as well as alternative models we 

developed, can be used to test whether postal price elasticities have changed as a result 

of recent events. Our primary finding is that the demand for postal products has 

remained own price inelastic. This implies that increases in the real prices of the market 

dominant postal products we studied will result in increased Postal Service revenue.

• As a theoretical matter, the total effect of all technological changes on the price 

elasticity of postal services is ambiguous. Factors such as increased modal competition 

from electronic alternatives on the demand for postal services may be expected to 

increase the elasticity of postal demands, other things equal. However, these effects can 

be offset, in whole or in part, by other interrelated changes. In particular, more elastic 

postal volumes may tend to be diverted to other modes first, so that remaining demand 

may be smaller and less elastic.

• The Postal Service’s January 2012 demand equations are usable as a baseline for testing 

whether own price elasticities have changed over time. While the Postal Service’s 

models have lost some economic content over successive model revisions, particularly 

insofar as they have dropped terms that explicitly modeled postal cross-product and 

electronic substitution effects, we do not view the models’ limitations as disqualifying. 

The Postal Service’s demand models otherwise are conceptually similar to time series 

models advanced in recent CRRI conference papers using time-series analysis.

• Neither the Postal Service’s January, 2012 models nor the alternative models in the CRRI 

conference papers explicitly allow for own price elasticities that change over time.

However, the log-linear specifications used in the Postal Service models and in time 

series models from the CRRI conference papers can be augmented with interaction 

 2 The January 2012 filing incorporates data through the end of FY 2011. The Postal Service released an update 

incorporating FY 2012 data and other changes on January 22, 2013. Our analysis incorporates the FY 2012 data 

from the 2013 filing, but otherwise uses the January 2012 demand models as its baseline. 3 We refer to these below as “CRRI conference papers” for short.
6

terms between time variables and price to allow for time-varying elasticities. We 

specifically estimated dummy variable interaction models to allow for structural shifts in 

own price elasticities following the Great Recession.

• Rolling and recursive coefficient analysis, applied to appropriately specified models, also 

provide an indication of underlying trends in demand elasticities. These analyses 

effectively relax the log-linear demand models’ assumption of constant elasticity over 

the full sample period. These methods are somewhat limited in that they require 

relatively long samples of quarterly data to obtain reasonable estimates of the own 

price elasticity, among other demand model parameters. As a result, it is not possible to 

run the demand models solely on data after the Great Recession or other recent events.

• We discovered errors in the Postal Service’s calculation of specification test statistics 

needed to justify the functional form of its baseline econometric demand equations. 

The errors appear to have led the Postal Service’s analysts to believe that the demand 

data are stationary, when correct implementations of the tests indicate otherwise. We 

investigated both the USPS baseline models and alternative specifications, called error 

correction models (ECMs), to address the specification error. We found that own price 

elasticities from the ECMs were qualitatively, and to some extent quantitatively, similar 

to the USPS baseline results. We strongly recommend that the Postal Service develop 

appropriate revisions to its baseline models in line with corrected specification test 

results.

• Our analysis shows that own price elasticities for the Postal Service’s market dominant 

products are relatively stable over longer sample periods, and that there is no evidence 

of significant recent structural breaks in own price elasticities. The baseline demand 

models and the alternative ECM specifications can produce unstable elasticity results 

over shorter sample periods, but most of the instability is in the direction of less elastic 

demand, with the notable exception of the Commercial Standard Mail Enhanced Carrier 

Route product.

I.B. Scope of Analysis

There are several potentially important issues in Postal Service demand measurement that are 

outside the scope of our analysis.

First, our analysis does not address the level or stability of own price elasticities for product 

categories other than those reported in the Postal Services’ January 2012 filing, including 

product definitions used for regulatory reporting since the implementation of the Postal 

Accountability and Enhancement Act (PAEA). In particular, Postal Service’s January 2013 filing 

incorporated a number of changes to the First-Class Mail demand models to the end of 

improving alignment with PAEA product categories. Our analysis carries forward the older FirstClass Mail product categories. The Postal Service reports that models for some PAEA product 

categories within Standard Mail are under study, but not yet sufficiently reliable for public 
7

release; we did not conduct a detailed analysis of alternative Standard Mail product groups in 

the absence of a Postal Service baseline model.4

Second, we did not revisit a number of details of the demand model specifications. The Postal 

Service’s models incorporate a great deal of practical experience with “nuisance” variables in 

the analysis, such as seasonal control variables, as well as selection of explanatory variables 

such as macroeconomic activity indicators where economic theory is relatively silent as to the 

details of the variable choice. In these cases, our review standard was whether the choices of 

the Postal Service’s modelers are justifiable, and not whether they are ideal. We also did not 

attempt to conduct further fine-tuning of the Postal Service models’ choice of explanatory 

variables. Rather, we focused on major specification issues such as the non-stationary data 

problem that led us to examine alternate ECM specifications of the demand models.

Finally, market dominant Package Services products—e.g., market dominant Parcel Post, Bound 

Printed Matter, and Media Mail—were excluded from the analysis, as were competitive 

shipping products. Demands for these market dominant products have a potentially complex 

relationship with competitive shipping products, and public data on competitive products are 

limited during the PAEA period. The analysis, then, focuses on products whose demands can be 

estimated using publicly available data.

II. PRICE ELASTICITY AND THE STRUCTURE OF POSTAL DEMANDS

II.A. Price Elasticity

The price elasticity of demand is a concept that measures purchasers’ responsiveness to a 

change in the price of a good. Price elasticity of demand is important to pricing strategy. It 

indicates a firm’s pricing power for a particular product and that product’s ability to generate 

profit or “contribution” to fixed cost recovery.

Technically, the price elasticity of demand εd is defined as the percentage change in quantity 

demanded Qd resulting from a one percent change in price P. That is, 

(1) εd = %∆Qd / %∆P = (∆Qd /∆P) (P/Qd) ≤ 0.

The demand elasticity εdmeasures consumer response to a change in the price of a good, all 

other factors the same. It is negative because consumers are willing to buy more of a good at 

lower prices than at higher prices (i.e., the law of demand). The demand elasticity reflects the 

shape of the demand curve, but differs from a simple slope measure. Itis a scale-free number in 

the sense that the demand elasticity does not depend on the measurement units of Q or P.

If the elasticity measure has a magnitude (absolute value) greater than unity (εd < -1), then 

demand is classified as elastic and an increase in price results in a decrease in total revenue. If 

 4 We carried out limited exploratory analysis to evaluate some Postal Service statements regarding its analysis, 

including its claim that alternative Standard Mail models are not yet sufficiently reliable for public release. 
8

the elasticity measure has a magnitude less than unity (εd > -1), then demand is inelastic and an 

increase in price results in an increase in total revenue. If total revenue is at its maximum, then 

εd = -1. The importance of the price elasticity of demand for pricing behavior is discussed in 

more detail in Appendix A.

Relative elasticity is a comparison of different or changing demand situations. Relative elasticity 

statements include phrases like “demand is less elastic” or “the more elastic demand,” 

regardless of the whether the magnitude of εd is greater or less than unity. Figure 1 shows two 

demand schedules. Demand depicted by D1 is relatively more elastic than demand represented 

by D2. That is, at any price level, the magnitude of the elasticity of demand is greater for D1 than 

for D2. 

Figure 1: Relative Elasticity

The 

graphs in Figure 2 represent two special cases of (or limits to) price elasticity of demand. First, 

Figure 2a represents perfectly elastic demand. In this case the demand curve for the seller’s 

product is horizontal and εd = -∞. The seller has many competitors, each selling a product which 

is completely acceptable by the consumer as a substitute for the seller’s product. Consequently, 

the seller has no pricing power because any increase in price would result in the loss of all the 

seller’s sales to its rivals. The second limiting case, illustrated in Figure 2b is perfectly inelastic 

demand. With perfectly inelastic demand, εd = 0 and the demand curve is vertical. That is, there 

would be no check on the ability of the seller to raise price. Perfectly inelastic demand for a 
9

seller’s good would require that the seller have no competitors and that the good be an 

absolute necessity at the observed quantities demanded. 

Figure 2: Perfectly Elastic Demand and Perfectly Inelastic Demand

(a) (b)

Perfectly Elastic Demand Curve Perfectly Inelastic Demand Curve 

Both of these special cases are hypothetical cases that exist mainly in theory. Perfectly elastic 

demand may be approximately accurate when there are many sellers selling a commodity and 

there are low barriers to entry into and exit from the industry. Perfectly inelastic demand, on 

the other hand, is a more unrealistic extreme. Even a pure monopolist will face demand 

elasticity as consumers have ability to just consume less of the good as price rises.5

 

II.B. Household and Business Demand for Postal Services

Households use postal services for many reasons. These include personal correspondence, 

business purchases, bill payments, and the transfer of materials to other persons. The demands 

for these postal services by individuals are founded in the behavior of households as they 

choose how to save, or to spend incomes across the vast array of goods and services. 

Economists see the household’s objective as one of attaining the maximum satisfaction (also 

called utility) possible given an income or budget. 

Some household consumption of postal services, such as writing a personal letter, directly 

produces satisfaction. Other uses of postal services, such as paying a utility bill, do not produce 

satisfaction in and of themselves, but are intermediate goods used in the process of obtaining 

final consumption goods, such as air conditioning. To the extent that use of a postal service is 

an intermediate input, then the demand determinants and properties are derived from the 

 5 When we observe zero or positive own price elasticities empirically, as in the rolling coefficient analyses in 

Section IV, below, we would normally view those as examples of regression model “failure.” However, it is possible 

both that demands are highly inelastic over some ranges of prices and/or highly inelastic in the short run.
10

demand for the final product and are thus similar to the business demand for postal services 

discussed below.6

 

Businesses use postal services as inputs in the process of making and marketing their products. 

The business demands for postal services include direct mail (solicitation and advertising), 

merchandise transport, business and legal communications, and bill presentation. The demands 

for these postal services are founded in the behavior of businesses pursing their objectives. 

Consequently, the demand for an input of production is derived from the demand for the final 

product and also from the supply of other factors of production. This theory of derived 

demand, first developed by Alfred Marshall,7 typically assumes the business is an enterprise 

that produces and sells its product in an effort to achieve maximum profit. However, even if the 

firm is a not-for-profit enterprise pursuing some other objective, its demand for inputs is still 

derived from the final product market.8

II.C. Determinants of the Price Elasticity of Demand

There are several factors that determine the elasticity of demand for a good. Demand 

determinants commonly include:

• Availability of substitutes 

• Necessity 

• Importance in budget or share of production cost

• Consumer loyalty and extent of product differentiation

• Macroeconomic variables

• Time

We examine determinants of the price elasticity of demand further in Appendix A.

II.D. The Distinction between a Change in Demand and a Change in the Elasticity of Demand

It is important to note that a change in demand does not necessarily mean a change in the 

elasticity of demand. Specifically, a decrease in demand does not necessarily imply that 

demand has become more elastic. This is illustrated by the graphs in Figure 3. A decrease in 

demand is represented by the demand curve shifting to the left. Figure 3a depicts a parallel 

shift in the demand curve. In this case at any price, demand is more elastic after the decrease in 

demand. In contrast, Figure 3b represents a decrease in demand where the demand curve has 

rotated somewhat to become relatively less elastic after the decrease in demand. In this case, 

the elasticity measure at a given price has decreased in magnitude. This could be the result of 

 6 A considerable literature exists on household production. A seminal article is Richard F. Muth, "Household 

Production and Consumer Demand Functions,” Econometrica, Vol. 34, No. 3 (Jul., 1966), pp. 699-708. 7 Marshall, Alfred (1948). Principles of Economics (Eighth Edition). New York: Macmillan pp. 383-386. 8 A not-for-profit firm may have an objective of maximizing sales subject to remaining financially solvent. Even in 

this case, if the firm operates in a competitive market and/or with weak demand, pursing its objective may end up 

being close to maximizing profit.
11

the decrease in demand being the result of the departure of the more price sensitive 

customers. 

Figure 3: Demand Decreases and Impacts on Elasticity of Demand

(a) (b)

Demand elasticity increases Demand elasticity decreases 

The evidence is clear that there has been a decline in demand for postal services in recent 

years. However, the impact on the price elasticity of demand remains an empirical question. 

While it is clear in both cases that the demand curve has shifted, it may not be readily apparent 

from the change in quantities whether the demand curve has become steeper (less elastic) or 

flatter (more elastic). Reviewing the decline in demand against the determinants of elasticity 

also gives mixed signals. Readily available electronic substitutes would make demand for postal 

services more elastic. The recession may decrease demand and make demand more elastic as 

businesses view postage and printing bills as areas to extract cost savings. However, economic 

recovery may strengthen demand and lessen price elasticity. And if expenditures on postal 

services become a smaller share of household expenditures and business production cost, 

demand may become less elastic. Finally, as the Postal Service market share decreases, the 

impact on elasticity depends on which customers are being lost and which are being retained. If 

the alternative services draw away customers with relatively elastic demands, the remaining 

postal demand may be less elastic than before the market share loss. The issue is an empirical 

question and the answer will be in the data.
12

III. ECONOMETRIC ESTIMATION METHODS FOR POSTAL SERVICE DEMANDS

III.A. Postal Service Baseline Models

The Postal Service describes its demand equations as log-linear functions of the form:

ln Vt = β0 + ∑ εiln xi,t

N

i=1 + ut.

Vt is a volume measure; xi,t (i = 1 to N) are explanatory variables; ut is a residual (error) term; 

and β0 and εi (i = 1 to N) are parameters. The Postal Service indicates that its log-linear models 

have “been found to model mail volume quite well historically” and notes two “desirable 

properties” of the model. First, the model “satisfies traditional least squares assumptions” and 

can be estimated using ordinary least squares (OLS) regression methods. Second, the 

parameters can be directly interpreted as elasticities, so the estimate of εi is the elasticity of 

volume with respect to explanatory variable xi. In this model, the elasticities are constants that 

“do not vary over time, nor do they vary with changes to either the volume or any of the 

explanatory variables.”9

In fact, the constant-elasticity restriction can be relaxed with relatively simple variations on the 

log-linear model. Estimating the model over different sample periods effectively holds the 

elasticities constant over those periods. If the true elasticities are changing substantially over 

time, we would expect the estimated elasticities to vary when estimated over sufficiently 

different sample periods. Also, by including interactions between explanatory variables and 

time-related variables in the regression, time-varying effects can be included in the model. Our 

analysis makes use of both sample period variation and interaction-based model-structure 

changes to detect potential variations in the own price elasticities over time.

We used the models from the Postal Service’s January, 2012 filing of demand equations for 

market dominant products as the baseline for our analysis (“USPS baseline models”). Our 

analysis covers domestic First-Class Mail, Periodicals, and Standard Mail products.10

The USPS baseline models are descended from a line of ancestor models used to forecast 

volumes and revenues in Postal Reorganization Act rate cases. Accordingly, there is a longrunning history of own price demand elasticities derived under similar econometric methods, a 

portion of which is shown in Table 1, below. The exact specifications for the demand models 

have been subject to frequent revision with the goal of producing accurate demand forecasts. 

Thus, the history of elasticity estimates does not reflect a true constant methodology—major 

changes have been made to model specifications, and to the sets of products included in the 

 9 United States Postal Service, “Narrative Explanation of Econometric Demand Equations for Market Dominant 

Products Filed with Postal Regulatory Commission on January 20,2012,” p. 2. 

http://www.prc.gov/Docs/83/83424/NarrativeExplanationMarketDominant.doc. 10 We also extended the analysis through FY 2012 using the data set provided with the Postal Service’s January 

2013 demand model filing.
13

analysis. Nevertheless, the overall picture of the elasticity history is one of fairly stable, inelastic 

demands for the major market dominant products.

The USPS baseline models’ dependent variable is quarterly mail volume for a given product, 

normalized by the number of working days in the quarter and an estimate of the U.S. adult 

population. The latter normalization treats population growth as a constant source of 

exogenous demand pressure. The explanatory variables include measures of macroeconomic 

activity Mt,

11 a distributed lag of a “real” (CPI-deflated) price index Pt, and a number seasonal, 

trend, and “intervention” variables to capture the effects of other factors affecting mail 

volumes Zt. Thus the USPS baseline models can be written as:

Ln Vt = β0 + εM ln Mt + ∑ εiln Pt−i

4

i=0 + γ′Zt + ut.

The Postal Service’s demand models have had more explicit economic content in the past, 

including prices of other postal services (postal cross price effects), non-postal prices, and 

variables measuring factors such as Internet adoption that may drive electronic diversion. The 

Postal Service’s analysts have justified dropping these additional economic variables on the 

grounds that they do not help explain (or predict) mail volumes. Our view is that the current 

state of the Postal Service demand equations is justifiable by inherent challenges in measuring 

cross-price and Internet diversion effects. The theoretical desirability of including such effects is 

limited by data availability and limitations of regression modeling of low frequency time 

series.12

For example, simple measures of broadband Internet market penetration in the U.S. show 

adoption rates slowing even as postal volume losses from electronic diversion appear to be 

accelerating for some products. While the apparent disconnection between Internet adoption 

rates and diversion trends may be explicable—at least in theory—via factors such as long lags 

between adoption and mail volume effects, or hard-to-observe qualitative characteristics of 

electronic information services, incorporating such factors in the demand model may well be 

impractical. From the standpoint of accurately measuring the own price elasticity with an 

econometric analysis, the most important thing is that the model should include workable 

control variables to minimize the possibility that the own price elasticities partly reflect 

‘confounding’ effects due to correlation of the own price with other explanatory factors.

 11 The Postal Service develops trend and cyclical components of the macroeconomic variables using a HodrickPrescott filtering procedure. The baseline models vary in whether they specify trend and/or cyclical components. 

Our ECM specifications use unfiltered macroeconomic activity variables. 12 The regression samples range from 52 quarterly observations for First-Class Workshared Cards to 108 quarters 

for First-Class Single Piece Letters, Flats, and Parcels.
14

Table 1. Own Price Elasticity History

Class Subclass or Product Category 1990 1994 1997 2000 2001 2005 2006 2007 2008 2009 2010 2011 2012

First-Class 

Mail

Letters, Flats & Parcels (LFP) 0.245 0.188

Single Piece LFP 0.189 0.262 0.311 0.175 0.184 0.232 0.218 0.192 0.182 0.189

Single Piece Letters & Cards 0.090

Single Piece Flats 0.265

Workshared LFP 0.289 0.251 0.071 0.329 0.130 0.246 0.250 0.436 0.346 0.436

Workshared Letters, Flats, & Cards 0.392

Parcels 0.213

Postal Cards 1.242 0.248 0.168 0.761 0.808

Private Cards 1.242 0.985 0.944 0.860 1.157

Postcards 0.376

Single-Piece Postcards 0.258 0.110 0.117 0.397 0.249 0.063

Workshared Postcards 0.540 0.533 0.835 1.427 1.397 0.292

Periodicals

Regular Rate 0.291 0.145 0.143 0.148 0.166 0.193 0.294 0.245 0.260 0.082

Within County 0.546 0.395 0.530 0.142 0.157 0.235 0.141 0.165 0.152 0.207

Nonprofit 0.221 0.121 0.228 0.236

Classroom 1.305 0.994 1.178 0.407

Nonprofit &Classroom 0.092 0.237 0.212 0.258 0.330 0.276

Total 0.133 0.122 0.126

Standard 

Mail

Third Class Single Piece 0.476 0.484

Third Class Regular Bulk 0.624

Regular (Commercial non-ECR) 0.331 0.382 0.570 0.388 0.267 0.296 0.368 0.311 0.244 0.286 0.335 .0437

Enhanced Carrier Route (ECR) 0.662 0.598 0.808 0.770 1.093 1.079 0.771 0.911 0.839 0.727 0.782 .0704

Nonprofit Bulk/Nonprofit 0.258 0.442 0.136 0.162 0.230 0.319

Nonprofit 0.306 0.105 0.176 0.165 0.177 0.265 0.299

Nonprofit ECR 0.284 0.539 0.525 0.524 0.513 0.542 0.560

Source: Various PRC omnibus rate case and annual PAEA compliance filings. Elasticities are reported in absolute value.
15

A recent paper by Cigno, Patel, and Pearsall sharply criticized the USPS baseline models for 

omitting prices for other postal products (cross-price terms) from the demand equations, and 

indeed contends that all possible postal cross-prices should be entered into the demand 

equations to produce statistically valid elasticity estimates.13 This reflects the theoretical result 

that all prices in the demand system, including prices of non-postal substitutes, can appear in 

the demand function as a general matter. Cigno, et al., recognize that limitations of sample size 

and multicollinearity among price measures can make estimation of the full set of cross-price 

elasticities impractical using some methods. We note that there is also considerable room for 

postal analysts to apply a priori knowledge to exclude many cross effects. Many postal products 

have content or mailer restrictions that limit their substitutability, and others feature 

preferential rates that mailers will not find uneconomical in the presence of small rate changes. 

We also generally agree with the Postal Service’s analysts’ contention that major productsubstitution episodes tend to be driven by one-time events such as mail classification changes 

or broader changes to pricing structures rather than small price variations on the margin. 

Consequently, we do not regard the omission of postal cross prices to be a disqualifying defect 

for the USPS baseline models.

We view the Postal Service’s demand equations serve as a workable baseline for investigating 

whether own price elasticities of demand for market dominant products have changed over 

time. While it may be possible to implement somewhat richer econometric demand models, we 

must view the question of what explanatory variables belong in the models as ultimately an 

empirical matter that the Postal Serivce’s analysts have explored in some depth.

We did discover one significant econometric error in the code for the January 2012 USPS 

baseline models, which also affects the January 2013 demand filing. We discuss the error, and 

the underlying econometric issue, in the next section.

III.B. Nonstationarity and Error Correction Models

Implicit in the claim that the Postal Service demand equations satisfy “traditional least squares 

assumptions” is a significant qualification that the data—the dependent variable (volume) and 

explanatory variables—must be “stationary.” Data arising from stationary time series have 

stable distributions over time, at least after trends are removed from the data.14

A large body of research in time series econometric methods established that conventional OLS 

regression methods could be inappropriate when applied to non-stationary data.15 A classic 

problem, called “spurious regression,” occurs when a regression of y on x results in high R-

 13 Margaret M. Cigno, Elena S. Patel, and Edward S. Pearsall, “Estimates of U.S. Postal Price Elasticities of Demand 

Derived from a Random-Coefficients Discrete-Choice Normal Model,” p. 1. http://www.prc.gov/prcdocs/library/refdesk/techpapers/CignoPatelPearsall%20Paper_2761.pdf

14 A stationary time series satisfies a number of technical conditions, including having a constant expected value, 

bounded (finite) variance, and restrictions on the intertemporal correlation structure of the data.

15 For an intuitive and even entertaining discussion of nonstationarity and cointegration, see Michael P. Murray, “A 

Drunk and Her Dog: An Illustration of Cointegration and Error Correction.” The American Statistician, vol. 48(1), 

1994.
16

squared values and statistically significant coefficient estimates, because the variables are 

highly correlated, even when x does not have a causal effect on y. Regressing stationary 

variables on non-stationary variables (or vice-versa) also can lead to problems in large samples 

as the observed relationships may tend to zero (or infinity).16

Nonstationary variables are often described by the differencing that is required to produce a 

stationary result. A variable is “integrated of order 1” or I(1) if it is nonstationary but its first 

difference is stationary. Violations of stationarity assumptions are important in econometrics 

because economic theories predict that many macroeconomic and financial variables should 

follow nonstationary data generating processes. Significantly for the Postal Service’s demand 

analysis, these include quantities such as aggregate consumption, income, investment, and 

output, which serve as or are closely related to economic activity drivers in the demand models.

A common test of stationarity is the Augmented Dickey-Fuller (ADF) test. The test is based on 

the OLS regression:

Δyt = b0 + b1t + φyt−1 + ∑ γiΔyt−i

N

i=1 + ut

The null hypothesis of the ADF test is that yt is I(1), or φ = 0. The ADF test statistic is the tstatistic for φ from the above regression (the coefficient estimate divided by the OLS estimated 

standard error), though the ADF statistic does not follow a t distribution. Rejecting the null 

hypothesis implies that yt is stationary. However, the ADF test has been criticized as having low 

statistical power, that is, it may fail to reject the I(1) null hypothesis when the null is false and 

the data are stationary. Alternative test statistics, such as the KPSS test, establish trend 

stationarity as the null hypothesis against which the presence of a unit root is the alternative.17

Two variables xt and yt that are I(1) are said to be “cointegrated” if a linear combination of the 

variables is stationary. That is, we can write:

yt − βxt = ut,

with ut stationary. When xt and yt are cointegrated, the variables are related by an “error 

correction model” (ECM) of the form:

∆yt = α0 + θ∆xt + φ(yt−1 − βxt−1) + et.

The ECM differs from a regression of y on x in first differences by inclusion of the “equilibrium 

error” term yt−1 − βxt−1, which is the effect of y and x being out of their “equilibrium” 

 16 See, e.g., James H. Stock and Mark W. Watson, “Variable Trends in Economic Time Series.” Journal of Economic 

Perspectives, Vol. 2(3), 1988, p. 163-167. 17 Denis Kwiatkowski, Peter C.B. Phillips, Peter Schmidt, and Yongcheol Shin, “Testing the null hypothesis of 

stationarity against the alternative of a unit root.” Journal of Econometrics, vol. 54, 1992.
17

relationship. The differenced variables and the equilibrium error term are all stationary, so the 

ECM can be estimated via least squares regression methods.18

The Postal Service’s analysts clearly have been aware of the potential for nonstationarity of the 

demand data. The demand model filings report ADF test results for the volume variables 

employed in the demand models, and for the demand models’ residuals. The reported test 

results have rejected the null hypotheses of nonstationarity, and thus ostensibly justified the 

use of traditional regression methods for stationary time series.

However, while reviewing the Postal Service’s estimation code, we found major errors in the

implementation of the ADF tests. The econometric code filed in January 2012 had errors in both 

the implementation of the ADF regression and the calculation of the ADF t-statistic. The code in 

the January 2013 filing corrected the regression specification but not the t-statistic calculation. 

We computed the results of ADF tests for the volumes, unfiltered economic activity variables, 

and prices in the demand equations we studied, based on a corrected version of the ADF test 

implemented in the Postal Service’s demand model filing.19 We also conducted a set of parallel 

tests using the KPSS statistic. We used the Johansen trace statistic to test for the presence of 

cointegtration where the stationarity testing indicated the data to be I(1).20 Results are 

provided in Table 2, below. 

The ADF tests uniformly fail to reject the null hypothesis of nonstationarity for the volumes of 

market dominant products and for the economic activity variables. Results for prices are mixed. 

The ADF tests reject the I(1) null hypothesis in favor of stationarity at the 10 percent 

significance level (or better) for Standard Mail prices except for Nonprofit Standard Mail 

Regular (non-ECR). Additionally, the ADF statistics for Periodicals, First-Class Single Piece 

Letters, and First-Class Workshared Cards prices are very close to the 10 percent critical values. 

The KPSS test statistics also reject the null of trend stationarity for the volumes and economic 

activity variables; they also tend to reject trend stationarity for the price variables.

 18 Variations on the ECM include seasonal differencing (sometimes applied to quarterly data, where the SPLY 

difference yt - yt-4 may be more economically significant than the first difference), and the inclusion of stationary 

regressors and additional lags of the I(1) variables. The ECM is a type of autoregressive model that also can be used 

to analyze stationary data.

19 The volumes and prices were transformed, and natural logarithms taken of the transformed variables, as in the 

econometric demand models. We tested the unfiltered economic activity variables in natural logarithms.

20 S. Johansen, Likelihood-Based Inference in Cointegrated Vector Autoregressive Models. Oxford University Press, 

1995, chapters 11-12.
18

Table 2. Results of Stationarity and Cointegtration Tests for Postal Service Demand Variables

Table 2a. KPSS and Augmented Dickey-Fuller Tests for Stationarity

H0: Variable is Trend 

Stationary H0: Variable is I(1)

Product/Variable KPSS Statistic p-Value ADF Statistic p-Value

1. Volumes

Commercial Standard Mail Regular 0.44 < 0.01 -1.21 0.909

Commercial Standard Mail ECR 0.41 < 0.01 -2.42 0.369

Nonprofit Standard Mail Regular 0.34 < 0.01 -1.23 0.904

Nonprofit Standard Mail ECR 0.41 < 0.01 -2.54 0.310

First-Class Single Piece Letters 0.70 < 0.01 2.02 1.000

First-Class Workshared Letters 0.47 < 0.01 -0.66 0.976

First-Class Single Piece Cards 0.54 < 0.01 1.06 1.000

First-Class Workshared Cards 0.37 < 0.01 -1.39 0.865

Periodicals 0.44 < 0.01 -0.11 0.993

2. Price Indexes

Commercial Standard Mail Regular 0.14 < 0.1* -3.76 0.019

Commercial Standard Mail ECR 0.19 < 0.025*** -4.26 0.004

Nonprofit Standard Mail Regular 0.19 < 0.025*** -2.60 0.282

Nonprofit Standard Mail ECR 0.12 < 0.1* -3.24 0.076

First-Class Single Piece Letters 0.20 < 0.025*** -3.13 0.099

First-Class Workshared Letters 0.29 < 0.01 -2.24 0.465

First-Class Single Piece Cards 0.26 < 0.01 -2.09 0.554

First-Class Workshared Cards 0.13 < 0.1* -3.03 0.123

Periodicals 0.16 < 0.05** -3.01 0.130

3. Economic Activity Variables

Investment (1988Q1-2012Q4) 0.45 < 0.01 -1.35 0.876

Employment (1983Q1-2012Q4) 0.54 < 0.01 -1.59 0.796

* Reject H0 at 10% significance level but not 5%

** Reject H0 at 5% significance level but not 2.5%

*** Reject H0 at 2.5% significance level but not 1%

Table 2b. Johansen Trace and Maximum Eigenvalue Tests for Cointegration (H0: Cointegrating Rank is 0)

Product

Trace 

Statistic p-Value

Max 

Eigenvalue 

Statistic p-Value

Estimated # 

of 

cointegrating 

vectors

Commercial Standard Mail Regular 18.04 < 0.05 15.47 < 0.05 1

Commercial Standard Mail ECR 37.58 < 0.01 27.39 < 0.01 1

Nonprofit Standard Mail Regular 95.15 < 0.01 84.86 < 0.01 1

Nonprofit Standard Mail ECR 26.47 < 0.01 23.87 < 0.01 1

First-Class Single Piece Letters 41.51 < 0.01 25.10 ~0.01 1-2*

First-Class Workshared Letters 47.87 < 0.01 36.00 < 0.01 1

First-Class Single Piece Cards 29.35 ~0.05 18.87 > 0.05 1

First-Class Workshared Cards 18.70 < 0.05 10.05 > 0.05 1

Periodicals 12.79 > 0.05 12.79 > 0.05 0-1**

* Higher p-value for 2 cointegrating vectors

** Can reject H0 on sample through FY 2011
19

The result that the price variables are not trend stationary is somewhat counterintuitive. Over 

the long run, indexes of U.S. postal prices have not tended to diverge significantly from the 

Consumer Price Index (CPI). To the extent the fixed-weight price indexes for the postal products 

are proportional to CPI, then their ratio—the “real” price—would be stationary. The CPI price 

caps under PAEA would be expected to impose such a relationship for the product aggregates 

where the caps apply; pre-PAEA pricing policies may have served to limit divergence between 

some Postal Service rates and CPI as well.21 On the other hand, pre-PAEA price adjustments led 

to occasional large changes in “real” prices, and the PAEA caps do not necessarily constrain 

prices at the product level (within classes) to CPI.

The Johansen trace tests showed the volumes, prices, and economic activity variables to be 

cointegrated for the products under study, generally with a single cointegrating vector. The 

main exception was Periodicals, where the trace test could not reject the hypothesis of no 

cointegration for the full sample (1993 Q1-2012 Q4) at a p-value of 0.05, though other tests 

showed the presence of a cointegrating vector.22

Given the results in Table 2, we conducted our analysis using both a modified USPS baseline 

model and ECM implementations of the Postal Service demand equations. Because the USPS 

baseline models have been the source of official demand elasticities, the behavior of those 

models may still be of interest. Additionally, since there is much less experience with ECM 

specifications for USPS demand models than with the USPS baseline models, understanding the 

current models’ (mis)behavior under alternative samples and other specification changes may 

provide a useful yardstick for evaluating the performance of the ECMs.

III.C. Modified USPS Baseline Demand Models

While the Postal Service demand models are based on log-linear demand functions, the specific 

econometric implementation of the models introduce some nonlinearities and multi-step 

estimation procedures. To avoid some computational issues with the rolling and recursive 

parameter analyses, we employed one-step linear models that yield very similar results to the 

Postal Service’s filed models.

One set of changes concerns the distributed lag of price variables on the right-hand side of the

regression equation. Since the current and lagged prices are highly intercorrelated, 

unconstrained estimates of the coefficients for the distributed lag are often highly volatile; 

 21 The lower frequency of rate cases under the Postal Reorganization Act tended to result in larger nominal 

increases than the more frequent but smaller rate changes under the PAEA price cap system, but the effects of 

inflationary erosion of the real value of the increases leave relatively little long-run trend in the real fixed-weight 

price indexes for the products under study in either the PRA or PAEA periods. A recent study found that UK postal 

prices deflated by the Retail Price Index (RPI) were stationary or I(0). The study noted that UK postal prices have 

subject to an RPI-X price cap since 2003. See Leticia Veruete-McKay, Soterios Soteri, John Nankervis, and Frank 

Rodriguez, “Letter Traffic Demand in the UK: An Analysis by Product and Envelope Content Type,” Review of 

Network Economics, Vol. 10(3), September 2011. 22 These included the Johansen maximum eigenvalue test and the trace test performed on the subset of data 

through FY 2011.
20

anomalous results such as large positive elasticities are not uncommon. We used a polynomial 

distributed lag (PDL) model, which constrains the coefficients of the distributed lag to fall on a 

second-order (quadratic) polynomial. The PDL model can be implemented as a set of linear 

constraints on the demand model parameters. The Postal Service’s approach uses a method 

which does not require the coefficients to fall exactly on the lag polynomial (called the Shiller 

“smoothness prior” method), but which requires setting a parameter in advance of the model 

estimation. Postal Service analysts had previously reported that the Shiller method and the PDL 

model produce similar results.23 Additionally, we use four lags of the price index variable for all 

products. In some cases, the Postal Service’s baseline models constrain the elasticities to zero 

for certain lags. While the criteria for lag selection are not explained in the Postal Service’s 

recent filings, we expect that the primary motivation was to avoid cases where the elasticities 

for certain lags had the “wrong” sign. In a number of cases, we found that the estimated 

elasticities for lags that were set to zero in the Postal Service models were not anomalous. 

The other change concerns nonlinear “interventions” included in the demand models for some 

(but not all) products. The interventions are included in the models to reflect the effects of 

exogenous determinants of demand that are not otherwise measured, such as electronic 

diversion effects. The interventions generally take the form:

It = ω0Pt + ω1(Pt−1 + δPt−2 + δ2Pt−3 + ⋯ ) + ω2St + ω3Tt.

24

It is linear in the variables Pt, St, and Tt, but nonlinear in the parameters due to the coefficient δ

on the lagged pulse terms. We used the Postal Service’s estimates of δ to compute “decay” 

variables:

Dt = Pt−1 + δ̂Pt−2 + δ̂2Pt−3 + ⋯

and we estimated the other transfer function parameters using:

It = ω0Pt + ω1Dt + ω2St + ω3Tt.

In some models, notably for single piece and workshared First-Class Mail letters, flats, and 

parcels, the interventions in the Postal Service models assume (at least) ω1 = 0, in which case 

our implementation is not restricted relative to the Postal Service baseline models.

Finally, the Postal Service models incorporate a Cochrane-Orcutt transformation of the data to 

adjust for autocorrelation of the regression residuals. This involves obtaining an estimate of the 

residual autocorrelation coefficient from an OLS regression, transforming the data, and rerunning the regression using the transformed data. Since the transformation is not required to 

obtain consistent coefficient estimates, we omitted it. However, standard variance formulas are 

 23 Postal Rate Commission, Docket No. R90-1, Direct Testimony of George S. Tolley (USPS-T-2), pages I-43 to I-46. 24 United States Postal Service, “Narrative Explanation of Econometric Demand Equations for Market Dominant 

Products Filed with Postal Regulatory Commission on January 20,2012,” p. 11.
21

not appropriate for OLS coefficient estimates are inappropriate when the disturbances are 

autocorrelated. We computed standard error estimates using heteroskedasticity- and 

autocorrelation-consistent methods.

We based our modified baseline models on the Postal Service’s January 2012 demand model 

filing with the Postal Regulatory Commission, which incorporated data through the end of 

FY2011. We extended our analysis through FY2012 using the dataset provided with the Postal 

Service’s January, 2013 demand model filing. We maintained the January 2012 methodology, to 

the extent possible, in extending our models into FY2012. An exception is that we added 

dummy variables, trends, or other interventions for events specific to FY2012, which would 

have been unobservable in the data through FY2011. We found that adding FY2012 

observations to the FY2011 models had little effect on the own price elasticities for the full 

sample periods.

The long-run elasticity estimates from the USPS filings and our modified baseline models are 

reported in Table 3, below. The results are qualitatively and quantitatively quite similar. Note 

that since there were a number of changes in the January 2013 USPS baseline models over 

2012, results from the most recent USPS baseline models are not directly comparable in a 

number of cases.

Table 3. Comparison of Long-Run Own Price Elasticities from USPS Demand Models and LRCA 

Modified Baseline Models, Full Sample Periods Ending Q4 FY2011 and Q4 FY2012

Long-Run Own Price Elasticities (Standard Errors in Parentheses)

USPS Baseline Modified Baseline

Product

First Sample 

Quarter [1]

January 2012 

(Data through 

FY2011)

January 2013 

(Data through 

FY2012)

Data through 

FY2011

Data through 

FY2012

Standard Regular FY1988,PQ1 -0.335 -0.437 -0.354 -0.359

(0.109) (0.102)

Standard ECR FY1988,PQ1 -0.782 -0.704 -0.777 -0.782

(0.051) (0.053)

Standard Nonprofit FY1988,PQ1 -0.265 -0.299 -0.302 -0.293

(0.087) (0.095)

Standard Nonprofit ECR FY1988,PQ1 -0.542 -0.560 -0.568 -0.618

(0.136) (0.112)

Periodicals FY1993,PQ1 -0.122 -0.126 -0.069 -0.104

(0.027) (0.039)

First-Class Single Piece Cards [2] FY1989,PQ1 -0.062 n/a 0.008 -0.005

(0.067) (0.067)

First-Class Workshared Cards [3] FY2000,PQ1 -0.291 n/a -0.395 -0.504

(0.168) (0.109)

First-Class Single Piece Letters [4] FY1983,PQ1 -0.189 -0.090 -0.331 -0.347

(0.036) (0.036)

First-Class Workshared Letters [5] FY1994,PQ1 -0.434 -0.391 -0.449 -0.456

(0.040) (0.040)

Notes

[1] USPS January 2012 models

[2] Combined with First-Class Single-Piece Letters in January 2013 USPS Baseline

[3] Combined with First-Class Workshared Letters in January 2013 USPS Baseline

[4] Includes cards, and excludes flats and parcels, in January 2013 USPS baseline

[5] Includes cards, and excludes workshared parcels, in January 2013 USPS baseline
22

III.D. Error Correction Models

As noted above, when we correctly implemented ADF and cointegration tests for Postal Service 

volumes and other economic data in the demand model, we could not reject the null 

hypothesis that the variables were nonstationary and cointegrated. Accordingly, we 

investigated ECM specifications of the Postal Service’s demand models.

The primary ECM specification we employed treats the volume, price index, and economic 

activity variables as I(1) and cointegrated, based on the test results reported in Tables 2a and 

2b. The estimating equations have the form:

Δ ln Vt = α0 + φ(ln Vt−1 − β1 ln Mt−1 − β2 ln Pt−1) + θ1Δ ln Mt + θ2Δ ln Pt + α′

Zt + et.

Where Vt is the normalized volume, Xt is the unfiltered economic activity variable, Pt is the own 

price index, and Zt includes seasonal, trend, intervention, and any other control variables. The 

coefficient β2 is interpreted as the long-run (equilibrium) own price elasticity, while θ2 is a 

short-run adjustment effect with respect to the own price.25

The long-run elasticity estimates from the ECMs are reported in Table 4, below. Results are 

qualitatively similar to the USPS baseline models. The demand elasticities are less than one in 

absolute value, and thus provide a broadly similar picture of inelastic demands to the baseline 

models. Products with relatively large (more elastic) demands in the USPS baseline models, 

such as Commercial and Nonprofit Standard Mail ECR, also have somewhat larger own price 

elasticities in the ECMs.

 25 We also investigated a second ECM specification suitable for cases where the price index is stationary, with the 

volume and economic activity variables cointegrated. This model included volume and the economic activity 

variable in the equilibrium error, and a polynomial distributed lag of prices (in levels) like the modified baseline 

model. We found generally similar results from this model, the baseline model, and the main ECM specification.
23

Table 4. Long-run Own Price Elasticities from Error Correction Models, Full Sample Periods Ending Q4 

FY2011 and Q4 FY2012

Long-RunOwn Price Elasticities (Standard Errors in Parentheses)

Baseline Models Error Correction Model

Product

USPS Baseline, 

January 2012

LRCA Modified, 

Data through 

FY2011

Data through 

FY2011

Data through 

FY2012

Standard Regular -0.335 -0.354 -0.306 -0.312

(0.109) (0.101) (0.094)

Standard ECR -0.782 -0.777 -0.555 -0.549

(0.051) (0.111) (0.093)

Standard Nonprofit -0.265 -0.302 -0.191 -0.180

(0.087) (0.030) (0.031)

Standard Nonprofit ECR -0.542 -0.568 -0.577 -0.589

(0.136) (0.082) (0.069)

Periodicals -0.122 -0.069 -0.085 -0.114

(0.027) (0.017) (0.027)

First-Class Single Piece Cards -0.062 0.008 -0.203 -0.179

(0.067) (0.100) (0.091)

First-Class Workshared Cards -0.291 -0.395 -0.347 -0.683

(0.168) (0.229) (0.105)

First-Class Single Piece Letters -0.189 -0.331 -0.151 -0.144

(0.036) (0.045) (0.047)

First-Class Workshared Letters -0.434 -0.449 -0.385 -0.393

(0.040) (0.034) (0.030)

IV. TESTING STABILITY OF OWN PRICE ELASTICIITES

IV.A. Rolling and Recursive Coefficient Analysis

The standard theory of linear regression analysis posits an estimating equation that holds over 

the entire sample period:

yt = xt ∙ β + ut,t = 1, ⋯ , T;

where xt and β are K x 1 vectors of explanatory variables and parameters, respectively, ut is a 

random disturbance term uncorrelated with xt and with zero mean, and T > K. As noted above, 

the Postal Service demand equations make this type of structural assumption, with the 

implication that the elasticities (the coefficients) are constant over the sample period. Of 

course, if the regression equation holds for the full sample, it also holds for every subsample:

yt = xt ∙ β + ut,t = t1, ⋯ ,t2; 1 ≤ t1 < t2 ≤ T.

Regression estimates of β from the full sample and subsamples will, under the standard 

assumptions, equal the “true” value of β plus a mean-zero error—i.e., the estimates will be 

unbiased. However, estimates from shorter subsamples will tend to have larger error variances 

compared to longer subsamples. If the coefficients are, in fact, constant over the sample 

period, then graphs of estimates taken from a series of adjacent subsamples will show an 
24

absence of a trend, since the estimates will be a constant (the “true” parameter value) plus 

noise. The noise term will tend to have a larger standard error for shorter subsamples.

“Rolling” and “recursive” coefficient analyses employ coefficient estimates from sequences of 

adjacent subsamples to investigate the stability of regression coefficients. The methods differ in 

the sequences of subsamples, and have advantages and disadvantages in identifying certain 

types of changes to the coefficients.

In the “rolling” analysis, the first subsample begins at period 1 and ends at period T0, where 

K<T0<T. T0 is sometimes called the “window” length for the rolling analysis. The second 

subsample consists of the T0 observations from period 2 to period T0+1, and so on, until the 

final subsample of T0 observations ends in period T. The “recursive” analysis starts with the first 

T0 observations, like the rolling analysis, but subsequent subsamples do not drop the early 

observations. Thus the second subsample is from period 1 to period T0+1, and so on, until the 

last recursive subsample is the full sample from period 1 to period T. The recursive analysis 

shows the effect of adding observations to the end of subsequent samples, and ends with the 

full-sample estimate. Finally, a “reverse recursive” analysis shows the effects of dropping 

observations from the start of the full sample period. It starts with the full sample t=1,...,T, and 

drops early observations from subsequent subsamples, so that the second subsample is from 

period 2 to period T, and the last subsample is estimated over the final window of length T0

ending at T—i.e., the final subsample from the rolling analysis.

Rolling and reverse recursive analysis will tend to be more sensitive to changes in the 

coefficients in later time periods, compared to the recursive analysis, since later rolling and 

reverse recursive subsamples drop observations from early in the sample that might reflect a 

different underlying model structure. However, the estimates from rolling subsamples will tend 

to be “noisier” than the longer subsamples for the recursive analysis as the shorter sample 

periods compared to the recursive analysis will tend to increase the sampling variance of the 

coefficient estimates. Conversely, retaining earlier data tends to reduce the variance of the 

coefficient errors in longer recursive subsamples (which approach the full sample period), but 

may attenuate the effects of structural changes.

All three methods are limited in that the shortest subsample that can be estimated is K+1 

periods, where K is the number of explanatory variables in the model. In practice, the shortest 

subsamples that produce reasonable results may be much longer. If a regression model using 

quarterly data has 19 explanatory variables, then the minimum sample window is 20 quarters, 

or five years’ worth of data. This may not be sufficient to draw out changes that may have 

occurred near the end of the full sample period. Indeed, the USPS baseline models typically 

have upwards of 20 explanatory variables, most of which are seasonal, trend, and intervention 

terms. We ran the rolling and recursive analysis using windows of 40 and 60 quarters. We found 

some elasticity estimates using 40-quarter sample windows to be highly volatile, though the 

recursive coefficient analyses showed relatively stable elasticities using both the modified USPS 

baseline models and ECM specifications.
25

IV.B. Results of Rolling and Recursive Parameter Analysis

The rolling and recursive analyses of the USPS baseline and ECM demand model specifications 

show some model instability over some rolling subsamples, while the recursive analysis shows 

relatively stable own price elasticities as the sample periods are lengthened. With a few 

exceptions, most of the instability of the elasticities in the rolling samples is in the direction of 

zero elasticity rather than larger elasticities.

IV.B.1. Commercial Standard Mail Regular

Figures 4a and 4b show long-run elasticities for Commercial Standard Mail Regular from rolling 

and recursive analysis using the modified USPS baseline and the ECM specification, respectively. 

In these graphs (and similar figures for other products), we show the end period for the rolling 

and recursive samples. This helps identify whether apparent trend breaks correspond with the 

inclusion of data from periods of interest such as the Great Recession.26

In both models, the own price elasticities from nearly all of the rolling samples are smaller than 

in the recursive samples. This indicates that including older observations does not necessarily 

result in less elastic measured demands; in this case, the older data appear to be keeping the 

measured elasticities larger than they would be with more recent samples.

The 60-quarter rolling samples through the sample ending in FY2009 quarter 1 are mostly 

between about -0.15 and -0.25.27 Beginning with the sample including FY2009 quarter 2—i.e., 

quarter 1 of calendar 2009, the quarter following severe financial-market disruptions prior to 

the 2008 election—the rolling samples jump towards zero, and mostly stay in the vicinity of 

zero or produce “wrong sign” elasticities. However, the 40-quarter rolling samples show 

increased volatility prior to the onset of the recession. The recursive samples are much more 

stable over time in all models, though a shift to smaller elasticities at FY2009 quarter 2 is still 

visible in the graphs. Cumulative sum (CUSUM) test indicate a possible structural break in both 

the baseline and ECM models, though the results are not statistically significant. 

The timing of the shifts in the Commercial Standard Mail Regular elasticities could reflect 

uncontrolled effects of the Great Recession. The January 2012 USPS baseline model includes a 

nonlinear intervention variable to capture Great Recession effects on volume. However, the 

start period for the intervention is FY2008 quarter 2, so the intervention variable does not 

account for the worsening recession in FY2009.28 Another possible factor is that the included 

macroeconomic activity variable, investment, has diverged from Commercial Standard Mail 

Regular volumes in the recovery.

 26 Note that the scales of the graphs are the same for each product, but owing to differences in the levels and 

variability of the results, not across products. 

27 A reverse recursive analysis shows that starting the sample slightly later than the FY1988 Q1 start of the sample 

for the USPS baseline model would also result in a smaller elasticity for Commercial Standard Mail Regular. 28 The NBER calendar date for the start of the recession was December, 2007, which is in quarter 1 of the 2008 

Postal Service fiscal year.
26

Figure 4a. Rolling and Recursive Analysis for Standard Regular, Modified Baseline

Figure 4b. Rolling and Recursive Analysis for Standard Mail Regular, ECM Version 1

Standard Mail Commercial Regular, Own-Price Elasticities from Rolling and Recursive Samples

Modified USPS Baseline

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

1997q41998q21998q41999q21999q42000q22000q42001q22001q42002q22002q42003q22003q42004q22004q42005q22005q42006q22006q42007q22007q42008q22008q42009q22009q42010q22010q42011q22011q42012q22012q4

Sample End Period

Long-Run Elasticity

Recursive Rolling40 Rolling60

Standard Mail Commercial Regular, Own-Price Elasticities from Rolling and Recursive Samples

Error Correction Model

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

1997q41998q21998q41999q2

1999q42000q22000q42001q22001q42002q22002q4

2003q22003q42004q22004q42005q22005q4

2006q22006q42007q22007q42008q22008q42009q2

2009q42010q22010q42011q22011q42012q22012q4

Sample End Period

Long-Run Elasticity

Recursive Rolling40 Rolling60
27

IV.B.2. Commercial Standard Mail Enhanced Carrier Route (ECR)

Figures 5a and 5b show long-run elasticities from rolling and recursive analyses for Commercial 

Standard Mail ECR. In contrast to the results for Commercial Regular, the rolling samples for 

Commercial ECR mostly produce larger elasticities than the recursive samples. A number of 

rolling samples for the both the USPS baseline model show results in the vicinity of unit 

elasticity.29 However, later rolling samples are closer to the recursive estimates. The recursive 

estimates are relatively stable over time, and show little evidence of trends. In the ECM, the 

rolling elasticities fluctuate in the vicinity of -0.8 for some time, with a large departure from 

trend for 40-quarter samples ending in FY2004 and FY2005, but eventually rejoin the recursive 

trend. Neither the rolling nor the recursive samples show signs of structural breaks in the 

elasticities associated with the Great Recession.

Figure 5a. Rolling and Recursive Analysis for Standard ECR, Modified Baseline

 29 CUSUM tests indicate a structural break around FY 1999-FY 2000, which is statistically significant in the ECM 

though not the baseline model.

Standard Mail Commercial ECR, Own-Price Elasticities from Rolling and Recursive Samples

 Modified USPS Baseline

-1.6

-1.4

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

1997q41998q21998q41999q21999q42000q22000q42001q22001q42002q22002q42003q22003q42004q22004q42005q22005q42006q22006q42007q22007q42008q22008q42009q22009q42010q22010q42011q22011q42012q22012q4

Sample End Period

Long-Run Elasticity

Recursive Rolling40 Rolling60
28

Figure 5b. Rolling and Recursive Analysis for Standard ECR, ECM Version 1

IV.B.3. Nonprofit Standard Mail Regular

Figures 6a and 6b show long-run elasticities from rolling and recursive analyses for Nonprofit 

Standard Mail Regular. Like Commercial Regular, the elasticities from the rolling samples are 

mostly smaller than the elasticities from recursive samples. In the ECM version, the rolling 

samples show some divergence from the recursive trend towards zero in the late PAEA period, 

then return to the recursive series during FY2009. The 40- and 60-quarter rolling elasticities 

from both the baseline model and ECM show considerable volatility in the last rolling samples, 

possibly indicating a FY2012 event that the January 2012 baseline models do not handle. The 

elasticities from the recursive samples show a slight trend towards smaller elasticities over time 

in the baseline model; the recursive elasticities from the ECM show little trend. There is no 

indication from CUSUM tests of significant structural breaks in the models. Unlike the other 

Standard Mail equations, the Nonprofit Regular equation includes an intervention variable 

dated to FY2009 quarter 2.

Standard Mail Commercial ECR, Own-Price Elasticities from Rolling and Recursive Samples

Error Correction Model

-1.6

-1.4

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

1997q41998q21998q41999q21999q42000q22000q42001q22001q42002q22002q42003q22003q42004q22004q42005q22005q42006q22006q42007q22007q42008q22008q42009q22009q42010q22010q42011q22011q42012q22012q4

Sample End Period

Long-Run Elasticity

Recursive Rolling40 Rolling60
29

Figure 6a. Rolling and Recursive Analysis for Standard Nonprofit, Modified Baseline

Figure 6b. Rolling and Recursive Analysis for Standard Nonprofit, ECM Version 1

Standard Mail Nonprofit Non-ECR, Own-Price Elasticities from Rolling and Recursive Samples

Modified USPS Baseline

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

1997q41998q21998q41999q21999q42000q22000q42001q22001q42002q22002q42003q22003q42004q22004q42005q22005q42006q22006q42007q22007q42008q22008q42009q22009q42010q22010q42011q22011q42012q22012q4

Sample End Period

Long-Run Elasticity

Recursive Rolling40

Rolling60

Standard Mail Nonprofit Non-ECR, Own-Price Elasticities from Rolling and Recursive Samples

Error Correction Model

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

1997q41998q21998q41999q21999q42000q22000q42001q22001q42002q22002q42003q22003q42004q22004q42005q22005q42006q22006q42007q22007q42008q22008q42009q22009q42010q22010q42011q22011q42012q22012q4

Sample End Period

Long-Run Elasticity

Recursive Rolling40

Rolling60
30

IV.B.4. Nonprofit Standard Mail ECR

Figures 7a and 7b show long-run elasticities from rolling and recursive analyses for Nonprofit 

Standard Mail ECR. Like Nonprofit Regular, the rolling samples mostly produce smaller 

elasticities than the longer recursive samples. The 40-quarter rolling samples from the baseline 

model show highly variable own price elasticities in late 2001 and early 2002, but similar 

volatility is not shown in the rolling samples from the ECM. The later rolling samples show some 

convergence with the recursive estimates, particularly in the ECM implementation in Figure 7b. 

The recursive elasticities are relatively stable, with evidence of a downward trend, though the 

elasticities show relatively little decline in recursive samples ending in FY2003 or later.

Figure 7a. Rolling and Recursive Analysis for Standard Nonprofit ECR, Modified Baseline

Standard Mail Nonprofit ECR, Own-Price Elasticities from Rolling and Recursive Samples

 Modified USPS Baseline

-1.6

-1.4

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

1997q41998q21998q41999q21999q42000q22000q42001q22001q42002q22002q42003q22003q42004q22004q42005q22005q42006q22006q42007q22007q42008q22008q42009q22009q42010q22010q42011q22011q42012q22012q4

Sample End Period

Long-Run Elasticity

Recursive Rolling40 Rolling60
31

Figure 7b. Rolling and Recursive Analysis for Standard Nonprofit ECR, ECM Version 1

IV.B.5. Periodicals

Figures 8a and 8b show long-run elasticities from rolling and recursive analyses for Periodicals. 

Since the full sample period is relatively short, we have relatively few replicate samples with the 

60-quarter rolling window, though the exercise does extend over the Great Recession quarters. 

The recursive elasticities show little variation, and while later recursive samples have slightly 

larger elasticities in absolute value, demand for Periodicals is highly own price inelastic. The 

rolling samples do not show a clear direction of divergence from the recursive samples, though 

they are somewhat volatile. Like the Standard Mail Regular model, the Periodicals model 

features a nonlinear intervention variable dated to FY2008 quarter 2, but not for the worsening 

conditions in FY 2009. Rolling samples from 40-quarter windows do not show systematic 

divergence from the recursive results; elasticities from 40-quarter rolling samples are more 

variable in the baseline model than the ECM.

Standard Mail Nonprofit ECR, Own-Price Elasticities from Rolling and Recursive Samples

Error Correction Model

-1.6

-1.4

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

1997q41998q21998q41999q21999q42000q22000q42001q22001q42002q22002q42003q22003q42004q22004q42005q22005q42006q22006q42007q22007q42008q22008q42009q22009q42010q22010q42011q22011q42012q22012q4

Sample End Period

Long-Run Elasticity

Recursive Rolling40 Rolling60
32

Figure 8a. Rolling and Recursive Analysis for Periodicals, Modified Baseline

Figure 8b. Rolling and Recursive Analysis for Periodicals, ECM Version 1

Periodicals, Own-Price Elasticities from Rolling and Recursive Samples

 Modified USPS Baseline

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

2002q42003q12003q22003q32003q42004q12004q22004q32004q42005q12005q22005q32005q42006q12006q22006q32006q42007q12007q22007q32007q42008q12008q22008q32008q42009q12009q22009q32009q42010q12010q22010q32010q42011q12011q22011q32011q42012q12012q22012q32012q4

Sample End Period

Long-Run Elasticity

Recursive Rolling40 Rolling60

Periodicals, Own-Price Elasticities from Rolling and Recursive Samples

Error Correction Model

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

2002q42003q12003q22003q32003q42004q12004q22004q32004q42005q12005q22005q32005q42006q12006q22006q32006q42007q12007q22007q32007q42008q12008q22008q32008q42009q12009q22009q32009q42010q12010q22010q32010q42011q12011q22011q32011q42012q12012q22012q32012q4

Sample End Period

Long-Run Elasticity

Recursive Rolling40 Rolling60
33

IV.B.6. First-Class Single Piece Letters, Flats, and Parcels

Figures 9a and 9b show long-run elasticities from rolling and recursive analyses for First-Class 

Single Piece Letters, Flats, and Parcels. There is little variation in the own price elasticities from 

the recursive samples. The rolling samples generally track the recursive trend in the baseline 

model. In Fig 9b, 60-quarter rolling samples using the ECM show the own price elasticity 

declining to zero in rolling samples that incorporate data from the Great Recession. However, 

we did not observe a similar trend in the recursive samples or 40-quarter rolling samples. Note 

that while the USPS baseline model includes trend variables to allow for accelerating electronic 

diversion of Single Piece First-Class Mail, it does not incorporate a Great Recession intervention 

variable in the style of the Periodicals and most of the Standard Mail models.

Figure 9a. Rolling and Recursive Analysis for Single Piece First-Class Mail, Modified Baseline

First-Class Single Piece Letters, Own-Price Elasticities from Rolling and Recursive Samples

 Modified USPS Baseline

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

1992q41993q21993q41994q21994q41995q21995q41996q21996q41997q21997q41998q21998q41999q21999q42000q22000q42001q22001q42002q22002q42003q22003q42004q22004q42005q22005q42006q22006q42007q22007q42008q22008q42009q22009q42010q22010q42011q22011q42012q22012q4

Sample End Period

Long-Run Elasticity

Recursive Rolling40 Rolling60
34

Figure 9b. Rolling and Recursive Analysis for Single Piece First-Class Mail, ECM Version 1

IV.B.7. First-Class Workshared Letters, Flats, and Parcels

Figures 10a and 10b show long-run elasticities from rolling and recursive analyses for First-Class 

Workshared Letters, Flats, and Parcels. Since the USPS baseline sample period is relatively 

short, we estimated the rolling regressions using only a 40-quarter window. The recursive 

elasticities are, as with other products, quite stable over successive samples, though the results 

for later recursive samples using the ECM show slight trends towards increasing elasticities. 

However, CUSUM tests do not indicate a significant structural break. The shorter rolling 

samples roughly track the recursive results for the USPS baseline model, though the samples 

ending in FY2012 show volatile results. The rolling samples for the ECMs mostly produce 

smaller elasticities than the recursive samples, and are volatile for samples ending in FY2012. As 

with First-Class Single Piece Letters, the First-Class Workshared Letters baseline model does not 

contain an intervention variable to account for effects of the Great Recession on volume.

First-Class Single Piece Letters, Own-Price Elasticities from Rolling and Recursive Samples

Error Correction Model

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

1992q41993q21993q41994q21994q41995q21995q41996q21996q41997q21997q41998q21998q41999q21999q42000q22000q42001q22001q42002q22002q42003q22003q42004q22004q42005q22005q42006q22006q42007q22007q42008q22008q42009q22009q42010q22010q42011q22011q42012q22012q4

Sample End Period

Long-Run Elasticity

Recursive Rolling40 Rolling60
35

Figure 10a. Rolling and Recursive Analysis for Workshared First-Class, Modified Baseline

Figure 10b. Rolling and Recursive Analysis for Workshared First-Class, ECM Version 1

First-Class Workshared Letters, Own-Price Elasticities from Rolling and Recursive Samples

 Modified USPS Baseline

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

2003q42004q22004q42005q22005q42006q22006q42007q22007q42008q22008q42009q22009q42010q22010q42011q22011q42012q22012q4

Sample End Period

Long-Run Elasticity

Rolling40 Recursive

First-Class Workshared Letters, Own-Price Elasticities from Rolling and Recursive Samples

Error Correction Model

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

2003q42004q22004q42005q22005q42006q22006q42007q22007q42008q22008q42009q22009q42010q22010q42011q22011q42012q22012q4

Sample End Period

Long-Run Elasticity

Rolling40 Recursive
36

IV.B.8. First-Class Single Piece Cards

Figures 11a and 11b show long-run elasticities from rolling and recursive analyses for First-Class 

Single Piece Cards. The USPS baseline model has recursive elasticities mostly in a narrow band 

around zero. The recursive elasticities from the ECM in Fig. 11b show negative elasticities 

gradually changing from about -0.4 to -0.2, with steps in FY2004 quarter 3 and FY2006 quarter 

3. However, the recent rolling samples in Fig. 11b diverged from the recursive samples and 

show near zero elasticities. The separate Single Piece Cards demand equation was dropped in 

the Postal Service’s January 2013 demand model filing

Figure 11a. Rolling and Recursive Analysis for Single Piece First-Class Cards, Modified Baseline

First-Class Single Piece Cards, Own-Price Elasticities from Rolling and Recursive Samples

 Modified USPS Baseline

-1.4

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1998q41999q21999q42000q22000q42001q22001q42002q22002q42003q22003q42004q22004q42005q22005q42006q22006q42007q22007q42008q22008q42009q22009q42010q22010q42011q22011q42012q22012q4

Sample End Period

Long-Run Elasticity

Recursive Rolling40

Rolling60
37

Figure 11b. Rolling and Recursive Analysis for Single Piece First-Class Cards, ECM Version 1

IV.B.9. First-Class Workshared Cards

Figures 12a and 12b show long-run elasticities from rolling and recursive analyses for First-Class 

Workshared Cards. We used a shorter estimation window, since the full sample period from the 

USPS baseline model uses fewer than 60 quarters of data. The 40-quarter window provides a 

limited trend showing the effects of adding relatively recent data to the regression samples. 

Some rolling samples show larger elasticities than the recursive samples, but the samples 

including FY2012 data yield volatile results. The ECM shows increasing elasticities in for 

recursive samples as FY2011 and FY2012 data are added, though the results from rolling 

samples shift in the opposite direction. The separate Workshared Cards demand equation was 

dropped in the Postal Service’s January 2013 demand model filing.

First-Class Single Piece Cards, Own-Price Elasticities from Rolling and Recursive Samples

Error Correction Model

-1.4

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1998q41999q21999q42000q22000q42001q22001q42002q22002q42003q22003q42004q22004q42005q22005q42006q22006q42007q22007q42008q22008q42009q22009q42010q22010q42011q22011q42012q22012q4

Sample End Period

Long-Run Elasticity

Recursive Rolling40 Rolling60
38

Figure 12a. Rolling and Recursive Analysis for Workshared First-Class Cards, Modified Baseline

Figure 12b. Rolling and Recursive Analysis for Workshared First-Class Cards, ECM Version 1

First-Class Workshared Cards, Own-Price Elasticities from Rolling and Recursive Samples

 Modified USPS Baseline

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

2009q42010q1

2010q2

2010q32010q4

2011q1

2011q22011q3

2011q42012q1

2012q2

2012q32012q4

Sample End Period

Long-Run Elasticity

Rolling40 Recursive

First-Class Workshared Cards, Own-Price Elasticities from Rolling and Recursive Samples

Error Correction Model

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

2009q4

2010q12010q22010q32010q42011q12011q22011q32011q42012q12012q22012q32012q4

Sample End Period

Long-Run Elasticity

Rolling40 Recursive
39

IV.C. Dummy Variable Interaction Models

The effects of explanatory variables in regression models can be allowed to vary, while 

remaining within the standard regression framework, by specifying some of the regressors as 

interaction variables. Consider a dummy variable Dt defined so that Dt =1 for t ≥T* and Dt =0 

otherwise, and the interaction variable Pt

∗ = Dt × ln Pt. Including Pt∗ in the baseline regression 

model gives (for instance):

ln Vt = α0 + ⋯ + ∑ βi ln Pt−i

4

i=0 + β∗Pt

∗ + α′

Zt + et.

In this model, the elasticity of demand with respect to the current-period price is β0 for t<T*

and β0 + β∗ for t ≥ T*. A version of the constant-elasticity hypothesis can be tested by testing 

whether β∗ = 0. An advantage of this method, compared to the rolling parameter analysis on a 

constant-elasticity model, is that it can potentially detect breaks for values of T* that may be 

much closer to the end of the available data than the shortest practical rolling window.

By defining other interaction variables, it is possible for the elasticities to have multiple 

structural breaks, be parametric functions of time, or depend on the values of other variables. 

Ultimately, the interaction exercise is limited by the available observations and the underlying 

variability of the data.

For the analysis of the demand models, the distributed-lag specification of prices in the USPS 

baseline model gives dummy variable interactions model essentially the same estimation 

problem caused by prices being highly correlated with their lags as in the original model. That 

is, we would expect unconstrained estimates of the interaction effects to be highly volatile. In 

principle, interactions should be introduced for the current and lagged prices, to allow all of the 

component coefficients of the long run elasticity to shift, so the model becomes:

ln Vt = α0 + ⋯ + ∑ βi ln Pt−i

4

i=0 + ∑ βi

∗

Pt−i

4 ∗ i=0 + α′

Zt + et.

If ln Pt and its lags are highly collinear, then we would expect Pt

∗ and its lags to be collinear as 

well, and thus we would have difficulty obtaining precise estimates of all of the βi

∗ coefficients. 

To mitigate the multicollinearity problem, we imposed restrictions so that the interaction 

coefficients represent a common shift of the PDL coefficients, so that the βi

∗ coefficients are the 

same for all i:

ln Vt = α0 + ⋯ + ∑ βi ln Pt−i

4

i=0 + ∑ β∗Pt−i

4 ∗ i=0 + α′

Zt + et.

We investigated three breakpoints with the dummy variable analysis: the first quarters of fiscal 

years 2008, 2009, and 2010. The FY2008 quarter 1 breakpoint includes the December, 2007 

NBER date for the start of the Great Recession. FY2009 quarter 1 includes months, notably 

October, 2008, of severe financial market disruptions. The latest breakpoint was intended to 

reflect possible later decoupling of Postal Service demand recovery from the general economic 
40

recovery. We implemented dummy variable interactions in the modified USPS baseline and the 

ECM models. In the ECM, we specified the interaction to allow a shift in the long-run elasticity.

Based on the rolling and recursive coefficient analyses, we would not expect to see structural 

breaks resulting in significantly higher own price elasticities in recent years. The dummy 

variable model results in Table 5a and 5b, below, confirm that the elasticities are little changed 

across breakpoints covering the Great Recession. We found that the interactions produced 

unusually large shifts in the elasticities in models where the interaction timing closely coincided 

with nonlinear intervention variables specified to capture recession effects. Thus, we do not 

report post-breakpoint elasticities for certain breakpoints.30 Otherwise, we found that the 

standard errors of the shift coefficients β∗ were relatively small—on the order of a few 

percentage points or less—so if there were large, systematic shifts in the elasticities, the 

models would appear to have been able to resolve any such shifts.

Table 5. Results from Dummy Variable Interaction Models

a. Modified USPS Baseline Model

Long-Run Own Price Elasticities

Breakpoint

Product Period FY2008Q1 FY2009Q1 FY2010Q1

Standard Regular No Break - Full Sample -0.354

Before Breakpoint -0.343 -0.347 -0.343

After Breakpoint * -0.346 -0.333

Difference * 0.001 0.010

Standard ECR No Break - Full Sample -0.780

Before Breakpoint -0.814 -0.768 -0.777

After Breakpoint -0.804 -0.774 -0.773

Difference 0.010 -0.005 0.005

Standard Nonprofit No Break - Full Sample -0.289

Before Breakpoint -0.274 -0.322 -0.350

After Breakpoint -0.294 * -0.390

Difference -0.020 * -0.040

Standard Nonprofit ECR No Break - Full Sample -0.617

Before Breakpoint -0.634 -0.636 -0.611

After Breakpoint * -0.551 -0.616

Difference * 0.085 -0.005

Periodicals No Break - Full Sample -0.071

Before Breakpoint -0.103 -0.066 -0.095

After Breakpoint * -0.086 -0.092

Difference * -0.020 0.004

First-Class Single Piece Cards No Break - Full Sample 0.013

Before Breakpoint 0.007 0.011 -0.012

After Breakpoint 0.022 0.001 -0.022

Difference 0.015 -0.010 -0.010

First-Class Workshared Cards No Break - Full Sample -0.383

Before Breakpoint -0.547 -0.255 -0.459

After Breakpoint -0.537 -0.335 -0.449

Difference 0.010 -0.080 0.010

 30 The FY2008 quarter 1 breakpoints are affected for Standard Regular, Standard Nonprofit ECR, and Periodicals, 

which incorporate interventions at FY2008 quarter 2; Standard Nonprofit (non-ECR) has a FY2009 intervention 

variable, affecting the FY2009 quarter 1 breakpoint.
41

First-Class Single Piece Letters No Break - Full Sample -0.275

Before Breakpoint -0.324 -0.344 -0.358

After Breakpoint -0.314 -0.359 -0.348

Difference 0.010 -0.015 0.010

First-Class Workshared Letters No Break - Full Sample -0.446

Before Breakpoint -0.442 -0.447 -0.455

After Breakpoint -0.445 -0.462 -0.452

Difference -0.002 -0.015 0.003

b. Error Correction Model

Long-Run Own Price Elasticities

Breakpoint

Product Period FY2008Q1 FY2009Q1 FY2010Q1

Standard Regular No Break - Full Sample -0.312

Before Breakpoint -0.308 -0.342 -0.312

After Breakpoint * -0.308 -0.313

Difference * 0.034 -0.001

Standard ECR No Break - Full Sample -0.549

Before Breakpoint -0.556 -0.543 -0.548

After Breakpoint -0.549 -0.545 -0.551

Difference 0.007 -0.002 -0.004

Standard Nonprofit No Break - Full Sample -0.180

Before Breakpoint -0.169 -0.189 -0.192

After Breakpoint -0.185 * -0.207

Difference -0.016 * -0.015

Standard Nonprofit ECR No Break - Full Sample -0.589

Before Breakpoint -0.574 -0.617 -0.589

After Breakpoint * -0.537 -0.589

Difference * 0.079 0.000

Periodicals No Break - Full Sample -0.114

Before Breakpoint -0.104 -0.119 -0.115

After Breakpoint * -0.115 -0.116

Difference * 0.003 -0.001

First-Class Single Piece Cards No Break - Full Sample -0.179

Before Breakpoint -0.187 -0.212 -0.185

After Breakpoint -0.181 -0.196 -0.180

Difference 0.006 0.016 0.005

First-Class Workshared Cards No Break - Full Sample -0.683

Before Breakpoint -0.544 -0.484 -0.680

After Breakpoint -0.568 -0.521 -0.681

Difference -0.023 -0.038 -0.001

First-Class Single Piece Letters No Break - Full Sample -0.144

Before Breakpoint -0.146 -0.161 -0.154

After Breakpoint -0.142 -0.182 -0.138

Difference 0.004 -0.021 0.016

First-Class Workshared Letters No Break - Full Sample -0.393

Before Breakpoint -0.379 -0.408 -0.392

After Breakpoint -0.373 -0.419 -0.395

Difference 0.005 -0.010 -0.003

* Not estimated due to conflict with intervention variable in baseline model; see text.
42

V. CONCLUSIONS

The significant volume losses of recent years have, understandably, led observers to consider a 

broad range of potential factors that may account for the declines, including increasing price 

sensitivity of mailers. Real U.S. postal rates have shown very little variation in recent years, and 

cannot themselves be a major factor of volume losses, compared to modal competition and 

recessionary drops in economic activity drivers. Nevertheless, it is possible that U.S. demands 

for postal services could have become more own price elastic with significant implications for 

pricing policies. The relatively long time periods needed for the estimation samples of the 

demand models, combined with constant elasticity assumptions in the log-linear demand 

equations, could in theory have attenuated changes in the own price elasticities.

We tested the stability of the Postal Service’s demand models for market dominant products 

both by varying the regression sample periods and by investigating whether there is evidence 

for recent structural breaks in the elasticity estimates. We found some technical deficiencies in 

the Postal Service’s baseline models related to time series properties of the volume and 

economic activity variables, and possibly also the price indexes. We recommend that the Postal 

Service’s analysts address these issues in future demand model updates.

We find no evidence that the Postal Service’s demand models are systematically understating 

own price elasticities of demand for the market dominant products we studied. Indeed, to the 

extent the analysis shows own price elasticities to be “in flux,” the changes are predominantly 

in the direction of lower own price elasticities. Additionally, the data do not suggest that the 

inclusion of older observations in the demand regressions result in smaller elasticity estimates. 

The overall picture is that while demands for market dominant postal products have shifted 

substantially due to a combination of factors other than postal prices, they remain own price 

inelastic.
43

APPENDIX A: PRICE ELASTICITY AND THE ECONOMIC STRUCTURE OF POSTAL DEMANDS

A.1. Pricing and the Importance of the Elasticity of Demand

The price elasticity of demand (εd ), a concept that measures consumers’ responsiveness to a 

change in the price of a good, is defined as the percentage change in quantity demanded (Qd ) 

resulting from a one percent change in price (P). That is, 

(A.1) εd = %∆Qd / %∆P = (∆Qd /∆P) (P/Qd ) ≤ 0.

From a seller’s point of view, the price elasticity of demand for that seller’s product is important 

information in the determination of price. The seller has less pricing power as demand for its 

product becomes more elastic. However, the impact on total revenue depends on the price 

elasticity of demand. Raising price would increase total revenue if demand is inelastic, but 

lower revenue if demand is elastic. Raising price also reduces total cost because of lower 

production. 

When demand is inelastic the seller can always increase profit by raising price -- total revenues 

would go up and total costs would go down, each effect contributing to the profit increase. 

However the case is not so clear when demand is elastic. A price decrease would increase 

revenue but also increase total cost as more output is produced and sold. Alternatively, with 

elastic demand, a price increase decreases both revenue and cost. Thus, in the case of elastic 

demand, the impact on profit from a price change depends on how the revenue and cost 

impacts net out. 

What we can conclude is that a profit-maximizing firm will operate in the elastic region of 

demand (again, the demand for its product) at a price point where any extra revenue that could 

be generated by lowering price would be just offset by the extra cost incurred.31 This is the 

familiar profit-maximization condition that “marginal revenue equals marginal cost.” 

Marginal revenue (MR) is the change in total revenue resulting from changing the quantity sold 

by one unit. As the discussion above suggests, marginal revenue is related to the elasticity of 

demand measure. That is,32

(A2) MR = P∙ (1 + 1/ εd )

Profit-maximization requires that marginal revenue equals marginal cost, 

(A3) MR = MC.

 31 This is also the point where the incremental revenue lost from raising price would be just offset by the reduction 

in cost. 

32 MR = ∆TR /∆Qd = ∆(P∙Qd) /∆Qd) = P∙ (∆Qd /∆Qd) + Qd ∙(∆P /∆Qd) = P (1 + (∆P /∆Qd)∙( Qd/P) = P∙ (1 + 1/ εd )
44

Substituting (A3) into (A2) and rearranging gives the profit-maximizing markup equation

(A4) (P – MC) / P = -1/ εd 

which is also known as the Lerner Index of Market Power.33 This measure shows that a firm’s 

ability to price above cost is inversely related to the elasticity of demand for its product.34

In the case where marginal cost is a constant, marginal cost and average variable cost are the 

same and multiplying the left-hand side of (A4) by Q/Q (=1) gives

(A5) Contribution/Revenue ≡ (TR – TVC)/TR = -1/εd.

That is, the inverse of the price elasticity of demand for the seller’s product indicates the 

seller’s ability to generate contribution as a share of revenue (or, equivalently, per unit margin 

as a share of price). If there is no fixed cost, then total variable cost is total cost and 

contribution is profit. 

For a firm selling multiple products and/or in multiple markets, where the products have 

independent demands and independent marginal costs,35 (A5) shows that each product’s ability 

to contribute a share of its revenues toward fixed cost recovery is inversely related to the price 

elasticity of demand for that product.36

In summary, the price elasticity of demand indicates a firm’s pricing power for a particular 

product and that product’s ability to generate profit or contribute to fixed cost recovery.

A.2. Determinants of the Price Elasticities of Household Demand

A change in price of a household good or service has two distinct effects on consumer demand. 

The substitution effect involves using more of a good whose relative price has decreased and 

less of a good whose relative price has increased. The extent to which substitution is possible is 

determined by the ability of one good to replace another good in terms of generating consumer 

satisfaction. When the price of a good increases, other things the same, the relative price of all 

other goods decrease and the consumer will use less of the good whose price increased and 

 33 Lerner, A. P. (1934). "The Concept of Monopoly and the Measurement of Monopoly Power". The Review of 

Economic Studies 1 (3): 157–175. 34 This result has been derived for the single-product profit-maximizing firm. A similar result can be derived for a 

multi-product not-for-profit firm with fixed costs. Also, closely related is the derivation of Ramsey pricing rules in 

which second-best efficient fixed cost recovery is achieved through greater price markups in markets with less 

elastic demand.

35 Independent demands means that the products are neither substitutes nor complements in consumption – the 

cross-price elasticities of demand are all zero. Independent marginal costs means that the products are neither 

substitutes nor complements in production – the cross-price elasticities of supply are all zero. 36 The mathematics are more complicated when demands are not independent. In that case, pricing power is 

inversely related to a “superelasticity of demand” involving the own- and the cross-price elasticities of demand. 
45

more of the other goods. Conversely, when the price of a good decreases, consumers will try to 

substitute it for other goods. 

The other effect of a price change is the income effect. As the price of a good goes up, the 

household has less purchasing power for the same budget. Consequently, to remain within its 

budget constraint a household has to reduce purchases overall. In most cases this means 

purchasing less of the good. When the price of a good decreases, the household has more 

purchasing power, and can increase the consumption of some or all goods while remaining on 

budget. Again, in most cases this means purchasing more of the good.37 

We can now identify and discuss some basic determinants of the household’s elasticity of 

demand for a good. 

A.2.a. Substitutes

Demand for a good is more elastic when it is feasible to substitute another good than when it is 

infeasible. Feasibility of substitution has two conditions. The first condition is technical 

substitution possibility. That is, can the same satisfaction be generated using the alternative 

good? The greater the degree of technical substitution of other goods, the more elastic the 

demand for the good in question. 

The second condition is availability of the substitute goods. Can the alternative readily be 

purchased? This condition relates to the price elasticity of supply of the alternative good. The 

more elastic the supply of a substitute good, the more elastic the demand for the good in 

question.

The demand for a good broadly defined (such as transportation) is less elastic than the demand 

for a more specific market (such as a particular car make and model). That is because there are 

few, if any, substitutes for the broadly defined good and more substitutes for the specific good. 

In the example of transportation goods, the possible substitutes for transportation are limited 

(walk, bus, taxi, etc.) and imperfect, while there is plethora of close substitutes for a particular 

model of car from a particular car dealer. 

A.2.b. Necessity

The more essential a good is, the less elastic the demand for the good. The necessity of a 

generic good is reinforced by the absence of feasible substitutes. 

Historically, postal services have been essential to long distance communication and transport 

of correspondence. Even though the demand for communication services seems to be always 

increasing, the development of telephones and subsequent methods of electronic 

 37 A good is a “normal good” if an increase in incomes results in the consumer purchasing more of that good. A 

good is an “inferior good” if an increase in income results in the consumer buying less of the good. The income 

effect reinforces the substitution effect for a normal good and opposes the substitution effect for an inferior good.
46

communications has made postal services per se less essential. Thus, the demand for postal 

services has been relatively inelastic, but may be becoming more elastic as the essentiality of 

the services decreases.

A.2.c. Importance in the Household Budget

The larger the share of the household budget allocated to purchase of a good, the more 

sensitive the consumer is to price. This is because it is worth the effort for the consumer to 

search out substitution alternatives for these big purchases while it might not be so for 

purchases that are a very small share of the budget. Also, when the purchases of the good 

comprise a larger share of the budget, the impact of the income effect from a price change can 

be substantial. 

Purchases of postal services have never been a large share of household expenses. 

Consequently, the demand for these services by households has been relatively inelastic. 

A.3.d. Consumer Loyalty and Product Differentiation:

Brand recognition and consumer loyalty to the brand leads to less elastic demand for a good. 

Advertising by a firm attempts to increase the demand for its product as well as make that 

demand less elastic. 

In the postal service context, customer loyalty and product differentiation probably make the 

demand less elastic for final consumption goods (e.g., a personal letter) but not for 

intermediate goods which are perceived as commodity inputs. 

A.3.e. Time:

Demand is more elastic in the longer run than in the short run. When the price of a good 

changes, consumers might not be able to immediately search for substitutes and necessity 

might require keeping purchases largely unchanged. However, with time, the consumer can 

identify some substitution possibilities that mitigate the impact of a price increase or find 

additional consumption opportunities in the case of a price decrease. Also, in the very long run, 

if the price change is viewed as permanent, new products and technologies might be 

developed. 

A.3. Determinants of the Price Elasticities of Business Demand

A change in the price of an input has two distinct impacts on a business’ demand for that input. 

As with household demand, there is a substitution effect. However, the demand for production 

inputs by businesses differs from the demand for goods by households because there is no 

income constraint. Consequently, there is no corresponding income effect as the result of a 

change in the price of an input. The second effect of a price change on a business’ demand for 

an input is the scale effect. 
47

The substitution effect reflects that the firm can change its mix of inputs to produce a given 

level of output. As the price of an input increases, the firm, in its effort to minimize cost,38 will 

substitute other inputs. Conversely, a price decrease for an input will cause the firm to use 

more of that input and less of other inputs for a given level of production. The extent to which 

substitution in production can occur is determined by technology. 

The second impact from a change in the price of an input is the scale effect. The scale effect 

(also called the expansion effect), takes into account that by changing the firm’s cost 

(particularly marginal cost), the change in an input price changes the optimal output of the firm. 

Typically, an increase in the price of an input will shift up (increase) the firm’s marginal cost.39

This results in the profit maximizing output (determined by the equation of marginal revenue 

and marginal cost) now being less. Conversely, an input price decrease leads to an expansion of 

output by the firm. If the input price change impacts all firms in the final product industry and 

the industry is competitive, then the scale effect is enhanced as the industry adjusts to a new 

equilibrium. That is, an input price increase would result in an initial contraction in output by 

each firm. However, the increased cost reduces profits and over time leads some firms to exit 

the industry, further decreasing employment of the input. Conversely, an input price decrease 

ultimately leads to competitive entry and increasing use of the input.

Marshall, in his development of the theory of derived demand, examined the factors on which 

the elasticity of derived demand depends.40 Marshall identified four conditions, now known as 

“Marshall’s Rules,” affecting the elasticity of demand for labor. John Hicks undertook a more 

rigorous mathematical derivation of Marshall’s Rules. 41 Although Marshall and Hicks focused 

on demand for labor, with the interest being on the effects on the distribution of income 

among the factors of production in the economy, the analysis is applicable at a more 

microeconomic level and to any factor of production. Marshall’s Rules (in the order he 

presented them) are that the demand for an input will be more elastic (1) the greater the ease 

of technical substitution of other inputs in the production process; (2) the greater the elasticity 

of demand for final output; (3) the greater the factor’s share of the production cost; and (4) the 

greater the elasticity of supply of other inputs. 

Rules (1) and (4) go directly to the substitution effect and are the business demand parallel to 

the substitution determinant in the household demand discussion above. Because an input is 

an intermediate good rather than a final good, the input is not a “necessity” in and of itself. 

However, an input may be essential to the production of the final good. How essential an input 

is depends on the technical substitution possible. The greater the ease of substitution of other 

inputs, the less essential the input and therefore the greater the elasticity of demand for it. 

 38 Cost minimization is a necessary condition for profit maximization. Cost minimization is also consistent with 

several alternative objectives, such as sales maximization subject to breaking even.

39 There is the theoretical possibility of an “inferior input” whose usage goes down as production increases, and as 

a result, the marginal cost would decrease. Inferior inputs are atypical, if they exist at all. There is no reason to 

think that postal services are inferior inputs.

40 Marshall, Alfred (1948). Principles of Economics (Eighth Edition). New York: Macmillan pp. 383-386. 41 Hicks, John R. (1964). Theory of Wages (Second Edition). London: Macmillan pp. 241-47.
48

Rule (4) regarding the elasticity of supply of other inputs holds in aggregate; however, for a 

specific other input the conclusion presumes the other input is a production substitute rather 

than complement.42

Rule (2) goes to the scale effect. As discussed above, an increase in the price of an input will 

increase production cost and ultimately lead to an increase in the price of the final good as the 

industry adjusts to a new equilibrium. The amount of the price increase depends on the extent 

to which substitution can mitigate the cost increase. However, any cost increase will lead to an 

increase in the price of the final good. At the higher price, consumers will purchase less which 

means less will be produced and less of all inputs will employed. The extent of production and 

employment cutback depends on the consumers’ sensitivity to price for the final good, that is, 

the price elasticity of demand for final output. 

Rule (3) is similar to the household demand being influenced by the importance in the budget. 

However, Rule (3) is directly derived from the firm’s profit-maximizing (and also costminimizing) behavior. Hicks challenged the importance of this rule. He demonstrated that this 

condition depends on the balance between the ease of technical substitution and the elasticity 

of demand for the final good. As long as the demand for the final good is fairly elastic while 

factor substitution is relatively difficult, the rule holds. But, as Hicks showed mathematically, 

the rule is reversed if technical substitution is easy and final demand is inelastic. He deftly 

summarized the finding as “(I)t is ‘important to be unimportant’ only when the consumer can 

substitute more easily than the entrepreneur.”43

Rules (1) and (4) are the most relevant to possible changes in the price elasticity of demand for 

postal services as an input in production. The development of the email, the Internet and other 

means of electronic transmission of communication has resulted in the emergence of much 

stronger substitutes to mail. Besides being feasible substitutes, technological change has made 

the alternatives readily available (i.e., their supplies are elastic). Automatic electronic transfer 

of funds and online bill payment have wrested away a majority of the bill payments from the 

Postal Service. The Postal Service has, so far, managed to hold onto most of the bill 

presentation market, but nevertheless lost a substantial share to electronic diversion. 44 

To the extent that the Internet has increased business and consumer purchases of 

merchandise, the demand for delivery of those purchases by U.S. mail may have increased. The 

Postal Service continues to face competition for providing the delivery of merchandise, but 

because of its extensive network, it appears to maintain a competitive advantage in last-mile 

delivery. 

 42 Not all inputs can be complements in production. In aggregate, other inputs have to be a substitute for the input 

in question, with the limiting case being a production function characterized by fixed proportions among inputs 

(i.e., no substitution possible).

43 Hicks, John R. (1964). Theory of Wages (Second Edition). London: Macmillan pp. 245-46. (emphasis in original).

44 See, e.g., 2011 USPS Household Diary Report. Table 4.10, p. 3.3; Table 4.13, p. 3.7.
49

A.4. All Other Things Aren’t the Same: How the Demand and the Elasticity of Demand for 

Postal Services Might—Or Might Not—Be Changing

The discussion of the price elasticity demand concerns the response of buyers to price changes 

and the general factors determining the degree of responsiveness. Most of the statements 

about elasticity have a key phrase included either explicitly or implicitly. That phrase, a favorite 

among economists, is “all other things the same.” But over long periods of time, all other things 

don’t stay the same. Consequently, quantitative and qualitative conclusions about price 

elasticities and the relative importance of their various determinants can change.

What are the other things relevant to the demand for postal services that might have changed?

A.4.a. Consumer Tastes and Preferences:

Economists generally think that consumers are fairly stable in terms of what generates utility or 

satisfaction. However, consumers do like new products and the introduction of new products 

causes reallocation of expenditures. Expanded choices usually mean increased substitution 

possibilities. 

A.4.b. Technology:

Technological improvements occur tend to occur regularly such that over time output is 

produced more and more efficiently. Some of this process technical change reflects steady 

continuous refinements in production and management methods. Breakthrough innovations, 

such as the printing press, the steam engine, and electrification, dramatically increase a 

society’s production possibilities. Technological progress might not impact all factors of 

production the same. Much of the technological change since the industrial revolution has been 

embodied in new capital and has resulted in less labor required per unit of output produced 

and production occurring at a greater ratio of capital to labor. At a more microeconomic level, a 

question can be asked as to the extent to which recent communication advances (e.g., the 

Internet) are “mail-saving” technological changes. How technological change alters the 

production function for a good directly impacts the input substitution possibilities and thereby 

impacts the price elasticities of demand for the inputs. 

Product innovation is another form of technological change. Product innovation is the 

development and introduction of completely new products. New products used to produce 

other goods feed into process technical change. New consumer goods present households with 

more goods over which to allocate their budgets and add more consumption substitution 

possibilities. Furthermore, the introduction of new final products may influence the evolution 

of consumer tastes and preferences. 

A.4.c. Availability of other goods and inputs:

A society’s production possibilities depend upon technology and the stock of inputs. Product 

innovation can introduce goods and inputs that were not available before. Pure chance can lead 

to the discovery of additional raw material resources. Process technical change may make 

extraction of previously unavailable resources feasible. Changes in the amount of goods and 
50

inputs available can change the relative scarcity of goods and inputs, impacting the 

consumption and production substitution feasibilities and thereby impacting the elasticities of 

demand.

A.4.d. Macroeconomic variables:

Changes in macroeconomic variables can impact the demands and demand elasticities for 

goods and inputs. These macroeconomic variables include population, consumer income, and 

overall economic activity. 

A.5. Conclusion 

The elasticity of demand is a measure of how customers respond to a change in the price of a 

good. Several factors affect the degree to which consumers respond. The price elasticity of 

demand is important in pricing strategy because it indicates a firm’s pricing power for a 

particular product and that product’s ability to generate profit or contribute to fixed cost 

recovery.

The demand for postal services comes from households and from businesses. These sectors 

have multiple needs to be met by the variety of postal services. As a result, the price elasticity 

of demand differs, even within a firm or household, depending on the need underlying the 

demand for a specific postal service. 

It is apparent that the demand for postal services has decreased in recent years as more 

electronic alternatives have become available. However, it is not certain how the market 

downturn has changed the price elasticity of demand for the different postal services. Theory 

suggests several effects, not all the same direction. As a result, how price elasticities have 

changed is an empirical question. To let the data answer the question requires judicious 

modeling. Specifically, it is necessary to recognize the distinct demands for different postal 

services, to be able to distinguish between changes in demand and changes in price elasticity of 

demand, and to allow flexibility in the elasticity measures to be estimated (i.e., don’t overly 

restrict the elasticity prior to estimation). 
51

APPENDIX B: SUMMARY OF CRRI CONFERENCE PAPERS REVIEWED

B.1. Time Series Models

The CRRI conference papers using time series methods employ demand models with similar 

economic content to the USPS baseline models, but differ notably in their use of time series 

econometric models more suitable for analyzing “cointegrated” data. These include studies by 

Veruete-McKay et al. (VM)45 and Jarosik, Nankervis, Pope, Soteri, and Veruete-McKay (JNPSV)46

of the UK; Martin, Paterson, Nikali, and Li (MPNL)47 employ data from Finland. 

The use of the ECM in both JNPSV and MPNL is motivated by cointegration of mail volumes and 

macroeconomic demand drivers. However, the VM paper reports that UK letter prices deflated 

by the retail price index (RPI) are stationary—the result is not unexpected in that a binding 

postal price cap based on RPI (CPI in the US) would yield relatively constant “real” postal prices. 

The MPNL paper uses annual data from 1990-2010. With relatively few observations in the 

annual time series, MPNL specify relatively rudimentary estimating equations with explanatory 

variables including own price, GDP per capita, an “electronification” measure, population 

growth (described as a measure of short-run demand pressure), and a global financial crisis 

dummy variable. They find that consumer-sent mail has highly inelastic demand, while 

business-to-consumer and business-to-business invoices are nearly unit elastic. However, the 

long-run own price elasticities for B2B and B2C invoice volumes are not very precisely 

estimated.

JNPSV employ relatively long series of quarterly data and, similar to the USPS baseline models, 

include a number of seasonal and trend variables in addition to own price and macroeconomic 

activity measures. The JNPSV paper also includes some cross-price terms, allowing for postal 

and (for presort and access volumes) nonpostal substitution possibilities. Conceptually similar 

cross-price and price differential (discount) terms are not currently specified in the USPS 

baseline models, but have been incorporated in the past—e.g., a number of price differentials 

were included in the demand models presented in the R2006-1 rate case. Finally, the JNPSV 

paper includes annual relative price terms in the equations for Second Class and presort/access 

volumes, to allow for “increasing levels of competition” in the sense of increased sensitivity of 

volume to product price differentials. In principle, similar interaction terms could be employed 

to test the stability of own price effects.

 45 Leticia Veruete-McKay, Soterios Soteri, John Nankervis, and Frank Rodriguez, “Letter Traffic Demand in the UK: 

An Analysis by Product and Envelope Content Type,” Review of Network Economics, Vol. 10(3), September 2011. 46 Marzena Jarosik, John Nankervis, Jonathan Pope, Soterios Soteri, and Leticia Veruete-McKay, “Letter Traffic 

Demand in the UK: Some New Evidence and Review of Econometric Analysis over the Past Decade.” Paper 

presented at the CRRI 20th Conference on Postal & Delivery Economics, Brighton, England, 2012. 47 Vance L. Martin, Chris J. Paterson, Heikki Nikali, and Qiubang Li, “Dynamic Letter Volume Models: How Does an 

Economic Downturn Affect Substitutuion Propensities.” Paper presented at the CRRI 20th Conference on Postal & 

Delivery Economics, Brighton, England, 2012.
52

In addition to the empirical papers, we reviewed a theoretical and simulation-based paper by 

Fève, Florens, Soteri, and Veruete-McKay48 examining a model of mail demand under changes 

in the composition of the postal customer base to include customers with access to electronic 

communication alternatives and hence more elastic demands for hardcopy mail. Fève et al. 

show that the average price elasticity during the demographic transition can remain low, as 

mail demand becomes relatively concentrated in customers with less elastic demands (due to 

lack of interest in or access to electronic alternatives). Using simulated data, they show that 

routine time series econometric techniques can produce reasonable own price elasticities, 

though measuring e-substitution can be difficult due to relatively poor proxy measures. 

Discrete Choice Model of Cigno, Pearsall, and Patel

Cigno, Patel, and Pearsall (CPP)49 depart radically from the time series approaches of the USPS 

baseline models and the other CRRI time series models. The core of the CPP paper’s critique of 

the USPS models is a claim that the exclusion of cross-price terms is a fatal deficiency. However, 

they acknowledge that the large number of cross-price effects and the high degree of 

multicollinearity of postal price series make it difficult to reliably measure the effects using 

traditional time series methods.

The CPP paper instead uses a discrete choice model based loosely on a model originally 

presented by Berry, Levinsohn, and Pakes (BLP).50 The BLP model is widely used in the empirical 

industrial organization literature. However, the CPP paper departs significantly from the BLP 

methodology, mainly in order to reduce the computational complexity of the method to a level 

that allows the estimator to be implemented in a Lotus 1-2-3 workbook. Additionally, the CPP 

model has a number of questionable features, which we feel make it a work in progress.

First, the CPP model frames all mailing decisions in terms of consumers’ utility-maximizing 

consumption choices, whereas much postal demand arises more directly from a variety of 

business (production) decisions. While demands derived from consumption and production 

theories can be generically similar—for example, in both cases, all prices in the relevant choice 

set enter demand functions in theory—they are likely to result in distinct explanatory variables 

for different products or product categories. This makes it relatively likely that the limited nonprice variables in the models omit important demand drivers.

 48 Frédérique Feve, Jean-Pierre Florens, Soterios Soteri, and Leticia Veruete-McKay, “Are Letter Price Elasticities 

Higher than Econometricians Think?” Paper presented at the CRRI 20th Conference on Postal & Delivery 

Economics, Brighton, England, 2012. 49 Margaret M. Cigno, Elena S. Patel, and Edward S. Pearsall, “Estimates of U.S. Postal Price Elasticities of Demand 

Derived from a Random-Coefficients Discrete-Choice Normal Model.” Paper presented at the CRRI 31st Annual 

Eastern Conference. (Advanced Workshop in Regulation and Competition), Shawnee, Pennsylvania, May 17, 2012, 

and the 20th Conference on Postal & Delivery Economics, Brighton, England, June 1, 2012.

http://www.prc.gov/prc-docs/library/refdesk/techpapers/CignoPatelPearsall%20Paper_2761.pdf 50 Steven Berry, James Levinsohn, and Ariel Pakes, “Automobile Prices in Market Equilibrium.” Econometrica, Vol. 

63(4), July 1995. See also Aviv Nevo, “A Practitioner’s Guide to Estimation of Random-Coefficients Logit Models of 

Demand.” Journal of Economics & Management Strategy, Vol. 9(4), Winter 2000.
53

Second, the CPP results show some implausible cross-elasticities. We suspect these are artifacts 

of failing to apply reasonable a priori knowledge regarding market segmentation within the 

array of postal products under study. Likewise, findings of large (negative) own price elasticities 

for market dominant products that receive preferential rates are highly suspect.

Third, the CPP paper makes a number of unjustified and implausible assumptions, particularly 

with respect to specification of the “outside good” in the model (representing choices of 

nonpostal products). The outside good is assumed to have static characteristics and prices 

(both normalized to zero for computational convenience, which is particularly troubling as 

electronic alternatives to postal services are marked by rapidly falling prices and improving 

quality. Since the CPP paper lacks needed quantity information for its outside good, it computes 

the outside good’s market share (needed to estimate model parameters) from the assumption 

that the total postal plus outside good market size is fixed over the sample period. This 

characterizes the Postal Service as enjoying a growing share of a fixed market until the volume 

peak in the 2000s rather than, as seems more likely, a declining share of a rapidly growing 

communications market. This could lead to inappropriate estimates of coefficients on price 

variables in the share equations, which subsequently feed into the CPP paper’s elasticity 

estimates.

As a practical matter, the CPP model’s Lotus 1-2-3 implementation is extremely cumbersome 

and not well suited to exploratory analysis. It appears that basic model changes including 

adding or removing variables, and altering the model time period, would require considerable 

spreadsheet modification. We would strongly encourage researchers pursuing postal 

applications of the BLP methodology to employ more standard econometric analysis software.
RARC-WP-13-008 Analysis of Postal Price Elasticities

U.S. Postal Service Office of Inspector General May 1, 2013

U.S. Postal Service Office of Inspector General

1735 N. Lynn Street

Arlington, VA 22209

Telephone: 703-248-2100

www.uspsoig.gov

For media inquiries, contact Agapi Doulaveris

Telephone: 703-248-2286

adoulaveris@uspsoig.gov