Use terminology related to inflation
Choose a base year
Calculate constant dollars
Choose a deflator
We use the term inflation to indicate the declining purchase power of money over
time. The general reason for inflation is that the quantity of money seeking to
purchase goods and services increases faster than the quantity of goods and
services offered for purchase. Because there are many complexities, such as the
speed at which money passes from one purchase to the next, inflation is best
measured by tracking the actual purchase price of typical goods—called a market
basket—repeatedly over time. Doing this allows for construction of an index, that
is, a series of numbers associated with dates that show the change in the price from
a base point. At the base point, the value is set at 1, 100%, or sometimes 100. If it
is 100, the value means 100%, so if you take the actual purchase price of all the
goods in the market basket and divide it by the actual purchase price on the base
date (the date when the base point is set), the result is 1 or 100%.1 Values on
subsequent dates tend to be higher because the purchase price of a market basket
tends to go up. Sometimes earlier dates are also shown, based on either historical
data or estimation, and these values typically will be smaller because the purchase
price of the market basket was less. The index that most readers hear about from
popular news sources is the Consumer Price Index for All Urban Consumers,
usually abbreviated as CPI. As the full title indicates, it is focused on urban
consumer prices, meaning the prices of goods and services that members of a
household in a city or suburb might purchase.
Nominal Versus Constant or Real Dollars
The dollars subject to inflation (i.e., those in the actual world used for actual
purchases) are sometimes called nominal dollars, which means that they are
perceived to reflect the value of a dollar on the date that they are used. Comparing
amounts of money available (revenue or appropriations) or spent in the form of
these dollars at different times is confusing. That’s because we cannot distinguish
between the effects of inflation and the effects of other changes on the expenditure
side and the revenue side. These might include, for example, differences in demand
or efficiency on the expenditure side or differences in population or tax rates on
the revenue side. To correct this, we make calculations using constant dollars,
also sometimes called real dollars. Constant dollars start with nominal dollars
and are then adjusted using an index.
Figure 7.1 shows a comparison between nominal dollars and constant dollars.
The series is sales and gross receipts “tax” for Alabama as reported by the US
Census Bureau.2 The central solid line that rises from $2.5 million to a little more
than $4.5 million is nominal dollars. The flatter dotted lines above and below the
solid line both show constant dollars and, in fact, are roughly the same except for
their levels (height) on the chart.3 They are at different levels on the chart because
they have different base years,4 but first, there is a difference between either of
these and the nominal series. On the left side, we see that the nominal series grows
every year until 2003, when it drops slightly. In the constant series, after a drop in
1994, the series grows until 1999 and stays roughly flat until 2003, when it takes
a sharp drop. Both series then grow until 2007, with the constant series growing
at a slower rate. The nominal series continues to grow into 2008 at a slower rate;
then it takes a sharp drop in 2009. It then recovers slightly above its former level
in 2010 and continues to grow. The constant series begins to drop sharply in 2008
and 2009, partly recovers in 2010, and then continues to slowly decline.
Alabama Revenues in Constant Dollars and Nominal Dollars (1993–2012)
Sources: US Census Bureau, 2013, http://www.census.gov/govs/statetax/.
These two views of the series tell very different stories. The nominal series
grows in almost all years, rapidly recovers from declines, has almost doubled over
the last two decades, and is growing as of the last date represented on the graph.
The constant series has grown in 9 of 19 intervals, saw most of its growth between
2003 and 2007, has grown less than 20% over the last two decades, and is
currently in modest decline. The constant series provides a more realistic
understanding of the changes in the purchasing power of Alabama’s revenue from
this source. Thus, for many purposes, a first step to effective analysis may involve
converting nominal dollars to constant dollars.
Figure 7.1 shows two constant series that reflect the need for the analyst to make
a choice. In the calculation (math) of constant dollars, the base year—meaning
the year when the constant dollars and the nominal dollars have the same value—
used in producing the constant series is arbitrary. But the choice is not. For many
purposes, an analysis is conducted to communicate something specific. The
message might be “If the value of money were what it was in 1993, we would only
have $2.9 million (1993) in taxes right now. Real revenue has declined for four of
the last five years. We need to find a new revenue source.” This is a largely
backward-looking message aimed at telling a story about constant dollars and
revenue-related policy implications. Here, where the emphasis is on storytelling
and not on estimation for the current period, the use of the earlier base year may
For other purposes, the main goal of the conversion of nominal dollars to
constant dollars is to aid in estimation for the current period or the near future.
When making estimates for the present, it is unhelpful to have dollar values that
are substantially out-of-date. While the conversion to constant dollars will take
away anything from the data that pushes values up to the near future, estimates
that are in the near to current base period are still much more useful than those in
substantially eroded dollars. Consequently, the base year should be the most
recent year for which data and an appropriate index are available. If absolute
precision is required, estimates made in this form may be projected into future
years using assistance from projected index values; however, such inflating of
estimates may be subject to rules in many budget environments. Where the user
is uncertain which approach to use, the most recent period’s base should be
Calculation of Constant Dollars
The calculation of constant dollars is straightforward. The formula is as follows:
This formula says that constant dollars in a time period, Ct, are found by
multiplying the nominal dollars for that time period, Nt, by the fraction in which
the numerator is the base year index value, IB, and the denominator is the periodic
index number, It.
This calculation is shown in Table 7.1. In the spreadsheet labeled Tables,
Data,Worksheets-M07.xlsx, represented by Table 7.1, “Sales and Gross Receipts” is
in column B, CPI is column C, row 4 contains 1993 data, and row 23 contains 2012
data. We used rounding to eliminate the unnecessary and sometimes confusing
long decimal results generated, but often not revealed, by spreadsheet formats.
Alabama Revenue in Nominal Dollars (CPI) and Constant Dollars, With CPI (1993–
Sources: US Census Bureau, 2013, http://www.census.gov/govs/statetax/. Federal Reserve Bank of
St. Louis, http://research.stlouisfed.org/fred2/.
The Excel formula used for the Constant 2012 Dollars column for 1993 is as
This formula can be used to select any base year by changing the row number after
the $ sign in the numerator of the fraction.
Deflators and Indexes
This demonstration uses CPI because it is the most common price index that users
know. However, governments are not typical urban consumers. The US Bureau of
Economic Analysis computes a consumption expenditures price deflator for
urban governments. The series label is A829RD3A086NBEA, and it can be
Figure 7.2 shows the data series shown in Figure 7.1 with nominal dollars,
constant dollars calculated using CPI, and constant dollars calculated using the
state and local implicit price deflator. This deflator more specifically shows how
inflation affects governmental spending power based on what governments
purchase. Based on this calculation of constant dollars, any limited gains in
revenue have been entirely eroded away in recent years. While analyses using CPI
may be important for communicating how taxes affect the burden experienced by
taxpayers (the data should also be adjusted to reflect per-capita or per-household
information), analyses using the price deflator reflect the ability of the government
to purchase goods and services with the money it has acquired. When selecting a
deflator or index, the analyst should be careful to select the one that is most
appropriate for the intended purpose.
Comparing the Indexes
Sources: US Census Bureau, 2013.
Inflation is the declining purchasing power of money over time. The dollars subject
to inflation, meaning those in the actual world used for actual purchases, are
sometimes called nominal dollars, while real dollars are those adjusted for
inflation using an index. The most commonly used index is the CPI, or Consumer
Price Index. An index used by government is the US Bureau of Economic Analysis’s
index, which computes a consumption expenditures price deflator for
governments that reflects government spending power based on what
government bodies typically purchase.
1. Define the following:
a. Nominal dollars
b. Constant dollars
2. Lake City’s park gazebo is available for residents to rent for picnics and other gatherings.
You have been tasked with building a compelling financial story to convince the city
council to raise the rental rates. The rental revenue history is shown in Table 7.2, along
with the CPI for each of the years.
Lake City: Park Gazebo Revenues and CPI (1984–2012)
a. Calculate 2012 constant dollars for the rental revenue.
b. Calculate 1984 constant dollars for the rental revenue.
c. Create a line graph displaying the nominal dollars, 2012 constant dollars, and 1984
constant dollars across all years of data.
d. How would you use these data to create a compelling financial argument to increase
rental rates? Would you use all of the data?
3. A member of Lake City’s town council—who has been on the city council for almost 25
years, remembers everything, and has a particular fondness for the park—questions the
data you have presented. He presents you with a newspaper clipping from 1996 that
claims the revenue in 1984 was just under $20,000 per year. Back at your desk, you tackle
your new task of determining where this “under $20,000 per year” figure came from as
well as how to explain nominal dollars and constant dollars to this member of the town
a. Using the same nominal dollars as in assignment 2, add a column and calculate 1995
b. Add the 1995 constant dollars data to your graph.
c. Using this graph, write a simple explanation about nominal dollars and the use of
different base years to create constant dollars. The explanation should be no more
than a page and written for an audience that does not have a financial background.
4. Big East City’s Public Works Department is asking for an additional $100,000 for sign
repairs in the next budget cycle because its costs have increased by at least that much
since 1995. The department has provided you with the information in Table 7.3. Big East
City has adjusted funding for each of its departments every year to keep up with the
buying power of money.
a. Calculate 2012 constant dollars for the expenditures.
b. Calculate 1995 constant dollars for the expenditures.
c. Create a line graph displaying the nominal dollars, 2012 constant dollars, and 1995
constant dollars across all years of data.
d. Based on the data provided and the calculations you have completed above, does
the Public Works Department’s request make sense? How much additional
funding do you think it might need?
Big East City: Expenditures for Sign Repairs and Price Deflator (1995–2012)
Understand sensitivity analysis as a general tool that is applicable to many methods
Apply scenario analysis
Apply quantitative sensitivity analysis
Prepare for use of sensitivity analysis with respect to other techniques
Sensitivity analysis is a general term for determining the potential range of
uncertainty when precise statistical methods are unavailable. There are several
practices that sometimes serve this purpose. The basic idea of sensitivity analysis
is to examine the effect of adjusting uncertain values across their possible
range. This practice can be performed both quantitatively and qualitatively. The
following discussion focuses on relatively easy-to-apply methods. However, at the
end, more sophisticated methods are mentioned, and some of the resources refer
to complex methods.
With qualitative information, scenario analysis may be used. Scenario analysis
consists of writing realistic stories (scenarios) that examine the anticipated way
that events may happen. If scenario writing does not come naturally, the analyst
might think of them as brief “What if?” problems such as these: “What if we close
the fire station at 10th Street and …?” “What if we open a senior center at the
armory on Main Street and …?” Think about what could realistically follow the and.
What if a fire happened at a nearby apartment building, or what if the potential
senior center were built in in a neighborhood where the number of senior citizens
did not fill the center’s capacity? Creating realistic extreme, but not silly, scenarios
will help determine the degree of uncertainty associated with cost estimates and
related policy recommendations.
Example of Scenario Analysis
Summerville is a retirement mecca in the Southwest. With a population of
180,000, it has 40,000 residents over the age of 65 and 18,000 over the age of 75.
Because of high-quality in-home care programs, 9,000 of the population age 75
and older live in independent or semi-independent housing. Roughly half of the
senior population relies on Social Security, Supplemental Security Income, or
similar government programs as their sole source of income. Most of these
individuals are eligible for the Supplemental Nutritional Assistance Program
(SNAP, formerly food stamps), although some are not enrolled. Presently,
Summerville provides seniors with group meals and other similar senior services
seven days a week at five multifunctional community centers. Summerville makes
these available to all who come, regardless of income status, and it also provides
meals-on-wheels to roughly 4,000 enrolled seniors who are unable to leave their
home. Because of population growth, the community centers are crowded, and
there are conflicts between the seniors and other users, particularly teens who
want to use the same spaces for sports activities. The group meals program is
thought to be underused. Summerville is proposing to open senior centers in
facilities that are adjacent to the multifunctional community centers. These
facilities will share kitchen facilities but will otherwise operate separately. Seniors
will continue to have access to community centers, but non-seniors will generally
not have access to the senior centers except as needed to assist seniors.
Scenario 1: Particularly because of the relocation of meals and programming, the
seniors adapt to the separate senior centers over the first 3 months. Conflicts over
space no longer occur. After a few months, there is a small increase in senior center
usage because individuals who were discouraged by the prior conflicts find the
new arrangement more pleasant. Likewise, usage of the community center by nonseniors increases slightly, reflecting the additional capacity. The overall small
increase in community center usage has little apparent budgetary impact, except
for a small increase in maintenance and cleaning costs and a small increase in the
Scenario 2: With the relocation of meals and programming, the seniors move to
the new senior centers within a short time. The publicity associated with the new
senior centers attracts large numbers of seniors who were not even aware of the
services in the community centers, as the latter had not been labeled senior
centers. Soon, the senior centers are filled to capacity, and the facilities are looking
to expand back into the community centers for needed extra space. The conflict is
not resolved, and non-seniors begin to demand new sports facilities that are not
associated with the community centers. The budgetary impact involves
substantial increases for meals and new staff (to manage the unexpected growth
in participation) and a longer-term capital cost of constructing three sports
facilities located away from the community centers.
Scenario 3: The seniors see the relocation of meals and programming as rejection
by the community. Over the next year, participation dwindles, and two facilities
are closed for lack of use. This leads to further lack of trust between seniors and
other residents. With the decline in use of the senior centers, there are also other
effects. The meals-on-wheels program has an increase in enrollment of over 1,000
individuals. The in-home care program sees a decline in success, with more
individuals moving into nursing homes. Because of a lack of nursing home beds in
the area, the seniors begin to demand that the community build and operate a
nursing home. Budgetary impacts include the decreased cost of operating the
senior meals program and other programs, the increased cost of meals-on-wheels,
and the capital and possible operating costs associated with the nursing home
(although these may eventually be paid by third parties).
Understanding Sensitivity Analysis
When an estimate of any sort includes a value that has been included based on
judgment, the range of uncertainty can be estimated through sensitivity analysis.
The first estimate should be based on the value or values that are judged to be
correct. Then at least two more estimates should be made. These should be the
two most extreme realistic estimates reflecting possible scenarios. If only one
variable is included in the estimate, the analyst estimates the value the variable
will have, then makes two more estimates using the highest and lowest possible
values of that variable. With two or more variables, all combinations should be
calculated, and the reported values should be the expected value and the highest
and lowest possible values.
Consider the senior center scenario analysis. One element of that analysis is the
group meals program. A concern is that the meals program can be affected by the
building of new senior centers. In Table 8.1, we consider what happens when the
number of users changes. At present, there are 4,000 users, and the number is
stable. So the estimate is 4,000. Based on current plans, the cost per meal for
feeding these 4,000 seniors one meal a day is approximately $6 per meal. The
annual cost is $8.76 million. If the number of users declines to 3,000 (a possible
result if the service becomes less popular), the cost of this element of the program
drops to $6.57 million. If the number of users increases to 5,000 (if the service
becomes more popular), the cost increases to $10.95 million. So the possible cost
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