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Weighted Indexes and Raw Indexes: Understanding Inflation and Escalation in Defense Acq - Video 9 - YouTube
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Welcome to the ninth video in our series:
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Understanding Inflation and Escalation in Defense
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Acquisition: Best Practices for Cost Analysis.
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Today we will present an overview on how the
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Department of Defense utilizes the weighted and raw
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indexes to support the development of certain
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figures in cost estimates and budgets. Let's
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begin. Let's say you're performing a cost estimate
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for the Department of Defense and you need to
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adjust cost values. While the Department of Defense
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will provide a weighted inflation index to suit
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your needs, it is unlikely that you will be
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provided a weighted escalation index. This video
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will help you understand the difference between
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raw and weighted indexes and how to calculate your
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own weighted escalation index. Recall the concept
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of a price index from the first video in our
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series. A price index depicts the rate of change over
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a period of time for the price of a class of goods
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or services. In the earlier video, we discuss two
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types of price indexes: escalation and inflation,
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and how these indexes support developing cost
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figures and cost estimates. Whether you're
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adjusting costs with an escalation index such as
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developing CERs or adjusting with an inflation
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index such as an affordability analysis, you will
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need to know the concepts of raw and weighted
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indexes. A raw index reflects the change in value
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from one year to the next. It is used to normalize
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for the effects of price changes. A weighted index
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is created specifically to account for the
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additional costs of price change expected to be
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incurred from expenditures beyond the year of
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obligation. So what exactly are raw and weighted
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indexes used for? First, raw indexes are used to
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normalise expenditures at a specific point in time
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whereas weighted indexes are used to normalise
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obligations where dollars provided in one year
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will be spent over a period of years. Before we
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move from defining these indexes to calculating
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them, we next need to understand the difference
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between expenditures and obligations. So what are
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expenditures and obligations? To start, expenditures
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are transactions that occur at a specific point in
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time. For example, if I want to buy a computer from
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an electronic store, I pay the price of the
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computer, and the merchant gives me a computer. In
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this example the transaction occurs and it is
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completed at a point in time. Please note that the
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term expenditure is frequently used
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interchangeably with the term outlay. Obligations
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represent dollars which will be spent over a
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period of time. They are binding agreements that
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will result in outlays immediately or in the
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future. Unfortunately there's no store the
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government can go to to buy ready made submarines,
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so the government must contract with a firm to
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produce submarines which may take several years to
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build after the agreement, and because these
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products may take several years to produce, if the
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government didn't account for the expected amount
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of price change over the construction period then
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they would be severely underfunding the production.
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Because the firm will be expending dollars over
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several years to build a submarine, the amount of
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dollars the government obligates must include
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the amount of price change expected to occur.
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Before we jump into creating a weighted index,
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let's quickly define the term base year which we
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discussed in an earlier video. A base year is the
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year used as a basis of comparison whenever an
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index is calculated. Using a base year helps an
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analyst normalize data for a consistent
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comparison across years. If we had a period of 20
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years that we wanted to calculate an index for, and
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we wanted to compare everything relative to the
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first year then that first year would be our base
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year. We should also note that when calculating
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raw indexes, the base year always has an index
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value of 1. Now that we've gone over definitions
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and explanations, let's open up Microsoft Excel and
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review how to develop a weighted index
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Next, let's explore how to create a weighted index.
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First, we need a raw index starting with a value of
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1 in the base year which will be 2005 in this
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example. We're going to suppose the index pertains
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to the cost changes of U.S. Navy ships which for
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simplicity will increase at a constant rate of 3%
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per annum. Using this information we can
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calculate the raw index for the subsequent years
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2006 through 2020. To do this we take the previous
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index value and multiply it by one plus the
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escalation rate of 0.03. We then
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drag the formula down which provides us the
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complete listing of raw indices from 2005 to
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2020 for U.S. Navy ships. If you look at the year
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2020 you can see that the value is 1.558.
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This means that U.S. Navy ships cost
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55.8% more in current
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year dollars in 2020 than they did in 2005.
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Assuming the quality of a U.S. Navy ship is
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constant over that time. Note that escalation
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indexes are often quality or content constant.
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This means that performance increases due to new
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or more advanced subsystems that are excluded. An
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important assumption that necessitates a weighted
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index is that U.S. Navy ships often take several
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years to produce because they are large and
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complex items. Let's say for simplicity that a
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U.S. Navy ship on average will be produced over the
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course of four years. Let's further assume that 25
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percent of the cost of the ship is expended and
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each of the four years. How do we carry a weighted
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index from this information? First, we must
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determine what the weighted index value for our
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base year is. For 2005, this can be done by
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starting the outlay rate for year 1, 25 percent,
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divided by the raw index for 2005 which is one.
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We can drag this formula down for each of the four
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years and the outlay profile, and we will get the
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deescalated values for the proportions and each
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year for a total obligation in 2005. Well, in the
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first year because there's no escalation that has
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occurred that has the purchasing power of 25 cents.
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But what happens in year two? We give the
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contractor 25 cents to expend in year two; however,
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escalation has occurred over the time period such
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that the 25 cents has been eaten away by 3 percent
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through escalation, and the contractor feels as if
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they only receive 24.3 cents of
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what was expected. This logic continues throughout
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the four years. In year four, the contractor is
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only receiving 22.9 cents of
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value from what was 25 cents due to the cumulative
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escalation of 9.3 percent over 2005
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price levels. If we sum the values, we can find
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that the contractor is only receiving 95.7%
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of the dollars they needed to
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produce the Navy ship due to the escalation that
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has occurred between 2005 and 2008. In order to
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provide the contractor enough money to produce the
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end product, we'll need to convert the one dollar. We
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take one divided by the sum of the deescalated
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values, 0.957, and that yields
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the weighted index value of 1.045 meaning
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that if we wanted to provide the contractor with
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enough funds to fill the production order over
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four years with an outlay rate of 25 percent each
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year, we'll need a budget for 1.045
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dollars for every dollar of purchasing power we
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need them to have in 2005 terms. So how do we
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find the weighted index value for each and every
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year? At this point, we have only provided the
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weighted index for 2005. We can generalize by
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observing that the weighted index value is the
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reciprocal of the weighted sum of the reciprocals
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of the raw indices across a given range of years
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where the weights are given by the outlay profile.
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For you math geeks out there, this is called the
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weighted harmonic mean. We can cleverly encapsulate
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this in a single Excel array formula. We take one
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divided by the sum of the outlay rates divided by
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the respective raw index values, and we control+
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shift+enter to enter that formula as an array, and
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we note that our weighted index value for 2005
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corresponds to what we previously calculated using
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more spreadsheet geography. When we drag the
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formula down, the raw index range will also shift
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down appropriately. For example, the 2006 weighted
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index pulls from the raw indices for 2006 through
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2009, the years needed to produce a ship starting
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in 2006. We will not get the 2018 weighted index
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value because the four year outlay profile means
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an obligation in 2018 will have expenditures
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extending to 2021 for which we do not have a raw
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index value.
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If we extend the formula one more down, you will
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see that the outlay rates are the same, but the raw
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index is now including a missing value. Of course
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in a simplified example, we can always generate
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raw indices under the constant escalation
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assumption, but it remains a practical constraint
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that we require raw indices projected further into
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the future than weighted indices. Thank you for
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watching. This concludes video 9 in our series:
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Understanding Inflation and Escalation in Defense
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Acquisition: Best Practices for Cost Analysis.
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For more information or additional resources on
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how inflation and escalation are used in defense
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acquisition, please visit our website at
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CADE.OSD.MIL/POLICY/INFLATION
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