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This note describes the calculation of chain-type quantity and price indexes used in the NIPA's.
Changes in current-dollar GDP measure changes in the market value of goods, services, and structures produced in the economy in a particular period. These changes can be decomposed into quantity and price components. Quantities, or "real" measures, and prices are expressed as index numbers with the reference year--at present, the year 1996--equal to 100.
The annual changes in quantities and prices are calculated using a Fisher formula that incorporates weights from two adjacent years. (Quarterly changes in quantities and prices are calculated using a Fisher formula that incorporates weights from two adjacent quarters; quarterly indexes are adjusted for consistency to the annual indexes before percent changes are calculated.) For example, the 1998-99 annual percent change in real GDP uses prices for 1998 and 1999 as weights, and the 1998-99 annual percent change in GDP prices uses quantities for 1998 and 1999 as weights. These annual changes are "chained" (multiplied) together to form time series of quantity and price indexes. The Fisher formula produces percent changes in quantities and prices that are not affected by the choice of reference years. In addition, because the changes in quantities and prices calculated in this way are symmetric, in general, the product of a quantity index and the corresponding price index equals the current- dollar index. (BEA also publishes a measure of the price level known as the "implicit price deflator (IPD)," which is calculated as the ratio of current- dollar value to the corresponding chained-dollar value, multiplied by 100. The values of the IPD are very close to the values of the corresponding "chain-type" price index for all periods.)
Chain-type quantity and price indexes for GDP and its major components are presented in this release as index numbers in table 5 and in the form of percentage changes from the preceding period in tables 1, 4, 6 and from the quarter one year ago in table 7. Contributions by major components to changes in real GDP are presented in table 2. BEA also prepares measures of real GDP and its components in a dollar-denominated form, designated "chained (1996) dollar estimates." For GDP and most other series, these estimates, which are presented in table 3, are computed by multiplying the 1996 current-dollar value by a corresponding quantity index number and then dividing by 100. For example, if a current-dollar GDP component equaled $100 in 1996 and if real output for this component increased 10 percent in 1997, then the chained (1996) dollar value of this component in 1997 would be $110 ($100 x 1.10).
For analyses of changes over time in an aggregate or in a component, the percentage changes calculated from the chained-dollar estimates and from the chain-type quantity indexes are the same; any differences will be small and due to rounding. However, because the relative prices used as weights for any period other than the reference year differ from those used for the reference year, the chained-dollar values for the detailed GDP components will not necessarily sum to the chained-dollar estimate of GDP or to any intermediate aggregate. A measure of the extent of such differences is provided by a "residual" line, which indicates the difference between GDP (or another major aggregate) and the sum of the most detailed components in the table. For periods close to the reference year, when there usually has not been much change in the relative prices that are used as weights for the chain-type index, the residuals tend to be small, and the chained (1996) dollar estimates can be used to approximate the contributions to growth and to aggregate the detailed estimates. As one moves further from the reference year, the residual tends to become larger, and the chained- dollar estimates become less useful for analyses of contributions to growth. Thus, the contributions to percent change shown in table 2 provide a better measure of the composition of GDP growth. In particular, for components for which relative prices are changing rapidly, calculation of contributions using chained-dollar estimates may be misleading even just a few years from the reference year.
References: "A Preview of the 1999 Comprehensive Revision of the NIPA's: Statistical Changes," October 1999 Survey, pp. 6-17; "A Guide to the NIPA's," March 1998 Survey, pp. 36-40; "BEA's Chain Indexes, Time Series, and Measures of Long-Term Economic Growth," May 1997 Survey, pp. 58-68.
Changes in current-dollar GDP measure changes in the market value of goods and services produced in the economy in a particular period. For many purposes, it is necessary to decompose these changes into quantity and price components. To compute the quantity indexes, changes in the quantities of individual goods and services are weighted by their prices. (Quantity changes for GDP are often referred to as changes in "real GDP.") For the price indexes, changes in the prices for individual goods and services are weighted by quantities produced. (In practice, the current-dollar value and price indexes for most GDP components are deter-mined largely using data from Federal Government surveys, and the real values of these components are calculated by deflation at the most detailed level for which all the required data are available.)
The annual changes in quantities and prices are calculated using a Fisher formula that incorporates weights from 2 adjacent years. For example, the annual percent change in real GDP in 1997-98 uses prices for 1997 and 1998 as weights, and the 1997-98 annual per-cent change in the GDP price index uses quantities for 1997 and 1998 as weights. Because the Fisher formula allows for the effects of changes in relative prices and in the composition of output over time, the resulting quantity or price changes are not affected by the substitution bias that is associated with changes in quantities and prices calculated using a fixed-weighted formula.1 These annual changes are "chained" (multiplied) together to form time series of quantity and price; the percent changes that are calculated from these time series are not affected by the choice of reference period.
The quarterly changes in quantities and prices are calculated with weights from two adjacent quarters. As part of an annual or comprehensive revision, the quarterly indexes through the most recent complete year are adjusted to ensure that the average of the quarterly indexes conforms to the corresponding annual index. In addition, BEA prepares measures of real GDP and its components in a dollar-denominated form, designated "chained (1996) dollar estimates." These estimates are computed by multiplying the 1996 current-dollar value of GDP, or of a GDP component, by the corresponding quantity index number. For example, if a current-dollar GDP component equaled $100 in 1996 and if real output for this component 1.
In addition, because the changes in quantities and prices calculated using these weights are symmetric, the product of a quantity index and the corresponding price index is generally equal to the current-dollar index. increased by 10 percent in 1997, then the "chained (1996) dollar" value of this component in 1997 would be $110 . Note that percentage changes in the chained (1996) dollar estimates and the percentage changes calculated from the quantity indexes are identical, except for small differences due to rounding.
Because of the formula used for calculating real GDP, the chained (1996) dollar estimates for detailed GDP components do not add to the chained-dollar value of GDP or to any intermediate aggregates. A "residual" line is shown as the difference between GDP and the sum of the most detailed components shown in each table. The residual generally is small close to the base period but tends to become larger as one moves further from it. Accurate measures of component contributions to the percentage changes in real GDP and its major components are shown in NIPA tables 8.2-8.6.
BEA also publishes the "implicit price deflator" (IPD), which is calculated as the ratio of current-dollar value to the corresponding chained-dollar value, multiplied by 100; the values of the IPD and of the corresponding "chain-type" price index are very close.
For quarters and months, the estimates are presented at annual rates, which show the value that would be registered if the rate of activity measured for a quarter or a month were maintained for a full year. Annual rates are used so that time periods of different lengths--for example, quarters and years--may be compared easily. These annual rates are determined simply by multiplying the estimated rate of activity by 4 (for quarterly data) or by 12 (for monthly data).
Percent changes in the estimates are also expressed at annual rates. Calculating these changes requires a variant of the compound interest formula:
Quarterly and monthly NIPA estimates are seasonally adjusted, if necessary. Seasonal adjustment removes from the time series the average impact of variations that normally occur at about the same time and in about the same magnitude each year--for example, weather, holidays, and tax payment dates. After seasonal adjustment, cyclical and other short-term changes in the economy stand out more clearly.
Using the Enhanced Table Viewer (Java)
The Enhanced Table Viewer is a Java Applet which runs on your computer in your browser. It holds the row and column headings on screen as you browser through a table. It also allows you to display rows which you have selected and hide the other rows from view. In addition you can select rows using a checkbox and then graph up to 5 at a time. Or, you can graph all rows, 5 at a time.
In order to use the viewer your browser must support Java and Java must
be enabled. All recent versions of Netscape, Internet Explorer and Opera support Java. In addition to supporting Java the
security setting on your browser must be set to enable Java. The best test to see if you can use the viewer is to click on
the link Try our Enhanced Table Viewer with Locking Column and Row Headings and Graphing.
either here or on the NIPA table home page. If this link gives you an error or an error page
is displayed you can not use the viewer. If no errors are displayed you are ready to use the viewer and no further action is
required on your part.
Data Selection The check boxes on the left side of the table enable you to select specific lines in the table. The selected lines can the be graphed, see Graphing in the Enhanced Table Viewer below, or they can be displayed by themselves by clicking on the View Selections button. Note that the parents of all indented selections are shown even if they are not selected themselves.
Graphing in the Enhanced Table Viewer - You can use one of two methods to graph data, Graph All and Graph 5 Selections.
Graph All will graph all of the data, in groups of five time series. Clicking on the Graph All button will cause the first five time series to be graphed. Once the graph is displayed the Graph All button label changes to Next 5. Clicking the Next 5 button will then graph the next five time series. This will go on until the end of the table is reached when it will start with the first 5 again.
Graph 5 Selections really means graph no more than the first 5 selections, but that won't fit on a button. When this button is clicked the first 5 selected, checked, time series will be graphed.
Graph Types Some tables allow four type of graphing: