## Index NumbersStatistical agencies often report time series data in the form of
index numbers. For example, the consumer price index is an important
economic indicator. Therefore, it is useful to understand how index numbers
are constructed and how to interpret them. An introduction to index
numbers is in Paul Newbold [ First, consider computing a price index for a single item.
Suppose that price data is
100 (P The price index expresses the price in every period as a percentage of the base period price.
The price index variable shows that the wool price in 1993 was 65% of the price in 1986. An aggregate price index for a group of commodities can be constructed by using some weighted average of the prices where the weights are quantities. Statistical agencies use this method to obtain the consumer price index. Various formula have been proposed by researchers and an illustration with SHAZAM is given in the next section below. When price index variables are used as explanatory variables in a regression equation the estimated coefficients must be interpreted appropriately. Consider time series Y and X where X is a price index that is 100 in the base year. The linear regression equation is: Y where e Now consider the log-linear regression equation: ln(Y where u
## Calculating price indexesThe
where ## ExampleThis example uses a data set provided by Newbold.
The SHAZAM commands (
The The SHAZAM output can be viewed.
[SHAZAM Guide home] ## SHAZAM output - Calculating price indexes|_SAMPLE 1 12 |_* Weekly stock prices for major car manufacturers. |_READ P1 P2 P3 P4 4 VARIABLES AND 12 OBSERVATIONS STARTING AT OBS 1 |_* Volume of shares, in hundreds of thousands, traded in each week. |_READ Q1 Q2 Q3 Q4 4 VARIABLES AND 12 OBSERVATIONS STARTING AT OBS 1 |_* Compute a price index for the 1st car manufacturer - base period is week 8. |_GEN1 PBASE1=P1:8 |_GENR PINDEX1=100*P1/PBASE1 |_* Compute an aggregate price index |_INDEX P1 Q1 P2 Q2 P3 Q3 P4 Q4 / BASE=8 LASPEYRES=PALL BASE PERIOD IS OBSERVATION 8 LASPEYRE WILL BE STORED AS VARIABLE: PALL PRICE INDEX QUANTITY DIVISIA PAASCHE LASPEYRES FISHER DIVISIA PAASCHE LASPEYRES FISHER 1 .930 .935 .929 .932 1623. 1614. 1625. 1619. 2 .925 .941 .914 .927 877.2 862.3 887.6 874.9 3 .911 .920 .909 .915 788.3 780.3 789.6 784.9 4 .929 .932 .926 .929 804.0 801.3 806.8 804.0 5 .972 .971 .970 .970 1218. 1220. 1221. 1221. 6 .974 .975 .973 .974 1000. 999.6 1002. 1001. 7 .957 .958 .956 .957 685.3 684.5 686.1 685.3 8 1.000 1.000 1.000 1.000 1304. 1304. 1304. 1304. 9 1.033 1.034 1.031 1.033 992.8 991.6 994.1 992.9 10 1.031 1.036 1.025 1.031 1301. 1295. 1308. 1302. 11 1.114 1.127 1.095 1.111 1656. 1637. 1685. 1661. 12 1.073 1.077 1.063 1.070 1267. 1262. 1278. 1270. |_GENR PALL=100*PALL |_GENR OBS=TIME(0) |_FORMAT(F10.0,5X,2F13.2) |_PRINT OBS PINDEX1 PALL / FORMAT OBS PINDEX1 PALL 1. 103.18 92.88 2. 101.27 91.38 3. 96.82 90.95 4. 100.64 92.60 5. 103.18 96.95 6. 101.27 97.33 7. 98.73 95.58 8. 100.00 100.00 9. 107.64 103.13 10. 114.01 102.55 11. 127.39 109.48 12. 117.20 106.31 |_STOP [SHAZAM Guide home] |