Producer Price Index Manual: Theory and Practice ... - METAC

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Producer Price Index Manual tm , t+ 1, m 0, m (22.8) PAL ( p , p , s ) m = 1, 2,...12; n∈S( m) tm , t+ 1, m 0, m (22.9) PAP ( p , p , s ) m = 1, 2,...12; ( + ) = ∑ s p p ; 0, m t 1, m t, m n n n −1 −1 ⎡ ⎤ 0, m t+ 1, m t, m = ⎢ ∑ sn ( pn pn ) ⎥ ⎢⎣n∈ S( m) ⎥ ; ⎦ t, m t+ 1, m 0, m 0, m (22.10) PAF ( p , p , s , s ) tm , t+ 1, m 0, m tm , t+ 1, m 0, m PAL ( p , p , s ) P ( p , p , s ) ≡ ; m = 1, 2,...,12 −1 −1 ⎡ ⎤ tm , t+ 1, m tm , tm , t+ 1, m tm , = ∑ sn ( pn pn ) ⎢ ∑ sn ( pn pn ) ⎥ n∈S( m) ⎢⎣n∈S ( m) ⎥⎦ . 22.23 The approximate Fisher year-over-year monthly indices defined by equation (22.10) will provide adequate approximations to their true Fisher counterparts defined by equation (22.6) only if the monthly revenue shares for the base year 0 are not too different from their current year t and t+1 counterparts. Thus, it will be useful to construct the true Fisher indices on a delayed basis in order to check the adequacy of the approximate Fisher indices defined by equation (22.10). 22.24 The year-over-year monthly approximate Fisher indices defined by equation (22.10) will normally have a certain amount of upward bias, since these indices cannot reflect long-term substitution toward products that are becoming relatively cheaper over time. This reinforces the case for computing true year-over-year monthly Fisher indices defined by equation (22.6) on a delayed basis, so that this substitution bias can be estimated. 22.25 Note that the approximate year-over-year monthly Laspeyres and Paasche indices, P AL and P AP defined by equations (22.8) and (22.9), satisfy the following inequalities: tm , t+ 1, m 0, m (22.11) PAL ( p , p , s ) t+ 1, m t, m 0, m PAL ( p p s ) × , , ≥ 1; m = 1, 2,...,12; + P p , p , s tm , t 1, m 0, m (22.12) AP ( ) t+ 1, m t, m 0, m PAP ( p p s ) m = 1, 2,...,12; × , , ≤ 1; with strict inequalities if the monthly price vectors p t,m and p t+1,m are not proportional to each other. 13 Equation (22.11) says that the approximate yearover-year monthly Laspeyres index fails the time reversal test with an upward bias while equation (22.12) says that the approximate year-over-year monthly Paasche index fails the time reversal test with a downward bias. As a result, the fixedweights approximate Laspeyres index P AL has a built-in upward bias while the fixed-weights approximate Paasche index P AP has a built-in downward bias. Statistical agencies should avoid the use of these formulas. However, they can be combined, as in the approximate Fisher formula in equation (22.10). The resulting index should be free from any systematic formula bias, although some substitution bias could still exist. 22.26 The year-over-year monthly indices defined in this section are illustrated using the artificial data set tabled in Section B. Although fixedbase indices were not formally defined in this section, these indices have similar formulas to the year-over-year indices that were defined, with the exception that the variable base year t is replaced by the fixed-base year 0. The resulting 12 yearover-year monthly fixed-base Laspeyres, Paasche, and Fisher indices are listed in Tables 22.3 to 22.5. 22.27 Comparing the entries in Tables 22.3 and 22.4, it can be seen that the year-over-year monthly fixed-base Laspeyres and Paasche price indices do not differ substantially for the early months of the year. However, there are substantial differences between the indices for the last five months of the year by the time the year 1973 is reached. The largest percentage difference between the Laspeyres and Paasche indices is 12.5 percent for month 10 in 1973 (1.4060/1.2496 = 1.125). 13 See Hardy, Littlewood, and Pólya (1934, p. 26). 560
22. Treatment of Seasonal Products Table 22.3. Year-over-Year Monthly Fixed-Base Laspeyres Indices Month 1 2 3 4 5 6 7 8 9 10 11 12 1970 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1971 1.1085 1.1068 1.1476 1.1488 1.1159 1.0844 1.1103 1.0783 1.0492 1.0901 1.1284 1.0849 1972 1.2060 1.2442 1.3062 1.2783 1.2184 1.1734 1.2364 1.1827 1.1049 1.1809 1.2550 1.1960 1973 1.3281 1.4028 1.4968 1.4917 1.4105 1.3461 1.4559 1.4290 1.2636 1.4060 1.5449 1.4505 Table 22.4. Year-over-Year Monthly Fixed-Base Paasche Indices Month 1 2 3 4 5 6 7 8 9 10 11 12 1970 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1971 1.1074 1.1070 1.1471 1.1486 1.1115 1.0827 1.1075 1.0699 1.0414 1.0762 1.1218 1.0824 1972 1.2023 1.2436 1.3038 1.2773 1.2024 1.1657 1.2307 1.1455 1.0695 1.1274 1.2218 1.1901 1973 1.3190 1.4009 1.4912 1.4882 1.3715 1.3266 1.4433 1.3122 1.1664 1.2496 1.4296 1.4152 Table 22.5. Year-over-Year Monthly Fixed-Base Fisher Indices Month 1 2 3 4 5 6 7 8 9 10 11 12 1970 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1971 1.1080 1.1069 1.1474 1.1487 1.1137 1.0835 1.1089 1.0741 1.0453 1.0831 1.1251 1.0837 1972 1.2041 1.2439 1.3050 1.2778 1.2104 1.1695 1.2336 1.1640 1.0870 1.1538 1.2383 1.1930 1973 1.3235 1.4019 1.4940 1.4900 1.3909 1.3363 1.4496 1.3694 1.2140 1.3255 1.4861 1.4327 Table 22.6. Year-over-Year Approximate Monthly Fixed-Base Paasche Indices Month 1 2 3 4 5 6 7 8 9 10 11 12 1970 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1971 1.1077 1.1057 1.1468 1.1478 1.1135 1.0818 1.1062 1.0721 1.0426 1.0760 1.1209 1.0813 1972 1.2025 1.2421 1.3036 1.2757 1.2110 1.1640 1.2267 1.1567 1.0788 1.1309 1.2244 1.1862 1973 1.3165 1.3947 1.4880 1.4858 1.3926 1.3223 1.4297 1.3315 1.1920 1.2604 1.4461 1.4184 561
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Contents Foreword..................
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Contents D. The Incorporating of Ne
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Contents E. Industry Price Indices
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Contents Table 19.23 Manufacturing
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Foreword This Producer Price Index
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Preface The ILO, IMF, OECD, UNECE,
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Preface source (rather than requiri
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Preface tremendous concern with sam
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Preface among countries. However, t
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Preface Chapter 6 Chapter 7 Chapter
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Reader’s Guide International manu
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Reader’s Guide the System of Nati
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Abbreviations ABS ABS AF ANZIC ATM
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Abbreviations OLS Ottawa Group P C
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PART I Methods, Uses, and Coverage
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Producer Price Index Manual The exp
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Producer Price Index Manual B.1 Pri
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Producer Price Index Manual D. The
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Producer Price Index Manual theoret
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Producer Price Index Manual C. Geog
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PART II Compilation Issues
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Producer Price Index Manual C. Appr
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Producer Price Index Manual Figure
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Producer Price Index Manual source
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Producer Price Index Manual prices
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5. Sampling Issues in Price Collect
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Producer Price Index Manual • Wil
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Producer Price Index Manual tory su
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Producer Price Index Manual D.1.2 C
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Producer Price Index Manual (5.2) f
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Producer Price Index Manual Table 5
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Producer Price Index Manual ances.
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Producer Price Index Manual RESPOND
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7. Treatment of Quality Change A. I
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Producer Price Index Manual 7.12 Co
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Producer Price Index Manual current
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Producer Price Index Manual success
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Producer Price Index Manual per uni
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Producer Price Index Manual variety
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Producer Price Index Manual (7.31b)
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Producer Price Index Manual B. Samp
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Producer Price Index Manual in resp
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9. PPI Calculation in Practice clud
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Producer Price Index Manual (a) Res
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Producer Price Index Manual 10. Rec
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Producer Price Index Manual USAGE C
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11. Errors and Bias in the PPI disp
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Producer Price Index Manual of the
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Producer Price Index Manual unitary
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12. Organization and Management A.
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12. Organization and Management ass
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12. Organization and Management of
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12. Organization and Management rie
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12. Organization and Management det
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12. Organization and Management Vis
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12. Organization and Management fou
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13. Publication, Dissemination, and
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14. The System of Price Statistics
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I 14. The System of Price Statistic
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15. Basic Index Number Theory 371 k
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15. Basic Index Number Theory 373 1
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15. Basic Index Number Theory 395 C
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15. Basic Index Number Theory 399 A
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16. Axiomatic and Stochastic Approa
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17. Economic Approach A. Introducti
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17. Economic Approach possibilities
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17. Economic Approach the numerator
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17. Economic Approach 17.28 The new
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17. Economic Approach 17.36 The abo
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17. Economic Approach 17.49 Suppose
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17. Economic Approach perlative ind
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17. Economic Approach (17.35) C 0 (
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17. Economic Approach (17.46) P T (
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17. Economic Approach ing flexible
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17. Economic Approach P W (p 0 ,p 1
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17. Economic Approach constraint, f
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18. Aggregation Issues A. Introduct
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18. Aggregation Issues (18.4) R 0 (
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18. Aggregation Issues (18.14) R(p
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18. Aggregation Issues Then, this n
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18. Aggregation Issues (18.28) P 1
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18. Aggregation Issues , = 1 N M
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18. Aggregation Issues (18.56) p t
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18. Aggregation Issues 18.67 Howeve
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19. Price Indices Using an Artifici
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