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

7. Treatment of Quality Change
Table 7.4. Hedonic Regression Results for Dell and Compaq PCs
Dependent Variable Price ln Price
Constant –725.996 (2.71)** 6.213 (41.95)***
Speed (Processor, MHz) 2.731 (9.98)*** 0.001364 (9.02)***
RAM (random access memory, MB) 1.213 (5.61) *** 0.000598 (5.00) ***
HD (hard drive capacity, MB) 4.517 (1.96)* 0.003524 (2.76)**
Brand (benchmark: Compaq Deskpro)
Compaq Presario –199.506 (1.89)* –0.152 (2.60)**
Compaq Prosignia –180.512 (1.38)* –0.167 (2.32)*
Dell -1,330.784 (3.74)*** –0.691 (3.52)***
Processor (benchmark: AMD Athlon)
Intel Celeron 393.325 (4.38)*** 0.121 (2.43)**
Intel Pentium III 282.783 (4.28)*** 0.134 (3.66)***
Rom-drive (benchmark: CD-ROM) †
CD-RW (compact disk-rewritable) 122.478 (56.07)*** 0.08916 (2.88)**
DVD drive (digital video disk) 85.539 (1.54) 0.06092 (1.99)*
Dell × Speed (MHz) 1.714 (4.038)*** 0.000820 (3.49)***
N 63 63
2
R 0.934 0.934
† Read-only memory.
Figures in brackets are t-statistics testing a null hypothesis of the coefficient being zero.
***, **, and * denote statistically significant at a 0.1 percent, 1 percent, and 5 percent level, respectively,
tests being one-tailed.
(OLS) regression. Facilities for regression are
available on standard statistical and econometricsoftware,
as well as spreadsheets. The estimated
(linear) equation in this instance is
(7.22) ˆPrice =− 658.436 + 3.261Speed,
2
R = 0.820 .
The coefficient on speed is the estimated slope of
the line: the change in price (£3.261) resulting
from a 1 MHz change in speed. This can be used to
estimate quality-adjusted price changes for PCs of
2
different speeds. The R finds that 82 percent of
price variation is explained by variation in processing
speed. A t-statistic to test the null hypothesis of
the coefficient being zero was found to be 18.83;
recourse to standard tables on t-statistics found the
null hypothesis was rejected at a 1 percent level.
The fact that the estimated coefficient differs from
zero cannot be attributed to sampling errors at this
level of significance. There is a probability of 1
percent that the test has wrongly rejected the null
hypothesis.
7.128 However, the range of prices for a given
speed—933 MHz for example—can be seen from
Appendix 7.1 to be substantial. There is a price
range of about £1,000, which suggests other quality
characteristics may be involved. Table 7.4 provides
the results of a regression equation that relates
price to a number of quality characteristics
using the data in Appendix 7.1. Such estimates can
be provided by standard statistical and econometric
software, as well as spreadsheets.
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