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Comments by Paul Armknecht
NBER/CRIW Conference
June 28, 2004
Introduction
In this paper, White and Berndt present a new data source for measuring price change in softwareNDP Intelect. The advantage of this new source is that it allows computation of average prices using actual transaction prices and quantities. Previous work by the authors used list prices to estimate both hedonic and matched-model price indices. The current paper is a first attempt to extend their work using actual transaction prices. In future revisions the authors may wish to change the title. Although it is catchy, the article could confuse Internet search engines and turn up under searches for Weight Watchers!
Weighted vs. Unweighted Indices
The authors pose the question as to whether weighted or unweighted indices are preferred and will provide evidence of the differences weighting makes in estimating hedonic and matched-model indices. Before reading the paper I came up with my a prior assumptions about what the results should show.
No question about it: everyone prefers weighted indices;
Weighted chained indices should eliminate most substitution bias;
Laspeyres indices will be greater than Paasche indices (the markets considered measure transaction prices for purchasers rather than revenues received by suppliers);
Matched models do not eliminate all quality change bias; and
Hedonic models should provide the best estimates of quality effects.
Results
The NDP Intelect dataset provides broader coverage of actual PC software transactions than those previously used by the authors. As expected the chained Laspeyres matched model indices showed higher growth rates than the chained Paasche matched model indices. For example, the annual average growth rate (AAGR) for operating systems showed the Laspeyres growing at 4.01 percent and the Paasche at 1.22 percent. For productivity suites, the Laspeyres AAGR was 0.22 percent while the Paasche AAGR was 1.37 percent. The differences between Laspeyres and Paasche were even greater of during 19982003 period.
The Fisher index shows little price change while the unweighted geometric mean reflects large declines. For example, in operating systems the geometric mean shows 11 percent and, for productivity suites, a similar 13 percent. In White and Berndts March 2004 paper the unweighted geometric mean and the unweighted Fisher index both show AAGRs of 7percent. Thus, the introduction of weights appears to make a significant difference.
However, direct comparisons of weighted indices with their unweighted counter parts are missing from the current paper. For operating systems, the quarterly chained Fisher index shows an AAGR of 1.36 percent. This index should be compared with an unweighted Fisher-type index (the Carruthers, Sellwood, Ward, and Daln index) to provide an estimate of the effects of weighting. Similarly, the unweighted geometric mean index, which shows an AAGR of 11.3, should be compared with a geometric Laspeyres index to measure the effects of weighting. For productivity suites, The quarterly chained Fisher index shows an AAGR of 0.58 percent and the geometric mean index AAGR is 13.2 percent. To obtain measures of the weighting effects, these indices should be compared with the Carruthers, Sellwood, Ward, and Daln index and the geometric Laspeyres, respectively.
Another comparison that can be made is to calculate a geometric Paasche index that then can be used with the geometric Laspeyres index to calculate a Trnqvist index. The Fisher and Trnqvist should show similar results.
An important result that is not shown are the development of hedonic indices. One of the major contributions of White and Berndts March 2004 paper was the various hedonic indices. This current paper could be greatly improved with the addition of the estimation and analysis of hedonic indices. It would be very interesting to see if the quality adjusted hedonic results are similar between this new dataset and the earlier work (AAGRs of 15 percent).
Other issues
The prices used in compiling the indices represent the average price paid per user. As such, the prices may not reflect differences due to volume discounts as some users may purchase large quantities and receive a discount that varies by the quantity purchased. The overall index may not reflect the full effects of such discounts.
The authors also assert in Section 4 that the annual chained Laspeyres index drifts upward and is greater than the quarterly chained Paasche index. This is not what is presented earlier in the paper. For operating systems the AAGR for the annual chained Laspeyres index is 2.7 percent versus an AAGR of 4.0 percent for the quarterly chained Paasche. For productivity suites, the Laspeyres AAGR is 0.2 percent compared with 1.1 for the Paasche. One reason for the atypical relationship is that the quarterly chained Paasche index my suffer from upward drift from too frequent chaining. This can occur if there are significant seasonal patterns in the data that result in price bouncing. Such seasonal patterns may exist as evidenced in the March 2004 paper where the hedonic indices show significant seasonal effects. Because both price and quantity data are available, it is possible to measure the contributions of each to the price index change using decomposition techniques such as the Edgeworth-Marshall cross.
Next steps
The authors should calculate the geometric Laspeyres price indices and the geometric Paasche indices to compare with unweighted geometric mean indices to estimate the effects that weights have on the basic level indices. They should also calculate the unweighted Carruthers, Sellwood, Ward, and Daln index to compare with the Fisher index to provide a separate estimate of the effects of weights.
Finally, the authors need to develop the hedonic indices similar to those in their earlier work. This will be most useful to see what differences occur when transaction prices and actual quantity weights are available for the measurement of true hedonic indices. Such information will provide a more accurate indication of the movement in quality adjusted price indices.
(continued)
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