"The Apple iPod iTunes Anti-Trust Litigation"

Filing 665

Declaration in Support of 663 Response ( Non Motion ) to Professor Noll's July 18 Declaration filed byApple Inc.. (Related document(s) 663 ) (Kiernan, David) (Filed on 7/22/2011)

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Robert A. Mittelstaedt #60359
[e-mail]
Craig E. Stewart #129530
[e-mail]
David C. Kiernan #215335
[e-mail]
555 California Street, 26th Floor
San Francisco, CA 94104
Telephone:
[phone]
Facsimile:
[phone]
Attorneys for Defendant
APPLE INC.

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UNITED STATES DISTRICT COURT

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NORTHERN DISTRICT OF CALIFORNIA

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SAN JOSE DIVISION

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THE APPLE iPOD iTUNES ANTITRUST LITIGATION

Lead Case No. C 05-00037 JW (HRL)
[Class Action]

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__________________________________

SUPPLEMENTAL REPORT OF
DR. MICHELLE M. BURTIS

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This Document Relates To:

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ALL ACTIONS

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Supp. Burtis Expert
C 05-00037 JW (HRL)

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1.

In his most recent report filed July 18, 2011 (“Supplemental Noll Declaration”),

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Professor Noll updated his “preliminary regression” analysis set forth in his March 28, 2011

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declaration (“Noll Reply Declaration”) in an attempt to account for iTunes 7.0. Counsel for

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Apple has asked me to review the Supplemental Noll Declaration and address whether this

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preliminary analysis demonstrates that impact and damages can be shown on a class-wide basis.

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2.

Professor Noll’s new declaration does not show that his proposed methods will

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work. Rather than demonstrating that iTunes 7.0 resulted in any class-wide damage, his latest

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analysis actually shows that iTunes 7.0 reduced iPod prices—the opposite of plaintiffs’ theory of

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class-wide harm. Moreover, although Professor Noll has admitted that his previous regression

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analysis was not reliable and could not be used to show any causal effect on iPod prices, he has

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done nothing in his current model to correct the deficiencies he previously identified.

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Professor Noll’s Model, if Anything, Shows that iTunes 7.0 Had No Impact

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3.

Professor Noll asserts that his new model shows that iTunes “caused the wholesale

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price of iPods to be elevated by $4.85.” 1 He relies for this assertion on the coefficient his model

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estimates for his new iTunes 7.0 variable. But Professor Noll misinterprets this coefficient, which

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he obtains in a manner that is inconsistent with his treatment of other similar variables. In

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particular, Professor Noll has specified the iTunes 4.7 variable to be “on” over the period

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beginning with the iTunes 4.7 update in October 2004 and ending when the 7.0 update occurred

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on September 12, 2006. 2 The specification of this variable is different from the way in which

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Professor Noll previously specified variables associated with the iTunes 4.7 update and it is

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different from the way that Professor Noll has specified all of the other “dummy,” or indicator,

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variables in his regressions. All of the other “dummy” variables are specified to be “on”

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Supplemental Noll Declaration at p. 4.

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Professor Noll claims that he is “separating” the period affected by update 4.7 from the period
affected by update 7.0.” Supplemental Noll Declaration at p. 2 (“Hence, the econometric model
in my period report would need to be amended to separate the period affected by update 4.7 from
the period affected by update 7.0.”) While the model may separate the periods, Professor Noll
does not correctly describe the “separate” effect from 7.0. And if he had modeled a “separate”
effect like he modeled the effects of other variables in his model, he would have found the effect
to be negative, not positive.
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beginning with the particular event and staying “on” throughout the remainder of the estimation

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period. This is true of the “Post-iTMS” variable, the “Harmony launched” variable, the “iTunes

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7.0” variable, the “iTMS competitiors fully DRM-free” variable, and the “iTMS fully DRM free”

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variable. 3 Had Professor Noll specified the “iTunes 4.7” variable as he had in his previous

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regression and consistent with the other dummy variables in his previous and current regressions,

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the coefficient on the 7.0 update variable would have been negative, and equal to -1.69. If

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Professor Noll’s model were otherwise valid, this negative coefficient means that iTunes 7.0

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caused iPod prices to decrease rather than increase as plaintiffs claim.

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4.

That Professor Noll’s model actually shows a price decrease from iTunes 7.0 can

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be seen by comparing the relevant coefficients. According to Professor Noll, the iTunes 4.7

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update “caused” the price of iPods to be $6.54 higher over the period beginning with the iTunes

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4.7 update and ending with the iTunes 7.0 update. The results then show that the impact of the

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iTunes 4.7 update fell from $6.54 to $4.85 over the period beginning with the iTunes 7.0 update

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throughout the rest of the class period. The difference between 4.85 and 6.54 is -1.69. Again, his

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regression shows that plaintiffs’ theory is wrong—iTunes 7.0 caused a decline in price, not an

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increase. This is what his regression would show if he had specified his iTunes 4.7 consistently

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with his other dummy variables, and consistently with his treatment of iTunes 4.7 in his prior

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report.

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5.

Thus, when Professor Noll asserts that iTunes 7.0 “caused the wholesale price of

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iPods to be elevated by $4.85,” what his analysis actually shows is only that iTunes 7.0 “caused”

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the amount by which the price was allegedly elevated from iTunes 4.7 to decrease from $6.54 to

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Professor Noll’s specification of the iTunes 4.7 variable is clearly a departure from his treatment
of other variables. For example, consider the variables included in his model that attempt to
capture the impact of DRM-free music on iPod prices—i.e., “iTMS competitors fully DRM-free”
and “iTMS fully DRM-free.” Similar to his interpretation of the 4.7 and 7.0 variables, these
variables could be interpreted to measure the impact of some change in the marketplace that
changed over time. The first variable would measure the impact of certain suppliers offering
DRM-free music and the second would measure the impact from Apple offering DRM-free music.
Professor Noll models each of these variables to be equal to one (or “on”) at the beginning dates
and then throughout the sample period.
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$4.85. Similarly, when Professor Noll claims that his specification allows him to analyze whether

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the iTunes 7.0 update “perpetuated” the elevation in prices caused by the iTunes 4.7 update, 4 all

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he is actually measuring is whether some of that increase in price (from the no longer implicated

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4.7 update) continued to exist after the 7.0 update. In other words, Professor Noll is not testing,

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or claiming to test, whether 7.0 independently “caused” iPod prices to be higher. He is simply

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measuring (if his methods were otherwise valid) how much of the alleged impact of 4.7 remained

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after 7.0 was released. That the alleged impact from iTunes 4.7 supposedly continued after

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iTunes 7.0, however, does not establish that iTunes 7.0 had any anticompetitive impact.

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Professor Noll’s Statistical Measures Do Not Show That His Model is Valid

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Professor Noll’s claim that his proposed regression results are “highly significant

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and very precisely estimated” 5 is mistaken. The claim is based on Professor Noll’s calculation of

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the “standard errors” of his estimated coefficients. Standard errors reflect that, because each

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coefficient is estimated, there is an “error” around the estimation. Thus, Professor Noll’s finding

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that the coefficient on his iTunes 7.0 variable is 4.85 is, in actuality, a finding not of the single

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number 4.85, but of a range with 4.85 in the middle. The size of the range is determined by the

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standard error. The smaller the standard error, the tighter the range, and in Professor Noll’s

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words, the more “precise” the estimate.

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7.

The standard errors that Professor Noll reports are artificially small because he is

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using observations in his data set that are not independent from one another. Standard errors are

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determined, in part, by the number of observations in a sample (more data, in general, means

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more precise estimates). But the observations must be independent. If they are not, the

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calculated standard errors will be artificially small unless the model is appropriately corrected.

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Consider, for example, a model that uses a given set of data, resulting in a set of coefficients with

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Supplemental Noll Declaration at p. 2. (“Regardless of whether the 4.7 update was
anticompetitive, my prior analysis found that the 4.7 update elevated iPod prices. If the 7.0
update caused increased lock-in to iPods, the effect would have been to perpetuate at least some
of the elevation in prices arising from update 4.7.”)

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Noll Supplemental Declaration at p. 4.
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a calculated standard error. If the size of that data set is then doubled by simply duplicating the

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original data, the standard error of the estimated coefficients using the doubled data will fall. But

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the explanatory value of the model will not have increased because the observations in this

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duplicated data are not independent of the previous data.

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Professor Noll’s results suffer from this problem. As I described in my earlier

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report, Professor Noll’s data has very little variation. 6 For example, on a given day, Professor

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Noll may have many price observations for a given product, but the prices are all the same and

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they are not independent from one another. Put differently, the price one reseller pays on a given

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day (or in a given quarter) is not independent of the price another reseller pays. Without

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correction, this has the effect of reducing the standard errors and generating coefficient estimates

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that Professor Noll claims are precise. But the precision has little to do with the underlying

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variation and information in the sample, but instead is due to the number of repetitive data

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observations. This problem, well known in empirical economics, is called clustering. 7 When

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observations are clustered, it means that they are not independent from one another, but rather are

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correlated with each other within groups (or clusters). In his deposition, Professor Noll

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recognized this problem but claimed that he did not investigate it because he “ran out of time.” 8

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Exhibit B shows the standard errors for Professor Noll’s coefficients when the data is corrected to

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account for clustering. As that exhibit shows, once corrected, the standard errors associated with

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the iTunes 4.7 and iTunes 7.0 coefficients are not only not “highly significant,” they are not

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statistically significant at either the 1% or the 10% level. In fact, the coefficient on the iTunes 7.0

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2011 Burtis Reply Report at ¶ 15.

See for example, Larry B. Hedges and Christopher H. Rhoads, “Correcting an analysis of
variance for clustering,” British Journal of Mathematical and Statistical Psychology, (2011), 64,
pp. 20-37 at p. 20. (“A great deal of educational and social data arises from cluster sampling
designs where clusters involve schools, classrooms, or communities. A mistake that is sometimes
encountered in the analysis of such data is to ignore the effect of clustering and analyze the data
as if it were based on a simple random sample. This typically leads to an overstatement of the
precision of results and too liberal conclusions about precision and statistical significance of mean
differences.”)
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Noll Deposition at pp. 112-113.
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variable would be significant at the 70% level. This means the coefficient has very little, if any,

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significance and for all practical purposes can be considered to be zero.

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9.

Professor Noll also claims that the “fit” of the regression is “very high, with an

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adjusted R2 of 0.98.” 9 Professor Noll asserts that this statistic shows that “all but two percent of

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the variation in prices of iPod models is explained by the regression.” It is well known, however,

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that a high R2 may or may not be associated with capturing a true underlying relationship.

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Dummy variables in a model (such as used by Professor Noll) may generate a high R2 even

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though they have little actual explanatory power. See A Guide to Econometrics, Peter Kennedy,

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Second Edition at p. 185.

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10.

That Professor Noll’s purported statistical measures do not show that his model is

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valid is confirmed by the fact that Professor Noll made the same assertions about his previous

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model—i.e., that the previous model had an adjusted R2 of 0.98 and very low standard errors. 10

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Despite that assertion, however, Professor Noll admitted at his deposition (as discussed in the

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following section) that his previous model was not reliable and could not support any conclusion

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that iTunes 4.7 caused any effect on prices. The same is true of his current model.

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Professor Noll’s Current Model Does Not Address the Deficiencies He Admitted Existed in

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His Previous Model

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At his deposition, Professor Noll testified that his earlier preliminary regression

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analysis with respect to iTunes 4.7 was unreliable, incomplete, had omitted variables, may be

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biased, may be affected by spurious correlation, did not take Apple’s pricing strategy into

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account, and should not be used to draw any inferences about issues fundamental to the case, such

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as the price effect of the launch of iTS, the entry of Harmony, or the disabling of Harmony. 11

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Professor Noll thus acknowledged that he could not make any “causal inferences” from the

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Supplemental Noll Declaration at p. 4.

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Noll Reply Declaration at pp. 38-39

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2011 Burtis Reply Report at ¶ 7.

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regression. 12 In other words, the regression could not, and thus did not, show that iTunes 4.7 had

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any impact on iPod prices.

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12.

Professor Noll’s new model does not address these issues. He has simply taken

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the same model he used previously and made only a few adjustments to purportedly measure the

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effect of the iTunes 7.0 update. He does not remedy the problems he previously identified. With

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the exception of adding a new variable for the U2 Special Edition and a variable for iTunes 7.0,

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he has not attempted to identify the omitted variables and try to include them in his model. He

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has not corrected for bias or spurious correlation. He has not taken Apple’s pricing strategy into

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account. He states that he has corrected some (but not all) data problems. But the omitted

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variable, bias, spurious correlation and other problems he identified with his model are

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independent of the data issues to which he refers. They are problems with the model’s

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specification. And this has not meaningfully changed.

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Professor Noll’s Model Remains Flawed for Additional Reasons

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13.

Professor Noll’s regression returns a single estimate that is an average across

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proposed class members that buy different iPod models and who purchase iPods at different

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times. 13 The measure of impact obtained from this model is an average amount across those

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products that are sold in the periods both before and after the 7.0 update. He finds a single

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estimate of price elevation (which he incorrectly interprets as $4.85), which would be applied,

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apparently, to iPod shuffles that are priced at retail as low as $49 as well as to iPod touch models

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that are priced at retail as high as $499. Similarly, the average will apparently be applied to all

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iPods purchased after September 2006, whether they were purchased one week or two years after

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the update. Impact on different products purchased by different proposed class members at

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different times cannot be inferred based on an average.

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Further, Professor Noll’s model does not, and indeed cannot, be used to measure

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impact for iPod models that were introduced for the first time after the introduction of

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Noll Deposition at 90, (“I drew no causal inferences from that regression.”)

2011 Burtis Reply Report at ¶ 11. Professor Noll admitted the result was an average. See Noll
Deposition at p. 142.
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Exhibit A

Professor Noll's Regression with Clustered
Standard Errors
Dependent variable
Adjusted R2
Number of Observations

iPod transaction price
0.9762
2,098,663

Variable

Coefficient Estimate

Standard Error

301.65
-47.41
-62.81
-35.58
-49.23
-206.39
-139.68
-119.62
-94.52
-194.62
-131.18
-94.41
-123.57
-39.10
-0.14
-48.13
-5.88
201.09
-19.16
32.99
63.49
-183.99
-0.26
4.16
0.34
-0.07
-0.17
12.09
4.00
0.36
3.52
-5.17
-1.81
-0.06
-2.03
-7.10
2.69
-1.64
-3.99
5.70
-0.50

70.58
9.19
14.44
10.25
14.22
39.01
36.81
37.10
34.91
40.59
119.69
31.77
43.53
26.90
36.27
38.45
25.74
69.06
37.50
98.69
39.96
52.09
1.04
1.77
0.92
0.95
1.02
5.62
8.49
0.89
3.42
1.89
1.13
2.09
0.98
2.10
2.74
5.74
1.72
1.77
0.45

Intercept
Classic
Mini
Nano
Shuffle
Capacity 512MB
Capacity 1024MB
Capacity 2048MB
Capacity 4096MB
Capacity 5120MB
Capacity 6144MB
Capacity 8192MB
Capacity 10240MB
Capacity 15360MB
Capacity 16384MB
Capacity 20480MB
Capacity 30720MB
Capacity 32768MB
Capacity 40960MB
Capacity 61440MB
Capacity 81920MB
Capacity 122880MB
Time trend
Time Trend * Capacity 512MB
Time Trend * Capacity 1024MB
Time Trend * Capacity 2048MB
Time Trend * Capacity 4096MB
Time Trend * Capacity 5120MB
Time Trend * Capacity 6144MB
Time Trend * Capacity 8192MB
Time Trend * Capacity 10240MB
Time Trend * Capacity 15360MB
Time Trend * Capacity 16384MB
Time Trend * Capacity 20480MB
Time Trend * Capacity 30720MB
Time Trend * Capacity 32768MB
Time Trend * Capacity 40960MB
Time Trend * Capacity 61440MB
Time Trend * Capacity 81920MB
Time Trend * Capacity 122880MB
Medium volume purchaser

***
***
***
***
***
***
***
***
***
***
***
***

***

***
**

**

***

**
***

**
***

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Exhibit A
High volume purchaser
1 to 5 units purchased
1st quarter
2nd quarter
3rd quarter
Photo capability
Video and photo capability
Post-repricing transaction
Post-end of life transaction
Post-iTMS
Harmony launched
iTunes 4.7
iTunes 7.0
iTMS competitors fully DRM-free
iTMS fully DRM-free
Size (in3)
Standard cost per unit

-0.75
2.94
5.01
13.73
5.10
9.73
-6.34
-11.35
-19.95
-50.49
-31.07
5.50
3.34
-9.78
-13.79
-3.16
0.80

***
**
***
**

***
**
***
***

**
***
***

0.62
0.61
1.97
2.41
2.32
7.02
5.17
3.77
8.32
14.73
9.96
7.31
8.71
4.33
4.31
4.60
0.08

Source: Noll Reply Declaration Backup
Note:
Standard errors are clustered around iPod model and the quarter during which the model
was sold.
*** Denotes statistical significance at the 1% level.
** Denotes statistical significance at the 5% level.
* Denotes statistical significance at the 10% level.

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Exhibit B

Professor Noll's Regression on iPod Touch
Transactions Only
Dependent variable
Adjusted R2
Number of Observations

iPod transaction price
0.9668
353,669

Variable

Coefficient Estimate

Intercept
Classic
Mini
Nano
Shuffle
Capacity 512MB
Capacity 1024MB
Capacity 2048MB
Capacity 4096MB
Capacity 5120MB
Capacity 6144MB
Capacity 8192MB
Capacity 10240MB
Capacity 15360MB
Capacity 16384MB
Capacity 20480MB
Capacity 30720MB
Capacity 32768MB
Capacity 40960MB
Capacity 61440MB
Capacity 81920MB
Capacity 122880MB
Time trend
Time Trend * Capacity 512MB
Time Trend * Capacity 1024MB
Time Trend * Capacity 2048MB
Time Trend * Capacity 4096MB
Time Trend * Capacity 5120MB
Time Trend * Capacity 6144MB
Time Trend * Capacity 8192MB
Time Trend * Capacity 10240MB
Time Trend * Capacity 15360MB
Time Trend * Capacity 16384MB
Time Trend * Capacity 20480MB
Time Trend * Capacity 30720MB
Time Trend * Capacity 32768MB
Time Trend * Capacity 40960MB
Time Trend * Capacity 61440MB
Time Trend * Capacity 81920MB
Time Trend * Capacity 122880MB
Medium volume purchaser

807.62
-245.89
-120.35
146.58
-7.59
3.39
1.02
-6.28
-0.32

Standard Error
0.52
0.24
0.23
0.22
0.01
0.01
0.01
0.01
0.18

Page 1

Exhibit B
High volume purchaser
1 to 5 units purchased
1st quarter
2nd quarter
3rd quarter
Photo capability
Video and photo capability
Post-repricing transaction
Post-end of life transaction
Post-iTMS
Harmony launched
iTunes 4.7
iTunes 7.0
iTMS competitors fully DRM-free
iTMS fully DRM-free
Size (in3)
Standard cost per unit

-0.29
2.97
9.04
20.97
10.67
-60.39
-5.86
-7.56
-81.88
0.32

0.17
0.52
0.00
0.01
0.01
0.09
0.02
0.01
0.05
0.00

Source: Noll Reply Declaration Backup
Note:
Coefficients that are not able to be estimated are denoted by a "-".
Standard errors have been calculated using Professor Noll's methodology.

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