Internet Service Providers Report

Appendix 2: Analysis of Copyright Notices over Time using Panel Data

All ISPs able to report monthly numbers of subscribers and infringement notices for a period of at least six months are pooled and analyzed using panel data techniques. The relationship between subscribers of various types and infringement notices over time was tested using a random effect model for cross-section and time-series data of the form:

y[i,t] = B*x[i,t] + u[i] + e[i,t]

Random effects is considered the appropriate specification of the u[i] term because (a) the firms represent a sample of the population, and (b) the u[i] are expected to be orthogonal to the number of subscribers. In total, there were 162 observations of infringement notices at a particular ISP in a particular month. The earliest observations are from 2001, and the latest from January of 2005.

The results of this analysis are in Table 6. As a baseline, Model 1 reproduces the analysis without time effects. For large ISPs, the number of copyright notices is positively and significantly related to the number of high-speed subscribers (i.e., Cable and DSL) but unrelated to the number of dial-up subscribers.

A linear time effect is introduced in Model 2 using a month variable that starts at 1 in the first month in the sample and increases by 1 for each subsequent month. The impact of the month variable is so strong (the explanatory power of the model, measured by percentage of variance explained, jumps markedly) that all of the estimates for the effects of subscribers become insignificant. Obviously there is a significant time trend in the number of notices received by large ISPs; Model 3 explores a quadratic time trend with the introduction of month squared. However, the squared term is insignificant, so time appears to have a linear effect within the sample data. Finally, Model 4 breaks this time trend into an interaction of the month variable with each subscriber type. All three of these interactions are significant, although two are positive (DSL and Cable) and one (dial-up) negative. Thus, the number of notices received per DSL and Cable subscriber per month has been increasing over time whereas the number of notices received per dial-up subscriber per month has been decreasing. As with the cross-sectional analysis above, the direct impact of time could not be included along with the interaction terms due to extreme multicollinearity.

Taking Model 4 as the preferred specification, the analysis of the number of ISP notices generated by subscriber type over time indicate:

• The number of copyright notices received per high-speed subscriber (Cable or DSL) has been increasing over time at a constant rate.
• The number of copyright notices received per dial-up subscriber has been falling over time at a constant rate.