construct placebo state-level laws on female wages and perform difference-in-difference regressions on CPS data. Despite the placebo nature of the laws, they find significant results for up to 45% of the placebo laws that they construct. As such, they conclude that using heteroskedastic-robust standard errors grossly underestimates the true standard errors of the estimate and suggest using clustered standard errors to control for possible autocorrelation of error terms across time. Nevertheless, KÊzdi (2004) shows that 50 clusters is sufficient for clustered standard errors to be roughly equal to true standard errors, but that a smaller number of clusters has a higher probability of producing incorrect results. To take into account that shifts in Spotify usage and piracy rates are not random within a country, I cluster my standard errors at the country level, addressing some of the concerns raised by Bertrand, Duflo, and Mullainathan (2002). Nevertheless, since I look at a relatively small number of states (15 total), the clustered standard errors may not allow us to draw accurate conclusions – that is, estimates that use clustered standard errors may produce estimates that are not close to their theoretical values. Thus, I look at both heteroskedastic-robust standard errors as well as clustered standard errors. 3.3.2
Robustness Tests
In order to test the robustness of the results obtained by the baseline regressions, I expand upon the baseline regressions in three ways: (1) I look at a different measure of music piracy, (2) I look at two different measures of Spotify usage rates, and (3) I add in a control variable to account for the possibility that other music streaming services account for changes in music piracy rates, rather than Spotify itself. I obtained data only for one possible substitute: Grooveshark, a similarly popular music streaming service that aims to change the way that music is listened to in such a way that diminishes music piracy rates. As discussed in section 2, Spotify’s impact on music piracy may not necessarily be its introduction into a country but rather the volume of new Spotify users. Thus, I look also at two other measures of the variable Spotify: (1) the flow of new Spotify users,
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