Well, to an economist, there's a bit of a problem. Both iTunes and Spotify, at least in their basic versions, are free -- and when goods are free, the notion of competition gets cloudy.
The idea can't get off the ground without a price. Most of the time, that's not a problem. Ford competes with Toyota, apples with oranges. No price, no scarcity -- and, it might seem, no economics. But the growing amount of economic activity on the Internet, where competition is so obvious and yet so many products are free, requires a more flexible notion of competition.
Let's stick with iTunes and Spotify as a case study of two high-profile Internet competitors. In the data analysis that follows, I find that iTunes loses a user for every five new users of Spotify and that the introduction of Spotify has so far reduced iTunes use by 15 percent globally. There is, in other words, competition on the Internet -- and competition even when goods are free.
[See update below: More data, bigger results.]
Using Google Trends, I downloaded weekly Google search data for iTunes and Spotify for 57 countries between 2004 and 2015. These, I think, are good proxies for signups for iTunes and Spotify, since people will search on Google to download either. (In my conversation with Josh Gans, I found that searches with "Spotify" or "iTunes" are usually about downloading them.) And the search data seem to match what we see in the limited public data on iTunes and Spotify use. I picked the countries based on where iTunes and Spotify had launched, looking for their target markets.
iTunes was initially released in 2001, and Spotify was in October 2008, both in select countries only. What we see in the Google data is that iTunes has been trending downwards since 2012. Perhaps not coincidentally, that was also when Spotify began expanding beyond its initial markets in northern Europe. That, of course, hardly proves that Spotify was responsible.
For iTunes or Spotify to enter a country, they must strike deals with big music labels in the context of local intellectual property law. Spotify negotiated for two years, for instance, before entering the US. As a result of this legal thicket, Spotify rolled out gradually across my sample of countries -- and I can exploit that gradual expansion to measure the effect of Spotify on iTunes. Using official Spotify press releases, like this one, I added Spotify's entry dates (or lack of entry, for some of the 57 countries) to my dataset. You can download my data here.
To measure the effect of Spotify on iTunes, I'll use an instrumental variables regression, one simple enough that even people who aren't stats nerds or economists can follow.
This method requires an important, but believable, assumption: The only way the timing of Spotify's market entry affects iTunes use is through Spotify use. Said differently, nobody decided to stop listening to music, or switch to Pandora, because Spotify became available. Which wouldn't make much sense. Formally, for the economists, my claim to instrument exogeneity follows from the independence of irrelevant alternatives.
The first step is to build a simple regression model that predicts Spotify use in a given country in a given week from whether Spotify was available in that country, whether it had launched in that country in that week, and how many weeks it had been available in that country.
I found, not surprisingly, that Spotify use was higher in countries where Spotify had entered, higher in the launch week, and growing in the number of weeks since launch. (I also included a term to capture the fact that this growth slowed eventually.) What is perhaps surprising is that my simple model explains 75 percent of the variance in Spotify use among the 57 countries from 2004 to 2015.
Here, for instance, is what the model's predictions look like versus actual data for the US:
Next, I take my model's predicted values for Spotify use for the 57 countries and use those to predict iTunes use. That regression, under our assumptions, actually measures the causal effect of Spotify on iTunes.
I find that, for every one new user of Spotify, iTunes loses -0.23 users -- although the 95-percent confidence interval is quite wide, at -0.40 users to -0.05 users. Roughly speaking, for every five that Spotify gains, iTunes loses one.
I can also use that conversion rate to figure out the total effect of Spotify on iTunes use over time. iTunes use is 15 percentage points lower because of Spotify use than it would have been in a world without Spotify.
Spotify thus explains around a third of the decline in iTunes use since its peak in 2012. There seems to be more to iTunes' decline than competition alone. Yet competition does exist, quite clearly, online and among goods without prices. It would be worth doing a similar analysis for MySpace and Facebook, or Netflix and Hulu and HBO GO.
Note about graphs: It doesn't affect any of the results, but the year labels are slightly off.
Update (1/18/16): I have expanded my dataset to 72 countries, and the marginal effect of Spotify on iTunes is -0.33, with a 95% confidence interval of (-0.51,-0.16). This implies that Spotify has caused a 20-percent drop in iTunes use, and I am thus able to explain about half of the decline of iTunes since 2012. The rest, presumably, must be related to the fact that iTunes is just an awful piece of software.