On one level the decline in over-the-air household is counter-intuitive; the price of multichannel television has gone up much faster than inflation over the last decade. Higher prices usually lead to lower sales for the same product. I see the three factors -- two external to the multichannel value proposition and one internal -- that supported the decline in the use of over-the-air television.
First, the conversion of broadcast TV to digital made decades of analog-only TV sets obsolete for receiving TV stations (or required a digital converter box to make broadcast TV signals usable by these sets). In contrast, all of the top multichannel subscription services work just fine with an analog TV set (without even the need for a set-top box on many cable systems).
Second, the number of households with high speed Internet connections has dramatically expanded since 2003 and such households have a large amount of video content available to them both for free (e.g., YouTube, Hulu) and for pay (e.g., Netflix, iTunes). A light TV viewer might get all the video he or she needs from the Internet and not bother with an antenna and/or converter box.
Finally, a strong argument can be made that the content available via multichannel television has advanced faster than its price, rendering it a better value than it was earlier. In 2003, the top college bowl games were on broadcast television as were virtually all of the top dramas. By 2012, all of the top college bowl games were on ESPN networks (well, all but 3 of the top 36 bowl games, per this link), AMC's The Walking Dead was the top rated drama on television and cable networks like Food, E!, History and Showtime were attracting significantly more viewing and this was no accident as they are all spending significantly more on original programming. Not to mention that the multichannel subscription is much more likely to include VOD, HD and online streaming/TV Everywhere access to substantially more content than it did in 2003.
|Click the graphic to see it in its full sized glory|