Do economists think TV is good for you?

In a nutshell, yes:

The variation Mr. Gentzkow
and Mr. Shapiro exploited was the timing of the introduction of TV into
different cities. Television began taking off in the U.S. in 1946,
after a wartime ban on TV production was lifted. But the Federal
Communications Commission stopped granting new commercial television
licenses from September 1948 to April 1952 while it made changes in
allocating broadcast spectrum. There was a long lag between when some
cities got television and when others did.

The economists then
looked at results of a survey of 800 U.S. schools that administered
tests to 346,662 sixth-grade, ninth-grade and 12th-grade students in
1965. Their finding: Adjusting for differences in household income,
parents’ educational background and other factors, children who lived
in cities that gave them more exposure to television in early childhood
performed better on the tests than those with less exposure.

The
economists found that television was especially positive for children
in households where English wasn’t the primary language and parents’
education level was lower. "We don’t exactly know why that is, but a
plausible interpretation is that the effect of television on cognitive
development depends on what other kinds of activity television is
substituting for," says Mr. Shapiro, 28.

Here is much more.  And yes the "Mr. Shapiro" is in fact Wunderkind Jesse Shapiro, a familiar figure to MR readers everywhere.  You’ll find two versions of the paper here.

Addendum: Here is Alex’s excellent post on the topic.