The difference between significant and non-significant is not itself statistically significant

One of my favorite points arose in the seminar today. A regression was fit to data from the 2000 Census and the 1990 Census, a question involving literacy of people born in the 1958-1963 period. The result was statistically significant for 2000 and zero for 1990, which didn’t seem to make sense, since presumably these people were not changing much in literacy between the ages of 30 and 40. The resolution of this apparent puzzle was . . . the difference between the estimates was not itself statistically significant! (The estimate was something like 0.003 (s.e. 0.001) for 2000, and 0.000 (s.e. 0.002) for 1990. So both data points were consistent with an estimate of 0.002 (for example). But at first sight, it really looked like there was a problem.

P.S. These was a small effect, as can be seen by the fact that it was barely statistically significant, even though it came from the largest dataset one could imagine: the Chinese census. Well, just a 1% sample of the Chinese census, but still . . .