I am using survey data with a huge amount of observations, such as the World Value Surveys. Large sample sizes are obviously very nice, but I have have encountered some downsides as well.
To give an example, in almost every econometric model I specify, about 90% of the variables is highly significant. So I will have to decide whether, in addition to an estimate being statistically significant, it is also economically significant, which is not always an easy thing to do.
The biggest issue is however, that when resorting to Instrumental Variables, the Hausman test for over identification is always very, very, very significant. See to this extent THIS POST.
How do I deal with with this consequence of large sample sizes?
The only thing I can think of is to reduce the sample size. This however seems a very arbitrary way to get the test statistic down.