I followed up my last post by looking at the correlation between perceived corruption in 2006 and opinions on whether politics played a part in the administration of relief in 1937. My idea was that states would have an enduring political culture, so that the ones that were corrupt (or perceived that way) in 1937 would still be in 2006. The correlation between the scores at the different times was .05, with a p-value of .75. The means are from samples, pretty small samples in many cases, but when you start from that near zero, correcting for sampling error won't make much difference.
Then it occurred to me that the alleged role of politics in the administration of relief was a Republican issue in the late 1930s, so you should control for the political inclinations of the states. I regressed 1937 perceptions on vote for Roosevelt in 1936 and perceived corruption in 2006. This produced an R-square of 0.3 and an adjusted R-square of zero. It's not looking good for my hypothesis.