One of my favorite parts of Milton Friedman's and Anna J. Schwartz's modern classic, A Monetary History of the United States, 1867-1960, is a lengthy footnote on pp. 463-64. It's their explanation of why they think the reported amount of gold in the United States, prior to FDR's confiscation order, was unrealistically low. A key part of the footnote:
If the estimates of gold lost and gold exported without record are added to the gold coin returned to the Treasury since 1934, we are still far short of accounting for even half of the $287 million. We therefore concluded that in Jan. 1934 the bulk of the $287 million was retained illegally in private hands. For this reason we restored to the gold stock and gold circulation the $287 million which the Federal Reserve subtracted for 1914-33 from the figures as originally published.
In other words, as they show in the footnote, the Fed had reported a lower number for the amount of gold than was justified by the earlier data on gold held. Presumably, although Friedman and Schwartz don't explicitly say this, if the Fed had reported a more-realistic number, it would have had to admit that a substantial amount of gold was held by people who said, in effect, "the hell with you Fed; this gold is mine." But governments often don't want to admit, especially in official documents, the extent of civil disobedience.
Update: I received an e-mail from a regular reader of this blog saying that my (Friedman's and Schwartz's) point isn't clear. Here it is, hopefully clearer. The government thought that x gold existed in, say, 1930. Then, when people were supposed to turn their gold over by law in 1934, the government calculated that there was only 0.8x. Rather than concluding that people were withholding 0.2x of gold, the government went back and said, "Oops, we overestimated the amount of gold in 1930. It must have been falling due to factors y and z."