In conformity with your figures the correlation is spurious and there is no question about it.
The problem is that, by the time that the interest rates got stuck against the zero lower bound the variations in unemployment should by the statitical data would have to be irrelevant because only a return to full employment would have been able to move the interest rates in the only possible way, which was and still is up. In other words, if the interest rates could have gone negative then maybe a different picture would have emerged.
Although Krugman said that one could expect the price of gold to have gone up in terms of the model he never excluded the possibility of gold being at the time in a bubble and well above the hotelling price.
This is very important because since interest rates are still at 2011 levels what he basically said is that the Hotelling price seems to be the current price. The is one of the reasons why I do laugh at the gold bugs and their futile attenpts at trying to make sense of what is going on.
