Bank runs increased before FDR's inauguration in part because some people feared he would abandon the gold standard and reduce the value of?

the dollar

Explanation:

Gold standard refers to a monetary system when we determine the value of different currencies based on how much gold that currency can obtain. (For example, if you can give $10 for an ounce of gold, we can say that the value of that currency is 1/10th of an ounce of gold)

When FDR took the positon, people were scared that he would abandon the gold standard. (He hinted a couple of times before he won the election)

This made people scared that the value of the money that they have will fall. In response, people start to withdraw the money that save in the bank (this is what they called increased Bank Runs) So they exchange their money with goods.