Final answer:
The largest change to the Federal Reserve's balance sheet between March 2007 and May 2013 was the significant jump in depository institution deposits on the liability side. This was due to the Federal Reserve's activities to stabilize the economy during the financial crisis through open market operations and other measures that expanded its balance sheet.
Step-by-step explanation:
The biggest change in the Federal Reserve's balance sheet between March 2007 and May 2013 was the jump in depository institution deposits on the liability side of the balance sheet. The Federal Reserve's activities, such as open market operations and emergency lending programs, led to a significant increase in the liabilities on its balance sheet, including deposits from depository institutions.
During this period, the Fed conducted open market operations like the open market sale and purchase of treasury bonds, affecting both assets and liabilities of banking institutions. When the Fed conducts an open market sale, it sells treasury bonds to a bank, which in turn decreases the bank's reserves as it pays for these bonds and respectively decreases its loans to maintain the required reserve ratios. Conversely, when the Federal Reserve buys bonds, the bank gains reserves, which can be converted into new loans, increasing the bank's lending capacity.
In response to the Great Recession, these kinds of transactions by the Federal Reserve widely expanded its balance sheet, primarily seen in the dramatic increase in depository institutions' reserves—a liability for the Fed, but an asset for the banks.