History of the Federal Reserve

Early conditions

In the early history of what is now the United States, the settlers used the currency of their previous country, base metals (gold and Silver and others), or simple barter. Over time, as the individual states became organized, the states set up their own central banks and printed money by the authority (and obligation) of the state government. The money supply was unplanned and unrelated to the productivity of the citizens, so the value of that money fluctuated quite a bit and the value was lower the farther you were from that state. (Why that happened - and still does.)

Bank of the United States

The first bank of the United States was formed with a 20 year charter in 1791 by congress. There were political issues having to do with banking that caused the charter not to be renewed, so in 1811 the bank was disbanded. The War of 1812 made obvious the need for a central authority in banking.
In 1816 the Second bank of the United States was founded with another 20 year charter.
In 1832 President Jackson vetoed the renewal of the charter, so in 1836 the second bank was disbanded.

Banking Acts

Finally in 1836 (in the midst of the Civil War) the National Banking Act created National banks with authority across state lines. It also made individual state bank currency illegal. Now at least the money would all be on a national basis.
In 1907 there was a banking panic and a major bank failed due to the inability of that bank to obtain enough cash on hand to cover the "run" on the bank. The money supply was not elastic, so the economy went through wild gyrations in currency value and job stability.
In 1908 the Aldich-Vreeland Act was passed. It allowed for the emergency issue of currency. This was to cover things like the bank collapse and times of war.
In 1911 the Aldrich Plan was proposed. It provided for a National Reserve Association to centrally control currency, interest rates, and the gold supply. It was "shot down" by William Jennings Bryan.

Federal Reserve

December 23rd, 1913 President Woodrow Wilson signed into law the Federal Reserve Act. Wilson wisely put William Jennings Bryan in the position of Secretary of State. Wilson assured Bryan that the Federal Reserve banks would be controlled by the Federal Reserve board of governors and that the board would be in the control of the government. Federal Reserve notes were defined as obligations of the United States government.
In 1914 the system was better defined with 12 member banks and 7 board members. One member would be the comptroller of the currency (an employee of the treasury). Another member of the board would be the Secretary of the Treasury himself. The other 5 members would come from the member banks (each having a board of 9 members as well). All of these board members would be appointed by the President of the United States. The Secretary of Treasury would serve as the chairman.
In 1922 an eighth member was added to the board to allow more influence from the farming communities.

Federal Open Market Committee

The FMOC was formed in 1922 to help regulate interest rates. This was accomplished by buying and selling government bonds on the open market. The FMOC was formalized in 1933 as part of the workings of the Fed.

Federal Deposit Insurance Corporation

The FDIC was formed in 1933 by the Glass-Steagall Act. It serves to insure deposits of account holders up to $100,000 per person. In case of catastrophy or bank run, you are guaranteed to get at least that much back from the government.

Further refinements

In 1935 the Banking Act was passed. This required the Federal Reserve board to appoint the 12 bank governors. It redefined the board to be made up of 7 members, none of which were the Secretary of Treasury or the Comptroller of the currency. The FMOC was to be the 7 board members plus another 5 members from the 12 regional Reserve banks.
This act also gave authority to the Fed to define and change deposit ratios for member banks without any emergency.
In 1951 the Treasury - Federal Reserve Accord was passed. This act defined and emphasised the fact that the Fed was independent of the Treasury department and could make decisions without the President's approval. This became necessary because the politicians were using the Fed to manipulate the economy to their short term advantage. (If people feel good about the economy, they are more likely to vote for the incumbent).
In 1980 the Monetary Control Act changed the demand deposit reserves requirement from 16.25% to 12% (in effect, giving the banks a tax break of $5 billion). It also forced the banks not in the system to hold the same amount of reserves (thus encouraging them to join rather than sit out).
Today, the Fed is working to remove the barriers of distinction between banks and brokerages or investment firms. This would increase the power of the Fed even more! Look for this legislation coming to a congression floor near you :-)

Fed Chairmen

1914 Benjamin Strong became the first Fed chairman (other than Secretaries of Treasury). He had to deal with an oversupply of currency because of the high regard other nations of the world had of America. (They kept sending their cash to the USA).
1934 Marriner S. Eccles became the seventh Chairman of the Fed. He helped write a plan that became the Banking Act of 1935. Prior to 1935 the Chairman role had less power and influence than it did after the Banking Act. Eccles was the first Fed Chariman with any significant power.
1948 Thomas B. McCabe became the chairman of the Fed. He had a disagreement with President Truman over priorities. Truman invited the entire FMOC board to the White house and "encouraged" them to keep interest rates low. 4 weeks later McCabe resigned.
In 1951 President Truman appointed William McChesney Martin to be the Fed Chairman. Martin did a great job of keeping interest rates and inflation low and maintained a predictable economy.
In 1970 Arthur Burns became chairman. He endured the inflationary 70's and let President Nixon dictate a loose money supply policy. The oil embargo of 1973-4 and again in 1979 exacerbated the inflationary spiral.
In 1978 G. William Miller was appointed Fed Chairman. He was a man President Carter could rely on to set interest rates where he wanted. This made things worse. Miller resigned in 1979 to become Secretary of Treasury.
In 1979 Paul Volcker became chairman of the Fed and really shook things up. (He was 6 foot 7 and was sometimes referred to as the jolly green giant). He tightened the money supply with a change in the reserve rate and interest rate manipulations in order to take the 20% inflation down to 1% by 1986. He knew what he was doing to bring confidence in the government back to the world, but he induced a recession along the way. He is known for making the position of the Fed chairman a position of power. He didn't even consult the President before putting his plan into action.
In 1987 Alan Greenspan became the Fed chairman. He responded correctly to the stock market crash of 1987 by loosening the money supply (opposite of the crash of 1929). All along Greenspan did a fine job through difficult economic conditions. He dealt with the dot com boom and bust of the late 90's keeping the "new economy" arguements in perspective. The 90's saw around 4% productivity gains year over year - much higher than historically seen.
2/1/2006 Ben Bernanke was appointed by President George W Bush and renewed by President Barack Obama. Bernanke is known for deftly handling the "Great Recession" of 2008. He increased the money supply and took decisive action to rescue major banks in the housing crisis that occured that year. He was a noted student of the Great Depression and it's causes.
Bernanke is also noted for his controversial roles in the bailouts of various banks and the refusal to bail out certain other banks. As a result, some banks failed and others were merged into other banks.
Bernanke is also known for the drastic "quantitative easing" executed from 2008 to 2011.
2/3/2014 Janet Yellen was appointed by President Barack Obama. She served under Ben Bernanke and was well versed on how to handle the low inflation environment she found herself in.
2/5/2018 Jerome Powell was appointed by President Donald Trump and presided over the Pandemic time frame.

This history summary was largely gathered from "The Federal Reserve System" (part of the Know Your Government series) by Gary Taylor. (332.11)

Also see How Money Works and the Constitution