The Federal Reserve identifies its goals as maximization of production output, maximization of employment, and stabilization of prices. This last point, stabilization of prices, is where combating inflation and stagnation come in.
The government should not regulate the economy, either through the Fed or any other governmental agency. The very fact that it attempts to do so has more to do with the expansion and intrusion of political power where it simply does not belong. The government does not create wealth, but as we have all seen, it can certainly destroy it through poor laws and tax policy. "Regulating the economy" is not a power granted to the government; it should cease in any attempt to do so.
I agree with #7: since the Fed is not accountable, and since their positions are appointed rather than elected, there is no real oversight and criticism falls on deaf ears. If the Fed can continue as an institution, it needs drastic overhaul and reform in every area, but simple oversight or an objective audit would help immensely.
This question highlights one of the major failings of the Federal Reserve, in my opinion, and this is its complete lack of accountability. This is something that we could argue leaves it open to massive misuse and abuse, as once an official is appointed to work in the Federal Reserve, they are free to see through their term and cannot really be "fired" in the traditional sense.
The Fed is responsible for US monetary policy. They regulate the amount of money in circulation by basically determining discount rates (the interest rates charged to commercial banks on loans they get from their regional Federal Reserve bank). In the recent financial crisis, the Fed also took more unconventional steps to maintain liquidity in the economy. In particular, they purchased bank-held debt, a practice known as quantitative easing. The Federal Reserve is not, as others have said, subject to much executive or legislative oversight.
As stated above, the job of the Federal Reserve is to, essentially, look out for the financial well-being (overall) of the government and country. Money brought into the Federal Reserve fluctuates based upon need by the Reserve to try to control inflation. Accountability of the Federal Reserve officials is relatively low. They simply cannot be held solely accountable for the state of the financial world.
The Federal Reserve exists to ensure that inflation is at a reasonable rate, and the economy does not get hurt too much by any movement. This is why the Fed raises and lowers interest rates, to control inflation in the US economy as best it can.
Like post two states the Federal Reserve's job is to keep the economy growing with modest inflation. However, this is to be matched with increase in pay, which has not happened. The oddest thing about the Federal Reserve is that they are not voted in by anyone. For this reason they have little accountability. Many are getting fed up with the Federal Reserve and their lack of transparency and power.
The Federal Reserve's goal is to help keep the economy going without excessive inflation or excessive unemployment. The officials are not accountable in any real way. The president can decline to reappoint the when their term is up, but that is about it.