Definition: Contractionary monetary policy is when the Federal Reserve is using its tools to put the brakes on the economy to prevent inflation. This usually means raising the Fed Funds rate to decrease the money supply. This will cause mortgage rates to increase, consumers to borrow and spend less, and businesses to stop raising prices and giving raises. This usually heads off inflation.
The Fed's goal is to do this without pushing the economy into a recession. The opposite is expansionary monetary policy.
Examples: Federal Reserve Chairman Ben Bernanke says that contractionary monetary policy caused the Great Depression of 1929.

