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I would say they both effect each other........
Government monetary policy aims to infleunce the overall level of monetary demand in the economy so that it grows broadly in line with the economys ability to produce goods and services. This stops output rising to quickly or slowly. Interest rates are increased to moderate demand and inflation, and they are reduced to stimulate demand. If interest rates are set to low, this may encourage the build up of inflationary pressure; If they are set to high, demand will be lower than necessary to control inflation.
Basically both short term and long term interest rates are affected by economic factors such as inflation, the strength of the US Dollar in your case, and the pace of economic growth. But by raising or lowering interest rates you can also effect and control inflation.
So to say that one leads the other ie last periods interest rate increase leads to this periods inflation rate or vice versa, i would say that that cant strictly be true because of many other factors in a given economy.
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