Under what program did president nixon proposed a shift of federal money to states and cities

The program is known as New Federalism.

The goal of New Federalism was to limit the power of the federal government and give more power to the state governments. For example instead of the federal government telling state governments how to spend their money, the New Federalism policy instead called for the federal government to give a large sum of money to the states and then the state government would decide the best way to use it. This gave state government more control over how to solve social issues in their respective state.

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