how much was the goverment the cause of the 1920 economic boom USA?

I don't think the government was much of the cause of it. The two republican Presidents who presided over the 1920's both followed 'hands off the economy' policies. Harding's officials were all found to be busy taking bribes in the 'Tea Pot Dome' scandal and he died of a stroke after even more corruption might have been revealed. Coolidge was very old fashioned and conservative and refused to be involved in anything saying problems would just go away. He refused to stop the stock market, bubble, the too easy credit, the over supply of money, and business corruption that resulted in the 1929 'Crash' and the Great Depression that started the year after he left office.

The cause of the 'boom' was most likely natural US recovery after the down of WWI (because the US homeland was untouched). Easy credit, lots of speculation blowing up in 'bubbles', lots of printed money.