The Republican Presidents of the 20's (like Calvin Coolidge and Herbert Hoover) were advocates of the laissez faire ideology. Laissez faire economics is based around the idea that the government should be involved as little as possible in terms of the economy. Instead, this system relies on competition for customers between businesses as a means to regulate their behavior.
These policies partly lead to the Great Depression. However, a lot of the blame can be place on individuals who used reckless spending as a means to buy material objects. However, the governments failure to regulate the stock market helped lead to the Stock Market Crash of 1929. This was one of the major factors behind the beginning of the Great Depression.