Methods of Regulation
The government agency that oversees and enforces regulation differs for every nation.
In the United States, the government body is the Securities and Exchange Commission (SEC). Its primary mission is to monitor and enforce laws created to govern the existence of securities and other related assets in the United States. It "licenses every exchange in the U.S., from main exchanges like the New York Stock Exchange and NASDAQ to the Chicago Stock Exchange, National Stock Exchange, and other minor markets". The US Securities and Exchange Commission works to ensure that laws under the Securities Act of 1933 are enforced.
Securities and Exchange Commission
China Securities Regulatory Commission
Financial Superviory Service
In general, governments say that they don't control the stock market. However, the policies they make have a significant impact on the stock market, whether directly or indirectly.
Fiscal policy is changes in government spending and taxes and to fight recessions or inflations. Government spending and taxation can influence the economy because it changes the supply and demand balance. During a recession, the government increase its level of spending and/or reduce taxes. Tax cuts and government spending can stimulate the stock market and could encourage investors to invest in stocks.
Monetary Policy is changes in money supply to fight recessions or inflations. The ultimate goal of monetary policy is to maximize employment, stabilize prices, and moderate long term interest rates. Monetary policy is created through the actions of the central bank on the money supply and interest rates. It works to either create a business friendly economy to spur employment and growth, or a policy to reduce national spending to try to lower the inflation rate.
India: Case Study
In India, the 2013 Prime Minister elections influenced a lot of investors to invest in S&P Bombay Stock Exchange Sensitive Index (India's market index). During the course of the elections, Modi, the prime minister candidate, called for development at the highest pace possible. He put forth policies such as Make in India, Startup India, Goods and services tax bill, and Bankruptcy code stimulated the market to grow.