Stock Market Experiments
Read first the section "Stock Market Valuation and the Share of Profits in GDP" in the paper Fed Policy and the Effects of a Stock Market Crash on the Economy. The following experiments rely on this section. It uses a standard stock-price formula to point out that the high level of stock prices that existed on June 30, 1999, implied a high future growth rate of earnings. The growth rate of earnings was so high as to imply an unrealistically large ratio of profits to GDP in the future.

The results in the paper are based on a particular set of assumptions about 1) the length of the horizon, 2) the discount rate, 3) the growth rate of dividends, and 4) the PE ratio at the end of the horizon. It is easy to modify the assumptions in the paper and compute alternative earnings growth rates. This can be done for any time period. The paper used data as of June 30, 1999, but more recent data can be used. The following link allows you to use your own assumptions and see what they imply. The default values that are used for these computations are based on data as of June 30, 2016, but you can change these values. The goal is to find a set of assumptions that seems sensible and that does not imply an unrealistically high ratio of profits to GDP in the future. Can you find such a set? The paper essentially argued that such a set did not exist for the June 30, 1999, data.
Compute growth rate of earnings

It is also possible to use the stock-price formula to compute what the S&P stock price should currently be for alternative assumptions about the future growth rate of earnings. The following link allows you to do this. Again, the default values are based on data as of June 30, 2016, but you can change these. You should compare your computed stock price with the current S&P stock price in deciding whether the current S&P stock price is too high or too low. Again, can you find a sensible set of assumptions that justifies the current S&P stock price and that does not imply an unrealistically high ratio of profits to GDP in the future?
Compute S&P stock price

Related Papers:

Testing for a New Economy in the 1990s, Business Economics, January 2004, 43-53.

Risk Aversion and Stock Prices, February 2003.

Shock Effects on Stocks, Bonds, and Exchange Rates, Journal of International Money and Finance, 2003, 307-341.

Events that Shook the Market, Journal of Business, October 2002, 713-732.