Empirical relation between interest rate and stock market performance

Question

Disclaimer: Originally I asked this question on the personal finance site (see here) where it was (rightfully) closed since it does not directly relate to personal finance but is rather a general economics question.

From the answers to my earlier question I learned that the expected return on the stock market is positively correlated with the interest level at the beginning of the considered time period. The reason is that otherwise the Efficient Market Hypothesis would be contradicted since the expected return is the risk-free rate plus a risk premium (the higher the risk the higher the premium).

Now I am wondering if this could be used to validate the Efficient Market Hypothesis empirically: A bit oversimplified, one could look at the stock market performance in all years where the the risk free interest rate was 5% at the beginning of that year and compare the average performance to the average performance of all years where the risk free interest rate was 1% at the beginning of the year. If the Efficient Market Hypothesis holds in practice, then the former should be significantly higher than the latter (or the volatility of the stock market is negatively correlated to the interest rate, so to make this analysis more precise one would have to account for effects on the volatility, too).

Has it been analyzed whether the interest rate at the beginning of the considered time period and the development of the nominal performance of the stock market are positively correlated empirically? Would this approach be suitable to analyze the empirical applicability of the Efficient Market Hypothesis?

Edit: I just found this very similar question which describes essentially the same considerations. I think the difference between both questions is small, but the focus of my question is slightly different: I want to understand whether the Efficient Market Hypothesis is considered to be (more or less) true in practice and whether the described considerations are suitable in order to validate the Efficient Market Hypothesis. Therefore, in this question, the relation between the interest rate and the stock market performance is mostly considered as a way to validate the Efficient Market Hypothesis.

Answer 1

Yes, this has been studied. The seminal work is Robert J. Shiller, "Do Stock Prices Move Too Much to be Justified by Subsequent Changes in Dividends?", published in the American Economic Review in 1981. He won the Nobel Prize in 2013 in large part for his work testing the efficient markets hypothesis.

Answer 2

There is a certain positive correlation between the stock market and interest rates. During the long-term rise in interest rates, it must be the Fed’s incremental currency. The expected inflation rate is higher than the interest rate rise. In this case, the real interest rate (real interest rate = nominal interest rate - inflation rate) < stock market Income, people will put money into the more profitable stock market. However, the rise in short-term interest rates can be seen as the result of the sudden monetary tightening by the Federal Reserve. The expected rise in interest rates will be higher than the inflation rate. In this case, the real interest rate (nominal interest rate - inflation rate) > stock market returns, people are more willing to save rather than Invest in the stock market. In addition, if the efficient market hypothesis is established, there will be no government (including the Federal Reserve and government policies) intervention in the stock market, but the actual situation is that the government introduces political policies, and the market effectively ferments the influence of political policies.