One of Summers' arguments for fiscal policy is that the low interest rates generated by monetary policy results in excessively high asset prices.
While it is true that given the expected return on an asset, a lower interest rate raises the asset's present value, the problem is supposed to be "secular stagnation." There is an excessively high supply of saving and excessively low demand for investment.
But the low demand for investment is being generated by low expected returns on real investment. Given the interest rate, that results in a lower present value of an asset. And to the degree that excessive saving is driving down the marginal return on investment, the result is the same.
And so, secular stagnation should lower asset prices at a given interest rate. The lower interest rate, then, simply dampens the decrease in asset prices.
To the degree there is a decrease in the quantity of saving supplied and increase in consumption due to the lower interest rates, the fundamental value of the assets falls.
If the supply of saving were perfectly inelastic with respect to the interest rate, then the interest rate must fall enough so that despite the lower expected return on investment, asset prices remain the same, and so it remains profitable to maintain real investment expenditure.
Now, it is also true that if there are fewer low risk, high yield projects available, the rational approach to investment is not simply to exploit equally low risk, lower yield projects. It is also sensible to exploit higher risk, equally high yield projects as well. There is nothing wrong with "a reach for yield." It is perfectly rational.
Of course, it would probably be more sensible for households to purchase equity to avoid lower yields rather than keep their money in banks that claim to promise the same safety without a reducing yield. In other words, to the degree a bank wants to promise depositors the same safety, it should lower the interest rate it pays enough to make it possible to fund a lower yield, equally safe asset portfolio. Those depositors who want a higher yield should buy stocks.
But if depositors want to earn a higher return and take a higher risk on deposits, should it be forbidden? I don't think so. But I don't think they should have government deposit insurance or even a lender of last resort.
What should be done instead? Option clauses and rapid resolution of insolvent institutions.
And most importantly, nominal GDP level targeting so that financial problems don't cause persistent shifts in the growth path of spending on output.
Finally, if the central bank is using a policy interest rate to target inflation, and the growth path of spending falls, and the lower spending results in depressed real output, and it is that depressed real output that reduces expected future returns and so equity prices, then if the central bank shows a willingness to shift to a more sensible policy, stock prices will rise because of the higher expected returns.
Now, suppose that to keep stock prices from rising, a foolish monetary policy is maintained. Instead, the national debt is increased enough so that national saving is low enough, that the interest rate that keeps saving and private investment equal prevents any increase in expected returns so that stock prices remain depressed. Further aiding this policy is the possibility that business profits will be taxed in the future to pay the interest on the national debt. By reducing expected future after tax profits, that will also keep stock prices depressed.
I think this would be a really bad policy.