The conclusion of this paper on deflation is that putting money under your mattress greatly helps productivity growth by eliminating low yield assets and concentrating all efforts in producing high yield assets. In the extreme case, the most risk tolerant person will own all assets worldwide.The paper assumes that return on investment is purely technological and that the period of ownership of intellectual property is short. This prevents the accrual of assets by risk tolerant investors, which would allow them to recuperate the bulk of the cash held by low risk investors through the sale of some of their assets (this would allow them in effect to corner the market).
In conclusion, it would seem that low variance investors increase the overall variance in GDP growth by allowing other risk savvy individuals to decide which investments are made. Cash is simply a non-voting share in an investment vehicle which invests in/owns the entire economy. Indeed, investing their money with a negative interest rate is the only way to regain their voting rights and reduce macroeconomic variance.
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In the (unforeseen) transition from inflation to deflation, banks would all go bust as risk adverse depositors pull their funds out of bank accounts and start placing them in mattresses (the reserve ratio of 10% is not going to be enough). This is because banks do not finance their lending with instruments of matching maturities.
To protect themselves against such an outcome (while maintaining some form of money multiplier), banks would have to restrict deposits to "term deposits" only. In effect, the reserve ratio for checking accounts would be 100%, and thus the interest rate would be 0%.
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