The Economist has an article on negative nominal interest rates, pointing out how common they are now in Europe. Most interesting is that nominal interest rates are negative on Swiss government bonds with terms to maturity of up to 10 years.
One problem with the argument is that that there is some notion that the goal of negative interest rates on central bank liabilities is to prevent people from saving.
The key purpose of negative interest rates on central bank liabilities is to reduce the demand to hold them. Given the quantity, the result will be higher demand for output. Or, the quantity can be reduced for any given demand for output, reducing the size of a central bank's balance sheet.
Whether or not people save more or less is not directly relevant, since it is only saving by accumulating money balances that adversely impacts the demand for output. If people save by accumulating assets other than money, that really isn't a problem.
Of course, looking at the demand for output, spending on consumer goods and services is an important form of demand, and for that to expand, saving must decrease. However, investment spending is another source of demand for output. I am enough of a "classical" economist to think that more saving and more investment is on the whole a good thing. Of course, really what is important is that interest rates coordinate saving and investment so that everyone can best achieve their own goals which most certainly involve consumption at some time or other.
Perhaps the most interesting fact in the article is that banks are passing on the negative interest rate on reserves by imposing a negative return on large deposit holdings. According to the article, banks are not charging for small depositors but are rather taking a loss.
Why would they do this? Perhaps they are just nice to small depositors, but that isn't a very satisfying answer for an economist.
One possibility is that many small depositors would be willing to withdraw currency if they were charged for holding deposits. It would be small for each depositor in an absolute amount, though large relative to their deposits, resulting in large withdrawals in aggregate. While hiding a few thousand dollars around my house might be foolish, it would not be technically difficult.
For large depositors, holding large amounts of currency would be difficult. It is important to keep in mind that the difficulty of storing currency will greatly deter currency withdrawals if interest rates on deposits are temporarily negative. What people would do in a word with permanently negative nominal interest rates is likely very different from when this is something that happens only occasionally.
Another possibility involves the stability of deposits as a funding source for banks. De jure, checkable deposits are payable on demand and would appear to be a very risky source to fund loans. In practice, "consumer accounts," in aggregate are considered by bankers to be a very stable source of funds most of which can be used to fund quite long loans. On the other hand, "hot" money, which has traditionally taken the form of relatively large deposits, sometimes with terms to maturity that are longer than "consumer deposits," are rightly considered a more risky source of funds for an individual bank. If deposits are exceptionally large in aggregate, with large firms holding unusally large amounts of "cash," then each bank will rightly see that much of its funding is such that it is too risky to tie up in longer term loans. It needs to be kept in short and liquid assets--the ones with negative nominal yields.
And so, this suggests that if nominal yields on short and safe assets become highly negative, then banks can be expected to provide negative yields on large deposits. This is both because the large depositors cannot handle huge amounts of currency and because the banks so not want to tie up the money in large loans. While small depositors will be shielded, because many of them can store amounts of currency that are small absolutely though large relative to their deposits and also because banks can depend on those funds in the longer run and lend them in longer term loans with higher nominal yields.
Now, if we were to imagine a world where negative nominal yields on short and safe assets were a permanent feature, then large depositors might well be motivated to develop the infrastructure to handle large amounts of currency.