As other answers have pointed out it isn't as simple to alter the bank's records in a way that wouldn't be instantly obvious. There is no "create money" button on the bank's computer. However, a sufficiently complex and skillful manipulation of the bank's records might in fact increase the money supply, although what most criminals would want to do is simply to get money into some account that they control, so they could withdraw it. This is both ethically and legally a form of theft, not in any meaningfully sense different from taking dollar bills out of the bank's vault. It would result in some other account (or more likely many other accounts) having less money while the total money in the bank's accounts was unchanged, because this is much easier and more profitable for the thief than changes that might actually increase the money supply.
The thief in this case would, in addition to other laws, violate the Computer Fraud and Abuse Act (CFAA) codified at 18 U.S.C. § 1030 This provides, in subsection (a) (4) that:
Whoever ... knowingly and with intent to defraud, accesses a protected computer without authorization, or exceeds authorized access, and by means of such conduct furthers the intended fraud and obtains anything of value, unless the object of the fraud and the thing obtained consists only of the use of the computer and the value of such use is not more than $5,000 in any 1-year period; ... shall be punished as provided in subsection (c) of this section.
Subsection (c)(3)(A) specifies:
a fine under this title or imprisonment for not more than five years, or both, in the case of an offense under subsection (a)(4) or (a)(7) of this section ...
Subsection (c)(3)(B) increases this to ten years where previous or offenses, or other offenses at the same time, under the same law have occurred.
Other provisions of the CFAA make it a crime to access a computer without proper authorization in many cases. Some of those might also be violated by the thief described in the question.
The Money Supply
Some other answers have said or implied that the money in a bank is tightly tied to the amount of physical currency that people have deposited there. This is not correct, although it once was. Most deposits are now made by electronic transactions, such as the direct deposit of paychecks or transfers from other financial institutions. Most of the rest are made by paper checks, not physical currency.
The Wikipedia article discusses several measures of the money supply, but note as particularly useful "MZM" or 'Money Zero Maturity' defined for the US as: (The total of all physical currency including coinage outside of the private banking system) plus (the amount of demand deposits, travelers checks and other checkable deposits) plus (most savings accounts). The article also defines for the US M0, M1, M2, M3, M4-, M4, and MB. Other countries use somewhat different definitions of some of these.
The article section "Money creation by commercial banks" says:
Commercial banks play a role in the process of money creation, especially under the fractional-reserve banking system used throughout the world. In this system, CREDIT is created whenever a bank gives out a new loan. This is because the loan, when drawn on and spent, mostly finishes up as a deposit in the banking system (an asset), which is counted as part of money supply (and offsets the LOAN - which has yet to be repaid). After putting aside a part of these deposits as mandated bank reserves, the balance is available for the making of further loans by the bank. This process continues multiple times, and is called the multiplier effect.
As the iterations continue, this multiplier is balanced (or nullified) by the equal and cumulative value of the loans, between the banks, creating a zero sum gain, and annulling the "money creation" claims or fears, that generally do not include or provision for the reality of reciprocating balancing, and net-offsets in their calculations, excluding double entry (balanced book) accounting principles.
This new money, in net terms, makes up the non-M0 components in the M1-M3 statistics. In short, there are two types of money in a fractional-reserve banking system:
- central bank money — obligations of a central bank, including currency and central bank depository accounts
- commercial bank money — obligations of commercial banks, including checking accounts and savings accounts.
It is incorrect to describe money not represented by physical currency as "imaginary" or "fictional", just as it would be incorrect to describe an ebook as "imaginary" because it is not printed on paper. Much of what people and companies buy and sell is done with non-physical money.
For the matter of that, paper currency is itself a governmental creation. It was once tightly tied to gold, silver, or other physical commodities. That has not been true in the US since 1933, and not true anywhere in the world for a long time.