Currently project managers, and other officials with the authority to spend money, are appropriate dollars mainly on a fiscal year basis. Successful PMs are those who, having met the requirements of their project, have also spent all their money. This is immensely important. Those who don't spend all their money are regarded as not fully successful. There is no incentive whatsoever to look for ways to save money. In fact saving is disincentivized.
For example, let’s say two PMs are given the same project and $100,000 to accomplish the goals of the project. Let’s say they both, at the end of the fiscal year, have satisfactorily met the goals of the project. PM1, will call him, has done so with only $20 remaining in his budget. While the other, PM2, has done so with $20,000 remaining. Current norms are that PM1 will receive approval and perhaps tangible rewards from his management. PM2, rather than being complemented for saving the government $20k, will be questioned as to why he's "left so much money on the table.”
Money can be saved by changing the current norm of operating and instead rewarding those whose accidentally or intentionally spend less money than they are allocated.
While this is written of NASA I’m almost certain it’s true of other government agencies.