It's nearly impossible for a government to invest money. Quite a bald, bland statement. I hope to show you that it's true. What does it mean to invest money? Well, one reasonable definition is to spend money now with the hope and expectation of getting more money back later. It's not sufficient to get back the same money later (aka a zero-interest loan). Life is uncertain. Any reasonable person (and a few unreasonable such) prefers money now to money later. This preference is expressed in the interest rate you have to pay for even the most secure loan (with no risk of loss of capital).
Let me argue against myself. Let's say that a government is going to invest money in something. The Village of Potsdam recently considered putting in another water tower to the north of town. Various developers want to put stores on land out there. They were hoping that the village would annex the land and put in water and sewer services. The assumption is that it would be cheaper for the developers and the village since the village already has a source of clean water and has a water treatment plant. In order to do that, though, the village would have to put in a water tower, at a cost of millions of dollars.
The village made a reasonable profit and loss calculation, weighing the increased property taxes plus the price paid for water. They ended up deciding against putting in the water tower. Just not a profitable investment. Isn't that evidence against my thesis that a government cannot invest? (Hint to the unwary: I'm right, of course, so that even your best argument isn't going to work)
My thesis doesn't depend on that kind of evidence, even though you think it might. Let's say that the water tower would have been profitable. Isn't that now evidence that a government can invest? Nope, still not. The missing context is: where does the money come from to invest?
Where is the government going to get the money for this theoretically profitable investment?
It could borrow the money. It could get a commercial loan if the investment is short-term, or it could issue bonds. Either way, the money for both of those is consuming capital. In the first, the capital has already been invested in a bank for it to loan out. In the second, these new bonds are competing for the existing capital base. No new capital has been created, so when the government invests in this manner, they're causing something else to be devested. They're consuming capital -- to create capital?!? Perpetual motion machines don't exist, even if you use rotating magnets.
Some governments have the ability to print money. There's a bunch of different ways to print money apart from actually cranking up the printing press. It could change the rules on how much float on check payments are allowed, or how much reserve a bank needs to keep on hand. It could reduce interest on the money it loans to banks. Regardless of the details, these governments can cause the amount of money in circulation to change in such a manner that they spend the new money first.
Increasing the amount of money doesn't increase the amount of liquid wealth. It just scribbles out one number on the paper money and writes in a different number. Not all at once, though, so that the economy is irrevocably distorted by spending this new money. It's not real capital, it's just doing a negative-sum transfer from those who already own capital.
Finally, the government could just take the capital from someone. From the point of view of the investor, paying taxes is the same thing as consumption. How does an investor fund consumption? You got it -- by liquidating some of his capital. It's possible that an investor will curb consumption, and that the government will invest those taxes. Only in this rare circumstance can a government invest.
I want to mention that the presumption here is that the government is investing wisely. Look at the things your government spends money on. Are any of them investments or are they consumption? The vast majority of them are consumption. Some are investments. Only some are wise investments. The others, the foolish ones, must be treated as consumption, from an economics point of view.
Why is capital so important? Only one thing enables employers to pay employees more: when the employees produce more. Only one thing enables employees to be more productive: the use of capital. Anything that reduces the amount of capital in a society makes the society poorer in the long run. To a large extent, government spending is capital consumption.