> The money tracks the value in the economy,
Does not imply this
> so the inflation is zero.
I do agree that the assertion holds true in most cases, but it break down during extreme environments - widespread bank collapses or when the productive ability of the economy is sharply reduced. Loans that cannot be repaid break the equation at some point.
As for government spending, it greatly depends on what it does with the money, and also on taxation. The government promises to pay back money based on future taxation, and if the taxation grow faster than the debt then there won't be any inflation.
Borrowing using assets as collateral means the money created matches the value of the collateral.
US government debt is around 31.5 Trillion $$ at the moment. If the US government were to pay its debt today, all that liquidity will be removed from the market and this will have enormous deflationary pressures.
In the same way for private individuals, if you can always keep renewing your debt and pricing your assets higher (a bubble would help), you’d create inflation.
What the fed does is create money that is backed solely by the fed promising to pay it back in the future. But the money is paid back by issuing more debt! Hence, inflation.