The non-government sector is immediately wealthier if the government matches it deficit with new debt issues compared to a situation where no debt was issued.
Answer: False
The answer is False.
Within a fiat monetary system we need to understand the banking operations that occur when governments spend and issue debt. That understanding allows us to appreciate what would happen if a sovereign, currency-issuing government (with a flexible exchange rate) ran a fiscal deficit without issuing debt?
Like all government spending, the Treasury would credit the reserve accounts held by the commercial bank at the central bank. The commercial bank in question would be where the target of the spending had an account. So the commercial bank's assets rise and its liabilities also increase because a deposit would be made.
The transactions are clear: The commercial bank's assets rise and its liabilities also increase because a new deposit has been made. Further, the target of the fiscal initiative enjoys increased assets (bank deposit) and net worth (a liability/equity entry on their balance sheet). Taxation does the opposite and so a deficit (spending greater than taxation) means that reserves increase and private net worth increases.
This means that there are likely to be excess reserves in the "cash system" which then raises issues for the central bank about its liquidity management. But at this stage, M1 (deposits in the non-government sector) rise as a result of the deficit without a corresponding increase in liabilities. In other words, fiscal deficits increase net financial assets in the non-government sector.
What would happen if there were bond sales? All that happens is that the banks reserves are reduced by the bond sales but this does not reduce the deposits created by the net spending. So net worth is not altered. What is changed is the composition of the asset portfolio held in the non-government sector.
The only difference between the Treasury "borrowing from the central bank" and issuing debt to the private sector is that the central bank has to use different operations to pursue its policy interest rate target in the absence of paying a return on excess reserves.
If it debt is not issued to match the deficit then it has to either pay interest on excess reserves (which most central banks are doing now anyway) or let the target rate fall to zero (the Japan solution).
There is no difference to the impact of the deficits on net worth in the non-government sector. Later as interest payments flow from the outstanding debt, then incomes rise in the non-government sector, which may translate into higher saving and more wealth.
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