Modern Money Theory – Part 1. The Basics of Macroeconomic Accounting – L. Randall Wray. 

​You cannot possibly understand the debate about the government’s budget (and critique the deficit hysteria that has recently gripped many nations) without understanding basic macro accounting.

It is a fundamental principle of accounting that for every financial asset there is an equal and offsetting financial liability.
A government deficit is the flow of government spending less the flow of government tax revenue measured in the money of account over a given period (usually a year). This deficit accumulates to a stock of government debt – equal to the private sector’s accumulation of financial wealth over the same period.
If the government always runs a balanced budget, with its spending always equal to its tax revenue, the private sector’s net financial wealth will be zero.
One sector’s deficit equals another’s surplus.
Domestic Private Balance + Domestic Government Balance + Foreign Balance = 0
For example, let us assume that the foreign sector runs a balanced budget (in the identity above, the foreign balance equals zero). Let us further assume that the domestic private sector’s income is $100 billion while its spending is equal to $90 billion, for a budget surplus of $10 billion over the year. Then, by identity, the domestic government sector’s budget deficit for the year is equal to $10 billion. The domestic private sector will accumulate $10 billion of net financial wealth during the year, consisting of $10 billion of domestic government sector liabilities.
As another example, assume that the foreign sector spends less than its income, with a budget surplus of $20 billion. At the same time, the domestic government sector also spends less than its income, running a budget surplus of $10 billion. From our accounting identity, we know that over the same period the domestic private sector must have run a budget deficit equal to $30 billion ($20 billion plus $10 billion). At the same time, its net financial wealth will have fallen by $30 billion as it sold assets and issued debt. Meanwhile, the domestic government sector will have increased its net financial wealth by $10 billion (reducing its outstanding debt or increasing its claims on the other sectors), and the foreign sector will have increased its net financial position by $20 billion (also reducing its outstanding debt or increasing its claims on the other sectors).
It is apparent that if one sector is going to run a budget surplus, at least one other sector must run a budget deficit. In terms of stock variables, in order for one sector to accumulate net financial wealth, at least one other sector must increase its indebtedness by the same amount. It is impossible for all sectors to accumulate net financial wealth by running budget surpluses. We can formulate another “dilemma”: if one of three sectors is to run a surplus, at least one of the others must run a deficit.
No matter how hard we might try, we cannot all run surpluses simultaneously. It is a lot like those children in Lake Wobegon (an imaginary town featured in Garrison Keillor’s Prairie Home Companion weekly radio show in the United States) who are supposedly all above average. For every kid above average there must be one below average. And for every deficit there must be a surplus.

No matter how much others might want to accumulate financial wealth, they will not be able to do so unless someone is willing to deficit spend (services a debt).
We conclude that while causation is complex, and while “it takes two to tango”, causation tends to run from individual deficit spending to accumulation of financial wealth, and from debt to financial wealth. Since accumulation of a stock of financial wealth results from a budget surplus, that is, from a flow of saving, we can also conclude that causation tends to run from deficit spending to saving.
Aggregate spending creates aggregate income. At the aggregate level, taking the economy as a whole, causation is more clear cut. A society cannot decide to have more income, but it can decide to spend more. Further, all spending must be received by someone, somewhere, as income. Finally, as discussed earlier, spending is not necessarily constrained by income because it is possible for households, firms, or government to spend more than income. Indeed, as we discussed, any of the three main sectors can run a deficit with at least one of the others running a surplus. However, it is not possible for spending at the aggregate level to be different from aggregate income since the sum of the sectoral balances must be zero. For all of these reasons, we must reverse causation between spending and income when we turn to the aggregate; while at the individual level, income causes spending, at the aggregate level, spending causes income.
Deficits in one sector create the surpluses of another.
Of course, much of the debt issued within a sector will be held by others in the same sector. For example, if we look at the finances of the private domestic sector we will find that most business debt is held by domestic firms and households.
this is “inside debt” of those firms and households that run budget deficits held as “inside wealth” by those households and firms that run budget surpluses. However, if the domestic private sector taken as a whole spends more than its income, it must issue “outside debt” held as “outside wealth” by at least one of the other two sectors (domestic government sector and foreign sector). Because the initiating cause of a budget deficit is a desire to spend more than income, the causation mostly goes from deficits to surpluses and from debt to net financial wealth. While we recognize that no sector can run a deficit unless another wants to run a surplus, this is not usually a problem because there is a propensity to net save financial assets. That is to say, there is a desire to accumulate financial wealth – which by definition is somebody’s liability.
It is necessary to emphasize that everything in this narrative applies to the macro accounting of any country. While examples used the Dollar, all of the results apply no matter what currency is used. Our fundamental macro balance equation, Domestic Private Balance + Domestic Government Balance + Foreign Balance = 0, will strictly apply to the accounting of balances of any currency. Within a country there can also be flows (accumulating to stocks) in a foreign currency, and there will be a macro balance equation in that currency also.

Note that nothing changes if we expand our model to include a number of different countries, each issuing its own currency. There will be a macro balance equation for each of these countries and for each of the currencies. Individual firms or households (or, for that matter, governments) can accumulate net financial assets denominated in several different currencies; vice versa, individual firms or households (or governments) can issue net debt denominated in several different currencies. It can even become more complicated, with an individual running a deficit in one currency and a surplus in another (issuing debt in one currency and accumulating wealth in another). Still, for every country and for every currency there will be a macro balance equation.

L Randall Wray

From his book: Modern Money Theory, a primer on Macroeconomics for Sovereign Montary Systems. 

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