## Why a fiscal rule can’t work for the left: some economic theory

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I wrote recently about why I felt fiscal rules were bad news for any government seeking to offer a Keynesian / left of centre approach to economic management using a narrative logic to support my arguments. When doing so I suggested I might also offer a mathematical justification for the position I have taken. Let me do that now.

The logic that follows is based upon what is usually called national income accounting: what is offered are accounting identities that have to be right as a matter of fact; that is why they are called identities.

The analysis starts by looking at the composition of GDP from a number of perspectives. One is these is:

GDP = C + I + G + (X — M)

What this identity says is that total national income (GDP) is the sum of total final consumption spending (C) plus total private investment (I) plus total government spending (G) and the sum of net exports (X — M) where (X) is exports and (M) is imports.

Why the identities are useful is because GDP can be looked at it in more than  one way, As a result this identity is also true:

GDP = C + S + T

This identity says that GDP is made up of household consumption (C) (as before) plus total saving (S) and total taxes paid (T).

It's pretty straightforward to then say that:

C + S + T = GDP = C + I + G + (X — M)

And without too much effort it's also possible to reorganise the expressions from this point to eliminate GDP from the equation and consumption (C) as well as it appears on both sides of the identity and so cancels out. The result is the following expression which is generally said to represent  the sectoral balances within the national accounts, about which I have written quite often on this blog:

(I — S) + (G — T) + (X — M) = 0

In effect the the three sums have to balance to zero because they represent financial flows that are either net saving or borrowing and as a matter of fact every saver needs a borrower in double entry book-keeping terms.

It's important to note what expressions mean though.  (I — S) is in effect the private sector balance: if investment exceeds saving the sector is borrowing and vice versa.

(G — T) is the government sector balance: either government spending is more or less than taxation.

And again  (X — M) is the current account balance with the rest of the world and represents whether we are saving abroad, which happens when outflows including for goods, services and finance (X) exceed (M) for inflows, or vice versa.

To this point I should add that there is nothing exceptional about what I have noted: this is pretty basic economics. I have no idea whether what follows is normal or not: I haven't bothered to search the literature to find out. It's my analysis using the arguments to this point as a starting point.

Remember what I am trying to analyse is the impact of a fiscal rule. That rule can be fairly easily inserted into these identities. The fiscal rule being considered is that which says government spending in current items, which I will call (Gc) should balance tax income (T) but that government spending on investment, which I will call (Gn) may be funded by borrowing.

To put this another way:

G = (Gc + Gn)

and

(Gc - T) = 0

In that case this identity (for that is what fiscal rule has made it) can be cancelled out of this expression:

(I — S) + (G — T) + (X — M) = 0

which now becomes:

(I — S) + (Gn) + (X — M) = 0

This has now to hold true. Rearrange it and the following can also be said to hold true:

Gn = (S - I) + (M - X)

This is, I suggest, when things become interesting. What this says are are a number of things.

The first, and most obvious, is that government investment does not impact consumption. (C) is not a component in this identity.

Second, the identity says that government investment is funded by one of:

• An increase in private sector saving: this would be represented by new bank deposits if cash was created to pay for the investment or by new holdings of bonds sold to fund that expenditure; or
• By a reduction in private sector investment: this could be said to be the classic government spending crowding out private sector activity argument; or
• By a net inflow of funds from importers or overseas investors taking advantage of the bonds made available to fund the government investment; or
• By a reduction in exports, which would imply that productive resources otherwise diverted to this activity was instead allocated to the creation of the newly funded government infrastructure.

You can play around with these explanations, but I suggest that these are sufficient for the purpose of this analysis.

There is one important thing to add at this juncture though, based on the economic climate that has prevailed since 2008, which cannot be ignored if we are going to suggest which, if any of these factors is more important than the others. This additional factor is that there is now and has been for some time spare capacity in the UK economy.

There is argument about how much spare capacity there is: I tend (like Danny Blanchflower) to think that actual spare capacity is much bigger than that which the Bank of England estimate. It does not greatly matter for this argument; what I think is clear is that quite considerable sums could be expended by any government on investment activity right now without in any way reducing the capacity of the private sector to invest (which it is showing some reluctance to do) or impairing the UK economy's capacity to export.

I could go into differential calculus here but I won't because at that point most who have reached this point will depart the scene and that is not my wish. Suffice to say that whilst it may be rash to say that in the last noted identity that there is no possibility of a relationship between a change in (Gn) and either (I) or (X) that it is also not unreasonable, given the point just noted on excess capacity in the economy, to suggest that the relationships in question are very weak indeed. In fact, I'll suggest that they are likely to be so insignificant that for all practical purposes it can be said that in the identity in question that for all practical purposes:

I = 0

and

X = 0

implying that a change in government investment will have no impact on these two variables, which then leaves the identity as:

Gn = S + M

There should, perhaps, be no great surprise in this conclusion. Modern monetary theorists have long said that government debt is the same as private wealth. And that is exactly what this expression confirms: the net effect of borrowing to fund government investment (Gn) has been to either increase UK private savings (S), which can be owned by either individuals or companies, or to deliver an increase in the sums saved in the UK from those overseas (M) which will be reflected in the current account deficit. What will not change is (C), which is the apparent well being of households.

The proof of this might be considered to be the evidence from the economy. For more than a decade there has been government borrowing funded by deficits. Now admittedly there has been current government spending (Gc) funded by deficits as well (for a summary of the data to 2015 see here), which confuses the picture (I admit) but what is clear from the most cursory of headline data is that there has been GDP growth but that this has not fed through into wages which have been declining whilst private sector wealth and the trade deficit have grown.

In other words what the identity suggests has happened: what has been considered to be desirable investment has not lead to a growth in net consumption, which is what maters to most people. That;s not to say that there has been no growth, but most people have not benefitted.

The issues arising from that suggestion and most especially what can be done about (because I think there are actions to be taken that can have beneficial impact) need further theoretical exploration, which should follow (other work and holiday permitting) but for now I return to my opening thesis, which is that a fiscal rule of the type that has been proposed by John McDonnell and which was previously imposed by Gordon Brown on the apparent advice of Ed Balls will not assist those that Labour intend it to help. That fiscal rule will increase private sector wealth which, as we know, is poorly dispersed across the economy resulting in a cost of increasing inequality in the UK. And such a rule may make the UK feel as though it is increasingly dependent for anything to happen on an inward flow of foreign funds (sound familiar, anyone? Just think Hinckley C) but by itself such a rule will not deliver for the ordinary people of the UK.

This is not to say there is no growth: if the result of the investment is put back into this identity:

GDP = C + S + T

then S has grown, and so therefore has GDP, but the reward is going to savers with a low marginal propensity to consume and low effective tax rates (because that is UK policy on saving).

I should warn: of course these identities ignore spillover effects, of which there will be some, but the point I am making remains valid as far a I can see: a fiscal rule of the sort that John McDonnell has adopted permit investment but is likely to deliver many of its benefits to those with the greatest existing wealth. Unless linked to further policy measures (and this is the issue I am working on) that means the question has to be asked as to why Labour, irrespective of leadership, has been so keen to use such rules?

Comments are of course welcome. This has not been peer reviewed so I may have missed something glaringly obvious. But if so please tell me what.