Fallacies of composition are a perennial problem in economics. What obviously works for an individual does not necessarily work for the whole economy. The classic case is that family frugality is no panacea if translated to national policy. The security which, for the individual, comes from income exceeding expenditure can easily translate into a depression if, at the level of the whole economy, there is insufficient demand to keep the economy on track.
It is against this background that we need to consider very carefully whether one of the central policies of the present government is likely to be achievable. This is to reduce the government deficit, probably to zero - a stance supported by much of the opposition although the Jeremy Corbyn camp may well disagree.
Certainly, there is a problem. Between 1991 and early 2015, gross government debt rose from 31% to 89% of GDP. The interest charges to finance this debt last year came to £43bn - roughly equal to the total amount spent on primary and secondary education taken together, or our total expenditure on defence. Because of subdued levels of economic growth and very little inflation, the two major means by which previous very high levels of national debt have been eroded away are largely absent.
In consequence, if the government deficit were to persist at, say, 6% of GDP per annum, inflation at 1% and growth at 2%, government debts as a percentage of GDP would go on rising at 3% per annum. Britain is not Greece, but an increase in gross government debt accumulated over the next 10 years of another 30% of GDP is not on anyone's wish list.
The obvious solution to reducing total government borrowing as a percentage of GDP - other than the contribution made by growth and inflation - appears to be to reduce expenditure and to increase taxation, and the present government is firmly committed on this basis to eliminating the deficit by 2020. Obviously, for an individual whose expenditure was more than his or her income, this would be the path to follow. The key issue, however, is whether this entails exactly the sort of fallacy of composition where what would might well be right for an individual makes no sense for the economy as a whole.
The reason for believing that this is the case is that the government deficit is not an independent entity but one which is largely the residual left over when all the other major surplus and deficit - and hence borrowing and lending - totals in the economy are taken into account. Every quarter the Office for National Statistics publishes a table showing the figures and, to provide some context, those covering all the years since 2000 to date are tabulated below.
The crucial point is that the government deficit, allowing for any net borrowing or lending by households or the corporate sector, has to equal the balance of payments deficit. It is then easy to see that, as the foreign payments deficit is soaring upwards, there would have to be completely implausible amounts of borrowing by both consumers and businesses to produce a zero government deficit by 2020 if, at the same time, we continue to have an annual balance of payments deficiency of £100bn or more.
If the real driver of the government deficit, therefore, at least in current conditions, is the foreign payments balance, and not, as seems obvious, the gap between the state's income and expenditure, what is the mechanism by which the government deficit would fail to fall when austerity policies are implemented? The answer is the government deficit is also not an independent entity.
Cutting expenditure or increasing taxation will not impact on the deficit independently from other factors. In particular, expenditure cuts and tax increases will depress the economy, leading to higher welfare expenditure and lower tax receipts, so that the effect of austerity programmes may be to leave GDP lower but the gap between income and expenditure as large as it was before.
If this analysis is correct, it has a crucial bearing on policy to reduce the government's deficit. It is not expenditure cuts or tax increases which will bring the deficit down. It is taking steps to reduce the balance of payments deficit. This is a policy objective which is now barely on any policy-maker's radar screen. Events, however, may shortly force it to become centre stage.