what is the difference between a structural budget deficit and a cyclical one

A structural budget deficit arises irrespective of the business cycle. It will exist whether the economy is in the boom or recession phase of its business cycle: in short, the government is spending beyond its means on a consistent basis, meaning that it has to borrow regularly in order to finance its expenditure. The danger is that sooner or later this overspending will become unsustainable. On the other hand, a cyclical deficit arises as a result of the operation of the automatic stabilisers: for example, when an economy enters a downturn, it will need to increase the level of its benefit payments (e.g JSAs for the unemployed) and will also receive less tax revenue. This will cause the cyclical deficit to swell. However, on the upswing the opposite will occur where benefits fall and tax revenues rise ( as rising incomes move into higher tax brackets) such that the deficit incurred on the downswing ‘melts’ away.

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