2 What is fiscal sustainability and how is it measured?

2.1  The inter-temporal budget constraint and fiscal sustainability

Fiscal policy can be examined through the three lenses of:

• Fiscal stability—the influence of fiscal policy on the business cycle and vice versa;
• Fiscal structure—the level and mix of public expenditure, taxation and government assets and liabilities; and
• Fiscal sustainability—the ability of the government to meet both current and future obligations (Barker et al., 2008).

Although fiscal sustainability is the main focus of this paper, these concepts are related because the choice of government expenditure programmes and how they are funded will impinge on fiscal stability and structure objectives. Fiscal sustainability can be expressed through the government's inter-temporal budget constraint over an infinite or a finite time horizon, as explained below.

Infinite horizon measures[3]

According to infinite horizon fiscal sustainability measures, the government's fiscal position is sustainable, if the government is solvent, that is, if over an infinite time horizon it will be able to repay all of its debt. This solvency condition can be expressed as the government's infinite horizon inter-temporal budget constraint as follows:

      (1)

where n is the current (initial) time period, t_s is the nominal level of government revenue-to-GDP in year s, g_s is the nominal level of government spending-to-GDP, d_n-1 is the inherited stock of public debt at time n-1, and r is the interest rate on government borrowing (defined as r=(i-y)/(1+y), where i is the nominal interest rate and y is the growth rate of GDP; often referred to as the growth-adjusted interest rate). In expression (1), the present discounted value of government revenue-to-GDP must equal the present discounted value of government spending-to-GDP plus the initial stock of public debt. The above configuration of the government's inter-temporal budget constraint is an approximation used for illustrative purposes and abstracts from a number of considerations including the financial assets of the government, cash and accruals measures, as well as inflation.

The infinite horizon inter-temporal budget gap (IBG) measures the extent of inter-temporal balance and can be expressed as follows:

      (2)

or

      (3)

where t_s - g_s denotes the primary balance-to-GDP ratio (henceforth referred to as the primary balance). If there is a positive fiscal gap, then to close the gap the government will need to increase revenues, reduce expenditure, or a combination of the two. Other policies, such as structural reform to lift growth rates can also help to close the fiscal gap.

Finite horizon measures

The above measures define fiscal sustainability over an infinite time horizon. Fiscal sustainability can also be defined over a finite time horizon as the government meeting a debt target that is deemed acceptable at a certain future date. Whereas the infinite horizon measure constrains the government to repay all of its debts, the finite horizon measure can be used in more flexible ways, including by examining the implications of different debt targets for fiscal policy. The finite horizon inter-temporal budget constraint can be expressed as follows:

      (4)

where d_h+n is the target debt-to-GDP ratio at time h+n, where h is the finite time horizon to reach the debt target after period n, and s is any future time period; and d_n-1 is the inherited stock of public debt-to-GDP. If the government wants the terminal debt-to-GDP target to equal the initial debt-to-GDP level, then it will need to run a primary surplus equal to the cost of servicing its debt, so that t_s - g_s = rd_n-1. This is often referred to as the debt-stabilising primary balance. As a simple numerical example, if the growth-adjusted real interest rate, r=(i-y)/(1+y) = (6-3.5)/(1+3.5)=0.55 and the initial stock of inherited debt, d_n-1 = 20% of GDP, then to stabilise government debt at 20% of GDP, the government needs to run a primary surplus of 0.55 x 0.2 = 0.11% of GDP.

Governments often set finite horizon debt targets, because lenders will impose limits on the cost or ability of the government to borrow, if debt reaches certain levels. However, it is not clear ex ante when this might occur, as it will depend on the particular circumstances.

A limitation of the measure (4) is that the expectation that the government will not exceed a terminal debt target is itself insufficient to ensure fiscal sustainability. The path to get to the debt target is also important. For example, borrowing in early years, say for investment in infrastructure, may generate gross financial returns, if the investment generates user-pays charges or indirect returns via improved economic growth and tax revenue receipts. Even if the investment would be met by future revenues sufficient to satisfy the government's future debt target, it would not be feasible, if the peak level of debt in an intervening year goes above the level that creditors would be prepared to finance. This is part of the reason for New Zealand's fiscal responsibility provisions requiring "a prudent level of debt over time," rather than at some point in the future. The above example does not of course suggest that all infrastructure investment will necessarily generate financial returns sufficient to fund the investment. This will depend, among other things, on the nature and quality of the investment.

Another factor to be borne in mind is that, while the expected present value of the sum of future net cash flows might satisfy the terminal debt target, the future is not known with certainty and so there will be a distribution of possible outcomes. Therefore, an extra margin (a "fiscal buffer") is desirable to obtain a suitable level of assurance around fiscal sustainability. There are some complex measurement and modelling issues associated with examining how the government's fiscal position is likely to change in the future, especially when looking over the long term. Some factors are within policy control, such as entitlements to government welfare schemes, while others are less so, such as interest rates, and some are the outcomes of long-run and well-known trends, such as demographic change. As was discussed in Section 1, demographic change in New Zealand may have a significant impact on future government primary balances and the future path of government debt. In this context, programmes like public health and superannuation, which when introduced involved a relatively large working-age population supporting a relatively small older population, if unchanged, will increasingly involve a relatively smaller working-age population supporting a relatively large older population.

From an institutional perspective, what is important for the debt target to be met and maintained is not necessarily that current policy be projected to satisfy the IBC in the future, but rather that the policy environment enables options for policy evolution to be explored and adopted over time as needed.

The inter-temporal finite horizon budget constraint can be rearranged to define the inter-temporal finite horizon fiscal gap, which is the change in the primary balance required to achieve a debt target at a certain point in time. This fiscal gap measure shows the change in the primary balance (via changes in taxes and/or spending) at a point in time required to reach a specified debt target at some point in the future, relative to where debt would be if the primary balance was determined by unchanged policy. The inter-temporalfinite horizon fiscal gap (FG) can be expressed as follows:

      (5)

or rearranging, as:

      (6)

If the inter-temporal finite horizon fiscal gap is positive, then that implies the need for the government to reduce future government expenditure or increase taxes to achieve the target debt ratio. If the fiscal gap is negative, then that implies the government is able to increase future government expenditure or reduce taxes and still achieve the target debt ratio. The fiscal gap measure will tend to be sensitive to the starting point that is chosen and where the economy is in the economic cycle.

The time horizon chosen over which to calculate the fiscal gap (n+h) may have an influence over whether policies are considered sustainable. For example, policies may be sustainable over a 10-year time horizon, but not over 40 years. This point is illustrated in Section 4 where we show how projections of government debt can look quite different as the time horizon is extended.