Long-run Fiscal Projections under Uncertainty: The Case of New Zealand

Ball, Christopher; Creedy, John; Scobie, Grant Working Paper Long-run Fiscal Projections under Uncertainty: The Case of New Zealand New Zealand Treasury Working Paper, No. 15/10 Provided in Cooperation with: The Treasury, New Zealand Government Suggested Citation: Ball, Christopher; Creedy, John; Scobie, Grant (2015) : Long-run Fiscal Projections under Uncertainty: The Case of New Zealand, New Zealand Treasury Working Paper, No. 15/10, ISBN 978-0-478-43694-5, New Zealand Government, The Treasury, Wellington This Version is available at: https://hdl.handle.net/10419/205688 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by/4.0/ Long-run Fiscal Projections under Uncertainty: The Case of New Zealand Christopher Ball, John Creedy and Grant Scobie New Zealand Treasury Working Paper 15/10 September 2015 DISCLAIMER The views, opinions, findings, and conclusions or recommendations expressed in this Working Paper are strictly those of the author(s). They do not necessarily reflect the views of the New Zealand Treasury or the New Zealand Government . The New Zealand Treasury and the New Zealand Government take no responsibility for any errors or omissions in, or for the correctness of, the information contained in these working papers. The paper is presented not as policy, but with a view to inform and stimulate wider debate. NZ TREASURY Long-run Fiscal Projections under Uncertainty: WORKING PAPER The Case of New Zealand 15/10 MONTH/YEAR September 2015 AUTHORS Christopher Ball Analyst New Zealand Treasury No. 1 The Terrace Wellington New Zealand Email: [email protected] Telephone: ++64 +4 890 7206 John Creedy Principal Advisor & Professor of Public Economics and Taxation New Zealand Treasury and Victoria University of Wellington No. 1 The Terrace Wellington New Zealand Email: [email protected] Telephone: ++64 +4 917 6893 Grant Scobie Principal Advisor New Zealand Productivity Commission No. 1 The Terrace Wellington New Zealand Email: [email protected] Telephone: ++64 +4 903 5178 ISBN (ONLINE) 978-0-478-43694-5 URL Treasury website at September 2015: http://www.treasury.govt.nz/publications/research-policy/wp/ 2015/15-10/twp15-10.pdf Persistent URL: http://purl.oclc.org/nzt/p-1777 ACKNOWLEDGEMENTS We are grateful to Mark Holmes, Martin Fukac and Renee Philip for comments on an earlier draft of this paper. NZ TREASURY New Zealand Treasury PO Box 3724 Wellington 6008 NEW ZEALAND Email: [email protected] Telephone: +64 4 472 2733 Website: www.treasury.govt.nz Abstract This paper introduces uncertainty into a fiscal projection model which incorporates population ageing along with a number of feedback effects. When fiscal policy responds in order to achieve a target debt ratio, feedback effects modify the intended outcomes. The feedbacks include the effect on labour supply in response to changes in tax rates, changes in the country risk premium in response to higher public debt ratios, endogenous changes in the rate of productivity growth and savings. Stochastic projections of a range of policy responses are produced, allowing for uncertainty regarding the world interest rate, productivity growth and the growth rates of two components of per capita government expenditure. The probability of exceeding a given debt ratio in each projection year, using a particular tax or expenditure policy, can then be evaluated. Policy implications are briefly discussed. WP15/10 Long-run Fiscal Projections under Uncertainty: The Case of New Zealand i Executive Summary In New Zealand, the Public Finance Act 1989 requires the Treasury to produce a statement on the Crown’s long-term fiscal position at least every four years. These statements provide 40-year projections of revenue, expenditure, the fiscal balance and public debt levels. They help to identify challenges that are likely to face future governments, such as those arising from society’s ageing population. The review of the Treasury’s most recent Long Term Fiscal Statement by the Controller and Auditor General argued that the uncertainty implicit in the projections may not be readily understood by readers. The present paper address that concern by treating explicitly selected sources of uncertainty. These are analysed with a model which also allows for feedbacks from the fiscal developments to the macro-economy. For example, a change in tax policy might be implemented to deal with a fiscal deficit. At the same time, the interest rate may vary as a result of risk-premium adjustments to consequent changes in the level of debt. But interest rates directly affect debt servicing costs, which may in turn have further consequences for fiscal sustainability. Four key variables of the model are subject to uncertainty. These are the growth rates of two components of expenditure (health and education, and other social expenditure), the world interest rate and the rate of productivity growth. The approach taken was to suppose that the observed variability in those four central variables over the forty-year period 1973 to 2013 provides a reasonable guide to future variability. Faced with the inevitable uncertainty associated with future values of these variables in the model, this paper employs Monte Carlo techniques to develop stochastic projections. The advantage of stochastic projections is that they allow probability statements to be generated about ranges of the debt ratio in each year, in particular the probability that any given debt ratio is exceeded. Uncertainty regarding the structure of the projection model itself, and the form of the various feedback relationships (as well as the many other variables which cannot be known with certainty), was ignored. The projected distributions can therefore be regarded as being conditional on these assumptions. While a much wider range of uncertainties are undoubtedly relevant in practice, this paper has limited the choice to four variables to make the WP15/10 Long-run Fiscal Projections under Uncertainty: The Case of New Zealand ii process manageable. Instead of specifying explicit functional forms for the distributions of the uncertain variables, random observations were taken from ‘blocks’ (of random length) of the past data. In this way the serial correlations and correlations among the variables were retained. Despite the limited nature of the uncertainty modelled here, it was found that the projections of the debt ratio over the forty-year period to 2053 are subject to extremely large variations, as well as being positively skewed in the later years. The results suggest that ignoring uncertainty leads to a very limited view of future debt paths. While the median level of the debt ratio might be similar with and without uncertainty, a single point projection provides very limited information on which to base a policy response. The distribution of possible outcome around that central point matters. These results raise the important question of the appropriate policy response. Faced with projections showing a divergence between expenditure and revenue, and the consequent rise in the debt ratio, it is sometimes argued that policy responses should be made as early as possible to prevent the debt reaching unsustainable levels, although such a recommendation is subject to inter-generational equity and other considerations. In the present context an increase in the tax rate in the first period, to accumulate a fund that can be used in the event of a future possible expenditure requirement, involves a sunk cost. However, with uncertainty, it is possible that there is an option value of waiting until some of the uncertainty is resolved, particularly where policy changes involve costs that cannot be reversed. Constraints on flexibility of government policy, such as the ability to change tax rates and expenditure, are also relevant. Faced with uncertainty, the inability to have frequent policy changes may well argue for early action. However, inaction may be chosen because of the inability to reverse any adverse effects on particular groups. The present model will be extended in future research to consider the question of optimal policy responses under uncertainty. WP15/10 Long-run Fiscal Projections under Uncertainty: The Case of New Zealand iii Contents Abstract i Executive Summary ii 1 Introduction 1 2 A Description of The Model 3 3 Introducing Uncertainty 5 3.1 PastVariations .................................. 6 3.2 Generating Stochastic Variables . . . . . . . . . . . . . . . . . . . . . . . . 9 4 The Benchmark Case 10 5 Meeting a Debt Target 13 5.1 TaxSmoothing .................................. 14 5.2 An Increasing Income Tax Rate . . . . . . . . . . . . . . . . . . . . . . . . . 15 6 Conclusions 17 1 GovernmentDebt ................................ 19 2 Income ...................................... 20 3 TaxRevenue ................................... 20 4 FeedbackEffects................................. 21 5 Details of Model Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 List of Figures Figure 1 – Outline of the Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Figure 2 – Labour Productivity Growth 1973 to 2013 . . . . . . . . . . . . . . . . . 7 Figure 3 – World Real Interest Rate 1973 to 2013 . . . . . . . . . . . . . . . . . . . 7 Figure 4 – Expenditure Growth Rates 1973 to 2013 . . . . . . . . . . . . . . . . . . 8 Figure 5 – Benchmark Stochastic Projections: No Policy Responses . . . . . . . . 11 Figure 6 – Probability of Exceeding Given Debt Ratios in Each Projection Year . . 11 Figure 7 – An Increase in Uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . 12 Figure 8 – Probability of Exceeding Debt Ratios where Uncertainty Arises from World Interest Rate Only . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Figure 9 – Tax Smoothing with Income Tax Rate of 18.5 Per Cent . . . . . . . . . . 14 Figure 10 – Probability of Exceeding Debt Ratios with Income Tax Rate of 18.5 Per Cent...................................... 15 Figure 11 – Gradual Tax Rate Increase of 0.14 Percentage Points each Year . . . . 16 Figure 12 – Probability of Exceeding Debt Ratios with Gradually Increasing Income TaxRate ................................... 16 Figure 13 – Stochastic Projections with Higher Base Productivity Growth Rate of 1.94PerCent................................. 24 Figure 14 – Probability of Exceeding Debt Ratios with Higher Base Productivity Growth .................................... 24 WP15/10 Long-run Fiscal Projections under Uncertainty: The Case of New Zealand iv List of Tables Table 1 – Summary Measures of Distributions: 1973-2013 . . . . . . . . . . . . . . 8 Table 2 – Correlation Matrix of Distributions: 1973-2013 . . . . . . . . . . . . . . . . 9 Table 3 – Probability of Exceeding Debt Ratios in 2053 as Income Tax Rate Varies . 14 Table 4 – Benchmark Parameter Values . . . . . . . . . . . . . . . . . . . . . . . . . 23 WP15/10 Long-run Fiscal Projections under Uncertainty: The Case of New Zealand v Long-run Fiscal Projections under Uncertainty: The Case of New Zealand 1 Introduction It has long been recognised that the provision of useful policy advice benefits from the construction of projections which describe the possible paths of relevant variables, under clearly stated assumptions. In New Zealand, this is a formal requirement of the Public Finance Act 1989, which requires Treasury to produce a statement on the Crown’s long-term fiscal position at least every four years. These statements provide 40-year projections, identify challenges that are likely to face future governments, such as those arising from society’s ageing population. 1 Such projections are crucial in assessing fiscal sustainability and the required adjustments in the face of projected debt growth: the issues are discussed by Buckle and Cruickshank (2014) in the New Zealand context.2 Projections are obviously subject to a number of limitations. For example, in reviewing the Treasury’s modelling work and its Long Term Fiscal Statement (LTFS), Ter-Minassain (2014, p. 50) suggested that, ‘the Treasury should continue to refine its analytical tools’ and ‘it would be desirable to present, in future versions of the LTFS, scenarios with different dynamic paths of the key macroeconomic assumptions, to allow for plausible feedbacks from the growth of the debt’. In this spirit, a long-term model incorporating a small number of feedbacks has recently been developed by Creedy and Scobie (2015). A further serious limitation is the need to deal explicitly with the inevitable and considerable uncertainty involved in making projections, particularly over such a long period. This was stressed in the review of the Treasury’s most recent Long Term Fiscal Statement, by the Controller and Auditor General; see Provost (2013). The review argued that: ‘Although a single projection makes it easier for a reader to understand, I am concerned that the level of uncertainty implicit in the projection may 1For previous reports see The Treasury (2006, 2009, 2013a). 2 Early definitions and measures were proposed by Blanchard et al. (1990). For a non-technical discussion of issues, see Schick (2005). The approach adopted by the European Union is set out in detail in European Commission (2006). For an example of its use, see also Kleen and Pettersson (2012). A recent review of approaches is by Pradelli (2012). WP15/10 Long-run Fiscal Projections under Uncertainty: The Case of New Zealand 1 Figure 4: Expenditure Growth Rates 1973 to 2013 normal distribution which has a kurtosis measure of 3; it is thus equal to the ratio of the fourth moment about the mean to the fourth power of the standard deviation, minus 3. Hence health and eduction, other social spending, and productivity growth are more peaked than the normal distribution, while the world real interest rate is flatter than a normal distribution. Table 1: Summary Measures of Distributions: 1973-2013 Growth rate of expenditure on Productivity World real Other social Health and growth rate interest rate expenditure Education ( per cent) Mean 0.0151 0.0209 0.0106 2.1763 Variance 0.0112 0.0020 0.0005 7.0509 Coeff of Variation 7.009 2.042 2.109 1.220 Skewness 0.1514 -0.3000 -0.3850 0.1532 Kurtosis (excess) 0.1208 0.6852 0.6087 -0.2445 Table 2 reports the correlations between the variables. This shows, for example, that two expenditure growth rates are slightly negatively correlated with the world interest rate. More important are the positive correlation between the two growth rates, along with the positive correlation between the growth of expenditure on health and education and the productivity growth rate, and between the latter and the world real interest rate. WP15/10 Long-run Fiscal Projections under Uncertainty: The Case of New Zealand 8 Table 2: Correlation Matrix of Distributions: 1973-2013 Growth rates of: Other social expenditure Health and education Productivity World real interest rate (per cent) Other social expend 1 – – – Health and Education 0.2884 1 – – Productivity growth 0.0862 0.2104 1 – World real interest rate (%) -0.0844 -0.0794 0.2856 1 3.2 Generating Stochastic Variables In order to capture the complex correlations between variables and the precise forms of their distributions, without having to estimate a fully specified joint distribution, the following approach was used. This was designed to capture the historical variation by sampling from the empirical distributions over the period 1973 to 2013, rather than taking random draws from specific functional forms of the relevant distributions. First, each empirical distribution was transformed to ensure that the respective geometric means are the same as the parameter values imposed in the deterministic projections examined by Creedy and Scobie (2015). 10 The method then involved taking a random selection of short ‘blocks’ of years, in moving over the 40 year projection period. The main properties of the empirical data of interest are the cross-correlations among variables and the serial correlation that is also evident in the diagrams. The first property was preserved by selecting data from the same past year for each variable. Hence, if 1985 is selected for one variable, the 1985 values are used for all other variables. The second property was covered by selecting a sequential run of years and randomly drawing a starting point and run length. Specifically, an initial run length was first obtained by taking a random draw from a uniform distribution over the integers three to seven. Hence each ‘block’ of years is allowed to vary from between three and seven years inclusive. Then, given the selected run length, the starting year was obtained by taking a random draw from a uniform distribution defined over those starting points which, given the run length, provide years that are completed within the dataset. 11 For example, at the start of the projection period, suppose the first random draw (from between 3 and 10 That is, if xi denotes the value of a particular variable in period i , and α is the value of the variable in the deterministic case (no stochastics), the transformed value is obtained as: {(1 + α) (1 + xi)/GM (1 + xi)} − 1. The deterministic case is then equivalent to all xi=α. 11 Further sensitivity analysis was carried out by sampling using only three and four year blocks of data. The main results are unchanged although there are minor differences in the percentiles. WP15/10 Long-run Fiscal Projections under Uncertainty: The Case of New Zealand 9 7 inclusive) gives 4, while the second draw give the year 1988. The values would be taken from the four (adjusted) distributions in the four years 1988, 1999, 2000, 2001. In carrying out the Monte Carlo analysis, 2000 sets of stochastic projections were obtained. For each projection year, the arithmetic mean and median of the resulting distribution of debt ratios were calculated, along with the quartiles and the 5th and 95th percentile. 4 The Benchmark Case As mentioned above, for the benchmark case where no policy responses take place over the period, the deterministic form of the model produced a projection for the debt ratio in New Zealand that closely matches that of the more disaggregated Treasury Long Term Fiscal Model. This produces the ‘expanding debt’ case that is recognised as being unrealistic and which corresponds in no sense to a forecast. For this case, the stochastic form of the model gives rise to Figure 5, which shows the time profiles of the mean and median debt ratio, two measures of location, along with various percentiles, The dotted lines are the 5 th and 95 th percentiles while the dashed lines are the two quartiles. The median value for the final projection year is a debt ratio of 143 per cent of GDP. This is similar to the deterministic case, where Creedy and Scobie (2015) found a debt ratio of (approximately) 150 per cent of GDP in the final year. The range shown by the 5th and 95th percentiles in the terminal year is vast. The mean is clearly strongly influenced in later years (after about 2033) by the long ‘right-hand’ tail of the debt ratio distribution as the distributions become more positively skewed as well as more dispersed. This is largely influenced by the dispersion of expenditure as a proportion of GDP, which is influenced by the rapid increase in debt servicing costs in the high-debt ranges, as the risk premium rises steeply. The spread shown in Figure 5 clearly underscores the considerable uncertainty involved in making projections over such a long period. Figure 6 shows the variation over time in the probability of exceeding three debt ratios, of 20, 50 and 100 per cent of GDP. Given that the starting point involves a debt level around 25 per cent of GDP, the probability of exceeding the first ratio is close to 1 in early years, while the probability of exceeding 50 or 100 per cent is zero. But as the dispersion increases, the probabilities of exceeding the higher debt ratios increase, while the probability of exceeding the lower ratio first WP15/10 Long-run Fiscal Projections under Uncertainty: The Case of New Zealand 10 Figure 5: Benchmark Stochastic Projections: No Policy Responses necessarily falls and then rises. A feature of these probability profiles is that at the end of the projection period the probabilities converge at around a debt ratio of 60 per cent. This arises because of the huge dispersion of the distribution, so that very little of the area under the distribution is contained between the 20 and 100 per cent debt ratio values. Figure 6: Probability of Exceeding Given Debt Ratios in Each Projection Year Consider the effect of increasing or decreasing the degree of uncertainty, reflected in the dispersions of the four variables concerned. Figure 7 illustrates two hypothetical distributions of the debt ratio in a particular year, where distribution A reflects more uncertainty than distribution B. These two distributions are shown as symmetric, with increased uncertainty resulting in a mean-preserving spread. In practice the distributions are skewed and the way in which the degree of uncertainty is specified affects the outcome. However, they illustrate a property that holds in the WP15/10 Long-run Fiscal Projections under Uncertainty: The Case of New Zealand 11 present case. Consider the lower debt ratio, xL . Letting DR denote the debt ratio and PA and PB the probabilities relating to the two distributions, it can be seen that PA ( DR > xL ) < PB ( DR > xL ). However, for the higher debt ratio, xH , the inequality is reversed and PA ( DR > xH ) > PB ( DR > xH ). Hence the probability of exceeding a relatively low debt ratio falls as uncertainty increases, while the probability of exceeding a relatively high value rises as uncertainty increases. Figure 7: An Increase in Uncertainty A further implication arises from these comparisons. Suppose the actual degree of uncertainty is greater than is thought; that is, distribution A reflects the actual uncertainty whereas B is generated from the assumptions used to generate the Monte Carlo experiment. In that case, the conclusions will be too pessimistic (attributing too high a probability) about exceeding low debt ratios and too optimistic (attributing too low a probability) about high debt ratios. Figure 8: Probability of Exceeding Debt Ratios where Uncertainty Arises from World Interest Rate Only WP15/10 Long-run Fiscal Projections under Uncertainty: The Case of New Zealand 12 As an example, suppose the only uncertainty arises from variations in the world real interest rate which, as seen above, has a relatively low coefficient of variation. Figure 8 shows the corresponding profiles over time of the probability of exceeding the three debt levels considered. All three probabilities approach unity by the end of the period because of the low dispersion of the distribution of the ratio of debt to GDP, with just the one variable being stochastic. The ‘dip’ in the profile for the probability of exceeding 20 per cent arises because of the slight reduction in the debt ratio profiles in the early years of the projection period. 5 Meeting a Debt Target It has been stressed that the benchmark projections provide, rather than any kind of forecast, information about fiscal sustainability and an indication of a likely need for future policy changes. An important question – to be examined in future research – concerns the policy implications of providing information about the uncertainty associated with the projections, in addition to the deterministic case. The present section instead examines the implications for the projected time path of the debt ratio of two simple policy responses designed to achieve a specified debt ratio target by the end of the projection period. The first policy, discussed in subsection 5.1, is the widely-discussed tax smoothing option, which implies a period when government surpluses are obtained. The incentive for tax smoothing arises from the fact that the excess burden of taxation increases disproportionately with the tax rate, so that a constant rate minimises the burden. An early modern discussion of tax smoothing is Barro (1979). Armstrong et al. (2007) also highlight the concave nature of the government’s revenue function, arising from adverse incentive effects. Davis and Fabling (2002) stress the ability of the government to obtain a rate of return, during periods of surplus, in excess of the cost of borrowing, although this feature is not examined here. The second policy, examined in subsection 5.2, involves using a gradual tax increase to achieve the same target debt ratio. The objective in comparing the policies is not at this stage to consider any type of optimal policy, but rather to compare the time paths of debt and the associated uncertainty, and also to compare results with those obtained when uncertainty is neglected. WP15/10 Long-run Fiscal Projections under Uncertainty: The Case of New Zealand 13 5.1 Tax Smoothing In the case where there is no uncertainty, Creedy and Scobie (2015) found that to achieve a 20 per cent debt ratio in 2053 using income tax smoothing, whereby a higher constant tax rate is imposed over the period, the tax rate needs to be increased to 18.5 per cent from the benchmark income tax rate of 16.25 per cent. 12 If the same policy, of imposing a rate of 18.5 per cent over the period, is imposed, the resulting stochastic projections are shown in Figure 9. As in the benchmark case, the dispersion of the probability distribution rapidly increases over time. The median debt ratio turns out to be about half of the ‘desired’ 20 per cent. Nevertheless, the median is increasing at the end of the period and would be expected to reach 20 per cent soon afterwards. The associated probabilities of exceeding 20, 50 and 100 per cent of GDP in each year are shown in Figure 10. Figure 9: Tax Smoothing with Income Tax Rate of 18.5 Per Cent Table 3: Probability of Exceeding Debt Ratios in 2053 as Income Tax Rate Varies Tax rate Ratio of debt to GDP ( per cent) ( per cent) 20 50 100 Mean 16.25 56 52 44 204 17 49 45 38 132 18 41 37 31 46 19 34 30 25 -31 20 27 25 20 -101 12 If only GST is adjusted, it needs to be raised, from the benchmark value of 15 per cent, to 18 per cent and held constant over the projection period. WP15/10 Long-run Fiscal Projections under Uncertainty: The Case of New Zealand 14 Figure 10: Probability of Exceeding Debt Ratios with Income Tax Rate of 18.5 Per Cent An alternative question which the stochastic projections are able to answer concerns how much the constant tax-smoothing income tax rate needs to be increased in order to achieve a specified probability of the debt ratio exceeding various levels. The result of gradually increasing the tax rate is shown in Table 3 for the final projection year, 2053. For example, if the income tax rate were to be increased from the benchmark case of 16.25 per cent to 20 per cent, the probability of the debt exceeding 20 per cent of GDP in 2053 would fall from 56 per cent to 27 per cent. This halving of the probability is similar for that of the debt ratio exceeding 50 per cent and 100 per cent of GDP. The relatively small difference in the probabilities, for the different debt ratios, arises for the reason explained above, namely that there is a very large dispersion in the final distribution. However, the associated variation in the expected value of the debt ratio in 2053 is huge: it falls from a ratio of 204 per cent in the benchmark case to a surplus of 101 per cent of GDP with the income tax rate of 20 per cent. 5.2 An Increasing Income Tax Rate In the deterministic case, it was found that a gradual increase in the income tax rate by 0.14 percentage points each year, so that the rate reaches 21.9 per cent in 2053, would result in a debt ratio of 20 per cent of GDP by the end of the projection period. In contrast to the tax-smoothing case which implies a period of surplus, there is less variation in the debt ratio over the projection period. It falls to a low of about 10 per cent of GDP in the middle of the projection period. WP15/10 Long-run Fiscal Projections under Uncertainty: The Case of New Zealand 15 Figure 11: Gradual Tax Rate Increase of 0.14 Percentage Points each Year If the same policy of gradually increasing the tax rate over time is followed, the resulting stochastic projections are illustrated in Figure 11. In this case the median debt ratio in 2053 is also about half of the value (of 20 per cent) obtained by the deterministic projections. Figure 12 shows the associate probabilities of exceeding three debt ratios in each year. These are similar to those obtained in the tax smoothing case. Figure 12: Probability of Exceeding Debt Ratios with Gradually Increasing Income Tax Rate WP15/10 Long-run Fiscal Projections under Uncertainty: The Case of New Zealand 16 6 Conclusions This paper has added uncertainty to the projection model introduced by Creedy and Scobie (2015), which allowed for a limited number of feedback effects in a model designed to examine fiscal sustainability in New Zealand over a long period. These modifications have been made in response to public criticisms of the Treasury’s Long Term Fiscal Statement (2014). Faced with the inevitable uncertainty associated with future values of important variables in the model, the approach taken has been to use stochastic projections in a Monte Carlo exercise. This has the substantial advantage over sensitivity analyses of being able to generate probability statements about projected debt ratios. The approach taken was to suppose that the observed variability in four central variables (the world interest rate, the base rate of productivity growth, and growth rates of two per capita expenditure categories) over the forty-year period 1973 to 2013, provided a reasonable guide to future variability. Instead of specifying explicit functional forms for the distributions, random observations were taken from ‘blocks’ (of random length) of the past data. In this way the serial correlations and correlations among the variables were retained. Uncertainty regarding the structure of the projection model itself, and the form of the various feedback relationships (as well as the many other variables which cannot be known with certainty), was ignored. The projected distributions can therefore be regarded as being conditional on these assumptions. Despite the limited nature of the uncertainty modelled here, it was found that the projections of the debt ratio over the forty-year period to 2053 are subject to extremely large variations, as well as being positively skewed in the later years. The results suggest that the basic deterministic projections provide a very partial view about future prospects, despite not departing substantially from the median values obtained from the stochastic projections. These results raise the important question of the appropriate policy response. Faced with deterministic projections showing a divergence between expenditure and revenue, and thus an expanding debt ratio, it is sometimes argued that policy responses should be made as early as possible, although such a recommendation is subject to inter-generational equity and other considerations. However, with uncertainty, it is possible that there is an option value of waiting until some of the uncertainty is resolved, particularly where policy changes involve costs that cannot WP15/10 Long-run Fiscal Projections under Uncertainty: The Case of New Zealand 17 Figure 13: Stochastic Projections with Higher Base Productivity Growth Rate of 1.94 Per Cent Figure 14: Probability of Exceeding Debt Ratios with Higher Base Productivity Growth WP15/10 Long-run Fiscal Projections under Uncertainty: The Case of New Zealand 24 References Auerbach, A.J. and Hassett, K. (1998) Uncertainty and the design of long-run fiscal policy. University of California Burch Working Paper, no. B98-01. Auerbach, A.J. and Hassett, K. (2002) Uncertainty and the design of long-run fiscal policy. In Demographic Change and Fiscal Policy (ed. by Auerbach, A. and Lee, R.), pp. 73-92. Cambridge: Cambridge University Press. Armstrong, A. Draper, N., Nibbelink, A. and Westerhout, E. 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WP15/10 Long-run Fiscal Projections under Uncertainty: The Case of New Zealand 26 The Treasury (2013c) Long-term Fiscal Model for the Statement of the Long-term Fiscal Position 2013. (Wellington, New Zealand). http://www.treasury.govt.nz/ government/longterm/fiscalmodel. WP15/10 Long-run Fiscal Projections under Uncertainty: The Case of New Zealand 27