Intergenerational Smoothing of New Zealand's Future Fiscal Costs

Guest, Ross Working Paper Intergenerational Smoothing of New Zealand's Future Fiscal Costs New Zealand Treasury Working Paper, No. 13/12 Provided in Cooperation with: The Treasury, New Zealand Government Suggested Citation: Guest, Ross (2013) : Intergenerational Smoothing of New Zealand's Future Fiscal Costs, New Zealand Treasury Working Paper, No. 13/12, ISBN 978-0-478-40351-0, New Zealand Government, The Treasury, Wellington This Version is available at: https://hdl.handle.net/10419/205636 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/ Intergenerational Smoothing of New Zealand’s Future Fiscal Costs Ross Guest New Zealand Treasury Working Paper 13/12 July 2013 NZ TREASURY WORKING PAPER 13/12 Intergenerational Smoothing of New Zealand’s Future Fiscal Costs MONTH / YEAR July 2013 AUTHOR Ross Guest Griffith University 170 Kessels Rd Nathan Brisbane QLD 4111 AUSTRALIA Email Telephone [email protected] +61 7 3735 7111 ISBN (O NLINE ) 978-0-478-40351-0 URL Treasury website at July 2013: http://www.treasury.govt.nz/publications/research-policy/wp/2013/13-12/ Persistent URL: http://purl.oclc.org/nzt/p-1569 NZ TREASURY New Zealand Treasury PO Box 3724 Wellington 6008 NEW ZEALAND Email Telephone Website [email protected] 64-4-472 2733 www.treasury.govt.nz 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. WP 13/12 | Intergenerational Smoothing of New Zealand’s Future Fiscal Costs i Abstract This paper applies an overlapping generations model in order to evaluate the implications of intergenerational smoothing of New Zealand’s future fiscal costs. The analysis complements the New Zealand fiscal projections of Bell et al. (2010) and the New Zealand tax smoothing analysis in Davis and Fabling (2002). It allows for feedback effects of the tax rate on labour supply through both intratemporal and intertemporal effects which in turn feed back to fiscal projections via taxation revenue. Under Treasury’s sustainable debt projections, which implies convergence to a stable 20% net debt to GDP ratio, generations born prior to 1990 are worse off and those born after 2000 are better off (measured by the impact on their remaining lifetime income). However, the magnitudes of the impact on the remaining lifetime income of all generations are small – no greater that 0.7% under the Medium demographic scenario. Those born around 1960 fare the worst, while those born after 2020 fare the best. The losses to current generations are weighed up against the gains to future generations through the social welfare function. The results show that net social gains are possible provided the gains to future generations are given sufficient weight by a low rate of social time preference and a high rate of aversion to variability in aggregate consumption over time. The parameter values required to generate net social gains are close to the bounds of plausible values. The magnitudes of the net social gains/losses range from minus $90 to plus $94 per capita per year. JEL CLASSIFICATION H31, H32, J18, E21 WP 13/12 | Intergenerational Smoothing of New Zealand’s Future Fiscal Costs ii Executive Summary This paper applies an overlapping generations model in order to evaluate the implications of intergenerational smoothing of New Zealand’s future fiscal costs. The approach here is to raise the average tax rate at the start of the projection period and keep it constant throughout the projection period in order to reach a target net debt to GDP of 20%. This differs from the approach adopted by New Zealand Treasury (Bell et al, 2010) which projects across the board spending cuts in order to reach a target net debt to GDP of 20%, the figure that Treasury adopts for its sustainable debt scenarios. The alternative approach here represents tax smoothing in the sense that the tax rate is higher initially but eventually lower than it would be if the tax rate were raised gradually in line with rising government spending in order to balance budgets. The model allows for feedback effects of the tax rate on labour supply through both intratemporal and intertemporal effects which in turn feed back to fiscal projections via taxation revenue. Tax smoothing implies that current generations will bear a greater tax burden, and future generations a lower burden, than they would under continuously balanced budgets. However the effects are arguably not large. For the baseline demographic projections, no generation is better or worse off by more than 0.7% of remaining lifetime income. This is perhaps not surprising given that the sustainable debt scenario requires only a small increase in the tax to GDP ratio of 0.5% at the most over a decade from 2015. Those born around 1960 fare the worst, but only suffer a 0.7% drop in their remaining lifetime incomes. This generation is at their peak earning capacity when the tax smoothing policy is introduced, which results in an initial jump in tax rates. They have also retired before the balanced budget scenario yields the payoff of a lower tax rate. Retired workers are also worse off because they pay higher tax rates on their retirement income. Future workers are better off because they escape the higher taxes on earlier generations and reap the gains from lower future taxes. The losses to current generations can be weighed up against the gains to future generations through the social welfare function. The results show that net social gains are possible provided the gains to future generations are given sufficient weight by appropriate choice of parameters in the social welfare function. The parameter values required to generate net social gains are close to the bounds of plausible values. Depending on the parameter values, the magnitudes of the net social gains/losses range from minus $90 to plus $94 per capita per year. WP 13/12 | Intergenerational Smoothing of New Zealand’s Future Fiscal Costs iii Table of Contents Abstract ............................................................................................................................. i Executive Summary ......................................................................................................... ii 1Introduction ................................................................................................................. 1 2 Intergenerational distribution of the national consumption burden of ageing through fiscal policy ...................................................................................... 2 2.1 Concepts.............................................................................................................................. 3 2.2The effects of demographic projections .............................................................................. 4 3The simulation model ................................................................................................. 5 3.1Intergenerational income analysis and social welfare analysis ........................................... 8 4Data and parameters .................................................................................................. 9 5Simulation results ..................................................................................................... 11 6Conclusion ................................................................................................................ 17 References ..................................................................................................................... 18 Appendix A – The Simulation Model ............................................................................ 20 List of Tables Table 1 – Effect on lifetime income from date of tax smoothing .................................................... 15 Table 2 – Effect on social welfare change of the sustainable debt scenario ................................. 16 List of Figures Figure 1 – Intergenerational allocation of the national consumption burden of population ageing through fiscal policy ............................................................................................ 3 Figure 2 – Support ratios. Effect of demographic projections .......................................................... 5 Figure 3 – Household labour income (after tax) and consumption .................................................. 7 Figure 4 – Effect of endogenous labour on aggregate participation rate ....................................... 11 Figure 5 – Government spending (ratio to GDP) ........................................................................... 12 Figure 6 – Tax to GDP ratios – Medium demographic projection .................................................. 12 Figure 7 – Budget balance (ratio to GDP) – Medium demographic projection .............................. 13 Figure 8 – Net debt to GDP ratios under alternative fiscal regimes – Medium demographic projection .................................................................................................................. 13 Figure 9 – Tax to GDP ratios for sustainable debt (=20% GDP) – Various demographic scenarios ........................................................................................................................................ 14 Figure 10 – Intergenerational equity with sustainable debt............................................................ 14 WP 13/12 | Intergenerational Smoothing of New Zealand’s Future Fiscal Costs 1 Intergenerational Smoothing of New Zealand’s Future Fiscal Costs 1 Introduction This paper reports modelling of a response to future fiscal cost pressures in New Zealand. The approach here is to raise the average tax rate at the start of the projection period and keep it constant throughout the projection period in order to reach a target net debt to GDP of 20%. This differs from the approach adopted by New Zealand Treasury (Bell et al, 2010) which projects across the board spending cuts in order to reach a target net debt to GDP of 20%, the figure that Treasury adopts for its sustainable debt scenarios. The alternative approach here represents tax smoothing in the sense that the tax rate is higher initially but eventually lower than it would be if the tax rate were raised gradually in line with rising government spending in order to balance budgets. Tax smoothing implies that current generations will bear a greater tax burden, and future generations a lower burden, than they would under continuously balanced budgets. The primary aim is to model the implications of this particular type of fiscal adjustment for the lifetime incomes of different generations and for national welfare. Different constant tax rates imply different debt paths and different intergenerational consequences. The methodology is similar to that in Guest (2008a) which was motivated by Australia’s Future Fund (FF). The FF is essentially a vehicle for spreading the fiscal costs of population ageing over time, as acknowledged in the Australian Government’s 2005-6 Budget Papers, Statement 7: “[the FF] will reduce calls on the budget in the future, at a time when significant intergenerational pressures are expected to emerge.” The accumulation of budget surpluses in the FF therefeore amounts to tax smoothing.1 The simulations for New Zealand in this paper imply alternative projections for net Government debt, rather than the accumulation of net assets in a sovereign wealth fund. Barro (1979) showed that, in a deterministic setting, a constant tax rate over time would minimize the distortions to behaviour arising from taxation. He pointed out that the distortions would increase more than proportionally to increases in the tax rate, drawing on Harberger (1964), cited in Browning (1987). An important distortion, or deadweight loss, arises from the substitution of leisure for work in response to taxation on labour. A policy of tax smoothing would reduce the magnitude of these distortions and therefore lead to a more efficient allocation of resources. 1 As at 31 March 2012 the FF held total assets of $77 billion or 5.3% of GDP. WP 13/12 | Intergenerational Smoothing of New Zealand’s Future Fiscal Costs 2 Empirical studies of tax smoothing have generally found small to modest positive gains in national output. For the U.S. see Cutler et al. (1990), for Europe see Floden (2003) and for Australia see Guest (2008). Cutler et al. (1990) found that the welfare gains from a constant tax rate that returned debt to its 1990 share of GNP after 60 years was 0.017% per year or, in present value terms, 1.1% of 1990 GNP. Floden (2003) found higher gains of up to 0.5% in annual consumption (for Italy but lower for most countries). The New Zealand study in Davis and Fabling (2002) found somewhat higher efficiency gains of between 3% and 5% of one year’s GDP (2008) in net present value terms. However most of these gains are due to their assumption that the assets accumulated under tax smoothing generate a rate of return above the government’s cost of borrowing. This assumption is ruled out in prior studies and here also. Guest (2008a) found even larger gains of around 1% in equivalent annual GDP over the projection period. The higher values in Guest (2008a) compared with Davis and Fabling (2002) and Cutler et al. (1990), which both assume a deadweight loss function, may be attributed to differences methodology – in particular a social aversion to variability in aggregate consumption over time, efficiency gains from lower distortions to intertemporal consumption, and a lower time preference rate, among other differences arising from the optimising approach. Floden (2003) uses a Ramsey intertemporal model which closer to that in this model and, interestingly, produces larger estimates than those in Cutler et al (1990) and, for some countries, larger than Davis and Fabling (2002). The model here complements the analyses of both Davis and Fabling (2002) and Bell et al (2010). A key difference is that the present study links feedback effects from the tax rate to labour supply through households’ optimal leisure-consumption choice over the lifecycle; this effect on labour supply in turn feeds back to tax revenue. In Davis and Fabling (2002), the feedback effects operates in one direction from the tax rate to labour supply through an assumed constant labour supply elasticity. In a life cycle optimising model the labour supply elasticity with respect to the tax rate is a complex non-liner function of parameters in the model (Ziliak and Kneisner, 2005). Other minor differences include: in Davis and Fabling (2002) labour productivity growth and interest rates are stochastic whereas here labour productivity growth zero here (discussed further below) and the interest rate is constant. The simulations use the fiscal projections from Treasury’s Long Term Fiscal Model (LTFM) adjusted for the labour supply response. Given the plans of each generation of households, aggregate consumption and labour supply in a given year are found by summing the consumption and labour supply generations alive in that year. This overlapping generations framework allows a tracking of the effect of policy changes such as fiscal adjustments on the lifetime incomes of different generations. The model also considers the effect of tax smoothing on national (or social) welfare. 2 Intergenerational distribution of the national consumption burden of ageing through fiscal policy Much of the projected fiscal cost pressures in New Zealand are attributed to population ageing (see Section 4 for numbers). Popular discussion of the costs of population ageing tends to conflate the national economic burden of ageing with the fiscal costs of ageing. The former refers to the effect of ageing on national consumption per capita over time, which occurs through the effects on the support ratio, labour productivity and the consumption share of GDP. WP 13/12 | Intergenerational Smoothing of New Zealand’s Future Fiscal Costs 9 The higher is  s the smaller are the future impacts on social welfare from changes in the aggregate consumption index. This will tend to reduce the social weight on the consumption gains relative to the losses because the gains occur in the future. The higher is  s the smaller the social weight placed on larger consumption gains or losses. This will tend to reduce the social weight on the consumption losses because they are generally larger than the gains even though the gains are spread over a longer period. The simulation outcomes are discussed below in Section 5. 4 Data and parameters The government spending share of GDP is equal to the values in Treasury’s LTFM for 2007 to 2060. Government spending9 is projected to increase by 6.4% of GDP from 29.6% to 36.0% over the 45 year period from 2014-15 to 2059-60.10 Health spending grows by 5% of GDP and New Zealand Superannuation (NZS) grows by 3.6% of GDP. However whereas all of the growth in NZS is due to demographic change, almost all of the health spending is due to “non-demographic volume growth” – income growth and input costs. Demographics accounts for roughly 1% of the 5% increase. This is consistent with the pattern in recent decades during which population ageing has accounted for only 10 to 15% of the growth in health spending in New Zealand (Bell et al., 2010). Hence the projected fiscal burden attributable to population ageing is somewhat less than the 6.4% of GDP of projected growth in total spending – approximately 4.5% to 5%. There are small reductions in other spending items as a share of GDP such as education and some welfare expenses. These figures are based on the “cost pressures” projection. This is a ‘no policy change’ projection based on bottom-up calculations of growth rates of the main budget expense categories. The growth rates for government consumption expenditure consist of the sum of the growth rates of input prices and output volumes. Input price growth consists of inflation plus (adjusted) real unit input costs which are based on (adjusted) labour productivity growth in the public sector. Output volume growth is the sum of demographically-driven and nondemographically-driven components. The demographically-driven component depends on the growth rates of recipient population age groups. For health spending, this is based on age and gender-specific shares of spending which are assumed constant throughout the projection period. For welfare spending, input price growth is simply equal to the inflation rate and volume growth is determined by demographic growth, in particular the growth rates of recipients for each category of spending. Hence unlike consumption expenditure, welfare spending does not grow with labour productivity growth. The Government spending share of GDP is assumed to remain constant at its 2055 level thereafter, and constant at its 2007 for all years up to 2007. The historic and projected age-specific population levels, age specific wage rates and exogenous11 labour force participation rates were accessed from Statistics New Zealand and not be socially optimal, as an implication of the axioms in Koopmans (1960). In particular, if  s=0, the consumption of generations near to the present would have negligible weightings in social welfare when H is large. The result would be that the future swamps the present in social importance. It could justify crushing the present generation to yield an infinitely small increase in the utility of each generation in the future. 9 Defined in the “cost pressures” projections as “core crown expenses excluding financing costs”. 10 Based on spreadsheet projections, derived from the LTFM, provided to the author by NZ Treasury officers. 11 Exogenous LFPRs are adjusted by households’ demand for leisure to generate the endogenous labour supply (see below and the Appendix). WP 13/12 | Intergenerational Smoothing of New Zealand’s Future Fiscal Costs 10 were provided by New Zealand Treasury officers.12 The population data are the same as those used in Treasury’s LTFM. Five demographic projections are compared. (i) A Medium projection which is the base case used for the LTFM and adopts the following long run assumptions: total fertility rate of 1.9, life expectancy at birth increases to 85.6 years for males and 88.7 years for females, and net migration of 10,000 p.a.; (ii) a (very) High Fertility projection which differs from the Medium projection only in that the long run fertility rate is 2.5; (iii) a (very) High Migration projection which differs from the Medium projection only in that long run net migration is 25,000 p.a. (iv) Zero Migration; and (v) Low Mortality in which life expectancy at birth increases to 95 for both males and females. A key parameter in analysing the welfare effects of tax smoothing is  , the intratemporal elasticity of substitution between leisure and consumption. This partly determines the elasticity of labour supply with respect to changes in the aftertax wage. Typical values of this parameter in the literature are in the range 0.5 to 1.0. For example, Foertsch (2004), Auerbach and Kotlikoff (1987) and Altig et al. (2001) all use a value of 0.8 in their dynamic models and this is the value chosen here. The relationship however between  and the labour supply elasticity in a lifecycle optimising model is a complicated non-linear function of the parameters of the model (Ziliak and Kneisner, 2005). Sensitivity tests are reported of labour supply responses over the lifecycle to the range of values of this parameter found in the literature. Figure 4 plots the effect of endogenous labour on the aggregate labour force participation rate (LFPR). The series plotted is the percentage change in LFPR given by the model compared with that given by the raw demographic data combined with the exogenous LFPR as given by Statistics New Zealand and used in Treasury’s LTFM. The endogenous LFPR averages about 0.2% below the exogenous LFPR over the full projection period, but the magnitude is greater (up to 1%) for the first two decades. This represents the response of households to rising tax rates. Note that the response is initially slightly larger under the sustainable debt scenario reflecting the higher initial tax rate. 12 Historical population tables from Estimated Resident Population by Age and Sex (1991+). Available from Infoshare http://www.stats.govt.nz/infoshare. Population projections from Projected Population of New Zealand by Age and Sex, 2006 (base) – 2061. Available from Table Builder http://www.stats.govt.nz/tools_and_services/tools/tablebuilder.aspx Age specific participation rates from Labour Force Status by Sex by Age Group (Qrtly-Mar/Jun/Sep/Dec). Available from Infoshare http://www.stats.govt.nz/infoshare/ . Age specific wage rates from Income by age, sex and labour force status Available from Table Builder: http://www.stats.govt.nz/tools_and_services/tools/tablebuilder.aspx Age specific earnings for those in paid employment from Earnings by region, sex and age groups. Available from Table Builder http://www.stats.govt.nz/tools_and_services/tools/tablebuilder.aspx. WP 13/12 | Intergenerational Smoothing of New Zealand’s Future Fiscal Costs 11 Figure 4 – Effect of endogenous labour on aggregate participation rate. % change in LFPR relative to exogenous LFPR ‐0.9% ‐0.8% ‐0.7% ‐0.6% ‐0.5% ‐0.4% ‐0.3% ‐0.2% ‐0.1% 0.0% 2015 2025 2035 2045 2055 Balancedbudgets Sustainabledebt There is zero technical progress in production. This allows for a more transparent analysis of the effects of ageing and accompanying fiscal regimes on labour supply and intergenerational welfare for the following reasons. One reason is that the effect of population ageing on technical progress is, although potentially important, highly uncertain in direction and magnitude according to the theoretical and empirical literature (Guest, 2007). A sensitivity analysis is one way to go but would lengthen the present analysis considerably as there are a number of potential mechanisms. Also, there is the well-known issue of modelling the leisure-consumption choice with technical progress. Technical progress drives up real wages which implies a rising price of leisure and therefore a falling leisure to consumption ratio – it would eventually decline to zero (Kulish et al., 2006; Auerbach and Kotlikoff, 1987). There are more complex utility functions that can deal with technical progress, but this is regarded as beyond the scope here. Other parameters are the interest rate, rate of time preference, depreciation rate and elasticity of marginal utility with respect to consumption. The values of these along with initial values for government debt, foreign liabilities and the capital stock are given in the Appendix. 5 Simulation results The Government spending share of GDP (G/Y) is plotted in Figure 5 for the five demographic projections. The patterns reflect those of the support ratios. Falling support ratios imply rising government spending due mainly to rising spending on NZS and health associated with higher old age dependency. The High Fertility scenario increases government spending to GDP by a maximum of 1.1% in 2035 and by 0.4% in 2060. The other demographic scenarios take longer to impact on GDP; indeed the effect is less than 0.2% of GDP up to 2035. After that the effect is greater. Zero Migration increases spending by the most, 1.7 % of GDP by 2060, compared with 1.2% under Low Mortality. High Migration reduces spending by 0.3% of GDP by 2060. WP 13/12 | Intergenerational Smoothing of New Zealand’s Future Fiscal Costs 12 Figure 5 – Government spending (ratio to GDP) 0.28 0.3 0.32 0.34 0.36 2015 2025 2035 2045 2055 ZEROMIG LOWMORT HIGHFERT MED HIGHMIG Three tax smoothing regimes are compared with a balanced budget regime. See Figure 6. Figure 6 – Tax to GDP ratios – Medium demographic projection 0.3 0.32 0.34 0.36 2015 2025 2035 2045 2055 Sustainabledebt Balancedbudget Zerodebt NetfinassetstoGDP=0.20 The first is a sustainable debt regime, where this is defined by NZ Treasury as a stable debt to GDP of 20% by 2060. This implies a tax to GDP ratio that starts at 30.9% in 2015 (compared with 30.5% under balanced budgets) and increases to 35.3% in 2060 (compared with 35.6% under balanced budgets). The sustainable debt tax path is very close to the balanced budget path. There is no more than 0.4% of GDP difference at any point over the projection period. Such a small increase in the balanced budget tax rate is all that is needed to reduce debt from the balanced budget level of 31.7% to 20% from 2015 to 2060. This is reflected in small/modest budget surpluses of between 1.3% and 0.6% of GDP over the projection period (see Figure 7 for budget surpluses). WP 13/12 | Intergenerational Smoothing of New Zealand’s Future Fiscal Costs 13 Figure 7 – Budget balance (ratio to GDP) – Medium demographic projection ‐0.05 ‐0.03 ‐0.01 0.01 0.03 0.05 2015 2025 2035 2045 2055 sustainabledebt zerodebt NetfinassetstoGDP=0.32 The third budget regime has debt to GDP stabilising at zero rather than 20% (see Figure 8 for the debt ratios in each regime). This requires higher initial budget surpluses of 2% of GDP declining to zero by 2060 (Figure 7). The fourth budget regime is even more extreme tax smoothing where the debt becomes negative and stabilises with net foreign asset of 20% of GDP. The budget surplus starts at 2.6% of GDP in 2015 and steadily declines to a stable budget deficit of 0.5% of GDP. Hence the three regimes represent progressive degrees of smoothing. A higher degree of smoothing implies greater transfer of the consumption cost of ageing to present generations and away from future generations, as discussed earlier. Figure 8 – Net debt to GDP ratios under alternative fiscal regimes – Medium demographic projection ‐0.3 ‐0.2 ‐0.1 0 0.1 0.2 0.3 0.4 2015 2025 2035 2045 2055 Sustainabledebt Balancedbudget zerodebt NetfinassetstoGDP=0.20 Sensitivity to the demographic projections is illustrated in Figure 9 which shows the tax to GDP ratios under the sustainable debt regime under the five demographic scenarios. It mirrors the pattern of government spending illustrated in Figure 5. The tax ratio is eventually highest under Zero Migration, being 1.6% above that under the Medium projection by 2060, although it takes at least 15 years (until 2030) for the tax ratio to rise above that of the Medium projection. Indeed that is the case for most of the alternative demographic projections – their fiscal implications are slow to take effect, the exception being the High Fertility scenario where the fiscal cost of higher dependents arises sooner. WP 13/12 | Intergenerational Smoothing of New Zealand’s Future Fiscal Costs 14 Figure 9 – Tax to GDP ratios for sustainable debt (=20% GDP) – Various demographic scenarios 0.3 0.32 0.34 0.36 2015 2025 2035 2045 2055 g ZEROMIG LOWMORT HIGHFERT MED HIGHMIG A key aim of the analysis is to determine whether households of different generations are better off or worse off under tax smoothing, and by how much. The method adopted here is to calculate the effect on lifetime income from the year of the policy shift which is 2015.13 The policy shift is assumed to be unexpected, prior to which balanced budgets are the actual and expected policy. The results are illustrated in Figure 10 and Table 1. Figure shows percentage effect on remaining lifetime income from 2015 of generations born in the year indicated, due to a change in fiscal regime from a balance. The sustainable debt scenario is compared with the balanced budget scenario for each of the five demographic projections. The balanced budget scenario is chosen as the counterfactual since the principal objective is to examine tax smoothing which implies a comparison with balanced budgets. Note that Table 1 provides more detail by including the extreme form of smoothing (resulting in stable net financial assets of 20% of GDP) for the Medium Fertility scenario, and also reporting results for each of the alternative demographic scenarios in the case of the sustainable debt regime. Figure 10 – Intergenerational equity with sustainable debt ‐4 ‐3 ‐2 ‐1 0 1 2 3 1940 1950 1960 1970 1980 1990 2000 2010 2020 2030 % Generationborninyearindicated Sustainabledebt(=20%GDP) Netfin.assets(=+20%GDP) 13 An alternative is to calculate the effect on remaining lifetime utility from 2015, expressed in units of equivalent annual income (see Guest, 2008, for an application of this method). WP 13/12 | Intergenerational Smoothing of New Zealand’s Future Fiscal Costs 15 Table 1 – Effect on lifetime income from date of tax smoothing High Fert High Mig Zero Mig Low Mort Individual born in year Sustainable debt (=20% GDP) Net fin. assets (=+20% GDP) Sustainable debt Sustainable debt Sustainable debt Sustainable debt 1940 -0.55 -2.43 -0.73 -0.57 -0.49 -0.53 1950 -0.59 -2.52 -0.74 -0.60 -0.52 -0.55 1960 -0.73 -3.12 -0.88 -0.76 -0.67 -0.71 1970 -0.60 -2.59 -0.72 -0.63 -0.56 -0.59 1980 -0.41 -1.78 -0.49 -0.44 -0.37 -0.41 1990 -0.20 -0.91 -0.24 -0.24 -0.17 -0.21 2000 0.00 -0.03 0.01 -0.04 0.03 -0.02 2010 0.25 1.03 0.29 0.20 0.29 0.23 2020 0.46 1.88 0.49 0.42 0.51 0.45 2030 0.64 2.55 0.67 0.62 0.70 0.65 Debt ratio in 2060 20% -20% 20% 20% 20% 20% Figures are percentage changes relative to balanced budget tax regime Median demo. projection The first and important point to note is that the magnitudes of effects on all generations are very small, at most no more than 0.9% on any generation under any demographic scenario. This is perhaps not surprising given the small adjustments to the tax rate required to achieve a sustainable debt (Figure 6). Generations born prior to 1990 are worse off and those born after 2000 are better off. (“Better off” and “worse off” is measured relative to the remaining lifetime income after the tax smoothing shock that occurs in 2015). Those born around 1960 fare the worst, albeit not by a large amount. They are 0.7% worse off in the Medium demographic scenario. This generation is aged around 45 and therefore at the peak of their earning capacity when the tax smoothing policy is introduced, which results in an initial jump in tax rates. Also this generation has retired before the balanced budget scenario yields a payoff in terms of a lower tax rate which occurs around the late 2030’s. Retired workers are also worse off because they pay higher tax rates on their retirement income. For those born a few years either side of 2000, the losses from higher tax rates for the 15 year period to 2030 are roughly balanced by the gains from lower taxation after 2030. Those who gain the most are future workers, particularly those born after 2020. They escape the higher taxes on earlier generations and reap the gains from lower future taxes. Even so, they are only better off by 0.6% under the sustainable debt scenario. The numbers are of course greater under the more extreme smoothing regime (Figures 10). Given that existing workers and retirees are worse off while future workers are better off, what is the social gain? This requires value judgements for which we apply the social welfare function (6). The impact on social welfare takes account not only of intergenerational equity but also implicitly the efficiency gains from tax smoothing arising from the reduction in distortions to both the labour-leisure choice arising from taxation of labour income and to the intertemporal consumption allocation arising from the taxation of capital income. The results are reported in Table 2 by expressing the effect in social welfare in terms of equivalent annual gains in GDP per annum generated by sustainable debt tax smoothing scenario. These were calculated by finding the annual increase in GDP under continual balanced budgets that would generate the same value of social welfare as in the tax smoothing scenario. Results are given for a range of values of the two key parameters in the social welfare function: the social time preference rate, θs, and the parameter measuring the social aversion to variability in aggregate consumption, βs. The values chosen for θs range from zero to 6%; and the values chosen for βs range from 0.2 to 5. The first point to note is that the effects are mostly small and negative. However gains from smoothing occur for a low WP 13/12 | Intergenerational Smoothing of New Zealand’s Future Fiscal Costs 16 rate of social time preference and a high rate of aversion to consumption variability (see the last row in the Table). The reasons for the gains under those parameter assumptions, as noted above, are that a low value of  s gives relatively more weight to the future gains from smoothing; and a higher value of  s gives a relatively low weight to the years of losses which are larger in magnitude but fewer in number. This will tend to reduce the social weight on the consumption losses because they are generally larger than the gains even though the gains are spread over a longer period. Hence net social gains are possible provided the gains to future generations are given sufficient weight. The parameter values required to generate net social gains are close to the bounds of plausible values. Table 2 – Effect on social welfare change of the sustainable debt scenario. Base case demographics (Medium fertility) Social Aversion to time pref variability in aggregate rate (θ s )consumption (β s ) % change in equiv . $ Change in equiv. annual % annual GDP GDP per capita* 0.0 2.0 -0.03% 13-$ 3.0 2.0 -0.10% 49-$ 6.0 2.0 -0.13% 66-$ 3.0 0.2 -0.11% 55-$ 3.0 1.0 0.00% 1-$ 3.0 5.0 -0.18% 90-$ 0.0 5.0 0.19% 94$ * Calculation is based on a projected 2015 GDP of $226 billion and a projected population of 4.6 million. The Table reports magnitudes in equivalent annual gains in GDP. This is done by finding the annual increase in GDP under the balanced budget case that would produce the same value of social welfare under the sustainable debt scenario. The magnitudes range from minus $90 to plus $94 per capita per year. Although the methodologies are different, these magnitudes are of the same order as those found in Davis and Fabling (2002) who calculated gains for New Zealand of between 3% and 5% of one year’s GDP (not annual GDP), would equate to roughly 0.1% of GDP per year. WP 13/12 | Intergenerational Smoothing of New Zealand’s Future Fiscal Costs 17 6 Conclusion This paper complements the New Zealand fiscal projections of Bell et al. (2010) and the New Zealand tax smoothing analysis in Davis and Fabling (2002). It allows for feedback effects of the tax rate on labour supply intratemporally and intertemporally which in turn feed back to fiscal projections via taxation revenue. The model allows for efficiency gains from tax smoothing arising from the reduction in distortions to both the labour-leisure choice arising from taxation of labour income and to the intertemporal consumption allocation arising from the taxation of capital income. The overlapping generations framework also allows an analysis of intergenerational income effects; and imposing a social welfare function allows a numerical calibration of the combined equity and efficiency effects of tax smoothing. For the Medium demographic projections, tax smoothing consistent with sustainable debt implies small gains and losses among generations amounting to no more than 0.7% of remaining lifetime income for any generation. This is not surprising given that the sustainable debt scenario requires only a small increase in the tax to GDP ratio of 0.5% at the most over a decade from 2015. Those born around 1960 fare the worst, but only suffer a 0.7% drop in their remaining lifetime incomes under the sustainable debt scenario for the Medium demographic projection. This generation is at their peak earning capacity when the tax smoothing policy is introduced, which results in an initial jump in tax rates. They have also retired before the balanced budget scenario yields the payoff of a lower tax rate. Retired workers are also worse off because they pay higher tax rates on their retirement income. Future workers are better off because they escape the higher taxes on earlier generations and reap the gains from lower future taxes. The losses to current generations can be weighed up against the gains to future generations through the social welfare function. The results show that net social gains are possible provided the gains to future generations are given sufficient weight by a low rate of social time preference and a high rate of aversion to variability in aggregate consumption over time. The parameter values required to generate net social gains are close to the bounds of plausible values. The magnitudes of the net social gains/losses for the combinations of parameter values simulated range from minus $90 to plus $94 per capita per year. There are well known limitations of the optimizing framework here, notably the assumption of fully forward looking households who have perfect foresight (except that they do not anticipate the switch in fiscal regime); a high degree of aggregation (the firm produces only one good); a perfect capital market; and a single tax rate applied to both income and capital. There are also a range of practical limitations, including political issues, in a pure form of tax smoothing considered in this paper (see the discussion in Davis and Fabling, 2002). Future work could begin to relax some of these constraints. WP 13/12 | Intergenerational Smoothing of New Zealand’s Future Fiscal Costs 18 References Auerbach, A.J. and Kotlikoff, L.J. (1987) “The Effects of a Baby Boom on Stock Prices and Capital Accumulation in the Presence of Social Security”, Econometrica 71, 2, 551-578. Barro, R. 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