Social Expenditure in New Zealand: Stochastic Projections (WP 13/06)

Abstract#

This paper presents stochastic projections for 13 categories of social spending in New Zealand over the period 2011-2061. These projections are based on detailed demographic estimates covering fertility, migration and mortality disaggregated by single year of age and gender. Distributional parameters are incorporated for all of the major variables, and are used to build up probabilistic projections for social expenditure as a share of GDP using simulation methods, following Creedy and Scobie (2005). Emphasis is placed on the considerable uncertainty involved in projecting future expenditure levels.

Acknowledgements#

We are grateful to Christopher Ball, John Bryant and Nicola Kirkup for comments on an earlier version of this paper.

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.

Executive Summary#

This paper reports projections of social expenditure in New Zealand, over the fifty-year period 2011 to 2061, which explicitly model uncertainty associated with a wide range of variables using a 'stochastic' approach.

The stochastic approach regards the parameters (fertility, labour force participation rates, age specific per capita expenditures, and so on) as being characterised by a distribution, rather than taking fixed values. A large number of projections of the variables of interest (such as total social expenditure in relation to GDP) can thus be made, in each case taking a random draw from each of the specified distributions. This generates a distribution of values in each year of the projection period, whose properties can be examined.

The first stage is the production of projections for the size of the population, together with its distribution by age and gender. This requires projections of trends in fertility, mortality and net migration. Projected labour force participation rates are then combined with age and gender specific unemployment rates to generate the size of the workforce. This is multiplied by average productivity per worker to obtain GDP. Social expenditures per capita are combined with population (by age and gender) to obtain total social expenditure on each of 13 categories for each age and gender group. The resulting total social expenditure is finally expressed as a share of projected GDP.

Focussing on 'pure ageing' results (whereby per capita social expenditure costs in each category grow at the same rate on average as productivity growth), the projections reveal considerable uncertainty regarding the ratio of total social expenditure to GDP as the time period increases.

In the benchmark case, the mean ratio of expenditure to GDP is projected to rise from its current level of 25 per cent to 28 per cent by 2061. However, the 5thand 95th percentiles are 22.5 per cent and 35 per cent.

A negligible part of the dispersion in this ratio is contributed by demographic uncertainty.

Much of the uncertainty was found to be contributed by uncertainty regarding future unemployment and labour force participation rates, and the rate of productivity growth. More optimistic assumptions regarding labour force participation and health costs among the aged produced lower average ratios of expenditure to GDP. A consistent finding was the tendency for the average expenditure ratio to fall slightly beyond around 2040, following the death of the post World War II baby boom generations.

1 Introduction#

The aim of this paper is to produce stochastic projections of social expenditure in New Zealand over the fifty-year period 2011 to 2061. By their very nature, expenditure projections cannot possibly provide accurate information about future levels. A very large range of parameters are held fixed or are assumed to change according to simple trends over the projection period. In considering the question of, 'what if recent trends were to continue and there were no endogenous policy changes?', such projections can at best provide an indication of the kind of stresses that could arise. There will inevitably be responses to those changes, including 'general equilibrium' types of response arising, for example, from changes in wage rates resulting from labour market pressures. While they cannot therefore be treated as forecasts, projections can stimulate and inform further analyses, considering for example whether market responses may be expected to mitigate or exacerbate the anticipated pressures.

Particular concern has been expressed regarding the consequences of the demographic transition in progress in New Zealand as in many industrialised countries. This involves the ageing of the baby-boom generations and, more importantly, continued reductions in fertility and especially mortality, with the latter producing the phenomenon of the 'ageing of the aged'. The fact that most types of social expenditure are age related makes this category of government expenditure a particularly important area of investigation. Of course, the present transition is merely one stage in earlier extensive demographic transitions experienced by developed economies. Furthermore, there have been very large changes in tax and expenditure ratios that have been quite independent of demographic changes.[1]

In view of the uncertainty that is inevitably involved in making projections, it is important to provide some indication of the potential range of values which could arise. Indeed, in considering possible policy action, and in particular the timing of such intervention (which may include tax smoothing in anticipation of higher future government expenditure), it is important to have some idea of the probability of future contingencies as well as their possible size.[2]

One approach is to consider a number of alternative 'scenarios', characterised by, for example, high labour force participation or higher mortality rates. However, there is no way to attach probabilities to such alternatives, and in the present context there are many parameters to consider. The starting point of the present stochastic approach is to regard the parameters (fertility, labour force participation rates, age specific per capita expenditures, and so on) as being characterised by a distribution, rather than being fixed values. A large number of projections of the variables of interest (such as total social expenditure in relation to GDP) can thus be made, in each case taking a random draw from each of the specified distributions. This kind of ‘Monte Carlo' approach thereby generates a distribution of values in each year of the projection period, whose properties can be examined. The method used here is based closely on the earlier work of Creedy and Scobie (2005).[3]

In specifying the form of the distribution (along with, say, the mean and standard deviation) of each relevant parameter, Creedy and Scobie (2005) used information about its past variability, which clearly involved the collection and analysis of a great deal of data. This was helped by, among other things, the existence of the Long Term Data Series, which was compiled within the Treasury. As this data series has not been maintained and regularly updated in more recent years (having been transferred to Statistics New Zealand), the present paper makes use of the growth rates and standard deviations obtained by Creedy and Scobie (2005). However, as indicated below, these were modified to some extent, either by ‘rounding' a number of values or by using a priori assumptions.[4]

Section 2 briefly describes the framework of analysis: for details see Appendix A. Section 3 presents the benchmark results. Sensitivity analyses are reported in Section 4. Conclusions are in Section 5.

2 The projection model#

This section provides a brief description of the projection model: further details are given in Appendix A.[5] Exogenous age-specific and gender-specific rates are used and, as mentioned above, no allowance is made for possible feedback effects, which may for example be generated by general equilibrium changes in price and wage rates, or endogenous policy responses.

The sequence of calculations is set out in Figure 1, where the grey boxes represent input data. The first stage is the production of projections for the size of the population, together with its distribution by age and gender. This requires projections of trends in fertility, mortality and net migration. Projected labour force participation rates are then combined with age and gender specific unemployment rates to generate the size of the workforce. This is multiplied by average productivity per worker to obtain GDP.

Figure 1: The Structure of the Model

 

Social expenditures per capita are combined with population (by age and gender) to obtain total social expenditure on each of 13 categories for each age and gender group. These categories are listed in Appendix Tables 4 and 5. The resulting total social expenditure is finally expressed as a share of projected GDP.

In moving through the sequence of calculations, a random draw from the distribution of each variable is made, as explained below. This process is repeated 5000 times, to produce a distribution of the social expenditure ratio for each projection year. The process therefore also generates distributions of the population by age and gender, as well as for each category of social expenditure.

Consider a relevant variable, Χ, which could be, for example, an unemployment rate, a fertility rate for women of a given age, or an item of social expenditure. In cases where the variable may take positive or negative values, it is assumed to be normally distributed. Where a variable is necessarily positive, and the distribution is positively skewed, the distribution is assumed to be lognormal.[6]

Where a variable is normally distributed with mean and variance μ and σ² respectively, Χ is distributed as N(μ,σ²) If r represents a random drawing from N(0,1), a simulated value, χ, can be obtained using χ = μ + r σ. In the lognormal case, μ and σ² refer to the mean and variance of logarithms. A random draw from a lognormal distribution is given by χ = exp (μ + r σ), where r is again a random N(0,1) variable.[7]

Each social expenditure projection is associated with its own demographic structure. The populations are necessarily derived using single-year age groups, but when calculating social expenditures and employment, some age grouping is necessary in view of the more limited data available for these variables.

The growth rates and standard deviations used in Creedy and Scobie (2005) were based on considerable information about past trends and the variability in several hundred fertility rates, mortality rates, migration rates, male/female birth ratios, labour force participation rates, unemployment rates and major categories of social expenditure. Their growth rates and standard deviations were estimated from the following regression:[8]

     log γ_t = α + β + u_t       (1)

Where γ_τ is per capita expenditure in the relevant category at time τ and u_t is an error term. This specification implies an estimated constant growth rate of

. Furthermore, Var(log γ_t) =

, so the standard deviations are derived from the estimated standard error of the regression,

. The log-linear specification was found to provide a good fit to the historical data.[9]

In producing the projections reported below, data were obtained for 2010 relating to male and female populations, inward and outward migrants by single year of age, along with male and female unemployment rates by five-year age groups. The details along with data sources are given in Tables 1-3 in Appendix B. The 2010 social expenditure costs per capita, again within 5-year age groups, were also obtained for 13 categories and are reproduced in Tables 4 and 5 of Appendix B. The standard deviations for demographic components of the model were adapted from Creedy and Scobie (2005), in view of the lack of more recent data.

3 Benchmark results#

This section presents the benchmark projections for the distribution of social expenditure as a proportion of GDP. The essential features are that all social expenditures are assumed to grow in real terms at 1.5 per cent per year, the same rate as labour productivity. The results therefore refer to a ‘pure ageing' assumption. Immigration is based on the average over recent years of 14,500 net immigrants each year (with total annual immigration of 82,500). Changes in mortality rates are assumed to continue (at values given in Table 1 of Appendix B) for 15 years, after which they remain constant. Changes in labour force participation rates, taken from Creedy and Scobie (2005), are assumed to apply for 10 years. Fertility rates are assumed to change for 10 years, after which no further changes in these rates are projected. The standard deviation of productivity growth is assumed to be 0.02, reflecting a high degree of uncertainty about this variable.

For the social expenditure categories, the standard deviations (in each age, gender and expenditure category) were set at 0.05 for each category and age group and gender.

Figure 2 shows the projected population pyramids for ten-year intervals over the 50-year projection period (for plotting purposes, the results are arranged into 5-year age groups). The figures actually show the arithmetic mean values of the various distributions. As expected, the population projections are associated with a relatively small degree of uncertainty, in that the confidence intervals around the mean values are very small. For this reason they are not shown here.

Figure 3 shows the time profile of various measures of the distribution of the projected ratio of total social expenditure to GDP from 2010 to 2060.[10] In addition to the mean, the profiles of upper and lower quartiles, and 5^th and 95^th percentiles are shown.[11] This diagram may be compared with Figure 3 of Creedy and Scobie (2005), which covers the period 2001 to 2051. The latter, as expected, starts from a similar base, but the present projections display slightly smaller ‘spreads' in the profiles over time. Nevertheless the most striking feature of Figure 3 is the increasing uncertainty regarding the social expenditure ratio.

As with earlier projections, the arithmetic mean ratio of total social expenditure to GDP increases relatively sharply from around 2020, as a result of the movement of the post World War II baby boomers into retirement and old age. In Creedy and Scobie (2005) the projected profile of this ratio becomes stable by around 2040. In the present case the mean ratio falls very slightly after this date. Given the assumption that mean per capita growth rates of social expenditure are the same as that of (mean) productivity growth, the profiles are affected largely by the changing age composition over time. The slight reduction in the projected mean expenditure ratio in later years therefore seems to be explained by the fact that the baby boom generations will have all died by that time. However, given the large degree of uncertainty (the high dispersion in the distribution of the expenditure ratio), these reductions cannot be treated as statistically ‘significant'.

The generally lower average social expenditure ratio in the present case is not explained by the much higher annual value of net immigration, compared with the earlier results (which were based on a long term average of only 5,000 (associated with gross immigration of 60,000), a value that has been substantially exceeded since 2001).[12] Higher immigration has very little effect, although it must be recognised that in the present model migrants are assumed to acquire existing New Zealand mortality, fertility and labour force participation characteristics as soon as they arrive (along with entitlements to benefits). And although the average age of immigrants is slightly lower than that of the New Zealand population, there are of course substantial numbers of migrants in the older age groups.[13]

Figure 2: Population Projections by Age Groups and Gender 2010-2060

 

Figure 3: Projected Social Expenditure as a Share of GDP: 2010-2060 (Benchmark Case)

 

To illustrate how the assumed standard errors of the per capita growth rates of social expenditures translate into standard errors of the costs, the projected growth in health and education costs per capita, for males and females separately, are shown in Figures 4 and 5. In each case the mean is plotted, along with two standard deviations either side of it. Health includes the five health categories aggregated; these are personal health, public health, mental health, DSS older, and DSS under 65. Education includes the two categories, primary and tertiary education.[14] The largest degree of uncertainty relates to unemployment benefits, since in this case the uncertainty also includes the age and gender-specific unemployment rates. Unemployment costs per capita are illustrated in Figure 6.

Figure 4: Health Expenditure per Capita: 2010-2060

 

Figure 5: Education Expenditure per Capita: 2010-2060

 

Figure 6: Unemployment Benefit Expenditure per Capita: 2010-2060

 

4 Sensitivity Analyses#

This section explores the impact on the projected levels of social expenditure of variations to the assumptions used in the benchmark case. In order to concentrate on the effects of the anticipated demographic transition, the sensitivity analyses retain the use of a ‘pure ageing' assumption (whereby average growth rates of the social expenditure categories are equal to average productivity growth).

First, it is of interest to examine the implications of having a higher age of eligibility for NZ Superannuation. The full effects cannot be modelled explicitly, but suppose that the age of eligibility is raised, for males and females, to aged 70.[15] To reflect this increase, the NZS costs per capita were changed: for males and females in age groups from 60 to 69 these were reduced to zero. For the age group 70-74 the annual per capita costs were changed to 10000 and 12000 for males and females respectively. Associated with these changes, the labour force participation rates for males in age groups 55-59, 60-64, 65-69, and 70-74 were changed to 0.9, 0.9, 0.75 and 0.1 respectively. For females in the corresponding groups the rates were increased to 0.8, 0.8, 0.75 and 0.1.

A related modification is a change to the assumed length of time over which mortality declines. This was changed from 15 to 30 years. The age-related health costs (DSS Older) for age groups from 50 to 64 were also reduced to zero. The modifications to labour force participation and health costs were, for simplicity, assumed to operate immediately. This modification from the benchmark case is thus one in which people continue to live longer, but this extra length of life is associated with improved health and hence also higher labour force participation. The extra longevity ultimately leads to higher stocks of retired individuals, though this is mitigated to some extent by the assumed higher labour force participation, which raises GDP.

The projected distribution of the ratio of social expenditure to GDP is shown in Figure 7. It is clear that these more optimistic assumptions imply a downward shift in the distribution, although the spread of values (between the 5^th and 95^th percentiles) remains similar to that of the benchmark case.

Figure 7: Projected Social Expenditure as a Share of GDP: 2010-2060 (Increased Longevity and Higher Labour Force Participation of Those Aged over 55)

 

Clearly a wide range of alternative assumptions could be examined, as discussed in Creedy and Scobie (2005), but in view of the present emphasis on uncertainty it is of interest to consider alternative assumptions about the standard errors of a number of the variables. First, the elimination of any uncertainty regarding demographic elements has very little effect, as expected; the resulting diagram (not shown here) is difficult to distinguish from the benchmark of Figure 3.

Two more cases are reported here. In the first variant, the standard deviations of expenditure categories in all age groups were set to zero. The uncertainty is thus attributed to demographic, labour market and productivity variations. In the second variant, the standard deviations of the unemployment and participation rates, and that of the productivity growth rate, were set equal to zero. The resulting projected distributions of the social expenditure to GDP ratio are shown in Figures 8 and 9. Comparison of these two figures shows that spread of the distributions arising from labour market and productivity variations is substantially higher than that arising from the uncertainty with regard to per capita social expenditures (as reflected in the observed variability over earlier years).

Figure 8: Projected Social Expenditure as a Share of GDP: 2010-2060: No Uncertainty Regarding Growth of all Social Expenditure Categories

 

Figure 9: Projected Social Expenditure as a Share of GDP: 2010-2060: No Uncertainty in Participation and Unemployment Rates, and Productivity Growth Rate

 

5 Conclusions#

This paper has projected social expenditures in New Zealand over the fifty-year period 2011-2061, based on a stochastic approach using 13 categories of social spending, decomposed by age and gender. By allowing for uncertainty about fertility, migration, mortality, labour force participation and productivity, and all categories of social spending, it has been possible to generate projections with accompanying confidence bands.

Focussing on ‘pure ageing' results (whereby per capita social expenditure costs in each category grow at the same rate on average as productivity growth), the projections reveal considerable uncertainty regarding the ratio of total social expenditure to GDP as the time period increases. In the benchmark case, the mean ratio of expenditure to GDP is projected to rise from its current level of 25 per cent to 28 per cent by 2061. However, the 5^th and 95^th percentiles are 22.5 per cent and 35 per cent.

A negligible part of the dispersion in this ratio is contributed by demographic uncertainty. Much of the uncertainty was found to be contributed by uncertainty regarding future unemployment and labour force participation rates, and the rate of productivity growth. More optimistic assumptions regarding labour force participation and health costs among the aged produced lower average ratios of expenditure to GDP. A consistent finding was the tendency for the average expenditure ratio to fall slightly beyond around 2040, following the death of the post World War II baby boom generations.

Appendix A: The Projection Model#

Population projections are obtained using a social accounting, or cohort component, framework.[16] There are N = 100 (single year) age groups. The square matrix of flows, f_ij, from columns to rows, has N - 1 non-zero elements which are placed on the diagonal immediately below the leading diagonal. The coefficients, a_ij, denote the proportion of people in the j th age who survive in the country to the age i, where p_j is the number of people aged j and

      (A1)

where only the a_i+1,i, for i = 1,..., N - 1 are non-zero. Males and females are distinguished by subscripts m and f, so that matrices of coefficients are A_m and A_f. Let p_m,t and p_f,t denote vectors of male and female populations at t, where the i-th element is the corresponding number of age i. The vectors of births and immigrants are b and m respectively. The forward equations:

      (A2)

      (A3)

In general the matrices A_m and A_f, along with the births and inward migration flows, vary over time.

Suppose that c_i represents the proportion of females of age i who give birth per year. In general the c_i values vary over time. Suppose that a proportion, δ, of births are male, and define the N-element vector τ as the column vector having unity as the first element and zeros elsewhere. Then births are:

      (A4)

      (A5)

where c′ is the transpose of the vector c. Equations (A2) to (A5) can be used to make population projections, for assumed migration levels.

The per capita social expenditures are placed in a matrix, S, with N rows and k columns, where there are k items of social expenditure and the i, j th element s_ij is the per capita cost of the j th type of social expenditure in the i th age group. Suppose the j th social expenditure is expected to grow in real terms at the annual rate ψ_j in each age group. Then define g_t as the k-element column vector whose j th element is equal to (1 + ψ_j )^t-1. Aggregate social expenditure at t,C_t, is thus:

      (A6)

Expenditure per person in each category and age differs for males and females, so that (A6) is suitably expanded.[17]

Projections of Gross Domestic Product depend on: initial productivity (GDP per employed person); productivity growth; employment rates; participation rates; and the population of working age. Total employment is the product of the population, participation rates and the employment rate. Employment is calculated by multiplying the labour utilisation rate by the labour force. If U_t is the total unemployment rate in period t, the utilisation rate is 1 - U_t. The aggregate unemployment rate is calculated by dividing the total number of unemployed persons, V_t, by the total labour force, L_t. The value of V_t is calculated by multiplying the age distribution of unemployment rates by the age distribution of the labour force, where these differ according to both age and sex.

Let vectors U_m and U_f be the age distributions of male and female unemployment rates. If ^∧ represents diagonalisation (a vector is written as the leading diagonal of a square matrix with other elements zero) unemployment in period t is:

      (A7)

The labour force, L_t, is:

      (A8)

If productivity grows at the rate, θ, GDP t is the product of the utilisation rate, 1 - U_t = 1 - V_t/L_t, the labour force, Lt, and productivity, so that:

      (A9)

Appendix B: The Data#

Notes:

P = population; I = immigration; E = emigration; M = mortality; ΔM/M = proportionate change in mortality; F = fertility; ΔF/F = proportionate change in fertility.

Population data are from New Zealand Treasury Fiscal Strategy Model: http://www.treasury.govt.nz/government/fiscalstrategy/model

Immigration and emigration data are from Statistics New Zealand Infoshare Database: http://www.stats.govt.nz/infoshare/ViewTable.aspx?pxID=492172f2-ccc5-407a-97e4-671786685d49 [Treasury adjusted URL at 02 Jul 2024 https://infoshare.stats.govt.nz/#]

The aggregated data provided a value for individuals aged 75+. This value has been apportioned across age years 75 - 99.

Mortality rates (2010 base year) are from New Zealand Treasury Long Term Fiscal Strategy Model: http://www.treasury.govt.nz/government/fiscalstrategy/model.

Fertility rates (2010 base year) from Statistics New Zealand Infoshare Database: http://www.stats.govt.nz/infoshare/ViewTable.aspx?pxID=ef4929f3-a56c-4ba9-9081-efefb05f4cfb [Treasury adjusted URL at 02 Jul 2024 https://infoshare.stats.govt.nz/#]

Appendix B: The Data (continued)#

Notes: Standard deviation values have been adapted from those in Creedy and Scobie (2002), and have been rounded to smooth out the variation between them.

Notes: (a) No data available for this value. It is assumed to be zero.

The labour force participation rates and unemployment rates are those for the base year 2010. Data are from Statistics New Zealand Infoshare Database: http://www.stats.govt.nz/infoshare/ViewTable.aspx?pxID=22810555-769b-4418-9f57-a62211a57972 [Treasury adjust URL at 02 July 2024 - https://infoshare.stats.govt.nz/#]
 

Standard deviation values have been adapted from those in Creedy and Scobie (2002), and have been rounded to smooth out the variation between them.

Appendix B: The Data (continued)#

Notes: DSS = Disability Support Services; NZS = New Zealand Superannuation; DPB = Domestic Purposes Benefit; WB = Widow's Benefit; IB = Invalid's Benefit; SB = Sickness Benefit.

Health Expenditure data for categories one to five are from New Zealand Treasury Fiscal Strategy Model: http://www.treasury.govt.nz/government/fiscalstrategy/model

Aggregate Education (Primary and Secondary) Expenditure data are from New Zealand Treasury calculations based on Ministry of Education administrative data. These data were disaggregated by age and gender using a weighted average approach according to the basic population demographic data in Table 1 for the relevant ages (4 - 17).

Aggregate Tertiary Education Expenditure data are from Statistics New Zealand: http://www.stats.govt.nz/browse_for_stats/education_and_training/Tertiary%20education/StudentLoansandAllowances_HOTP10/Tables.aspx  [Treasury adjusted URL at 02 July 2024: https://www.stats.govt.nz/topics/education]. These data were disaggregated by age and gender using a weighted average approach according to the basic population demographic data in Table 1 for the relevant ages (17 - 64). The aggregated data provided a value for individuals aged 60+. This value has been apportioned to the 60-64 age category.

Data for social expenditure data categories eight to thirteen are calculated using New Zealand Treasury model TaxWell, based on HES 08/09 and HES 09/10.

Notes: DSS = Disability Support Services; NZS = New Zealand Superannuation; DPB = Domestic Purposes Benefit; WB = Widow's Benefit; IB = Invalid's Benefit; SB = Sickness Benefit.

Health Expenditure data for categories one to five are from New Zealand Treasury Fiscal Strategy Model: http://www.treasury.govt.nz/government/fiscalstrategy/model

Aggregate Education (Primary and Secondary) Expenditure data are from New Zealand Treasury calculations based on Ministry of Education administrative data. These data were disaggregated by age and gender using a weighted average approach according to the basic population demographic data in Table 1 for the relevant ages (4 - 17).

Aggregate Tertiary Education Expenditure data are from Statistics New Zealand: http://www.stats.govt.nz/browse_for_stats/education_and_training/Tertiary%20education/StudentLoansandAllowances_HOTP10/Tables.aspx [Treasury adjusted URL at 02 July 2024: https://www.stats.govt.nz/topics/education]  These data were disaggregated by age and gender using a weighted average approach according to the basic population demographic data in Table 1 for the relevant ages (17 - 64). The aggregated data provided a value for individuals aged 60+. This value has been apportioned to the 60-64 age category.

Data for social expenditure data categories eight to thirteen are calculated using New Zealand Treasury model TaxWell, based on HES 08/09 and HES 09/10

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