Population Ageing and Social Expenditure in New Zealand: Stochastic Projections (WP 02/28)

Abstract#

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It is widely recognised that as the population ages there will be potentially significant implications for a wide range of economic variables, including in particular the fiscal costs of social expenditures. Long term fiscal planning requires estimates of the possible future path of public spending. This paper presents projections for 14 categories of social spending. 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. Attention is focussed on health expenditures which are disaggregated into seven broad classes. In addition we explore the impacts of alternative hypothesis about future health costs. While it can be predicted with some confidence that overall social expenditures will rise, the results suggest that long term planning would be enriched by recognising the distributions about point estimates of projected social costs.

Acknowledgements#

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The authors acknowledge assistance from Ivan Tuckwell and Statistics New Zealand in providing data, John Bryant and Grant Johnston for help with the health costs, Malcolm McKee for help with social expenditures, and a significant input to the analysis of the results contributed by Vito Schultz.

Disclaimer#

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The views expressed in this Working Paper are those of the author(s) and do not necessarily reflect the views of the New Zealand Treasury.  The paper is presented not as policy, but with a view to inform and stimulate wider debate.

1  Introduction#

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The fiscal costs of meeting public social expenditures are widely expected to rise in most industrialised countries as their populations age.[1] Policies are already being implemented to deal with the increased share of the Gross Domestic Product (GDP) expected to be devoted to meeting social expenditures. Some countries have reduced eligibility for publicly provided services and transfers, while others have reduced the level of benefits. In the case of the universal superannuation scheme in New Zealand, the government, based on expected increases in the fiscal cost, has introduced a prefunding mechanism. In this way, today’s taxpayers contribute to a common fund which can subsequently be drawn upon to reduce the tax burden on future generations. Expectations about future fiscal costs are reflected in policy initiatives taken today. This paper presents projections for social expenditures in New Zealand over the next 50 years, as a contribution to the stock of information on which such policies can be based. It is precisely on the basis of projections of future social expenditures that policy decisions are being taken by governments today.[2]

Projecting social expenditures requires a range of assumptions about future paths of fertility, mortality, migration, labour force participation, unemployment and productivity growth, together with assumptions about the social policies governing future expenditures. There is substantial uncertainty surrounding projections of these underlying variables. Demographic projections typically recognise this uncertainty by conducting a sensitivity analysis using, for example, high medium and low values for some of the key variables.[3] In contrast, this paper examines the statistical properties of social expenditure projections. By specifying distributions of the relevant variables, simulation methods are used to translate the inherent variability of the component variables into variability of the projected social expenditures. Scenario based approaches, while providing a general sense of the possible range of outcomes, do not offer these distributional insights. A principal contribution of this paper is to provide such distributions through stochastic simulation.

A US Congressional Budget Office study of the financial balances of the Social Security trust Fund described stochastic simulation as follows:[4]

The ideal approach would be to assign a probability to every possible combination of paths for input assumptions, solve for the system’s finances under each set of paths, and then use the probabilities associated with each set of inputs to assign probabilities to every set of outcomes. Although it is impossible technically to assign probabilities to every set of outcomes, it is feasible to create an arbitrarily large sample of input combinations, solving each time for system finances, and then evaluate how finances vary within that sample and draw conclusions about the probability distribution of the outcomes…that technique (is) called stochastic simulation.

(Congressional Budget Office 2001):53).

Other studies for New Zealand which project the fiscal costs of population ageing include Bagrie who used a simplified model with labour productivity growing at 1.9%, and per capita social expenditure for all ages growing at an equivalent rate (Bagrie 1997). His study focused on the implications for revenue and expenditure and the sustainability of the fiscal settings. Polackova used a similar approach to examine the public sector balance (Polackova 1997), while Cook and Savage included an exploration of the net debt position (Cook and Savage 1995).[5] While the overall results for social spending are in line with the findings of the present study, uncertainty was handled through the conventional approach of alternative scenarios.[6]

Section 2 provides an overview of the key relationships together with a formal statement of the model. In Section 3, details of the data are set out, while Section 4 presents the benchmark results. The effect of varying some key assumptions is explored in Section 5. Conclusions are in Section 6.

2  The projection model#

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2.1  An overview#

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The sequence of calculations is set out in Figure 1. The first stage in projecting social expenditures is the production of demographic projections for the size of the population, together with its distribution by age and gender. To achieve this requires forecasts of the underlying trends in fertility, mortality and net migration.[7] Estimates of the rates of labour force participation are then combined with age and gender specific unemployment rates to generate the size of the workforce. When this is multiplied by the average productivity per worker an estimate is obtained of GDP.

Combining the social expenditures per capita with the projected population by age and gender leads to the estimate of total social expenditure built up from the expenditure on each category for each of the age and gender groups. The resulting social expenditures are 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, and the resulting set of input values is used to compute the ratio of social expenditure to GDP for a given forecast year. This process is repeated 5000 times for each year, to produce a distribution of the social expenditure ratio for each year from 2001 to 2051. The process therefore also generates distributions of the population by age and gender, as well as for each of 14 categories of social expenditure.

The uncertainty about each variable is reflected in the standard deviation of its distribution. The values used below are based on an analysis of past trends and the variability in fertility, mortality, migration, male/female birth ratios, labour force participation rates, unemployment rates and major categories of social expenditure. The resulting estimated standard deviations are used, and it is assumed that these remain the same in the future.[8]

The projections are entirely mechanical in that they do not rely on economic models of fertility, mortality, migration, labour force participation and so on. Instead, various exogenous age and gender specific rates are used and no allowance is made for possible feedback effects, which may for example be generated by general equilibrium changes in wage rates.[9]

2.2  Population projections#

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Population projections are obtained using the standard social accounting, or cohort component, framework.[10] There are
N = 100(single year) age groups, and no one is assumed to survive beyond the age of N. 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 jth age who survive in the country to the age i, where p_j is the number of people aged j and

(1)    

 

 

where only the a _i+1,i for i= 1,..., ,N - 1 are non-zero. This framework applies to males and females separately, distinguished by subscripts m and f. Hence the matrices of coefficients for males and females are A_m and A_f respectively. Let p_m,t and p _f,t represent the vectors of male and female populations at time t, where the i-th element is the corresponding number of the aged i. The N-element vectors of births and immigrants are represented by b and m respectively, with appropriate subscripts; only the first element of b is non-zero, of course. The number of people existing in one year consists of those surviving from the previous year, plus births, plus immigrants. Hence the forward equations corresponding to this framework are:

(2)    P_m,t+1 = A_mP_m,t + b_m,t + m_m,t

(3)    P_f,t+1 = A_fP_f,t + b_f.t + m_f,t

Given population age distributions in a base year, and information about the relevant flows, equations (2) and (3) can be used to make projections. In general the matrices A_m and A_f, along with the births and inward migration flows, vary over time. Changes in the

 

matrices can arise from changes in either mortality or outward migration.

 

Suppose that c_i represents the proportion of females of age i who give birth per year. Many elements, for young and old ages, of the vector, c, are of course zero, and in general the c_is vary over time. Suppose that a proportion, δ, of all 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 in any year can be represented by:

(4)    b_m = δτc'p_f

(5)    b_f = (1- δ)τc'p_f

where c′ is the transpose of the vector c, that is, the column vector written as a row. The b vectors contain only one non-zero element. Equations (2) to (5) can thus be used to make population projections, for assumed migration levels.

Figure 1 - An overview of the key relationships in the model

 

Note: The shadowed boxes represent input data.

2.3  Social expenditure and GDP#

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The per capita social expenditures are placed in a matrix with N rows and k columns, where there are k items of social expenditure. If this expenditure matrix is denoted S , then the i, jth element S_ij measures the per capita cost of the jth type of social expenditure in the ith age group. Suppose that the jth type of social expenditure per capita 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 time t,c_t ,is thus equal to:

(6)    

 

 

where, as above, the prime indicates transposition. In the projections reported below, expenditure per person in each category and age differs for males and females, so that (6) is suitably expanded.[11]

Projections of Gross Domestic Product depend on assumptions about five factors, including: initial productivity (defined as 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 in period t, V_t, by the total labour force in that period, L_t. The value of V_t is in turn 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 the vectors U_m and U_f be the N-element age distributions of male and female unemployment rates. If the symbol ^ represents diagonalisation, whereby the vector is written as the leading diagonal of a square matrix with other elements equal to zero, the total number of people unemployed in period t is:

(7)    

 

 

The labour force in period t, L_t , is given by:

(8)    

 

 

Suppose productivity grows at the constant rate, θ. Then GDP in period t is calculated as the product of the utilisation rate,
1 - U_t = 1-Vt / L_t, the labour force, L_t, and productivity, so that:

(10)    

 

 

If the population age distribution, along with the gender and age specific participation and unemployment rates, are constant, the social expenditure to GDP ratio remains constant if all items of expenditure grow at the same rate as productivity; that is if θ = ψ_j for j = 1,...,k. From (10), the rate of growth of real GDP (g_y) is given by:

(11)     (1 + g_y) = (1 + θ)(1 + g_w)

where g_w is the rate of growth in the number of workers.

Many assumptions are required to make projections, and many potential interdependencies may exist, though they are not easy to model. For example, productivity may itself depend on social expenditures and the age distribution of workers. Furthermore, participation rates and population growth are likely to be interdependent. The changing age distribution is only one component of the ratio of aggregate social expenditure to GDP, and its influence may, for example, be substantially affected by other components. However, as mentioned above, such interdependencies are not modelled here.

2.4  A Stochastic specification#

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The above description of the projection model is deterministic in the sense that each component is assumed to be known with certainty. The future mortality, fertility and migration rates, along with the various unemployment and participation rates and growth rates of productivity and social expenditure costs, cannot be known with certainty. One way to allow for this uncertainty is to specify, for each appropriate variable, a distribution. Each observation is regarded as being drawn from the corresponding distribution. A large number of projections can be made, where each projection uses random drawings from each of the distributions. This exercise produces a ‘sampling distribution’ of the ratio of social expenditure to GDP.[12]

It is therefore necessary to specify the form of the various distributions. Consider a relevant variable, denoted by x. This could be, for example, an unemployment rate, a fertility rate for women of a given age, or an item of social expenditure. In some cases, indicated below, it is assumed to be normally distributed with mean and variance μ and σ respectively; that is, x ~ N(μ,σ). If r represents a random drawing from the standard normal distribution N(0,1), a simulated value of x, x_y, can be obtained using:

(12)   x_r = µ+rσ 

since (x = µ)/σ is N (0,1). In cases where the variable is assumed to be lognormally distributed as Λ(µ,σ²), where now µ and σ² refer to means and variances of logarithms, a corresponding draw can be obtained using:

(13)      x_r = exp(µ+rσ)

The use of lognormal distributions ensures that the random draws are always positive.[13]

3  Input data and projections#

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This section describes the key input variables, sources and the derivation of their projected values. In the case of fertility, mortality and labour force participation rates, their growth rates and standard deviations were estimated from the following regression:[14]

(14)      log y_t = α + β_t + u_t

This implies that the constant growth rate is given by

 

where

 

. As

 

, 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. The growth rates for male and female mortality rates and fertility rates are given in Appendix Table 1, and the respective standard deviations are documented in Appendix Table 2.[15]

 

3.1  Fertility rates#

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Fertility rates by single age year of mother from 1980 to 2001 were used to estimate the trend annual rates of change using a regression of the logarithmic rates against time, as described above.[16] The decision to truncate the data for the regressions and start at 1980 was based on the finding that there is a marked turning point in the fertility rates around 1980, especially for older mothers.[17] The trends prior to 1980 were quite distinct and reflected the substantial decline in fertility following the 1960s.[18] These rates were used to form the projections for the next ten years, after which fertility rates were assumed to remain constant.[19] A selection of the actual and projected values is presented in Appendix Figure 1.

3.2  Mortality rates#

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Mortality rates are available by single year age groups (from 0 to 99) for three-year averages centered on the years 1971, 1976, 1981, 1986, 1991, and 1996.[20] For 1999, values were only available for 5-yearly age brackets for 1999-2001. Single year values for that year were interpolated by using the same proportions as in 1996. The values for ages 96 to 100 in 1999 were taken to be equal to those for 1996 to 2001. The resulting data set of seven observations for each single year of age were used to estimate the trend annual rates of change using the regression of the logarithm of mortality rates against time, as discussed above. These rates were used to form the projections of the mean rates for each age. The standard deviations were taken from the standard errors of each regression. Hence, as with fertility, each rate is assumed to be lognormally distributed. The precise values are given in Appendix Table 2.

Changes in mortality rates were projected for the next twenty years, after which these rates were assumed to remain constant.[21] Given the relatively small numbers involved, it was assumed for simplicity that 100 years is the upper limit of the age distribution. The actual and projected values of mortality rates for selected ages are presented in Appendix Figure 2.

3.3  Migration#

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For the last 100 years net migration (permanent and long-term) has averaged 5,000 per year, although major swings have frequently occurred. This long-term average was adopted as the benchmark rate for net migration with a corresponding gross level of immigration of 50,000. We assume that future inward and outward migration flows have the same age and gender distribution as the average for the years 1997 –2001.[22] Data for this period were used to estimate the standard deviations of the arrival and departure rates for males and females by single year of age. The average for the age group 99+ were assigned to age 99, and migration flows for those aged 100 were arbitrarily assumed to be zero.

3.4  Labour productivity growth#

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Bagrie (1997) reported a long-term average for labour productivity growth of 1.5% per year based on the period 1955-56 to 1995-96. This is close to the value reported by Diewert and Lawrence (Diewert and Lawrence 1999), Table 4.2, p.66) of 1.66% for the period 1978 to 1998. The Long Term Fiscal Model at the Treasury assumes 1.5 percent.[23] Downing et al find similar rates for more recent time periods: 1.28% for 1993 to 1997 and 1.54% for 1999 to 2002.[24] The present study adopted a rate of 1.5% for the benchmark average annual growth in labour productivity, assumed to remain constant over the projection period. The standard deviation of 0.01707 was obtained using data from 1979-2002. The initial value of labour productivity in the base year 2001 was given by GDP ($114,374m) per worker (1.804m) ie $63,400.

3.5  Labour force participation rates#

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Labour force and social expenditure data are available only for certain age groups, rather than single years. Hence, having obtained the single year age distributions using the demographic component of the projection model, these needed to be grouped for each of the social expenditure projection years, for the purposes of calculating GDP and social expenditure.

Significant changes have occurred in participation rates over recent years. The rates have typically fallen amongst the younger age groups, associated with increased tertiary education rates. Male participation rates up to age 50 have fallen, while most female rates have been rising. Data on age-specific rates for the years 1987 to 2002 were used to estimate the trend rates of growth.[25] These in turn were used to generate projected rates for the next 10 years, after which no further change was assumed. There are some exceptions to this – specifically in the case of older males, where a rise in participation following 1990 can be attributed to an increase in the age of eligibility for universal superannuation; for this reason the trend was not extrapolated. Appendix Figure 3 shows the actual and projected rates for a selection of age groups, while the means and standard deviations for both the participation and unemployment rates are given in Appendix Table 3.

3.6  Social expenditures#

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Social expenditures are divided into 14 categories. These are: Age Related; Medical/Surgical; Mental Health; Pregnancy/Childbirth; Primary Diagnostics; Primary General; Public Health; Education; NZ Superannuation; Domestic Purposes Benefit; Sickness Benefit; Invalids’ Benefit; Other Benefits; Unemployment Benefits. Hence, categories 1 through 7 refer to health and categories 10 through 13 are denominated social security and welfare. Data from Treasury’s Long Term Fiscal model for Categories 1 to 7 of health expenditures were used to compute the shares of each category by age and gender. These shares were applied to estimates of total health expenditures by age group (Johnston and Teasdale 1999).

Data from the Household Economic Survey were used to find the distribution by age and gender of other categories. Where there was no division by gender (in the cases of education, invalids’ and other benefits) the rates for males and females were set equal. Payments under Category 10 were assumed to be received by females, and no payments under category 4 were assigned to males.[26] Data from the HES were for 1997-98 and indexed to 2001 prices using the Consumer Price Index. A complete set of the social expenditure data by category, age and gender is given in Appendix Tables 4 (for males) and 4 (for females).

The growth rate of total social expenditure in each category was applied to all age and gender groups. This is because in most cases relevant information was available only at an aggregate level. Growth rates and standard deviations were derived from per capita expenditure series for health, education and superannuation from 1960 to 2000, and 1980 to 2000 in the case of unemployment benefits which are calculated on a per recipient rather than per capita basis. These are reported in Table 1. In the case of NZ Superannuation, it was assumed that there was a 100% take-up by all those over the age of 65, and all received the rate applying to single persons. A series for Social Expenditure for 1960 to 2000 was used to derive the growth rate and standard deviation applied to the sub-category Social Security and Welfare.[27] The historical trends and annual changes of the major categories of social expenditure are shown in Appendix Figure 4.

Sources: All data are from unpublished Treasury sources from the Long Term Data Series, except for social security and welfare from (Dalziel and Lattimore 2001)

4  Benchmark results#

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This section presents the benchmark projections. The essential features are that all social expenditures are assumed to grow at 1.5% per year, the same rate as labour productivity. The results therefore refer to a ‘pure ageing’ assumption. Migration is set at the long-term average of 5,000 net migrants each year, and changes in fertility, mortality and labour force participation are assumed to apply for 10, 20 and 10 years respectively, after which no further change in these rates is projected. The demographic and social expenditure projections are discussed in turn.

4.1  Demographic projections#

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Starting from the initial age and gender structure of the population in 2001, randomly drawn values from the distributions of fertility, mortality and migration rates were used to project the population by single year of age and gender for each year until 2051. The age and gender structure is depicted in Appendix Figure 5. A summary is given in Table 2. The growth rates of the total population and for those 65 and over are given in Table 3. It can be seen that most of the anticipated change in the structure occurs by 2031. The 95% confidence limits on these estimates are relatively narrow. One explanation of the narrowness of the range, in addition to the relatively low standard deviations for many of the demographic variables, is that the projections assume independence between age groups and time periods. If, for example, changes in mortality rates were positively correlated across age groups, the confidence limits would be expected to be larger. As shown in Appendix Figure 6 there are significant shifts in the population shares. People aged 85 and over for example are projected to rise from 1.3% to 4.8% of the total population by 2051.

Two types of dependency measure are defined. The demographic dependency ratio is the total number of individuals aged from 0-14 and over 65, expressed as a ratio of those aged 15-64. The economic dependency ratio is equal to the number of non-workers divided by the number of workers. The number of workers is the product of the labour force and the employment rate, while the labour force is the product of the total working age population and the labour force participation rate.

Note: ^a The Demographic Dependency Ratio is defined as the population aged 0-14 and 65 over expressed as a ratio of the population aged 15-64

^bThe Economic Dependency Ratio is the number of non-workers divided by the number of workers

The number of workers in each age group between 15 and 64 is given by the product of the population of a given age and gender, and their corresponding rates of labour force participation and employment. Non-workers are the balance of the population. Both measures, together with their 95% confidence bands, are depicted in Figure 2. After an initial decline, the economic dependency ratio is projected to rise markedly from 2011 until 2031. In 2011 one worker is projected to support 1.1 non-workers; this ratio rises by over 20% to 1.33 by 2031. Already workers over age 40 comprise almost half of the workforce and this is projected to rise by five percentage points by 2051. For those aged 50 and over, their share of the workforce rises by over seven percentage points, as shown in Table 4.

Figure 2 - Projected economic and demographic dependency ratios : 2001-2051

 

An alternative measure is the elderly dependency ratio, defined as those 65 and older as a percentage of the population between 15 and 64. The present projections suggest that this ratio rises from 18% in 2002 to 34% by 2031, which is similar to the OECD average.[28]

4.2  Social expenditure#

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Future rises in social expenditures depend on three critical sets of factors. These are the population ageing effect, labour market changes and policy settings. The benchmark model can be viewed as providing estimates of the “pure” population ageing effect as it assumes that existing policies remain in place unaltered, and that all categories of social expenditure grow at an annual rate of 1.5%, equal to the underlying rate assumed for productivity growth.

Figure 3 summarises the changing distribution of the ratio over time, and shows that the steepest increase in the average is projected to occur between 2011 and 2031, flattening thereafter. The critical issue concerns the uncertainty surrounding this point estimates. Even after only ten years, these bands are 20.0% to 26.8%. While the central estimate for 2051 is 31% of GDP, the 95% confidence bands range from 21.1% to 44.7%. The upward drift in the mean and the widening spread of the estimates are depicted in Appendix Figure 7, which plots the histograms resulting from the simulations. These show that the distributions become not only more spread, but also more skewed, in the later periods. This explains why the 95% confidence intervals are not symmetric about the average value.

The benchmark model projects that mean social expenditures rise from 22.7% in 2001 to 31.0% of GDP by 2051. Comparable results from other New Zealand studies are from 22.9% to 35.6% (Polackova 1997) and from 23% to 33% (Bagrie 1997) while a similar study for Australia reports that in the base case, social expenditure is projected to rise from 20.7% to 28.0% of GDP by 2051(Guest and McDonald 2000).[29]

Table 5 presents a summary of the projected growth in major groups of social expenditure as a share of GDP, due solely to population ageing. These are graphed in Figure 4. The costs of superannuation rise most markedly from 5% today to 10% by 2051.

Education costs fall slightly and there is a small increase in social security and welfare costs. Under the benchmark growth rates of the per capita real costs of social expenditure, the share of health costs in GDP rises by 50%, or by 3 percentage points. When health expenditure is divided into the seven sub-categories, the first two (age related and medical/surgical) account for almost all of this increase, as shown in Figure 5. For further details, see Appendix Table 6.

Figure 3 - Projected social expenditure as a share of GDP : 2001-2051

 

 

Figure 4 - Projected mean total social expenditure and expenditure by major categories

 

Figure 5 - Projected increases in health costs

 

5  Impact of Varying Assumptions#

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This section explores the impact on the projected levels of social expenditure of variations to the assumptions used in the benchmark case. In each case, the benchmark model is taken and one assumption or associated set of assumptions is varied. In this manner the following sections show the impact, relative to the benchmark case, of changes in each of these critical assumptions.

5.1  Higher Rate of Migration#

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The effect of higher net migration was examined by raising the annual net migration level from 5,000 to 20,000. This latter figure corresponds to the upper level used by Statistics New Zealand (2000). Higher rates of migration are variously seen as adding to the burden of social expenditure on the one hand, or providing more workers and enhancing the tax base on the other. The result depends on the age distribution of the migrants relative to the resident population. In this study we assume that the higher migration levels would simply reflect the mix by age and gender of migrants between 1997 and 2001. The effect (see Table 6) is to lower the projected rise in social expenditure by 2051 rather modestly from 31.0% to 29.5%. Migrants are only slightly younger on average than the New Zealand population. Given the estimates of the standard errors this change cannot be regarded as statistically significant.[30]

5.2  Changes in Labour Market Parameters#

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Two adjustments were made to the labour market parameters. The first raised the average growth in labour productivity to 1.75% from 1.50% per year. This, as expected, reduces the projected mean ratio of social expenditure, from 31.0% to 28.7% by 2051. Details are given the final column of Table 6. In the second case higher rates of female labour force participation were used. All female rates were increased to match those of the males (where male rates were higher), with the exception that for women between 20 and 29 their participation rates were held at a maximum of 90% of the male rates for those age groups. The results are also shown in Table 6, where it can be seen that the higher participation resulted in only a modest and statistically insignificant decline in the mean projected share of social expenditure in GDP.

5.3  Changes in Standard Deviations of Social Expenditures#

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The standard deviations of the growth rates of major categories of social expenditure were estimated from historical data, as discussed earlier (see Table 1). Their size reflects considerable uncertainty. They contribute significantly to the overall confidence band around social expenditure projections. By 2051, the 5 and 95 percentile bands around the mean estimate of 31.0% are from 21.1% to 44.7%. To explore what would happen if the variability in social expenditure programmes were lower in the future, two sets of simulations were made. For the first simulation, all the standard deviations were set to zero; this provides a useful point of comparison since the variation arises entirely from demographic and labour market distributions. In the second simulation, the standard deviations were reduced by 50 percent.

The effects on the final distributions of social expenditures are shown in Table 7. When the standard deviations of social expenditures are set to zero, the 5 and 95 percentile bands for the ratio of social expenditure to GDP in 2051 are reduced to 25.3% to 37.4%. The confidence intervals therefore remain substantial, reflecting the high standard deviations on participation and unemployment rates.

Note: ^a Variability only contributed by population, labour force participation rate, unemployment rates and productivity

5.4  Higher Growth Rates of Social Expenditure#

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The initial benchmark results, based on the assumption that real unit costs of social expenditure grow on average at the same rate as overall productivity, were important to isolate the pure effect of population ageing. However, this assumption is unlikely to be true. This subsection considers a different set of assumptions. This alternative uses historical annual rates of growth of real per capita social expenditures over the last 40 years, reported in Table 1 above.[31] The average annual changes exceed 1.5%, the rate of growth used in the benchmark simulations, by a considerable margin. The resulting projections are summarised in Table 8; detailed results with standard deviations for all 14 categories and for males and females are shown in Appendix Table 7.

Total social expenditures rise to a mean of over 55% of GDP by 2051. Health costs alone represent 35% of total social expenditure and rise from 6% of GDP in 2001 to a projected level of 20% by 2051. It is immediately evident that these results are improbable. When the uncertainty is taken into account there is a 5% chance that social expenditures could exceed 78% of GDP in 2051 if the costs per capita were to continue to grow in real terms at their historical rates and productivity in the economy were to grow on average at no more than its historical rate. It is most unlikely that the growth rates of social expenditures in past decades could be sustained without intolerable fiscal pressures.In fact it could be argued that, with the exception of health costs, the annual average growth rates of the other major groups of social expenditure have been slowing through time, and the rates over the last decade are below those of earlier periods, or the 1960 to 2000 span as a whole. Were this the case and were the more recent levels of higher productivity growth to prove sustainable over a very long period, then conceivably current policy settings might be manageable.

Unlike some other items, (as shown in Appendix Figure 4) the annual rates of growth in health costs, while showing some variability, do not appear to have abated. The following section explores further the impact of the growth in health expenditures.

5.5  Changes in Future Health Costs#

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The results of Section 4 show that increased health costs represent a significant share of the projected rise in social expenditures. This is particularly so if per capita social expenditures were to continue to grow at their historical rates. This section further explores the growth in health costs, and extends the basic model to allow for differential growth rates of health expenditures by age groups.

It has been stressed that the growth rates in real per capita public health expenditures have been highly variable; see Appendix Figure 4. As shown in Table 9 the selection of the historical period influences the annual average estimated growth rate in health expenditures. Most accounts of long-term changes in medicine and health make the period around World War II a watershed. It therefore probably makes sense to look at average growth rates from then until the present. As is apparent in Table 9, this gives a growth rate of around 3% per year. The corresponding average for the entire OECD for 1960-1995 is around 4.7% per year (Mayhew 2000b).[32]

Source: NZ Treasury; unpublished data from the Long Term Data Series

For present purposes it is necessary to eliminate the contribution of population ageing to this expenditure growth. Strictly speaking, this cannot be done without knowing the age-profile of spending in the past. A Ministry of Health report (Johnston and Teasdale 1999) nevertheless makes an estimate, presumably by assuming a constant age-profile. The report’s estimate is that ageing was responsible for about 0.4 percentage points in expenditure growth per year between 1977 and 1997. Mayhew (2000a: Table 2.3) derives an estimate of 0.35 percentage points per year for the OECD during the years1960 to 1995.

Subtracting an ageing component of 0.4% per year from an average growth rate of 3.0% per annum gives an adjusted rate of increase in per capita public spending on health of 2.6%. This is rounded to 2.5%, a figure in line with international estimates.[33] Mayhew (2000a: Table 2.3) assumes an underlying growth rate of 3.0% for the OECD over the period 1995-2050.

Table 10 presents a comparison of the projected level of social expenditures as a share of GDP under three different growth rates for health costs. In the benchmark estimates all social expenditures grow at 1.5%, equal to the rate of labour productivity growth. In the second case all social expenditures grow at their historical rates, which implies health costs grow at 3.1% (a figure which is not adjusted for the effect of population ageing). In the third case, health costs for all age groups grow at 2.5% while other categories of social expenditure continue to grow at 1.5% per year. Even in the third case, where only health costs are permitted to grow at a higher rate, the projected mean level of social expenditures rises substantially compared with the benchmark case; yet because of the large degree uncertainty, the differences are not statistically significant.

The projections have all assumed that any given rate of growth in health costs applied to all age groups. There is a possibility that the costs for the elderly will rise more steeply than those for younger age groups.[34] Recognising this, the projection model was modified to allow for the annual growth rates for all categories of social expenditure category to vary with age. The mean growth rates for health expenditures in the higher age groups were thereby allowed to be higher than the corresponding rates for lower ages. However, the standard deviation of the growth rate for each age group was set equal to the common value previously used for each social expenditure category (as there was insufficient information on which to base any differences). This increase in the number of distributions from which random draws are made raises a question regarding the correlation between age groups (with the values being jointly normally distributed). Indeed, the earlier projections are equivalent to an equal mean growth rate for each age group, combined with an implicit assumption that the values are perfectly correlated. The allowance for a lower degree of correlation is expected to reduce the standard deviation of the ratio of aggregate social expenditure to GDP, since the selection of higher than average values in one age group in a particular year can be partially offset by the selection of lower than average values for other age groups. For this reason, the two extremes of zero and perfect correlation between the growth rates in different age groups were examined.

Note: ^a Benchmark case

gij refers to the projected growth rate of the i-th category of social expenditure (i=1,...,14) for the j-th age group (j=1,...,19)

ρ refers to the correlation coefficient of growth rates between age groups.

The first two columns of Table 11 show the benchmark case for the two extreme values of the correlation across ages. The mean estimates remain virtually unchanged but the standard deviations are reduced. The final two columns allow growth rates to vary by age; health expenditures were assumed to grow at 2% for those from 0-64 and 3.5% pa for those 65 and over. All remaining categories of social expenditure were held to the benchmark growth rate of 1.5%. The accelerated growth rate of elderly health costs adds some 7 percentage points to the mean share of GDP with the standard deviations again varying according to the assumption about the correlation across age groups. A detailed breakdown of the components of health costs for the case of a unit correlation coefficient (third column in Table 11) is given in Appendix Table 8.

6  Conclusions#

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This paper has projected social expenditures in New Zealand over 50 years, based on a stochastic approach using 14 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 forecasts with accompanying confidence bands. The results show that there is considerable uncertainty and future projections have wide confidence intervals.

This uncertainty has implications for fiscal policy and the management of the Crown debt. The Fiscal Responsibility Act 1994 states that, as a principle of responsible fiscal management, a New Zealand government should ensure total Crown debt is at a prudent level by ensuring total operating expenses do not exceed total operating revenues. In the face of uncertain levels of future expenditure, the best that can be achieved is to estimate the ex ante cash budget balance needed to achieve an actual cash budget balance, at a given level of probability (Buckle, Kim and Tam 2001). To the extent that the approach adopted in this paper can improve the estimates of the probability distribution surrounding key areas of government expenditure, then it should be possible to make more reliable estimates of the ex ante budget balance needed to sustain a particular level of the Crown’s debt.

It would however be premature to conclude from these results that increased outlays will constitute a burden on society. First place, the well-being of older citizens is presumably enhanced by the receipt of health and pension benefits. Offsetting this is the loss to those who must bear higher rates of taxation to meet the transfers. We have not explored the costs to society of the deadweight losses of extra taxation.[35] Second, as argued by Guest and McDonald (2000) the absolute incomes of future generations will be higher given continued growth in productivity. In fact, even if productivity growth were to remain at its longer term average rate of 1.5%, future workers in 30 years time would be enjoying real incomes more than 50% higher than at present. The implication is that even after allowing for higher relative transfers, they would still have a level of well-being substantially greater than that enjoyed by workers today.

In focussing on the task of explicitly incorporating uncertainty into the projections, we have set aside some other potentially difficult issues. For example, while we have forecast some changes in labour force participation rates, these have relied on projections of past trends. With increased labour scarcity combined with better health and extended life spans, significant increases in the participation rates of older workers may occur. Offsetting that is the increased demand for leisure that comes with higher real incomes. While the demographic projections are based on reasonably disaggregated data, no allowance has been made for other demographic characteristics such as ethnicity or marital status.

The projection model allows for the growth of every category of social spending to differ for every age group. This constitutes a more disaggregated approach than has been applied in other studies. When combined with the extensive stochastic elements this comes at a cost of increased complexity. The empirical work is still at a rudimentary stage. We have often relied on crude assumptions such as the variability of underlying distributions remains constant over time, or across several sub-categories as in the case of health spending. Further we have paid scant attention to the question of covariances across categories of spending.

We have relied, like others, on examining the sensitivity of the projections to different assumptions. More remains to be done to explore different policy settings such as adjustments to the age of eligibility for publicly provided retirement benefits or to the criteria for certain classes of welfare benefits. Above all, even after the extensive disaggregation in the present study together with stochastic simulation of over 500 variables, the approach is vulnerable to the criticism that it fails to capture potential behavioural responses to changes in relative prices and incomes. Those advances remain as challenges.

References#

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Appendix Figures#

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Appendix Figure 2 - Mortality rates: 1971-2011

 

Appendix Figure 2 - Mortality rates: 1971-2011 (continued)

 

Appendix Figure 3 - Labour force participation rates: 1987-2011

 

Appendix Figure 3 - Labour force participation rates: 1987-2011 (continued)

 

Appendix Figure 4 - Historical trends in major categories of social expenditures

 

Appendix Figure 5 - Population projections by age group and gender: 2002-2051

 

Note: Population is measured in thousands

Appendix Figure 6 - Changes in the age structure of the population between 2001 and 2051

 

Appendix Figure 7 - Frequency distributions for projected total social expenditure as a share of GDP for 2002, 2011, 2031 and 2051

 

Appendix Tables#

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Notes: P = population

I = immigration

E = emigration

M = mortality

Δ M/M = proportionate change in mortality

F = fertility

Δ F/F = proportionate change in fertility

Notes: In = immigration

Out = emigration

Note: (a) No data are available for these values. They were assumed to be zero.

Sources: The unemployment rates are those for the base year 2001. The standard deviations are computed from annual data from 1987-2002 using INFOS Series HLFA.SAF1AA to HLFA.SAF1AK (male) and Series HLFA.SAF2AA to HLFA.SAF2AK (females). The labour force participation rates are those for the base year 2001. The standard deviations are the standard errors from the regressions of participation rates on time, using time series data from 1987-2002, and using INFOS Series HLFA.SAE1AA to HLFA.SAE1AK (male) and Series HLFA.SAE2AA to HLFA.SAE2AK (females). The data from INFOS for the oldest age category is for 65+; it was assumed that this applied to the group aged 65-69.

Note: ^a Unemployment expenditure per recipient

DPB = Domestic Purpose Benefit

NZS = New Zealand Superannuation

Note: ^a Unemployment expenditure per recipient

DPB = Domestic Purposes Benefit

NZS = New Zealand Superannuation

- Projected social expenditures by category ($millions) with benchmark growth rates

Note: Based on assuming that health expenditures for those aged 0-64 and 65+ grow at 2% and 3% pa respectively, and the correlation across age groups is unitary.