Modelling Retirement Income in New Zealand

Transcription

1 Modelling Retirement Income in New Zealand Christopher Ball Abstract A microsimulation model is presented to project the fiscal impacts of retirement income policy in New Zealand, while extending the range of policies that can be evaluated. Socioeconomic variables, such as income and education, are projected along with demographic variables, such as labour force participation and mortality, to provide a more comprehensive analysis of the impacts of pension reform in New Zealand. Mortality differentials are constructed based on socioeconomic and demographic variables, and are used to derive future fiscal costs. The fiscal impact of four types of pension reform are presented. The reforms include an increase in the age of eligibility, a change in the annual adjustment process, a move to communal prefunding and a move to compulsory private savings with abatement. J. E. L. CLASSIFICATION C50 Econometric Modelling, General; D31 Personal Income, Wealth and Their Distribution KEYWORDS Retirement Income; Quantitative Methods 1

2 Contents Abstract 1 1 Introduction 1 2 Model overview 2 3 Demographics Cohort population assumptions Education Differential effects of education Modelling approach for differential education outcomes Couple formation Modelling couple formation Income Base income profiles Income dynamics Differential mortality Differential mortality modelling framework Applications of the retirement income model Adjustments to the age of eligibility for NZS Annual adjustment of NZS payments Communal funding Compulsory private savings with abatement Conclusions 15 List of Figures 1 Overview of the retirement income model Couple formation flow diagram Age-standardised mortality rates per 100,000 by gender and income, New Zealand, List of Tables 1 Conditional transition probabilities of study status by gender and age from Cohort specific age differences distributional parameters for couple formation Regression parameters for income statics Projected fiscal cost of NZS as % of GDP

3 1 Introduction New Zealand, like most developed countries, is experiencing a structural demographic shift due to lower fertility and increasing life expectancy. New Zealand Superannuation 1 (NZS) expenses are projected to increase significantly, due to a rate structure that will increase effectively in line with wages and an increasing proportion of the population receiving NZS as life expectancy increases (see, for example, New Zealand Treasury (2013)). As the labour force is projected to contain a smaller proportion of the population this implies a progressively increasing burden on future workers if current policy settings continue. There are several ways in which Government could respond to adverse projections, including considering public pension reform. In the New Zealand context, most modelling of retirement income has focussed on the aggregate fiscal costs. This approach, seen in New Zealand Treasury (2013), Financial Services Council (2013), and OECD (2012b), typically uses demographic data on population and labour force provided by Statistics New Zealand, and assumptions on the future paths of variables such as inflation and GDP. If the retirement income outcomes for the individual are considered, it is usually a representative individual earning a fixed proportion of the median or average wage throughout their working life. Over the longer time horizon typically considered when projecting retirement income, the cumulative effect of small deviations from the representative individual can cause a divergence of the projected representative individual and the characteristics of the future population. The aim of this paper is to extend current modelling of retirement income in three ways. Firstly, income dynamics are added to existing demographic and economic modelling methodology. This allows evaluation of both the individual impact and fiscal impact of policy changes to the financing of NZS through, for example, a hypothecated payroll tax. Secondly, by using a microsimulation approach a broad range of transmission mechanisms can be modelled. Thirdly, detailed distributional implications of policy change can be analysed in a way which is internally consistent with the aggregate fiscal costs. In analysing the effects of a specified pension or superannuation scheme, one approach would be to examine the implications for a particular cohort (of individuals born in a specific year) as the individual members grow older, participate in the labour force, form partnerships, retire and eventually die. The fundamental components of such a model would include a way of simulating, for each age and individual, partnership formation and break-up along with both systematic changes in income over the life cycle (influenced particularly by education), and transitory movements within the distribution. Pension receipt over the retirement period is then affected by partnership status, the age-income profile (particularly for income-related contribution schemes) as well as age at death. A desirable component of a pension simulation model is the ability to generate differential mortality rates, based on empirical associations between mortality, education and lifetime income. To examine the implications for the evolution over time of aggregate measures, such as savings, pension payments and tax revenue, it is necessary to model the experience of all cohorts who are alive at each date. The lifetime experience of cohorts differs for a variety of reasons. For example, productivity growth means that the age-earnings profiles of succeeding cohorts overtake each other (young cohorts earn more, on average, at comparable ages). Labour force participation rates vary. Some cohorts are close to retirement age when a pension or tax system is changed, while other cohorts spend a much longer period subject to the new structure. The model outlined here is thus an overlapping-generations lifetime simulation model. Values are 1 NZS is New Zealand s universal public pension system available to almost all New Zealand residents over the age of 65. 1

4 obtained over a specified period of calendar time for all individuals and cohorts alive at each date, allowing for systematic and stochastic variations over the lifetimes of individual members of each cohort as well as systematic differences between cohorts. As explained below, some of the central relationships, in particular the component generating the changing distribution of income for each cohort, are obtained using econometric estimates, while others are based on calibration methods. Furthermore, the simulation model is capable of analysing a wide range of implications of alternative tax and pension systems, including the complex intra- and inter-cohort redistribution involved. The paper provides a flavour of the results of simulating several superannuation reforms options and their impact on total fiscal costs in New Zealand. The structure of the paper is as follows. An overview of the model is provided in section 2. Section 3 presents the demographic projections used in the model. Space limitations mean that the present paper is able to give only a brief description of the model. The role and influence of education, which is an important determinant of lifetime income and mortality differentials within a cohort, is presented in Section 4. Couple formation has redistributive impacts on retirement income between males and females and is discussed in section 5. Section 6 describes the approach used to construct income profiles for cohorts, which allow for the quantification of the impact that income-linked policies, such as compulsory private savings, have on fiscal costs and distributional measures. Differential mortality is considered in section 7, which also reviews the evidence for different mortality rates based on demographic variables such as education and income. Section 8 concludes by presenting a selection of applications of the model. 2 Model overview The model introduced in this paper is a cohort-based microsimulation model, with the cohorts based on birth year and gender. In generating the demographic and socioeconomic variables for the individuals within a cohort, a particular causal ordering has been chosen, as shown in Figure 1. The causal ordering imposed is designed to capture the associations between the variables that are drawn from administrative and survey data. Any causal ordering, including the approach taken in prior related work of largely assuming no causal ordering, is open to criticism on the direction and magnitude of the interrelationships. It is argued in this paper that the causal ordering presented in Figure 1 is a tractable modelling methodology that captures the associations between variables in the model and the impacts that heterogeneity in these variables have on the distribution of retirement income. The model is formed by linking modules designed to capture the critical demographic elements that are considered important in determining lifetime and retirement income. The imposed causal ordering is shown by directional arrows in Figure 1. Education and labour force participation are the first variables generated for the cohort, which are used as inputs to the modelling of income, couple formation and mortality according to the directional arrows in Figure 1. While there are links between education and labour force participation, the associations are captured in the income component, owing to the difficulty of modifying labour force participation projections. Education has a direct effect on couple status in the model through the partner s education level, which assumes that education level influences couple formation. Similarly education, couple status and labour force participation are assumed to affect lifetime earnings potential income in the model, through the methodology explained in section 6. Using a non-behavioural model it was not possible to include reverse causality with relation to lifetime earnings potential. Mortality differentials are assumed to be caused by differences 2

5 Figure 1: Overview of the retirement income model Cohort enters model Education Labour force participation Couple formation Lifetime earnings potential Mortality Lifetime Income in lifetime earnings potential and educational attainment, consistent with previous modelling work such as Creedy (1982). 3 Demographics Demography is a key component of any retirement income model. Since many of the people who are considered in the modelling are alive today, it is also one of the more certain components. The demographic assumptions are based on Statistics NZ s population and labour force projections. These projections have been extended to 2110/11 to allow enough time for the full impacts of retirement income options to be evaluated. Customised data obtained from Statistics NZ are used for the base survival rates and expected remaining years of life. The assumptions underlying the demographic projections from Statistics New Zealand are detailed in Bascand (2012). 3.1 Cohort population assumptions Data provided by Statistics NZ aggregate the 90+ population for males and females, which is needed by single year of age as an input to the model. The disaggregation was performed by extrapolating the survival rates provided by Statistics NZ until they reach 0 (implying the cohort has no survivors) and using the survival rates to proportionally distribute the population projections category of 90+ for males and females separately. The size of the decline in survival rates was assumed to double every 10 years following an exponential curve, using the decline in survival rates for people aged 90 through to 100 years old as the base. This was done for each gender in each period, so acceleration in the survival rate decline for year olds flows through into higher survival rates for progressively older cohorts in the period. With the data provided by Statistics NZ the extrapolated period and cohort survival rates are decreasing, so older cohorts have lower survival rates than younger ones. 3

6 Based on the survival rates, the 90+ population was proportionally distributed into single year of age groups. The logic is that the survival rates imply a relative probability of survival (so if there were only two age groups, one with a 60% survival rate and one with a 20% survival rate we would expect 75% to be in the first group and 25% to be in the second group). This ignores cohort effects, which would alter the relative proportion of survivors within a group. Survival rates in the 90+ age groups are strictly decreasing, at a rate that is sufficient for this method to produce strictly decreasing cohort sizes by single year of age. The aggregate-level fiscal costs are not sensitive to the allocation to single year of age for the 90+ cohort, as the total number of people in the cohort remains consistent with the population projections. There is no effect on the distributional measures due to single year of age allocation as these are based on survival rates. However differing specifications of survival rates can have an effect. The specification of the survival rates affect the average life expectancy, which changes the cost of NZS and the proportion of NZS that an annuity can fund. However, most of the movement in life expectancy is captured by the official population projections, so to the extent that official population projections accurately reflect changes in mortality this is reflected in the model. 4 Education This section considers the effects of education on retirement income. There are indirect effects captured through the model through the influence of education on income, couple formation and mortality. The remainder of section 4 explains the links between education and income and couple formation and how education is included in the model. The relationship between education and mortality is discussed in section Differential effects of education The impacts of education on an individual are complex, and would be significantly more complex to include in a modelling methodology if intergenerational educational effects were considered. There is evidence suggesting a significant link between parental education achievement and child educational achievement, see OECD (2012a). Intergenerational educational inequality may be accentuated if, as the evidence suggests, there is a tendency for people with similar educational attributes to form couples. 2 There are offsetting factors to educational assortative mating which are discussed in Kalwij & Gustafsson (2006). For instance, fertility rates and couple formation rates may vary inversely with educational attainment and since assortative mating relies on the availability of suitable partners, these factors may reduce intergenerational effects over time. As intergenerational transmission of educational attainment is very difficult to model, the focus of this model is to capture the associations between education, income, couple formation and mortality. 4.2 Modelling approach for differential education outcomes Years of formal education from the age of 15 leading to a formal qualification are used as the proxy for an individual s level of education. For cohorts with the possibility of existing formal qualifications, Census data for the cohort s 5 year age band and gender are used to provide a probability distribution of highest qualification. As each individual in these existing cohorts is created, they are assigned a 2 See Mare (1991) and the references within for a discussion in the context of the U.S. and Blossfeld & Timm (2003) for a cross country comparison. 4

7 qualification as a draw from the cohorts highest qualification distribution, which is then converted into the number of years of full-time study from age 15 needed to typically attain the formal qualification. Cohorts under the age of 15 in 2010/11 are assigned 0 years of formal education as a starting value. Educational attainment does not decrease over time, although the rate of return from educational attainment may decrease over time as average educational attainment increases. Most formal full-time educational study in New Zealand occurs before the age of 30. It is therefore assumed that educational attainment occurs before the age of 65, with most of that educational attainment occurring before the age of 35 based on Census 2006 data. Some modification was needed to capture the tendency for people who are in formal study to be more likely to remain in formal study. This was done by increasing the conditional probability of educational attainment in the following future year for people who were in formal study the previous year and offsetting that by adjusting the conditional probabilities for people not in study to maintain the same aggregate participation rate. The final conditional probabilities of study status by gender and selected ages, given the study status in the previous year, are included in Table 1. Table 1: Conditional transition probabilities of study status by gender and age from Age Male conditional on previous year study Male conditional on previous year not studying Female conditional on previous year study Female conditional on previous year not studying Couple formation Couple formation needs to be considered in projections of fiscal costs and distributional measures as intra-household sharing of resources influences the relative positions of males and females. With males on average earning more than females over the life cycle, any change from a defined benefit scheme, such as NZS, to a defined contribution scheme, such as a compulsory version of KiwiSaver, would impact on the retirement outcomes of women more than men. Both the fiscal savings and distributional impacts are likely to be biased if couple formation is not considered, as resource sharing within the couple to maximise the benefits under a policy change is not only possible, but likely. The model does not explicitly incorporate behavioural responses to policy changes, but it does include 5

8 Figure 2: Couple formation flow diagram Impute marriage indicator 15+ Enter the system Under 15 Married Single Stay with same marriage indicator until death Yes 65+? No Add 1 to Age adjustments such as a wealthy spouse providing for a less wealthy spouses annuities before asset-tested government transfers are considered. Marriage is a channel for redistribution between males and females. Under current legislation KiwiSaver is considered a relationship asset, so that in the event of divorce a reasonable first approximation would be that the assets saved for retirement are split equally. Similarly if one partner in a marriage dies, the survivor would have the ability to claim at least half of the private savings balance or any benefit derived from decumulation through products such as an annuity. 5.1 Modelling couple formation Current marriage stocks have been estimated from 2006 Census data. The modelling was also informed by the changes in marriage rates since Census By considering the changes since 1996 the decreasing marriage rate can be decomposed into trends by age cohort, so that the trend in marriage rates is not being driven by a shifting demographic profile that has been induced by the post war baby boom. Marriage rates have been declining over the 10 years 1996 to 2006 for all cohorts except for females over 65 and males over 85. This has generally been offset by an increase in the Other partnership category, showing a preference shift to de-facto relationships. The assumption is that we are projecting the combined total of marriage and other partnership. Both these categories would be likely to have KiwiSaver and other private savings considered as relationship property. The formation rate of marriage and other partnership by cohort is projected as constant from 2006 Census level. An important advantage of this approach that it does not require an assumption about the relative prevalence of marriage and de-facto relationships, with the two treated equivalently in the modelling. When a cohort enters the system, a marriage indicator is randomly assigned for each individual based on the proportions in the 2006 Census data. From there until the cohort reaches 65 the couple status is updated annually (single people may marry or not, married people may remain married or separate due to divorce or bereavement). Once a person reaches 65 their indicator will change only upon the death of one member of the couple. 6

9 The update status step in Figure 2 requires knowing how separation is dealt with and how the characteristics of a partner are imputed. An assumption is made about the split of couples which will separate. Historical data suggests 40% is not unreasonable although there is significant uncertainty. When the couple is formed a variable is generated which has value 1 with probability 0.4 and value 0 with probability 0.6. If separation occurs, then the duration of the relationship is generated from a Poisson random variable with mean of 15 years increasing at a rate of 0.08 per year from 2010/11. This reflects the pattern of administrative data drawn from the last 20 years for the increasing median duration of marriage ending in divorce. The final step is to impute a profile for the partner of the reference individual if a couple is formed. Similar to the reference person, the partner needs an evolving path of age, education, income and mortality, but we also need the information to be consistent with known cross-sectional associations between partners drawn from Census and HES. The education status of the partner is equal to the reference person, income is imputed using the process outlined in section 6 and mortality is taken from the partner s appropriate cohort survival rates provided by Statistics N.Z. 3 The age difference was estimated from the pooled HES data, from couples with an age difference over the range of the female being 20 years younger to the female being 10 years older. This was refined by restricting the age difference to the 5th and 95th percentile for cohorts under 40 to deal with the funneling effect that is seen in couple formation, namely that in general as people age the spread of the age difference between partners in the couple increases. The distribution of the age difference is assumed to be Binomial with a gender specific offset reflecting that on average the male is older than the female and an age/gender specific p parameter to reflect the age difference changes relative to the age of the cohort. Let X i,j be a Binomial random variable for age cohort i (i = 1 represents 15-19, i = 2 represents 20-24, etc. until 65+) and gender j (0 for males and 1 for females). Let N i,j = 30 be the number of trials associated with the Binomial distributions for age cohort i and gender j, and let p i,j be the age difference Binomial distributional parameters for age cohort i and gender j in Table 2. Then the final age difference Y i,j for age cohort i and gender j is defined in terms of a random draw from an intermediate Binomial random variable X i,j as: 4 P {X i,j = x} = 30! (30 x)!x! px i,j(1 p i,j ) 30 x x = 0, 1,..., 30 (1) Y i,j = X i,j 10j 20(1 j) (2) The final distributions of age difference distributional parameters based on pooled HES data are presented in Table 2. Table 2: Cohort specific age differences distributional parameters for couple formation Age Group Male p Female p It is not possible to apply the differential mortality framework presented to the partner(s) of the reference person. 4 Sampled until the partner s age remains within the 5th to 95th percentile bounds for each reference person age. 7

10 6 Income This section explains how the income distribution is constructed for the base year 2010/11, and how the individuals which form the core of the model are projected forward. The framework used to project individual income is built up from two parts. One part is how the base income profiles are estimated from pooled cross-sectional data. The other part is how an individual shifts within the income distribution over time relative to the other members of the cohort. 6.1 Base income profiles Following Ball & Creedy (2014) and Creedy (1997) a regression was fitted to the Household Economic Survey data of individual incomes to find an age-related parameterisation of lognormal distributional parameters for the New Zealand population in the base year 2010/11. The parameters of an individuals lognormal distribution, namely µ and σ, were estimated using the following regression equations: µ i = α 0 + α 1 i + α 2 i 2 + α 3 i 3 + ζ 1 K + ζ 2 C (3) σ 2 i = γ 0 + γ 1 i (4) where i is the age of the individual, K is years of formal education, C is an indicator variable for in a couple, µ i is the mean of log-income for age i, σ i is the standard deviation log-income for age i and α 0, α 1, α 2, α 3, γ 0, γ 1, ζ 1 and ζ 2 are regression parameters. Male and female parameters were estimated separately. By assumption, α 3 = 0 for males. The above model is slightly different from that estimated in Ball & Creedy (2014). However it is estimated using the same data set augmented with an education and couple status variables. The static distributional parameters for the regression parameters are in Table 3. 5 Table 3: Regression parameters for income statics Parameter Male Female α α α α ζ ζ R 2 for (3) γ γ R 2 for (4) Income dynamics Given the base year income for a cohort, denoted y i,0, we now need a way to project income forward. Some key observations from income data suggest that the projection process should capture the characteristics of mean reversion and autoregression, represented by an AR(1). These characteristics 5 Ball & Creedy (2014) include a more detailed discussion on the preparation and how the regressions were performed. 8

11 are evident in the work of Carey et al. (2012) and Creedy (1997, 1982) and the process of income dynamics adopted in this paper is influenced by their work. Consider projecting this base income out to time t: t = 1, 2, 3,..., 80 i. As a cohort ages they experience both economy wide wage growth and age-related productivity growth, where the latter affects the cohort s income growth and income distribution. Economy wide wage growth is incorporated by modifying the mean of the lognormal distribution by M i+t = µ i+t + βt (5) where β is the natural logarithm of the economy wage growth. An autoregressive term is included through the variance of the lognormal distribution u i,t : u i,t = ηu i,t 1 + ɛ i,t (6) where η is the autoregressive term and ɛ i,t is an independent draw from the normal distribution N(0, σ 2 i+t ). Finally, the income projections are tied together to produce a draw for income y i,t for cohort i in period t. y i,t = ( yi,t 1 m i,t 1 ) ξ exp(m i,t + u i,t) (7) where m i,t 1 is the cohort i s geometric mean income from period t 1 and ξ is the parameter which determines the degree of mean reversion, with ξ = 0 implying a Markov process, 0 < ξ < 1 implying mean reversion and ξ > 1 implying divergence from the mean. Estimates for the parameters η and ξ are taken from Carey et al. (2012), who apply the framework above to administrative tax data to estimate that η = and ξ = Differential mortality Differential mortality allows variations in income and education to have systematic influence on the survival rates. Assuming an equal length of life or a random process independent of demographic and socioeconomic characteristics may significantly bias savings accumulation and the value of annuities used. This theoretical modelling framework for differential mortality is based heavily on earlier work by Creedy (1982). The following sections consider the empirical evidence and literature underpinning differential mortality, and our modelling of this for retirement income. The pioneering work in differential mortality is Kitagawa & Hauser (1973), which illustrated the relationship between education and mortality rates for population subgroups based on age, sex and race. Kitagawa & Hauser (1973) also estimate the relationship between income and mortality. They state, In our judgement, the education differentials probably provide more reliable indicators of socioeconomic differentials in mortality in the United States in 1960 than do the income differentials (p. 23). The key concept is that mortality rates have a correlation with lifetime resources, with the more commonly used proxies for lifetime resources being education, income and wealth. 6 Prior research, 6 Both in the New Zealand context and international studies ethnicity has also been explored as an explanatory variable for differential mortality. Given the lack of New Zealand ethnic population projections over the required time period this is beyond the scope of the current modelling approach. 9

12 such as the literature review by Feinstein (1993), has generally found that education and income has an independent effect on mortality. However both have a negative correlation with mortality rates. 7 It may be tempting to move from correlation to a causal relationship between education/income and differential mortality, but it is not a simple relationship. Considering health as the channel for mortality, international evidence suggest that health disparities are only partially mitigated when controls are included for access to health care and health risk behaviours (such as smoking and highfat diet that are more prevalent among lower socioeconomic groups). The possibility of mutually reinforcing interactions among education, income, wealth, health and mortality make it very difficult to identify the influence of these individual elements on health outcomes and consequently differential mortality. For a discussion on the interactions of these variables see Smith (1999). Blakely et al. (2007) finds a relationship between differential mortality and income in New Zealand, illustrated in Figure 3. 8 One of the important conclusions drawn in Blakely et al. (2007) is that the increasing size in the mortality differential seems to have slowed. 9 Fawcett et al. (2005) shows that differential mortality trends by level of education in New Zealand are broadly similar; that is higher education levels have an additional independent effect to reduce mortality rates. Blakely et al. (2007) prefer the relationship between income and mortality to the relationship between income and education due to the changing profile of returns to education, as well as the increasing attainment of progressively higher levels of education over time. Figure 3: Age-standardised mortality rates per 100,000 by gender and income, New Zealand, Source: Based on data in Blakely et al. (2007), Table S18. We conclude therefore that there is strong evidence to support differential mortality that is correlated with income and education. The next subsection describes how differential mortality is incorporated into the retirement income modelling framework. 7 Income and education are generally positively correlated, however there is evidence that the marginal return to an additional year of education may be decreasing over time as educational attainment increases. 8 The definition of income used is equivalised household disposable income, which adjusts household disposable income (income after taxes and government transfers) by a factor that allows accurate comparisons based on estimated economies of scales in household consumption. 9 Carter et al. (2010) find that the difference between life expectancies for the upper third of the income distribution and the lower third was 4.4 years in 1981 and 6.5 years in

13 7.1 Differential mortality modelling framework With the rather complicated interactions between differential mortality and other variables incorporated into the model, three key assumptions are necessary to make the inclusion of differential mortality tractable. The first assumption is that differential mortality is determined by the other demographic variables. The second assumption is that differential mortality has a proportional effect on the survival rates. The third is that differential mortality is linked to the final educational attainment and lifetime earnings potential. The second and third assumptions deserve a more thorough explanation. With the links between education, income and mortality, an individual s survival rates would be expected to vary over the lifetime as education and income profiles change. This is challenging from a modelling perspective as it would require recalculating survival rates for every year, while still maintaining consistency with the aggregate differentials, that is ensuring that two people who end up with the same educational attainment and lifetime income have the same differential mortality. By linking the differential to the final outcome of lifetime income and educational attainment and smoothly altering survival rates, consistency with the aggregate differential can be maintained while still capturing the important individual effects of differential mortality. The final mortality differential for person i is calculated as: 10 Mortality = 0.5(Education i ι Education ) + 3 min ( ) Lifetime income 1, 2 GM LI where ι Education is the average education level of the individual s cohort and GM LI is the geometric mean of lifetime income of the individuals cohort. The parameters of 0.5 for education and 3 for income were calibrated to be consistent with Figure 3, making allowances for the difference in base years. With differing definitions of income and education, as well as a different base year, it is not possible fully to reconcile the differential mortality estimates for New Zealand with the projection methodology used in the model. With the mortality differential determined, all that remains is to modify the survival rates appropriately. The modifications to survival rates begin at age 15, from which, using the assumptions detailed above, we can modify the survival rates. The idea is to shift the survival curve by the mortality differential, substituting 1 for each year of positive mortality differential. To give a concrete examples, if the mortality differential is -2 (expected to die 2 years earlier than the representative individual) then at age 15 the individual has the mortality rates of a representative 17 year old. If the mortality differential is +2, then the individual would definitely live to age 17, where they would have the mortality rates of a representative 15 year old. This transformation ensures that the life expectancies are consistent, survival rates are feasible ( 1) and the change occurs in the area of the distribution that has the least effect on retirement income measures. 8 Applications of the retirement income model This section presents aggregate fiscal costs for four policies that have been evaluated with this model. The four policies are (i) raising the age of eligibility for NZS, (ii) changing the rate of annual adjustments to superannuation payments, (iii) communal prefunding from a payroll tax, and (iv) compulsory 10 For cohorts that are aged over 40 in 2010/11 only the education term is used, with a constant of 0.75 replacing

14 private savings with abatement, funded from a payroll tax. These options were selected because they have the potential to reduce the fiscal cost of NZS. 8.1 Adjustments to the age of eligibility for NZS As an increase in the number of recipients due to an increase in life expectancy is a significant factor influencing the increasing fiscal cost, raising the age of eligibility attempts to ensure that different age cohorts spend a comparable proportion of their life receiving NZS. The age of eligibility for NZS is currently 65. This also explicitly linked with the age of eligibility for withdrawing KiwiSaver, which is important when considering the interactions with the public and private prefunding options. Only age of eligibility increases are currently supported in the model, and currently it is not possible to have separate eligibility ages for access to KiwiSaver or compulsory savings and NZS. 11 The results of changes in the age of eligibility for NZS whereby the eligibility age is increased to 67 and 70 at 6 months per year starting in 2020, are shown in Table 4. This shows that raising the eligibility age results in a downward shift in the level of fiscal costs. These options have a noticeable impact on the fiscal cost of NZS over the period to They reduce the fiscal cost relative to the base scenario of no policy change by 0.6% of GDP and 1.5% of GDP respectively. However, as raising the age of eligibility in this way does not address pressures from further increases in life expectancy, fiscal costs are only reduced from the base scenario a further 0.1% of GDP and 0.2% of GDP respectively over the following 40 years. 8.2 Annual adjustment of NZS payments In the base model it is assumed that NZS is indexed to economy-wide wage growth, 12 which is the same assumption used to determine the cohort wage growth of the income component of the model. 13 This is the other significant influence on the increased fiscal cost. Reducing the annual adjustments would be expected to lower retirement incomes for the elderly. Existing superannuitants affected by the reduced entitlement may not have the ability to alter their behaviour by working longer or saving more, implying that consumption will likely decrease for this cohort. 14 We consider two options for modelling a change to the annual adjustments in NZS payments. The scenarios presented in Table 4 are alternative options involving CPI inflation indexing of NZS rates and indexing the rates by a 50% mixture of CPI inflation and economy wide wage growth. of these options have a noticeable 50 year and 100 year impact on fiscal costs, reducing fiscal costs relative to the base scenario by 1.9% of GDP and 1% of GDP respectively in 2061, and reducing fiscal costs by 5.4% of GDP and 3.3% of GDP in In the absence of significant behavioural responses to raise private savings rates, they have implications for elderly poverty rates because pension rates 11 When the age of eligibility in a given year is not an integer, the fractional part is used to determine the proportion of the cohort who receive it in the first year, with the remainder receiving NZS in the subsequent year. Individuals are allocated using a Bernoulli variable with the appropriate parameters of success p determined by the fractional part of the age of eligibility. 12 This is due to the differential between CPI inflation and wage growth causing NZS to remain on the legislated wage floor over the projection period. 13 This may seem to lead to a slight inconsistency in that aggregate wage growth from the income model is not the wage growth used to adjust NZS, however the wage growth used for adjusting NZS does not depend on the hours worked whereas economy-wide wage growth implied by the income component does. The differences are ± 0.05% for the period 2010/11 to 2060/61 which is not unreasonable to ignore considering the variability in wage growth over the last 20 years. 14 There are other avenues, such as decumulation of assets, which could be used to maintain consumption. However, existing superannuitants will be under more financial pressure relative to the other options presented which do not reduce entitlements for existing superannuitants. Both 12

15 progressively diverge below average real wages. 8.3 Communal funding This section examines options for funding the current NZS payment rates, The current system is funded predominately through current taxation. We examine the implications of a system involving a greater amount of pre-funding. Communal pre-funding in the New Zealand context would most likely involve an expansion of the New Zealand Superannuation Fund, beyond the capital contributions that have already been committed under current policy. Communal prefunding will most likely increase the total amount available for income support to future retirees through the effect of compounding returns. This will also cause some cohorts effectively to pay for part of the previous cohort s tax financed NZS and part of their own future NZS, which is substantially more than some previous cohorts would have contributed, see Coleman (2011). Communal prefunding does not necessarily reduce the future NZS liabilty, as it does not necessarily change the number of recipients or the rates. 15 What communal funding does, similar to private prefunding, is to sacrifice consumption in the present for the prospect of increased consumption in the future. One of the key assumptions underlying this prospect is that the rate of return to capital will be higher than the per capita growth rate of the economy, see Coleman (2011, 2012). The first and most important choice for the modelling of communal funding is to decide how to decumulate the savings to offset NZS costs. The option considered here is to construct separate accounts for each cohort, and to purchase annuities for all remaining survivors at the age of eligibility for the cohorts account balance. Any shortfall would be covered by the government through contemporaneous taxation, and any surplus would be available to the government. The other parameters included in the model which are relevant to the communal funding option are a payroll tax rate and the rate of return. The annuities considered are actuarially fair-value individual annuities priced by gender (women tend to live longer which results in an increased fair-value cost for an annuity of the same payment per period relative to a male in the same cohort). 16 The cohorts account is split to the survivors at the age of eligibility in such a way that everyone receives an annuity with the same payment per year. The scenarios presented are the base scenario compared with a 3% and 6% payroll tax, shown in Table 4. The reduction in fiscal costs from the base scenario in 2061 is modest, 0.5% of GDP and 1.1% of GDP respectively. By 2111 a dramatic reduction in fiscal costs is observed, 8% of GDP and 3.9% respectively. The timing profile is understandable given that the communal funding option take until the 15 year old cohort in the year of change retires to reach a steady state. Looking at only the fiscal cost misses some key intergenerational issues. Some cohorts will have to pay relatively more for a larger share of previous cohorts superannuation while saving to fund their own pension, while not fully experiencing the lower taxes that future cohorts will enjoy due to prefunding of the pension system. 15 This is not entirely true as the implementation of a payroll tax would reduce the net of tax average wage, similar to the ACC levy, which would reduce the wage floor lowering the cost of NZS. This could be offset by reducing personal income rates to ensure that marginal tax rates remain constant. There may also be savings impacts, through avenues such as capital deepening, which could increase future productivity growth and real wages and consequently increase the rates of future NZS. 16 A fair-value annuity is one where the initial sum paid is equal to the net present value of the expected payments the individual could receive. 13

16 8.4 Compulsory private savings with abatement Another funding option considered is abatement of a compulsory private savings account, similar to a compulsory version of KiwiSaver, where a percentage of the balance at retirement is used to purchase an annuity, with the government providing a top-up if necessary to ensure that everyone receives at least the current level of NZS. 17 Compared to communal pre-funding this will more closely align contributions with retirement income outcomes as higher earners will receive higher levels of retirement income. For a more thorough treatment of compulsory private savings with abatement, see Kirkup et al. (2012). Almost all of the considerations and parameters transfer over to this case from the communal pre-funding case. However, we have added a split between the amount contributed by the employee and the amount contributed by the employer. The justification is that employer and employee contributions may have different macroeconomic impacts on, for example wage growth. For the scenarios presented here it is assumed that there are no macroeconomic impacts from either employer or employee contributions. The two compulsory private savings scenarios presented are as follows. One is a 4% contribution from the employer and a 6% contribution from the employer, with 50% of the balance at the age of eligibility used to offset government NZS expenses. The other scenario is a 3% contribution from both the employer and employee with 50% offset. In both scenarios, if the person dies before reaching the age of eligibility then no money is taken from the account, unlike the communal funding scenarios. The profile for a compulsory savings scheme is similar to a communal funding scheme, except at a given contribution rate the communal funding scheme can be expected to reduce fiscal costs more. The reduction in fiscal costs from the base scenario in 2061 is 0.9% of GDP and 0.6% of GDP respectively. In 2111 the reduction in fiscal costs is 4.7% of GDP and 3.5% respectively. This is primarily because in the compulsory savings options considered once an individual can fully fund the equivalent of NZS, they are not expected to contribute towards the pensions of others. As the options are currently modelled wealthier individuals are still required to contribute to a communal savings scheme once they have fully funded their own publicly provided pension. There is also a smaller secondary impact due to the retention of decedents contributions in the communal funding options. Table 4: Projected fiscal cost of NZS as % of GDP Year Base NZS Eligibility Age to Eligibility Age to CPI Indexation CPI /Wage Mixture Indexation Communal Savings 6% Communal Savings 3% Private Savings 4%/6% Private Savings 3%/3% As with communal funding the annuity is assumed to be purchased at an actuarially-fair price based only on pricing by gender. 14

17 9 Conclusions This paper has outlined a model designed to provide a framework for analysing a broad range of policy options for New Zealand Superannuation. It brings together previous work to project additional demographic indicators, such as education and couple status, and link them with a consistent method of projecting income. The approach can be used to present detailed disaggregation of fiscal measures and distributional analysis, beyond what has been previously available for New Zealand. After describing the structure of the model, four policy simulations were carried out to investigate the fiscal costs of alternative reforms. These reforms have been discussed in public debates, but the present paper does not attempt a complete evaluation of their implications and thus makes no policy recommendations. Nevertheless, estimation of cost implications is an important component of any policy evaluation. Firstly, it was found that of the four options examined, changing the age of eligibility is the only one which will give short-term fiscal savings. However, compared with the other options, the long-term savings are more moderate. Secondly, while changing the indexation and pre-funding of superannuation have similar fiscal cost profiles, the level of payments and incidence of taxation can be significantly different. The microsimulation approach presented in this paper can be extended, for example by including analysis of the distributional measures for alternate retirement income policies. Other modifications to the modelling methodology that could open interesting avenues for future research include simulating behavioural responses, such as the substitution of private savings to offset public pension reform, and expanding the scope of the study to include variables such as health, ethnicity and migration. Acknowledgements Special thanks to John Creedy for helpful assistance throughout both the research and editorial process. The author would like to acknowledge the helpful reviews of an earlier version by Robert Buckle, Robert Clark, Malcolm Menzies, Katherine Meerman and Anton Samoilenko. The views, opinions, findings, and conclusions or recommendations expressed in this Working Paper are strictly those of the author. 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. References Ball, C. & Creedy, J. (2014). Population ageing and the growth of income and consumption tax. New Zealand Economic Papers, Special Issue (Forthcoming). Bascand, G. (2012). Demographic Projections from Statistics New Zealand: Aims, Methods and Results. Available at ltfep-s1-06.pdf. Blakely, T., Tobias, M., Atkinson, J., Yeh, L.-C., & Huang, K. (2007). Tracking disparity: Trends in ethnic and socioeconomic inequalities in mortality, Wellington: Ministry of Health. Available at 15