4  Data and parameters

The government spending share of GDP is equal to the values in Treasury's LTFM for 2007 to 2060. Government spending[9] is projected to increase by 6.4% of GDP from 29.6% to 36.0% over the 45 year period from 2014-15 to 2059-60.[10] Health spending grows by 5% of GDP and New Zealand Superannuation (NZS) grows by 3.6% of GDP. However whereas all of the growth in NZS is due to demographic change, almost all of the health spending is due to “non-demographic volume growth” - income growth and input costs. Demographics accounts for roughly 1% of the 5% increase. This is consistent with the pattern in recent decades during which population ageing has accounted for only 10 to 15% of the growth in health spending in New Zealand (Bell et al., 2010). Hence the projected fiscal burden attributable to population ageing is somewhat less than the 6.4% of GDP of projected growth in total spending - approximately 4.5% to 5%. There are small reductions in other spending items as a share of GDP such as education and some welfare expenses.

These figures are based on the “cost pressures” projection. This is a ‘no policy change' projection based on bottom-up calculations of growth rates of the main budget expense categories. The growth rates for government consumption expenditure consist of the sum of the growth rates of input prices and output volumes. Input price growth consists of inflation plus (adjusted) real unit input costs which are based on (adjusted) labour productivity growth in the public sector. Output volume growth is the sum of demographically-driven and non-demographically-driven components. The demographically-driven component depends on the growth rates of recipient population age groups. For health spending, this is based on age and gender-specific shares of spending which are assumed constant throughout the projection period. For welfare spending, input price growth is simply equal to the inflation rate and volume growth is determined by demographic growth, in particular the growth rates of recipients for each category of spending. Hence unlike consumption expenditure, welfare spending does not grow with labour productivity growth.

The Government spending share of GDP is assumed to remain constant at its 2055 level thereafter, and constant at its 2007 for all years up to 2007.

The historic and projected age-specific population levels, age specific wage rates and exogenous[11] labour force participation rates were accessed from Statistics New Zealand and were provided by New Zealand Treasury officers.[12] The population data are the same as those used in Treasury's LTFM. Five demographic projections are compared. (i) A Medium projection which is the base case used for the LTFM and adopts the following long run assumptions: total fertility rate of 1.9, life expectancy at birth increases to 85.6 years for males and 88.7 years for females, and net migration of 10,000 p.a.; (ii) a (very) High Fertility projection which differs from the Medium projection only in that the long run fertility rate is 2.5; (iii) a (very) High Migration projection which differs from the Medium projection only in that long run net migration is 25,000 p.a. (iv) Zero Migration; and (v) Low Mortality in which life expectancy at birth increases to 95 for both males and females.

A key parameter in analysing the welfare effects of tax smoothing is Ψ, the intratemporal elasticity of substitution between leisure and consumption. This partly determines the elasticity of labour supply with respect to changes in the after- tax wage. Typical values of this parameter in the literature are in the range 0.5 to 1.0. For example, Foertsch (2004), Auerbach and Kotlikoff (1987) and Altig et al. (2001) all use a value of 0.8 in their dynamic models and this is the value chosen here. The relationship however between Ψ and the labour supply elasticity in a lifecycle optimising model is a complicated non-linear function of the parameters of the model (Ziliak and Kneisner, 2005). Sensitivity tests are reported of labour supply responses over the lifecycle to the range of values of this parameter found in the literature.

Figure 4 plots the effect of endogenous labour on the aggregate labour force participation rate (LFPR). The series plotted is the percentage change in LFPR given by the model compared with that given by the raw demographic data combined with the exogenous LFPR as given by Statistics New Zealand and used in Treasury's LTFM. The endogenous LFPR averages about 0.2% below the exogenous LFPR over the full projection period, but the magnitude is greater (up to 1%) for the first two decades. This represents the response of households to rising tax rates. Note that the response is initially slightly larger under the sustainable debt scenario reflecting the higher initial tax rate.

Figure 4 - Effect of endogenous labour on aggregate participation rate. % change in LFPR relative to exogenous LFPR

There is zero technical progress in production. This allows for a more transparent analysis of the effects of ageing and accompanying fiscal regimes on labour supply and intergenerational welfare for the following reasons. One reason is that the effect of population ageing on technical progress is, although potentially important, highly uncertain in direction and magnitude according to the theoretical and empirical literature (Guest, 2007). A sensitivity analysis is one way to go but would lengthen the present analysis considerably as there are a number of potential mechanisms. Also, there is the well-known issue of modelling the leisure-consumption choice with technical progress. Technical progress drives up real wages which implies a rising price of leisure and therefore a falling leisure to consumption ratio - it would eventually decline to zero (Kulish et al., 2006; Auerbach and Kotlikoff, 1987). There are more complex utility functions that can deal with technical progress, but this is regarded as beyond the scope here.

Other parameters are the interest rate, rate of time preference, depreciation rate and elasticity of marginal utility with respect to consumption. The values of these along with initial values for government debt, foreign liabilities and the capital stock are given in the Appendix.