Appendix:
Assumptions for Stochastic Simulations
The stochastic simulations were based on 1000 fifty-year scenarios for each of: labour productivity growth; New Zealand bond returns; New Zealand equity returns; foreign bond returns; and foreign equity returns. All series were modelled in nominal terms but, since the inflation rate is deterministic in our fiscal model, the implicit assumption is that the real series are stochastic. The series were modelled as jointly-dependent normally-distributed variables with the following population parameters:
| Variables | Mean | Standard Deviation |
|---|---|---|
| Labour Productivity Growth (LPG) | 3.0% | 1.9% |
| New Zealand Bond Returns (NZB) | 7.0% | 4.6% |
| New Zealand Equity Returns (NZE) | 8.6% | 17.1% |
| Foreign Bond Returns (FBD) | 6.7% | 10.4% |
| Foreign Equity Returns (FEQ) | 12.5% | 14.9% |
Sources: Statistics New Zealand, MSCI and authors’ estimates
| Correlation Coefficients[23] | LPG | NZB | NZE | FBD | FEQ |
|---|---|---|---|---|---|
| LPG (GDP)[24] | 1.00 | 0.22 | 0.32 | -0.16 | 0.03 |
| NZB | 0.22 | 1.00 | 0.11 | 0.34 | 0.06 |
| NZE | 0.32 | 0.11 | 1.00 | -0.24 | 0.41 |
| FBD | -0.16 | 0.34 | -0.24 | 1.00 | 0.18 |
| FEQ | 0.03 | 0.06 | 0.41 | 0.18 | 1.00 |
Sources: Statistics New Zealand, MSCI and authors’ estimates
The parameters represent the sample means, standard deviations and correlation coefficients for representative series over the period 1991:Q1 to 2001:Q3.[25] There is one exception: the calculated return on foreign bonds was adjusted downwards by two percentage points to be lower than the return on New Zealand bonds.
Notes
- [23]The balanced portfolio has a correlation of 0.17 with LPG and has a mean return of 8.7% and standard deviation of 7.5%.
- [24]Since LPG is the only stochastic input that affects GDP growth, the volatility of LPG (and the correlations with other series) represents the volatility of GDP growth. For this reason, we used a nominal GDP series to derive the volatility and correlations of the LPG series. Hence, the volatility and correlation parameters should be interpreted as relating to GDP rather than LPG.
- [25]All series means were measured in real terms and increased by 1.5% to obtain nominal values. The representative series are Statistics New Zealand nominal GDP and the MSCI gross return indices for New Zealand (3-5 yr) bonds, New Zealand equities, World Sovereign bonds (3-5 yr), and World equities.
