Appendix 1: Econometric analysis of revenue windfalls and asset prices

Approach

The hypothesis that asset price deviations have explanatory power for revenue surprises, controlling for growth surprises, is tested using the following regression specification:

RS_t = β₀ + β₁G_t + β₂RE_t+ β₃DE_t + β₄GE_t + ε_t

where:

RS_t = nominal revenue surprise

G_t = nominal GDP growth surprise

RE_t = real estate price “gap” (deviation from benchmark)

DE_t = domestic equity price “gap” (deviation from benchmark)

GE_t = global equity price “gap” (deviation from benchmark)

ε_t = residual error term

Data

For the revenue surprises, errors are the one-year-ahead Budget forecasts of tax receipts over 1991 to 2009.

Growth surprises are measured using errors in Treasury's one-year-ahead forecasts of nominal GDP growth. The forecast value used is taken from the published Budget forecasts. For the actual value, the first vintage outturn is used as subsequent revisions incorporate information which was not available at the time of the forecast.

Domestic real estate prices are measured using an index of median dwelling prices deflated by consumer prices. The benchmark, or structural, level of house prices is estimated by applying a constant growth rate to the base (1990) value. Two benchmarks are tested: the first uses a constant growth factor using the average growth from 1990 to the end of the forecast horizon (2014). Using this assumption, prices have converged to their benchmark level by the end of the forecast by construction. The alternative assumption, which is used to test sensitivity, uses the average of the quarterly growth rates over 1990 to 2000. Under this assumption, the rise in house prices in the 2000s can be seen as a bubble, with house prices in 2010 still well above the benchmark level (by around 40%). This latter view is in common with some fundamental indicators such as price-to-income ratios.

Appendix Figure 1 – New Zealand house prices

Source:  The Treasury, Quotable Value NZ, Statistics New Zealand, author's calculations

Note: Index is QV median dwelling price deflated by CPI.

Real domestic equity prices are measured using an index of the New Zealand stock market (NZX), deflated by consumer prices. For the trend component, an HP filter is used (with quarterly data and a smoothing parameter of 1600).

Appendix Figure 2 – New Zealand equity prices

Source:  Datastream, author's calculations

US equity prices are also controlled for since New Zealanders' financial portfolios are likely to be exposed to, or correlated with, US equity prices. The MSCI US equity price index, deflated by US consumer prices, is used. For the benchmark level, both an HP filter and constant growth assumptions are used (the latter based on the average monthly growth rate over this period).

Appendix Figure 3 – US equity prices

Source:  Datastream, author's calculations

Regression results

The results for regressions under different specifications are reported in Table 9. Caveats of course must apply given the relatively limited data and simple regression methodology. The main conclusion drawn is that growth surprises have high explanatory power, whereas the other variables to do not.

* significant at 10% level; ** significant at 5% level; *** significant at 1% level