2.4  Sensitivity of revenues to the cycle

The values used for the revenue elasticity parameters in Treasury's existing indicator are reported in Table 1. These are the same values used by the OECD, originally estimated in Girouard and André (2005). These estimates are the most recently made for New Zealand and, since they are used by the OECD, have the advantage of being validated by an independent, international body.

Source: The Treasury

The elasticity of each revenue type with respect to the output gap can be decomposed into the product of an elasticity of revenue with respect to the relevant revenue base (eg, wages or profits) and an elasticity of the revenue base with respect to the output gap:

^εR_i,YGAP = ^εR_iB_i X ^εB_i,YGAP (11)

where B_i denotes the associated macroeconomic base for revenue type i.

The remainder of this section assesses each of these revenue elasticity estimates.

2.4.1  Sensitivity of tax revenues to changes in the base (^εR_iB_i)

For personal income tax, the relevant base is the total wage bill. In Girouard and André (2005), the elasticity of personal income tax revenue with respect to the wage bill is found by computing the marginal and average tax rates of a representative household for several points in the earnings distribution. Per capita elasticity of income tax with respect to earnings can be evaluated as follows:

(12)

With Y_i = weight of earnings-level i in total earnings, MA_i = marginal income tax rate at point i on the earnings distribution and AV_i = average income tax rate at point i on the earnings distribution.

The existing elasticity estimate is 1.3, which is estimated on the basis of the 2003 tax code and earnings distribution data from 1999 to 2001. This is at the bottom end of the range of estimates for OECD economies (see Figure 5). New Zealand’s tax settings have changed since this time, including significant changes entering into effect from 1 October 2010. The range of estimates for the tax-to-base elasticity, based on this new tax code, is 1.33 to 1.40 (see Table 2). This is based on both the method of equation 12 and other microsimulation and econometric procedures.

The relevant bases for corporate income tax and indirect tax are corporate profits and taxable consumption respectively. The OECD assumes a tax-to-base elasticity of unity due to measurement difficulties and uncertainties, and there remains no obvious way of overcoming these issues.

Figure 5 – OECD estimates of income tax elasticities

Source:  Girouard and André (2005)

Source: Bell (2010)

2.4.2  Sensitivity of tax bases to the output gap (^εB_i,YGAP)

For the personal income tax elasticity, Girouard and André (2005) econometrically estimate the elasticity of the wage bill with respect to the output gap. A pooled panel regression approach is used in which New Zealand is calibrated to a pool consisting of similar Anglo economies (United Kingdom, United States, Australia and Canada). The New Zealand time series is too short to give robust results. The estimated coefficient used is 0.66. This is near the median of OECD economies and there is minimal dispersion amongst countries, suggesting further attempts at refining this estimate would probably not have a high payoff.

For corporate income tax, the elasticity is derived from equation 13 by recognising that the corporate tax base (profits) is the reciprocal of the wage bill. The relationship is defined by:

(13)

where ^εB_c,YGAP is the elasticity of the corporate income tax base (ie, profits) with respect to the output gap, P is the profit share in GDP, and ^εB_w,ygap is the elasticity of the wage bill with respect to the output gap. Because of the assumption that corporate income tax revenues change proportionally to the tax base, equation 13 also equals the overall elasticity of corporate tax with respect to the output gap. Girouard and André's data has a profit share of 44.8% for New Zealand, which combined with the wage bill-output gap elasticity of 0.66, means an estimated elasticity of 1.4 for corporate tax revenue with respect to the output gap. Profits, proxied by the gross operating surplus in the national accounts, have remained a relatively stable share of GDP since the early 1990s at around 45%. Thus this continues to be a robust estimate.

Indirect taxes, including GST, are assumed to have unit elasticity with respect to their bases for all countries due to measurement difficulties.

2.4.3  Summary of evidence for tax revenue elasticities

The available evidence suggests that the OECD estimates remain reasonable values for the revenue elasticities. They are also widely accepted, used by the IMF and European Commission. Therefore there is sense in retaining the practice of using the OECD elasticity estimates.

It was noted that the estimate of the elasticity of personal income tax to the wage bill had increased slightly with the recent change in tax settings (increasing from about 1.3 to about 1.4). This is not large enough in magnitude to change the revenue-to-output gap elasticity value without introducing spurious precision (since 1.3 X 0.66 ≅ 0.9 and 1.4 X 0.66 ≅ 0.9).

2.4.4  Sensitivity of non-tax revenues to the cycle

Non-tax revenues make up a significant share of total Crown revenue (32% in 2009).

Investment income is not cyclically adjusted. Although financial returns will have some relationship with the cycle, the covariance will be specific to the nature of the financial instrument and the growth shock. Given the difficulties inherent in estimating these reliably, no cyclical adjustment is made to either investment income or financing costs. In any case, examining the primary balance (which is the fiscal balance excluding net finance costs) enables analysis which is not sensitive to this assumption.

Source: The Treasury

The existing Treasury indicator treats the sales of goods and services and other revenue (including levies and fines) as sensitive to the cycle (with an assumed elasticity of unity). There is not sufficient data to estimate the elasticity. The Crown derives much of its sales revenue from low-volatility industries (predominantly in the energy sector), where it seems likely that both revenue and expenses would tend to co-vary over the business cycle. Therefore net profit, which impacts the operating balance, would have a relatively small cyclical component. This would also hold for levies and fines, which typically reflect expenses. Thus, it appears advisable to remove the cyclical adjustment for all non-tax revenue. This is consistent with the OECD's approach, which does not cyclically-adjust the profits of state-owned enterprises. The quantitative difference arising from this methodological change would be material but not large: in the existing approach, an output gap of one percentage point is associated with a cyclical adjustment of 0.2% of GDP.

2.4.5  Unemployment-related expenditures

The existing Treasury indicator uses an Okun's law relationship to derive a structural rate of unemployment. The Okun coefficient is assumed to be 0.5, meaning that an output gap of 1% of GDP is associated with the actual unemployment rate differing from its structural rate by 0.5 percentage points.

As a rule of thumb, 0.5 is broadly consistent with the established literature looking at major economies such as the United States. Harris and Silverstone (2000) investigate the Okun coefficient using New Zealand data from 1979 to 1999. Using an OLS regression, they found an estimate of 0.4. Using the same methodology on data over the period 1988 to 2009 also produces an estimate of 0.4. Harris and Silverstone also found that a standard estimate of the Okun's coefficient is likely to be understated due to misspecification of the adjustment process. Specifically, they found that expansions and contractions in output have an asymmetric relationship with unemployment.

The key advantage of using an Okun's law relationship is that it ensures consistency between the output gap and structural unemployment assumptions. However, while the empirical relationship holds on average over time, there may well be significant divergences at any particular point in time. An alternate approach to the Okun's law relationship would be use a direct estimate of the NAIRU. The Treasury's preferred method is a time-varying estimate using a Kalman filter (Szeto and Guy, 2004). This estimate of the NAIRU has a much less cyclical pattern than the rate implied by Okun's law.

The use of Kalman filter estimate of the NAIRU is more consistent with a medium-term perspective and is consistent with the Treasury's general equilibrium forecasting model. However, in scenarios which use a different output gap from the official forecast, it would be necessary to decide whether to use an alternative NAIRU estimate (in which case, the Okun's law relationship could be employed as a rule of thumb).

The actual difference in structural unemployment rates is bounded by 2 percentage points using data from 1994 until 2014 (the end of the Budget 2010 forecast horizon). Unemployment expenses currently make up only about 1% of total Crown expenses. Thus, even with a divergence in the estimated structural rate of unemployment of 2 percentage points, the total difference to the CAB would only be 0.1% of GDP.