3.1 Elasticities of government revenues and expenditures

The six coefficients that need to be identified using external information are the elasticities of real net taxes and real net spending per capita with respect to each of output, inflation and the interest rate. These correspond to the coefficients , and a_ti.

The elasticity of tax revenue with respect to GDP is set to 1 (a_ty = 1.0). This is consistent with the assumption of Claus et al. (2006), which was based on the estimations in Girouard and Andre (2005).

The elasticity of government spending with respect to output is set to zero (a_ty = 0). This is based on an assumption that real government spending (which excludes transfer payments, such as the unemployment benefit) would not respond to contemporaneous changes in GDP in a quarter^[2]. This is consistent with Claus et al. (2006) and Blanchard and Perotti (2002).

The price elasticity of tax revenue is set at 0.2 (a_tΔp = 0.2). The price elasticity of personal income tax can be estimated by subtracting 1 from the elasticity of tax revenues per person to average earnings (Perotti, 2005). This latter elasticity is estimated to be 1.3 for New Zealand by Girouard and Andre (2005) and a range of methods indicate a range of 1.3 to 1.4 reported in Parkyn (2010). Subtracting 1 from these estimates indicates a price elasticity of around 0.3 to 0.4. Corporate taxes have a very uncertain relationship with price in both directions and so we assume a price elasticity of zero. Indirect taxes are also assumed to have a price elasticity of zero as they have a typically proportional rate. Individual tax has accounted for around half of total tax revenue over 1990 to 2010, and therefore a weighted average of these price elasticities is about 0.2.

The price elasticity of real government spending is set to -0.5 (a_gΔp = 0.5). This is consistent with the assumption used by FG, following Perotti (2005). Perotti reasons that the wage component of government spending is fixed within the quarter. This implies that the elasticity of real government spending on wages with respect to the GDP deflator is ­1. The non-wage component of spending is more likely to be effectively indexed to price inflation (although some spending is likely to be fixed in nominal terms in a quarter). This implies that the price elasticity for non-wage spending is likely to be closer to 0. Since direct wage costs account for a significant proportion of real government spending, it seems reasonable to assume that the price elasticity of real government spending must be well below 0 but higher than -1.

The elasticity of government spending with respect to the interest rate is set to zero (a_gi = 0). This is justified on the grounds that we only consider primary fiscal variables (that is, excludes debt servicing costs and investment income).

The elasticity of tax revenue with respect to the interest rate is set to zero (a_ti = 0). This follows the assumption of FG and Perotti (2005), noting that this assumption may be slightly uncertain since the tax base does include interest income, although the effects may be quite complex given that dividend streams may also be affected by interest rate movements.