2  Model and data

This section outlines the modelling framework used to assess the impact of fiscal policy on New Zealand output. The framework of analysis is a structural vector autoregression (VAR) model, employing estimation and identification techniques used by Blanchard and Perotti (2002). This section derives the fiscal VAR model and the restrictions used to identify the effects of net tax and government spending on gross domestic product (GDP). It describes the fiscal and economic data and discusses their time series properties and trend specification.

2.1  Fiscal VAR and identification

The fiscal VAR model is described by a system of reduced-form equations. Ignoring constant terms, it is given by

(1)     A(L) y_t = ε_t

where A(L)is a P^th order matrix polynomial in the lag operator L, such that A(L)t =I -A₁L - A₂L² - ... - A_pL ^p . Throughout, is set equal to four as quarterly data are used in the analysis.[2] In this model, is a three-dimensional vector in the logarithms of quarterly net tax (government tax revenue less transfer payments), government spending and GDP, although our extension of this model also disaggregates net tax into taxes and government transfers. Each variable is expressed in real per capita terms, where all nominal variables are deflated using the GDP deflator. is the vector of reduced form residuals for net tax, government spending and GDP respectively. The reduced form residuals are unexpected movements in net tax, government spending and GDP and are composite errors of the shocks to the economy. The reduced form VAR model was estimated using quarterly data for the period September 1982 to September 2004.

To gauge the impact of fiscal policy on GDP, restrictions need to be imposed on the reduced form errors. To derive the identification scheme adopted in this paper, write:

(2)    

(3)    

(4)    

where , , and are the mutually uncorrelated structural residuals for net tax, government spending and GDP. These structural shocks need to be recovered to identify the impact of net tax and government spending on GDP.

Equation (2) shows that unexpected movements in net tax are a function of unexpected movements in GDP and structural shocks to government spending and net tax. Equation (3) states that unexpected movements in government spending are also owing to unexpected movements in GDP and structural shocks in net tax and government spending. Finally, equation (4) states that unexpected movements in GDP are related to unexpected movements in net tax and government spending and structural shocks to GDP.

The key challenge is to estimate the parameters of equations (2) to (4). This is done using the identification procedures developed by Blanchard and Perotti (2002) and Perotti (2004) for the purpose of evaluating the effects of fiscal policy on GDP for the United States and a group of OECD economies.

Contemporaneous changes in net tax and government spending in response to GDP movements could potentially occur for two reasons. First, net tax and government spending may automatically change in response to GDP movements under existing fiscal policy settings. Second, the government may discretionarily vary net tax and spending in response to movements in GDP by changing fiscal policy settings. However, as noted by Blanchard and Perotti (2002), the use of quarterly data virtually eliminates the operation of the second channel owing to recognition and implementation lags with regards to discretionary fiscal policy. Therefore, ^a1 and ^b1 can be obtained from independent estimates of elasticities of net tax and government spending to output.

Girouard and André (2005) provide estimates of output elasticities for direct taxes on individuals, corporate income taxes, and indirect taxes for a number of OECD countries. They estimated New Zealand tax to output elasticities using annual data for the period 1989 to 2003. Based on these estimates ^a 1 is set equal to one. This means that a one percentage point increase in GDP leads to a one percentage point increase in taxes. Following Blanchard and Perotti (2002) and Perotti (2004) it is assumed that government spending does not automatically respond to unexpected movements in GDP, therefore ^b1 is set equal to zero.

Estimates for ^a1 and ^b1 provide the basis for estimating the parameters ^c1 and ^c2 of equation (4). Following Blanchard and Perotti (2002), cyclically adjusted reduced form net tax and government spending residuals are used as instrumental variables to estimate ^c1 and ^c2. The cyclically adjusted net tax and government spending reduced form residuals are calculated as and . The cyclically adjusted reduced form residuals and can be used as instruments as they are not correlated with the structural GDP shock .

Finally, estimates are required for ^a2 and ^b2. As noted by Blanchard and Perotti (2002), it is difficult to determine the ordering of government net tax and spending decisions. Do governments make a decision to tax first and then spend, or do they spend and then tax? In the baseline model net tax is ordered before government spending. But because there is no clear answer to the question, the reverse ordering is considered in the sensitivity analysis in section 4. When net tax is ordered before government spending ^a2 and ^b2 is estimated. When government spending is ordered before net tax ^b2 and ^a2 is estimated. As is discussed in Section 4, in practice this issue is of little consequence because the dynamic response of GDP to both net tax and government spending shocks is basically invariant to the ordering of net tax and government spending.