2.2  Data

To estimate the fiscal VAR for New Zealand at least three variables are required: net tax (i.e. government tax revenue less transfer payments), government spending (purchases of goods and services), and GDP. GDP is measured by Statistics New Zealand’s real production GDP series. The net tax variable is the sum of direct and indirect taxes less total transfer payments. Government spending includes both current (consumption) and capital (investment) spending. All data enter the model in real per capita, seasonally adjusted terms. Fiscal data are deflated using the implicit GDP deflator. The real per capita data are plotted in Figure 1.

Quarterly aggregate data are collated for all variables from June 1982. All fiscal series cover central government with the exception of government investment, which also includes local government, because a central government investment series is unavailable. The purchase of frigates in 1997 and 1999 are removed from both the purchases of government goods and services and the goods and services tax (GST) series.

Quarterly fiscal data were constructed using two data sources: Statistics New Zealand National Accounts Data and the New Zealand Crown Accounts (and their supporting financial data). Data on government purchases of goods and services (both current and capital) were drawn from the National Account (1993) expenditure GDP series for the period June 1987 to date, and were backdated to June 1982 using the National Accounts (1968) expenditure GDP series.

For direct taxes (source deductions and gross companies tax payments), data are available on a quarterly basis from June 1982. These series account for in excess of 73 percent of annual total tax receipts prior to the introduction of GST in December 1986, and in excess of 86 percent thereafter. Where quarterly data at a disaggregate level are unavailable (between June 1982 and June 1987), quarterly data are estimated by allocating the annual figures in the crown financial statements over the quarters based on the distribution of receipts in the later period (post June 1987). Total tax receipts and the sum of direct and indirect tax have been reconciled back to the crown financial statements from 1983/84 to 1990/91. In 1991/92 the crown accounts moved from a cash basis to accruals basis. Due to GST and source deductions being on a cash basis, our cash receipts figures no longer reconcile back to the Crown Financial Statements. However, the variance between the calculated total tax receipts and the crown financial statements is small, with the average error being around 1.4 percent. Prior to 1994 transfer payments data are available on a less frequent basis. Based on the known relative quarterly allocations, the quarterly transfer payments data can be constructed.[3]

Figure 1 – Variables used in the estimation of the fiscal VAR

2.3  Time series properties of the data and trend specification

Figure 1 shows that per capita real GDP, net tax and government spending have grown over time. To account for the upward trend in the data structural VAR models are often specified to identify shocks that move variables temporarily away from their long-run paths. Structural VARs in this tradition include Sims (1980), Bernanke and Blinder (1992) and Dungey and Pagan (2000). This modelling approach is also adopted by Buckle, Kim, Kirkham, McLellan and Sharma (2002) for their structural VAR model of the New Zealand economy. It is also the modelling approach followed by Blanchard and Perotti (2002) and in this paper.

Blanchard and Perotti (2002) adopt two trend specifications for their United States fiscal VAR: one allowing for deterministic time trends in the data and the other allowing for stochastic trends. The deterministic specification includes time and time squared as additional regressors on the logarithms of per capita net tax, government spending and GDP. The assumption here is that variables grow along long-run equilibrium paths that are a function of time. The stochastic specification is estimated using the first differences of the logarithms of net tax, government spending, and GDP less a changing mean that is calculated as the geometric average of past first differences with a decay parameter set equal to 0.025 per quarter.[4] The stochastic specification allows for persistent shocks to variables’ long-run equilibrium paths. Variables that exhibit persistent shocks (upward or downward movements) are said to be non-stationary.

One way to assess the appropriateness of the deterministic versus stochastic trend specification is to test whether time series are stationary. A test of stationarity is the unit root test. Appendix A reports the results for the augmented Dickey and Fuller (Said and Dickey, 1984) unit root test. The results provide evidence that the level of per capita net tax, government spending, and GDP are non-stationary, suggesting the stochastic specification may be more appropriate. Therefore, in the sensitivity analysis in section 4 two alternative stochastic trend specifications are considered. First, net tax, government spending and GDP are first differenced. Second, the data are detrended by removing time varying stochastic trends using the Hodrick and Prescott (1997) filter. The second alternative specification is consistent with previous work that examines the impact of international and domestic shocks on the New Zealand economy using structural VAR methodology (Buckle et al, 2002 and Buckle, Kim and McLellan, 2003).