5.2 Comparison with Treasury’s measure of fiscal impulse
This section compares a measure of fiscal impulse, developed by Philip and Janssen (2002), with those produced by various specifications of the fiscal VAR. We start by noting the conceptual similarities and differences between the alternative measures of fiscal impulse and then compare quantitative estimates.
The Philip and Janssen indicator of fiscal impulse is defined as the change in the estimated structural primary cash balance. The structural primary cash balance is constructed by taking cyclically-adjusted tax receipts and subtracting cyclically-adjusted government spending (which includes some capital items that are deemed to have an impact on aggregate demand) and net interest payments. At a general level (and ignoring net interest payments) this measure of fiscal impulse 
can be denoted as follows:
(6) 
where the superscript * indicates the variable has been cyclically adjusted. This indicator of fiscal impulse is seen as measuring whether changes in fiscal policy are adding to, or subtracting from, aggregate demand pressure in the economy (although it is not always specified how aggregate demand is being measured) and is usually estimated using annual data.
This type of measure of fiscal impulse has two widely cited limitations. First, the composition of fiscal policy changes are not taken into account, so for example tax decreases and government spending increases are treated symmetrically in terms of their impact on aggregate demand. Second, at best, this type of indicator only captures the first round impacts of changes in fiscal policy, and not additional dynamic effects.
Interpreting measures of fiscal impulse from VAR models depends on the trend specification adopted. To see this, first denote fiscal impulse (Fl2) from the Hodrick-Prescott fiscal VAR specifications as follows:
(7) 
where the superscript M indicates model-adjusted government spending and net tax (adjusted to isolate the discretionary components of fiscal policy) and the superscript * indicates the time or Hodrick-Prescott trend in net tax and government spending. In this specification fiscal impulse arises from discretionary changes in fiscal policy in which net tax and government spending deviate from their long-run growth paths (as measured by their Hodrick-Prescott trends) and is estimated using quarterly data.
The measure of fiscal impulse (
) that emerges from the first difference specification of the fiscal VAR can be denoted as follows:
(8) 
In this specification fiscal impulse arises because of changes in taxes and government spending. This measure of fiscal impulse gauges the contribution of fiscal policy to GDP growth.
The VAR measures of fiscal impulse overcome the two main limitations of indicator type measures of fiscal impulse. First, the VAR measures of fiscal impulse account for changes in the composition of fiscal policy. This is because they feed through a system of equations that allows for different impacts of tax and spending changes on GDP. Second, because dynamic interactions are specifically modelled within the VAR model, second round effects are captured.
Figure 8 shows the two measures of fiscal impulse from the first difference and Hodrick-Prescott specifications of the fiscal VAR and compares them with the Philip and Janssen indicator measure of fiscal impulse. The first chart of Figure 8 corresponds to the first difference fiscal VAR specification and shows the contribution of fiscal impulse to annual GDP growth. The second chart of Figure 8 corresponds to the Hodrick-Prescott fiscal VAR specification and shows the contribution of fiscal impulse to deviations in GDP from trend (that is, the output gap). The Philip and Janssen measure of fiscal impulse has been inverted, compared to the way it is usually presented, to aid comparison with the fiscal VAR measures of fiscal impulse. Because initial conditions can make substantial contributions to GDP growth or deviations in GDP from trend this analysis focuses from the mid-1980s onwards.
Figure 8 suggests that in general the sign and magnitude of the first difference fiscal VAR specification and the Philip and Janssen measures of fiscal impulse are similar, although there are periods where there are differences. It is interesting to note that Treasury’s current measure of fiscal impulse tends to display larger absolute changes than the measure of fiscal impulse from the first difference fiscal VAR model.
In the late 1980s both measures of fiscal impulse suggest that fiscal policy was acting to dampen GDP growth; this was more so for the Philip and Janssen measure of fiscal impulse. During the 1991 and 1992 recession, the measure of fiscal impulse from the first difference fiscal VAR suggests that fiscal policy made a larger negative contribution during this period, than is suggested by the Philip and Janssen measure of fiscal impulse. Throughout the remainder of the 1990s both measures are in broad agreement about the contribution of fiscal policy to GDP growth (although the stimulus from fiscal policy in 1997 is considerably larger for the Philip and Janssen measure compared to the VAR measure of fiscal impulse). In the period from 2002, at least until more recently, the two measures suggest different impacts of fiscal policy on GDP growth.
In general, there has also been some degree of congruence between the measure of fiscal impulse produced from the Hodrick-Prescott VAR specification and the Philip and Janssen measure of fiscal impulse, particularly over the last five years. However, one period where the two measures noticeably differ is in the mid-1990s, when the Philip Janssen measure suggests discretionary fiscal policy was subtracting from positive deviations in GDP from trend, whereas the fiscal VAR measure suggests fiscal policy was adding to positive deviations in GDP from trend.
