3 Model and data

The model is adopted from Perotti (2005) which uses a five-variable VAR comprising government spending, taxes net of transfers, output, interest rates and inflation. The debt equation is added to this system in a deterministic way (ie, as an identity). The identification of structural shocks in this approach relies on institutional information about tax and transfer systems and on the existence of decision lags in fiscal policy.

The reduced form residuals u_t in (3) are correlated and therefore not purely exogenous. The problem then is to take the observed values of the reduced form residuals, u_ts, and to restrict the system so as to achieve identification and recover the uncorrelated structural shocks. The identification restrictions of the Blanchard and Perotti SVAR can be expressed as an AB model, see Amisano and Giannini (1997), with:

           (5)

where Α is a n x n matrix of contemporaneous relations among variables, Β is a n x n matrix that allow some shocks to affect directly more than one endogenous variable, u_t is the vector of reduced form residuals with variance-covariance matrix and e_t is the vector of structural policy and non-policy shocks we want to identify. Using the specification in Perotti (2005) and denoting the five variables as government spending, taxes, output, inflation and interest rates respectively, (4) can be represented as follows:

          (6)

Each row in (6) is an equation that defines a relationship among the reduced-form residuals and structural shocks that we want to estimate. However, the above system of equations is not identified and needs to be restricted to achieve identification. It is important to note that the debt-to-GDP ratio is an identity and therefore deterministic. This means that equation (2) plays no role in the identification of structural shocks. The identification problem can be described as follows:

By construction, the reduced form disturbances and the underlying structural shocks are related as,

         (7)

from which the variance-covariance matrices of e_ts and u_ts can be derived as follows:

where is an identity matrix (ie, e_t is a vector of uncorrelated structural shocks). Substituting the population moments with sample moments, we obtain:

            (8)

Equation (8) shows that the reduced form and the structural variance-covariance matrix are related to each other and is key to understanding the identification problem. OLS estimation allows us to obtain consistent estimates of the reduced form parameters , the reduced form errors u_ts and the variance-covariance matrix . Since is symmetric, the left-hand side of (8) contains 15 distinct elements. Therefore, the maximum number of identifiable parameters in matrices Α and Β is also 15. The number of free parameters to be estimated in the Α and Β matrices in (6), on the other hand, is 22 (ie, coefficients excluding zeros and ones). Therefore, the system is under-identified, requiring 7 identifying restrictions.

Using Blanchard's identification strategy, the six parameters in the first two rows of matrix Α are identified using external information. The next section discusses the identification of these coefficients for New Zealand in more detail. Since the focus of our analysis is studying the effects of fiscal policy shocks on macroeconomic variables, we are particularly interested in identifying the structural shocks in the first two rows of the matrix A. Therefore, the structural shocks and are identified by using a recursive structure on the last three rows of A and B which is fairly standard in the VAR literature.

The identification of the two off-diagonal elements of the B matrix (b₁₂,b₂₁) is not straightforward and depends on our view of the functioning of fiscal policy. We assume that government expenditure decisions are prior to tax decisions (b₁₂ = 0) and test the sensitivity of the results to this assumption. In line with other studies, we find that the results are not sensitive to this assumption[1].