Annex III.1. Technical Description of the Fiscal SVAR Framework
The basic VAR specification is:
where zt is a nx1 vector of endogenous variables,
where the nxn matrices A and B describe (i) the instantaneous relation between the variables and (ii) the linear relationship between the structural shocks and the reduced form residuals, respectively. The structural shocks are assumed to be orthogonal, which allows for impact analysis of an isolated shock. The structural form of the VAR can be obtained by multiplying (1) by A and using the relation defined in (2):
Solving (3) for zt yields the structural specification:
Where I is a nxn identity matrix. In the simplest specification used in this study, zt = [yt et rt] consists of three variables for Singapore: real private domestic demand, yt; real government expenditure (consumption and investment), et; and real current government revenue, rt. 4 The data used are seasonally adjusted and at a high frequency (quarterly) in order to identify the structural shocks. The VAR is estimated in log levels with a constant, time dummies, and G7 growth added as exogenous explanatory variables. The number of lags chosen is five as suggested by Akaike and other information criteria.5
Estimation basically proceeds in four steps. In the first step, the reduced form VAR is estimated, yielding the reduced form residuals
As suggested by Perotti (2005), the innovations in
Given that the reduced form residuals are correlated with the structural shocks, exogenous elasticities are used to estimate the automatic/cyclical response of the fiscal variables.7 With these, one can then construct the cyclically adjusted fiscal shocks, which constitutes the second step of the estimation procedure:
The structurally adjusted expenditure shock is, consequently, equal to the cyclically adjusted expenditure shock. With this, it is now possible to estimate the response of revenues to structural expenditure shocks,
In the fourth and final step, the coefficients in the equation for private domestic demand residuals (5) can be determined. Combined, the four steps, which are effectively done simultaneously, allow us to estimate the A and B matrices presented in (2):
In turn, these are used to compute the structural impulse responses of private domestic demand to discretionary expenditure and revenue shocks.
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Prepared by Leif Lybecker Eskesen
See IMF World Economic Outlook, April 2008.
Singapore does not have a comprehensive unemployment benefit scheme and corporate taxes are assessed based on previous year’s income.
Quarterly data for special transfers were unfortunately not available and are, therefore, not included in the expenditure data.
The models specified in this paper are robust to alternative specifications and residuals do not appear to suffer from autocorrelation. Tests for normality of error terms suggest there is not an issue with skewedness, but they cannot reject the hypothesis that there may be an issue with kurtosis.
Representation of the exogenous variables are excluded here to allow for a simplistic illustration of the model.
For Singapore, the elasticity of expenditures with respect to changes in economic activity is assumed to be close to zero within the quarter, as commonly assumed in many other empirical studies. The elasticity of revenues is estimated at around ½ percent within the quarter. The relatively low number partly reflects that corporate taxes are based on past year’s rather than contemporaneous earnings, leaving taxes less responsive to contemporaneous changes in economic activity. While the parameterization is plausible, the magnitude has implications for the estimated multipliers.