Appendix A. VAR Modeling and Diagnostics
Appendix B. Additional Impulse Responses and Variance Decompositions
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The author would like to thank Rex Ghosh, Yasser Abdih, Fabiano Bastos, Rainer Köhler, and Issouf Samake for helpful comments and suggestions. Special thanks also to the second deputy governor of the Bank of Mauritius Dr. Ahmad Jameel Khadaroo, Jitendra Bissessur, Mahendra Punchoo, and seminar participants at the Bank of Mauritius for useful comments and discussions on an earlier draft of the paper. The usual disclaimer applies.
Although VARs were traditionally used for forecasting, Sims’ work initiated their use for policy analysis.
For more details about the historical evolution of monetary policy in Mauritius see Heerah-Pampusa, Khodabocus, and Morarjee (2006).
The MPC includes the BoM Governor and two Deputy Governors, two Board Directors and four members.
Staff estimates of the reaction function
For more details on the calculation of various measures of core inflation see Bissessur and Morarjee (2006).
Both the headline and core CPI’s (i.e. the levels) are highly negatively correlated with the repo rate. Looser monetary policy translates to increases in the (core and headline) price level.
Technically, (1) represents a VARX model (that is, a VAR with exogenous variables), an extension of Sims’s (1980) original approach which treats every variable in the system as endogenous. The exogeneity of the variables used in a VARX model can be justified on a priori grounds but also established statistically by testing for weak exogeneity. In our case, exogeneity tests performed establish that the variables used are indeed weakly exogenous, in the sense that Yt does not Granger cause Xt.
Before performing the Cholesky decomposition is imposed we test the correlations between the reduced form residuals which were found to be low (see Appendix). This suggests that the reduced form shocks are fairly orthogonal to each other and ensures that the results presented are robust with respect to the ordering of the variables. Nevertheless, we carry through both identifications to compare the robustness of the results.
The unit root tests are based on specifications with a constant term included. Alternative specifications including both a constant and a deterministic time trend were also used with similar results.
Dummy variables were used as needed to capture effects of “structural” changes in the economic environment (such as changes in monetary statistics in 2003, the 2006 abolition of the Lombard rate, and the 2008 financial crisis) as well as the presence of outliers.
The diagnostic tests mentioned in the text are tests performed on each equation of the VAR separately and on the entire system and yield the same results.
The basic idea behind recursive estimation is to fit the VAR to an initial sample of M-1 observations, and then fit the VAR to samples of M, M+1, … up to T observations, where T is the total sample size.
The dynamic out of sample forecast is estimated using a VAR model from 1999 Q1 to 2008Q1. Using static forecasting (i.e. where series’ forecasts are based on one-step forecasts) the forecasted inflation series is even closer to the actual.