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Prepared by Daniel Kanda
This approximation of the coefficients of equation (14) is accurate to one decimal place, and the simplification enables us to derive analytical solutions for the optimal fiscal path below. As a check, equation (14) was also used directly in the optimization problem, and the coefficients obtained in the policy functions for the different countries from a numerical solution method closely matched those obtained algebraically using equation (15) even for values of ∂ as high as 1.
Strictly speaking, there are three solutions found, but only one where both A and B are positive.
In the case of Germany, another issue that arises is that estimating the structural primary balance using the output gap (as in equation (6)) may have biased downward our estimates of the annual structural fiscal adjustment, because labor market indicators showed significantly smaller economic slack than indicated by the size of the output gap. In that case, the value of alpha for Germany could be significantly smaller than estimated here.