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Universitá di Bologna and International Monetary Fund. I wish to thank for their comments Fabrizio Balassone, Mark De Broeck, Allan Drazen, Olivier Jeanne, Manmohan S. Kumar, Eduardo Ley, Alessandro Missale, Alessandro Rebucci, and Alessandro Turrini. The standard disclaimer applies.
I have tried to keep technicalities to a minimum, or to relegate them into Appendix I. For a dynamic stochastic model of optimal taxation with debt and in the presence of spending barriers, see Manasse, 1996.
Thus, d≡ln(D/Yp), e≡ln(Y/Yp), and D, Y, Yp denote the deficit, actual and trend (potential) output, respectively.
I follow the convention of indicating a partial derivative with a subscript, e.g., Wx is the partial derivative of W with respect to x.
The term c(e) enters separately from the choice variable, d, so it does not affect the analysis (but only the welfare calculations). The chosen functional form can be interpreted as a linearization of an increasing and concave function, or, in expected terms, as a constant absolute risk-aversion (CARA) utility function.
For example, Feldstein (2005) argues that a monetary union creates a strong deficit bias because a deficit in a single nation does not cause the rise in the nation’s interest rate nor a depreciation of the domestic currency. Under this interpretation, Wp represents the national government’s objective function, and W denotes the welfare of the representative union-wide agent.
Note that each of the N consumers’ utility becomes W’=W-w(d)/N ≈W for N large.
Recall that d≡ln(D/Yp) and e≡ln(Y/Yp), so that d-e represents the logarithm of the deficit-output ratio, d-e=ln(D/Y). Hence D/Y≤ X implies, taking logs of both sides, d-e ≤ x
This requires that