# Issues on fiscal policy TaxSmoothing Barro 1979 Romer

Issues on fiscal policy

Tax-Smoothing (Barro 1979) Romer (2012) section 12. 4 Distortion costs from raising Tt: The government chooses the path that minimizes this distortion:

Costs are minimized when: This result is very interesting under uncertainty:

Discussion: T/Y follows a random walk (no predictable changes in T/Y. 1) Important role for debt financing: War 2) Recessions

Model of debt crisis, Romer 4 th edition section 12. 10 • One period model • D debt has to be rolled over (issue D of new debt to pay off the debt coming due) • T tax revenues the following period, • Government want investors to hold the debt for one period • T is random with cumulative function F() • R is the interest factor (1+r) and R-1 is the interest rate r • If T is less than RD full default • Default is all-or-nothing • Investors are risk neutral • The riskless interest factor RMIN is independent of R and D. • π is the expected probability of default

Arbitrage between risky and riskless assets implies • (1 -π)R = RMIN • Or π = (R-RMIN)/R (12. 42) • Example European debt crisis • 12. 42 is plotted in the following graph

Condition for investors to be willing to hold government debt From 12. 42 1 π RMIN R

Second equilibrium condition: government defaults if T < RD • • • T distribution function is F() π = F(RD) (12. 43) The maximum value of T is TMAX The minimum value of T is TMIN Density function is bell-shaped The cumulative distribution function is Sshaped

The probability of default as a function of the interest factor 1 π TMIN/D TMAX/D R

The determination of the interest factor and the probability of default 1 B π πA TMIN/D B is unstable (p. 636) Two stable equilibria, A And π=1 A RMIN TMAX/D R

Analysis • So there are two equilibria, one when the interest factor and the probability of default are low, one where no investor want to hold the debt • For a sufficiently large riskless rate RMIN (Figure 12. 6 next) the red curve is on the right of the blue curve and the only equilibrium is π=1. You don’t need large change in fundamental to have π moving from a low πA to π=1 • For RMIN below this point, and increase in RMIN increase the low πA • Read page 637 -638 (the conclusion on expectation, beliefs about fundamentals is Keynesian).

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