The name is absent

whose Lagrangean is:

U(p) - C(x,z) - λ₁ [p + rb - yb - z - W] - λ₂ [p + rb - x - H]                 (6.7)

with first order conditions:

U’ - λ1 - λ2 = 0                                                            (6.8a)

- Cx + λ2 = 0                                                               (6.8b)

- Cz + λ1 = 0                                                               (6.8c)

λ1 ≥ 0            p + rb - yb - z - W ≤ 0     λ1[p + rb - yb - z - W] = 0 (6.8d)

λ2 ≥ 0            p + rb - x - H ≤ 0           λ2[p + rb - x - H] = 0       (6.8e)

Since Cx ,Cz> 0 by assumption, from (6.8b) and (6.8c) it follows that λ1, λ2 > 0, which in
turn we use in (6.8d) and (6.8e) to get:

z = p + rb - yb - W                                                    (6.9)

x = p + rb - H                                                           (6.10)

We use these equations as the basis for our econometric analysis and estimate the
following two regressions:

zt = α0 + α1 dt + α2 ytbt-1 + α3 Wt + εa                                         (6.11)

xt = β0 + β 1 dt + β 2 Ht + εb                                                    (6.12)
where d=p+rb is the “true deficit”; Wt=0 if bt-1>60, Wt=60-bt-1, if bt-1<60; and Ht=3 if
d^mt-1<3, Ht=d^mt-1 if d^mt-1>3.

From the signs in (6.9) and (6.10), we expect:

(a)       α1 > 0 ; α2 , α3 < 0

(b)       β 1> 0 ; β 2 < 0

We expect both types of SFA to be positively related to the level of the “true deficit”
(α1, β1 > 0): the higher the “true deficit”, the higher the x and z values required for formal
compliance with the rules (see also Buti et al., 2007).

The debt level plays no direct role, and it only affects the debt-specific SFA through the
“growth effect” (i.e. the reduction of the debt ratio determined by GDP growth, which is
larger the larger the debt). The use of z to keep debt dynamics under control becomes less
necessary when the growth impact is higher, hence the negative sign expected for α2.

The constraints determined by the deficit and debt fiscal rules enter directly the
corresponding estimating equations. We expect the levels of z and x to be negatively
correlated with, respectively, the maximum allowed change in debt and the maximum

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