El derecho al olvido y el derecho de acceso a la documentación judicial.

Again, we use the household problem for parents of adults described in equation (54) in order to demonstrate the exogenous grid method. First order and envelope conditions were given by:

FOCC : uC(C, 1 − `) 1+ τc −βRn<sub>t+1</sub>Eη0<sub>|η</sub>V0 X0 j+ 1, X0, q, γ, η0
 −µ<sub>A</sub>0 = 0 (72) FOC1−`: u1−`(C, 1 − `) − wnt, j,qβRnt+1Eη0|ηV 0 X0 j+ 1, X0, q, γ, η0
+ µ_A0  −µ` = 0 (73) EVLPX : VX( j, X, q, γ, η) = βRnt+1Eη0|ηV 0 X0 j+ 1, X0, q, γ, η0
+ µ_A0, (74)

From equations (72) and (74) we get:

VX( j, X, q, γ, η) = βRnt+1Eη0|ηV 0 X0 j+ 1, X 0_{, q, γ, η}0
 = uC(C, 1 − `) 1+ τc . (75)

Households’ budgets read as:

X0 = Rnt+1A

0_{+ (1 − τ}

ss)wt+1, j+1,qγη0

A0 = X − (1 + τc)C − (1 − τss)wt, j,qγη(1 − `) − Tt(Yt) ≥ −Ψ(q)A_j,t.

In contrast to the endogenous grid method, the exogenous grid method starts the solution with an exogenous asset level A which, given our cash-on-hand definition, also determines X = Rn

household cannot ”fall off” and no extrapolation is required. For the lower end we simply set A1 = −Ψ(q)A_j,t. For the upper end we look at the asset grid for the respective household and

identify the highest asset level A0

max a solution is stored for. Then we set An such that it is

impossible for the household to save A0 > A0_max. In the same fashion as in the endogenous grid method we now graze the asset regions described in figure (23) as follows, given an asset level Ai from GA:

(i) Check whether we are in the region where agents choose not to work (see regions in Figure 23.a and an analytic description in Section B.5.2):

Given assets and labor ` = 0 we know X = Rn

tA+ (1 − τss)wt, j,qγη and net wage wn_{t, j,q}γη =

(1 − τss) wt, j,qγη. In contrast to the endogenous grid method we do not know A0and in turn

V0

X0(·), so we need to balance equation (72) with a solver. However, each consumption

level C pins down savings via A0 = X − (1 + τc)C − (1 − τss)wt, j,qγη. As we know that

the consumption level balancing (72) has to be between C =  and ¯C = X82_{, we hand this}

bracket over the solver and receive C(` = 0) as well as A0(` = 0). Next, we compute µ`

via (73).

(a) If µ` > 0 optimal labor is ` = 0:

i. If savings A0 = X − (1 + τc)C − (1 − τss)wt, j,qγη ≥ −Ψ(q)A_j,t we have found a

valid solution and can compute VX following (75).

ii. Else the household is borrowing constraint. The solution is found via the intra- temporal Euler equation as described in Section B.5.3.

(b) Else proceed to next step.

(ii) Check whether we are in the region where agents choose ` ∈0, ¯` = Zt (1−0.5τss)wt, j,qγη

i

(Figure 23.b):

Given net wage wn_{t, j,q} = (1 − τss) wt, j,qγη, would the solution for optimal leisure imply

82_{This is due to the Inada Condition. In case lim}

C→0∂u(C,1−`)_∂C = ∞ and (72) has to be larger than zero. On the

contrary, if C = X we not only have a small marginal utility of consumption today, it also minimizes potential savings and thereby drives up V0

`∗ <sub>∈</sub> <sub>0, ¯`</sub>i_{? Given we are searching for an interior solution, we know that the intra-}

temporal Euler equation (87) between consumption and leisure has to hold. So we can (i)guess a consumption level C and (ii) back out the corresponding leisure level via the intra-temporal Euler equation. With consumption and leisure we (iii) also know savings A0 = X − (1 + τ

c)C − (1 − τss)wt, j,qγη(1 − `) and (iv) are able to compute X0 as well

as (v) the right hand side of equation (72) in order to verify our choice of C. Again, given that optimal consumption has to be between C =  and ¯C = X, we let a solver perform steps (i)-(v) in this interval until it found optimal consumption and leisure given wn

t, j,q = (1 − τss) wt, j,qγη.

(a) If ` < ¯` then

i. If savings A0 _{= X − (1 + τ}

c)C − (1 − τss)wt, j,qγη(1 − `) ≥ −Ψ(q)A_j,t we have

found a valid solution and can compute VX following (75).

ii. Else the household is borrowing constraint. The solution is found via the intra- temporal Euler equation as described in Section B.5.3.

(b) Else proceed to next step.

(iii) Check whether agent is at the border of being a (labor-) taxpayer (Figure 23.c): Set `= ¯` = Zt

(1−0.5τss)wt, j,qγη and compute optimal C from (72) as described in step (i) under

` = 0. Plug C and (1− ¯`) in (73) in order to compute µ`. Note that increasing ` implies be-

coming a taxpayer, so we need to compute µ`with wnt, j,q = 1 − τss−τ`,t(1 − 0.5τss)
wt, j,qγη.

(a) If µ` > 0 the agent would prefer to work less given this wage. But as we ruled out

` < ¯` in the previous step, we found a solution in ` = ¯`. Once more we perform the following check:

i. If savings A0 = X − (1 + τ

c)C − (1 − τss)wt, j,qγη(1 − ¯`) ≥ −Ψ(q)A_j,t we have

found a valid solution and can compute VX following (75).

ii. Else the household is borrowing constraint. The solution is found via the intra- temporal Euler equation as described in Section B.5.3.

(b) Else proceed to next step.

(iv) After eliminating all other possibilities, it has to be the interior solution with T (Yt), τ`,t > 0

(Figure 23.d):

The solution method is identical to the one in step (ii) under ` ∈ 0, ¯`i, with the difference being that now labor taxes have to be taken into account. Thus, we solve for optimal con- sumption, leisure and savings under net wage wn

t, j,q = 1 − τss−τ`,t(1 − 0.5τss)
wt, j,qγη

as described above.

(a) If savings A0= X − (1 + τc)C − (1 − τss)wt, j,qγη(1 − `) ≥ −Ψ(q)A_j,t we have found a

valid solution and can compute VX following (75).

(b) Else the household is borrowing constraint. The solution is found via the intra- temporal Euler equation as described in Section B.5.3.

Note that ` ≥ 1 can be excluded (for borrowing unconstraint households) via Inada Con- ditions, in particular lim`→1∂u(C,1−`)<sub>∂(1−`)</sub> = ∞.