The Dynamic Cost of the Draft

cannot exceed the present value of lifetime wage income:

59                                   59

∑(1⅛“(1 - ^τ'>∙'<∙' ≥∑ (1⅛             (5)

t=0 ^{v       !}                       t=0 ^{v !}

where w is the marginal productivity of labor services, and τ' is the tax rate on
wage income. Therefore, w(1 — τ') is the return to labor services after tax. The
price of the consumption good is chosen as numéraire and normalized at unity.
Each individual maximizes the present value of lifetime utility, U, subject to the
time endowment constraint, the law of motion with respect to human capital,
and the intertemporal budget constraint.

2.2 Conscription

Having established the intertemporal maximization problem for each individual,
we next describe how the draft system is introduced in the model. We assume
that conscripts are forced to spend available time in the first period of the life
cycle on work, i.e. q_c∙₀ = e. Wage income during conscription can be subject to
supplementary taxation, and the intertemporal budget constraint for conscripts
changes to:

59      ₁                                                  59      ₁

X (1+7)7^{w(1 — τ}') ∙ ^l<∙t^{— τ} ∙ ^{w(1 — τ}') ∙ ^lc∙0 ≥ X (1+7)7 ∙ <W’     ⁽⁶⁾

t=0 `` '                                                                        t=0 '` ' '

where τ is the supplementary tax rate on wage income during conscription. Since
w(1 — τ') is the return to labor services after tax, τ = 0 corresponds to a situation
where conscripts receive the market value of labor (net of income taxes), whereas
τ = 1 corresponds to a situation where conscripts receive no pay. The true value
of τ is di∏icull to estimate; it furthermore varies with family and educational
status.⁹

The use of time is constrained to work in the first period of the life cycle
for conscripts, and the extra payments from conscripts do not further distort
the allocation of time. However, the extra payment reduces private saving by
conscripts since private consumption is determined by lifetime income and follows
an exponential pattern over the life cycle, where the consumption growth rate
is determined by the Euler condition (the difference between the real interest
rate and the rate of time preference divided by the intertemporal elasticity of
substitution).

The intertemporal budget constraint for non-conscripts is:

59                                    59

Σ (T⅛w(1 — τ') ∙ l_at ≥ ∑ ʌ ∙ ..         (7)

⁹ Schleicher (1996) estimates that net income foregone for an average German conscript in
1993 was 2.4 times the pay during conscription — which implies that τ = 2.4/3.4 = 0.7.

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