Labour income taxation, child rearing policies and fertility
Luciano Fanti Luca Gori
University of Pisa University of Pisa
Abstract
We examine how subsidy policies to support child-rearing affect the fertility rate in a textbook general equilibrium overlapping generations model extended to account for endogenous fertility decisions of individuals. It is shown the counter-intuitive result that increasing the child grant may actually reduce the long-run fertility rate.
Citation: Fanti, Luciano and Luca Gori, (2007) "Labour income taxation, child rearing policies and fertility." Economics Bulletin, Vol. 10, No. 20 pp. 1-10
Submitted: December 2, 2007. Accepted: December 20, 2007.
! " # $%&&'( ) * $%&&+( , $%&&&( % -./) $0 123( +4 $ ( . 5 $ ( 6 - 7 ! % ! + / " 0 t $Nt( $cty( $ct+1o( $nt( ' ) 4 $ 112( - $wt( 4 m $ ( , 8 8 β∈
( )
0,m 0 $st( rt+1 - t " { }(
)
(
)
( )
( )
( )
t o t y t t o t y t t n c cty t o t U c c n c c n ln ln ln 1 , , max 1 1 , , +1 + = −φ +γ + +φ 9 %- , 5 $%&&&( 0 , $%&&&( +7 '9 t n nt −11
(
t) (
)
t t t t y t w m n r c c = −τ − −β + + + + 1 1 1 1 1 0<τt < 0<γ <1 1 0<φ < - " 1 1 1 1 + + ⋅ − = + t y t o t r c c γφ $:.; ((
β)
φ φ = − − m c nt ty 1 $:.;%( < $:.; ( < $:.;%( 9 t n m−β >0 = $:.; ( $:.;%( "(
)
β τ γ φ − − ⋅ + = m w n t t t 1 1 $ ((
t)
t t w s τ γ γ ⋅ − + = 1 1 $%( - -t " t t t w n τ β = $+( 4 7 $+( $ ( τt "(
γ)(
β)
φβ φ + − + = m w n t t 1 $'( 9 $%( $+( $'( "(
)
(
γ)(
β)
φβ β γ + − + − = m w m s t t 1 $3( - $ ( ; 0 Yt =AKtαLt1−α 3 t Y Kt t t N L = t A>0( )
0,1 ∈ α 5 0 kt :=Kt /Nt yt :=Yt/Nt α t t Ak y = " 31 1 − =α α− t t Ak r $2(
(
α)
α t t Ak w = 1− $>( ? Nt+1 =ntNt t t tk s n +1 = ! n s < $'( $3( "( )
(
β)
φ γ β = m− k* $@( < $@( $ β − m (( )
0 * > − = ∂ ∂ φ γ β β k 4 A -./) - "( )
[
]
{
β * * β}
* * ,w k n n = $1( < $1( β "2 − − + + + ∂ ∂ ⋅ ∂ ∂ ⋅ ∂ ∂ + ∂ ∂ = β β β * * * * * * * k k w w n n d dn $ &( < $ &( " $ ( $ ( $%( $ ( 7 $ ( ) $, : < ( w* - < $'( $>( $@( β "( )
(
(
γ)
)(
φ(
β)
φββ)
γ α φ β α + − + − − = m m A n 1 1 * $ ( " α α < - $ ( 0 = β " 203
( )
( )
[
(
)
]
(
φγ)
α γ γ ββ β = ⋅ + −+ − + ∂ ∂ = 1 1 1 0 * 0 * m n n $ %(( )
( )
< > ∂ ∂ < > ∂ ∂ = = α α β β α α β β β β iff n iff n 0 0 0 * 0 * $ +( γ φ γ α + − + ≡ 1 1 α α < *( )
β n β =β* α α > 0 < $ ( β "( )
( )
{
[
(
)
]
(
)(
)
}
(
γ βφ)(
[
α β)(
γ γβ)
φβα]
γ φ β ββ − − + + − + − − + − − + ⋅ = ∂ ∂ 1 1 1 1 1 * * m m m n n $ '( 7 α <α( )
n n β β ββ > < ⇔ < > ∂ ∂ 0 * $ 3((
)
[
]
(
γα)(
φ γα φ)
γ β − + − + − − + ≡ 1 1 1 1 m n > $ 2( 7 α >α( )
0 * < ∂ ∂ β β n m < <β 0 B 5 $ C ( B % $ C 5 ( n β β ≤ D ! -./) $0 123( - " $ ( 5 D $%( 5 >7 m n < β α φ γC " - " - " $ ( $%( $+( E F " 7 7 "
