Diaspora remittances finance and economic development

Munich Personal RePEc Archive

Diaspora remittances finance and economic development

Jellal, Mohamed

Al Makrîzi Institut D’économie, Rabat , Morocco

18 July 2014

Online at https://mpra.ub.uni-muenchen.de/57410/

MPRA Paper No. 57410, posted 18 Jul 2014 23:48 UTC

𝐴𝐾(𝑡)

𝐾 𝑡 + 1 = 𝐼 𝑡 + 1 − 𝛿 𝐾 𝑡

𝐾(𝑡) 𝑡 𝛿 𝐼(𝑡)

1− ∅

∅

∅

𝑆(𝑡)

𝐼 𝑡 = ∅.𝑆(𝑡)

𝑌 𝑡 = 𝐴𝐾(𝑡

𝑠 𝑡 = ^𝑆(𝑡)

𝐴𝐾(𝑡)

g(t) = ^{K t+1 −K(t)}

K(t) = ^{I t + 1−δ K t −K(t)}

K(t)

𝑔 𝑡 = ^{∅𝑆 𝑡}

𝐾 𝑡 − 𝛿 = 𝐴∅𝑠 𝑡 − 𝛿

𝐴,∅,𝑒𝑡 𝑠 𝑡

𝐴

∅.

𝑔(𝑡) = 𝐴∅𝑠 𝑡 − 𝛿

𝜕 𝑔(𝑡)

𝜕∅𝜕𝑠(𝑡) = 𝐴 > 0

𝐼 𝑡 = ²_𝑖=1𝐼(𝑡)_𝑖 = ²_𝑖=1∅_𝑖 𝑆(𝑡)_𝑖

𝑡 = ^{𝑖 ∅𝑖}

𝑖=2=1 𝑆 𝑡 _𝑖

𝐾 𝑡 − 𝛿 = 𝐴. ^𝑖_𝑖⁼²₌₁∅_𝑖𝑠(𝑡)_𝑖 − 𝛿

𝑔 𝑡 = ^𝐼(𝑡)

𝐾 𝑡 − 𝛿 = ^{𝐼(𝑡)𝑖}

2𝑖=1

𝐾 𝑡 − 𝛿 = 𝐴. ^𝑖_𝑖⁼²₌₁∅_𝑖𝑠(𝑡)_𝑖 − 𝛿

0 < 𝑚 < 1

𝑛

𝑈 𝑛 = 𝜋 − 1 +𝜌 𝑟𝐼

𝜋 𝐼

𝑟 𝜌

𝑚 𝑀

𝑈 𝑚 = 𝜋 − 1 + 𝜌 𝑟(𝐼 − 𝑀)

𝑟.𝑀

𝜋 = 𝐻. 1 +𝑠𝐼(𝑡 − 1) +𝜖 𝐻

𝑠 > 0 𝐼(𝑡 −1)

𝜖

𝜖) = − ,

𝑈 𝑛 = 𝜋 − 1 +𝜌 𝑟𝐼 > 0

𝐻 1 +𝑠𝐼(𝑡 −1) +𝜖 > 1 +𝜌 𝑟𝐼

𝜖 > 1 + 𝜌 𝑟𝐼 − 𝐻(1 +𝑠𝐼 𝑡 − 1 )

𝑃 𝑛 = 𝑃𝑟𝑜𝑏 𝑖𝑛𝑣𝑒𝑠𝑡𝑖𝑠𝑠𝑒𝑚𝑒𝑛𝑡

= 𝑃𝑟𝑜𝑏 𝜖 > 1 + 𝜌 𝑟𝐼 − 𝐻 1 + 𝑠𝐼 𝑡 −1 = 1 − 𝐺(𝜖 )

1 +𝜌 𝑟𝐼 − 𝐻 1 +𝑠𝐼 𝑡 −1 𝜖 (𝑛)

1 + 𝜌 𝑟𝐼

𝐻 1 + 𝑠𝐼 𝑡 −1

𝐼 𝑛,𝑡 = 1 − 𝑚 . [1− 𝐺( 1 +𝜌 𝑟𝐼 − 𝐻 1 +𝑠𝐼 𝑡 −1 ]

𝜕𝐼 𝑛,𝑡

𝜕𝜌 = − 1− 𝑚 𝑔 . 𝑟𝐼 < 0

𝜕𝐼 𝑛,𝑡

𝜕𝐻 = 1− 𝑚 𝑔 . 1 + 𝑠𝐼 𝑡 −1 > 0

𝜕𝐼 𝑛,𝑡

𝜕𝐼(𝑡−1) = 1 − 𝑚 𝑔 . 𝐻𝑠 > 0

𝜕𝐼 𝑛,𝑡

𝜕𝜌 = − 1 − 𝑚 𝑔 . 𝑟.𝐼 < 0

𝜕𝐼 𝑛,𝑡

𝜕𝐻 = 1 − 𝑚 𝑔 . 1 + 𝑠𝐼 𝑡 −1 > 0

𝜕𝐼 𝑛,𝑡

𝜕𝐼(𝑡 −1) = 1− 𝑚 𝑔 . 𝐻𝑠 > 0

𝐻

𝑈 𝑚 = 𝜋 − 1 +𝜌 𝑟(𝐼 − 𝑀) > 𝑟𝑀

𝐻 1 +𝑠𝐼(𝑡 − 1) +𝜖 > 1 +𝜌 𝑟 𝐼 − 𝑀 +𝑟𝑀

𝜖 > 1 +𝜌 𝑟𝐼 − 𝜌𝑟𝑀 − 𝐻(1 +𝑠𝐼 𝑡 − 1 = 𝜖 (𝑚)

𝜖 (𝑚)

𝜖 𝑛 = 1 +𝜌 𝑟𝐼 − 𝐻 1 +𝑠𝐼 𝑡 − 1

𝑃 𝑚 = 𝑃𝑟𝑜𝑏 𝑖𝑛𝑣𝑒𝑠𝑡𝑖𝑠𝑠𝑒𝑚𝑒𝑛𝑡

= 1− 𝐺( 1 +𝜌 𝑟𝐼 − 𝜌𝑟𝑀 − 𝐻 1 + 𝑠𝐼 𝑡 −1

𝑃 𝑚 > 𝑃(𝑛)

𝜖 (𝑚) < 𝜖 (𝑛)

𝑃 𝑚 = 1− 𝐺(𝜖 𝑚 ) > 𝑃 𝑚 = 1− 𝐺(𝜖 𝑛

𝐼 𝑚,𝑡 = 𝑚. [1− 𝐺( 1 +𝜌 𝑟𝐼 − 𝜌𝑟𝑀 − 𝐻 1 + 𝑠𝐼 𝑡 −1 ]

𝜌 𝜃 𝜌(𝜃)

𝜌^′ 𝜃 < 0.

𝐼(𝑚,𝑡,𝜃) = 𝑚. [1− 𝐺( 1 + 𝜌 𝜃 𝑟𝐼 − 𝜌(𝜃)𝑟𝑀 − 𝐻 1 + 𝑠𝐼 𝑡 −1

𝜕𝐼 𝑛,𝑡

𝜕𝜃 = −𝑚𝑔 . 𝑟(𝐼 − 𝑀)𝜌^′ 𝜃 > 0

𝜕𝐼 𝑛,𝑡

𝜕𝐻 = 𝑚𝑔 . 1 + 𝑠𝐼 𝑡 −1 > 0 ^{𝜕𝐼 𝑛,𝑡}

𝜕𝐼(𝑡−1) = 𝑚𝑔 . 𝐻𝑠 > 0

𝜕𝐼 𝑛,𝑡

𝜕𝑀 = 𝑚𝑔 . 𝑟𝜌 𝜃 > 0

𝑆𝑖𝑔𝑛𝑒 ^𝜕_{𝜕𝜃𝜕𝑀}^{2𝐼 𝑛,𝑡} = 𝑆𝑖𝑔𝑛𝑒 𝑚𝑔 . 𝑟𝜌^′ 𝜃 < 0

𝜃 𝑀

𝐼 𝑡 = 1 − 𝑚 . [1− 𝐺 1 +𝜌 𝑟𝐼 − 𝐻 1 + 𝑠𝐼 𝑡 − 1 +𝑚. [1

− 𝐺( 1 +𝜌 𝜃 𝑟𝐼 − 𝜌(𝜃)𝑟𝑀 − 𝐻 1 +𝑠𝐼 𝑡 − 1

𝐼 𝑡 = 1 − 𝑚 𝐼(𝑛,𝑡,𝜃) +𝑚𝐼 𝑚,𝑡,𝜃

𝐵 ≥ 0

1 +𝜌(𝜃) + 𝜏 𝑟(𝐼 − 𝑀) 𝜏 ≥ 0

𝑈 𝑛 = 𝜋 − 1 + 𝜌 𝑟𝐼 − 𝐵 > 0

𝐻 1 +𝑠𝐼(𝑡 − 1) + 𝜖 > 1 +𝜌 𝑟𝐼 + 𝐵

𝜖 > 1 +𝜌 𝑟𝐼 − 𝐻 1 +𝑠𝐼 𝑡 − 1 + 𝐵

𝑃 𝑛 = 𝑃𝑟𝑜𝑏 𝑖𝑛𝑣𝑒𝑠𝑡𝑖𝑠𝑠𝑒𝑚𝑒𝑛𝑡

= 𝑃𝑟𝑜𝑏 𝜖 > 1 +𝜌 𝑟𝐼 + 𝐵 − 𝐻 1 +𝑠𝐼 𝑡 −1

= 1− 𝐺(𝜖 (𝑛,𝐵)

1 +𝜌 𝑟𝐼 +𝐵 − 𝐻 1 +𝑠𝐼 𝑡 −1 𝜖 (𝑛,𝐵)

𝐼 𝑛,𝐵,𝑡 = 1− 𝑚 . [1− 𝐺( 1 +𝜌 𝑟𝐼 +𝐵 − 𝐻 1 + 𝑠𝐼 𝑡 −1 ]

𝜕𝐼 𝑛,𝑡

𝜕𝐵 = − 1− 𝑚 .𝑔 . < 0

𝐼 𝑚,𝐵,𝑡 = 𝑚. [1− 𝐺( 1 +𝜌+𝜏 𝑟𝐼 − (𝜌+𝜏)𝑟𝑀 +𝐵

− 𝐻 1 + 𝑠𝐼 𝑡 −1 ]

𝜕𝐼 𝑚,𝐵,𝑡

𝜕𝐵 = −𝑚.𝑔 . < 0

𝜕𝐼 𝑚,𝐵,𝑡

𝜕𝜏 = −𝑚𝑔 . 𝑟(𝐼 − 𝑀) < 0

𝜏 = 𝜌_𝐼−𝑀^𝑀

1 +𝜌+𝜏 𝑟𝐼 − 𝜌 +𝜏 𝑟𝑀 +𝐵 − 𝐻(1 +𝑠𝐼 𝑡 −1 = 𝜖 (𝑚,𝐵,𝜏)

1 +𝜌 𝑟𝐼 +𝐵 − 𝐻(1 +𝑠𝐼 𝑡 − 1 = 𝜖 (𝑛,𝐵)

𝜖 (𝑚,𝐵,𝜏) ≤ 𝜖 (𝑛,𝐵)

𝜏 ≤ 𝜏 = 𝜌_𝐼−𝑀^𝑀

𝐼 𝑡 = 1 − 𝑚 . [1− 𝐺 1 +𝜌 𝑟𝐼 +𝐵 − 𝐻 1 + 𝑠𝐼 𝑡 − 1 + 𝑚. [1− 𝐺( 1 +𝜌 𝜃 + 𝜏 𝑟𝐼 − 𝜌 𝜃 + 𝜏 𝑟𝑀 +𝐵 − 𝐻 1 + 𝑠𝐼 𝑡 − 1

- - - - - -

- -

𝐼_𝑡 = 𝐼_𝑡−1,

𝜖

𝜖) = − ,

1 +𝜌 𝑟𝐼 +𝐵 − 𝐻(1 + 𝑠𝐼 𝑡 − 1 = 𝜖 (𝑛,𝐵) 1 + 𝜌+𝜏 𝑟𝐼 − 𝜌 +𝜏 𝑟𝑀 +𝐵 − 𝐻(1 +𝑠𝐼 𝑡 − 1 = 𝜖 (𝑚,𝐵,𝜏)

𝐼 𝑡 = 1 − 𝑚 . [1− 𝐺 𝜖 (𝑛,𝐵) + 𝑚. [1− 𝐺( 𝜖 (𝑚,𝐵,𝜏)

𝐼 𝑡 = 1 − 𝑚 . [¹

2− ₂¹_∆ 𝜖 (𝑛,𝐵) +𝑚. [¹

2− ₂¹_∆ 𝜖 (𝑚,𝐵,𝜏)

𝑡 =.¹

2−₂¹_∆[(1− 𝑚) 𝜖 𝑛,𝐵 +𝑚𝜖 (𝑚,𝐵,𝜏)

lim⁡𝐼 𝑡 = 1 2− 1

2∆[ 1− 𝑚 𝜖 𝑛,𝐵 +𝑚𝜖 𝑚,𝐵,𝜏 = 1/2 ⟺

→

𝜖 (𝑛,𝐵) 𝜖 (𝑚,𝐵,𝜏)

𝐼 𝑡 = ¹

2 −₂¹_∆ 1 +𝜌 𝑟𝐼 +𝐵 − 𝐻 − 𝑚 𝜌 +𝜏 𝑟𝑀 + ¹

2∆𝑠𝐻𝐼(𝑡 −1)

𝐼_𝑡 = 𝐼_𝑡−1,

1

2 −₂¹_∆ 1 +𝜌 𝑟𝐼 +𝐵 − 𝐻 − 𝑚 𝜌 +𝜏 𝑟𝑀 =

𝐼 𝑡 = + ¹

2∆𝑠𝐻𝐼(𝑡 − 1)

𝜕𝐼(𝑡)

𝜕(𝑚𝑀) = 1

2∆ 𝜌 + 𝜏 𝑟 > 0

1

2∆𝑠𝐻 < 1

𝜕𝐼(𝑡)

𝜕𝐼(𝑡−1) = ¹

2∆𝑠𝐻 < 1

𝑠𝐻 < 2∆

I = 1

(2∆ −sH) ∆ − 1 + ρ rI− B + H + m ρ+τ rM )

𝐼 𝑡 = + 1

2∆𝑠𝐻𝐼(𝑡 − 1)

𝐼 𝑡 = 𝐼 𝑡 − 1 = 𝐼 ∀𝑡 𝐼 = + ¹

2∆𝑠𝐻𝐼 𝐼 = 1

(1 − 1

2∆ 𝑠𝐻)

𝜕𝐼

𝜕𝐵 < 0

𝜕𝐼

𝜕𝐻 > 0

𝜕𝐼

𝜕𝑠 > 0

−^𝜕𝐼 _𝜕𝜌 > 0

𝜕𝐼

𝜕𝑀 > 0

𝜕𝐼

𝜕𝑚 > 0

−^𝜕_{𝜕𝑀𝜕𝜌}^𝐼 < 0

= 2,23 + 0,062. R + 0,008. F −0,002. RF + 0,03. HK + 0,034. INST + 0,015. INFRAS

“

”

“ ”

”

”

“

”

”

”

“

”

“

… ”

“

”

“

”

”

“

”

“

”

“

”

“

”

“

”

“

”

“

”

“ ”

“

”

“ ”

“

“

”

”

“ ”