Exceptional Argentina Di Tella, Glaeser and Llach - Thomas Piketty

ρ
1/
1
ρ ρ
1
( ξ ξ ) 1
TT
K , aK
A
A +
ρ
1/
2
ρ ρ
2
( ξ ξ ) 2
LLM
K , mK
M
M +
where A and M are productivity parameters,
i
s
i are the elasticity of substitution. Notice that:
∈{ 1,2}
0
ρ Case Elasticity of
i
Substitution
− ∞ Leontieff:
Perfect
complements
0
1
Cobb-Douglas
1 Perfect
substitutes
∞
'
−
ξ are share parameters and ( 1−
) 1
ρ for
i
The production function for services is still: Y
N
= NLN
, where N is a productivity parameter.
Consumer's preferences are represented by:
ρ
d
ρ
d
ρ 1/ ρ
d
( φ c
) d
1 A
+ φ2cM
+ (1−φ1
−φ2)
cN
We are interested in the effect of the exogenous variables (Tˆ , Kˆ , Lˆ , Â , Mˆ , Nˆ , where
T ˆ = dT/
T ) on the capital and labor employment share: λˆ and κˆ . The following table shows the
sign of these effects as a function of the elasticity of substitutions ρ
1
, ρ
2
and ρ
d
. For instance,
the first row shows that the effect of an increase in the amount of land, Tˆ , on κ (i.e., d / ˆκ dTˆ
) has
the same sign as ρ 1
− ρd
, whereas the effect on λ (i.e. d / ˆλ dTˆ
) has the same sign as
− ( ρ2 − ρd )( ρ1
− ρ d
). The next rows show the sign of the effect for the other 5 exogenous
variables.
dT
ˆ
d κˆ
d λˆ
ρ 1
− ρd
− ρ2
− ρ ρ1
ρd
− ρ
ρd − ρ ρ2
− ρd
ρ
ρ − ρ d
ρ
dK
ˆ (footnote)
2
dL
ˆ 2
dA
ˆ
d
2
dM
ˆ
( )( − )
− ( ) d
ρ
d
dN
ˆ ( ρ − ρ d
) ρ d
ρ
d
− ρ
2 d
d
ρ d