Workshop Modelli Dinamici in Economia e Finanza Urbino, September 25-26-27, 2008

Local populations in front of big external investors:

an opportunity or a risk?

Elisa Ticci (University of Florence)Angelo Antoci (University of Sassari)Paolo Russu (University of Sassari)

Presentation outline

Objective and literature references Presentation of the model Main results Concluding remarks

Overview of literature on foreign investments

Positive effects on host economies (Brems, 1970, De Mello 1997, Findlay 1978, Lall 1978; Blomstrom and Wang, 1992, Barrios et al. 2003): Increase in capital stock Positive externalities and spill-over effects Upstream and downstream links

Key conditions under which host economies are more likely to derive these benefits (Alfaro et al., 2004; Balasubramanyam et al. 1996, Blomstrom et al. 1994, Borenzstein et. al., 1998, Lim 2001).

Crowding-out of local firms in the same industry (Saltz 1992, Aitken and Harrison 1999, Konings 2001, Herzer et. al. 2005

Impact of FDI on inequality (Bonassi, Giovannetti and Ricchiuti 2006; Te Velde 2003, Benassy-Queré and Salins 2005)

Context

Small open economy. Production of two goods with exogenous price.

Two populations: Local agents (L-agents), external investors (I-agents).

Each population is constituted by a continuum of identical individuals and the size of each population is equal to 1.

I-agents• “Unlimited” physical capital (KI) : they will

continue to invest physical capital in the economy until capital return is higher than its cost.

• They employ local agents as wage workers (1- L)

• We denote their production as “external sector”. 1(1 )I IY K L

L-agents• They have to choose the distribution of their

labor between two activities: independent self-employment or wage work for the External Investors.

• Self-employment activities use three productive factors: free access renewable natural resources (E), labor (L), physical capital (KL).

• Local Agents can invest only their savings.

• Production function of the local sector(1 )

L LY K E L

Main result of the modelIn this context a decline in the opportunity cost of external

capital investment prompts a process of diversification in the local economy: expansion of the external sector, higher levels of physical capital and wage labor employment.

The impact on well-being of local population, however, is not always positive.

If the external sector is “relatively” much more polluting than the local sector, the utility of local agents declines.

The problem of the representative I-agent • The I-agents choose L and KI in order to maximize their

profits (πI):

ω = wage

r = interest rate

(1)

(2)

(1 )I I IY L rK

0 (1 ) (1 )IIK L

L

1 10 (1 )IIK L r

K

The problem of the representative L-agent

, ,0 0

max ( ) max (ln )L L

t tL L

L C L CU C e dt C e dt

s.t. (1 ) (1 )L L LK K E L L C

( ) L IE E E E Y Y

and average values of and L I L IY Y Y Y

ε and η = positive parameters measuring environmental impacts caused by production of L- and I-agents

carrying capacityE

The problem of the representative L-agent• Maximization of the continuous time current value

Hamiltonian function (H):

(3)

(4)( )0 (1 ) L

HK E L

L

10

L L

H

C C

(1 )ln (1 ) 0L L LH C K E L L C

• The fixed point value of L is obtained by optimality conditions (1)-(2)-(3)-(4) and by equilibrium condition in labor market (i.e. wages and labor allocation between the two sectors change until labor demand is equal labor supply):

(5)

(6)

(7)

( )(1 ) (1 ) (1 )L IK E L K L

1

LL K E

1

1

1

(1 ) / r

Possible regimes• By definition L≤1, then

(8)

• Therefore two cases are distinguished according to the equilibrium value of labor allocation– Case with specialization → L=1

– Case without specialization

1

1LL K E

1

min 1, LL K E

1

1LK E

Delimitation between the two regimes• In the plane (E,KL), fixed points without

specialization are below the straight line

while stationary points with full specialization will be above the straight line

where

LK

LK

1(1 ) /

(1 )

r

Complete specialization• Dynamics:

• In the plane (E ; KL) the condition is satisfied along the graph of the function f1(E), while the condition is satisfied along the graph of the function g1(E).

1

1

( )

( )

L L

L

L

K K E

E E E E K E

K E

0

0E

1/1

1

1

( ) /

( ) / ( )

L

L

f E K E

g E K E E E

Uncompleted specialization

• In the plane (E ; KL) the condition is satisfied along the graph of the function f(E), while the condition is satisfied along the graph of the function g(E).

1/ 1 1/1

1/1 1

1 1/

( ) (1 ) / 1 ( ) 1/

( ) / ( ) /

( )

L L L

L

L

L

K K E T r K E

E E E E r K E r

K E

K

0

0E

( )

( ) ( ) /

L

L

f E K E

g E K E E E

Fixed points• In the plane (E , KL), the intersections between

f1 (E) and g1 (E) which are above the straight line and the intersections between f(E) and g(E)

which are below the straight line identify the fixed points.

( )

( ) ( ) /

L

L

f E K E

g E K E E E

LK

1/1

1

1

( ) /

( ) / ( )

L

L

f E K E

g E K E E E

1(1 ) /

(1 )

r

Existence of fixed points

EA < EB< EA1 < EB1 (9)

The dynamic systems admit no more than four fixed points, A and B , A1 and B1

where

Stability of fixed points

• Numerical simulations show that no more than one reachable fixed point can exist.

• If one reachable fixed point exists, then it is the point associated with the highest level of E, namely B1 or, if B1 is not admissible (in this case neither A1 is admissible), B is the unique reachable stationary state.

Comparative statics

Given that the fixed points B and B1 are the unique reachable equilibria, comparative statistics investigate the impact of a change in parameters on stationary values of KL, KI, L, E and CL in these points.

In the paper we have studied the impact of a

change in carrying capacity and in parameters ε, η and r

Impact of a change in r• Negative relation between r and KI

• Positive relation between r and KL

• The consequences of changes in r on equilibrium value of natural capital and of L-agent's utility depend on the difference between the two sectors in terms of environmental impact

(10)

(11)

1

1

→ Positive relation between r and E

1

1

→ Negative relation between r and CL

1

1

AND η is sufficiently low (ε is sufficiently high)

→ negative relation between r and CL.

1

1

AND η is sufficiently high (ε is sufficiently low)

Positive relation between r and CL

Negative relation between r and CLMoreover there exist sufficiently high values of ε (or low values of η) and r so that an increase in r leads to a decrease in E.

1

1

Conclusions

• A reduction in r can be interpreted as a reduction in cost opportunity of external agents' decision to invest physical capital in the considered economy.

• This event is usually regarded as beneficial for economic growth and indirectly for poverty reduction.

• In all scenarios a decline in r leads to a labor ri-allocation towards the external sector and an expansion of this sector but…

Conclusions

• …the growth of external investments results in decrease in CL if the

external sector is much more polluting than local sector i.e.

• This economic transition leads to an increase in natural capital only

if the local sector is much more polluting than external sector i.e..

• Final caveats: no positive externalities, no backward and forward

linkages, local producers cannot employ wage labor.

1 is "sufficiently positive"

1

1 is "sufficiently negative"

1