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APPENDIX

( 4 1 ) t P a t P a t P a t P a t T T 3 2 2 2 0 1 2 * 2 2 ( + + + + =

US 2 )dt =

Pat µ pat 2 * .2

e

µPat

2t

( 4 2 ) t P a t P a t P a t P a t T T 3 3 2 3 0 1 3 * 3 3 ( + + + + =

US3 )dt =

Pat µ pat 3 * .3

e

µPat

3t

( 4 3 ) * 3 1 * 2 1 * 1 1 P a t P a t P a t P a t + + +

* US1

= Pat

* .1

( 4 4 ) * 3 2 * 2 2 * 1 2 P a t P a t P a t P a t + + +

* US 2

= Pat

* .2

( 4 5 ) * 3 3 * 2 3 * 1 3 P a t P a t P a t P a t + + +

* US 3

= Pat

* .3

(46)T * =

1

* .1

Pat µ pat

1

* 2

(47)T =

* .2

Pat µ pat

2

* 3

(48)T =

* .3

Pat µ pat

3

We now solve the system for the rates of growth and initial levels for the endogenous variables. We consider only the solution for country 1 which can be easily replicated for the remaining countries.

The following system, based on the undetermined coefficient method, is derived by imposing the condition that the condition of the steady-state in the model is identically satisfied in each moment of time i.e, the constant terms and time coefficients are constrained to be zero in each equation:

Output

l o g l (49) o g 1 2 1 * 1 1 1 1 1 0 1 + + h S T α α α α α α

* sh1

l o g 1 2 1 + m S α α

* sm1

0 l o g l o g l o g 1 * 1 1 * 1 1 4 1 * 1 1 3 1 = + + + y Y L K µ α α α α α

( 5 0 ) 1 1 2 1 1 1 1 1 + S h h p µ α α µ α α

1 1 2 1 + S m m µ α α

0 1 1 1 1 4 1 1 1 3 1 = + + Y L K µ α ρ α α ρ α α

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