
10 
with i=1,… n
(6)
⎪ ⎨ l o g P a t DlogPat_{USj }d U S j
( = l o g P a t d U S j U S j β
−logPat_{USj})
= 0 U S j β
+ 1 U S j β
+ + ) ( 2 d i s t b t a U S j U S j β
+ l o g 3 H K U S j s h U S β
+ l o g 3 S U S j s m h j β
+ l o g 4 S U S j m j β
l o g Y j
+ 5 U S j β
l o g H K j
In each of the n countries the stock of technology is then given by
( 7 ) d t P a t P a t P a t P a t P a t T T u s j n j j j t j j j ) . . . ( 3 2 0 1 0 + + + + + + = ∫
To summarize, for each country j, the following are the endogenous and exogenous variables. Endogenous
Y j , P a t i j , P a t U S j , , T j , , S h j , S m j
Exogenous
H K i , H K R j , S T R j , I C T j , R E G j , d i s t i j , L j , K j , t
with i, j =1,..n
It is worth noting that having assigned some variables as exogenous does not require that they assume specific rates of growth for the study of the steadystate proprieties of the model as shown in the Appendix.
The model is a set of non linear differential equations for each country. The degree of the system is one. Eqs (7) define the domestic stock of technology in each country as the cumulated flow of patents obtained both through production and diffusion. Note that such equations may be written in differential form:
u s j n j j j j j P a t P a t P a t P a t P a t D T + + + + + = . . . 3 2 1
T h e n o n l i n e a r i t y o f t h e s y s t e m i s i n t r o d u c e d t h r o u g h t h e s e e q u a t i o n s a s P a t i j a n d T j a r e n o necessarily expressed in logs. Country fixed effects are not shown for sake of simplicity but they are included in each equation of the model replacing, as usual, the constant term with as many constants as the number of countries. t
Additional constraints have to be introduced on distance, expressed in kilometers:
( 8 ) d i s t j j = 0