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The stock of technology in each country evolves over time from t-1 to t as follows, given the initial condition of the stock of knowledge T. In the n countries case for each country j we will have:

(4) T t j = T t - 1 j + P a t i j w i t h i = 1 , n

Where the first subscript of Pat indicates the sender country and the second subscript the recipient country. In (4) the process starts at t-1 while Patii indicates the domestic accumulation of patents and Patij indicates the amount of technology produced in country i that is actually received by country j.

Technology accumulation in each country can be disaggregated in the following elements: technology accumulated domestically and the amount of technology accumulated in each of the other countries that is transferred to the recipient country through diffusion. In addition we consider transfer of technology generated in the “rest of the world”, e.g. in the United States. F o r e a c h c o u n t r y w e s p e c i f y a d o m e s t i c t e c h n o l o g y a c c u m u l a t i o n c o m p o n e n t ( P a t i i ) a n d a n i m p o r t e d t e c h n o l o g y c o m p o n e n t f r o m e a c h o f t h e o t h e r c o u n t r i e s c o n s i d e r e d ( P a t i j ) i n c l u technology imported from the “rest of the world”. The impact of technology diffusion depends on distance as well as on the sending and receiving countries’ human capital. As mentioned, while distance affects diffusion negatively, the impact of distance decreases over time (t) if technological progress and/or integration decrease the costs of transferring technology. However, over time, the value of technology decreases with obsolescence. So over time the impact of diffusion increases if the first effect prevails. We consider these two effects by separating the overall impact of distance into two components, a fixed component (coefficient d i n g

a ) a n d a t i m e - v a r y i n g c o m p o n e n t ( c o e f f i c i e n t b ) w h i l e t h e c o e f f i c i e n t i j 1 β c a p t u r e s t h e o v e r a l l

impact of technology transfer (net of the impact of human capital) which may include elements additional to “distance” 8

In the n country case, we have n×(n+1) equations to describe technology accumulation, where the last (n+1) equations represent the technology transfer from the rest of the world to the n countries of interest. In the estimation analysis we consider as the rest of the world the United States and Japan. In particular for each country j (with j=1,…n) we will have: Technology

(5)

( ) + + + = = ) ( l o g l o g l o g l o g 2 1 0 d i s t b t a P a t P a t P a t P a t D i j i j i j i j d i j i j d i j i j i j β β β β

+ l o g 3 H K i j s h i β

+ l o g 3 S i j s m h j β

+ + l o g l o g l o g 5 4 H K R Y S j i j j i j m j β β

8

Such as cultural or linguistic factors, as discussed in Peri (2004).

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