maintain countries in the trap. On the other hand, countries enjoying constant technological improvement fall in the area of higher equilibrium (top right quadrant) within the vicinity of the global technology frontier (Point A).

The consistent increase in income and technological endowment of countries in the higher equilibrium set is illustrated by a shift towards the global technology frontier in panel II. Since the poverty and technology trap hypothesis assumes the existence of self-reinforcing mechanisms which cause countries to remain poor on the technology ladder and welfare score, _B B_ Δ _tYt_ ≡ 0 because Δ _tTt_ = 0 (no technology jump in a low-technology trap).

_A A A_ On the other hand, technology jump ( δ _tn_ ( _T_ ) = δ _t_ 0 ( _T_ ) + Δ _t_ δ _t_ ( _T_ )) leads to increase aggregate _A A_ output in the higher equilibrium set ( Δ _tYt_ ( • | _T_ ) > 0 and Δ _tTt_ > 0) . Assuming that the more technological endowed country A is setting the pace of technological advances at the global level, the point A is located on the global technology frontier; while the point B falls in the first quadrant of dual traps.

The frontier is shown as being curve inwards (increasing returns to scale assumption) intersecting the 45 degree line in the fourth quadrant (panel I). At time<sup>_t_</sup> 0 , the technology gap between countries A and B in the _x-axis_ is mirrored by the output gap on the _y-axis_ . The rightward shift on the global technology frontier in the second Panel is the result of technology jump in country

> A ( Δ _t_<sup>δ</sup> _tA_ ( _T_ ) > 0) . Under the technology trap assumption there is no technology jump in country _B_ B ( Δ _t_<sup>δ</sup> _t_ ( _T_ ) = 0) . The widening technology gap between the two countries (illustrated by the increasing distance from the global technology frontier along the 45 degree line) leads to increasing productivity and output gap between the two countries.

r Now suppose that the initial random matrix _X_ of dimension ( _n_ , _p_ ) is reduced to a vector of nr _T_ rows and 2 columns; that is _X_ = ( _x_ 1, _x_ 2 ) , following the construction of a composite index summarizing technology endowment and knowledge. The focus of the analysis is to assess the degree of co-variation between technological progress and income growth. Suppose that the first vector<sup>_x_</sup> 1 represents the Knowledge Economy Index (KEI), proxy for technological endowment, and<sup>_x_</sup> 2 the distribution of Purchasing Power Parity-adjusted per capita income following a logarithmic transformation, both of which are deviated from their mean. The KEI is an aggregate and composite index representing the overall level of development of a country and its progress towards the knowledge economy. 24

> 24 The Knowledge Economy Index is produced by the World Bank for cross-countries comparisons on the scale of knowledge and economic development. This index is constructed from the normalized performance scores of a country averaged across four criteria: economic incentives and institutional framework, human resource development and knowledge accumulation, innovation system, information and communication technology and scientific infrastructures. The development and adoption of this composite index which has become very popular is the resultant of increasing emphasis on the contribution of knowledge, research and development for long-run growth over the past few decades [World Bank (2007)].

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