Distance to the Frontier: How and When should the countries reduce the gap?

1. Distance to the Frontier: How and When should the countries reduce the gap? Bruno Cruz Université Catholique de Louvain IRES – Institut de Recherches Économiques et Sociales The objective of this paper is to study: how should one design the policies for developing countries regarding the optimal adoption of new technologies? When should they incur in a massive effort to adopt new technologies? Supposing that the government can affect the amount to be learned by the developing countries, which is the optimal time to switch to an intensive regime of adoption of new technologies? Furthermore, is it possible to determine which is the optimal amount of capital necessary to switch to the intensive adoption regime.

2. Introduction • David (1975) argues that it was the connection of a national network that foster the adoption of new technologies in the US and contributed to explaining US growth in the nineteenth century. • David and Wright(1995) compare the adoption of Dynamo, a so-called general propose technology (GPT), in US and Britain.

3. Introduction • Networks can indeed help the reduction in the amount to be learned. In 2000, a network financed by a public agency decode a the genetic code of a pathogen. “It was the first time that a free-living plant pathogen had been sequenced anywhere, a breakthrough for southern-hemisphere science.” [The Economist(2001)]

4. Introduction

5. Introduction • The Global Information Technology Report 2003-04 (World Economic Forum): • There is a threshold to Readiness: a country needs to have a certain level of Readiness with regards to ICT before there can be an effective usage of ICT, and a consequent impact.

6. Introduction • Golder and Tellis (1997): non-smooth diffusion of durabale goods • The main point: • The marginal impact of infrastructure or the set-up of network is increasing and discontinuous.

7. Introduction • Supposing the government can set-up the infrastruture, the expenditure will just have a significant impact above a certain threshold level.

8. “There was no point in giving people computers when they had no electricity” Ted Turner, the Economist (2001) • The propose of this paper is tackle this point. One can state the question as: • Should a developing country invest in reduction of the technological divide, or should it accumulate capital and then try to invest?

9. Model The Production Function is defined as: Where: A* is the aumont to be learned l speed of learning

10. Model • The A* aumont to be learned is defined as: G is the public spendings. q is a parameter to capture the complexity of the technology The function F(g) is defined to fit with the empirical fact that the marginal impact on the learning is increasing and discountinous.

11. Model The function F(g) is continous, but not smooth:

13. The problem is defined as:

14. The Case of a Poor Country • K<G1 for sure the country starts in regime I • G=0 for all t, not optimal. • Is the switching time finite? So, the economy goes to regime II. • If so, how does the control variable G behaves? • Finally, once we are in regime II, do the economy go back to regime I, or even to G=0? .