Schumpeterian Growth Model And Convergence Theory Economics Essay

Schumpeterian Growth Model And Convergence Theory Economics Essay The Schumpeterian model, developed by Aghion and Howitt (1992) is an economic growth model that includes technological improvements, or innovation. This leads to the process of creative destruction where the advancement of new technologies renders the old obsolete. To give a theoretical example, colour mobile phones have replaced the old black and white ones in stores. Also the advancement of mobile phone technology could mean less need for wrist watches or cameras. This is based on the work pioneered by Joseph Schumpeter (1950) where innovators are the drivers of economic growth. He popularised the use of the term creative destruction or Schà ¶pferische Zerstà ¶rung. The efficiency frontier, used interchangeably with technological frontier, is based on growth with technological progress. It describes how technological implementation affects the growth rate of countries depending on their relative level of technological development. An industrialising country is far behind the frontier so has a large advantage by adopting the technologies of wealthier countries. As the economy moves closer to the frontier the effectiveness of this practise is abated. Hence policies that are effective in one economy could be detrimental in another depending on their level of industrialisation. This has implications on the theory on convergence. If a country is positively investing in RD they should be able to maintain economic growth. The way a country converges and if convergence is possible depends party on its comparative level of development and in part on its economic policies. Hence the Schumpeterian theory is that of club convergence. there are different lev els of convergences; a country moves towards the same frontier to that of his technological peers. This paper looks at the basic model of Schumpeterian growth and then applies it examine why growth rates differ across countries. The remainder of the paper is set out as follows: section 2 provides a brief literature review, section 3 presents the model. An application of the Schumpeterian model is looked at in section 4 where the effect of technological advancement is used to examine the technological frontier. Section 5 is an empirical testing of the model including the efficiency frontier is looked at in section 4. Section 6 looks at convergence due to technological advancement. and section 7 concludes and suggests areas for future research. Section 2: Literature review Majority of the work in this field has been undertaken by Aghion and Howitt. They developed the original model and have released a number of papers, together and corroborating with others, that expand the model. They have also done work on the technological frontier. Acemoglu has also published a prominent amount of literature in this field. Barro and Sala-i-Martin (2004) have provided a good algebraic model which is replicated in the next section. Jones (1995), Young (1998) and subsequently Dinopoulos and Thompson (1998) have developed neo-Schumpeterian models to remove scale affects. Empirical literature testing the accuracy of the model is rare, especially for countries outside the EU (excluding the USA). Most empirical literature discovered is testing other theories within the context of the Schumpeterian growth model. Zachariadis (2002) gives an overview of previous empirical literature and finds that most conform to the Schumpeterian model. He then does his own analysis and concurs that an increase in technological progress has a positively affects the growth rate of output. Teixeira and Vieira (2004) examine the relationship between productivity and human capital in Portugal. They find the pattern conforms to the Schumpeterian model of creative destruction. A problem with the literature is that they all use statistics on patent approval as a measure of technological development. The Schumpterian growth model is concerned with technological improvement in general, not just new innovations, so in this case imitation could also be included. The problem is that it is difficult to find data on imitation rates in an economy. Xu (2000) attempts to solve this problem by using data on the rate of technology transfers from US multinational enterprises to both developed and developing economies. Empirical literature also tends to focus on the USA, whom is at the forefront of the efficiency frontier. This could result in an underestimation on the effects of RD on growth because there is no effect from technological transfer at the head of the frontier. Once again Aghion and Howitt are prominent researchers in the field of Schumpeterian convergence. Howitt (2000) provided a framework which was later developed into a model (Howitt Mayer-Foulkes, 2004). Krugmans paper (1994) was seminal in literature on growth accounting, an early paper on Schumpeterian convergence. He argued the miraculous growth rates experience by the Soviet Union and in Asia were simply a product of large scale increases in input. There must be technological change for growth to be sustainable. Section 3: The model In the Schumpeterian growth paradigm, growth in driven by technological change. Here new technologies replace the old in a process described as creative destruction (Durlauf, 2010). In this model we assume new technologies are completely substitutable for the old ones. So as new technologies are invented they completely drives out the old technology from the marketplace. Innovation leads to a higher level of output being achieved for a given level of capital and labour than was previously possible which enables the economy to transcend the law of diminishing returns (Weil, 2005). Figure 1 in the appendix shows the law of diminishing returns where the purple line indicates the higher output possibility with technological improvement. The country acquires this new technology either through innovation or imitation. There are three players in the model: producers, innovators and consumers (Barro Sala-i-Martin, 2004). Innovators perform RD in order to develop new technologies. Those that are successful receive monopoly rents from the product due to patents. Note that the latest innovator has a efficiency advantage compared to the previous innovator but he has a disadvantage compared to the next. This is because the latest innovator is able to expand upon past knowledge in his creation of new technologies. This is shown in Figure 2. The successful innovator has the right to sell his idea to a final good producer, at this stage the profit stream to the previous innovator is terminated. The model makes several assumptions about the producers. There are a fixed amount Ñ products in the economy of varying quality. Each new producer is different from the old producer. So when innovations are made the old producer receives no more profit and the new producer takes over the market. Therefore the industry leader has the first mover advantage. The duration of dominance in the market is random (Barro Sala-i-Martin, 2004). The products are placed on a quality ladder, as shown in Figure 3. There are Ñ different goods of quality K. An improvement in a certain good corresponds with a movement up the ladder, an increase in K. Figure 4 shows the quality ladder for an individual product. Here we can see that duration between quality improvements and the size of quality improvements are both random. An incomplete, simplistic version of the growth model is as follows: in an economy with a fixed amount Ñ products, output is given by Yi = ALi1-ÃŽÂ ± .à ¢Ã‹â€ Ã¢â‚¬ËœNj=1 (qKjXij)ÃŽÂ ± where Yi is output in industry i, given A is the technology parameter, L is labour input and qKjXij is the quality, K, adjusted amount of the jth type of intermediate good X in industry i. If P is price, a firm maximises profit with Yi wLi à ¢Ã‹â€ Ã¢â‚¬ËœNj=1 Pjxij Demand for product X equals the marginal cost of production Xj = L. [AÃŽÂ ±qÃŽÂ ±Kj/Pj]1/(1-ÃŽÂ ±) The monopoly profit, à Ã¢â€š ¬Kj, for the innovator is the difference between the price of the product and marginal cost of production à Ã¢â€š ¬Kj =(Pj -1)Xj If Zj Kj is the flow of resources (as in figure 1) and à Ã¢â‚¬ ¢ is random then an innovator faces probability of success pKj = Zj Kj.à Ã¢â‚¬ ¢Kj and with ÃŽÂ ¶ as a parameter equal to the cost of doing research à Ã¢â‚¬ ¢ is equal to à Ã¢â‚¬ ¢kj = (1/ÃŽÂ ¶). q-(kj+1).ÃŽÂ ±/(1-ÃŽÂ ±) which is an endogenous variable (Barro Sala-i-Martin, 2004: 321-22). The consumers are interested in consuming the latest good. If ÃŽÂ ¸ is a constant representing the elasticity of marginal utility, in other words the willingness to substitute and (r à Ã‚ ) is a marker of growth over time then household consumption grows by ÄÅ  /C = (1/ÃŽÂ ¸).(r à Ã‚ ) The interest rate can be defined as a function of profit flow, ÃÅ'„à Ã¢â€š ¬, the cost of doing research, ÃŽÂ ¶, and the probability of success r =( ÃÅ'„à Ã¢â€š ¬/ÃŽÂ ¶) p So the amount of resources devoted to RD in sector j at k quality can be defined as Zkj = q(kj+1).ÃŽÂ ±/(1-ÃŽÂ ±).(ÃÅ'„à Ã¢â€š ¬ rÃŽÂ ¶) Hence aggregate RD spending is à ¢Ã‹â€ Ã¢â‚¬ËœNj=1 Zkj= qÃŽÂ ±/(1-ÃŽÂ ±)Q.(ÃÅ'„à Ã¢â€š ¬ rÃŽÂ ¶) Q is the aggregate level of quality improvements. The growth rate of Q is equal to ÃÅ'†¡Q/Q = ( ÃÅ'„à Ã¢â€š ¬/ÃŽÂ ¶ r).[qÃŽÂ ±/(1-ÃŽÂ ±) 1] If we algebraically substitute the above equation into the the consumption growth equation, allowing for r =( ÃÅ'„à Ã¢â€š ¬/ÃŽÂ ¶) p we get the growth rate ÃŽÂ ³ ÃŽÂ ³ = [qÃŽÂ ±/(1-ÃŽÂ ±) 1] . [( ÃÅ'„à Ã¢â€š ¬/ÃŽÂ ¶) à Ã‚ ] 1+ÃŽÂ ¸ . [qÃŽÂ ±/(1-ÃŽÂ ±) 1] We can see growth increases with economic profit flows, ÃÅ'„à Ã¢â€š ¬, and quality enhancements, q, but decreasing with the cost of research, ÃŽÂ ¶, and the utility parameters à Ã‚  and ÃŽÂ ¸ (Barro and Sala-i-Martin, 2004: 91, 327-31). The basic model has been expanded upon in recent literature. Aghion et al (2001) relaxes the assumption that the monopoly rent receiver will cease to innovate while he receives the rents. In this model there are two firms in an industry so the rent receiver must continue to innovate in order to keep up with the industry leader. This is important because leap frogging is not possible in this model and competition is important for growth. I was unable to find empirical testing of this framework but the assumptions made are more realistic to the real world. For example, when Nintendo invented the gameboy in the 1990s, they did not wait for the competitors to develop hand held gaming devices before they made improvements to the original gameboy. The paper also proposes that a small level of imitation is always good for growth because it encourages competition. Contrastingly, large levels of imitation is detrimental. This issue is explored further in the next section. Aghion et al. (2005) introduce credit constraints into there model. In reality poorer countries are restricted in how much they can imitate because they do not have enough money. Poorly functioning financial institutions or markets limit the flow of credit to potential entrepreneurs. Another line of research was pioneered by Jones (1995) we he brought into light the problems with assuming scale affects. Scale affects arise because the in the classic Schumpeterian model, Aghion and Howitt (1992) assume productivity will rise as the population increases but this has not been empirically supported (Durlauf, 2010). Aghion and Howitt (1998) acknowledged the correction to their model and have also incorporated growth effects into their new model. Dinopoulos and Thompson (1998) have also based work on Jones model by modifying the welfare effects. Section 4: Efficiency Frontier The Schumpeterian model describes growth due to technological progress. The productivity parameter is shown as a change in technology between two periods. If ÃŽÂ ¼n is the frequency innovations take place, ÃŽÂ ¼m the frequency of implementation and ÃŽÂ ³ is a multiple of the new technology we can write the productivity parameter as At+1 At = ÃŽÂ ¼n(ÃŽÂ ³-1)At + ÃŽÂ ¼m(At-At) and we can describe the growth rate,g, as the percentage change in productivity between the two periods (At+1 At)/At g = ÃŽÂ ¼n(ÃŽÂ ³-1) + ÃŽÂ ¼m(ÃŽÂ ±-1-1) where ÃŽÂ ±-1 = At/Äâ‚ ¬t (Durlauf 2010: 232). This leads us to the theory of the technological frontier. The country at the forefront of the frontier is the most technologically progressive economy, which has typically been the USA (Griffth et al. year). The distance of a country to the frontier impacts the effectiveness of adopting technologies and policies on growth. This is used to explain the experience of the slowdown of european growth after the 1970s. It cannot be explained by the Solow model as Europe had much higher levels of savings (Aghion Howitt 2006: 270). An alternative explanation is the lower frequency of technological implementation in Europe meant the continent could not keep up with the USA in terms of growth during the technological revolution during the 1980s. The technological frontier is captured algebraically by à £ = ÃŽÂ ¼m/(g + ÃŽÂ ¼m ÃŽÂ ¼n(ÃŽÂ ³-1)) which is the steady state value of at (Durlauf 2010: 233). Gerschenkrons theory of backwardness is incorporated into the model above. Gerschenkron (1962) proposed that relatively backwards economies could achieve high levels of growth by investing RD into imitating technologies of the advanced countries. Relating it to this model, economies far behind the frontier could move closer to à £ by enabling a large increase in ÃŽÂ ¼m because it is quicker to mimic technologies instead of inventing new ones. This result is true for OECD countries (Griffith et al 2000: 893) At the lower stage of development countries are advantaged by implementing anti-competitive policies that would encumber growth at later stages of development. For example, having many state owned enterprises means lower competition. This means an economy should not rely on investment based strategies for a prolonged period of time, at later stages of development they should start to encourage innovation instead. Investment based strategies are those that protect certain indus tries, foster strong relationships between firms and workers and between firms and banks, and encourage high levels of savings (Acemoglu et al 2006: 38-9). The German and Japanese economic model is an example of this. Although perhaps not the best example as both economies also place importance on innovation. Figure 6 shows the relationship between distance to the frontier and barriers to competition. This confirms that the closer a country is to the frontier, the more detrimental barriers to competition are to growth by the significant negative coefficient in all estimates for this relationship. The relationship between distance to the frontier and low barriers on growth is less negative and not significant (Acemoglu et al. 2006: 42-43). Most papers find tacit knowledge to be an important factor when adapting technologies. In this case location and close relationships with developed countries is important because the information can be easily passed on. An example was given in Grif fith et al (2004: 883) of when the British supplied the Americans with jet planes during the Second World War. The planes had to be redrawn to comply with American standards, a process which took ten months. Even once a country has sufficiently developed institutions or a high level of human capital it could still be at a disadvantage because it does not have the knowledge implicit in other regions. In the case of USA versus European economic growth, one aspect not covered by the model is that Europe is made up of many different countries with different attitudes. Hence fiscally responsible nations like Germany need to make up for large spending nations like Greece and Hungary. Countries like France and Sweden have highly developed social welfare systems, which impede growth, while the US welfare system is notoriously poor. On the other hand the social welfare systems can also play into the Schumpeterian model. For example, firm entry and exit rates are far lower in Europe, partly because Europeans tend to be more cautious in entrepreneurship and failure is not as heavily stigmatised in the US (Verheul et al 2002: 230). Firm turnover is part of creative destruction. Note that high entry and exit rates are only important at the head of the frontier. As described above, they should be low when a country is far behind the frontier, consistent with anti-competitive behaviour. The importance of technological progress for growth is seen in the examples of the Soviet Union in the 1950s and the East Asian miracle in the 1990s. These countries moved rapidly towards the frontier during their respective years of growth but it was unable to be sustained and they never reached the frontier. The high growth rates have been found to have resulted from large scale increases to input (Krugman, 1997) in other words from government investment and growing populations. The governments failed to successfully switch to innovation strategies and the growth rates faltered. A similar phenomenon appears to be unfolding at the moment in China. Once the population growth rate starts to decrease it remains to be seen whether they can continue to sustain their economic growth. An government then faces the problem of when to switch from policies promoting catch up growth to those enabling competition. Acemoglu et al. (2006: 64) has derived an algebraic model capturing the point where an economy should switch strategies The turning point is a function of ÃŽÂ ¼, innovation incentive, ÃŽÂ ´, anti-competition and à Ã¢â‚¬Å¾, the fraction of government subsidised investment. This equation also incorporates the spillovers, cost of the investment, the skills of the entrepreneur and the amount of high skilled agents in the economy. The full model is explained in Acemoglu et al (2006). If the economy were to transfer before the turning point was reached it would lose the advantage of backwardness and also may not have industries developed enough to compete globally. On the other hand if it remains in the investment stage for too long it may risk falling into the non convergence trap. Growth levels stagnate because total factor productivity is not increasing with the global standard. The problem with this model is that it is simplistic. There are many factors hard to capture in economic model. An example is poorly developed countries tend to have high levels of corruption. Powerful business leaders could influence the decision not to switch away from the investment strategy. In the case above with the Soviet Union there were political problems hindering growth when communism fell. Another problem is that the communist destroyed large amounts of resources with their inefficient techniques. Large amounts of land became in-arable due to pollution and untapped oil became inaccessible. Natural resources or geographic local could also affect growth. For example the EU has great benefits to member countries. There could be problems mobilising the population from rural to urban areas such as in Africa. Sociologist literature places emphasis in a national psyche that influences economic growth. This is common in entrepreneurial literature when examining regional motivatio nal difference but discredited somewhat in economic literature. The example previously used in this paper is that America is more entrepreneurial because of its emphasis on individualism and willing acceptance of change. This is a reason for their strong growth. The empirical testing of the above framework is looked at in the next section. Education is another important factor to consider in growth models. Does higher human capital result in economic growth. One might assume with a highly educated population there is greater likelihood of successful innovations. Yet as described in the above scale effects literature this is not automatically true. A country with a basic primary and secondary education may advance in the earlier stages of development but there are diminishing returns to scale as the country progresses towards the frontier. For countries near to the frontier a greater emphasis must be placed on tertiary education. Table 1 shows the educational attainments of 5 large OECD countries. USA and Japan both have relatively high levels and France has been quite low. Table 2 shows Japan and the US have had the highest levels of productivity growth over the period and the Netherlands was low. The amount of total patents shown in Table 3 shows a different ranking. The USA and Japan still at the top but Germany has also performed highly. France and Netherlands have granted a far lower amount of patents. These figures are too superficial to make any conclusions and further research should be done on this issue but it seems tertiary education is unrelated to patent number but could be one of many contributing factors towards productivity growth. It might be useful to look at increases in education rates and compare it to increases in patent rates to see if tertiary education has an affect on innovation when close to the frontier. Section 5: Empirical evidence There have been examples of data from various countries conforming to the Schumpeterian model of growth, as a closer fit than captured by the Solow model. Venturini (2010) have taken data from the US economy. He has expanded the model to include ÃŽÂ ´, the rate at which ideas become obsolete. He finds only a weak fit to the Schumpeterian model but acknowledges that this could be to do with a bias formed from the underlying assumptions of the framework. Teixeira and Vieira (2004) find the Schumpeterian model fits the case of regional Portuguese data. They estimated an econometric model of human capital, firm productivity and firm failure rates. The main finding is that regions with higher levels of income and human capital have higher failure rates on average, a process of creative destruction. Clydesdale (2007) finds the Chinese economic growth is hampered by not engaging a technological enhancement strategy. The Chinese economy is restricted by being overly ridgid and too special ised, making change difficult (Clydesdale, 2007: 71). Recent Chinese growth has been found to be resultant from a large scale increase in the quantity of inputs rather than from improvement in input quality. Historically this has not been a sustainable method of growth, for example the former USSR. Zachariadis (2010) used a neo-Schumpeterian model to estimate an RD steady state on the US manufacturing industry. He empirical evidence that scale effects do not exist in Schumpeterian growth (Figure 6). Between 1957 and 1989 levels of RD remained constant as did technological progress despite an obvious increase in population (Zachariadis, 2002: 569). The main finding in the paper is that RD has a strong positive affect on patent rates and is probably a cause of growth. Although most papers rely on data on patents to estimate technological progress, Xu (2000) measures technology spillovers from US multinational enterprises on 40 different countries. He finds that technology spillovers have a positive affect on productivity growth as long as they have met a certain level of human capital accumulation. This means countries that are relatively undeveloped like Brazil. These results are consistent with the findings of Aghion and Howitt (2006) above where developed countries have a greater emphasis on tertiary education and therefore a greater ability to innovate. Poorer countries need to reach a certain level of knowledge before they can successfully adapt technologies. As they move further towards the frontier the emphasis must shift to innovation in order to keep growing. Positive affects on productivity are still felt in the poorly developed economy but from other causes (Xu, 200: 479). Griffith et al (2000) made a study in OECD countries on the effe cts of RD imitation in catching up to the efficiency frontier. As with Zachariadis, Griffith et al. find an affect on patents from RD. They also find human capital affects innovation and imitation but international trade does not have a significant affect. Figure 7 was taken directly from their paper. TFPGAP is a measure of distance to the frontier and robust standard errors are in parentheses. Column 1 shows a positive, significant relationship of technology transfers on productivity growth, and in column 2 they introduce the effects of RD growth, also significant. In column 3 the level of RD and the relationship between RD is positive. The greater the distance to the frontier, the greater the chance of technology transfers to positively affect RD and growth but only at a ten per cent significance level. Aghion et al (2005) theoretically and empirically test the importance of financial development on convergence. This paper examines the role of financial development in supporting or hindering technological progress, the main force behind economic growth. Figure 8 shows average financial development and per capita GDP. There is a positive relationship between the two factors. There is no longer a positive affect of financial development on growth once a country reaches approximately a 39 per cent level of development, which is the level of Greece (Aghion et al 2005: 190) Section 6: Convergence Convergence is the concept that all countries will move towards the same economic growth rate. Convergence is theoretically possible because of the advantage of backwardness Gerschenkron (1962). Pritchett (1997) found that over the past 140 years that while the major economies moved towards convergence, there has been an overall divergence between the rich and the poor. This is the main idea driving the section on the efficiency frontier. First countries most mobilise resources, as seen with the large scale increases in inputs. They most also develop economic and financial institutions able to withstand and support prolonged growth. Technological progress is the last stage of convergence. This is the newer theory of club convergence (Howitt and Mayer-Foulkes, 2004). Based on Schumpeterian growth theory, countries move towards different steady states determined by their level of development. The richest countries benefit from technology transfers amongst each other but the poorer grou p must reach the appropriate level of human capital to be able to support advanced technology first. Global convergence begun in the later stages of the industrial revolution where European countries and the new world countries: USA, Canada, Australia and New Zealand began to move towards similar growth rates (Pritchett 1997). However the poorer countries were not able to match such progress. In fact the opposite happened; during the period 1870 to 1990 the ratio between rich and poor went from 8.7 to 45 times the GDP per capita (Krugman, 1997: 11). Howitt (2000) theorised that while countries are making positive investments in RD they should eventually converge to the long run growth path . This is because innovations in other countries can be easily adopted as long as the country has the appropriate underlying institutions (Howitt, 2000: 830). Hence we have club convergence as shown in Figure 9. Growth path A represents those countries investing in modern RD and at the forefront of the efficiency frontier. Line B are those countries in the catch-up stage who have not reach reached the innovation stage of development. This could be a representation of countries such as the BRIC nations (Brazil, Russia, India and China), or the eastern tigers of the 1990s. Countries that are growing rapidly but that must make a structural and political change before they are completely industrialised. Line C are those countries that started far behind the rest and are too poorly developed to start converging and, though they are growing, are classified third world countries. Countries that are not investing at all in RD would be a flat line along the x axis. This is probably only the experience of remote amazonian tribes and other communities removed from the modern world and so are not included in the model. Mayer-Foulkes (2000) proposes there are five clubs of convergence, experiencing divergence between groups. The richest group has the highest average steady state growth. Of the five groups, three describe different levels of development. In Mayer-Foulkes (2000) model development is defined by level of income, to represent propensity to innovate, and by average life expectancy, to show the level of human development. Groups 1, 3 and 5 represent high, medium and low levels of development, respectively. The other two groups, 2 and 4, are transiting to a higher level of development. Figure 10 shows the geographic locations were groups members are situated. This is mostly what is expected above except the BRIC nations are not in the one group. India for example is in group 4 (Mayer-Foulkes, 2002: 8). Interestingly Argentina Uruguay are in the highest group. and Latin America dominates the third group and the lowest group has only two non African members. Note that Eastern Europe has not b een included. Three groups have been recognised as existing outside the model: the ex-Soviet countries; other countries that were previously, or are currently socialist; and countries that are mainly oil-exporting. These groups experience a different growth pattern to the rest of the world and so are not converging to any of the steady states in other groups. In this model the economy produces a single good Zt with output dependent on the input of intermediate goods i at date t, denoted by x(i)t and à Ã¢â‚¬  , a parameter representing the non-technological aspects of total factor productivity Zt = à Ã¢â‚¬  L1-ÃŽÂ ± à ¢Ã‹â€ Ã‚ «o1 At(i)1-ÃŽÂ ±xt(i)ÃŽÂ ± di The probability that an entrepreneur innovates, ÃŽÂ ¼, is increasing with the skill level of entrepreneurs, St, the productivity of the innovation, ÃŽÂ », and the quantity of inputs, zt. ÃŽÂ · is the Cobb-Douglas exponent of skills in innovation and Äâ‚ ¬t+1 is the global frontier. Such that and the division by the global frontier represents the fact that as technologies become more advanced innovation becomes harder (Howitt Mayer-Foulkes, 2004:8,10). Note, this last assumption may not be realistic because inventions such as the steam train, electricity and computers have resulted in large increases in innovation. St = à Ã¢â‚¬ ºAt where à Ã¢â‚¬ º is the entrepreneurs level of education. It follows that the equilibrium rate of innovation is As at = At / Äâ‚ ¬t the local human capital level is compared to the global standard and the difficulty of coming from behind is captured in the equation. Greater values of At mean the country is at an advantage. Howitt and Mayer-Foulkes refer to this as the absorption affect (2004: 11) because the probability of innovation is proportional to the skill level. Diving the national factors by the world growth rate gt implies an increase in growth globally hinders the rate of innovation. These are important because it represents the countries ability to effectively incorporate new technologies into its own economy, thus the basis of the club convergence model. A low value of at implies a disadvantage of backwardness. Hence a countrys productivity can advance in to ways; independently or towards the global standard On average At+1 = ÃŽÂ ¼tÄâ‚ ¬t+1 + (1-ÃŽÂ ¼t)At dividing both sides by the world productivity in the next period yields In this case there is no absorption effect, so Gerschenkrons (1962) advantage of backwardness would apply (Howitt Mayer-Foulkes, 2004: 12). In the above section the USA was acknowledged as the efficiency frontier. The USA is still a country, therefore the productivity rate of the efficiency frontier can be written as ÃŽÂ ¼tUS = ÃŽÂ ¼US.atUS 1 + gt The growth of the USA would be the world growth rate. In this case gt = à Ã†â€™ÃƒÅ½Ã‚ ¼tUS where à Ã†â€™ is a spillover affect from similarly advanced countries, line A in Figure