Copyright © The Authors 2007. Published by Oxford University Press.
Appropriate technology in a Solovian nonlinear growth model
* Università di Pisa, e-mail: dfiaschi{at}ec.unipi.it
** Università di Palermo, e-mail: lavezzi{at}unipa.it
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We propose a Solovian growth model with a convex–concave production function and international technological spillovers. We test the empirical implications of the model, analysing the effects of the productivity slowdown that followed the oil shocks of the 1970s. We argue that this slowdown, altering the world income distribution, affected the pattern of international technological spillovers, taking the poorest countries further away from the technological leaders, and therefore unable to exploit their technologies. The result is the emergence of a poverty trap for low-income countries.
Key Words: convex–concave production function • distribution dynamics • productivity slowdown • international technological spillovers
The material in this paper is based on our ‘Nonlinear Growth and the Productivity Slowdown’, presented at the American Economic Association 2006 Annual Meeting in Boston in the session ‘1956 Contribution to Economic Growth Theory by Robert Solow: The 50th Anniversary Celebration’. We are grateful to O. De La Grandville for organizing the session and to Prof. Solow for his comments. Thanks also to J. Stachurski. The usual caveat applies.
1 In this model the capital stock should be interpreted as a composite index of physical and human capital and therefore, for simplicity, we are assuming that the rates of obsolescence of both types of capital coincide.
2 A longer discussion on this type of functions is in Barro and Sala-i-Martin (2004, pp. 74–7).
3 The AK model has been criticized on the grounds of results on conditional convergence (see, for example, Barro and Sala-i-Martin, 2004, p. 167). However, if the growth path is nonlinear in the transition, the evidence on conditional convergence may not be sufficient to reject the AK model. In fact, with a nonlinear path, countries in the sample may display a period of convergence, in which poor countries grow faster than rich countries. The problem in this case would consist in discerning between a nonlinear AK model and a model which is asymptotically AK, but satisfies the neoclassical assumptions otherwise (Barro and Sala-i-Martin, 2004, p. 161). To the best of our knowledge, an empirical test of a nonlinear AK model has not been provided yet.
4 We abstract from the consideration of explicit investment in the accumulation of knowledge, e.g. in R&D.
5 In addition, standard international economics suggests that the process of catching up by laggard countries may hurt leading countries’ growth because it worsens their terms of trade (see, for example, Krugman and Obstfeld, 2004, ch. 5). We thank Alberto Chilosi for pointing this out to us.
6 This differs from the model by Basu and Weil (1998), where the cardinality of Zi matters. That is, if all countries in Zi are identical, an increase in 
increases the productivity of country i. This effect can be obtained by raising 
in equation (2) to an exponent lower than 1.
7 This partition was originally proposed in Fiaschi and Lavezzi (2003).
8 For simplicity, in the present discussion the hypothesis 
H > L is assumed to guarantee that when P receives positive spillovers from R, R is not harmed by the interaction with P.
9 This threshold is implicitly defined as:
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10 See Appendix for the country list. Figures are in 1990 constant dollars.
11 Typically, the dynamics of the distribution is represented as a Markov chain when the income space is discretized. See, for example, Quah (1997) for more details.
12 The use of absolute per capita GDP imposes care on the interpretation of the long-run predictions, given that the growth behaviour identified for some GDP levels may not be assumed to remain the same in distant periods. For further discussion on the use of absolute or relative values of GDP, see Fiaschi and Lavezzi (2007).
13 For all the non-parametric estimates we used R (2005). The statistical package mgcv, if not stated differently, is used for the non-parametric regressions (see Wood, 2006). This package has an advantage in terms of computational time, and is used when the database is particularly large. Ninety-five per cent confidence bands in Figure 3 are calculated by an appropriate resampling method (wild bootstrap), suggested by Härdle et al. (2004, p. 127). Data sets and codes used in the empirical analysis are available on the authors' websites (http://www-dse.ec.unipi.it/fiaschi and http://www.unipa.it/
lavezzi).
14 For details on this choice, see Fiaschi and Lavezzi (2003).
15 The distribution of observations is not symmetric, given our criterion for the choice of the GDP classes. In particular, the distribution of observations is: 0.29, 0.48, 0.15, 0.08 (first period); 0.19, 0.39, 0.20, 0.22 (second period).
16 In these figures we also reproduce the grid used in Tables 2 and 3. The procedure to compute the ergodic distribution follows Johnson (2005) (the author kindly helped us, by providing the instructions now available at http://irving.vassar.edu/faculty/pj/pj.htm). The ergodic distribution solves 
, where z and x are two GDP levels, g
(z|x) is the density of z, given x, periods ahead. In our computations we set = 10. To estimate g(z|x) it is necessary to estimate the joint density of z and x, g(z, x), and the marginal density of x, f(x). In the estimation of g(z|x) we used the adaptive kernel estimator suggested by Johnson (2005) (see Silverman, 1986, p. 100), in which the kernel window increases when the density of observations decreases.
17 These non-parametric regressions are obtained with R (2005), in particular with the statistical package sm (see Bowman and Azzalini, 1997). Given the smaller number of observations for every regression, we adopted the adaptive kernel procedure of Silverman (1986), where the bandwidth increases as the density of observations decreases (the parameter regulating the sensitivity of the window width to the density of observations is set to 0.5). For the pilot estimate of the densities of observations we used the optimal normal bandwidth with Gaussian kernel.
18 In Fiaschi and Lavezzi (2006) we control for the appropriateness of Bi as an index of the level of technology in a country by regressing it against an index of competitiveness based on the structure of trade, and generally find a positive relation.
19 We report the estimation of 3 years as they are sufficient to highlight the most important features of the dynamics of B across countries.
20 Baily and Schultze (1990, p. 397), note that Tobin's q in the USA fell well below unity after the first shock, indicating a low evaluation of installed capital (and therefore an increase in the rate of obsolescence), while in 1987 it reached a value of 0.91, indicating the reversal of the previous tendency.
21 In Fiaschi and Lavezzi (2006) we analyse the relationship between investment rates and growth rates before and after 1973. We find that in GDP classes III and IV investment rates showed a strong decrease associated with a decrease in the growth rate. However, the growth rate decreases in GDP classes I and II despite an increase in the investment rate. See Fiaschi and Lavezzi (2006) for more details.
22 A more complete analysis of the growth rebound in recent years should consider the sectoral composition of GDP. For example, Nordhaus (2004, p. 23) shows that the rebound in productivity growth after 1995 in the USA does not concern all sectors. In particular, the energy-intensive sectors do not show substantial gains.
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