The Conditional Convergence Properties of Simple Kaldorian Growth Models

Abstract

Findings of conditional convergence are usually interpreted within a neoclassical growth framework. This follows from the methodology of testing for conditional convergence, whereby the estimating equation is explicitly derived from a neoclassical growth model. Given this explicit derivation, findings of conditional convergence might be thought to discriminate against alternative approaches to growth in general and the Kaldorian approach to growth in particular. This article shows, however, that this is not the case. It does so by examining the conditional convergence properties of the ‘core’ model of Kaldorian growth theory—the Kaldor‐Dixon‐Thirlwall (KDT) model. In particular, the paper demonstrates that this model predicts conditional convergence of a qualitatively identical nature to that predicted by the neoclassical growth model. A simple extension of the KDT model that is reconciled with quantitative estimates of the speed of conditional convergence is also presented.

Key Words:

• growth
• convergence
• Kaldor

Jel Classifications:

• E12
• O40
• C20

Acknowledgements

The author is grateful to John McCombie and two anonymous referees for their very helpful comments. All remaining errors are the sole responsibility of the author.

Notes

1. NUTS is an acronym for Nomenclature of Units of Territorial Statistics and represents a classification system for regions of the European Union (EU). This system was established by the EU’s statistical agency—Eurostat.

2. Henceforth, Barro & Sala‐i‐Martin will be referred to as BS.

3. This approach originates from the work of Nicolas Kaldor (see, inter alia, Kaldor, 1966, 1970, 1977, 1981). It has since been further developed by Cornwall (1977), Dixon & Thirlwall (1975), McCombie & Thirlwall (1994, 1997a, 1997b) and Setterfield (1997a, 1997b), to name but a few.

4. There are also differences between the neoclassical and Kaldorian approaches to growth at a methodological level. Thus, the former adopts an axiomatic‐deductive approach to modelling, whilst the latter stresses the importance of realistic, or, what Kaldor (1972), termed, ‘scientific’, assumptions in modelling.

5. Indeed, some of its central themes, such as the endogeneity of technical progress, have been incorporated into the neoclassical approach by ‘new’ growth theorists such as Aghion & Howitt (1998) and Romer (1986, 1990).

6. Examples are Swales (1983), Targetti & Foti (1996), De Benedictis (1998), Fingleton (2000), León‐Ledesma (2002), and Roberts (2002).

7. More generally, it was taken as evidence against neoclassical exogenous growth models, including not only the Solow‐Swan model, but also, for example, the Ramsey model as developed by Cass (1965) and Koopmans (1965).

8. Sala‐i‐Martin (1996) terms this the ‘classical approach’ to testing for convergence.

9. Both absolute and conditional convergence are types of β convergence. Following BS (see, for example, BS, 2004, chapter 11), the convergence literature makes a further distinction between this type of convergence and σ convergence, where the latter is defined as a declining cross‐sectional dispersion of levels of per capita (or per worker) income or product.

10. BS (2004, pp. 464–465) point out that the assumption of an independently distributed disturbance term will be violated if there exist shocks that have a common influence on subgroups of economies. They view this possibility as being more likely when the economies in question are regions belonging to a single country or a common currency zone and, in such cases, supplement Equation (2) with a variable to control for the influence of such shocks.

11. This is a slightly unfair representation of BS (2004), if not Mankiw et al. (1992). This is because BS do allow different countries to exhibit different levels of efficiency by adopting a broad interpretation of A_t which sees it as capturing not only the level of technology, but various kinds of country‐specific government policies, distortions and so forth. They attempt to control for these factors by including proxies for them in . However, it is unlikely that the proxies capture all of the unobserved variations in A_t and, to the extent that this is the case, the problem of failing to control for non‐random variations in ln(A_t) remains.

12. Estimates towards the upper end of this range, such as those obtained by Canova and Marcet (1995), come from regional data. Islam (1995), meanwhile, obtains country estimates at the very bottom of this range. Caselli et al. (1996) argue, however, that this is because of simultaneity problems in growth regressions that Islam (1995) fails to control for.

13. Dixon & Thirlwall developed the model as an explicit formalisation of a growth model first outlined by Kaldor (1970).

14. Both w and τ are assumed to be exogenously determined. For an extension of the KDT model that endogenises w, see Roberts (2002).

15. Strictly speaking, the lag should also apply to the variables π_c and y_c in Equation (4). Their omission, however, does not affect any of the results derived below.

16. The importance of this difference cannot be understated. In particular, it is this difference that permits the KDT model to explain sustained long‐run differences in growth performance both between countries (and continents) in the world (for example, between Africa and South East Asia) and between regions within countries.

17. This follows from substituting Equation (13) into Equation (10) so as to obtain

18. Thus, integrating with respect to time gives . This corresponds to Equation (14) except that the constant of integration has been set to zero. This is because must hold in equilibrium.

19. Hooper and Marquez (1995) survey a wide range of studies reporting point estimates of η for the UK, whilst Anderson (1993), Bairam (1988, 1993), Driver and Wren‐Lewis (1999) and Landesmann and Snell (1989) also provide point estimates of η for the UK. The average point estimate of η from the studies surveyed by Hooper and Marquez and the other studies referred to is 0.43 (see Roberts, 1999). Meanwhile, surveys of the empirical literature (Bairam, 1987; McCombie & Thirlwall, 1994, chapter 2) on Verdoorn’s law reveal a value of 0.50 to be reasonable.

20. This result does, however, display a high degree of sensitivity to the assumed parameter values. Thus, in their original article setting out the KDT model, Dixon & Thirlwall (1975, p. 212) argue for a value of η = 1.5. With this value of η, the predicted speed of conditional convergence becomes 25% per annum. This removes further need for extension of the model along the lines set out below.

21. This is why neoclassical endogenous growth models of the simple AK variety do not predict conditional convergence—they possess no explicit transitional dynamics.

22. By contrast, the Solow‐Swan and augmented Solow‐Swan models predict slow rates of conditional convergence because, compared to the KDT model, their transitional dynamics are relatively unstable.

23. The simple Kaldorian models of growth investigated in this article suggest panel data studies allowing for economy‐specific fixed effects are to be preferred to simple cross‐sectional studies because of persistent variations in r* that might not otherwise be controlled for.