Abstract
We analyze aspects of long-run economic growth in stylized lagging and leading regions. Both regions use physical capital, research and development (R&D), and knowledgeable workers to produce a final consumption good. The lagging region faces two key economic disadvantages. Specifically, the constant fractions of the output of the final consumption good that are saved to enhance the stocks of physical capital and R&D are assumed to be twice as large in the leading region, as they are in the lagging region. In this scenario, we perform three tasks. First, we determine the ratio of the balanced growth path (BGP) value of output per knowledgeable worker in the leading region to its value in the lagging region. Second, we ascertain the ratio of the BGP value of R&D per knowledgeable worker in the leading region to its value in the lagging region. Finally, we show the extent to which the lagging region’s initial economic disadvantages are magnified on the BGP and then discuss some policy implications.
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Notes
We recognize that there are many studies on lagging and leading regions. Examples of such studies include, but are not limited to, Batabyal and Beladi (2015a), Brown et al. (2017), Batabyal (2018) and Boltho et al. (2018). That said, the point is not that such studies do not exist. Instead, our point here is twofold. First, there are a relatively small number of studies that have a direct bearing on the central question that we analyze in this paper. Second, we have cited these relevant studies in the present paper.
By “essential” we mean that if the value of any one of these three inputs is set equal to zero then the value of output is also zero. In other words, there is no way to produce output without using positive amounts of all three inputs.
The knowledge variable strengthens the raw labor variable in a multiplicative manner and hence the product of these two variables represents what we are calling “knowledgeable labor”. Put differently, knowledgeable labor is the outcome of raw labor augmenting knowledge. Note that the knowledge variable of interest here is distinct from the R&D that we have discussed previously. Therefore, there is no double counting whatsoever of R&D. Finally, we would like to point out that approaches that are similar to the approach we employ in this paper to study knowledgeable labor have been used previously in the literature by Batabyal and Beladi (2015b, c).
In the equations of motion described by Eqs. (2)–(5), the stock variables do not depend explicitly on time. As such, these differential equations are autonomous. Note that this feature of our model is not atypical at all because it is very common to work with this sort of autonomous formulation in the growth theory literature. See the many examples in either Acemoglu (2009) or Romer (2012) for a more detailed corroboration of this point.
Because \(\alpha + \beta < 1\) in our model, this model is characterized by decreasing returns to scale and hence it is not an endogenous growth model. If, in contrast, we specify that \(\alpha + \beta = 1\) then there would be constant returns to scale and the model would become an endogenous growth model. See Mankiw et al. (1992) for additional details on this point and see Romer (1986), Coe and Helpman (1995) and Jones (1995) for additional perspectives on, inter alia, the role of R&D in promoting economic growth. That said, for the central question that we wish to study in this paper—described in the last paragraph of Sect. 1.2—it is not necessary to analyze an endogenous growth model. Finally, although the results of all theoretical papers depend on the assumptions made and on the modeling strategy utilized, we have tried to be as general as possible in our analysis while making the minimum number of assumptions to obtain tractable results. In this regard, we note that our use of the Cobb–Douglas production function in Eq. (1) is not unusual at all and that many papers in the growth theory literature also use this production function. See Mankiw et al. (1992) for a prominent example. See Romer (2012) for a textbook example of the repeated use of Cobb–Douglas production functions to study questions concerning economic growth.
We realize that the analysis we conduct in this paper is based, in part, on using explicit numerical values for the α and the β parameters and that the two constant savings fractions are twice as large in the leading region as they are in the lagging region. We adopt this approach because of two reasons. First, consistent with our observation in footnote 5, it is not possible to illustrate the working of our model without using numerical values for some parameters and, in this regard, we have kept our use of numerical values to a minimum. Second, we use the “twice as large” values for the two constant savings fractions to help build intuition. We believe that it is easier to comprehend the impacts of “doubling differences” in initial conditions than it is to understand the effects of arbitrary differences in initial conditions. That said, we would like to point out that the magnification results we discuss in section 4 below are general in the sense that they hold for any positive integer z > 2 and not just for z = 2 or the “doubling” case. Finally, the reader should note that the practice of illustrating the working of a model with actual numbers is not without precedent. For instance, in their well-known paper on the empirics of economic growth, Mankiw et al. (1992) use actual numerical values for some of their model parameters to obtain results and to demonstrate the working of their model
Using the methodology of Batabyal and Nijkamp (2019), it can be shown that the economies of the leading and the lagging regions converge to a unique BGP. In other words, a BGP equilibrium in both economies exists.
The point of this first policy implication is not to emphasize the obvious. In other words, we are not just saying that “saving and investing more leads to higher output”. Instead, we are pointing to an explicit magnification effect on the BGP and we are also quantifying the exact nature of this magnification effect.
Having stated this third policy conclusion, we would like to point out that in general, it is unlikely that an apposite regional authority will be able to control any one of these three parameters.
We reiterate that our primary objective in this paper is to demonstrate how small differences in initial conditions that separate a leading and a lagging region can lead to dramatic and magnified impacts on the BGP. The reader should understand that our objective is not to study how spillovers such as migration or the potential movement of physical capital between two regions might affect economic growth on the BGP in these same two regions. That is why we do not study spillovers in this paper. Our modeling of the two savings fractions \(s_{\text{D}}\) and \(s_{\text{K}}\) as constants in the open interval (0, 1) is not without precedent. See, for instance, Mankiw et al. (1992) and Batabyal and Nijkamp (2019) for additional details on this point. Finally, the idea that allowing flows from one region to another can reduce disparities is not something that was believed to be true in the 1950s only. In fact, we now have evidence—see, for instance, Giannetti (2002)—that under some conditions, knowledge flows between regions can actually reduce disparities between them.
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Acknowledgements
For their helpful comments on a previous version of this paper, we thank the Editor-in-Chief Yoshiro Higano, two anonymous reviewers, and participants in The Regional Science Academy Workshop in the Lulea University of Technology, Lulea, Sweden, in June 2018, the Annual Meeting of the Regional Science Association International’s Japan Section in Hokkai-Gakuen University, Sapporo, Japan, in October 2018, and the Annual Conference of the North American Regional Science Council, San Antonio, Texas, in November 2018. In addition, Batabyal acknowledges financial support from the Gosnell endowment at RIT. The usual disclaimer applies.
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Batabyal, A.A., Nijkamp, P. The magnification of a lagging region’s initial economic disadvantages on the balanced growth path. Asia-Pac J Reg Sci 3, 719–730 (2019). https://doi.org/10.1007/s41685-019-00118-7
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DOI: https://doi.org/10.1007/s41685-019-00118-7