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Articles

A regional model of endogenous growth without scale assumptions

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Pages 5-35 | Received 03 Jan 2017, Published online: 21 Nov 2017

ABSTRACT

In this paper we model growth using a scale-neutral approach to innovation allowing differences between regions to emerge due to regional mechanisms. In this model, agglomeration is growth enhancing as the scale effect for innovation arises from greater access to knowledge rather than any assumed scale effects in growth-modelling techniques. Furthermore, entrepreneurs are assumed to choose the location of firms endogenously so as to minimize the costs of innovation, transport and living. The effects of such mechanisms are such that any policies that increase knowledge spillovers between locations will enhance growth and equality, but may be destabilizing for agglomeration.

ACKNOWLEDGEMENTS

For many helpful comments and suggestions, the authors are grateful to Jacques Poot, Martin Richardson, Henri de Groot, the editor and three anonymous referees, as well as participants at the Global Conference on Economic Geography, the North American Congress of the Regional Science Association International, and seminars at the University of Groningen and VU University Amsterdam. The usual disclaimer applies.

DISCLOSURE STATEMENT

No potential conflict of interest was reported by the authors.

SUPPLEMENTAL DATA

Supplemental data for this article can be accessed at https://doi.org/10.1080/17421772.2018.1392038

Notes

1 ‘Semi-endogenous’ growth refers to approaches where long-run growth is not influenced by R&D policy but proportional to population growth. Growth in fully endogenous models is influenced by R&D policy. While growth in Young (Citation1998) is not influenced by a proportional R&D subsidy, it is still considered fully endogenous because growth is influenced by an alternative R&D support policy that focuses on the intensity of R&D (Jones, Citation1999; Young, Citation1998). See Jones (Citation1999) and Dinopoulos and Thompson (Citation1999) for surveys and comparisons of ‘first-generation’ endogenous growth models with scale effects, ‘semi-endogenous’ growth models and ‘second-generation’ fully endogenous growth models without scale effects.

2 For example, if there were some kind of congestion cost for producing horizontal innovations, this could apply to the labour input to innovation rather than to the number of varieties. In absence of congestion, regional models might be expected to generate the opposite effect through mechanisms such as greater knowledge spillovers or a spatial sorting of heterogeneous workers. The latter would be similar to the approaches in the NEG literature supporting agglomeration to access knowledge spillovers (Baldwin et al., Citation2003) or approaches in the trade and growth literature that sorts more productive firms to locate in the more productive region (Melitz, Citation2003; Sampson, Citation2016).

3 The model uses a discrete-time specification because the growth model used is deterministic. This does not affect the results or conclusions drawn compared with a stochastic model in continuous time but is used to maintain analytical simplicity.

4 Other models (Baldwin et al., Citation2003) use a different measure of trade freeness where units must be shipped in order for one unit to arrive at the destination. Baldwin et al. (Citation2003) also use a corresponding freeness of trade measure . For direct comparison with the model here, and .

5 Davis (Citation1998) identifies that this is not a straightforward normalization in models without migration because equal transport costs for both the traditional good and differentiated goods eliminate the home-market effect if workers cannot migrate. However, the home-market effect still exists in models with migration because the concentration of migrants always reduces transport costs. Equal transport costs for all goods in a model with migration also create a home-market effect for traditional goods that pushes up the factor price of unskilled labour in the agglomerated home region and pushes it down in the foreign region, reducing the home-market effect for differentiated varieties but not eliminating it. The normalization that for traditional goods has the effect of nominal factor price equalization and removing the home-market effect for traditional varieties, greatly simplifying the analysis.

6 Alternatively, the results could be interpreted as the expected outcomes of a stochastic model.

7 Although this places a limit on calibrating the share of expenditure on differentiated varieties, it is a modelling assumption from Forslid and Ottaviano (Citation2003) made for simplicity and tractability in order to equalize wages for unskilled workers at the numeraire price for traditional goods without using Krugman’s (Citation1991) modelling trick and is not intended to reflect an empirical fact. Relaxing this assumption only leads to wage differences between regions for unskilled workers, reducing the tractability of the model but not changing the conclusions drawn.

8 The notation here is different from the above. The ambiguity is required because of the perspective of agents. The utility functions are from the perspective of consumers, so tilde refers to varieties imported and consumed by home consumers. In this part of the analysis, profit functions are from the perspective of the firm, so tilde refers to exported varieties and transport costs are treated as a cost of producing varieties for export.

9 Advancing variables by one period finds the market clearing skilled wage in the current period.

10 For more detail, see the supplemental data online.

11 Other regional mechanisms could include land rents, congestion costs, migration costs, cultural affinity, local amenities, climate or anything else that affects agents’ location decisions.

12 For a detailed wage pressure equation, see the supplemental data online.

13 The second condition is required to extend the ‘no black holes’ condition for . Although is always < 1 and is also typically < 1, there is a theoretical possibility for to be > 1.

14 Baldwin and Forslid (Citation2000) use a different measure of trade freeness, so a direct comparison of magnitudes is not possible. The important comparison to note is the effect of changes in knowledge spillovers on the overlapping stability of the ‘core–periphery stable and equal distribution stable’ steady states.

Additional information

Funding

This research was undertaken with financial support received at various times from the Marsden Fund [grant number 08-UOW-022-EHB] and The University of Waikato.

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