Market potential, spatial theories and spatial trends

ABSTRACT

Previous literature on European regions has shown that structural estimation of New Economic Geography (NEG) wage-type equations obtains results similar to those obtained using old regional economics techniques. I show that this similarity is due to the presence of global spatial trends in the variables (first-order non-stationarity), which produce spurious regressions. Formal tests and graphical models confirm that any variable displaying a core–periphery spatial pattern produces similar predictions for European regional per capita income. Empirical tests of spatial theories should thus pay attention to the geographical features of the administrative units and the global spatial trends of the variables analysed.

KEYWORDS:

• NEG
• core–periphery
• spurious regression
• observational equivalence

JEL Codes::

• C21
• F12
• R12

View correction statement:

Correction

ACKNOWLEDGEMENTS

Previous drafts of this paper have been presented in various forums, such as the Spanish Association of International Economics and Finance (Salamanca, Spain), Spanish Regional Science Association (Bilbao, Spain), European Regional Science Association (Lisbon, Portugal), Meeting of Economics at the National Polytechnic School (Quito, Ecuador), workshop in honour of Geoffrey Hewings (Santiago de Compostela, Spain), School of Geographical Sciences (Bristol, United Kingdom), Department of Global Economics and Management (Groningen, The Netherlands); and the Departments of Economics of the following universities: A Coruña and Autonomous University of Madrid (Spain), Catholic University of the North (Chile) and Porto (Portugal). I thank many colleagues and several anonymous referees for their comments. I am especially grateful for the advice of Coro Chasco, Paul Elhorst, James LeSage, Mariano Matilla-García, Román Mínguez and Isabel Neira. I also thank the C&D Research Group of the Universidade da Coruña and ECOBAS for their financial support. The usual disclaimers apply.

DISCLOSURE STATEMENT

No potential conflict of interest was reported by the author(s).

Correction Statement

This article was originally published with errors, which have now been corrected in the online version. Please see Correction (http://dx.doi.org/10.1080/17421772.2024.2339022)

Notes

1 The term ‘social physics’ refers to development since the 18th century of social theories inspired by the mathematical properties of physics. In the first half of the 20th century, demographers, geographers and economists applied Newton’s law of gravity to social phenomena, attributing attraction forces to them. This approach to social phenomena is not mere historical anecdote. As will be discussed, its tradition has used surface trend analysis, which was later ignored in general economics.

2 Some examples of studies using Harris’ indicator in a regression for European regions are Brakman et al. (2009), Clemente et al. (2009), Karahasan and López-Bazo (2013) and Bruna et al. (2016). Among many others, Boulhol et al. (2008) and Fallah et al. (2011) have used Harris’ index to study other geographical samples. See also Rokicki and Cieślik (2023).

3 See Fingleton (2006), Brakman et al. (2009), Fingleton and Fischer (2010) and Partridge (2010), among others.

4 Although these authors omitted the comparison to Harris’ indicator in their published version, their draft showed a third source of evidence demonstrating the results’ similarity to those obtained using Redding and Venables’ approach in analysis of a European sample. Fichet de Clairfontaine and Hammer’s (2018) estimation of gravity equations uses interregional trade data.

5 For Redding and Venables (2004), the dependent variable of the equation is the log of the price of the composite immobile factor of production, which they interpret as labour. Head and Mayer (2004) reinterpreted this variable as a cost-share weighted sum of logged primary factor prices.

6 The model includes many simplifications: $\sigma$ is the same for any consumer and any variety of goods; the share of $M$ consumption in total expenditure ($E_j$) is the same everywhere; and others.

7 $S_j^M$ is termed. ‘supplier access’ by Redding and Venables (2004) and ‘supply’ index by Head and Mayer (2006). $S_j^{M1/\left(1-\sigma \right)}$ is equivalent to Krugman’s (1992) ‘true’ price index, the unit utility cost for the consumer.

8 Empirical NEG literature has ignored maritime transport, a serious omission when testing a historical explanation on a European sample. See Donaldson and Hornbeck (2016) and Gambuli (2023) for estimations that include water transport.

9 Klaesson et al. (2015) survey different distance-decay functions used in the literature on accessibility. The general conclusions of the research presented here may be applied to any approach that uses distance-decay functions, such as those of Hanson (2005), based on Helpman’s (1998) model, or of Niebuhr (2006). See Gambuli (2023) for a comparison of different methods for computing market potential.

10 Rokicki and Cieślik (2023) argue that capturing regional price indices through fixed effects in panel data estimations (as in Redding and Venables (2004)) assumes that transport accessibility remains constant across time. This assumption may bias empirical estimates of market potential.

11 See, for instance, Tabuchi and Thisse (2011), Hsu (2012), Taylor and Hoyler (2021), and Díaz-Lanchas et al. (2022), among others.

12 A second-order source of non-stationarity is variance. Location frequently matters not only for the values of the variable but also for the data dependence structure. The latter property is called anisotropy (Arbia et al., 2013).

13 One exception is Head and Mayer’s (2006) instrumentation of market potential with an indicator of world centrality. I have reproduced the construction of their instrumental variable. This variable works well for Head and Mayer’s sample of NUTS 1 regions for nine European countries. For the NEG explanation, however, this instrument yields poor empirical results for samples of 16 or 32 European countries, as in my research.

14 Attending to the scale/level effect, I repeated the empirical estimations in this paper for NUTS 1 regional European territories, as used by Head and Mayer (2006), rather than for the more disaggregated level of NUTS 2 discussed here. The main results are the same.

15 Using French data and Harris’ indicator of market potential, Briant et al. (2010) studied the MAUP for different zoning systems. They use the terms ‘shape effect’ to refer to different empirical results derived from the level of aggregation (scale problem) and ‘size effect’ for those derived from drawing boundaries for a given spatial resolution (aggregation problem). They do not study the size effect of a spatial trend in regional area but conclude that MAUP also affects estimated trade elasticity to distance when using gravity equations. Fotheringham and Sachdeva (2022), in contrast, approach MAUP from the point of view of local differences in the data generation processes rather than of attributes of the data units. See also my latter discussion about Dijkstra et al.’s (2011) grid-based method.

16 The online supplementary Appendix summarizes discussion of how to measure regional internal market potential and presents the empirical results using a complete indicator of internal and external accessible market, HMP in Equation (3). See Bruna (2024a). Dijkstra et al.’s (2011) approach using GIS-based techniques eliminates the problem of measuring internal market sizes but is an exception in the literature.

17 See LeSage and Pace (2014) for a similar exercise regarding the weights matrix in spatial econometrics.

18 Bruna et al. (2016) also considered a SAR model. Fichet de Clairfontaine and Hammer (2018) studied spatial filtered data. I do not discuss possible spatial econometric models in detail. As argued in Section 3.2, the presence of global trends in the data induces detection of local spatial autocorrelation.

19 This quadratic approximation of the trend is frequently used in spatial trend analysis and is useful for the purposes of this paper, though alternative parametric and non-parametric procedures may be considered.

20 See https://ec.europa.eu/eurostat/web/nuts/background.

21 Breinlich (2006) and Fichet de Clairfontaine and Hammer (2018), among others, found that constructing market potential with current travel times instead of geographical distances does not significantly alter the results.

22 See https://en.wikipedia.org/wiki/Blue_Banana.

23 Population density is a standard indicator of urban agglomeration economies. It has been used to compare NEG and urban economics theories (Fingleton, 2006; Brakman et al., 2009). Fichet de Clairfontaine and Hammer (2018) therefore use an instrument from urban economics explanations to confirm the NEG explanation – another example of the observational equivalence of several theories discussed since Section 1.

24 It may be argued that the smaller size of geographically central European regions is explained historically by NEG or CPT. Definition of NUTS regions does in fact consider historical traditions and population thresholds. The standard literature testing theoretical models does not adopt this reasoning, however.

25 Figure A8 in the online supplementary Appendix repeats Figure 4 but constructs the indicators of ‘EMP’ as $\sum _{j\ne i}^{R_i-1}{d}_{\mathrm{ij}}^{-2}$or different numbers of nearest neighbours ($R_i=1,\dots ,217$). This paper’s conclusions do not depend on estimating the distance decay parameter using the gravity equation, as proposed by Redding and Venables (2004).

26 My sincere thanks to Mariano Matilla-García for providing me with the results of these tests.