Urban Footprints in Rural Canada: Employment Spillovers by City Size

Abstract

Ali K., Olfert M. R. and Partridge M. D. Urban footprints in rural Canada: employment spillovers by city size, Regional Studies. Growing rural-to-urban commuting epitomizes a de facto regionalization process that is unique for each urban area and its spatial setting. In evaluating these relationships, commuting patterns for 115 Canadian urban areas are estimated empirically. A novel weighted-averaging process reveals a rich spatial pattern that illustrates significant heterogeneity attributable to differences in urban size and to geographical diversity. Strong distance attenuation effects exhibit non-trivial variations in their intensity and geographic reach across the country. The general patterns are consistent with urban hierarchy notions of functional regions that both compete with and overlap one another. Governance and infrastructure planning would benefit from understanding these interdependencies.

Ali K., Olfert M. R. et Partridge M. D. Les traces urbaines en milieu rural au Canada: des excédents d'emplois par taille des grandes villes, Regional Studies. La croissance des migrations ruralo-urbaines quotidiennes incarnent de facto un processus de régionalisation qui est unique à chaque zone urbaine et à son cadre géographique. Pour évaluer ces rapports, on estime empiriquement les migrations quotidiennes pour 115 zones urbaines au Canada. Un processus original de moyennes pondérées laisse voir une riche distribution géographique qui illustre une importante hétérogénéité imputable aux différences de la taille urbaine et de la diversité géographique. D'importants effets de modération quant à la distance laissent voir des variations non-négligeables de leur intensité et de leur portée géographique à travers le pays. Les distributions générales conforment à des notions hiérarchiques urbaines de régions fonctionnelles qui se font la concurrence et se chevauchent. Une meilleure compréhension de ces interdépendances serait au profit de la gouvernance et de la planification de l'infrastructure.

Migrations quotidiennes Régionalisation Marchés du travail régionaux

Ali K., Olfert M. R. et Partridge M. D. Urbane Fußabdrücke in ländlichen Gebieten Kanadas: Übertragung von Beschäftigung je nach Stadtgröße, Regional Studies. Ein wachsender Pendlerverkehr von ländlichen in städtische Gebiete ist der Inbegriff eines De-facto-Regionalisierungsprozesses, der für jedes städtische Gebiet und seine räumliche Umgebung einzigartig ist. Zur Bewertung dieser Beziehungen wurden die Pendlerströme von 115 Stadtgebieten Kanadas empirisch geschätzt. Ein neuartiges Verfahren zur Ermittlung des gewichteten Durchschnitts führt zu einem erweiterten räumlichen Muster, das eine signifikante Heterogenität verdeutlicht, die durch Unterschiede hinsichtlich der Größe und geografischen Diversität der Städte verursacht wird. Starke entfernungsbedingte Abschwächungseffekte führen landesweit zu nicht vernachlässigbaren Variationen hinsichtlich der Intensität und geografischen Reichweite. Die generellen Muster stimmen mit der Auffassung von der urbanen Hierarchie funktionaler Regionen überein, die miteinander konkurrieren und sich zugleich überschneiden. Die Planung von Politik und Infrastruktur würde von einem Verständnis dieser Wechselwirkungen profitieren.

Pendlerverkehr Regionalisierung Regionale Arbeitsmärkte

Ali K., Olfert M. R. y Partridge M. D. Huellas urbanas en las zonas rurales de Canadá: desbordamientos de empleo según el tamaño de las ciudades, Regional Studies. El creciente proceso de desplazamientos al trabajo de un área rural a otra urbana epitomiza un proceso de regionalización de facto que es único para cada área urbana y su entorno espacial. Al evaluar estas relaciones, se calculan empíricamente los modelos de desplazamientos en 115 áreas urbanas de Canadá. Un nuevo proceso de promedios ponderados indica un amplio modelo espacial que ilustra una heterogeneidad significativa atribuible a las diferencias en el tamaño urbano y la diversidad geográfica. Los fuertes efectos de atenuación de las distancias muestran variaciones no triviales en su intensidad y alcance geográfico en todo el país. Los modelos generales son coherentes con las nociones de jerarquías urbanas de las regiones funcionales que compiten y se solapan entre ellas. La gobernanza y la planificación de infraestructura se beneficiaría si fuese capaz de entender estas interdependencias.

Desplazamietos al trabajo Regionalización Mercados laborales regionales

Keywords:

• Commuting
• Regionalization
• Regional labour markets

JEL classifications:

• R11
• R12
• R23

Acknowledgements

The authors thank James LeSage and Tom Johnson for providing helpful comments on earlier drafts of this paper. Earlier versions of this paper were presented at the Regional Science Association International World Congress, São Paulo, Brazil; the Southern Regional Science Association Annual Meetings in Arlington, Virginia, USA; Canadian Economics Association Annual Meetings in Vancouver, British Columbia; the Canadian Urban Institute–Canada Rural Revitalization forum ‘Developing the Regional Imagination: A National Workshop on Rural–Urban Interaction’, Toronto, Ontario; and at the Canadian Rural Revitalization Foundation Annual Meetings, ‘Connecting Communities: Rural and Urban’, Vermillion, Alberta. Production of this paper was made possible through a financial contribution from Infrastructure Canada. The views expressed herein do not necessarily represent the views of the Government of Canada. The authors also thank the Canada Rural Revitalization Foundation and the Federation of Canadian Municipalities for their support of this project, in particular Robert Greenwood.

Notes

1 There is a rich literature following Alonso (1964) exploring the intra-urban commuting patterns, where the commuting/housing decision is cast as a trade-off between a preferred residential setting and better access to the central business district. Extended, extra-urban commuting, the subject of the current paper, has, however, received much less attention. Though there are similarities between intra- and extra-urban commuting flows, there are also conceptual differences that lead to differing modelling approaches.

2 CA and CMA are defined as consisting of an urban core and one or more adjacent municipalities. The population required for an urban core to form a CMA is at least 100 000, and at least 10 000 to form a CA. To be included in the CA or CMA, adjacent municipalities must be highly integrated with the central urban area, as measured by commuting flows (Du Plessis et al., 2002).

3 For geographic consistency between the two censuses, the 2001 data are adjusted to reflect the 1996 boundaries. Persons who had no fixed work address or worked outside the country are excluded. The commuting flow matrix, however, is not square since information on place of work was withheld for confidentiality reasons in the case of a small number of sparsely populated communities.

4 Statistics Canada defines a CCS as a group of adjacent census subdivisions. Generally, small urban census subdivisions (towns, villages, etc.) are combined with a surrounding rural census subdivision (Du Plessis et al., 2002).

5 Statistics Canada, in delineating CMAs, considers only commuting to the urban core of the CMA. That is, for a CCS to be ‘attached’ to a CMA, it must be the case that more than 50% of its labour force is commuting to the core.

6 There are 137 CA/CMAs in Canada; however, twenty-two had too few surrounding CCSs within the 200-km limit to permit estimation.

7 A distance of 200 km is assumed to be the maximum for potentially regular commuting given well-connected highways and access to modern transportation facilities; beyond 200 km, commuters may not commute daily.

8 In initial exploration, the authors experimented with a general Tobit model to account for left-hand censoring at a zero commuting rate. Generally, the key distance coefficients were a little larger than currently reported, particularly for small urban areas with a larger share of zero commuting rates. These preliminary Tobit results indicate that the smallest urban areas have somewhat reduced regional labour markets than implied in the results given below. The results for the larger urban areas appear to be only slightly affected, or not affected at all, by this censoring, suggesting that the present conclusions are unchanged. However, estimating SEM Tobit models is problematic because of the simultaneous problem of addressing the censoring issue while estimating the λWu term, that is, surrounding county residuals simultaneously face the censoring issue (no suitable software available). Thus, the SEM model is preferred due to theoretical concerns about spillovers.

9 The authors also experimented with logit models to address another possible concern of non-normally distributed errors since commuting shares are bounded between zero and one. While these models are theoretically appealing for limited-dependent variables, fairly easy to estimate, and predict probabilities of the event of interest, some practical considerations related to their applicability to the data and prediction performance of the test models dissuaded the present authors to adopt these models for all commuting sheds (for further discussion, see the empirical result section and note 16 below about pooling).

10 The auxiliary regression of distance of the nearest urban area on the other explanatory variables suggested that the key distance variable is not highly correlated with the other explanatory variables. A further investigation of the potential effect of multicollinearity was conducted through the calculation of the variance inflation factor between all the independent variables. These factors range from 1.3 to 5.2, all well below the critical value of 10.0, suggesting that multicollinearity is not problematic (Kennedy, 1985, p. 153).

11 The authors experimented with including a quadratic term of the distance to the focal CA/CMA, but it was almost always insignificant, suggesting that linear distance decay for commuting patterns adequately represents the data. Possibly, the 200-km truncation limits the scope for non-linearity. A fourth distance variable, ‘distance to the nearest major highway’, initially included, was omitted because of multicollinearity concerns and statistical insignificance. A reviewer noted that one could employ other functional forms for the dependent variable, such as a logit or log-odds form:

• $\log \left(C/\right(1-C\left)\right)$where C is the commuting rate in equation (2)(2) $\mathit{C}=\mathit{X}\text{β}+\mathit{u}\mathit{u}=\lambda \mathit{W}u+\mathit{\epsilon }\mathit{\epsilon }\sim N(0,{\sigma }^2\mathit{I})$(2) . Though this model would no longer face censoring issues, it would be highly non-linear because many observations for C are either zero or near to zero, especially in more distant CCSs, while other values of C are near 1. Yet, as just noted, no significant non-linearities were uncovered and censoring does not appear to play a role in the conclusions after the averaging is done across multiple commuting areas. Distance to the two competing urban centres may exceed 200 km since they were not restricted to be within the commuting shed of 200-km radius.

12 Distinct commuting sheds would be much more difficult to disentangle in areas very densely populated with cities, such as Western Europe. In the Canadian setting relatively few areas have dense cities, and it is thus easier to isolate patterns that would not be apparent if all areas comprised numerous overlapping commuting sheds across the entire country, that is, as in many European countries or in most of Japan.

13 A difference, rather than a ratio, is used because job growth can be positive or negative and the ratio formulation misrepresents the sign if one or both of the numerator/denominator is negative.

14 Although there could potentially be more mobile education categories such as with a college or university degree, they were generally not significant predictors for commuting rates when considered in exploratory analyses.

15 Pesaran et al. (1999) refer to a sample size of thirty-two as ‘large’ and a sample size of seventeen as ‘small’. They show that the mean-group averaging works well in examples using these sample sizes.

16 When pooling the entire sample, this ‘unbalanced’ pooling problem can be illustrated with the following example. Take Essa CCS (3543021) in south-west Ontario. It falls in the following eight urban area samples determined by the 200-km radius: Hamilton, Toronto, Kitchener, Brantford, Barrie, Oshawa, Peterborough, and London. Using the notation of equation (2)(2) $\mathit{C}=\mathit{X}\text{β}+\mathit{u}\mathit{u}=\lambda \mathit{W}u+\mathit{\epsilon }\mathit{\epsilon }\sim N(0,{\sigma }^2\mathit{I})$(2) , if one were to pool the entire sample, one would have eight separate observations for Essa: (1)(1) $C_{ij}=C_{ij}(e_i,e_j,D_{ij},Z_{ij})$(1) C_Ham = X_Ham β_Ham + u_Ham; (2)(2) $\mathit{C}=\mathit{X}\text{β}+\mathit{u}\mathit{u}=\lambda \mathit{W}u+\mathit{\epsilon }\mathit{\epsilon }\sim N(0,{\sigma }^2\mathit{I})$(2) C_Tor = X_Tor β_Tor + u_Tor; … (8) C_Lon = X_Lon β_Lon + u_Lon. Thus, the eight residual vectors u_Ham, u_Tor, …, u_Lon will all be correlated in an unknown fashion, which is even further confounded by the underlying spatial autocorrelation in the sample. Adding further complications is that across the country the number of urban samples for which a given CCS will be included will vary from as low as one to as high as ten or more, and the particular urban areas will greatly vary when moving across the country. That is, though the problem is similar to that which underlies the use of the seemingly unrelated regression, the solution in this case is intractable given current methodologies and software. This stacking problem when pooling the data applies regardless of whether OLS, SEM, or logit are used, that is, when pooling the data there will be the multiple observations for a given CCS. Thus, treating each urban area individually and then averaging is a sensible way of avoiding this intractable statistical problem while still gaining efficiency from considering multiple urban areas. Pesaran and Smith (1995) and Pesaran et al. (1999) show that the averaging leads to results that compare favourably with pooled approaches.

17 By separating the regressions into separate urban area commuting models, one need not take into account the correlated error term structure that would result if the overlapping commuting models were pooled (see note 16). The use here of a spatial error model also helps take into account the spatial interdependence of overlapping commuting sheds.

18 The geographic size of the CA/CMAs varies from a minimum of 40.5 km² to a maximum of 610 456 km², with a mean area of 18 356 km². Generally, the outer fringe of the official CMA is very lightly populated.

19 Recent applications of this technique include Tan (2006) in the case of foreign aid and growth, and Martinez-Zarzoso and Bengochea-Morancho (2004) in the case of carbon dioxide (CO₂) emissions and per-capita income relationships.

20 Pesaran and Smith (1995) and Pesaran et al. (1999) faced similar problems in which the countries in their Organisation for Economic Co-operation and Development (OECD) sample, or the industries in their thirty-eight industry sample, were also unlikely to be perfectly independent of one another – though they still applied mean-group averages.

21 See note 16.

22 Results are available from the authors upon request.

23 The use of quadratic terms in these trend models was statistically insignificant, suggesting that larger urban centres do not dominate the fit of this line.

24 Excluding Toronto and Montreal from the regressions resulted in a poorer fit – R² drops to 13–29%, and flatter trend lines occur. Consequently, the threshold populations for various degrees of labour market linkages are unrealistically large.

25 By comparison, the out-commuting rates used by Statistics Canada are 50% to the core (Statistics Canada, 2004) in determining whether a locality is included in a metropolitan area, while the corresponding figure for the US Census Bureau to include a county as part of a metro area is 25% (US Office of Management and Budget, 2000).

26 These figures are derived as the anti-log of the log population, where the 50-km line crosses the 30%, 20%, and 10% lines, that is, exp(14.4), exp(12.7), and exp(11.0).

27 The authors have chosen an area relatively densely populated with urban centres in the Canadian context, acknowledging that in an even more densely populated area such as in Western Europe and the North-eastern United States, these patterns may be much more complex.

28 While the radii represent average distances, actual commuting sheds will have shapes that reflect competition between commuting destinations and the transportation network. Fig. 1 illustrates the ‘non-circular’ extent of the commuting shed surrounding London.

29 Quadratic distance terms are added for London's model to accommodate its unique commuting shed that comprised a large proportion of CCSs under the biggest agglomeration shadow of Toronto, while occupying the ‘neck’ of the southern Ontario peninsula with very few CCSs to the south and west.