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Spatial agglomeration and firm exit: a spatial dynamic analysis for Italian provinces

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Abstract

The paper investigates the effect of spatial agglomeration on firm exit in a dynamic framework. Using a large dataset at the industry-province level for Italy (1998–2007), we estimate a spatial dynamic panel model via a GMM estimator and analyze the short-run impact of specialization and variety on firm exit. Specialization negatively affects firm exit rates in the short-run. The effect is particularly significant for low-tech firms. The impact of variety on firm mortality rates at the industry level is instead less clear, although still negative and significant for low-tech firms.

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Notes

  1. Some authors distinguish between static and dynamic externalities (e.g. Glaeser et al. 1992; Henderson et al. 1995; Henderson 2003). Static externalities are one-time efficiency gains produced by spatial concentration. As such, they can account for spatial agglomeration in a homogeneous space, but not for long-run growth differentials between regions. Dynamic externalities are instead within- and across-industry knowledge spillovers able to explain sustained differentials in regional growth rates.

  2. With respect to age, the most debated are the “liability” of “newness” (Stinchcombe 1965; Geroski 1995), “aging” (Hannan 1998), “obsolescence”, “senescence” (Barron et al. 1994), and “adolescence” (Schindele et al. 2011). With respect to size, the most investigated is the so-called liability of “smallness” (Aldrich and Auster 1986; Geroski 1995; Honjo 2000).

  3. The widespread use the extant literature makes of the location quotient as an indicator of localization economies comes from the seminal studies by Glaeser et al. (1992) and Henderson et al. (1995), which somehow re-initiated this literature. However, Glaeser et al. (1992), who first express the idea that the location quotient can better capture the potential for Marshall–Arrow–Romer (MAR) externalities, do not provide a clear theoretical justification for this. In fact, it seems that Glaeser et al. (1992) and Henderson et al. (1995) use the location quotient only because the size-based indicator (the level of own industry employment) could not be used, as it was already included in the specification to account for mean reversion processes in the employment dynamics. This is explicitly, although incidentally, acknowledged also by Henderson (2003), who uses the number of own industry plants to proxy localization economies and observes that “it is difficult to disentangle dynamic externalities from mean reversion processes—both typically involve the same quantity, measures of past own industry employment” (p. 4).

  4. The role of the production and technological capabilities of the local firms is hard to disentangle from that of the regional ones, as the latter are not simply additive with respect to the former. On this point, see, for instance, Iammarino et al. (2012) and Simonen and McCann (2008).

  5. Italy is actually the country where Marshallian industrial districts, theorized by Becattini (1990), have received the largest attention, both in the academic research and in the policy analysis.

  6. Data availability prevented us from investigating to what extent the 2007 crisis affected firm exit in Italy. Although with a different econometric strategy, on this issue see Amendola et al. (2010).

  7. Among the other things, this control enabled us to reduce the incidence of possible operations of Mergers and Acquisitions (M&A) on the actual exit of firms from the market.

  8. As a robustness check, estimates have been also run by dropping the 20th percentile of the variable, referring to observations with less then 16 firms. As they remain substantially unchanged, these estimates will be not reported in the following and are available upon request.

  9. As our focus is on the impact of spatial agglomeration on firm mortality in manufacturing as a whole, we differentiate from Carree et al. (2011), who use different sectoral panels for different manufacturing industries.

  10. It is worth stressing that the indicator, as such, is not able to account for the level of industrial concentration of the sector or for other factors related with the average size of the firms belonging to a certain sector (for the interconnections between industrial and spatial concentration see Ellison and Glaeser 1997; for the interconnections between industrial and spatial concentration see Rosenthal and Strange 2001). Indeed, the number of firms per km² in a certain sector-province tends to be lower for the sectors characterized by structurally higher industrial concentration. Nonetheless, we account somehow for these factors controlling for the unobserved time-invariant heterogeneity in the econometric specification.

  11. We use the entropy index instead of the log of the (inverse) Herfindahl index to measure variety, as it does not require any further transformation (it is already a weighted average of logs) and as it is becoming a more standard measure of it, given its decomposability property (see, for instance, Frenken et al. 2007). The index is in fact what Frenken et al. (2007) call “unrelated variety”.

  12. The case of industrial districts is particularly illustrative. Their identification through the popular “Sforzi approach” and the “Iuzzolino approach” (Boccella et al. 2005; Sforzi 2009) actually show them to be very often trans-provincial.

  13. Both the correlations and all the subsequent specifications have also been estimated using (Euclidean) distance-based matrices with threshold cut-off equal to: 75 km (critical cut-off, i.e. min cutoff so that each province has got at least one neighbor); 100 km; 200 km; 300 km; 400 km. Results do not significantly differ and are available on request.

  14. This specification is a generalization of that analyzed, among the others, by Lee and Yu (2010c), where there is only one time lag and one spatial-time lag (L e  = 1). Lee and Yu (2010c) work out the sufficient and necessary stability conditions for the model with only one time lag and one spatial-time lag. The sufficient and necessary stability conditions for the more general model in (5) have not yet been worked out.

  15. Once again, the following cut-offs have been considered: 75 km (critical cut-off, i.e. min cutoff, so that each province has at least one neighbor); 100 km; 200 km; 300 km; 400 km. Industries in the same province have always been considered neighbors.

  16. We estimate all the specifications also by dropping the 20th percentile (units-periods with less than 16 firms) and the results, available on request, do not significantly differ.

  17. In order to check for economic opportunities and business cycle conditions affecting firm exit, which were not already captured by our spatial-time lags, we have also tried to include in the specification the growth rate of the GDP at the NUTS-3. However, and as expected, it turned out not significant and has therefore been omitted.

  18. Given the absence of a simultaneous spatial lag (λ = 0) in the estimated specification, the short-run ATI coincides with the coefficient attached to the variable.

  19. The first candidate would be what Frenken et al. (2007) call “related variety”, as distinguished from the variety indicator that we used, which correspond to the “unrelated” one in their framework.

  20. The derivation is similar to the ATI for the SAR model (see LeSage and Pace 2009, Ch. 2, for details).

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Acknowledgements

The authors would like to thank the participants to the VII Workshop of the European Network of the Economics of the Firm (ENEF) (Amsterdam, September 16–17, 2010) and the XXXII Annual Scientific Conference of the Italian Association of Regional Sciences (Milan, September 15–17, 2011) for their useful comments. They are particularly indebted to Alessia Amighini and Roberto Basile, for their suggestions on a previous version of the paper. The authors gratefully acknowledge support for this research from the Autonomous Province of Trento (OPENLOC Project). The usual disclaimers apply.

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Authors and Affiliations

  1. Department of Economics and Management, University of Padua, via del Santo 33, 35122, Padua, Italy

    Giulio Cainelli

  2. CERIS-CNR, Milan, Italy

    Giulio Cainelli

  3. Department of Economics, University of Bologna, Strada Maggiore 45, 40125, Bologna, Italy

    Sandro Montresor

  4. JRC-IPTS, European Commission, Seville, Spain

    Sandro Montresor

  5. Department of Sociology and Social Research, University of Milano-Bicocca, via Bicocca degli Arcimboldi 8, 20126, Milan, Italy

    Giuseppe Vittucci Marzetti

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Correspondence to Sandro Montresor or Giuseppe Vittucci Marzetti.

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Although the paper is the joint work of all the three authors and they share Sects. 1 and 5, Sect. 2 can be attributed to Sandro Montresor and Giuseppe Vittucci Marzetti, Sect. 3 to Giulio Cainelli and Giuseppe Vittucci Marzetti, Sect. 4 to Sandro Montresor.

Appendix: Long-run steady state Average Total Impact

Appendix: Long-run steady state Average Total Impact

Looking at the steady state relation of Eq. (5) we have:

$$ {\bar{\bf E}} = \ \lambda {\bf W} {\bar{\bf E}} + \sum_{l=1}^{L_e} \gamma_l {\bar{\bf E}} + \sum_{l=1}^{L_{e}} \rho_l {\bf W} {\bar{\bf E}} + \sum_{l=0}^{L_s} \delta_l {\bar{\bf S}} + \varvec{\mu} + {\bar{\bf X}} \varvec{\beta} $$

where \(\varvec{\beta} = (\beta_c,\beta_d)'\) and \({\bar{\bf X}} = ({\bar{\bf C}}, {\bar{\bf D}}). \)

$$ \begin{aligned} &\left ( \left ( 1- \sum_{l=1}^{L_e} \gamma_l \right ){\bf I} - \left ( \lambda + \sum_{l=1}^{L_{e}} \rho_l \right ){\bf W} \right ) {\bar{\bf E}} = \sum_{l=0}^{L_s} \delta_l {\bar{\bf S}} + \varvec{\mu} + {\bar{\bf X}} \varvec{\beta}\\ &{\bar{\bf E}} = {\bf B}(\lambda,\varvec{\gamma},\varvec{\rho}) \sum_{l=0}^{L_s} \delta_l {\bar{\bf S}} + {\bf B}(\lambda,\varvec{\gamma},\varvec{\rho}) \varvec{\mu} + {\bf B}(\lambda,\varvec{\gamma},\varvec{\rho}) {\bar{\bf X}} \varvec{\beta} \end{aligned} $$

where \({\bf B}(\lambda,\varvec{\gamma},\varvec{\rho}) = (( 1- \sum_{l=1}^{L_e} \gamma_l){\bf I} - (\lambda + \sum_{l=1}^{L_{e}} \rho_l){\bf W})^{-1}. \)

The ATI in the steady state of a regressor k is therefore given by: Footnote 20

$$ \begin{array}{ll} \frac{\beta_k}{n} \varvec{\iota}' {\bf B}(\lambda,\varvec{\gamma},\varvec{\rho})\varvec{\iota} &= \frac{\beta_k}{(1- \sum_{l=1}^{L_e} \gamma_l)}\left ( n^{-1} \varvec{\iota}' \left ( {\bf I} - \frac{\lambda + \sum_{l=1}^{L_e} \rho_l}{1-\sum_{l=1}^{L_e} \gamma_l}{\bf W} \right )^{-1} \varvec{\iota}\right )\\ &= \frac{\beta_k}{(1- \sum_{l=1}^{L_e} \gamma_l)} \left ( 1 - \frac{\lambda + \sum_{l=1}^{L_e} \rho_l}{1- \sum_{l=1}^{L_e} \gamma_l} \right )^{-1} = \frac{\beta_k}{1 - \lambda - \sum_{l=1}^{L_e} (\gamma_l + \rho_l)} \end{array} $$

where \(\varvec{\iota}\) is a column vector of ones and n the number of cross-sectional units.

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Cainelli, G., Montresor, S. & Vittucci Marzetti, G. Spatial agglomeration and firm exit: a spatial dynamic analysis for Italian provinces. Small Bus Econ 43, 213–228 (2014). https://doi.org/10.1007/s11187-013-9532-6

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