Competitive and Complementary Relationship between Regional Economies: A Study of the Great Lake States

Abstract

Since regional economies are exposed to the region common shock, the degree of co-movement of each region's business cycle is strong, possibly exaggerating or biasing the dependency on its neighbor regions. By separating out the common shock and the individual shocks using a multi-level dynamic factor model suggested by Bai and Wang, the possible misunderstanding of regional interdependency can be prevented. An application to the Great Lakes region revealed that much of the region-specific business activities can be explained by the region common shock, and the spillovers from neighbors are small or insignificant.

Résumé

étant donné que les économies régionales sont exposées au choc commun de la région, la degré de parallélisme dans le cycle commercial de chaque région est élevé, en exagérant ou en faussant éventuellement la dépendance de ses régions avoisinantes. En séparant le choc commun des chocs individuels, à l'aide d'un modèle de facteur dynamique multi-niveaux du type proposé par Bai et Wang, il est possible d'éviter d'éventuels malentendus d'interdépendance régionale. Une application à la région des grands lacs a révélé qu'une grande partie des activités commerciales spécifiques à la région peuvent être expliquées par le choc commun de la région, et que les retombées de régions voisines sont faibles, voire insignifiantes.

Resumen

dado que las economías regionales están expuestas al choque común regional, la proporción del comovimiento del ciclo comercial de cada región es elevada, posiblemente exagerando o influenciando la dependencia de sus regiones vecinas. A través de la separación del choque común y los choques individuales mediante un modelo de factor dinámico de multinivel sugerido por Bai y Wang, se puede evitar el posible malentendido de la interdependencia regional. Una aplicación a la Región de los Grandes Lagos reveló que una gran parte de las actividades comerciales específicas de la región puede explicarse mediante el choque común regional y los excedentes de las regiones vecinas son pequeños o insignificantes.

摘要

由于区域经济体暴露于区域常见的震荡, 每个地区的商业周期一 般都呈现很强的同步走向, 因而很可能会夸大或阻碍对相邻区域的依赖关系。通过采用 Bai and Wang 建议的多层次动态因素模型使共同震荡和个别震荡相分离的方法, 可以防止对区域相互依赖的误解。在大湖区的应用结果表明, 很多区域特有 的商业活动可通过区域的共同震荡得到解释, 而邻国的溢出效应则往往很小或微不足道。

Keywords:

• Regional business cycle
• dynamic factor model
• multi-level
• spillover effects

JEL Classification:

• C11
• C15
• C31
• R11

Disclosure statement

No potential conflict of interest was reported by the authors

Supplemental data

Supplemental data for this article can be accessed here.

Notes

1. Individual ‘region’ denotes each state in Great Lake Region, and ‘region common’ denotes Great Lake States.

2. The estimation of Equation (2) is equivalent to estimating a latent factor model, treating each shock as an unidentified parameter. Thus, a Kalman filtering method, as is used in Bai & Wang (2012)'s dynamic factor model used later in this paper, can be used to identify those shocks and parameters. For a more details about estimation procedures, refer to Clark & Shin (1998).

3. See Magalhães et al. (1999) for an example using a non-linear relative dynamics formulation and Marquez et al. (2013) for a case study using a spatial vector autoregressive approach

4. Although, Bernanke et al. (2005) does not specify a multi-regional framework in its model, the direct application of their work into a multi-regional framework can easily be expressed into Equations (5)–(7).

5. Typically, it is a Gaussian error term in its application, but it is allowed to have temporal lag in its theoretical form.

6. Also, for example, if the regional economy is triple layer structure with R local level regional units, S intermediate level regional units and 1 national level state of economy, then the number of units we consider should be . However, in practical applications, models with more than two layer structure are hard to implement because the size of the coefficient matrix becomes too large. For example, when the number of units that should be considered is , the number of the 1st lag coefficient in Equation (10) becomes .

7. In reality, it is somewhat vague to categorize which shock is local and which shock is global. For example, if there is a business decision on production increase of a multi-regional manufacturing company, this decision itself is a national level shock because the increased production will have a nationwide effect, but if the production facility is located in a particular region, and/or the products are consumed mostly in a particular region, then this positive production shock will be local in nature.

8. In Bai & Wang (2012)'s model, the factors in the state Equation (10) can be regarded as innovations of the observation Equation (8) that allow for temporal and spatial correlations.

9. Bai & Wang (2012) discuss the required restrictions needed to identify the dynamic factor model in more general cases.

10. Bayesian-inference Using Gibbs Sampling for Windows.

11. The Bayesian inference also relies on priors, which have to be assumed for all unknown parameters of the model. In this paper, uninformative priors were used. Using the likelihood and the priors, the Gibbs Sampling algorithm draws samples from the posterior distribution of parameters including the latent factors. After a sufficient burn-in period, the appropriate thinning period is set to eliminate the autoregressive relationship between each round of sampling, and the posterior distribution of each parameter is derived. Appendix 1 (Supplementary material) describes the likelihood and the priors used in the model for Equations (8) through (10).

12. CIRF is used in order to more conveniently compare the long-term signs of the responses of each factor against each shock.

13. Derivation of the multi-level structure model is provided in Appendix 2 (Supplementary material).

14. If the researcher believes that a single-level structure is the true structure of the Indonesian economy, then the multi-level model will pick up a spurious spatial dependency. However, since sub-national level Indonesian regions are exposed to a single national factor, it should be more appropriate to adopt the multi-level idea in this case.

15. The data are thus monthly frequency US state level aggregated data. The degree of the spatial spillovers can be dependent on the degree of aggregation over time and space. For example, Park & Hewings (2012) revealed that the degree of spatial dependency increases with the use of more disaggregated temporal data. Also, Arbia & Petrarca (2011) deal with the modifiable areal unit problem (MAUP), and showed that the estimated parameters changes with the aggregation of the spatial units. In this paper, since the focus is on the business cycle analysis of the six Great Lake states, and the more disaggregated temporal frequency is thought to best reveal the spatial dependency structure, monthly state level data are used. To see the longer term effect of spatial spillover effect, six-month ahead FEVD and cumulative impulse responses are shown later in this chapter allowing for an enough time period for the propagation of the spillover from a region to another.

16. The estimation results of parameters are presented in Appendix 3 (Supplementary material), and the estimation results of dynamic factors with their confidence intervals are provided in Appendix 4 (Supplementary material) for the multi-level dynamic factor, and in Appendix 5 (Supplementary material) for the single-level dynamic factor.

17. The estimated region common factor is, in fact, can be regarded as the common shock to the US states. As we can see in Appendix 6 (Supplementary material), the extracted region common shock and the CFNAI (Chicago Fed National Business Activity Index) are almost identical with different scales.

18. VAR(3) specification of the state equation was also tried, but it turned out that VAR(2) and VAR(3) both generate insignificant coefficients, thus only VAR(2) results are presented in this paper. Any longer lag structure had not been tried because of the limited computing power, but judging from the VAR(2) and VAR(3) results, estimation of higher order state equation does not seem to produce more significant estimators.

19. The cumulative impulse response functions for all those 6 alternative model structures and single-level structure model with 95% confidence intervals are provided in Appendix 7 (Supplementary material). In Table 7, the FEVD table using the disaggregated employment series shows very large portions of neighborhood spillovers compared to the original set of variables. This is because the sub-sectorial employment series have relatively higher correlation with each other than the aggregated series of regional macroeconomic variables including housing sector and unemployment rate. Thus, if the regional industrial performances are of more interest than the overall regional economic performances, more inter-regional dependencies will be found.

20. ( matrix for the multi-level model with R + 1-th element being the interaction between a factor and the region common factor, and for the single-level model without R + 1-th element.

21. Appendix 7 (Supplementary material) provides the whole set of CIRFs.

22. The latent factor model can be regarded as a tool to estimate the unknown controls for the regional business cycle.