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Assessing the regional business cycle asymmetry in a multi-level structure framework: a study of the top 20 US MSAs

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Abstract

Dating the regional business cycle phases using a multi-level Markov-switching model revealed that the regional cycle phase transition probability depends on the national cycle phase, although the propagation speed of the national phase into a regional cycle varies across the regions. The estimation of the national factor loadings on regional economies showed that the response of a regional economy to a national impact is mostly greater during a national contraction phase.

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Notes

  1. Examples include Garcia and Schaller (2002), Karras (1996) and Ravn and Sola (2004).

  2. When the national economy is at contraction phase, the time it takes for a regional economy to transit is much shorter. It is well known that agents react faster to bad news in time of recession because late response can greatly hurt the industry.

  3. Burns and Mitchell (1946) defined business cycle as the following: business cycles are a type of fluctuation found in the aggregate economic activity of nations that organize their work mainly in business enterprises: a cycle consists of expansions occurring at about the same time in many economic activities, followed by similarly general recessions, contractions and revivals which merge into the expansion phase of the next cycle. (p. 3)

  4. In NBER Web site of “U.S. Business Cycle Expansions and Contractions” section, it says:

    “The NBER does not define a recession in terms of two consecutive quarters of decline in real GDP. Rather, a recession is a significant decline in economic activity spread across the economy, lasting more than a few months, normally visible in real GDP, real income, employment, industrial production, and wholesale-retail sales.”

    This paper used a Markov-switching model in identifying the business cycle phases to let the statistical model work as the regional version of the business cycle dating committee.

  5. Thus, a dynamic factor model with a regime switching and an AR(1) structure will require at least four distinct phases defined in order to effectively identify the business cycle phase.

  6. Since many of the national economic indicators that are used in constructing the national business cycle index are aggregated series of regional economic indicators, the assumption that the national business cycle phase transition dynamics are independent from the regional business cycle phases might look unrealistic. However, as noted earlier in the previous section and Fig. 3, the unobserved state of the national economy is assumed to be mostly determined by non-regional factors such as monetary/fiscal policies, international commodity markets and conglomerates business decisions and innovations, national cycle phase works as an exogenous factor in regional cycle phase transition dynamics. Similar structures can be found in international business cycle analysis literature where international (or foreign) variables are exogenous to small open economies. See Buckle et al. (2007), Gjerde and Saettem (1999), Jacobson et al. (2001) and Uribe and Yue (2006) for more details.

  7. By assuming that the national cycle phase is exogenous to the regional cycle phase transition, the national transition dynamics become separated from the regional transition dynamics; thus, we estimate one national-level transition matrix and two regional-level transition matrices for each region. If we do not assume this hierarchical structure between the national and regional cycle phase dynamics, then the national and regional dynamics will become parallel, which is economically implausible. In other words, if regional units also have significant impacts on the national-level cycles, there should be four states (national expansion + regional expansion, national expansion + regional contraction, national contraction + regional expansion, and national contraction + regional contraction) for a region. This implies that if we expand this transition dynamics to 20 MSAs, the number of states will grow to \(2^{21}\), implying more than 4 million entries to estimate, which is practically impossible.

  8. The resulting phase probability, \(S_{rt}\), is not very different even when we use a conventional single-level structure phase transition matrix. The only difference between the multi-level structure Markov-switching model and the single-level structure Markov-switching model is the transition matrix itself.

  9. The list is provided in Appendix 1. All appendices are available at www.real.illinois.edu/d-paper/14/app.pdf.

  10. The list of the deleted observations is provided in Appendix 2.

  11. For the detailed description of IPCA algorithm, see Imtiaz and Shah (2008).

  12. The priors for the parameters are specified as below:

    • \(\mu _{Srt}^r\) and \(\mu _{St}\) are given an uninformative normal prior with mean 0 and precision 0.0001,

    • \(\sigma _{St}\) and \(\sigma _{Srt}^{r}\) are given an uninformative inverse gamma prior with parameter (0.0001, 0.0001), and

    • \(p_{i0} =1-p_{i1}\) and \(p_{r \, i0}^s =1-p_{r \, i1}^s\) are given an uninformative uniform prior Unif(0, 1).

    The state parameters, S and Sr are drawn from Bernoulli distribution.

  13. Bayesian inference Using Gibbs Sampling for Windows.

  14. The results for other cities are provided in Appendix 3.

  15. The transition matrices of other cities, and the test results whether the transition probability matrices are different during the national expansion phase and the national contraction phase are provided in Appendix 4.

  16. Although the original identification of the business cycle phase has already been incorporated in different variances for each phase, at this stage of analysis, the sources of shock on each regional economy are decomposed into national components, its own regional lag, and idiosyncratic components. Thus, the variance measured in Eq. (7) represents the variance of idiosyncratic part of the regional series, while the variance measured in phase identification stage denotes the total variance of the regional series.

  17. The responses of other cities are presented in Appendix 5.

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Acknowledgments

I would like to express my gratitude to Anil K. Bera, Bernard Fingleton, Michael T. Owyang, Jason Bram and other anonymous referees for their valuable comments on this paper. With their comments and the support from my greatest academic advisor, Geoffrey J.D. Hewings, this paper could win 2015 Tiebout Prize.

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Authors and Affiliations

  1. Economic Research Institute, Bank of Korea, Seoul, 04532, Korea

    Sungyup Chung

  2. Regional Economics Applications Laboratory, University of Illinois, Urbana, IL, 61801-3671, USA

    Sungyup Chung

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Chung, S. Assessing the regional business cycle asymmetry in a multi-level structure framework: a study of the top 20 US MSAs. Ann Reg Sci 56, 229–252 (2016). https://doi.org/10.1007/s00168-015-0732-7

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