## _wp11290 - References

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---

### Introduction
- Market context and scope
  - The market for US municipal bonds is a $2.9 trillion tax-exempt bond market amounting to about a third of the US treasury market.
  - Study period: 01/01/2005 to 01/13/2011 using daily 10-year municipal and treasury bond yields from Bloomberg.
  - The 10-year Treasury yield is the constant maturity yield. Municipal yields estimated from an option-free yield curve built using option adjusted spread model and contributed pricing to Bloomberg.
- Research questions
  - Whether and how shocks to individual state bond markets spread to other state bond markets.
  - Whether shocks to individual state bond markets spread to US Treasury securities and vice versa.
- Key contextual points
  - The housing bust, the financial crisis, and the recession reduced state and local tax revenues and increased borrowing costs for many states.
  - The largest recent municipal failure referenced is Jefferson County, Alabama in November 2011.
  - Focus: describing the nature of spillover effects rather than identifying specific transmission channels.

### Spillover literature and empirical test
- Theoretical framing
  - Two strands: non-crisis-contingent (“strong form of contagion”) and crisis-contingent (“weak form of contagion” or “shift-contagion”).
  - Forbes and Rigobon (2002) argue that increases in unconditional correlation during crises can be driven by increased volatility and propose a correction for this bias.
- Forbes-Rigobon (FR) correction (as presented)
  - FR correction formula: ρ̃ = ρu / sqrt(1 + δ).
  - Relative increase in variance δ: δ = σ_high^2 / σ_low^2 − 1, where σ_high^2 is VAR residual variance in the high-volatility sub-sample and σ_low^2 is variance in the low-volatility sub-sample.
- Test implementation choices
  - Use of the Dungey et al. (2005) recommended FR test where low and high volatility sub-samples are independent.
  - Robustness checks: two other FR versions and multivariate FR considered; main results unchanged (additional results available upon request).

### Main results
- Sample break date and volatility
  - Break date chosen to maximize increase in VAR residual variance: August 29th, 2008.
  - Twenty-two largest municipal issuers analyzed; municipal yields filtered by a VAR(2) conditioned on the ten-year US bond yield and S&P 500 return.
  - Examples from Table 1 (σ_low and σ_high):
    - California: σ_low 0.1661, σ_high 0.3647
    - Connecticut: σ_low 0.2053, σ_high 0.4430
    - Puerto Rico R.: σ_low 0.5062, σ_high 0.6068
- Within-muni spillover (Table 2; FR test)
  - FR test statistic interpretation: follows asymptotically a student distribution; a test statistic higher (lower) than 1:96 supports (rejects) the presence of spillover. The sign indicates direction of co-movement.
  - Primary finding: between most markets for individual U.S. state bonds there are negative spillovers—an increase in borrowing costs in one state tends to result in better borrowing conditions (lower yields) for other states.
  - Behavior interpreted as a “flight to safety” within the muni market during periods of volatility.
  - Notable issuers whose problems benefit other states: California, Georgia, Maryland, and the City of New York (spillover is negative when these issuers experience problems).
  - A few states show positive correlations (borrowing costs increase when another state has problems), e.g., Connecticut and Florida.
  - Possible explanations (not empirically tested): reallocations by domestic retail investors and muni bond funds, liquidity effects, rating-triggered rebalancing by institutional investors, and state-specific tax exemptions affecting local investor behavior.
- Bottom-up and top-down spillover between municipal and Treasury markets (Table 3; FR test)
  - Overall finding: no substantial spillover effects between shocks originating from state securities and federal markets, except for a few large issuers.
  - Evidence of positive spillover—albeit below conventional significance—between the U.S. Treasury market and markets for New Jersey, Texas, Washington state, and New York City, with the strongest result for New York City.
  - California shows a negative spillover with the U.S. Treasury market (yields move in opposite directions following a shock).
  - Results robust to using additional lags and controlling for S&P 500 returns; tests reported for VAR specifications with 2 lags and 4 lags, with and without conditioning on S&P 500 returns.
- Causality in the frequency domain (Breitung and Candelon, 2006)
  - Method: Granger causality test in the frequency domain to identify direction and whether causality is short-run (frequencies far from zero) or long-run (frequencies near zero).
  - Main causality findings:
    - The Treasury bond market directly causes changes in municipal bond markets in both the short and long run.
    - Some evidence of causality from municipal to Treasury markets, but only of a long-run nature.
  - Policy implication: structural reforms improving the federal budget in the long run will affect state borrowing conditions; state-level reforms will affect federal borrowing costs in the long run.

### Conclusions and policy implications
- Empirical conclusions
  - Most state bond markets exhibit negative spillovers (problems in one state tend not to worsen borrowing conditions in other states).
  - Only a few large municipal issuers are linked with the Treasury bond market in ways that could affect federal markets.
  - Treasury market causes municipal markets in both short and long run; municipal → Treasury causality exists only in the long run.
- Policy lessons
  - Fiscal unions and supranational authorities should analyze spillovers within their sub-national bond markets as well as linkages between sub-national and supra-national bond markets.
  - Risk management strategies should be informed by the sign (positive or negative) and time-horizon (short or long run) of spillovers.
  - Evidence suggests flight-to-quality dynamics rather than contagion within U.S. state bond markets; implications for whether deeper fiscal union would increase or reduce systemic risk require further research.

### References cited (select highlights)
- Ang, Andrew, and Francis Longstaff, 2011, “Systemic Sovereign Credit Risk: Lessons from the U.S. and Europe,” NBER Working Paper No. 16982.
- Bae, Kee-Hong, G. Andrew Karolyi and René M. Stulz, 2003, “A New Approach to Measuring Financial Contagion,” Review of Financial Studies, Vol. 16(3), pp.717–763.
- Breitung, Jörg, and Bertrand Candelon, 2006, “Testing for Short and Long-Run Causality: A Frequency Domain Approach,” Journal of Econometrics, Vol. 132, pp. 363–78.
- Dungey, M., R. Fry, B. Gonzalez-Hermosillo and V. Martin, 2005, "Empirical Modeling of Contagion: a Review of Methodologies," Quantitative Finance, Vol. 5(1), pages 9–24.
- Forbes, Kristin J., and Roberto Rigobon, 2002, “No Contagion, Only Interdependence: Measuring Stock Market Comovements,” Journal of Finance, Vol. 57, No. 5, pp. 2223–6.1.

*Source: _wp11290 - REFERENCES*

### References .............................................................................................................

### _wp11290 - References .............................................................................................................

### Introduction
- Market context and scope
  - The market for US municipal bonds is a $2.9 trillion tax-exempt bond market amounting to about a third of the US treasury market.
  - The study covers the period 01/01/2005 to 01/13/2011 and uses daily 10-year municipal and treasury bond yields from Bloomberg.
  - The 10-year Treasury yield is the constant maturity yield. Municipal yields are estimated from an option-free yield curve built using option adjusted spread model and contributed pricing to Bloomberg.
- Research questions
  - Whether and how shocks to individual state bond markets spread to other state bond markets.
  - Whether shocks to individual state bond markets spread to US Treasury securities and vice versa.
- Key contextual points
  - The housing bust, the financial crisis, and the recession reduced state and local tax revenues and increased borrowing costs for many states.
  - The largest recent municipal failure referenced is Jefferson County, Alabama in November 2011.
  - The paper focuses on describing the nature of spillover effects rather than identifying specific transmission channels.

### Spillover literature and empirical test
- Theoretical framing
  - Two strands: non-crisis-contingent (“strong form of contagion”) and crisis-contingent (“weak form of contagion” or “shift-contagion”).
  - Forbes and Rigobon (2002) argue that increases in unconditional correlation during crises can be driven by increased volatility and propose a correction for this bias.
- Forbes-Rigobon (FR) correction (as presented)
  - FR correction formula: ρ̃ = ρu / sqrt(1 + δ) where notation in the source describes the relationship between unadjusted/conditional correlation ρ̃, actual/unconditional correlation ρ, and relative increase in variance δ.
  - Relative increase in variance δ is given by δ = σ_high^2 / σ_low^2 − 1, where σ_high^2 is VAR residual variance in the high-volatility sub-sample and σ_low^2 is variance in the low-volatility sub-sample.
- Test implementation choices
  - The authors use the version of the Forbes and Rigobon test recommended by Dungey et al. (2005) where the low and high volatility sub-samples are independent.
  - Robustness checks: two other FR versions and multivariate FR were considered; main results unchanged (additional results available upon request).

### Main results
- Sample break date and volatility
  - Break date chosen to maximize increase in VAR residual variance: August 29th, 2008.
  - Key sample information: the twenty-two largest municipal issuers are analyzed; municipal yields are filtered by a VAR(2) conditioned on the ten-year US bond yield and S&P 500 return (see tables and notes).
  - Table 1 reports σ_low and σ_high for each issuer. Example entries:
    - California: σ_low 0.1661, σ_high 0.3647
    - Connecticut: σ_low 0.2053, σ_high 0.4430
    - Puerto Rico R.: σ_low 0.5062, σ_high 0.6068
- Within-muni spillover (Table 2; FR test)
  - Test interpretation: FR test statistic follows asymptotically a student distribution so that a test statistic higher (lower) than 1:96 supports (rejects) the presence of spillover. The sign of the test statistic indicates direction of co-movement.
  - Primary finding: between most markets for individual U.S. state bonds there are negative spillovers—an increase in borrowing costs in one state tends to result in better borrowing conditions (lower yields) for other states.
  - Observed behavior interpreted as a “flight to safety” within the muni market during periods of volatility.
  - Notable issuers whose problems benefit other states: California, Georgia, Maryland, and the City of New York (spillover is negative when these issuers experience problems).
  - A few states show positive correlations (borrowing costs increase when another state has problems), e.g., Connecticut and Florida.
  - Possible explanations discussed (not empirically tested): reallocations by domestic retail investors and muni bond funds, liquidity effects, rating-triggered rebalancing by institutional investors, and state-specific tax exemptions affecting local investor behavior.
- Bottom-up and top-down spillover between municipal and Treasury markets (Table 3; FR test)
  - Overall finding: no substantial spillover effects between shocks originating from state securities and federal markets, except for a few large issuers.
  - Evidence of positive spillover—albeit below conventional significance—between the U.S. Treasury market and markets for New Jersey, Texas, Washington state, and New York City, with the strongest result for New York City.
  - California shows a negative spillover with the U.S. Treasury market (yields move in opposite directions following a shock).
  - Results robust to using additional lags and controlling for S&P 500 returns; tests reported for VAR specifications with 2 lags and 4 lags, with and without conditioning on S&P 500 returns.
- Causality in the frequency domain (Breitung and Candelon, 2006)
  - Method: Granger causality test in the frequency domain to identify direction and whether causality is short-run (frequencies far from zero) or long-run (frequencies near zero).
  - Main causality findings:
    - The Treasury bond market directly causes changes in municipal bond markets in both the short and long run.
    - There is some evidence of causality from municipal to Treasury markets, but only of a long-run nature.
  - Policy implication drawn: structural reforms improving the federal budget in the long run will affect state borrowing conditions (benefit or worsen them depending on sign); state-level reforms will affect federal borrowing costs in the long run.

### Conclusions and policy implications
- Summary of empirical conclusions
  - Most state bond markets exhibit negative spillovers (problems in one state tend not to worsen borrowing conditions in other states).
  - Only a few large municipal issuers are linked with the Treasury bond market in ways that could affect federal markets.
  - Treasury market causes municipal markets in both short and long run; municipal → Treasury causality exists only in the long run.
- Policy lessons
  - Fiscal unions and supranational authorities should analyze spillovers within their sub-national bond markets as well as linkages between sub-national and supra-national bond markets.
  - Risk management strategies should be informed by the sign (positive or negative) and time-horizon (short or long run) of spillovers.
  - The evidence here suggests flight-to-quality dynamics rather than contagion within U.S. state bond markets; implications for whether deeper fiscal union would increase or reduce systemic risk require further research.

* _wp11290 - References .............................................................................................................*

### REFERENCES

### _wp11290 - REFERENCES

### References cited
- Ang, Andrew, and Francis Longstaff, 2011, “Systemic Sovereign Credit Risk: Lessons from the U.S. and Europe,” NBER Working Paper No. 16982 (Cambridge, Massachusetts: National Bureau of Economic Research).
- Bae, Kee-Hong, G. Andrew Karolyi and René M. Stulz, 2003, “A New Approach to Measuring Financial Contagion,” Review of Financial Studies, Vol. 16(3), pp.717–763.
- Baig, T. and I. Goldfajn, 1998, “Financial Market Contagion in the Asian Crisis,” IMF Working Paper No. 98–155, International Monetary Fund, Washington, D.C.
- Breitung, Jörg, and Bertrand Candelon, 2006, “Testing for Short and Long-Run Causality: A Frequency Domain Approach,” Journal of Econometrics, Vol. 132, pp. 363–78.
- Calvo, S. and C. M. Reinhart, 1995, “Capital Inflows to Latin America: Is There Evidence of Contagion Effects?,” in G. A. Calvo, M. Goldstein and E. Hochreiter (eds), Private Capital Flows to Emerging Markets After the Mexican Crisis, Washington, DC: Institute for International Economics.
- Dungey, M., R. Fry, B. Gonzalez-Hermosillo and V. Martin, 2005, "Empirical Modeling of Contagion: a Review of Methodologies," Quantitative Finance, Taylor and Francis Journals, Vol. 5(1), pages 9–24.
- Favero, Carlo A. and Giavazzi, Francesco, 2002, “Is the International Propagation of Financial Shocks Non-Linear? : Evidence from the ERM," Journal of International Economics, Vol. 57(1), pp. 231–246.
- Forbes, Kristin J., and Roberto Rigobon, 2002, “No Contagion, Only Interdependence: Measuring Stock Market Comovements,” Journal of Finance, Vol. 57, No. 5, pp. 2223–6.1.
- King, M. and S. Wadhwani, 1990, “Transmission of Volatility Between Stock Markets,” Review of Financial Studies 3, pp. 3–33.
- Masson, P. R., 1999, “Contagion: Monsoonal Effects, Spillovers, and Jumps between Multiple Equilibria,” in P. Agnor, M. Miller and D. Vines (eds), The Asian Crises: Causes, Contagion and Consequences, Cambridge: Cambridge University Press.
- Pesaran, Hashem M. and Andreas Pick, 2007, “Econometric Issues in the Analysis of Contagion,” Journal of Economic Dynamics and Control, Vol. 31, Issue 4, April, pp. 1245–1277.

### Methodological and topical emphases (as reflected by titles)
- Systemic sovereign credit risk and lessons from regional case studies.
- New approaches to measuring financial contagion and comovements.
- Empirical modeling and reviews of methodologies for contagion analysis.
- Testing for short- and long-run causality using frequency domain approaches.
- Transmission of volatility across stock markets.
- Non-linear international propagation of financial shocks (evidence from ERM).
- Capital inflows and contagion effects in emerging markets and crises.
- Econometric issues in the analysis of contagion.

*Source: _wp11290 - REFERENCES*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2011/_wp11290.pdf_