Structural Break Quantile-on-Quantile Regression
Also known as: SB-QQR, structural-break QQ regression, quantile-on-quantile with structural breaks, QQR with regime shifts
Structural Break Quantile-on-Quantile Regression (SB-QQR) extends the quantile-on-quantile framework of Sim and Zhou (2015) by allowing regression slopes to differ across regimes separated by structural breaks. It maps how the effect of a predictor's quantile on an outcome's quantile changes not only across the full distributional space but also across distinct historical periods or policy regimes.
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When to use it
Use SB-QQR when you have a long time series and you suspect that (a) the relationship between two variables differs across distributional quantiles (not just in the mean) and (b) this distributional relationship has shifted at one or more historical break points — for example, around financial crises, commodity price shocks, or major policy changes. It is particularly valuable in energy economics, financial contagion studies, and macroeconomic regime analysis. Do not use it for short samples (fewer than ~150 observations) — reliable kernel-based quantile surface estimation and break detection both require adequate data. Avoid it when structural breaks are theoretically implausible or when a simpler quantile regression or standard ARDL with a dummy variable would answer the research question.
Strengths & limitations
- Captures full distributional dependence between predictor and outcome at both tails, not just the conditional mean.
- Explicitly allows distributional dependence structure to shift across historical regimes — not imposed as constant.
- Combines nonparametric flexibility (local linear kernel) with established structural break detection theory.
- Produces intuitive heat-map visualisations that communicate how dependence varies over quantile space and across regimes.
- Particularly powerful for detecting asymmetric contagion at market extremes in different macroeconomic regimes.
- Computationally intensive: requires fitting a separate local linear quantile regression at every (theta, tau) grid point for each regime.
- Requires a sufficiently long time series to support reliable break detection and adequate observations within each regime.
- Results are sensitive to bandwidth choice in the kernel weighting and to the break-detection method used.
- The combined framework lacks a single unified asymptotic theory — practitioners must carefully justify both the QQR and the break-detection components.
Frequently asked
How does SB-QQR differ from standard quantile regression with a structural break dummy?
A dummy variable in quantile regression shifts the intercept (or a single slope) at a given quantile level. SB-QQR instead estimates an entirely separate two-dimensional QQ surface for each regime, capturing how the full distributional dependence — across every combination of predictor and outcome quantile — changes between regimes. The two approaches answer different questions.
How many observations do I need per regime?
As a rough guideline, each regime segment should contain at least 80-100 observations to support reliable kernel-based local linear quantile estimation across the quantile grid. With fewer observations, extreme quantile estimates become very noisy. If break detection leaves a segment with fewer observations, consider restricting the quantile grid to [0.15, 0.85] or using a wider bandwidth.
Which break-detection test should I use before running QQR?
The choice depends on assumptions: Bai-Perron allows multiple simultaneous breaks and is the most general; Zivot-Andrews identifies one endogenous break while accounting for a unit root; CUSUM-based tests are distribution-free. It is good practice to report results under at least two specifications and discuss sensitivity to the break date.
Can I apply SB-QQR to panel data?
The standard SB-QQR framework is designed for time series. Panel extensions exist that pool QQ estimation across cross-sectional units while allowing regime-specific surfaces, but these require specialised software and more complex inference. The simpler panel Granger causality or panel quantile regression with breaks is often a more tractable alternative.
What software can run SB-QQR?
There is no single off-the-shelf package. Researchers typically implement it in R by combining the 'quantreg' package for quantile regression with custom kernel weighting loops for the QQ grid, and use 'strucchange' or 'mbreaks' for break detection. MATLAB implementations also appear in published replication codes. StatWise provides an integrated interface for the full pipeline.
Sources
- Sim, N., and Zhou, H. (2015). Oil prices, US stock return, and the dependence between their quantiles. Journal of Banking and Finance, 55, 1-8. DOI: 10.1016/j.jbankfin.2015.01.013 ↗
- Bai, J., and Perron, P. (1998). Estimating and testing linear models with multiple structural changes. Econometrica, 66(1), 47-78. DOI: 10.2307/2998540 ↗
How to cite this page
ScholarGate. (2026, June 3). Structural Break Quantile-on-Quantile Regression. ScholarGate. https://scholargate.app/en/econometrics/structural-break-quantile-on-quantile-regression
Which method?
Set this method beside its closest kin and read them side by side — the library lays the books on the table; the choice is yours.
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