Structural break

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Econometric term

title: "Structural break" type: doc version: 1 created: 2026-02-28 author: "Wikipedia contributors" status: active scope: public tags: ["change-detection", "time-series", "panel-data", "econometric-modeling", "regression-analysis"] description: "Econometric term" topic_path: "general/change-detection" source: "https://en.wikipedia.org/wiki/Structural_break" license: "CC BY-SA 4.0" wikipedia_page_id: 0 wikipedia_revision_id: 0

::summary Econometric term ::

::figure[src="https://upload.wikimedia.org/wikipedia/commons/d/d1/Chowtest2.svg" caption="[[Linear regression]] with a structural break"] ::

In econometrics and statistics, a structural break is an unexpected change over time in the parameters of regression models, which can lead to huge forecasting errors and unreliability of the model in general. This issue was popularised by David Hendry, who argued that lack of stability of coefficients frequently caused forecast failure, and therefore we must routinely test for structural stability. Structural stability − i.e., the time-invariance of regression coefficients − is a central issue in all applications of linear regression models.

Structural break tests{{Anchor|Sup-Wald test|Sup-MZ test}}

A single break in mean with a known breakpoint

For linear regression models, the Chow test is often used to test for a single break in mean at a known time period K for K ∈ [1,T]. This test assesses whether the coefficients in a regression model are the same for periods [1,2, ...,K] and [K + 1, ...,T].

Other forms of structural breaks

Other challenges occur where there are: :Case 1: a known number of breaks in mean with unknown break points; :Case 2: an unknown number of breaks in mean with unknown break points; :Case 3: breaks in variance.

The Chow test is not applicable in these situations, since it only applies to models with a known breakpoint and where the error variance remains constant before and after the break. Bayesian methods exist to address these difficult cases via Markov chain Monte Carlo inference.

In general, the CUSUM (cumulative sum) and CUSUM-sq (CUSUM squared) tests can be used to test the constancy of the coefficients in a model. The bounds test can also be used. For cases 1 and 2, the sup-Wald (i.e., the supremum of a set of Wald statistics), sup-LM (i.e., the supremum of a set of Lagrange multiplier statistics), and sup-LR (i.e., the supremum of a set of likelihood ratio statistics) tests developed by Andrews (1993, 2003) may be used to test for parameter instability when the number and location of structural breaks are unknown. These tests were shown to be superior to the CUSUM test in terms of statistical power, and are the most commonly used tests for the detection of structural change involving an unknown number of breaks in mean with unknown break points. The sup-Wald, sup-LM, and sup-LR tests are asymptotic in general (i.e., the asymptotic critical values for these tests are applicable for sample size n as n → ∞), and involve the assumption of homoskedasticity across break points for finite samples; however, an exact test with the sup-Wald statistic may be obtained for a linear regression model with a fixed number of regressors and independent and identically distributed (IID) normal errors. A method developed by Bai and Perron (2003) also allows for the detection of multiple structural breaks from data.

The MZ test developed by Maasoumi, Zaman, and Ahmed (2010) allows for the simultaneous detection of one or more breaks in both mean and variance at a known break point. The sup-MZ test developed by Ahmed, Haider, and Zaman (2016) is a generalization of the MZ test which allows for the detection of breaks in mean and variance at an unknown break point.

Instead of assuming IID Normal errors as in standard regression, they created tests when errors form ARMA process and even more complex stochastic structures. This literature, and its applications, are reviewed in Hansen, B. (2001).

HOWEVER, all of this literature makes the same assumption that structural change occurs in the regression coefficients but NOT in the error process. Even the very complex error processes, with heteroskedasticity and autocorrelation (HAC), do not change in time. Recently, Maasoumi, Zaman, and Ahmad (2010) published a paper (“Tests for Structural Change, Homogeneity, and Aggregation” Economic Modelling Vol 27 no.6 (2010): 1382–1391) which relaxes this assumption and allows variances to change at the breakpoint, while also allowing for multiple known breakpoints. This test is called the MZ test by the authors. This test requires the breakpoints to be specified in advance. On the pattern of the rolling Chow, this test can also be used to detect unknown breakpoints by using it at all possible breakpoints, and then taking the maximum of all the statistics, leading to the sup MZ test. The performance of this test was evaluated recently by Ahmed, Haider, & Zaman (2016) Theoretical evaluations shows that small changes in variance across the breakpoint cause significant deterioration in performance of the sup F test. Of course the sup MZ test is designed for this situation and hence works much better. Empirical evaluation was done by taking several macroeconomic series and testing them for structural change using both sup F and sup MZ. In these GNP series, tests indicated that structural change frequently involved both regression coefficients and the variance, leading to substantially superior performance of the sup MZ.

Tests for multiple breaks

The MZ test is designed to handle the (unlikely) case that multiple breaks all occur at known breakpoints. There is a vast literature on more complicated cases. The simpler case arises when the number of breakpoints is known but their position is unknown. The more difficult case is where both the number of breakpoints, and their position is unknown. For these cases, the sup-Wald, sup-LM, and sup-LR tests developed by Andrews (1993, 2003) may be used to test for parameter instability when the change points (the structural break locations) are unknown.

Structural breaks in cointegration models

For a cointegration model, the Gregory–Hansen test (1996) can be used for one unknown structural break, the Hatemi–J test (2006) can be used for two unknown breaks and the Maki (2012) test allows for multiple structural breaks.

Statistical packages

There are many statistical packages that can be used to find structural breaks, including R, GAUSS, and Stata, among others. For example, a list of R packages for time series data is summarized at the changepoint detection section of the Time Series Analysis Task View, including both classical and Bayesian methods.

References

References

  1. (25 April 2018). "Structural breaks in panel data: Large number of panels and short length time series". Econometric Reviews.
  2. (December 2008). "Not So Fixed Effects: Correlated Structural Breaks in Panel Data". [[IZA Institute of Labor Economics]].
  3. (November 2001). "The New Econometrics of Structural Change: Dating Breaks in U.S. Labor Productivity". Journal of Economic Perspectives.
  4. (October 2016). "Detecting structural change with heteroskedasticity". Communications in Statistics – Theory and Methods.
  5. Gujarati, Damodar. (2007). "Basic Econometrics". Tata McGraw-Hill.
  6. (November 2001). "The New Econometrics of Structural Change: Dating Breaks in U.S. Labor Productivity". Journal of Economic Perspectives.
  7. (2012). "Econometric Analysis". Pearson Education.
  8. (2007). "bcp: An R Package for Performing a Bayesian Analysis of Change Point Problems". Journal of Statistical Software.
  9. "BEAST: A Bayesian Ensemble Algorithm for Change-Point Detection and Time Series Decomposition".
  10. (2001). "Bounds testing approaches to the analysis of level relationships". [[Journal of Applied Econometrics]].
  11. (July 1993). "Tests for Parameter Instability and Structural Change with Unknown Change Point". Econometrica.
  12. (January 2003). "Tests for Parameter Instability and Structural Change with Unknown Change Point: A Corrigendum". Econometrica.
  13. (January 2003). "Computation and analysis of multiple structural change models". Journal of Applied Econometrics.
  14. (November 2010). "Tests for structural change, aggregation, and homogeneity". Economic Modelling.
  15. Mumtaz Ahmed and Gulfam Haider and Asad Zaman. (2017). "Detecting structural change with heteroskedasticity". Taylor & Francis.
  16. (1996). "Tests for Cointegration in Models with Regime and Trend Shifts". Oxford Bulletin of Economics and Statistics.
  17. (2006). "Tests for Causality between Integrated Variables Using Asymptotic and Bootstrap Distributions: Theory and Application". [[Applied Economics (journal).
  18. (2008). "Applied Econometrics with R". Springer.
  19. "CRAN Task View: Time Series Analysis. Version 2023-09-26.".
  20. "strucchange: Testing, monitoring, and dating structural changes".

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