Threshold Regression
Threshold Regression Model · Also known as: threshold model, regime-switching regression, sample splitting model, Eşik Değer Regresyonu (Threshold Regression)
Threshold regression is a nonlinear, regime-switching model in which the regression parameters take different values above and below an estimated threshold value of a threshold variable. The sample-splitting and threshold-estimation framework was developed by Bruce E. Hansen (2000) and is widely used for time-series and panel data with structural breaks and regime-dependent relationships.
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When to use it
Use threshold regression when a continuous outcome plausibly follows different regimes split by a threshold variable that may be exogenous or a lagged dependent variable, and you have time-series or panel data with a reasonably large sample (about 100 observations or more). It is appropriate when you suspect a structural break or a nonlinear, regime-dependent relationship rather than a single global slope. The errors are assumed homogeneous across regimes; if that fails, robust standard errors should be used.
Strengths & limitations
- Captures structural breaks and regime-dependent relationships that a single linear model would miss.
- Estimates the threshold from the data rather than imposing it, and Hansen's bootstrap supplies a confidence interval for the break point.
- Coefficients remain interpretable within each regime, like a separate regression on each side of the threshold.
- Needs a fairly large sample (about 100 or more) so that each regime contains enough observations to estimate stable coefficients.
- Assumes homogeneous residuals across regimes; heteroscedasticity invalidates the standard errors unless robust ones are used.
- Inference on the threshold is nonstandard, requiring bootstrap methods rather than ordinary t-tests.
Frequently asked
What is the threshold variable?
It is the variable that decides which regime each observation falls into. It can be an exogenous variable or a lagged dependent variable; observations at or below the estimated threshold use one set of coefficients and those above it use another.
How is the threshold itself estimated?
By conditional least squares: the model is fitted for each candidate threshold and the residual sum of squares is recorded, and the threshold that minimises that sum is selected. Hansen's (2000) method then builds a bootstrap confidence interval around it.
How large a sample do I need?
Roughly 100 observations or more, because the sample is split into separate regimes and each side needs enough data to estimate its coefficients stably.
What if the residuals are not homogeneous across regimes?
The homogeneous-residual assumption underlies the standard inference; if it is violated, use robust standard errors so that the coefficient tests remain valid.
Sources
- Hansen, B. E. (2000). Sample Splitting and Threshold Estimation. Econometrica, 68(3), 575-603. DOI: 10.1111/1468-0262.00124 ↗
How to cite this page
ScholarGate. (2026, June 1). Threshold Regression Model. ScholarGate. https://scholargate.app/en/econometrics/threshold-regression
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