Note on panel data

If a panel dataset is used, xtbreak differentiates between five models.
The default is a model with fixed effects.
The second model has breaks in the fixed effects.
The third and forth models arewith a pooled constant (pooled OLS) with and without a break.
The last model is a model with neither fixed effects nor a pooled constant.

The following table gives an overview:

Model | Equation | xtbreak options,

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Fixed Effects | y(i,t) = a(i) + b1 x(i,t) + s1(s) z(i,t,s) + e(i,t) | *
with breaks | y(i,t) = a(i,s) + b1 x(i,t) + s1(s) z(i,t,s) + e(i,t) | breakfixedeffects *
Pooled OLS | y(i,t) = b0 + b1 x(i,t) + s1(s) z(i,t,s) + e(i,t) | nofixedeffects
with breaks | y(i,t) = s0(s) + b1 x(i,t) + s1(s) z(i,t,s) + e(i,t) | nofixedeffects breakconstant
No FE or POLS | y(i,t) = b1 x(i,t) + s1(s) z(i,t,s) + e(i,t) | nofixedeffects noconstant
* Option noconstant is implied.

where b0 is the pooled constant without break, a(i) the fixed effects,
a(i,s) fixed effects with breaks,
b(1) a coefficient without break, s0(s) a pooled constant with break
and s1(s) a coefficient with break.

A model with a constant and fixed effects, with or without breaks in both is a special case of the first two models above.
Since we are not interested in the estimation of the constant and/or the fixed effects,
we can treat them as the combination of both.

Covariance Estimators

xtbreak supports 4 different covariance estimator:

vce(type) | Description

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ssr | Variance Covariance estimator based on SSR: cov = (X'X)^(-1)*SSR
hc | heteroskedastic robust; HC0
hac | heteroskedastic and autocorrelation robust
np | non-parametric estimator of Pesaran (2006)