Chow test
Encyclopedia
The Chow test is a statistical and econometric test of whether the coefficients in two linear regression
s on different data sets are equal. The Chow test was invented by economist Gregory Chow. In econometrics, the Chow test is most commonly used in time series analysis to test for the presence of a structural break
. In program evaluation
, the Chow test is often used to determine whether the independent variables have different impacts on different subgroups of the population.
Suppose that we model our data as
If we split our data into two groups, then we have
and
The null hypothesis
of the Chow test asserts that
, 
, and 
.
Let
be the sum of squared residual
s from the combined data,
be the sum of squared residual
s from the first group, and
be the sum of squared residual
s from the second group.
and 
are the number of observations in each group and 
is the total number of parameters (in this case, 3). Then the Chow test statistic is
The test statistic follows the F distribution with
and 
degrees of freedom
.
Linear regression
In statistics, linear regression is an approach to modeling the relationship between a scalar variable y and one or more explanatory variables denoted X. The case of one explanatory variable is called simple regression...
s on different data sets are equal. The Chow test was invented by economist Gregory Chow. In econometrics, the Chow test is most commonly used in time series analysis to test for the presence of a structural break
Structural break
A structural break is a concept in econometrics. A structural break appears when we see an unexpected shift in a time series. This can lead to huge forecasting errors and unreliability of the model in general...
. In program evaluation
Program evaluation
Project evaluation is a systematic method for collecting, analyzing, and using information to answer questions about projects, policies and programs, particularly about their effectiveness and efficiency...
, the Chow test is often used to determine whether the independent variables have different impacts on different subgroups of the population.
| structural break | program evaluation |
|---|---|
At  there is a structural break, regression on the subintervals  and  delivers a better modelling than the combined regression(dashed) over the whole interval. |
Comparison of 2 different programs (red, green) existing in a common data set, separate regressions for both programs deliver a better modelling than a combined regression (black). |
Suppose that we model our data as
If we split our data into two groups, then we have
and
The null hypothesis
Null hypothesis
The practice of science involves formulating and testing hypotheses, assertions that are capable of being proven false using a test of observed data. The null hypothesis typically corresponds to a general or default position...
of the Chow test asserts that
, , and .Let
be the sum of squared residualErrors and residuals in statistics
In statistics and optimization, statistical errors and residuals are two closely related and easily confused measures of the deviation of a sample from its "theoretical value"...
s from the combined data,
be the sum of squared residualErrors and residuals in statistics
In statistics and optimization, statistical errors and residuals are two closely related and easily confused measures of the deviation of a sample from its "theoretical value"...
s from the first group, and
be the sum of squared residualErrors and residuals in statistics
In statistics and optimization, statistical errors and residuals are two closely related and easily confused measures of the deviation of a sample from its "theoretical value"...
s from the second group.
and are the number of observations in each group and is the total number of parameters (in this case, 3). Then the Chow test statistic isThe test statistic follows the F distribution with
and degrees of freedomDegrees of freedom (statistics)
In statistics, the number of degrees of freedom is the number of values in the final calculation of a statistic that are free to vary.Estimates of statistical parameters can be based upon different amounts of information or data. The number of independent pieces of information that go into the...
.