World Library  
Flag as Inappropriate
Email this Article

Chow test

Article Id: WHEBN0002883675
Reproduction Date:

Title: Chow test  
Author: World Heritage Encyclopedia
Language: English
Subject: Structural break, Chow, Econometrics, Statistical tests, Time series analysis
Collection: Econometrics, Regression Diagnostics, Statistical Tests, Time Series Analysis
Publisher: World Heritage Encyclopedia
Publication
Date:
 

Chow test

The Chow test is a statistical and econometric test of whether the coefficients in two linear regressions on different data sets are equal. The Chow test was invented by economist Gregory Chow in 1960. 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.

structural break program evaluation

At x=1.7 there is a structural break, regression on the subintervals [0,1.7] and [1.7,4] 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

y_t=a+bx_{1t} + cx_{2t} + \varepsilon.\,

If we split our data into two groups, then we have

y_t=a_1+b_1x_{1t} + c_1x_{2t} + \varepsilon. \,

and

y_t=a_2+b_2x_{1t} + c_2x_{2t} + \varepsilon. \,

The null hypothesis of the Chow test asserts that a_1=a_2, b_1=b_2, and c_1=c_2, and there is the assumption that the model errors \varepsilon are independent and identically distributed from a normal distribution with unknown variance.

Let S_C be the sum of squared residuals from the combined data, S_1 be the sum of squared residuals from the first group, and S_2 be the sum of squared residuals from the second group. N_1 and N_2 are the number of observations in each group and k is the total number of parameters (in this case, 3). Then the Chow test statistic is

\frac{(S_C -(S_1+S_2))/(k)}{(S_1+S_2)/(N_1+N_2-2k)}.

The test statistic follows the F distribution with k and N_1+N_2-2k degrees of freedom.


Remarks

- The global sum of squares (SSE) if often called Restricted Sum of Squares (RSSM) as we basically test a constrained model where we have 2K assumptions (with K the number of regressors).

- Some software like SAS will use a predictive Chow test when the size of a subsample is less than the number of regressors.



References

  • Chow, Gregory C. (1960). "Tests of Equality Between Sets of Coefficients in Two Linear Regressions". Econometrica 28 (3): 591–605.  
  • Doran, Howard E. (1989). Applied Regression Analysis in Econometrics. CRC Press. p. 146.  
  • Dougherty, Christopher (2007). Introduction to Econometrics. Oxford University Press. p. 194.  
  •  
  •  

External links

  • Computing the Chow statistic, Chow and Wald tests, Chow tests: Series of FAQ explanations from the Stata Corporation at https://www.stata.com/support/faqs/
  • [2]: Series of FAQ explanations from the SAS Corporation
This article was sourced from Creative Commons Attribution-ShareAlike License; additional terms may apply. World Heritage Encyclopedia content is assembled from numerous content providers, Open Access Publishing, and in compliance with The Fair Access to Science and Technology Research Act (FASTR), Wikimedia Foundation, Inc., Public Library of Science, The Encyclopedia of Life, Open Book Publishers (OBP), PubMed, U.S. National Library of Medicine, National Center for Biotechnology Information, U.S. National Library of Medicine, National Institutes of Health (NIH), U.S. Department of Health & Human Services, and USA.gov, which sources content from all federal, state, local, tribal, and territorial government publication portals (.gov, .mil, .edu). Funding for USA.gov and content contributors is made possible from the U.S. Congress, E-Government Act of 2002.
 
Crowd sourced content that is contributed to World Heritage Encyclopedia is peer reviewed and edited by our editorial staff to ensure quality scholarly research articles.
 
By using this site, you agree to the Terms of Use and Privacy Policy. World Heritage Encyclopedia™ is a registered trademark of the World Public Library Association, a non-profit organization.
 



Copyright © World Library Foundation. All rights reserved. eBooks from World eBook Library are sponsored by the World Library Foundation,
a 501c(4) Member's Support Non-Profit Organization, and is NOT affiliated with any governmental agency or department.