|
|
| Line 1: |
Line 1: |
| 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 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. | | The author's title is Andera and she believes it sounds fairly great. Her family members lives in Alaska but her spouse desires them to move. He is an order clerk and it's something he truly enjoy. One of the very best things in the globe for him is doing ballet and he'll be starting something else alongside with it.<br><br>Here is my site; [http://chungmuroresidence.com/xe/reservation_branch2/152663 love psychic] |
| | |
| {| class="wikitable"
| |
| |-
| |
| !structural break
| |
| !program evaluation
| |
| |-
| |
| |-
| |
| |style="width:450px" valign="top" halign="center" |
| |
| [[File:Chow test structural break.png|440px]]
| |
| |style="width:450px" valign="top" halign="center"|
| |
| [[File:Chow test substructures.png|440px]]
| |
| |-
| |
| |valign="top"|
| |
| At <math> x=1.7 </math> there is a structural break, regression on the subintervals <math>[0,1.7]</math> and <math>[1.7,4] </math> delivers a better modelling than the combined regression(dashed) over the whole interval.
| |
| |valign="top"|
| |
| 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
| |
| | |
| :<math>
| |
| y_t=a+bx_{1t} + cx_{2t} + \varepsilon.\,
| |
| </math>
| |
| | |
| If we split our data into two groups, then we have
| |
| | |
| :<math>
| |
| y_t=a_1+b_1x_{1t} + c_1x_{2t} + \varepsilon. \,</math>
| |
| | |
| and
| |
| | |
| :<math>
| |
| y_t=a_2+b_2x_{1t} + c_2x_{2t} + \varepsilon. \,
| |
| </math>
| |
| | |
| The [[null hypothesis]] of the Chow test asserts that <math>a_1=a_2</math>, <math>b_1=b_2</math>, and <math>c_1=c_2</math>, and there is the assumption that the [[errors and residuals in statistics|model errors]] <math> \varepsilon </math> are [[independent and identically distributed]] from a [[normal distribution]] with unknown [[variance]].
| |
| | |
| Let <math>S_C</math> be the sum of squared [[errors and residuals in statistics|residual]]s from the combined data, <math>S_1</math> be the sum of squared [[errors and residuals in statistics|residual]]s from the first group, and <math>S_2</math> be the sum of squared [[errors and residuals in statistics|residual]]s from the second group. <math>N_1</math> and <math>N_2</math> are the number of observations in each group and <math>k</math> is the total number of parameters (in this case, 3). Then the Chow test statistic is
| |
| | |
| :<math>
| |
| \frac{(S_C -(S_1+S_2))/(k)}{(S_1+S_2)/(N_1+N_2-2k)}.
| |
| </math>
| |
| | |
| The test statistic follows the [[F distribution]] with <math>k</math> and <math>N_1+N_2-2k</math> [[degrees of freedom (statistics)|degrees of freedom]].
| |
| | |
| ==References==
| |
| *{{cite journal | doi=10.2307/1910133 | first1=Gregory C.|last1=Chow | title=Tests of Equality Between Sets of Coefficients in Two Linear Regressions | jstor=1910133 | journal=Econometrica | year=1960 | volume=28 | pages=591–605 | issue=3}}
| |
| *{{cite book |last=Doran |first=Howard E. |year=1989 |title=Applied Regression Analysis in Econometrics |publisher=CRC Press |isbn=0-8247-8049-3 |page=146 }} ([http://books.google.de/books?id=JHzik5hkrIMC&pg=PA146&dq=Chow-Test+regression&lr=&as_brr=3&sig=ACfU3U1T_tmXj-sQbqDVHutF3RRPLFQTqg restricted online version (Google Books)])
| |
| *{{cite book |last=Dougherty |first=Christopher |year=2007 |title=Introduction to Econometrics |publisher=Oxford University Press |isbn=0-19-928096-7 |page=194 }} ([http://books.google.de/books?id=h0MTRO_3jYEC&pg=PA194&vq=chow+test&source=gbs_search_r&cad=1_1&sig=ACfU3U2ZXf7-rPaXyqzwpfAaEDtpqoy5MA restricted online version (Google Books)])
| |
| | |
| ==External links==
| |
| *[http://www.stata.com/support/faqs/stat/chow.html Computing the Chow statistic], [http://www.stata.com/support/faqs/stat/chow2.html Chow and Wald tests], [http://www.stata.com/support/faqs/stat/chow3.html Chow tests]: Series of FAQ explanations from the [[Stata]] Corporation at http://www.stata.com/support/faqs/
| |
| | |
| [[Category:Econometrics]]
| |
| [[Category:Time series analysis]]
| |
| [[Category:Statistical tests]]
| |
| [[Category:Regression diagnostics]]
| |
The author's title is Andera and she believes it sounds fairly great. Her family members lives in Alaska but her spouse desires them to move. He is an order clerk and it's something he truly enjoy. One of the very best things in the globe for him is doing ballet and he'll be starting something else alongside with it.
Here is my site; love psychic