CHOW TEST
Presented By:
Namrata Dewan (23902), Samyog Dhungel (23903), Anisha Karki
(23906), Nimesh Mani Risal (23916), Shristy Satyal (23917), Ashesh
Shrestha (23920)
WHAT IS CHOW TEST?
A statistical method that checks whether variables of two different
regression models are equal.
Primary purpose: To determine if any structural change occurs between
these variables.
Used mostly for TIME-SERIES and CROSS-SECTIONAL DATA.
Test depends on : k-distribution and includes a null and alternative
hypothesis.
HOW TO PERFORM CHOW TEST?
FORMULA:
Where, RSSR = RSS3 i.e. Restricted residual sum of squares for combined line
RSSUR= RSS1+RSS2 i.e. RSS of two separate lines (Unrestricted)
n1 and n2 = No. of samples
k = Degree of Freedom
PERFORMING CHOW TEST
This table gives data on disposable personal income and personal savings, in
billions of dollars, for the United States for the period 1970–1995. It is well known
that in 1982 the United States suffered its worst peacetime recession. The civilian
unemployment rate that year reached 9.7 percent, the highest since 1948. An
event such as this might disturb the relationship between savings and DPI. To see if
this happened, let us divide our sample data into two time periods: 1970–1981 and
1982–1995, the pre- and post-1982 recession periods.
Ho = There is no structural change.
Ha = There exists a structural change
COMBINED REGRESSION
Yc = 62.42267 + 0.0376791 Xc + uc
RSS = 23248.3 , RSSR = 23248.3, df = 24
Observation
Savings (Y)
Income (X)
Observation
Savings (Y)
Income (X)
1970
61
727.1
1983
167
2522.4
1971
68.6
790.2
1984
235.7
2810
1972
63.6
855.3
1985
206.2
3002
1973
89.6
965
1986
196.5
3187.6
1974
97.6
1054.2
1987
168.4
3363.1
1975
104.4
1159.2
1988
189.1
3640.8
1976
96.4
1273
1989
187.8
3894.5
1977
92.5
1401.4
1990
208.7
4166.8
1978
112.6
1580.1
1991
246.4
4343.7
1979
130.1
1769.5
1992
272.6
4613.7
1980
161.8
1973.3
1993
214.4
4790.2
1981
199.1
2200.2
1994
189.4
5021.7
1982
205.5
2347.3
1995
249.3
5320.8
REGRESSION : PRE- 1982
Ya= 1.016115 + 0.0803319Xa + ua
RSS1= 1785.03254, df = 10
REGRESSION: POST - 1982
Yb = 153.4947 + 0.0148624 Xb + ub
RSS2 = 10005.2214, df = 12
RSSUR= RSS1 + RSS2 = 11790.25394
CALCULATING F VALUE USING CHOW TEST
F = (23248.3 - 11790.25394) / 2
(11790.25394) / 22
Hence, F = 10.69, and from F-Table, Fo= 5.72. Since F > Fo, we can assume to
alternative hypothesis that the savings-income relation has undergone a
structural change.
F-TABLE (SIGNIFICANCE 0.01)
Drawbacks
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Sensitivity to Breakpoint Specification
Dependence on Sample Size
Difficulty in Interpreting Breaks
Lack of Robustness
No Information on Magnitude
Limited to Linear Regression