Data is taken from the Economic Survey of Pakistan 1991-1992. The data file link is at the end of the post “Goldfeld-Quandt Test Example for the Detection of Heteroscedasticity”.
Read about the Goldfeld-Quandt Test in detail by clicking the link “Goldfeld-Quandt Test: Comparison of Variances of Error Terms“.
Goldfeld-Quandt Test Example
For an illustration of the Goldfeld-Quandt Test Example, the data given in the file should be divided into two sub-samples after dropping (removing/deleting) the middle five observations.
Sub-sample 1 consists of data from 1959-60 to 1970-71.
Sub-sample 2 consists of data from 1976-77 to 1987-1988.
The sub-sample 1 is highlighted in green colour, and sub-sample 2 is highlighted in blue color, while the middle observation that has to be deleted is highlighted in red.
The Step-by-Step Procedure to Conduct the Goldfeld Quandt Test
Step 1: Order or Rank the observations according to the value of $X_i$. (Note that observations are already ranked.)
Step 2: Omit $c$ central observations. We selected 1/6 observations to be removed from the middle of the observations.
Step 3: Fit OLS regression on both samples separately and obtain the Residual Sum of Squares (RSS) for each sub-sample.
The Estimated regression for the two sub-samples are:
Sub-sample 1: $\hat{C}_1 = 1010.096 + 0.849 \text{Income}$
Sub-sample 2: $\hat{C}_2 = -244.003 + 0.88067 \text{Income}$
Now compute the Residual Sum of Squares for both sub-samples.
The residual Sum of Squares for Sub-Sample 1 is $RSS_1=2532224$
The residual Sum of Squares for Sub-Sample 2 is $RSS_2=10339356$
The F-Statistic is $ \lambda=\frac{RSS_2/n_2}{RSS_1/n_1}=\frac{10339356}{2532224}=4.083$
The critical value of $F(n_1=10, n_2=10$ at a 5% level of significance is 2.98.
Since the computed F value is greater than the critical value, heteroscedasticity exists in this case, that is, the variance of the error term is not consistent, rather it depends on the independent variable, GNP.
Your assignment is to perform the Goldfeld-Quandt Test Example using any statistical software and confirm the results.
Download the data file by clicking the link “GNP and consumption expenditure data“.
Learn about White’s Test of Heteroscedasticity
