# Breusch-Pagan Test vs. Harvey Test

## What's the Difference?

The Breusch-Pagan Test and Harvey Test are both used in econometrics to test for heteroscedasticity in regression models. The Breusch-Pagan Test is a parametric test that assumes a specific form of heteroscedasticity, while the Harvey Test is a non-parametric test that does not make any assumptions about the form of heteroscedasticity. The Breusch-Pagan Test is more commonly used in practice due to its simplicity and ease of interpretation, while the Harvey Test is preferred when the assumptions of the Breusch-Pagan Test are violated. Overall, both tests are valuable tools for detecting and correcting for heteroscedasticity in regression models.

## Comparison

Attribute | Breusch-Pagan Test | Harvey Test |
---|---|---|

Test Type | Heteroscedasticity test | Heteroscedasticity test |

Assumption | Homoscedasticity | Homoscedasticity |

Null Hypothesis | Homoscedasticity is present | Homoscedasticity is present |

Alternative Hypothesis | Heteroscedasticity is present | Heteroscedasticity is present |

Test Statistic | Chi-square | F-statistic |

## Further Detail

### Introduction

When it comes to econometric analysis, researchers often need to test for heteroscedasticity in their data. Two commonly used tests for this purpose are the Breusch-Pagan Test and the Harvey Test. Both tests aim to determine whether the variance of the errors in a regression model is constant or not. In this article, we will compare the attributes of these two tests to help researchers understand their differences and choose the most appropriate test for their analysis.

### Breusch-Pagan Test

The Breusch-Pagan Test, developed by Trevor Breusch and Adrian Pagan, is a statistical test used to detect heteroscedasticity in regression models. The test is based on regressing the squared residuals from the original regression model on the independent variables. The null hypothesis of the test is that the variance of the errors is constant (homoscedasticity), while the alternative hypothesis is that the variance is not constant (heteroscedasticity). The test statistic is then compared to a chi-squared distribution to determine whether to reject the null hypothesis.

- Based on regressing squared residuals on independent variables
- Null hypothesis: variance of errors is constant
- Alternative hypothesis: variance is not constant
- Test statistic compared to chi-squared distribution

### Harvey Test

The Harvey Test, developed by Andrew Harvey, is another statistical test used to detect heteroscedasticity in regression models. Unlike the Breusch-Pagan Test, the Harvey Test is based on regressing the absolute residuals from the original regression model on the independent variables. The null hypothesis of the Harvey Test is also that the variance of the errors is constant, while the alternative hypothesis is that the variance is not constant. The test statistic is then compared to a chi-squared distribution to determine the presence of heteroscedasticity.

- Based on regressing absolute residuals on independent variables
- Null hypothesis: variance of errors is constant
- Alternative hypothesis: variance is not constant
- Test statistic compared to chi-squared distribution

### Comparison of Attributes

Both the Breusch-Pagan Test and the Harvey Test are used to detect heteroscedasticity in regression models, but they differ in the way they calculate the test statistic. The Breusch-Pagan Test uses squared residuals, while the Harvey Test uses absolute residuals. This difference in calculation can lead to different results in practice, as the two tests may have different power to detect heteroscedasticity depending on the data and the model being tested.

Another difference between the two tests is the interpretation of the test statistic. In the Breusch-Pagan Test, the test statistic follows a chi-squared distribution under the null hypothesis of homoscedasticity. In contrast, the Harvey Test statistic also follows a chi-squared distribution under the null hypothesis, but with a different degrees of freedom. Researchers need to be aware of this difference when interpreting the results of the tests.

Furthermore, the Breusch-Pagan Test is more commonly used in econometric analysis compared to the Harvey Test. This may be due to the fact that the Breusch-Pagan Test is easier to implement and interpret, as it is based on squared residuals which are more commonly used in regression analysis. However, the Harvey Test can also be a useful tool for detecting heteroscedasticity, especially in cases where the assumptions of the Breusch-Pagan Test may not hold.

### Conclusion

In conclusion, both the Breusch-Pagan Test and the Harvey Test are valuable tools for detecting heteroscedasticity in regression models. While the Breusch-Pagan Test is more commonly used and easier to interpret, the Harvey Test offers an alternative approach that may be more suitable in certain situations. Researchers should consider the attributes of each test and choose the one that best fits their data and research question. By understanding the differences between these two tests, researchers can make more informed decisions in their econometric analysis.

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