The Hausman test helps choose between fixed effects and random effects models from "summary" of Introduction to Econometrics by Christopher Dougherty
The Hausman test is a statistical test used in econometrics to determine whether a fixed effects model or a random effects model is more appropriate for a particular dataset. Fixed effects models assume that each individual in the dataset has a unique intercept that is constant over time, while random effects models assume that the intercepts are randomly distributed across individuals. To conduct the Hausman test, researchers estimate both a fixed effects model and a random effects model using the same dataset. The test then compares the estimated coefficients from each model to see if they are significantly different. If the coefficients are significantly different, this suggests that the random effects model is inconsistent and that the fixed effects model is more appropriate. The intuition behind the Hausman test is that if the random effects model is consistent, the estimated coefficients should be similar to those from the fixed effects model. However, if the random effects model is inconsistent, the estimated coefficients will be biased and different from those of the fixed effects model. In practice, researchers typically calculate a test statistic using the estimated coefficients from the two models and compare it to a critical value from a chi-squared distribution. If the test statistic is greater than the critical value, researchers reject the null hypothesis that the random effects model is consistent, and choose the fixed effects model instead.- The Hausman test provides a formal way to choose between fixed effects and random effects models based on the assumption of consistency. By comparing the estimated coefficients from each model, researchers can determine which model is more appropriate for their dataset and ensure that their results are reliable and valid.
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