The Lagrange Multiplier Test for Random Effects in Panel Data Analysis

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In this video, we will introduce the Lagrange Multiplier Test, which is used to determine whether random effects are significant in panel data model. We will show you how to perform it step by step on our panel data, from which we presented the results in our article, published on Sustainability review in 2019.
In 1980, Breusch and Pagan developed a Lagrange multiplier test for random effects, so this test is also called Breusch-Pagan Lagrange Multiplier test. The test helps us choose between random-effects model regression and pooled OLS regression.
The null hypothesis of the Lagrange Multiplier Test assumes that, the random effects are not significant, and they can be excluded from the model without a substantial loss of information. Conversely, the alternative hypothesis suggests that, the random effects are indeed essential and contribute significantly to the overall model fit.
The LM statistic follows a chi-square distribution with 1 degree of freedom, because we are testing for one measure only - the variance of random effects term. If we reject the null hypothesis using this test, we conclude that the random effects are significant in the model, and the use of the Random Effects Model is appropriate.
We will show you how to implement the Lagrange Multiplier Test on our panel data, that includes 434 year-observations of 62 provinces as entities of our sample; each province has 7 year-observations. Our research aims to study the relationship between foreign direct investment and sustainability at provincial level, in a developing host country such as Vietnam, in the period between 2010 and 2016.