The Wald, LR, and LM Inequality. This is based on Baltagi (1994). The likelihood is given by Eq. (2.1) in the text

















Hence, using (4) and (8), one gets
Hence, using (3) and (11), one gets
where the last equality follows from (10). L(f, 52) is the restricted maximum; therefore, logL(ft, о2) < logL(ft, 52), from which we deduce that W > LR. Also, L(ft, &2) is the unrestricted maximum; therefore log L(ft, о2) > log L(ft, 52), from which we deduce that LR > LM.
An alternative derivation of this inequality shows first that LM W/n L...
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