1.4.6.md

Solution to Review Question

by Qiang Gao, updated at May 11, 2017

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Chapter 1 Finite-Sample Properties of OLS

Section 4 Hypothesis Testing under Normality

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Review Question 1.4.6 ($$t$$ vs. $$F$$)

“It is nonsense to test a hypothesis consisting of a large number of equality restrictions, because the $$t$$-test will most likely reject at least some of the restrictions.” Criticize this statement.

Solution

A joint test of multiple restrictions simultaneously is different from separately test multiple restrictions. As explained in the text, the overall significance increases with the number of restrictions to be tested if the $$t$$-test is applied to each restriction without adjusting the critical value.

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