Let T be a test statistic such that under H0, T d 23 Since P 23 7 815 0 05, an asymptotic 5 test of H0 rejects when T 7 815 An econometrician is interested in the Type I error of this test when n 100 and the data structure is well specified She performs the followingMonte Carlo experiment B 200 samples of size n 100 are generated from a distribution satisfying H0 On each sample, the test statistic Tb is calculated She calculates b p B1PBb 1 1 Tb 7 815 0 070 The econometrician concludes that the test T is oversized in this context it rejects too frequently under H0 Is her conclusion correct, incorrect, or incomplete Be specific in your answer

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Question: Let T be a test statistic such that under H0, T ! d 23 . Since P 23 7.815 0.05, an

Let T be a test statistic such that under H0, T ¡!

Â23

. Since P

Â23

È 7.815

Æ 0.05, an asymptotic 5% test of H0 rejects when T È 7.815. An econometrician is interested in the Type I error of this test when n Æ 100 and the data structure is well specified. She performs the followingMonte Carlo experiment.

• B Æ 200 samples of size n Æ 100 are generated from a distribution satisfying H0.

• On each sample, the test statistic Tb is calculated.

• She calculates b p Æ B¡1PBb

Æ1 1{Tb È 7.815} Æ 0.070.

• The econometrician concludes that the test T is oversized in this context – it rejects too frequently under H0.

Is her conclusion correct, incorrect, or incomplete? Be specific in your answer.

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