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13_InferenceB_handou - Inference II Single-equation hypothesis 73-261 Econometrics September 15 Readings Wooldridge 4.2 4.4 pp 4 7 8 12 updated

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Unformatted text preview: Inference II: Single-equation hypothesis 73-261 Econometrics September 15 Readings: Wooldridge 4.2, 4.4 pp. 4, 7, 8, 12 updated with info on testing inequalities Updates are highlighted with blue font and/or boxes See lecture note from Sep-27 for more detail p. 2 © CMU / Y. Kryukov 73-261 1.3 Inference II Overview – Inference Last time: Reject β j = 0 when t-statistic is large: p-value is low: Follows from: Today One-sided test: β j > 0 (Wooldridge 4.2) Testing β j = 1 (4.2) Confidence interval for β j (4.3) Testing β j > β m (4.4) ( ) c t t k N j j j = − > = − − − α β β 2 1 1 1 1 | ) ˆ ( se ˆ | | ˆ | ( ) α < − = − − j k N t t p ˆ 2 1 [ ] 1 2 ) ' ( , Normal ~ ˆ − X X σ β β α = significance level t N-k- 1 = c.d.f. t- 1 = inverse c.d.f. p. 3 © CMU / Y. Kryukov 73-261 1.3 Inference II t-stat and p-value in GRETL p. 4 © CMU / Y. Kryukov 73-261 1.3 Inference II One-sided tests Want to test if β j is positive H : β j = 0 – the boundary of β j > H 1 : β j < 0 – t j is likely to be below zero : Should we reject H ? Is this more likely under H or H 1 ? 5% significance: reject if where Pr{ t j > c 5% } = 5% p-value: (t-stat greater than the realized value) 10 ) ˆ s.e.( / ˆ ˆ = = j j j t β β % 5 ˆ c t j > } ˆ Pr{ j j t t p > = p. 5 © CMU / Y. Kryukov 73-261 1.3 Inference II Testing β j = 1 Hypothesis – H : β j = 1 Test statistic: Rejection rule (H 1 )– one-tail or two?...
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This note was uploaded on 01/21/2011 for the course ECON 73-261 taught by Professor Kyrkv during the Fall '09 term at Carnegie Mellon.

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13_InferenceB_handou - Inference II Single-equation hypothesis 73-261 Econometrics September 15 Readings Wooldridge 4.2 4.4 pp 4 7 8 12 updated

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