An economist estimates Y X0 11 X22 e by least squares and tests the hypothesis H0 2 0 against H1 2 6 0 Assume 1 2 Rk and 2 2 R She obtains a Wald statistic W 0 34 The sample size is n 500 (a) What is the correct degrees of freedom for the 2 distribution to evaluate the significance of the Wald statistic (b) The Wald statistic W is very small Indeed, is it less than the 1 quantile of the appropriate 2 distribution If so, should you reject H0 Explain your reasoning

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Question: An economist estimates Y X0 11 X22 e by least squares and tests the hypothesis H0 : 2 0 against H1 :

An economist estimates Y Æ X0 1¯1 Å X2¯2 Åe by least squares and tests the hypothesis H0 : ¯2 Æ 0 against H1 : ¯2 6Æ 0. Assume ¯1 2 Rk and ¯2 2 R. She obtains a Wald statistic W Æ 0.34. The sample size is n Æ 500.

(a) What is the correct degrees of freedom for the Â2 distribution to evaluate the significance of the Wald statistic?

(b) The Wald statistic W is very small. Indeed, is it less than the 1% quantile of the appropriate Â2 distribution? If so, should you reject H0? Explain your reasoning.

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