Powerful in the statistical sense in small samples

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powerful (in the statistical sense) in small samples because it tends to reject the true hypothesis or model more frequently than it ought to. 2. A Test for General Mis-specification: RESET Ramsey’s RESET test is a test for both omitted variables and incorrect functional form for the estimated equation (The population regression function may be nonlinear 1 ). Ramsey has proposed a test for general misspecification called RESET ( regression specification error test ). The Ramsey RESET test involves three steps: (1) Estimate the equation to be tested using OLS: 0 1 ˆ ˆ ˆ k t i ti i Y X (2) 1 For example, it may take any of the following forms: 0 1 ln t t Y X , 0 1 ln t t Y X or 0 1 1 t t Y X .
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ECON 301 - Introduction to Econometrics I May 2013 METU - Department of Economics Instructor: Dr. Ozan ERUYGUR e-mail: [email protected] Lecture Notes 7 (2) Take the ˆ t Y values from Equation (2) and create 2 ˆ t Y , 3 ˆ t Y 1 ˆ j t Y terms where j =1… p . Then add these terms to Equation (2) as additional explanatory variables and estimate the new equation with OLS: 1 0 1 1 ˆ p k j t t t i ti j i j Y X Y u (3) (3) In step three, we compare the fits of the two equations by using the F-test . Specifically, we test the hypothesis that the coefficients of all three of the added terms are equal to zero: 0 1 2 : ... 0 p H : A H otherwise The Q-statistic is given as: , 1 / . / ( 1) R U RESET p T k U SSR SSR p Q F SSR T k   where p is the number of restrictions and T-k-1 is the degrees of freedom of unrestricted model (equation 3). The same statistic can also be stated differently as follows:
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ECON 301 - Introduction to Econometrics I May 2013 METU - Department of Economics Instructor: Dr. Ozan ERUYGUR e-mail: [email protected]com Lecture Notes 8 2 2 , 1 2 / 1 / ( 1) U R RESET p T k U R R p Q F R T k   where p is the number of restrictions and T-k-1 is the degrees of freedom of unrestricted model (equation 3), 2 R R is the R square of restricted model (equation 2) and 2 U R is the R square of unrestricted model (equation 3). Note that, generally p=2 is a reasonable choice. Rejection of the null hypothesis merely indicates that the equation has been mis-specified in some way or other. One advantage of RESET is that it is easy to apply, for it does not require one to specify what the alternative model is. Example Suppose that you have the following model: (0.08) (0.01) ˆ 32.9 0.70 0.27 t t t Y PC YD (5) where T =44, SSR =185.66.
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ECON 301 - Introduction to Econometrics I May 2013 METU - Department of Economics Instructor: Dr. Ozan ERUYGUR e-mail: [email protected] Lecture Notes 9 For step two, we take ˆ t Y from Equation (5), calculate 2 ˆ t Y and 3 ˆ t Y , and then reestimate Equation (5) with the two new terms added in: 2 3 (1.71) (0.71) (0.08) (0.0011) ˆ ˆ ˆ 23.80 0.59 0.36 0.02 0.007 t t t t t Y PC YD Y Y where T =44, SSR =138.41.
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