The Limits of Mathematics and NP Estimation in ... - Chichilnisky

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Using the SUR Model of Tourism Demand for Neighbouring Regions in Sweden and Norway 113This gives us ˆt 2. Run an OLS on:ˆ X y ˆ ˆ ... ˆ uit t ti 1 t1 2 t2P tP tThis equation can be used for any AR(P) process. From this equation the unrestrictedresidual sum of squares (RSS u ).The restricted residual sum of squares (RSS R ) is given from the following equation:The null hypothesis is:3. Run an F-test: Xy ˆt t t 1t: .... 0H0 1 2 PF=((RSS R -RSS U )/p) / (RSS U /(T-k-P))This has a distribution: F(P,T-k-P) under the null hypothesis.The Breusch-Godfrey test can be tested for AR(P) processes which gives this test a clearadvantage over other available tests for autocorrelation.6.1.3 The Ramsey RESET-testRESET test stands for Regression Specification Error Test. The test is very general and canonly tell you if you have a problem or not. It tests for omitted variables and incorrectfunctional forms or misspecified dynamics and also if there is a correlation between theerror term and the independent variable. The null hypothesis is:H 0 : E (ε i /X i ) = 0H 1 : E (ε i /X i ) ≠ 0(and an omitted variable effect is present)Thus, by rejecting the null hypothesis indicates some type of misspecification. First a linearregression is specified:y X i i iThis gives the restricted residual sum of squares (RSSR). After the RSS R has been found theunrestricted model is presented by adding variables (three fitted values):y X yˆyû2 3t i 1 i 2i tThis gives us the unrestricted residual sum of squares (RSS U ). In the third step the RESETtestuses a F-test:F= ((RSS R - RSS U )/number of restrictions under H 0 ) / (RSS U / (N- number of parameters inunrestricted model))The F-test checks if θ 1 =θ 2 =0, if θ 1 =θ 2 ≠0 I have an omitted variable or a misspecification inthe model.
114Advances in Econometrics - Theory and Applications6.1.4 The White’s testThis test is a general test where I do not need to make any specific assumptions regardingthe nature of the heteroscedasticity, whether it is increasing, decreasing etc. The test onlytells us if I have an indication of heteroscedasticity.2 20 : iH iThe alternative hypothesis is not H 0 , anything other than H 0 .The test can be divided into several steps:1. Run an OLS on:y 1X1 ... X i i k ki iFrom this equation I get î which is used as a proxy for the variance.2. Run an OLS on:ˆ ... ... 2 2 2i 0 1X1i kXki k1X1i kkXkk kk1X1iXk iWhere k is the number of parameters. The variance is considered to be a linear function of anumber of independent variables, their quadratic and cross products. Thus, the X:s is usedas a proxy for Z.3. Calculate an F-test:Restricted model:2 ' 'î 0 i From this test the restricted residual sum of squares (RSS R ) is measured.The F-test is:WhereF=((RSS R -RSS U )/k) / (RSS U /(n-k-1))H0 : i 0 i1,2... k6.1.5 The ARCH Engel’s LM testThis is a test for AutoRegressive Conditional Heteroscedasticity (ARCH). The ARCHprocess can be modeled as:y X t t twhere the Variance of t conditioned on t i: Var( t \ t i ) = 0 + 1 t i1. Use OLS on the original model and get: ˆt . Square it and use it in the folloingunrestricted model:2 22. ˆ ˆt 0+ itii+t3. Test whether i = 0, for any i = 1, 2 , . . . By an F-test as before.2
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