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# task2 - Question 1 a Agree On average OLS slope coefficient...

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Question 1 a) Agree. On average OLS slope coefficient are on target even with heteroscedasticity, but are no longer efficient. b) true The classical t-test is valid when the regressor is fixed and trended and autocorrelation among errors is predominantly negative, and when the regressor is random and AR(1), like the errors, and autocorrelation is moderately negative or positive. Agree. Parameters estimates are fitted by minimizing a WLS of residuals where the weights are inversely proportional to the variance of the errors. This is in contrast to OLS. Disagree. The last slope B4 has for factor edi+agei. When we expand the expression we get 2*edi*agei but no explanatory variable appears to be linearly correlated to another.

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Disagree. The Durbin–Watson statistic is a test statistic used to detect the presence of autocorrelation We would need to add slope dummy variables and an intercept dummy variable as well. We want to test for a difference in the slope and the intercept. We therefore enter the categorical dummy variable children and estimate for its slope b5. Children = {0,1} – We jump between models by plugging-in 0 or 1. The model with children is written as: y= b1 + (b2+d1children)edi + (b3+d2children)agei + (b4+d3children)wagei + b5children + ut. We begin by testing to see if we can remove the dummy variables Setting up a test of hypothesis as follows: H(0): only edu, agei, wagei,and b1needed => b5 =0 – null hypothesis H(a): dummy variables are needed, => d(1-5)=/=0 Rejection: We use the following F test F(obs.) = (RSS(0) - RSS(a))/(df(0) - df(a)) __________________________________ RSS(a)/df(a) We will perform a t test on the coefficient of the dummy variable. 1. Work hour structure of married people without children = Work hour structure of married people with children b5, =0 b5 =/=0
Ha: Work hour structure of married people without children > Work hour structure of married people with children 2. Test for significant effect of dummy variable on pooled data H 0 : β 5 =0 H 1 : β 5 ≠0 Test for significant effect of children: H 0 : β 5 =0 H 1 : at least one of the parameters β 1-4 is not zero This hypothesis test follows the F-distribution The critical value of this test which is always one-tailed is, F α ,K,n-K-1 where α is the level of significance K represents the number of parameters set to zero (in this case two) n-K-1 is the degrees of freedom in the unrestricted model In the F-table, the numerator degrees of freedom is K and the denominator degrees of freedom is n-K-1 To test whether the multiple regression model with dummy variable for the “Children effect” improved the regression model with 4 explanatory variable, I conducted Wald’s F test. The test statistic is F, where the numerator is (SSEr – SSEur)/m, while denominator is SSEur divided by DoF. The unrestricted model is the multiple regression with the dummy, while the restricted model is the simple market model.

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