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Structural Change

  • Restricted RSS
  • Unrestricted RSS
  • DoF restricted model
  • Number of restrictions
  • 5% Critical value
  • F-test
  • DoF unrestricted model
  • 302
  • 26.10
  • 310
  • 4.68
  • 1.97
  • 23.22
  • 8

Using the information above, the model
 
ln(D)=\beta_0+\beta_1ln(Y_i)+\beta_2[ln(Y_i)]^2+\beta_3M_i+\beta_4school_i+\beta_5age_i+\gamma_1L_i+\epsilon_i
where L=1 if London, 0 otherwise was estimated and this yielded a RSS=25.41. Test the significance of the London dummy.


Using the information above, the model
 
ln(D)=\beta_0+\beta_1ln(Y_i)+\beta_2[ln(Y_i)]^2+\beta_3M_i+\beta_4school_i+\beta_5age_i+\gamma_1L_i+\gamma_2SO_i+\gamma_3MD_i+\epsilon_i
where SO=1 if South West or South East, 0 otherwise and MD=1 if East Midlands, West Midlands or East, 0 otherwise. This model was estimated and this yielded a RSS=24.20. Test this model against that with just a London dummy.


Using the information above, the model
 
ln(D)=\beta_0+\beta_1ln(Y_i)+\beta_2[ln(Y_i)]^2+\beta_3M_i+\beta_4school_i+\beta_5age_i+\gamma_1L_i+\gamma_2SO_i+\gamma_3MD_i+\epsilon_i
where SO=1 if South West or South East, 0 otherwise and MD=1 if East Midlands, West Midlands or East, 0 otherwise. This model was estimated and this yielded a RSS=24.20. When testing this model against that with all the regional dummies included, which of the following corresponds to the null hypothesis?

Consider the following model estimated on a sample of 316 individuals living in England on their own:
 
ln(D)=\beta_0+\beta_1ln(Y_i)+\beta_2[ln(Y_i)]^2+\beta_3M_i+\beta_4school_i+\beta_5age_i+\epsilon_i
where: where D is the level of debt in £, Y is the wage rate (in £), age=1 if the individual is less than 45 years old, 0 otherwise, M= 1 if male, 0 if female, school = number of years of schooling. Estimating by OLS yielded a RSS of 26.10. Estimating the model above separately for the 142 people living in the South (including London) and the 174 people not living in the South yielded RSS of 10.53 and 14.83, respectively. Test the hypothesis that the parameters of the model estimated across the 2 regions are the same (2 decimal places).


Consider the following model estimated on a sample of 316 individuals living in England on their own:
 
ln(D)=\beta_0+\beta_1ln(Y_i)+\beta_2[ln(Y_i)]^2+\beta_3M_i+\beta_4school_i+\beta_5age_i+\epsilon_i
where: where D is the level of debt in £, Y is the wage rate (in £), age=1 if the individual is less than 45 years old, 0 otherwise, M= 1 if male, 0 if female, school = number of years of schooling. Estimating by OLS yielded a RSS of 26.10. Including additional variables
 
M_i~\times~ln(Y_i)~ and ~M_i~\times~[ln(Y_i)]^2~ yielded a RSS 25.15. Test the joint significance of the coefficients on these two variables (2 decimal places)


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