distribution with one degree of freedom, and a sum of m such variables has a χ2 distribution with m degrees of freedom

INSTRUCTIONS TO CANDIDATES

ANSWER ALL QUESTIONS

1.a Use the t-test to individually test whether the coefficients β1 and β2 are individually zero at the 5% level of significance. That is, test whether β1 = 0 and then whether β2 = 0.

1.b Use the joint F-test to test whether the coefficients β1 and β2 are jointly zero at the 5% level of significance. That is, test whether β1 = β2 = 0.

1.c Use the Wald coefficient restriction test to test whether β1 = β2.

1.d The coefficient β2 measures the elasticity of population with respect to employment. It is frequently supposed that β2 = 1. Test whether it is. That is, test whether we can, at the 5% level of significance, reject the hypothesis that β2 = 1.

1.e The CUSUM test is based on the observation that the normalized one-step ahead forecast errors should (under the null hypothesis of intertemporal stability) be n(0,1), so their intertemporal sum should behave like a sum of n(0,1) variables. Use the CUSUM test to test whether this equation is intertemporally stable.

1.f The CUSUM of Squares test is based on the fact that the square of a n(0,1) variable follows a χ2 distribution with one degree of freedom, and a sum of m such variables has a χ2 distribution with m degrees of freedom. So the intertemporal sum of the square of the normalized one-step ahead forecast errors should follow a χ2 distribution under the null hypothesis of intertemporal stability. Use the CUSUM of Squares test to test whether this equation is intertemporally stable.

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