In the model y_t = ₀ + ₁x_t₁ + ₂x_t₂ + ….. + _kx_tk + u_t, the explanatory variables, x_t = (x_t₁, x_t₂ …., x_tk), are sequentially exogenous if:

Question

Quizplus · Accepted Answer

Sequential exogeneity requires that the error term is not correlated with any of the previous or current values of the explanatory variables, which is captured by the condition E(u|xt, xt-₁,…) = E(u) = 0. This means that the error term is not affected by the values of the explanatory variables, hence they are exogenous. Choice B is incorrect because it implies that the error term is perfectly predictable based on the values of the explanatory variables, which violates the assumption of exogeneity. Choices C and D are also incorrect because they imply a positive or non-zero correlation between the error term and the explanatory variables, respectively, which also violates the assumption of exogeneity. In the given model, the explanatory variables are sequentially exogenous if E(u_t|xt , xt-1, ……) = E(u_t) = 0, t = 1,2, ….

In the Model Yt = 0 + 1xt1

In the Model Y_t = ₀ + ₁x_t₁