Here Are Some Examples of the Instrumental Variables Regression Model $\chi _ { m - k } ^ { 2 }$

question 42

Essay

Here are some examples of the instrumental variables regression model. In each case you are given the number of instruments and the J-statistic. Find the relevant value from the $\chi _ { m - k } ^ { 2 }$ distribution, using a 1% and 5% significance level, and make a decision whether or not to reject the null hypothesis.
(a)Y_i = β₀ + β₁X_1i + u_i, i = 1, ..., n; Z_1i, Z_2i are valid instruments, J = 2.58.
(b)Y_i = β₀ + β₁X_1i + β₂X_2i + β₃W_1i + u_i, i = 1, ..., n; Z_1i, Z_2i, Z_3i, Z_4i are valid instruments, J = 9.63.
(c)Y_i = β₀ + β₁X_1i + β₂W_1i + β₃W_2i + β₄W_3i + u_i, i = 1, ..., n; Z_1i, Z_2i, Z_3i, Z_4i are valid instruments, J = 11.86.

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