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 + β₁X₁_i + u_i, i = 1, ..., n; Z₁_i, Z₂_i are valid instruments, J = 2.58.
(b)Y_i = β₀ + β₁X₁_i + β₂X₂_i + β₃W₁_i + u_i, i = 1, ..., n; Z₁_i, Z₂_i, Z₃_i, Z₄_i are valid instruments, J = 9.63.
(c)Y_i = β₀ + β₁X₁_i + β₂W₁_i + β₃W₂_i + β₄W₃_i + u_i, i = 1, ..., n; Z₁_i, Z₂_i, Z₃_i, Z₄_i are valid instruments, J = 11.86.

Question

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 + β₁X₁_i + u_i, i = 1, ..., n; Z₁_i, Z₂_i are valid instruments, J = 2.58.
(b)Y_i = β₀ + β₁X₁_i + β₂X₂_i + β₃W₁_i + u_i, i = 1, ..., n; Z₁_i, Z₂_i, Z₃_i, Z₄_i are valid instruments, J = 9.63.
(c)Y_i = β₀ + β₁X₁_i + β₂W₁_i + β₃W₂_i + β₄W₃_i + u_i, i = 1, ..., n; Z₁_i, Z₂_i, Z₃_i, Z₄_i are valid instruments, J = 11.86.

Quizplus · Accepted Answer

The Answer of 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 + β₁X₁_i + u_i, i = 1, ..., n; Z₁_i, Z₂_i are valid instruments, J = 2.58. (b)Y_i = β₀ + β₁X₁_i + β₂X₂_i + β₃W₁_i + u_i, i = 1, ..., n; Z₁_i, Z₂_i, Z₃_i, Z₄_i are valid instruments, J = 9.63. (c)Y_i = β₀ + β₁X₁_i + β₂W₁_i + β₃W₂_i + β₄W₃_i + u_i, i = 1, ..., n; Z₁_i, Z₂_i, Z₃_i, Z₄_i are valid instruments, J = 11.86.

Here Are Some Examples of the Instrumental Variables Regression Model χm−k2\chi _ { m - k } ^ { 2 }χm−k2​

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