Stataでインストルメント化された相互作用項を使用してインストルメンタル変数回帰を行う方法は？

Stata構文に少し問題があります。次の回帰を行う必要があります。

y = a x + b z + c (x z) + e

$y = ax + bz + c(xz) + e$

ここで、と両方が計測され、相互作用項は計測されたと値を使用します。 $x$ $z$ $xz$ $x$ $z$

と予測値を生成し、それらを回帰変数として使用するだけでは、誤った標準誤差が生じます。 $x$ $z$

編集：また、1つの変数のみが計測され、この1つの計測変数が相互作用項にある状態で、同様の回帰を行う必要があります。

stata interaction instrumental-variables

— ミロア
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$x_{1}$ $x_{2}$ $x$ $z$ $z$ $x_3 = x_1 \cdot x_2$

y = a x_{1} + b x_{2} + c x_{3} + e

$y = ax_1 + bx_2 + cx_3 + e$ which has three endogenous variables. Assuming that you have two variables

z_{1}

$z_1$ and

z_{2}

$z_2$ which are valid instruments for

x_{1}

$x_1$ and

x_{2}

$x_2$ , then a valid instrument for

x_{3}

$x_3$ is

z_{3} = z_{1} \cdot z_{2}

$z_3 = z_1 \cdot z_2$ . In Stata it is straightforward to generate the corresponding interactions and to use them in the appropriate estimation command like ivreg2, for instance.

Note though that models with more than one endogenous variable can be difficult to interpret and also you might be confronted with the question why you are tackling two causal questions at the same time. This issue is discussed on the Mostly Harmless Econometrics blog by Angrist and Pischke.

Your second problem is similar for the case where you interact an endogenous ( $x$ ) and an exogenous variable ( $w$ ) in a model of the type

y = a x + b w + c (x \cdot w) + e

$y = ax + bw + c(x\cdot w) + e$ If

z

$z$ is a valid instrument for

x

$x$ , then a valid instrument for

(x \cdot w)

$(x\cdot w)$ is

(z \cdot w)

$(z\cdot w)$ . This procedure was suggested in the Statalist. I just provide one link but there are many more discussions about this (most of which will pop up on Google when searching for: interaction of "two endogenous variables").

— Andy
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