<p>You need at least as many instruments as endogenous variables. If you use IV estimation, with <span class="math-container">$U_t$</span> and <span class="math-container">$U_{t-1}$</span> as endogenous and <span class="math-container">$U_{t-2}$</span> as instrument you are basically <em>`replacing'</em> <span class="math-container">$U_t$</span> and <span class="math-container">$U_{t-1}$</span> by a linear combination of <span class="math-container">$U_{t-2}$</span> giving the regression:
<span class="math-container">$$
\begin{align*}
D&amp;= a + b X_t+c \alpha U_{t-2} +d \beta U_{t-2} + \varepsilon\\
 &amp;=a + b X_t+(c \alpha+ d \beta) U_{t-2} + \varepsilon
\end{align*}
$$</span>
You can get estimates for <span class="math-container">$\alpha, \beta$</span> and <span class="math-container">$c \alpha + d \beta$</span>, which is not sufficient to estimate <span class="math-container">$c$</span> and <span class="math-container">$d$</span> separately.</p>
<p>You could try using instruments <span class="math-container">$U_{t-2}$</span> and <span class="math-container">$U_{t-3}$</span>.</p>

CC BY-SA 4.0
2024-11-15T10:03:11.200Z
2024-11-15T10:03:11.200Z
tdm
<p>i have to run the following  equation using IV method
D= a+bXt+cUt+dUt-1.
Could you please let me know if it is possible to define Ut and Ut-1 as endogenous variables and use Ut-2 as an instrument in STATA. To put it differently, to use for my two endogenous variable the same instrument (Ut Ut-1=Ut-2).
Many thanks</p>

<econometrics><regression>
Instrumental Variables
user51997
# Instrumental Variables

(Asked by: username_0 on 2024-11-13)

i have to run the following equation using IV method
D= a+bXt+cUt+dUt-1.
Could you please let me know if it is possible to define Ut and Ut-1 as endogenous variables and use Ut-2 as an instrument in STATA. To put it differently, to use for my two endogenous variable the same instrument (Ut Ut-1=Ut-2).
Many thanks

**Tags:** econometrics, regression

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## 1 answers

### Answer by username_1 on 2024-11-15. Score: 1

You need at least as many instruments as endogenous variables. If you use IV estimation, with $U\_t$ and $U\_{t-1}$ as endogenous and $U\_{t-2}$ as instrument you are basically *`replacing'* $U\_t$ and $U\_{t-1}$ by a linear combination of $U\_{t-2}$ giving the regression:
$$
\begin{align\*}
D&= a + b X\_t+c \alpha U\_{t-2} +d \beta U\_{t-2} + \varepsilon\\
&=a + b X\_t+(c \alpha+ d \beta) U\_{t-2} + \varepsilon
\end{align\*}
$$
You can get estimates for $\alpha, \beta$ and $c \alpha + d \beta$, which is not sufficient to estimate $c$ and $d$ separately.

You could try using instruments $U\_{t-2}$ and $U\_{t-3}$.


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