<p>You have a model</p>
<p><span class="math-container">$$(1)\  y = x \beta + e,$$</span></p>
<p>where <span class="math-container">$x$</span> is endogenous <span class="math-container">$\mathbb E[xe] \not =0$</span>. This is the structural model in the sense that the parameter you are interested in is <span class="math-container">$\beta$</span> interpreted by its appearance in (1). In your case</p>
<ul>
<li>y is civil conflict onset</li>
<li>x economic growth</li>
</ul>
<p>suggesting that you are interested in examining how economic growth affects propensity for civil conflict. So positive <span class="math-container">$\beta$</span> means economic growth increase propensity for civil conflict.</p>
<p>Using 2SLS you get an IV-estimate of <span class="math-container">$\beta$</span> which we can denote <span class="math-container">$\hat \beta_{IV}$</span>. When <span class="math-container">$\hat \beta_{IV}$</span> is positive it suggests that <span class="math-container">$\beta$</span> is positive and hence  economic growth increase propensity for civil conflict.</p>
<p>Interpretation is independent of <span class="math-container">$Cov(z,x)$</span> where <span class="math-container">$z$</span> is the instrument. Which in this case is</p>
<ul>
<li>z is natural disaster.</li>
</ul>
<p>For instrumental regression instruments must be relevant which in the simple univariate case reduces to <span class="math-container">$Cov(z,x) \not = 0$</span>, but the sign is irrelevant (you can try to use <span class="math-container">$w := -z$</span> as instrument then <span class="math-container">$Cov(z,x) &lt; 0 \Leftrightarrow Cov(w,x) &gt; 0$</span> but the 2SLS estimate <span class="math-container">$\hat \beta_{IV}$</span> will be the same).</p>

CC BY-SA 4.0
2021-01-27T14:07:18.257Z
Thanks a lot! Actually I am not really interested in examining how economic growth affects propensity for civil conflict. Instead I am interested in how natural disasters affect conflict THROUGH economic growth. I thought, due to the assumptions of relevance and exogeneity of an instrument, the coefficient in the table estimates exactly this indirect channel.
Hokkaido21
CC BY-SA 4.0
2021-01-27T16:32:23.840Z
Fair enough, still thats an entirely different story.
Jesper Hybel
CC BY-SA 4.0
2021-01-27T17:44:58.770Z
Yes! I do not really like this approach but I have to work on it. So assuming the approach would make sense, what would be the interpretation of the 2SLS coefficient?
Hokkaido21
CC BY-SA 4.0
2021-01-27T17:54:11.970Z
In the 2SLS context the interpretation is that the instrument is relevant. You do not have interpretation independent of theory so you have to make structural causal model. As I said this is a diffrent story and in this forum a new question.
Jesper Hybel
CC BY-SA 4.0
2021-01-28T12:03:02.553Z
@Hokkaido21 according to your profile you have 4 questions all have received answers with upvotes but you have accepted none. It is good custom accept when the question has been answered both as a way of showing appreciation of the free service you get but also to help other future users and close questions (this also helps getting Economic site of Beta version).
Jesper Hybel
CC BY-SA 4.0
2021-01-28T18:04:31.340Z
I am very sorry! I am still quite new to this forum and I did not know that I have the possibility to accept an answer. I only upvoted the answers. I really appreciate the free service and of course I appreciate your answer! My intention was not to signal anything else.
Hokkaido21
CC BY-SA 4.0
2021-01-28T18:34:19.520Z
No worries. Happy to be of help.
Jesper Hybel
CC BY-SA 4.0
2021-01-27T12:17:29.080Z
2021-01-27T12:17:29.080Z
Jesper Hybel
<p>I am a bit confused because of the interpretation of a coefficient in my analysis. I am using 2SLS in two different subsamples with economic growth as endogenous variable. It is instrumented by a variable for natural disasters. The outcome variable is a measure of civil conflict onset. The first stage shows that if natural disasters increase, economic growth decreases. The second stage then provides a positive coefficient for one subsample, while it produces a negative coefficient in the other subsample.</p>
<p>Does a positive coefficient in the second stage mean that a decrease in economic growth (as a consequence of increased natural disasters) decreases the risk of conflict onset?</p>
<p>I am confused because I do not know how to interpret the coefficients since the instrument is negatively correlated to the instrumented variable. If natural disasters would increase economic growth, then the interpretation would be easier since the direction is the same.</p>
<p>Below, you find my LaTeX Output Table. I hope this will help. The coefficients I am interested in are on the one hand -0.0312 and     0.0210 on the other hand.</p>
<p>I know, there is no F test and no control in the analysis. This analysis is not supposed to be sophisticated, it is basically just a means to understand the interpretation of those coefficients.</p>
<pre><code>
\begin{table}[t!]\centering
\begin{threeparttable}
\renewcommand{\arraystretch}{1.2} % Default value: 1
\def\sym#1{\ifmmode^{#1}\else\(^{#1}\)\fi}
\begin{tabular}{l*{3}{c}}
\hline\hline
            &amp;\multicolumn{1}{c}{(1)}&amp;\multicolumn{1}{c}{(2)}&amp;\multicolumn{1}{c}{(3)}\\
            &amp;\multicolumn{1}{c}{GDP growth p.c.}&amp;\multicolumn{1}{c}{Onset of Conflict}&amp;\multicolumn{1}{c}{Onset of Conflict}\\
\hline
GDP growth p.c.&amp;                     &amp;    -0.0312\sym{**}&amp;     0.0210\sym{**}        \\
            &amp;                     &amp;     (-2.01)         &amp;      (2.00)         \\
Natural Disasters&amp;      -18.02\sym{***}&amp;     Instrument&amp;              Instrument       \\
            &amp;     (-3.39)         &amp;              &amp;                     \\
\hline
Observations       &amp;        3894         &amp;        3894         &amp;        3894         \\

\end{tabular}
\end{threeparttable}
\end{table}
</code></pre>
<p>The code produces following table:
<span class="math-container">$$
\begin{array}{|l|c|c|c|} 
 \hline
   &amp; \text{(1)} &amp; \text{(2)} &amp; \text{(3)} \\
   &amp; \text{GDP growth p.c.} &amp; \text{Onset of Conflict} &amp; \text{Onset of Conflict} \\ \hline
\text{GDP growth p.c.} &amp; &amp; -0.0312^{**}  &amp; 0.0210^{∗∗} \\ 
 &amp; &amp; (-2.01) &amp; (2.00) \\ 
\text{Natural Disasters} &amp; -18.02^{***} &amp; \text{Instrument} &amp; \text{Instrument}  \\ 
 &amp; (-3.39) &amp; &amp; \\ \hline
 \text{Observations} &amp; 3894 &amp; 3894 &amp; 3894 \\ \hline
\end{array}
$$</span></p>

CC BY-SA 4.0
2021-01-26T22:27:56.593Z
I would personally recommend posting your output to ensure a good answer
EB3112
CC BY-SA 4.0
2021-01-27T07:44:49.593Z
@EB3112 thanks, I adjusted the post
Hokkaido21
CC BY-SA 4.0
2021-01-27T13:32:09.997Z
How do models (2) and (3) relate to different subsamples if no. of observations is the same for all three models?
E. Sommer
CC BY-SA 4.0
2021-01-27T14:08:45.770Z
@E.Sommer this is only an example. These are not my actual estimates. I only wanted to grasp the idea of interpreting the coefficients.
Hokkaido21
<econometrics><development-economics>
Interpretation of a 2SLS Coefficient - Civil War Determinants
Hokkaido21
# Interpretation of a 2SLS Coefficient - Civil War Determinants

(Asked by: username_0 on 2021-01-26)

I am a bit confused because of the interpretation of a coefficient in my analysis. I am using 2SLS in two different subsamples with economic growth as endogenous variable. It is instrumented by a variable for natural disasters. The outcome variable is a measure of civil conflict onset. The first stage shows that if natural disasters increase, economic growth decreases. The second stage then provides a positive coefficient for one subsample, while it produces a negative coefficient in the other subsample.
Does a positive coefficient in the second stage mean that a decrease in economic growth (as a consequence of increased natural disasters) decreases the risk of conflict onset?
I am confused because I do not know how to interpret the coefficients since the instrument is negatively correlated to the instrumented variable. If natural disasters would increase economic growth, then the interpretation would be easier since the direction is the same.
Below, you find my LaTeX Output Table. I hope this will help. The coefficients I am interested in are on the one hand -0.0312 and     0.0210 on the other hand.
I know, there is no F test and no control in the analysis. This analysis is not supposed to be sophisticated, it is basically just a means to understand the interpretation of those coefficients.

\begin{table}[t!]\centering
\begin{threeparttable}
\renewcommand{\arraystretch}{1.2} % Default value: 1
\def\sym#1{\ifmmode^{#1}\else\(^{#1}\)\fi}
\begin{tabular}{l*{3}{c}}
\hline\hline
            &\multicolumn{1}{c}{(1)}&\multicolumn{1}{c}{(2)}&\multicolumn{1}{c}{(3)}\\
            &\multicolumn{1}{c}{GDP growth p.c.}&\multicolumn{1}{c}{Onset of Conflict}&\multicolumn{1}{c}{Onset of Conflict}\\
\hline
GDP growth p.c.&                     &    -0.0312\sym{**}&     0.0210\sym{**}        \\
            &                     &     (-2.01)         &      (2.00)         \\
Natural Disasters&      -18.02\sym{***}&     Instrument&              Instrument       \\
            &     (-3.39)         &              &                     \\
\hline
Observations       &        3894         &        3894         &        3894         \\

\end{tabular}
\end{threeparttable}
\end{table}

The code produces following table:
$$
\begin{array}{|l|c|c|c|} 
 \hline
   & \text{(1)} & \text{(2)} & \text{(3)} \\
   & \text{GDP growth p.c.} & \text{Onset of Conflict} & \text{Onset of Conflict} \\ \hline
\text{GDP growth p.c.} & & -0.0312^{**}  & 0.0210^{∗∗} \\ 
 & & (-2.01) & (2.00) \\ 
\text{Natural Disasters} & -18.02^{***} & \text{Instrument} & \text{Instrument}  \\ 
 & (-3.39) & & \\ \hline
 \text{Observations} & 3894 & 3894 & 3894 \\ \hline
\end{array}
$$

**Tags:** econometrics, development-economics

> **Comments:**
> **username_1**: I would personally recommend posting your output to ensure a good answer  
> **username_0**: @username_1 thanks, I adjusted the post  
> **username_2**: How do models (2) and (3) relate to different subsamples if no. of observations is the same for all three models?  
> **username_0**: @E.Sommer this is only an example. These are not my actual estimates. I only wanted to grasp the idea of interpreting the coefficients.  

---

## 1 answers

### Answer by username_3 on 2021-01-27. Score: 7 | Accepted answer

You have a model

$$(1)\ y = x \beta + e,$$

where $x$ is endogenous $\mathbb E[xe] \not =0$. This is the structural model in the sense that the parameter you are interested in is $\beta$ interpreted by its appearance in (1). In your case

* y is civil conflict onset
* x economic growth

suggesting that you are interested in examining how economic growth affects propensity for civil conflict. So positive $\beta$ means economic growth increase propensity for civil conflict.

Using 2SLS you get an IV-estimate of $\beta$ which we can denote $\hat \beta\_{IV}$. When $\hat \beta\_{IV}$ is positive it suggests that $\beta$ is positive and hence economic growth increase propensity for civil conflict.

Interpretation is independent of $Cov(z,x)$ where $z$ is the instrument. Which in this case is

* z is natural disaster.

For instrumental regression instruments must be relevant which in the simple univariate case reduces to $Cov(z,x) \not = 0$, but the sign is irrelevant (you can try to use $w := -z$ as instrument then $Cov(z,x) < 0 \Leftrightarrow Cov(w,x) > 0$ but the 2SLS estimate $\hat \beta\_{IV}$ will be the same).

> **Comments:**
> **username_0**: Thanks a lot! Actually I am not really interested in examining how economic growth affects propensity for civil conflict. Instead I am interested in how natural disasters affect conflict THROUGH economic growth. I thought, due to the assumptions of relevance and exogeneity of an instrument, the coefficient in the table estimates exactly this indirect channel.  
> **username_3**: Fair enough, still thats an entirely different story.  
> **username_0**: Yes! I do not really like this approach but I have to work on it. So assuming the approach would make sense, what would be the interpretation of the 2SLS coefficient?  
> **username_3**: In the 2SLS context the interpretation is that the instrument is relevant. You do not have interpretation independent of theory so you have to make structural causal model. As I said this is a diffrent story and in this forum a new question.  
> **username_3**: @username_0 according to your profile you have 4 questions all have received answers with upvotes but you have accepted none. It is good custom accept when the question has been answered both as a way of showing appreciation of the free service you get but also to help other future users and close questions (this also helps getting Economic site of Beta version).  
> **username_0**: I am very sorry! I am still quite new to this forum and I did not know that I have the possibility to accept an answer. I only upvoted the answers. I really appreciate the free service and of course I appreciate your answer! My intention was not to signal anything else.  
> **username_3**: No worries. Happy to be of help.  

---

