<p>Let's take a hypothetical example of the SVAR with lag 1 (simplified specification for understanding):</p>
<p><span class="math-container">$ Inc_t = \alpha_1 + Inc_{t-1} + Con_{t-1} + Inv_{t-1} + e_1 $</span></p>
<p><span class="math-container">$ Inv_t = \alpha_2 + Inc_t + Inc_{t-1} + Con_{t-1} + Inv_{t-1} + e_2 $</span></p>
<p><span class="math-container">$ Con_t = \alpha_3 + Inc_t + Inv_t + Inc_{t-1} + Con_{t-1} + Inv_{t-1} + e_3 $</span></p>
<p>This SVAR represents an ordering of Income, Investment and Consumption.</p>
<p>We can observe that because Current period Income is only affected by the lagged terms in the first equation. But, income is contemporaneously affecting both investment and consumption. This implies that the current period investment and consumption are affected by current period Income along with lags.</p>
<p>Similarly, investment is contemporaneously affecting only consumption, that is, current consumption depends on current investment along with the lags.</p>
<p>This is also referred to as Cholesky Decomposition. The different choices of ordering will completely change the model. You could order it as Investment, income and consumption and so on, which will change the specification of the contemporaneous terms (variables which affect the others in the same period).</p>
<p>Hence, it is up to the researcher to decide the correct ordering based on some economic theory or other considerations. The decision has to be made on which variables may have a delayed effect on others and which can affect the others instantly in the same period.</p>
<p>The relative endogeneity/exogeneity is important here. Relatively less endogeneity would mean that the variable can affect the others contemporaneously (in the same time period). In this hypothetical example, income is the most exogenous and consumption is the most endogenous.</p>

CC BY-SA 4.0
2022-07-26T15:17:20.397Z
Thank you, I understand it better now :)
sowmyau
CC BY-SA 4.0
2022-07-26T08:03:42.227Z
2022-07-26T08:03:42.227Z
Spur Economics
<p>The ordering means placing the variables in the (decreasing) order of exogeneity. For example, if <span class="math-container">$y_1,y_2$</span> and <span class="math-container">$y_3$</span> are variables in the system and economic theory says <span class="math-container">$y_3$</span> is relatively more exogeneous than <span class="math-container">$y_1$</span> and <span class="math-container">$y_2$</span> and <span class="math-container">$y_1$</span>  is more exogeneous than <span class="math-container">$y_2$</span> but less exogenous than <span class="math-container">$y_3$</span>, then they should be ordered <span class="math-container">$y_3,y_1,y_2$</span>. It is also important to understand that while all variables are endogenous some are more/less endogenous, that is what I mean when I say relative exogeneity.</p>
<p>Exactly as the source says, if you mess up the order your results will be biased. To figure out the correct order you should survey theoretical literature on the issue you want to examine, or see past empirical papers that also used SVAR to examine same/similar topic and see their ordering (and justification for it).</p>

CC BY-SA 4.0
2022-07-25T14:10:27.347Z
2022-07-25T16:51:21.500Z
2022-07-25T16:51:21.500Z
1muflon1
<p>I am currently working on my dissertation where I try to analyze how macroeconomic shocks affect firms financing decisions. The research paper that I am currently reading says:<br />
&quot;Overall, this suggests that the results using the recursive scheme can be highly sensitive to the ordering of the variables—that is, the impulse responses can be subject
to large biases if the ordering is incorrect&quot;
What does this ordering of variables mean? I am confused. Thank you in advance!</p>

CC BY-SA 4.0
2022-07-25T14:03:49.027Z
Please give reference to the paper you got the quote from.
Herr K.
<svar>
What is ordering of the variables in a SVAR model
sowmyau
# What is ordering of the variables in a SVAR model

(Asked by: username_0 on 2022-07-25)

I am currently working on my dissertation where I try to analyze how macroeconomic shocks affect firms financing decisions. The research paper that I am currently reading says:  
"Overall, this suggests that the results using the recursive scheme can be highly sensitive to the ordering of the variables—that is, the impulse responses can be subject
to large biases if the ordering is incorrect"
What does this ordering of variables mean? I am confused. Thank you in advance!

**Tags:** svar

> **Comments:**
> **username_1**: Please give reference to the paper you got the quote from.  

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## 2 answers

### Answer by username_2 on 2022-07-26. Score: 4

Let's take a hypothetical example of the SVAR with lag 1 (simplified specification for understanding):

$ Inc\_t = \alpha\_1 + Inc\_{t-1} + Con\_{t-1} + Inv\_{t-1} + e\_1 $

$ Inv\_t = \alpha\_2 + Inc\_t + Inc\_{t-1} + Con\_{t-1} + Inv\_{t-1} + e\_2 $

$ Con\_t = \alpha\_3 + Inc\_t + Inv\_t + Inc\_{t-1} + Con\_{t-1} + Inv\_{t-1} + e\_3 $

This SVAR represents an ordering of Income, Investment and Consumption.

We can observe that because Current period Income is only affected by the lagged terms in the first equation. But, income is contemporaneously affecting both investment and consumption. This implies that the current period investment and consumption are affected by current period Income along with lags.

Similarly, investment is contemporaneously affecting only consumption, that is, current consumption depends on current investment along with the lags.

This is also referred to as Cholesky Decomposition. The different choices of ordering will completely change the model. You could order it as Investment, income and consumption and so on, which will change the specification of the contemporaneous terms (variables which affect the others in the same period).

Hence, it is up to the researcher to decide the correct ordering based on some economic theory or other considerations. The decision has to be made on which variables may have a delayed effect on others and which can affect the others instantly in the same period.

The relative endogeneity/exogeneity is important here. Relatively less endogeneity would mean that the variable can affect the others contemporaneously (in the same time period). In this hypothetical example, income is the most exogenous and consumption is the most endogenous.

> **Comments:**
> **username_0**: Thank you, I understand it better now :)  

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### Answer by username_3 on 2022-07-25. Score: 1

The ordering means placing the variables in the (decreasing) order of exogeneity. For example, if $y\_1,y\_2$ and $y\_3$ are variables in the system and economic theory says $y\_3$ is relatively more exogeneous than $y\_1$ and $y\_2$ and $y\_1$ is more exogeneous than $y\_2$ but less exogenous than $y\_3$, then they should be ordered $y\_3,y\_1,y\_2$. It is also important to understand that while all variables are endogenous some are more/less endogenous, that is what I mean when I say relative exogeneity.

Exactly as the source says, if you mess up the order your results will be biased. To figure out the correct order you should survey theoretical literature on the issue you want to examine, or see past empirical papers that also used SVAR to examine same/similar topic and see their ordering (and justification for it).


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