<blockquote>
<p>But I am wondering when we should use &quot;internal consistency&quot; and why the author need to perform the robustness test for it afterwards?</p>
</blockquote>
<p>You do not <em>use</em> internal consistency that is something that your model either <em>has</em> or <em>does not have</em>. Internal consistency is property not a method.</p>
<p>For example:</p>
<p><span class="math-container">$$a+b=1 \tag{1}$$</span></p>
<p><span class="math-container">$$5a+5b=15 \tag{2}$$</span></p>
<p>Is an inconsistent system of equations. The equation <span class="math-container">$(1)$</span> tells us that <span class="math-container">$a+b=1$</span>, but the equation <span class="math-container">$(2)$</span> tells different story:</p>
<p><span class="math-container">$$ 5a+5b=15 \implies  5(a+b) =15 \implies a+b=3 \tag{3} $$</span></p>
<p>Clearly, <span class="math-container">$a+b$</span> cannot be at the same time both 1 and 3, so here we have some internally inconsistent system. You can see it further by substituting 3 into 1. You will get:</p>
<p><span class="math-container">$$a+1-a=3 \implies 1 = 3$$</span></p>
<p>which is obvious contradiction.</p>
<p>People always strive to have internally consistent models, if you have internally inconsistent model that is tantamount of making a modeling mistake somewhere.</p>
<blockquote>
<p>why the author need to perform the robustness test for it afterwards?</p>
</blockquote>
<p>They do not do robustness test to check for internal consistency, they use robustness test, because <em>in order to make their model internally consistent</em>, they were forced to use real interest rate, but they were also interested in knowing if the effect holds for nominal interest rate as well even though that was not their preferred specification.</p>

CC BY-SA 4.0
2021-08-24T12:16:52.537Z
2021-08-24T22:37:46.430Z
2021-08-24T22:37:46.430Z
1muflon1
<p>From a paper of <a href="https://academic.oup.com/rfs/article/34/4/1834/5873590" rel="nofollow noreferrer">Gao (2021)</a>, I saw a paparagraph</p>
<blockquote>
<p>We deviate from this traditional specification in three ways: we
examine only money held by corporations, we include real GDP growth in
the regression to control for economic fluctuations over the business
cycle, and we use real instead of nominal interest rates. This last
choice is for <strong>internal consistency</strong> with the theoretical framework that
follows</p>
</blockquote>
<p>I understand the internal consistency from this description</p>
<blockquote>
<p>For example, if a respondent expressed agreement with the statements
&quot;I like to ride bicycles&quot; and &quot;I've enjoyed riding bicycles in the
past&quot;, and disagreement with the statement &quot;I hate bicycles&quot;, this
would be indicative of good internal consistency of the test.</p>
</blockquote>
<p>But I am wondering when we should use &quot;internal consistency&quot; and why the author need to perform the robustness test for it afterwards?</p>

<soft-question>
When should we use "internal consistency" test?
Phil Nguyen
# When should we use "internal consistency" test?

(Asked by: username_0 on 2021-08-24)

From a paper of [Gao (2021)](https://academic.oup.com/rfs/article/34/4/1834/5873590), I saw a paparagraph

> We deviate from this traditional specification in three ways: we
> examine only money held by corporations, we include real GDP growth in
> the regression to control for economic fluctuations over the business
> cycle, and we use real instead of nominal interest rates. This last
> choice is for **internal consistency** with the theoretical framework that
> follows

I understand the internal consistency from this description

> For example, if a respondent expressed agreement with the statements
> "I like to ride bicycles" and "I've enjoyed riding bicycles in the
> past", and disagreement with the statement "I hate bicycles", this
> would be indicative of good internal consistency of the test.

But I am wondering when we should use "internal consistency" and why the author need to perform the robustness test for it afterwards?

**Tags:** soft-question

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## 1 answers

### Answer by username_1 on 2021-08-24. Score: 2 | Accepted answer

> But I am wondering when we should use "internal consistency" and why the author need to perform the robustness test for it afterwards?

You do not *use* internal consistency that is something that your model either *has* or *does not have*. Internal consistency is property not a method.

For example:

$$a+b=1 \tag{1}$$

$$5a+5b=15 \tag{2}$$

Is an inconsistent system of equations. The equation $(1)$ tells us that $a+b=1$, but the equation $(2)$ tells different story:

$$ 5a+5b=15 \implies 5(a+b) =15 \implies a+b=3 \tag{3} $$

Clearly, $a+b$ cannot be at the same time both 1 and 3, so here we have some internally inconsistent system. You can see it further by substituting 3 into 1. You will get:

$$a+1-a=3 \implies 1 = 3$$

which is obvious contradiction.

People always strive to have internally consistent models, if you have internally inconsistent model that is tantamount of making a modeling mistake somewhere.

> why the author need to perform the robustness test for it afterwards?

They do not do robustness test to check for internal consistency, they use robustness test, because *in order to make their model internally consistent*, they were forced to use real interest rate, but they were also interested in knowing if the effect holds for nominal interest rate as well even though that was not their preferred specification.


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