<p>A <a href="https://en.wikipedia.org/wiki/Leontief_production_function" rel="nofollow noreferrer">Leontief production</a> does imply perfect multicollinearity between the inputs, since there is no substitutability between them. Thus, if a firm's production technology features non-substitutability between inputs, one would observe the firm choosing inputs in fixed proportions. </p>

<p>However, (perfect) multicollinearity does not necessarily imply non-substitutability. For instance, the Cobb-Douglas production technology of the form $y=x_1^{0.5}x_2^{0.5}$ is also consistent with a firm choosing inputs in fixed proportions. So the answer to your question is no (from a theoretical perspective). </p>

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2017-11-05T02:07:53.507Z
edited my question. Thanks for the definition
EconJohn
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2017-11-05T02:10:45.937Z
But in a case of fundamentally different $x_1$ and $x_2$ where they are not  a linear combination of one another is this contradiction still true
EconJohn
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2017-11-05T02:04:06.470Z
2017-11-08T22:16:04.037Z
2017-11-08T22:16:04.037Z
Herr K.
<p>I've been thinking about how to answer this question <a href="https://economics.stackexchange.com/questions/19005/how-to-econometrically-identify-perfect-complements-in-production">How to econometrically identify perfect complements in production?</a> and may think that multicollinearity has something to do with identifying such a process.</p>

<p>If I have a regression such that:</p>

<p>$$y=\beta_0+\beta_1x_1+\beta_2x_2+\mu$$</p>

<p>where $x_1$ and $x_2$ are correlated with each other. </p>

<p>does that imply that some function of the nature $\min\{x_1,x_2\}$ is present in the determination of $y$? </p>

<microeconomics><econometrics>
Does multicolinearity of variables imply complementary inputs?
EconJohn
# Does multicolinearity of variables imply complementary inputs?

(Asked by: username_0 on 2017-11-05)

I've been thinking about how to answer this question [How to econometrically identify perfect complements in production?](https://economics.stackexchange.com/questions/19005/how-to-econometrically-identify-perfect-complements-in-production) and may think that multicollinearity has something to do with identifying such a process.

If I have a regression such that:

$$y=\beta\_0+\beta\_1x\_1+\beta\_2x\_2+\mu$$

where $x\_1$ and $x\_2$ are correlated with each other.

does that imply that some function of the nature $\min\{x\_1,x\_2\}$ is present in the determination of $y$?

**Tags:** microeconomics, econometrics

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## 1 answers

### Answer by username_1 on 2017-11-05. Score: 1 | Accepted answer

A [Leontief production](https://en.wikipedia.org/wiki/Leontief_production_function) does imply perfect multicollinearity between the inputs, since there is no substitutability between them. Thus, if a firm's production technology features non-substitutability between inputs, one would observe the firm choosing inputs in fixed proportions.

However, (perfect) multicollinearity does not necessarily imply non-substitutability. For instance, the Cobb-Douglas production technology of the form $y=x\_1^{0.5}x\_2^{0.5}$ is also consistent with a firm choosing inputs in fixed proportions. So the answer to your question is no (from a theoretical perspective).

> **Comments:**
> **username_0**: edited my question. Thanks for the definition  
> **username_0**: But in a case of fundamentally different $x_1$ and $x_2$ where they are not  a linear combination of one another is this contradiction still true  

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