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I've been thinking about how to answer this question 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 $y$?

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A Leontief production 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).

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  • $\begingroup$ edited my question. Thanks for the definition $\endgroup$ – EconJohn Nov 5 '17 at 2:07
  • $\begingroup$ 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 $\endgroup$ – EconJohn Nov 5 '17 at 2:10

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