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In Econometrics, the Inverse Function Limits the Dependent Variable's Value

If you believe that the outcome (dependent variable) you’re modeling is likely to approach some value asymptotically (as X approaches zero or infinity), then an inverse function may be the way to go.

Inverse functions can be useful if you’re trying to estimate a Phillips curve (the inverse relationship between inflation and unemployment rates) or a demand function (the inverse relationship between price and quantity demanded), among other economic phenomena where the variables are related inversely.

Here is the mathematical representation of an inverse function econometric model:

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If you estimate this type of regression, you’re likely to see one of the following three outcomes:

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The graph in part (a) shows an inverse function with Y approaching positive infinity as X approaches zero and Y approaching

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as X approaches infinity.

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The graph in part (b) depicts an inverse function with Y approaching positive infinity as X approaches zero and Y approaching some negative value

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as X approaches infinity.

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The graph in part (c) shows an inverse function with Y approaching some positive value

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as X approaches positive infinity and Y approaching negative infinity as X approaches zero.

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