<p>I recently learned that EU characterized by independence and weak ordering is identifiable, but a utility function like: <span class="math-container">$U(x)=v_1(x)v_2(x)$</span> is not identifiable.</p>
<p>Does it mean that &quot;cardinal uniqueness = identifiability&quot;? Or cardinal uniqueness implies identifiability but not the other way?</p>
<p>I found the precise definition of &quot;identifiability&quot; parametric function. But for non-parameteric function, what is the precise definition of identifiability?</p>
<p>For example, does the simplest utility function <span class="math-container">$u(x)$</span> characterized by weak order and continuity identifiable by its own? (a.k.a does ordinal uniqueness implies identifiability?)</p>

CC BY-SA 4.0
2020-12-01T16:09:08.943Z
So what is the definition of identifiability for parametric functions and in what sense is EU parametric?
Michael Greinecker
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2020-12-01T16:34:31.947Z
@MichaelGreinecker EU is non-parametric in this case.
High GPA
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2020-12-01T17:15:33.533Z
That's not what I asked.
Michael Greinecker
CC BY-SA 4.0
2020-12-01T17:17:52.657Z
@MichaelGreinecker For parametric functions, identifiable means that any two different parameter vectors cannot give the same value.
High GPA
CC BY-SA 4.0
2020-12-01T17:30:12.787Z
Non-parametric does not mean there are no parameters, it usually means the parameter space is infinite-dimensional (which would also be the case with EU with infinitely many outcomes). So the same definition works in a non-parametric setting.
Michael Greinecker
<microeconomics><decision-theory><theory><identification>
Identifiability of Non-Parametric Utility Function?
High GPA
# Identifiability of Non-Parametric Utility Function?

(Asked by: username_0 on 2020-12-01)

I recently learned that EU characterized by independence and weak ordering is identifiable, but a utility function like: $U(x)=v\_1(x)v\_2(x)$ is not identifiable.

Does it mean that "cardinal uniqueness = identifiability"? Or cardinal uniqueness implies identifiability but not the other way?

I found the precise definition of "identifiability" parametric function. But for non-parameteric function, what is the precise definition of identifiability?

For example, does the simplest utility function $u(x)$ characterized by weak order and continuity identifiable by its own? (a.k.a does ordinal uniqueness implies identifiability?)

**Tags:** microeconomics, decision-theory, theory, identification
> **Comments:**
> **username_1**: So what is the definition of identifiability for parametric functions and in what sense is EU parametric?  
> **username_0**: @MichaelGreinecker EU is non-parametric in this case.  
> **username_1**: That's not what I asked.  
> **username_0**: @MichaelGreinecker For parametric functions, identifiable means that any two different parameter vectors cannot give the same value.  
> **username_1**: Non-parametric does not mean there are no parameters, it usually means the parameter space is infinite-dimensional (which would also be the case with EU with infinitely many outcomes). So the same definition works in a non-parametric setting.  

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## 0 answers

