<p>I believe the correct answer is (C). Both coefficients are identifiable. The cross-sectional variation identifies the alternative-specific coefficients.</p>
<p>It is probably easiest to see why if you assume <span class="math-container">$Z_n$</span> only takes two values and ignores the other variables. Then you observe two groups with different proportions of individuals choosing alternatives 1,2 and 3 respectively which is sufficient to pin down <span class="math-container">$\delta_1,\delta_2$</span> and <span class="math-container">$\delta_3$</span>.</p>
<p>The same argument goes for <span class="math-container">$\beta_j$</span> here you just also have variation across alternatives.</p>
<p>However, something that would be not identifiable is <span class="math-container">$\beta_jC_j$</span>.</p>
<p>So the identifying variation is the cross-section variation.</p>

CC BY-SA 4.0
2024-05-17T12:45:56.267Z
I find this tricky to believe, as technically (C) being true would imply (B) cannot be false. In our course, we emphasised that only differences in utilities for a given decision maker matter, so for decision maker attributes we cannot identify the deltas in levels – only their difference with respect to a control group (e.g. set delta_1 = 0).
Martin
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2024-05-17T11:31:40.373Z
2024-05-17T11:31:40.373Z
Jesper Hybel
<p><a href="https://i.sstatic.net/xVTybcWi.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/xVTybcWi.png" alt="Multiple choice question" /></a></p>
<p>In this random utility model, which of the five statements is true? I've been thinking about this question ever since the exam... I said (B).</p>

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2024-05-19T20:09:22.587Z
Could you please add a reference? Thanks a lot!
Beerus
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2024-05-19T23:36:07.100Z
MPhil Economics – Econometrics exam at Oxbridge.
Martin
<econometrics><applied-econometrics><theory><model><logit>
Random Utility Model Multiple Choice Question. Which one is correct?
Martin
# Random Utility Model Multiple Choice Question. Which one is correct?

(Asked by: username_0 on 2024-05-16)

[![Multiple choice question](https://i.sstatic.net/xVTybcWi.png)](https://i.sstatic.net/xVTybcWi.png)

In this random utility model, which of the five statements is true? I've been thinking about this question ever since the exam... I said (B).

**Tags:** econometrics, applied-econometrics, theory, model, logit
> **Comments:**
> **username_1**: Could you please add a reference? Thanks a lot!  
> **username_0**: MPhil Economics – Econometrics exam at Oxbridge.  

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## 1 answers

### Answer by username_2 on 2024-05-17. Score: 1

I believe the correct answer is (C). Both coefficients are identifiable. The cross-sectional variation identifies the alternative-specific coefficients.

It is probably easiest to see why if you assume $Z\_n$ only takes two values and ignores the other variables. Then you observe two groups with different proportions of individuals choosing alternatives 1,2 and 3 respectively which is sufficient to pin down $\delta\_1,\delta\_2$ and $\delta\_3$.

The same argument goes for $\beta\_j$ here you just also have variation across alternatives.

However, something that would be not identifiable is $\beta\_jC\_j$.

So the identifying variation is the cross-section variation.

> **Comments:**
> **username_0**: I find this tricky to believe, as technically (C) being true would imply (B) cannot be false. In our course, we emphasised that only differences in utilities for a given decision maker matter, so for decision maker attributes we cannot identify the deltas in levels – only their difference with respect to a control group (e.g. set delta_1 = 0).  

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