<p>The dependent variable is <em>level of concessions</em>, which takes on one of three values:</p>
<p><span class="math-container">$y_i \in \{\text{None, Partial, Full}\}$</span></p>
<p>If you know the ordered probit model, then you should see that a dependent variable with three levels implies the inclusion of two intercepts. For more information on ordered probit see for example <a href="https://www.eco.uc3m.es/%7Ericmora/miccua/materials/S13T31_English_handout.pdf" rel="nofollow noreferrer">this slidedeck</a>, especially slide 10.</p>
<p>Very short explanation by me:</p>
<p><strong>Ordered probit with three outcomes</strong></p>
<p>There is a latent model with observed explanatory variables and unobserved dependent variable <span class="math-container">$y_i^*$</span>, specified as follows</p>
<p><span class="math-container">$y_i^*=x_i'\beta+u_i \qquad u_i \sim N(0,1)$</span></p>
<p>The way in which <span class="math-container">$y_i^*$</span> translates into a value for the observed dependent variable <span class="math-container">$y_i$</span> is given by:</p>
<p><span class="math-container">$$y_i=a \times \mathbf{1}(y_i^*&lt;\alpha_1) + b \times \mathbf{1}(\alpha_1 &lt;y_i^*&lt;\alpha_2)+ c \times \mathbf{1}(\alpha_2 &lt;y_i^*)$$</span></p>
<p>where <span class="math-container">$\mathbf{1}(\cdot)$</span> is an indicator function (it equals 1 iff the condition in the parentheses is met). <span class="math-container">$a$</span>, <span class="math-container">$b$</span>, <span class="math-container">$c$</span> are the three different outcomes.</p>
<p>It can be solved with maximum likelihood for the parameters <span class="math-container">$(\beta, \alpha_1, \alpha_2)$</span></p>
<p><span class="math-container">$\alpha_1$</span> and <span class="math-container">$\alpha_2$</span> are the two intercepts.</p>

CC BY-SA 4.0
2022-11-10T08:29:45.483Z
2022-11-10T08:29:45.483Z
user18214
<p>I am currently reading a research paper(Developing Countries and General Agreement on Tariffs and Trade/World Trade Organization Dispute Settlement by Marc L. BUSCH and Eric REINHARDT) and in the part where they come to the regression where they use an ordered probit model for level of concession reached, in the descriptive table there is data for 2 coefficients, labeled &quot;intercept 1&quot; and &quot;intercept 2&quot;. I cannot understand why there 2? Only reason i can think for intercepts being different is the presence of a dummy variable, but the dummy variables are separately specified? Or is there some conceptual thing I'm missing? Could anyone help?</p>
<p>The paper:</p>
<p>Marc L. Busch, Eric Reinhardt, 'Developing Countries and General Agreement on Tariffs and Trade/World Trade Organization Dispute Settlement', (2003), 37, Journal of World Trade, Issue 4, pp. 719-735</p>

<regression><wto><model>
2 intercepts in a probit model about WTO/GATT concessions?
viktor nikiforov
# 2 intercepts in a probit model about WTO/GATT concessions?

(Asked by: username_0 on 2022-11-09)

I am currently reading a research paper(Developing Countries and General Agreement on Tariffs and Trade/World Trade Organization Dispute Settlement by Marc L. BUSCH and Eric REINHARDT) and in the part where they come to the regression where they use an ordered probit model for level of concession reached, in the descriptive table there is data for 2 coefficients, labeled "intercept 1" and "intercept 2". I cannot understand why there 2? Only reason i can think for intercepts being different is the presence of a dummy variable, but the dummy variables are separately specified? Or is there some conceptual thing I'm missing? Could anyone help?

The paper:

Marc L. Busch, Eric Reinhardt, 'Developing Countries and General Agreement on Tariffs and Trade/World Trade Organization Dispute Settlement', (2003), 37, Journal of World Trade, Issue 4, pp. 719-735

**Tags:** regression, wto, model

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## 1 answers

### Answer by username_1 on 2022-11-10. Score: 1

The dependent variable is *level of concessions*, which takes on one of three values:

$y\_i \in \{\text{None, Partial, Full}\}$

If you know the ordered probit model, then you should see that a dependent variable with three levels implies the inclusion of two intercepts. For more information on ordered probit see for example [this slidedeck](https://www.eco.uc3m.es/%7Ericmora/miccua/materials/S13T31_English_handout.pdf), especially slide 10.

Very short explanation by me:

**Ordered probit with three outcomes**

There is a latent model with observed explanatory variables and unobserved dependent variable $y\_i^\*$, specified as follows

$y\_i^\*=x\_i'\beta+u\_i \qquad u\_i \sim N(0,1)$

The way in which $y\_i^\*$ translates into a value for the observed dependent variable $y\_i$ is given by:

$$y\_i=a \times \mathbf{1}(y\_i^\*<\alpha\_1) + b \times \mathbf{1}(\alpha\_1

where $\mathbf{1}(\cdot)$ is an indicator function (it equals 1 iff the condition in the parentheses is met). $a$, $b$, $c$ are the three different outcomes.

It can be solved with maximum likelihood for the parameters $(\beta, \alpha\_1, \alpha\_2)$

$\alpha\_1$ and $\alpha\_2$ are the two intercepts.


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