<p>Using OLS on count and dummy variables is appropriate. The estimates are consistent. Using OLS instead of probit/logit is appropriate if the number of observations is sufficiently high. For example <a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3800113/#FN5" rel="noreferrer">Bleakley (QJE, 2007)</a> uses this approach on survey data.</p>
<p>I don't know why you would imagine that logit or probit needs to be used in the first stage either. The first stage is a simple projection of the instrumented variable on the rest. There is no room or necessity for a link function here.</p>

CC BY-SA 4.0
2021-07-29T13:58:50.180Z
2021-07-29T13:58:50.180Z
Grada Gukovic
<p>I assumed you would need to do an IV probit in this scenario, but it was not used in this AER paper - Children and Their Parents' Labor Supply (Angrist and Evans, 1998).</p>
<p>The first stage is estimated using OLS:</p>
<ul>
<li>more than 2 kids(1 or 0) = IV(1 or 0) + error</li>
</ul>
<p>The second stage is:</p>
<ul>
<li>labor force participation (1 or 0) = more than two kids (1 or 0) +
error</li>
</ul>
<p>These are all estimated using regular 2SLS, which involves OLS, and I thought that would not be appropriate?</p>
<p>The second stage uses different dependent variables which are usually continuous, but the first stage is always OLS with a dependent variable dummy. Why is this something that is okay for the first stage of a 2SLS?</p>

<econometrics>
When doing 2SLS, can you use OLS if the dependant variables are dummy variables?
amess
# When doing 2SLS, can you use OLS if the dependant variables are dummy variables?

(Asked by: username_0 on 2021-07-28)

I assumed you would need to do an IV probit in this scenario, but it was not used in this AER paper - Children and Their Parents' Labor Supply (Angrist and Evans, 1998).

The first stage is estimated using OLS:

* more than 2 kids(1 or 0) = IV(1 or 0) + error

The second stage is:

* labor force participation (1 or 0) = more than two kids (1 or 0) +
  error

These are all estimated using regular 2SLS, which involves OLS, and I thought that would not be appropriate?

The second stage uses different dependent variables which are usually continuous, but the first stage is always OLS with a dependent variable dummy. Why is this something that is okay for the first stage of a 2SLS?

**Tags:** econometrics

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## 1 answers

### Answer by username_1 on 2021-07-29. Score: 5

Using OLS on count and dummy variables is appropriate. The estimates are consistent. Using OLS instead of probit/logit is appropriate if the number of observations is sufficiently high. For example [Bleakley (QJE, 2007)](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3800113/#FN5) uses this approach on survey data.

I don't know why you would imagine that logit or probit needs to be used in the first stage either. The first stage is a simple projection of the instrumented variable on the rest. There is no room or necessity for a link function here.


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