I have a – so I guess – a simple question: I am using Stata 13 and I am running a Tobit model to understand differences in firm performance. Among others, I am controling for firm types $T_i$- i.e. Single-Owner-Firms $SOF$vs. Multiple-Owner-Firms $MOF$.

So far I dummied $T_i$ so that $MOF=0$ and $SOF=1$. Here is why:

Given a simple relationship such as

$y_i= a + beta_1x_i + beta_2T_i +beta_3x_iT_i$

We can show that

$y_i= (a + beta_1x_i) + T_i(beta_2+beta_3x_i)$

The lower order coefficients $beta_1$ shows the simple effect of $x_i$ on $y_i$ for $T_i=0$ since $y_i= (a + beta_1x_i)$ for $T_i=0$. Similar, $beta_2$ shows the simple effect of $T_i$ on $y_i$ since $y_i= a + T_ibeta_2$ for $x_i=0$.

Finally, and as far as I understand it, $beta_3$ depicts how the slopes differ the firm types $T_i=0$ and $T_i=1$

However, I now got the advice to contrast code $T_i$ so that $MOF=-1$ and $SOF=1$.

I have three questions:

- Is the interpretation scheme I put forward above correct?
- Why and when should one use dummy and contrast (effect) coding?
- And if I use contrast coding, how would I interpret thet resulting coefficients?

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#### Best Answer

- Yes, with the caveat that Tobit models have multiple marginal effects and it is not clear which ones you care about here.
- Contrast coding is typically used when you have a categorical variable with more than two levels (something like education: dropout, high school, college, and graduate) and you are interested in comparing the marginal effects to each other, not just to the omitted base level. However, with Stata's
`margins, contrast`

command, this is less useful than it once was. Since you only have two levels, contrast coding does not seem very useful here.

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