# Solved – When should I use contrast coding

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:

1. Is the interpretation scheme I put forward above correct?
2. Why and when should one use dummy and contrast (effect) coding?
3. And if I use contrast coding, how would I interpret thet resulting coefficients?
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2. 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.