I have a dependent variable, credit rating, and it is a limited dependent variable. Independent variables are profitability, firm size, stock return, etc.
I was advised to use Stata and run regression with fixed effects and then predict yhat in order to obtain a target rating that a certain firm wants to target in this way:
xtreg dependent independent, fe with regression equation below:
Credit rating = $\alpha + \beta_1$R&D $+\beta_2$Size $+\beta_3$Selling Expense $+\beta_4$Market to Book $+\beta_5$Profitability $+\beta_6$Operating Risk $+\beta_7$Tangibility + error term
Then run predict yhat in order to get a proxy for the credit rating a certain firm wants to target.
The dependent variable credit rating is limited, so is the panel regression for the model: xtreg, fe oK, or should an ordered probit model be used instead? (In other studies with credit ratings they use ordered probit.)
And if a probit model should be used, what command is the corresponding command predict yhat (in the case of xtreg fe) for the ordered probit model? Or in other words, how do I get the rating that a firm wants to target (from the panel regression with xtreg, fe and then predict yhat for the fitted values) from the ordered probit model?
Best Answer
If linear fixed effects or order probit are the only two available options for you then the linear fixed effects model is the better choice. Unless you have very strong reasons to believe that there is no unobserved heterogeneity among your firms it is important to account for these unobserved fixed effects as otherwise you are unlikely to obtain consistent estimates. Generally there is a lot of unobserved time-invariant heterogeneity among firms so rejecting fixed effects is unlikely.
However, I do believe that there are other options available to you like the fixed effects ordered logit estimator by Baetschmann et al. (2013). Another paper which might be of interest to you is Riedl and Geishecker (2012). They discuss conditions under which it is better to choose
and which of those alternatives have good properties in small and large samples.
In terms of predictions in Stata you can still use the
predictcommand afteroprobit(see the Stata manual on oprobit postestimation).