I am searching for a suitable regression method, when the dependent variable is a fraction or proportion. I am using an unbalanced panel data set.
Analyzing panel data set is based on assumptions. It's difficult or may inappropriate to decide an estimation technique without taking proper steps. Therefore, you may start from basic panel estimation distinguishing between OLS, FE and RE.
Based on F-test, you may decide which model between OLS and FE is better for you data set.
Based on LM test, you can see which model between OLS and RE is better for you data set.
Based on Hausman test, you may decide which model between FE and RE is suitable for your data set.
Moreover, if you face endogeneity issue, heteroscedasticity or serial correlation there is more advance method to solve these issues. However, to advice on that, I must know more details about you variables, T and N.
Actually, your data will choose the appropriate model for it based on its nature and appropriateness.
Hope it helps.
Do the following reading: Hahn and Newey (2004), Arellano and Hahn (2006), and Hahn and Kuersteiner (2011)
Probably I would use approach used in the last one - here fixed effect parameters and the lagged dependent variables are nonlinear
Panel data is very complicated and problematic. To keep your self in the right path, I think it is better to bind your self with the theory regarding whether the relationship between the variables are linear or nonlinear, dynamic or static in nature. Another thing you may want to keep in mind, is the structure of your data, whether you have long panel (time-series panel) or short panel (micro panel). There are various types of nonlinear models such as regime switching, and threshold models. These models are quite interesting but they could take time to be fully understood and are subject to some limitations. Therefore, I think you should restrict your self theory and then look for the method that accomplish your objective(s).
What is the size of your time period for each group and the number of groups that you have. If the number of groups is large enough, like more than 50 and your time for each group is less than 5, then you can use first difference GMM or system GMM. If your time period is long like more than 20 for each observation and your group is less than 50, then u can use macro panel data.
Thank you very much everyone for taking time to answer my question. I found that fractional probit model can be used to analyze this kind of data.
Thank you Divyakant for the reference and suggestion. I am following their 2008 paper as well.
Best Regards,
Pubuduni
Yes the write answer is
fractional probit model can be used to analyze this kind of data.