Hi Sagnik !

Thank you for the question, Well, let's start from the begin;

Because the dependent variable (y) is an index that lies within the range [0, 1] (are necessarily bounded between zero and one), standard linear models may not provide an accurate picture of the effects of the independent variables on the dependent variable ( mainly because the dependent variable are eventually predicted to be greater than one). Papke and Wooldridge (2008) method, based on "glm" / 'xtgee" under Stata, is applicable when dealing with balanced panels.

The methods of the correlated random effects model for unbalanced data developed by Wooldridge 2010 (attacched) are extensions of the Chamberlain-Mundlak approach for balanced panels.

In a linear panel data setting, it can be desirable to estimate the magnitude of the Fixed Effects, as they provide measures of the unobserved components.

Chamberlain's approach to unobserved effects models is a way of estimating the linear unobserved effects, under Fixed Effect (rather than Random Effects) assumptions, in the following unobserved effects model

yit = xitb + ci + uit (1)

where ci is the unobserved effect and xit contains only time-varying explanatory variables.

Rather than differencing out the unobserved effect ci, Chamberlain proposed to replace it with the linear projection of it onto the explanatory variables in all time periods. Specifically, this leads to the following equation

ci = d + xi1 λ1 + xi2 λ2 + ... + xiT λT + ei (2)

where the conditional distribution of ci given xit is unspecified, as is standard in Fixed Effects models. Combining equations (1) and (2) then gives rise to the following model.[2][3]

yit = d + xi1 λ1 + ... + xit (b+λt ) + ... + xiT λTb + ei + uit (3)

When it's the case of a Modeling Approach for Nonlinear Models, we sould be interested in the conditional distribution D(yit|xit,ci), Average partial effects are generally identified without restricting conditional dependence.

You Can then use a host of quasi-log likelihoods on the selected sample, including the Bernoulli for fractional responses, the gamma for nonnegative (continuous) responses, and the Poisson for non negative (count) responses.

Hope this Help

Please don't hesitate to contact me if you need more technical details, like Stata Codes

Hi Sagnik !

Thank you for the question, Well, let's start from the begin;

Because the dependent variable (y) is an index that lies within the range [0, 1] (are necessarily bounded between zero and one), standard linear models may not provide an accurate picture of the effects of the independent variables on the dependent variable ( mainly because the dependent variable are eventually predicted to be greater than one). Papke and Wooldridge (2008) method, based on "glm" / 'xtgee" under Stata, is applicable when dealing with balanced panels.

The methods of the correlated random effects model for unbalanced data developed by Wooldridge 2010 (attacched) are extensions of the Chamberlain-Mundlak approach for balanced panels.

In a linear panel data setting, it can be desirable to estimate the magnitude of the Fixed Effects, as they provide measures of the unobserved components.

Chamberlain's approach to unobserved effects models is a way of estimating the linear unobserved effects, under Fixed Effect (rather than Random Effects) assumptions, in the following unobserved effects model

yit = xitb + ci + uit (1)

where ci is the unobserved effect and xit contains only time-varying explanatory variables.

Rather than differencing out the unobserved effect ci, Chamberlain proposed to replace it with the linear projection of it onto the explanatory variables in all time periods. Specifically, this leads to the following equation

ci = d + xi1 λ1 + xi2 λ2 + ... + xiT λT + ei (2)

where the conditional distribution of ci given xit is unspecified, as is standard in Fixed Effects models. Combining equations (1) and (2) then gives rise to the following model.[2][3]

yit = d + xi1 λ1 + ... + xit (b+λt ) + ... + xiT λTb + ei + uit (3)

When it's the case of a Modeling Approach for Nonlinear Models, we sould be interested in the conditional distribution D(yit|xit,ci), Average partial effects are generally identified without restricting conditional dependence.

You Can then use a host of quasi-log likelihoods on the selected sample, including the Bernoulli for fractional responses, the gamma for nonnegative (continuous) responses, and the Poisson for non negative (count) responses.

Hope this Help

Please don't hesitate to contact me if you need more technical details, like Stata Codes

Dear Sagnik Bagchi ,

Look the link, maybe useful.

https://www.stata.com/statalist/archive/2010-11/msg00846.html

https://www.youtube.com/watch?v=mJzrWocdWGY

Regards, Shafagat

Thank you Aymen, for your reply. Thank you for sharing the paper. I will be contacting you in due time.

Let me understand first, what you have mentioned.

Thanks,

Sagnik

Thanks, Shafagat for your answer. I have had looked into it.

Sagnik

Aymen Ammari : Please provide stata code for fractional response model for unbalanced panel data set.

your mail please

[email protected]

Aymen Ammari: I am using unbalanced panel dataset with t=18 and i=118. My dependent variable is bounded between zero and one. I have read paper " correlated Random effects Models with unbalanced Panels". But I don't know how to technical apply it in Stata. Should I include time dummies for 18 years, as suggested by this paper.

Panika Jain You may also look into this paper by Ramalho et al. (2016), "Exponential Regression of Fractional-Response Fixed-Effects Models with an Application to Firm Capital Structure"

Sagnik Bagchi Yes, I am following this paper only. I have run exponential fractional regression model on my dataset. But, Should I include 18 time dummies in my model?. My dependent variable varies little over time in each cross-sectional unit. If I am including both time and cross-sectional effect in G( ) function, command provided by them is not running. I got result for logit(QMLp, QMLpfe); Probit(QMLpfe, QMLcre); Cloglog(QMLp, QMLpfe) , Loglog(QMLpfe). But without timed matrix used by them.

In other cases I got this result:

ALGORITHM DID NOT CONVERGE OR STOPPED AT A BOUNDARY VALUE There were 20 warnings (use warnings() to see them).

I would like to know that after estimating these models, how we can select the appropriate one. As my pooled and fixed effect model gives different sign of the coefficient of the variable, I am most interested in.

Biefly, you use only the complete cases in computing the time averages, and you also define dummy variables indicating how many time periods you observe for the different units. These become explanatory variables in the fractional probit/logit along with the time averages. You can make this flexible, too, by interacting those dummies with the time averages and maybe other variables. Best regards Aymen

egen newx=mean(x), by(id)

is this command fine for creating time averages for the explanatory variables??

also, do we have to add time averages in addition to the explanatory variables or only time averages would suffice?

Aymen Ammari

please provide me with the stata codes for beta regression panel data.

email: [email protected]

Thank you