Panel regression

Panel regression

Date- 20-02-2014
Unobserved unit specific heterogeneity- In panel regression, we generally face the situation that heterogeneity of individuals. Due to heterogeneity of individuals, we divide the estimation techniques into two parts (1) Fixed effect estimation (Fixed effect) (2) Random effect.
                    Panel model:
                                   yit = β0 +β1x1it +· · ·+βkxkit + γ1z1i +· · ·+γj zji +ui +eit
Here: Yit= dependent variable of i th observation at T th time.
Xit------Xkit: are the independent variables ( time varying variables)
γ1z1i............γj zji : are the independent variables (time constant variables)
Time in-varying variables mean- Where variables are not changed over time. Ex- Ethics , education, religion etc.
Time Varying variables- Where variables are changed over time- performance of employees, Efficiency etc.
Based on the two variables we decide when and how we will apply two different models in different scenario to get the efficient of parameter of interest and independent error term ( Mean zero and constant variance).
 ui-  This is error term of model, this error arises due to heterogeneity of individuals of the model. For example we have 50 different firms with 10 years data. We assume for simplicity time has no effect on dependent variable (yit), (that is why βt= β0) only heterogeneity of firms have impact on dependent variables. Here 50 firms have different properties, so no firms have equal in behavior. So to control the heterogeneity behavior of the 50 firms, we add another variable that is called unobserved variable or unobserved unit specific heterogeneity. To know the effect of heterogeneity on dependent variable (yit), we decide which model is the best estimator of our parameter of interest. That is way we take fixed effect model and random effect model.
Here we will discuss two different models (1) random effect model and (2) fixed effect model.
Random effect model-  Assumption (1)  ui  should not be related with any of the variables that may be time varying (Xit) variables or time in-varying variables (time constant)  (z1i )
(2) Error should be random in nature (white noise), some people treat it as idiosyncratic
 error.
If the two assumption is satisfied, in that case we apply random effect estimator to get the parameter of interest. This is only possible if we have large data set. Data should be assumed that it was collected from population in random basis. If that is true, then the inference will be valid and reliable in our model. This is otherwise called population specific.
Fixed effect model-  Some way, in realistic our unobserved unit specific heterogeneity is related both of the variables like time in-varying variables and time constant variable. To control that effect, we take the fixed effect model.  In this model we are interested to judge the effect of unobserved unit specific impact on time varying and time constant variables in the model. This error arises due to small sample. so it is called sample specific error. The basic difference between random effect model and fixed effect model is ui (unobserved unit specific heterogeneity) is seen population specific and sample specific. When you have large data set, assume that random effect model is good for estimating parameter of interest, When you have small sample data set, assume that fixed effect model is better.
 Difference between random effect model and fixed effect model- Random effect model is population specific and fixed effect model is sample specific effect.

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