Panel Data Analysis

QUESTION 1

Do Panel Data Analysis of "Produc" data analyzing  on three types of model :
   a.   Pooled affect model
   b.   Fixed affect model
   c.   Random affect model

Determine which model is the best by using functions:
       pFtest : Fixed vs Pooled
       plmtest : Pooled vs Random
       phtest: Random vs Fixed

Pooled Model

Command: 

pool<-plm( log(pcap) ~ log(hwy) +  log(water) + log(util) + log(pc) + log(gsp) + log(emp) + log(unemp)

, data= Produc, model = ("pooling"), index = c("state","year"))

Fixed Model

Command: 

fixed<-plm( log(pcap) ~ log(hwy) +  log(water) + log(util) + log(pc) + log(gsp) + log(emp) + log(unemp)

, data= Produc, model = ("within"), index = c("state","year"))

 Random Model

Command: 

random<-plm( log(pcap) ~ log(hwy) +  log(water) + log(util) + log(pc) + log(gsp) + log(emp) + log(unemp)

, data= Produc, model = ("random"), index = c("state","year"))

Pooled vs Fixed 

Null Hypothesis: Pooled Model

Alternate Hypothesis : Fixed Model

Since the p value is negligible so we reject the Null Hypothesis and hence Alternate hypothesis is accepted which is to accept Fixed Model is better than Pooled Model

Pooled vs Random 

Null Hypothesis: Pooled Model

Alternate Hypothesis: Random Model

Since the p value is negligible so we reject the Null Hypothesis and hence Alternate hypothesis is accepted which is to accept Random Model is better than Pooled Model

Random vs Fixed 

Null Hypothesis: No Correlation . Random Model

Alternate Hypothesis: Fixed Model

Since the p value is negligible so we reject the Null Hypothesis and hence Alternate hypothesis is accepted which is to accept Fixed Model.

Conclusion: 

 So after making all the comparisons we come to the conclusion that Fixed Model is best suited to do the panel data analysis for "Produc" data set.

Hence , we conclude that within the same id i.e. within same "state" there is no variation.