Assignment- 8TH March,2013

Assignment no:-1

Perform Panel Data Analysis of “Produc” data

Solution:

There are three types of models:

•       Pooled affect model
•       Fixed affect model
•       Random affect model 

We will be determining which model is the best by using functions:
      1) pFtest : for determining between fixed and pooled
      2) plmtest : for determining between pooled and random
      3) phtest: for determining between random and fixed

The data can be loaded using the following commands:-
data(Produc , package =”plm”)
head(Produc)

Screenshot:-

Pooled Affect Model 

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”))
summary(pool)

Screenshot:-

Fixed Affect Model:

 

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”))

summary(fixed)

 

Screenshot:-

 

 

 

Random Affect Model:

 

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”))

> summary(random)

 

Screenshot:-

 

 

 

Testing of Model

 

This can be done through Hypothesis testing between the models as follows:

 

H0: Null Hypothesis: the individual index and time based params are all zero

H1: Alternate Hypothesis: atleast one of the index and time based params is non zero

 

Pooled vs Fixed

 

Null Hypothesis: Pooled Affect Model

Alternate Hypothesis : Fixed Affect Model

 

Command:

 > pFtest(fixed,pool)

 

Result:

data:  log(pcap) ~ log(hwy) + log(water) + log(util) + log(pc) + log(gsp) + log(emp) + log(unemp)
F = 56.6361, df1 = 47, df2 = 761, p-value < 2.2e-16
alternative hypothesis: significant effects 

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

 

Pooled vs Random

 

Null Hypothesis: Pooled Affect Model

Alternate Hypothesis: Random Affect Model

 

Command :

> plmtest(pool)

 

Result:

 

 Lagrange Multiplier Test – (Honda)

data:  log(pcap) ~ log(hwy) + log(water) + log(util) + log(pc) + log(gsp) + log(emp) + log(unemp)

normal = 57.1686, p-value < 2.2e-16
alternative hypothesis: significant effects 

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

 

 

Random vs Fixed

 

Null Hypothesis: No Correlation . Random Affect Model

Alternate Hypothesis: Fixed Affect Model

 

Command:

 > phtest(fixed,random)

 

Result: 

 

 Hausman Test

data:  log(pcap) ~ log(hwy) + log(water) + log(util) + log(pc) + log(gsp) + log(emp) + log(unemp)

chisq = 93.546, df = 7, p-value < 2.2e-16
alternative hypothesis: one model is inconsistent . 

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

 

Conclusion: 

 

So after making all the tests we come to the conclusion that Fixed Affect 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.