We will be doing Panel Data Analysis of "Produc" data
We will be analysing on three types of model :
Pooled affect model
Fixed affect model
Random affect model
Then we will be determining which model is the best by using functions:
pFtest : for determining between fixed and pooled
plmtest : for determining between pooled and random
phtest: for determining between random and fixed
Commands:
Loading data:
> data(Produc, package ="plm")
> head(Produc)
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)
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)
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)
Comparison
The comparison between the models would be a Hypothesis testing based on the following concept:
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 comparisons 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.
