Business App IT Lab - Session 8

Assignment

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)

 Data

Pooled Effect 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)

 Pooled Effect Model

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)

Fixed Effect Model

Random Effect 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)

Random Effect Model

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 Effect Model
Alternate Hypothesis : Fixed Effect 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 Effect Model.

pFtest

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 Effect Model.

plmtest

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 Effect Model.

phtest

Conclusion: 

So after making all the comparisons we come to the conclusion that Fixed Effect 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.