ITBA lab Session # 8 - 12 March 2013

#this post is created as a solution for assignment for IT & Business Applications Lab, Spring Semester, VGSoM, IIT Kharagpur Class of 2014.

Panel Data Analysis of "Produc" data

We will be analyzing 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 Affect Model

> pool <- br="" data="Produc," emp="" gsp="" hwy="" index="c(" log="" model="(" pc="" pcap="" plm="" pooling="" state="" unemp="" util="" water="" year=""> > summary(pool)

Pooled Affect Model

Fixed Affect Model:

> fixed <- data="Produc," emp="" gsp="" hwy="" index="c(" log="" model="(" pc="" pcap="" plm="" span="" state="" unemp="" util="" water="" within="" year="">

> summary(fixed)

Fixed Affect Model

Random Affect Model:

> random <- data="Produc," emp="" gsp="" hwy="" index="c(" log="" model="(" pc="" pcap="" plm="" random="" span="" state="" unemp="" util="" water="" year="">

> summary(random)

Random Affect 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 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.

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 Affect 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 Affect Model.

phtest

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.