Assignment
- Panel Data Analysis
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
> data(Produc , package ="plm")
> head(Produc)
state year pcap
hwy water util
pc gsp emp unemp
1 ALABAMA 1970 15032.67 7325.80 1655.68 6051.20 35793.80 28418
1010.5 4.7
2 ALABAMA 1971 15501.94 7525.94 1721.02 6254.98 37299.91 29375
1021.9 5.2
3 ALABAMA 1972 15972.41 7765.42 1764.75 6442.23 38670.30 31303
1072.3 4.7
4 ALABAMA 1973 16406.26 7907.66 1742.41 6756.19 40084.01 33430
1135.5 3.9
5 ALABAMA 1974 16762.67 8025.52 1734.85 7002.29 42057.31 33749
1169.8 5.5
6 ALABAMA 1975 17316.26 8158.23 1752.27 7405.76 43971.71 33604
1155.4 7.7
> 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)
Oneway (individual) effect Pooling Model
Call:
plm(formula = log(pcap) ~ log(hwy) + log(water) + log(util) +
log(pc) + log(gsp) +
log(emp) + log(unemp), data = Produc,
model =
("pooling"), index = c("state", "year"))
Balanced Panel: n=48, T=17, N=816
Residuals :
Min. 1st Qu.
Median 3rd Qu. Max.
-0.04950 -0.01940 -0.00412
0.01150 0.08690
Coefficients :
Estimate
Std. Error t-value Pr(>|t|)
(Intercept) 0.7496721 0.0271054
27.6577 < 2.2e-16 ***
log(hwy)
0.5248704 0.0048326 108.6099 <
2.2e-16 ***
log(water)
0.1077579 0.0040454 26.6370 < 2.2e-16 ***
log(util)
0.4127255 0.0038337 107.6574 <
2.2e-16 ***
log(pc)
-0.0330829 0.0048219 -6.8610 1.361e-11 ***
log(gsp)
0.0758341 0.0108650 6.9797 6.170e-12 ***
log(emp)
-0.0891772 0.0076891 -11.5978
< 2.2e-16 ***
log(unemp)
0.0043878 0.0029465 1.4891
0.1368
---
Signif. codes: 0 ‘***’ 0.001
‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Total Sum of Squares:
724.14
Residual Sum of Squares: 0.56734
R-Squared : 0.99922
Adj. R-Squared
: 0.98942
F-statistic: 147217 on 7 and 808 DF, p-value: < 2.22e-16
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)
Oneway (individual) effect Within Model
Call:
plm(formula = log(pcap) ~ log(hwy) + log(water) + log(util) +
log(pc) + log(gsp) +
log(emp) + log(unemp), data = Produc,
model =
("within"), index = c("state", "year"))
Balanced Panel: n=48, T=17, N=816
Residuals :
Min. 1st Qu.
Median 3rd Qu. Max.
-0.069800 -0.005280 -0.000327
0.005360 0.061200
Coefficients :
Estimate Std.
Error t-value Pr(>|t|)
log(hwy) 0.5418395 0.0109565 49.4536 < 2.2e-16 ***
log(water) 0.1215676 0.0053719 22.6304 < 2.2e-16 ***
log(util) 0.3909247 0.0065771 59.4368 < 2.2e-16 ***
log(pc) 0.0177190 0.0096372
1.8386 0.0663624 .
log(gsp) 0.0568433 0.0126569
4.4911 8.184e-06 ***
log(emp) -0.0851515 0.0146508 -5.8121 9.073e-09 ***
log(unemp) -0.0092135
0.0024988 -3.6872 0.0002429 ***
---
Signif. codes: 0 ‘***’
0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Total Sum of Squares:
9.4468
Residual Sum of Squares: 0.12613
R-Squared : 0.98665
Adj. R-Squared
: 0.92015
F-statistic: 8033.41 on 7 and 761 DF, p-value: < 2.22e-16
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)
Oneway (individual) effect Random Effect Model
(Swamy-Arora's
transformation)
Call:
plm(formula = log(pcap) ~ log(hwy) + log(water) + log(util) +
log(pc) + log(gsp) +
log(emp) + log(unemp), data = Produc,
model =
("random"), index = c("state", "year"))
Balanced Panel: n=48, T=17, N=816
Effects:
var std.dev share
idiosyncratic 0.0001657 0.0128743 0.221
individual 0.0005848
0.0241825 0.779
theta: 0.8719
Residuals :
Min. 1st Qu.
Median 3rd Qu. Max.
-0.06500 -0.00624 -0.00195
0.00454 0.06450
Coefficients :
Estimate
Std. Error t-value Pr(>|t|)
(Intercept)
0.6625006 0.0530786 12.4815 <
2.2e-16 ***
log(hwy)
0.5021294 0.0074551 67.3537 <
2.2e-16 ***
log(water)
0.1191683 0.0049801 23.9289 <
2.2e-16 ***
log(util)
0.3944635 0.0060802 64.8768 <
2.2e-16 ***
log(pc) 0.0101901 0.0075870
1.3431 0.1796
log(gsp)
0.0599363 0.0122997 4.8730 1.323e-06 ***
log(emp)
-0.0767378 0.0125556 -6.1119
1.531e-09 ***
log(unemp)
-0.0034020 0.0022591 -1.5059 0.1325
---
Signif. codes: 0 ‘***’
0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Total Sum of Squares:
21.167
Residual Sum of Squares: 0.13965
R-Squared : 0.9934
Adj. R-Squared
: 0.98366
F-statistic: 17380.4 on 7 and 808 DF, p-value: < 2.22e-16
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
> pFtest(fixed,pool)
F test for
individual effects
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
> plmtest(pool)
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
> phtest(fixed,random)
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.
