Do Panel Data Analysis of "Produc" data analyzing on three types of model :
Pooled affect model
Fixed affect model
Random affect model
Determine 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
Pooled 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)
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 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 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
Pooled vs Fixed
Null Hypothesis: Pooled Model
Alternate Hypothesis : Fixed 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 Model is better than Pooled Model
Pooled vs Random
Null Hypothesis: Pooled Model
Alternate Hypothesis: Random 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 Model is better than Pooled Model
Random vs Fixed
Null Hypothesis: No Correlation . Random Model
Alternate Hypothesis: Fixed 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 Model.
Conclusion:
So after making all the comparisons we come to the conclusion that Fixed 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.
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