Thursday, 14 March 2013

Assignment 8 : Panel Data Analysis

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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