> mdata <-read.table("panel.csv", header=T, sep=",")
> id <-mdata[,1]
> year<-mdata[,2]
> y <-mdata[,3]
> x <-mdata[,4]
> ols_result <-lm(y~x)
> summary(ols_result)
Call:
lm(formula = y ~ x)
Residuals:
Min 1Q Median 3Q Max
-2.52559 -0.39145 0.07648 0.51871 1.61471
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 1.43810 0.10262 14.01 <2e-16 ***
x 0.84544 0.03498 24.17 <2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.799 on 313 degrees of freedom
Multiple R-squared: 0.6511, Adjusted R-squared: 0.65
F-statistic: 584.1 on 1 and 313 DF, p-value: < 2.2e-16
> mydata <-data.frame(id,year,y,x)
> library(lattice)
> xyplot(y[1:28]~year[1:28]|as.character(id[1:28]), data=mydata, xlab="year", ylab="y", type="l", as.table=TRUE)
> xyplot(y[1:28]~year[1:28], groups=as.character(id[1:28]), data=mydata, xlab="year", ylab="y", type="l", as.table=TRUE, auto.key = list(x = 0.1, y = 0.8, corner = c(0, 0)))
> library(plm)
> fixed <-plm(y~x, data=mydata, index=c("id","year"), model="within")
> summary(fixed)
Oneway (individual) effect Within Model
Call:
plm(formula = y ~ x, data = mydata, model = "within", index = c("id",
"year"))
Balanced Panel: n = 45, T = 7, N = 315
Residuals:
Min. 1st Qu. Median 3rd Qu. Max.
-1.2919733 -0.1525946 0.0088823 0.2231488 1.0914112
Coefficients:
Estimate Std. Error t-value Pr(>|t|)
x 0.195584 0.081855 2.3894 0.01757 *
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Total Sum of Squares: 36.917
Residual Sum of Squares: 36.15
R-Squared: 0.020783
Adj. R-Squared: -0.14303
F-statistic: 5.70919 on 1 and 269 DF, p-value: 0.017565
> pFtest(fixed,pool)
F test for individual effects
data: y ~ x
F = 27.683, df1 = 44, df2 = 269, p-value < 2.2e-16
alternative hypothesis: significant effects
# fixed effects: alpha+u_i
> summary(fixef(fixed))
Estimate Std. Error t-value Pr(>|t|)
1 3.28080 0.15422 21.2742 < 2.2e-16 ***
2 3.11843 0.29516 10.5653 < 2.2e-16 ***
3 3.02394 0.25892 11.6790 < 2.2e-16 ***
4 2.80321 0.20902 13.4113 < 2.2e-16 ***
5 4.26975 0.33127 12.8891 < 2.2e-16 ***
6 1.75536 0.26685 6.5780 2.475e-10 ***
7 2.72358 0.15102 18.0342 < 2.2e-16 ***
8 4.49926 0.35651 12.6202 < 2.2e-16 ***
9 3.76266 0.26940 13.9666 < 2.2e-16 ***
10 5.37197 0.40826 13.1582 < 2.2e-16 ***
11 2.74967 0.26812 10.2553 < 2.2e-16 ***
12 2.51395 0.21171 11.8744 < 2.2e-16 ***
13 3.20393 0.19897 16.1023 < 2.2e-16 ***
14 3.20121 0.25105 12.7513 < 2.2e-16 ***
15 2.85323 0.21248 13.4281 < 2.2e-16 ***
16 3.59978 0.28924 12.4457 < 2.2e-16 ***
17 3.12772 0.35804 8.7356 2.639e-16 ***
18 3.79249 0.32649 11.6161 < 2.2e-16 ***
19 3.92342 0.30444 12.8874 < 2.2e-16 ***
20 2.64026 0.26174 10.0872 < 2.2e-16 ***
21 1.84157 0.23136 7.9596 4.853e-14 ***
22 0.68081 0.20937 3.2517 0.001293 **
23 4.29891 0.38487 11.1698 < 2.2e-16 ***
24 3.29837 0.24475 13.4766 < 2.2e-16 ***
25 3.55406 0.31790 11.1797 < 2.2e-16 ***
26 3.86666 0.22426 17.2416 < 2.2e-16 ***
27 3.88323 0.30878 12.5761 < 2.2e-16 ***
28 0.65306 0.14345 4.5524 8.042e-06 ***
29 2.94679 0.23379 12.6046 < 2.2e-16 ***
30 1.28630 0.17853 7.2052 5.843e-12 ***
31 5.10160 0.39886 12.7905 < 2.2e-16 ***
32 1.23127 0.14624 8.4197 2.278e-15 ***
33 2.40025 0.14390 16.6800 < 2.2e-16 ***
34 4.96925 0.42253 11.7608 < 2.2e-16 ***
35 0.92362 0.14194 6.5070 3.729e-10 ***
36 2.61346 0.19394 13.4754 < 2.2e-16 ***
37 4.51959 0.41697 10.8390 < 2.2e-16 ***
38 4.32519 0.31243 13.8437 < 2.2e-16 ***
39 2.36210 0.28097 8.4069 2.484e-15 ***
40 3.27609 0.28583 11.4618 < 2.2e-16 ***
41 2.90388 0.24818 11.7007 < 2.2e-16 ***
42 4.08466 0.28724 14.2204 < 2.2e-16 ***
43 3.58245 0.22082 16.2232 < 2.2e-16 ***
44 3.70293 0.30053 12.3213 < 2.2e-16 ***
45 3.28288 0.30251 10.8520 < 2.2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
> random <-plm(y~x, data=mydata, index=c("id","year"), model="random")
> summary(random)
Oneway (individual) effect Random Effect Model
(Swamy-Arora's transformation)
Call:
plm(formula = y ~ x, data = mydata, model = "random", index = c("id",
"year"))
Balanced Panel: n = 45, T = 7, N = 315
Effects:
var std.dev share
idiosyncratic 0.1344 0.3666 0.213
individual 0.4954 0.7038 0.787
theta: 0.8068
Residuals:
Min. 1st Qu. Median 3rd Qu. Max.
-1.358754 -0.206733 0.053443 0.251733 0.815222
Coefficients:
Estimate Std. Error t-value Pr(>|t|)
(Intercept) 2.29119 0.19784 11.5810 < 2.2e-16 ***
x 0.52182 0.06180 8.4438 1.164e-15 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Total Sum of Squares: 56.909
Residual Sum of Squares: 46.351
R-Squared: 0.18553
Adj. R-Squared: 0.18292
F-statistic: 71.2972 on 1 and 313 DF, p-value: 1.1642e-15
> phtest(random, fixed)
Hausman Test
data: y ~ x
chisq = 36.942, df = 1, p-value = 1.217e-09
alternative hypothesis: one model is inconsistent
> pool <-plm(y~x, data=mydata, index=c("id","year"), model="pooling")
> summary(pool)
Pooling Model
Call:
plm(formula = y ~ x, data = mydata, model = "pooling",
index = c("id", "year"))
Balanced Panel: n = 45, T = 7, N = 315
Residuals:
Min. 1st Qu. Median 3rd Qu. Max.
-2.525593 -0.391450 0.076475 0.518710 1.614709
Coefficients:
Estimate Std. Error t-value Pr(>|t|)
(Intercept) 1.438101 0.102621 14.014 < 2.2e-16 ***
x 0.845438 0.034983 24.167 < 2.2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Total Sum of Squares: 572.75
Residual Sum of Squares: 199.84
R-Squared: 0.65108
Adj. R-Squared: 0.64997
F-statistic: 584.061 on 1 and 313 DF, p-value: < 2.22e-16
> plmtest(pool, type=c("bp"))
Lagrange Multiplier Test - (Breusch-Pagan) for balanced panels
data: y ~ x
chisq = 516.79, df = 1, p-value < 2.2e-16
alternative hypothesis: significant effects