# [R] plm "within" models: is the correct F-statistic reported?

Liviu Andronic landronimirc at gmail.com
Tue Mar 16 23:24:12 CET 2010

```Dear R users
I get different F-statistic results for a "within" model, when using
"time" or "twoways" effects in plm() [1] and when manually specifying
the time control dummies [2].
[1] vignette("plm")
[2] http://cran.r-project.org/doc/contrib/Farnsworth-EconometricsInR.pdf

Two examples below:
library("AER")
data("Grunfeld", package = "AER")
library("plm")
gr <- subset(Grunfeld, firm %in% c("General Electric",
"General Motors", "IBM"))
pgr <- plm.data(gr, index = c("firm", "year"))
> dim(pgr)
[1] 60  5

## the first example is actually on "individual" effects
> gr_fe <- plm(invest ~ value + capital, data = pgr,
+  model = "within", effect="individual")
> summary(gr_fe)
Oneway (individual) effect Within Model

Call:
plm(formula = invest ~ value + capital, data = pgr, effect = "individual",
model = "within")

Balanced Panel: n=3, T=20, N=60

Residuals :
Min. 1st Qu.  Median 3rd Qu.    Max.
-167.00  -26.10    2.09   26.80  202.00

Coefficients :
Estimate Std. Error t-value    Pr(>|t|)
value     0.1049     0.0163    6.42 0.000000033 ***
capital   0.3453     0.0244   14.16     < 2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Total Sum of Squares:    1890000
Residual Sum of Squares: 244000
F-statistic: 185.407 on 2 and 55 DF, p-value: <2e-16
> summary(fixef(gr_fe))
Estimate Std. Error t-value Pr(>|t|)
General Motors      -70.6       67.8   -1.04     0.30
General Electric   -239.6       32.8   -7.29    3e-13 ***
IBM                 -24.6       16.2   -1.52     0.13
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
> gr_lm <- lm(invest ~ 0+value + capital + firm, data = pgr)
> summary(gr_lm)

Call:
lm(formula = invest ~ 0 + value + capital + firm, data = pgr)

Residuals:
Min      1Q  Median      3Q     Max
-167.33  -26.14    2.09   26.84  201.68

Coefficients:
Estimate Std. Error t value     Pr(>|t|)
value                   0.1049     0.0163    6.42 0.0000000330 ***
capital                 0.3453     0.0244   14.16      < 2e-16 ***
firmGeneral Motors    -70.5629    67.8196   -1.04         0.30
firmGeneral Electric -239.5560    32.8400   -7.29 0.0000000012 ***
firmIBM               -24.6480    16.1726   -1.52         0.13
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 66.6 on 55 degrees of freedom
Multiple R-squared: 0.974,	Adjusted R-squared: 0.972
F-statistic:  420 on 5 and 55 DF,  p-value: <2e-16

In the first case, plm(..., effect="individual"), F-statistic: 185.407
and in the second F-statistic:  420, while all other regression
coefficients and standard errors are the same. Which F-statistic
should be considered?

## A second example with "twoways" effects
> gr_fe1 <- plm(invest ~ value + capital, data = pgr,
+   model = "within", effect="twoways")
> summary(gr_fe1)
Twoways effects Within Model

Call:
plm(formula = invest ~ value + capital, data = pgr, effect = "twoways",
model = "within")

Balanced Panel: n=3, T=20, N=60

Residuals :
Min. 1st Qu.  Median 3rd Qu.    Max.
-153.00  -29.10    2.23   34.80  125.00

Coefficients :
Estimate Std. Error t-value Pr(>|t|)
value     0.1295     0.0224    5.77  1.4e-06 ***
capital   0.4184     0.0353   11.85  5.5e-14 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Total Sum of Squares:    957000
Residual Sum of Squares: 138000
F-statistic: 107.246 on 2 and 36 DF, p-value: 6.84e-16
> #summary(fixef(gr_fe1, "time"))
> gr_fe2 <- plm(invest ~ value + capital + year, data = pgr,
+   model = "within", effect="individual")
> summary(gr_fe2)
Oneway (individual) effect Within Model

Call:
plm(formula = invest ~ value + capital + year, data = pgr, effect =
"individual",
model = "within")

Balanced Panel: n=3, T=20, N=60

Residuals :
Min. 1st Qu.  Median 3rd Qu.    Max.
-153.00  -29.10    2.23   34.80  125.00

Coefficients :
Estimate Std. Error t-value Pr(>|t|)
value           0.1295     0.0224    5.77  1.4e-06 ***
capital         0.4184     0.0353   11.85  5.5e-14 ***
year[T.1936]  -83.9625    53.6143   -1.57   0.1261
year[T.1937] -150.9206    58.3282   -2.59   0.0139 *
year[T.1938]  -81.2343    50.7175   -1.60   0.1180
year[T.1939] -137.4579    53.4385   -2.57   0.0144 *
year[T.1940]  -96.3584    53.9837   -1.78   0.0827 .
year[T.1941]  -56.5587    53.0089   -1.07   0.2931
year[T.1942]  -36.6539    50.9966   -0.72   0.4769
year[T.1943]  -78.0794    52.0249   -1.50   0.1421
year[T.1944]  -66.4725    52.5047   -1.27   0.2136
year[T.1945]  -89.5562    54.2876   -1.65   0.1077
year[T.1946]  -59.1147    55.3115   -1.07   0.2923
year[T.1947]  -87.5444    52.6530   -1.66   0.1051
year[T.1948] -119.9125    53.3167   -2.25   0.0307 *
year[T.1949] -167.9552    54.1999   -3.10   0.0038 **
year[T.1950] -172.7676    55.0212   -3.14   0.0034 **
year[T.1951] -191.1369    57.6114   -3.32   0.0021 **
year[T.1952] -195.4503    59.6377   -3.28   0.0023 **
year[T.1953] -174.6639    66.3451   -2.63   0.0124 *
year[T.1954] -181.1273    68.5794   -2.64   0.0121 *
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Total Sum of Squares:    1890000
Residual Sum of Squares: 138000
F-statistic: 21.8327 on 21 and 36 DF, p-value: 1.32e-14

In the first case, F-statistic: 107.246 , while in the second
F-statistic: 21.8327. Again, which one is correct? Thank you
Liviu

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