# plm

##### Panel Data Estimators

Linear models for panel data estimated using the `lm`

function on
transformed data.

- Keywords
- regression

##### Usage

```
plm(
formula,
data,
subset,
weights,
na.action,
effect = c("individual", "time", "twoways", "nested"),
model = c("within", "random", "ht", "between", "pooling", "fd"),
random.method = NULL,
random.models = NULL,
random.dfcor = NULL,
inst.method = c("bvk", "baltagi", "am", "bms"),
restrict.matrix = NULL,
restrict.rhs = NULL,
index = NULL,
...
)
```# S3 method for plm.list
print(
x,
digits = max(3, getOption("digits") - 2),
width = getOption("width"),
...
)

# S3 method for panelmodel
terms(x, ...)

# S3 method for panelmodel
vcov(object, ...)

# S3 method for panelmodel
fitted(object, ...)

# S3 method for panelmodel
residuals(object, ...)

# S3 method for panelmodel
df.residual(object, ...)

# S3 method for panelmodel
coef(object, ...)

# S3 method for panelmodel
print(
x,
digits = max(3, getOption("digits") - 2),
width = getOption("width"),
...
)

# S3 method for panelmodel
update(object, formula., ..., evaluate = TRUE)

# S3 method for panelmodel
deviance(object, model = NULL, ...)

# S3 method for plm
predict(object, newdata = NULL, ...)

# S3 method for plm
formula(x, ...)

# S3 method for plm
plot(
x,
dx = 0.2,
N = NULL,
seed = 1,
within = TRUE,
pooling = TRUE,
between = FALSE,
random = FALSE,
...
)

# S3 method for plm
residuals(object, model = NULL, effect = NULL, ...)

# S3 method for plm
fitted(object, model = NULL, effect = NULL, ...)

##### Arguments

- formula
a symbolic description for the model to be estimated,

- data
a

`data.frame`

,- subset
see

`stats::lm()`

,- weights
see

`stats::lm()`

,- na.action
see

`stats::lm()`

; currently, not fully supported,- effect
the effects introduced in the model, one of

`"individual"`

,`"time"`

,`"twoways"`

, or`"nested"`

,- model
one of

`"pooling"`

,`"within"`

,`"between"`

,`"random"`

`"fd"`

, or`"ht"`

,- random.method
method of estimation for the variance components in the random effects model, one of

`"swar"`

(default),`"amemiya"`

,`"walhus"`

, or`"nerlove"`

,- random.models
an alternative to the previous argument, the models used to compute the variance components estimations are indicated,

- random.dfcor
a numeric vector of length 2 indicating which degree of freedom should be used,

- inst.method
the instrumental variable transformation: one of

`"bvk"`

,`"baltagi"`

,`"am"`

, or`"bms"`

(see also Details),- restrict.matrix
a matrix which defines linear restrictions on the coefficients,

- restrict.rhs
the right hand side vector of the linear restrictions on the coefficients,

- index
the indexes,

- …
further arguments.

- x, object
an object of class

`"plm"`

,- digits
number of digits for printed output,

- width
the maximum length of the lines in the printed output,

- formula.
a new formula for the update method,

- evaluate
a boolean for the update method, if

`TRUE`

the updated model is returned, if`FALSE`

the call is returned,- newdata
the new data set for the

`predict`

method,- dx
the half--length of the individual lines for the plot method (relative to x range),

- N
the number of individual to plot,

- seed
the seed which will lead to individual selection,

- within
if

`TRUE`

, the within model is plotted,- pooling
if

`TRUE`

, the pooling model is plotted,- between
if

`TRUE`

, the between model is plotted,- random
if

`TRUE`

, the random effect model is plotted,

##### Details

`plm`

is a general function for the estimation of linear panel
models. It supports the following estimation methods: pooled OLS
(`model = "pooling"`

), fixed effects (`"within"`

), random effects
(`"random"`

), first--differences (`"fd"`

), and between
(`"between"`

). It supports unbalanced panels and two--way effects
(although not with all methods).

For random effects models, four estimators of the transformation
parameter are available by setting `random.method`

to one of
`"swar"`

SWAM:AROR:72plm (default), `"amemiya"`

AMEM:71plm, `"walhus"`

WALL:HUSS:69plm, or `"nerlove"`

NERLO:71plm.

For first--difference models, the intercept is maintained (which
from a specification viewpoint amounts to allowing for a trend in
the levels model). The user can exclude it from the estimated
specification the usual way by adding `"-1"`

to the model formula.

Instrumental variables estimation is obtained using two--part
formulas, the second part indicating the instrumental variables
used. This can be a complete list of instrumental variables or an
update of the first part. If, for example, the model is `y ~ x1 + x2 + x3`

, with `x1`

and `x2`

endogenous and `z1`

and `z2`

external
instruments, the model can be estimated with:

`formula = y~x1+x2+x3 | x3+z1+z2`

,`formula = y~x1+x2+x3 | . -x1-x2+z1+z2`

.

If an instrument variable estimation is requested, argument
`inst.method`

selects the instrument variable transformation
method:

`"bvk"`

(default) for BALE:VARA:87;textualplm,`"baltagi"`

for BALT:81;textualplm,`"am"`

for AMEM:MACU:86;textualplm,`"bms"`

for BREU:MIZO:SCHM:89;textualplm.

The Hausman--Taylor estimator HAUS:TAYL:81plm is
computed with arguments `random.method = "ht"`

, `model = "random"`

, `inst.method = "baltagi"`

(the other way with only
`model = "ht"`

is deprecated).

##### Value

An object of class `"plm"`

.

A `"plm"`

object has the following elements :

the vector of coefficients,

the variance--covariance matrix of the coefficients,

the vector of residuals (these are the residuals of the (quasi-)demeaned model),

(only for weighted estimations) weights as specified,

degrees of freedom of the residuals,

an object of class `"pFormula"`

describing the model,

the model frame as a `"pdata.frame"`

containing the
variables used for estimation: the response is in first column followed by
the other variables, the individual and time indexes are in the 'index'
attribute of `model`

,

an object of class `"ercomp"`

providing the
estimation of the components of the errors (for random effects
models only),

named logical vector indicating any aliased
coefficients which are silently dropped by `plm`

due to
linearly dependent terms (see also `detect.lindep()`

),

the call.

It has print, summary and print.summary methods. The summary method creates an object of class "summary.plm" that extends the object it is run on with information about (inter alia) F statistic and (adjusted) R-squared of model, standard errors, t--values, and p--values of coefficients, (if supplied) the furnished vcov, see summary.plm() for further details.

##### References

AMEM:71plm

AMEM:MACU:86plm

BALE:VARA:87plm

BALT:81plm

BALT:SONG:JUNG:01plm

BALT:13plm

BREU:MIZO:SCHM:89plm

HAUS:TAYL:81plm

NERLO:71plm

SWAM:AROR:72plm

WALL:HUSS:69plm

##### See Also

`summary.plm()`

for further details about the associated
summary method and the "summary.plm" object both of which provide some model
tests and tests of coefficients. `fixef()`

to compute the fixed
effects for "within" models (=fixed effects models).

##### Examples

```
# NOT RUN {
data("Produc", package = "plm")
zz <- plm(log(gsp) ~ log(pcap) + log(pc) + log(emp) + unemp,
data = Produc, index = c("state","year"))
summary(zz)
# replicates some results from Baltagi (2013), table 3.1
data("Grunfeld", package = "plm")
p <- plm(inv ~ value + capital,
data = Grunfeld, model = "pooling")
wi <- plm(inv ~ value + capital,
data = Grunfeld, model = "within", effect = "twoways")
swar <- plm(inv ~ value + capital,
data = Grunfeld, model = "random", effect = "twoways")
amemiya <- plm(inv ~ value + capital,
data = Grunfeld, model = "random", random.method = "amemiya",
effect = "twoways")
walhus <- plm(inv ~ value + capital,
data = Grunfeld, model = "random", random.method = "walhus",
effect = "twoways")
# summary and summary with a funished vcov (passed as matrix,
# as function, and as function with additional argument)
summary(wi)
summary(wi, vcov = vcovHC(wi))
summary(wi, vcov = vcovHC)
summary(wi, vcov = function(x) vcovHC(x, method = "white2"))
# nested random effect model
# replicate Baltagi/Song/Jung (2001), p. 378 (table 6), columns SA, WH
# == Baltagi (2013), pp. 204-205
data("Produc", package = "plm")
pProduc <- pdata.frame(Produc, index = c("state", "year", "region"))
form <- log(gsp) ~ log(pc) + log(emp) + log(hwy) + log(water) + log(util) + unemp
summary(plm(form, data = pProduc, model = "random", effect = "nested"))
summary(plm(form, data = pProduc, model = "random", effect = "nested",
random.method = "walhus"))
## Hausman-Taylor estimator and Amemiya-MaCurdy estimator
## replicate Baltagi (2005, 2013), table 7.4
data("Wages", package = "plm")
ht <- plm(lwage ~ wks + south + smsa + married + exp + I(exp ^ 2) +
bluecol + ind + union + sex + black + ed |
bluecol + south + smsa + ind + sex + black |
wks + married + union + exp + I(exp ^ 2),
data = Wages, index = 595,
random.method = "ht", model = "random", inst.method = "baltagi")
summary(ht)
am <- plm(lwage ~ wks + south + smsa + married + exp + I(exp ^ 2) +
bluecol + ind + union + sex + black + ed |
bluecol + south + smsa + ind + sex + black |
wks + married + union + exp + I(exp ^ 2),
data = Wages, index = 595,
random.method = "ht", model = "random", inst.method = "am")
summary(am)
# }
```

*Documentation reproduced from package plm, version 2.2-5, License: GPL (>= 2)*