pvcm function

Variable Coefficients Models for Panel Data

Estimators for random and fixed effects models with variable coefficients.

pvcm(
  formula,
  data,
  subset,
  na.action,
  effect = c("individual", "time"),
  model = c("within", "random"),
  index = NULL,
  ...
)

## S3 method for class 'pvcm'
summary(object, ...)

## S3 method for class 'summary.pvcm'
print(
  x,
  digits = max(3, getOption("digits") - 2),
  width = getOption("width"),
  ...
)

Arguments

• formula: a symbolic description for the model to be estimated,
• data: a data.frame,
• subset: see lm,
• na.action: see lm,
• effect: the effects introduced in the model: one of "individual", "time",
• model: one of "within", "random",
• index: the indexes, see pdata.frame(),
• ...: further arguments.
• object, x: an object of class "pvcm",
• digits: digits,
• width: the maximum length of the lines in the print output,

Returns

An object of class c("pvcm", "panelmodel"), which has the following elements:

• coefficients: the vector (numeric) of coefficients (or data frame for fixed effects),

• residuals: the vector (numeric) of residuals,

• fitted.values: the vector of fitted values,

• vcov: the covariance matrix of the coefficients (a list for fixed effects model (model = "within")),

• df.residual: degrees of freedom of the residuals,

• model: a data frame containing the variables used for the estimation,

• call: the call,

• args: the arguments of the call,

random coefficients model only (model = "random"): - Delta: the estimation of the covariance matrix of the coefficients,

• single.coefs: matrix of unbiased coefficients of single estimations,

• single.vcov: list of variance-covariance matrices for single.coefs,

• single.std.error: matrix of standard errors of single.coefs,

• chisq.test: htest object: parameter stability test (homogeneous coefficients),

separate OLS estimations only (model = "within"): - std.error: a data frame containing standard errors for all coefficients for each single regression.

Details

pvcm estimates variable coefficients models. Individual or time effects are introduced, respectively, if effect = "individual"

(default) or effect = "time".

Coefficients are assumed to be fixed if model = "within", i.e., separate pooled OLS models are estimated per individual (effect = "individual") or per time period (effect = "time"). Coefficients are assumed to be random if model = "random" and the model by \insertCite SWAM:70;textualplm is estimated; it is a generalized least squares model which uses the results of the OLS models estimated per individual/time dimension (coefficient estimates are weighted averages of the single OLS estimates with weights inversely proportional to the variance-covariance matrices). The corresponding unbiased single coefficients, variance-covariance matrices, and standard errors of the random coefficients model are available in the returned object (see Value).

A test for parameter stability (homogeneous coefficients) of the random coefficients model is printed in the model's summary and is available in the returned object (see Value).

pvcm objects have print, summary and print.summary methods.

Examples

data("Produc", package = "plm")
zw <- pvcm(log(gsp) ~ log(pcap) + log(pc) + log(emp) + unemp, data = Produc, model = "within")
zr <- pvcm(log(gsp) ~ log(pcap) + log(pc) + log(emp) + unemp, data = Produc, model = "random")

## replicate Greene (2018), p. 452, table 11.22/(2012), p. 419, table 11.14
summary(pvcm(log(gsp) ~ log(pc) + log(hwy) + log(water) + log(util) + log(emp) + unemp, 
             data = Produc, model = "random"))
             
## replicate Poi (2003) (need data adjustment, remaining tiny diffs are due 
## Poi's data set having more digits, not justified by the original Grunfeld data)
data(Grunfeld) # need firm = 1, 4, 3, 8, 2
Gr.Poi.2003 <- Grunfeld[c(1:20, 61:80, 41:60, 141:160, 21:40), ]
Gr.Poi.2003$firm <- rep(1:5, each = 20)
Gr.Poi.2003[c(86, 98), "inv"] <- c(261.6, 645.2)
Gr.Poi.2003[c(92), "capital"] <- c(232.6)

mod.poi <- pvcm(inv ~ value + capital, data = Gr.Poi.2003, model = "random")
summary(mod.poi)
print(mod.poi$single.coefs)
print(mod.poi$single.std.err)

## Not run:

# replicate Swamy (1971), p. 166, table 5.2
data(Grunfeld, package = "AER") # 11 firm Grunfeld data needed from package AER
gw <- pvcm(invest ~ value + capital, data = Grunfeld, index = c("firm", "year"))
# close replication of Swamy (1970), (7.4) [remaining diffs likely due to less 
# precise numerical methods in the 1970, as supposed in Kleiber/Zeileis (2010), p. 9]
gr <- pvcm(invest ~ value + capital, data = Grunfeld, index = c("firm", "year"), model = "random")
## End(Not run)

References

\insertAllCited

\insertRef SWAM:71plm

\insertRef GREE:18plm

\insertRef POI:03plm

\insertRef KLEI:ZEIL:10plm

Author(s)

Yves Croissant, Kevin Tappe