plm (version 1.2-3)

pgmm: Generalized Method of Moments (GMM) Estimation for Panel Data

Description

Generalized method of moments estimation for static or dynamic models with panel data.

Usage

pgmm(formula, data, effect = c("individual","twoways", "none"),
     model = c("onestep", "twosteps"),
     instruments = NULL, gmm.inst, lag.gmm, lag.form,
     transformation = c("d", "ld"),
     fsm = NULL, ...)
## S3 method for class 'pgmm':
summary(object,robust, ...)
## S3 method for class 'summary.pgmm':
print(x, digits = max(3, getOption("digits") - 2),
    width = getOption("width"),...)

Arguments

formula

a symbolic description for the model to be estimated. Should be an object of class "dynformula" or of class "formula". In the latter case, a lag.form argument should be provided,

object,x

an object of class "pgmm",

data

a data.frame,

effect

the effects introduced in the model, one of "individual" or "twoways",

model

one of "onestep" or "twosteps",

instruments

a one-sided formula containing the normal instruments,

gmm.inst

a one-sided formula containing the GMM instruments,

lag.gmm

a list containing the lags to use for each GMM instrument, or a list of two named lists ("d" for difference and "l" for level) in case of ``system GMM'',

lag.form

a list containing the lags to use for each variable of the formula. Only relevant if formula is a standard formula and not a dynformula,

transformation

the kind of transformation to apply to the model: either "d" (the default value) for the ``difference GMM'' model or "ld" for the ``system GMM'',

fsm

the matrix for the one step estimator : one of "I" (identity matrix) or "G" ($=D'D$ where $D$ is the first-difference operator) if transformation="d", one of "GI" or "full" if transfor

digits

digits,

width

the maximum length of the lines in the print output,

robust

if TRUE, robust inference is performed in the summary,

...

further arguments.

Value

• An object of class c("pgmm","panelmodel"), which has the following elements:
• coefficients
  the vector (or the list for fixed effects) of coefficients,
• residuals
  the vector of residuals,
• fitted.values
  the vector of fitted.values,
• vcov
  the covariance matrix of the coefficients,
• df.residual
  degrees of freedom of the residuals,
• model
  a list containing the variables used for the estimation for each individual,
• W
  a list containing the instruments for each individual (two lists in case of ``sys--GMM''),
• K
  a list containing K the number of explanatory variables, Ky the number of lags of the dependent variable and Kt the number of time dummies,
• A1
  the weighting matrix for the one--step estimator,
• A2
  the weighting matrix for the two--steps estimator,
• call
  the call.
• It has print, summary and print.summary methods.

Details

pgmm estimates a model for panel data with a generalized method of moments (GMM) estimator. The description of the model to estimate is provided with a dynformula. The GMM instruments are provided by filling the pgmm.inst argument with a one-sided formula. By default, all the variables of the model which are not used as GMM instruments are used as normal instruments with the same lag structure as the one specified in the dynformula, but the user may also specify a one-sided formula to indicate expicitly the variables to use as normal instruments. The lags used for the GMM instruments are indicated with the lag.gmm argument. For each instrument, it is either a vector of length 2 (e.g., c(99,3) indicates to use all the lags available up to t-3), or a scalar (e.g, 2 indicates to use the lags 0, 1 and 2). If a single vector (or scalar) is written, then this lag structure is replicated for all GMM instruments. Otherwise, lag.gmm should be a list of length equal to the number of GMM instruments. transformation indicates how the model should be transformed for the estimation. "d" gives the ``difference GMM'' model (see Arellano and Bond (1991)), "ld" the ``system GMM'' model (see Blundell and Bond (1998)). pgmm is an attempt to adapt GMM estimators available within the DPD library for GAUSS (see Arellano and Bond 1998) and Ox (see Doornik, Arellano and Bond 2006) and with the xtabond2 library for STATA (see Roodman 2009).

References

Arellano, M. and Bond, S. (1991) Some Tests of Specification for Panel Data: Monte Carlo Evidence and an Application to Employment Equations, The Review of Economic Studies, vol. 58(2), 1991, pp.227--297. Arellano, M. and Bond, S. (1998) Dynamic Panel Data Estimation Using DPD98 for GAUSS: A Guide for Users. Blundell, R. and Bond, S. (1998) Initial Conditions and Moment Restrictions in Dynamic Panel Data Models, Journal of Econometrics, vol. 87, pp.115--143. Doornik, J., Arellano, M. and Bond, S. (2006) Panel Data Estimation using DPD for Ox. http://www.doornik.com/download/dpd.pdf Roodman, D. (2009) How to do xtabond2: An Introduction to ``difference'' and ``system'' GMM in Stata, Stata Journal, vol. 9(1), pp. 86--136. Working Paper version at http://ideas.repec.org/p/cgd/wpaper/103.html

See Also

dynformula for dynamic formulas, sargan for Sargan tests and mtest for Arellano--Bond's tests of multicollinearity.

Examples

data("EmplUK", package = "plm")

## Arellano and Bond (1991), table 4b 
z1 <- pgmm(log(emp) ~ log(wage) + log(capital) + log(output),
            lag.form = list(2,1,0,1), data = EmplUK, 
            effect = "twoways", model = "twosteps",
            gmm.inst = ~log(emp), lag.gmm = list(c(2,99)))
summary(z1)

## Blundell and Bond (1998) table 4 (cf DPD for OX p.12 col.4)
z2 <- pgmm(dynformula(log(emp) ~ log(wage) + log(capital), list(1,1,1)), 
            data = EmplUK, effect = "twoways", model = "onestep", 
            gmm.inst = ~log(emp) + log(wage) + log(capital), 
            lag.gmm = c(2,99), transformation = "ld")
summary(z2, robust = TRUE)