plm (version 1.6-5)

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, subset, na.action, effect = c("twoways", "individual"), model = c("onestep", "twosteps"), collapse = FALSE, lost.ts = NULL, transformation = c("d", "ld"), fsm = NULL, index = NULL, ...) 
"summary"(object, robust, time.dummies = FALSE, ...)
"print"(x, digits = max(3, getOption("digits") - 2), width = getOption("width"), ...)

Arguments

formula

a symbolic description for the model to be estimated. The preferred interface is now to indicate a multi--part formula, the first two parts describing the covariates and the gmm instruments and, if any, the third part the 'normal' instruments,

object,x

an object of class "pgmm",

data

a data.frame (neither factors nor character vectors will be accepted in data.frame),

subset

see lm,

na.action

see lm,

effect

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

model

one of "onestep" (the default) or "twosteps",

collapse

if TRUE, the gmm instruments are collapsed,

lost.ts

the number of lost time series: if NULL, this is automatically computed. Otherwise, it can be defined by the user as a numeric vector of length 1 or 2. The first element is the number of lost time series in the model in difference, the second one in the model in level. If the second element is missing, it is set to the first one minus one,

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 transformation="ld",

index

the indexes,

digits

digits,

width

the maximum length of the lines in the print output,

robust

if TRUE, robust inference is performed in the summary,

time.dummies

if TRUE, the estimated coefficients of time dummies are present in the table of coefficients,

...

further arguments.

Value

An object of class c("pgmm","panelmodel"), which has the following elements: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 multi--part formula which is (or which is coerced to) a Formula object. The first right--hand side part describes the covariates. The second one, which is mandatory, describes the gmm instruments. The third one, which is optional, describes the 'normal' instruments. 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 model.

y~lag(y, 1:2)+lag(x1, 0:1)+lag(x2, 0:2) | lag(y, 2:99) is similar to y~lag(y, 1:2)+lag(x1, 0:1)+lag(x2, 0:2) | lag(y, 2:99) | lag(x1, 0:1)+lag(x2, 0:2) and indicates that all lags from 2 of y is used as 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 within 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(1), pp. 115--143.

Doornik, J., Arellano, M. and Bond, S. (2006) Panel Data Estimation using DPD for Ox. http://www.doornik.com/download/oxmetrics7/Ox_Packages/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. http://www.stata-journal.com/article.html?article=st0159.

See Also

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

Examples

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

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

## Blundell and Bond (1998) table 4 (cf. DPD for OX p. 12 col. 4)
z2 <- pgmm(log(emp) ~ lag(log(emp), 1)+ lag(log(wage), 0:1) +
           lag(log(capital), 0:1) | lag(log(emp), 2:99) +
           lag(log(wage), 2:99) + lag(log(capital), 2:99),        
           data = EmplUK, effect = "twoways", model = "onestep", 
           transformation = "ld")
summary(z2, robust = TRUE)

## Not run: 
# ## Same with the old formula or dynformula interface
# ## Arellano and Bond (1991), table 4, col. b 
# 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)
# ## End(Not run)