For GMM on panel data with Stata

Title

[XT] xtabond -- Arellano-Bond linear, dynamic panel-data estimation

Syntax

xtabond depvar [indepvars] [if] [in] [, options]

options description -------------------------------------------------------------------------- Model noconstant suppress constant term diffvars(varlist) already differenced exogenous variables inst(varlist) additional instrument variables lags(#) use # lags of dependent variable; default is lags(1) maxldep(#) maximum lags of dependent variable for use as instruments maxlags(#) maximum lags of predetermined variables for use as instruments twostep compute the two-step estimator instead of the one-step estimator

Predetermined, More predetermined pre(varlist[...]) predetermined variables; see Options for details pre(varlist[...]) pre() can be specified more than once

SE/Robust vce(vcetype) vcetype may be robust robust synonym for vce(robust)

Reporting level(#) set confidence level; default is level(95) small report small-sample statistics artests(#) use # as maximum order for AR tests; default is artests(2) -------------------------------------------------------------------------- You must tsset your data before using xtabond; see tsset. indepvars and all varlists may contain time-series operators; see tsvarlist. The specification of depvar may not contain time-series operators. by, statsby, and xi may be used with xtabond; see prefix. See xtabond postestimation for features available after estimation.

Description

Dynamic panel-data models allow past realizations of the dependent variable to affect its current level. xtabond fits a dynamic panel-data model using the Arellano-Bond estimator. Consider the model

y_it = y_(it-1)a_1 + ... + y_(it-p)a_p + x_(it)b_1 + w_(it)b_2 + v_i + e_(it) i={1,...,N{c )-}; t={1,...,T_i},

where

the a_1,...,a_p are p parameters to be estimated

x_(it) is a (1 X k_1) vector of strictly exogenous covariates

b_1 is a (k_1 X 1) vector of parameters to be estimated

w_(it) is a (1 X k_2) vector of predetermined covariates

b_2 is a (k_2 X 1) vector of parameters to be estimated

v_i are the random effects that are independent and identically distributed (iid) over the individuals with variance s_v*s_v

and e_(it) are iid over the whole sample with variance s_e*s_e.

The v_i and the e_(it) are assumed to be independent for each i over all t.

First differencing the above equation removes the v_i and produces an equation that can be estimated using instrumental variables. Arellano and Bond derive a generalized method-of-moments estimator for a_1,...,a_p, b_1, and b_2 using lagged levels of the dependent variable and the predetermined variables and differences of the strictly exogenous variables. xtabond implements this estimator, known as the Arellano-Bond dynamic panel-data estimator. This method assumes that there is no second-order autocorrelation in the e_(it). xtabond includes the test for autocorrelation and the Sargan test of over-identifying restrictions for this model.

Options

+-------+ ----+ Model +-------------------------------------------------------------

noconstant; see estimation options.

diffvars(varlist) specifies a set of variables that already have been differenced to be included as strictly exogenous covariates.

inst(varlist) specifies a set of variables to be used as additional instruments. These instruments are not differenced by xtabond before including them into the instrument matrix.

lags(#) sets p, the number of lags of the dependent variable to be included in the model. The default is p=1.

maxldep(#) sets the maximum number of lags of the dependent variable that can be used as instruments. The default is to use all T_i-p-2 lags.

maxlags(#) sets the maximum number of lags of the predetermined variables that can be used as instruments. The default is to use all T_i-p-2 lags of the dependent variable. If the predetermined variables are endogenous, the default is to use all T_i-p-2 lags of these endogenous variables. If the predetermined variables are not endogenous, the default is to use all T_i-p-1 lags of these variables.

twostep specifies that the two-step estimator be calculated.

+-----------------------------------+ ----+ Predetermined, More predetermined +---------------------------------

pre(varlist [, lagstruct(prelags, premaxlags) endogenous]) specifies that a set of predetermined variables be included in the model. Optionally, one may specify that prelags lags of the specified variables also be included. The default for prelags is 0. Specifying premaxlags sets the maximum number of further lags of the predetermined variables that can be used as instruments. Additionally, if you specify endogenous, xtabond treats these variables as endogenous instead of predetermined. The default is to include T_i-prelags-1 lagged levels as instruments for predetermined variables and T_i-prelags-2 lagged levels as instruments for endogenous variables. You may specify as many sets of predetermined variables as you need within the standard Stata limits on matrix size. Each set of predetermined variables may have its own number of prelags and premaxlags.

+-----------+ ----+ SE/Robust +---------------------------------------------------------

vce(vcetype); see vce_option.

robust; see estimation options. robust may not be specified with twostep.

+-----------+ ----+ Reporting +---------------------------------------------------------

level(#); see estimation options.

small specifies that t statistics be reported instead of Z statistics and that F statistics instead of chi-squared statistics.

artests(#) specifies the maximum order of the autocorrelation test to be calculated and reported. The maximum order must be less than or equal to p+1. The default is 2.

Examples

. xtabond n l(0/1).w l(0/2).(k ys) yr1980-yr1984, lags(2)

. xtabond n l(0/1).w l(0/2).(k ys) yr1980-yr1984, lags(2) twostep pre(w, lag(1,.)) pre(k,lag(2,.))

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Hope to be of help