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help for xtlsdvc (SJ5-4: st0091)
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Bias corrected LSDV dynamic panel data estimator
xtlsdvc depvar [indepvars] [if], initial(estimator) [level(#) bias(#) vcov(#) first lsdv]
where estimator is
ah Anderson-Hsiao
ab Arellano-Bond
bb Blundell-Bond
my initial values supplied by the user
xtlsdvc is for use with time-series data. You must tsset your data before using xtlsdvc; see tsset.
However, since xtlsdvc calls xtreg, indepvars may not contain time-series operators; see xtreg.
xtlsdvc shares the features of all estimation commands; see estcom.
The syntax of predict following xtlsdvc is
predict [type] newvarname [if] [in] [, statistic]
where y[i,t] = y[i,t-1]a + x[i,t]b + u + e[i,t] and statistic is
xb y[i,t-1]a + x[i,t]b, fitted values; the default
ue u + e[i,t], the combined residual
(*) xbu y[i,t-1]a + x[i,t]b + u, prediction, including fixed effect
(*) u u, the fixed effect
(*) e e[i,t], the observation-specific error component
Unstarred statistics are available both in and out of sample; type predict ... if e(sample) ... if wanted
only for the estimation sample. Starred statistics are calculated only for the estimation sample, even when
if e(sample) is not specified.
Description
xtlsdvc calculates bias-corrected least-squares dummy variable (LSDV) estimators for the standard
autoregressive panel-data model using the bias approximations in Bruno (2005a), who extends the results by
Bun and Kiviet (2003), Kiviet (1999), and Kiviet (1995) to unbalanced panels
x[i,t] is a (1 X (k-1)) vector of strictly exogenous covariates
b is a ((k-1) X 1) vector of parameters to be estimated
u are the individual effects, for which no distributional assumption is made apart being fixed over time,
and e[i,t] are iid over the whole sample with variance s_e*s_e.
It is also assumed that the u and the e[i,t] are independent for each i over all t.
A more detailed description of xtlsdvc can be found in Bruno (2005b).
Options
initial(estimator) is required and specifies the consistent estimator chosen to initialize the bias
correction.
estimator description
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ah AH estimator, with the dependent variable lagged two times, used as an instrument for the
first-differenced model with no intercept (ivreg)
ab standard one-step AB estimator with no intercept (xtabond)
bb standard BB estimator with no intercept, as implemented by the user-written Stata routine
xtabond2 by Roodman (2003)
my a row vector of initial values supplied directly by the user
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To implement the last instance of this option, the user must create a {1 x (k+1)} matrix to be named my,
the i element of which serves as an initial value for the coefficient on the i variable in varlist and
the last, (k+1), element as an estimate for the error variance. This may be useful in Monte Carlo
simulations or if the user wishes to try initial estimators other than ah, ab, or bb.
level(#) specifies the confidence level, as a percentage, for confidence intervals of the coefficients. The
default is level(95) or as set by set level.
bias(#) determines the accuracy of the approximation: #=1 (default) forces an approximation up to O(1/T);
#=2 forces and approximation up to O(1/NT); #=3 forces an approximation up to O(N^{-1}T^{-2}).
vcov(#) calculates a bootstrap variance-covariance matrix for LSDVC using # repetitions (# may not equal 1).
Normality for errors is assumed. This procedure continues to work also in the presence of gaps in the
exogenous variables, although in this case, bootstrap samples for each unit are truncated to the first
missing value encountered. Gaps in the dependent variable, instead, bear no consequence to the bootstrap
sample size.
first requests that the first-stage regression results be displayed.
lsdv requests that the original LSDV regression results be displayed.
Options for predict
xb calculates the linear prediction; that is, y[i,t-1]a + x[i,t]b. This is the default.
ue calculates the prediction of u + e[i,t].
xbu calculates the prediction of y[i,t-1]a + x[i,t]b + u, the prediction including the fixed component.
u calculates the prediction of u, the estimated fixed effect.
e calculates the prediction of e[i,t].
Remarks
xtlsdvc does not report analytical standard errors. Only bootstrap standard errors are reported, provided
that vcov(#) is given.
Bootstrap standard errors are downward biased when values for the unknown parameters are supplied through
the matrix my, since the procedure, keeping my fixed over replications, neglects a source of variability of
the bias-corrected LSDV estimator.
Saved results
xtlsdvc saves in e():
Scalars
e(N) number of observations
e(Tbar) average number of time periods
e(sigma) estimates of sigma through the within
residuals from the first-stage regression
e(N_g) number of groups
Macros
e(cmd) xtlsdvc
e(ivar) panel variable
e(depvar) name of dependent variable
e(predict) program used to implement predict
Matrices
e(b) xtlsdvc estimate
e(b_lsdv) coefficient vector of the uncorrected LSDV
e(V_lsdv) variance-covariance matrix of the uncorrected LSDV
e(V) variance-covariance matrix of the estimators
Functions
e(sample) marks estimation sample
Examples
. xtlsdvc n w k ys yr1980-yr1984, initial(ah)
. xtlsdvc n w k ys yr1980-yr1984, initial(ab) bias(3)
. xtlsdvc n w k ys yr1980-yr1984, initial(ab) bias(3) vcov(50)
References
Bruno, G. S. F. 2005a. Approximating the bias of the LSDV estimator for dynamic unbalanced panel data
models. Economics Letters 87: 361-366.
------. 2005b. Estimation and inference in dynamic unbalanced panel data models with a small number of
individuals. CESPRI WP n.165. Universit?Bocconi-CESPRI, Milan.
Bun, M. J. G. and J. F. Kiviet. 2003. On the diminishing returns of higher order terms in asymptotic
expansions of bias. Economics Letters 79: 145-152.
Kiviet, J. F. 1995. On bias, inconsistency, and efficiency of various estimators in dynamic panel data
models. Journal of Econometrics 68: 53-78.
------. 1999. Expectation of expansions for estimators in a dynamic panel data model; some results for
weakly exogenous Regressors. In Analysis of Panel Data and Limited Dependent Variables, ed. c. Hsiao,
K. Lahiri, L.-F. Lee, and M. H. Pesaran, 199-225. Cambridge: Cambridge University Press.
Roodman, D. M. 2003. XTABOND2: Stata module to extend xtabond dynamic panel-data estimator. Statistical
Software Components S435901, Boston College Department of Economics.
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