------------------------------------------------------------------------------- help forxtlsdvc-------------------------------------------------------------------------------Bias corrected LSDV dynamic panel data estimator

xtlsdvcdepvar[varlist] [ifexp],initial(estimator)[level(#)bias(#)lsdvfirstvcov(#)]where

estimatoris

ahAnderson-HsiaoabArellano-BondbbBlundell-Bondmyinitial values supplied by the user

xtlsdvcis for use with time-series data. You musttssetyour data before usingxtlsdvc; see help tsset. However, sincextlsdvccallsxtregvarlists may not contain time-series operators; see help xtreg.

xtlsdvcshares the features of all estimation commands; see help estcom.

The syntax of predict following

xtlsdvcis

predict[type]newvarname[ifexp] [inrange] [,statistic]where y[i,t] = y[i,t-1]a + x[i,t]b + u[i] + e[i,t] and

statisticis

xby[i,t-1]a + x[i,t]b, fitted values; the defaultueu[i] + e[i,t], the combined residual (*)xbuy[i,t-1]a + x[i,t]b + u[i], prediction including fixed effect (*)uu[i], the fixed effect (*)ee[i,t]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

xtlsdvccalculates bias corrected 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 panelsy[i,t] = y[i,t-1]a + x[i,t]b + u[i] + e[i,t] i={1,...,N}; t={1,...,T_i},

where

a is a parameter to be estimated

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[i] 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[i] and the e[i,t] are independent for each i over all t.

A more detailed description of

xtlsdvccan be found in Bruno (2005b).

Options

level(#)specifies the confidence level, in percent, for confidence intervals of the coefficients; see help level.

initial(estimator)specifies which consistent estimator among Anderson-Hsiao (ah), Arellano-Bond (ab) and Blundell-Bond (bb) is to initialize the bias correction. In alternative, users may want to supply their own values, which can be done by creating beforehand the (1 X (k+1)) matrixmy, the i.th element of which serves as an initial value for the coefficient on the i.th variable invarlist, i=1,...,k and the last element as an estimate for the error variance. This may be useful in Monte Carlo simulations or when the user wants to try initial estimators other thanah,aborbb.

bias(#)determines the accuracy of the approximation: up to O(1/T) (1); up to O(1/NT) (2); up to O(1/NT^2) (3).

firstrequests that the first-stage regression results be displayed.

lsdvrequests that the lsdv regression results be displayed.

vcov(#)calculates a bootstrap variance-covariance matrix for LSDVC using#repetitions. 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.

Options forpredict

xbcalculates the linear prediction; that is, y[i,t-1]a + x[i,t]b. This is the default.

uecalculates the prediction of u[i] + e[i,t].

xbucalculates the prediction of y[i,t-1]a + x[i,t]b + u[i], the prediction including the fixed component.

ucalculates the prediction of u[i], the estimated fixed effect.

ecalculates the prediction of e[i,t].

Remarks

xtlsdvcdoes not report analytical standard errors. Only bootstrap standard errors are reported, provided thatvcov(#)is given.Bootstrap standard errors are downward biased when values for the unknown parameters are supplied through the matrix

my, since the procedure, keepingmyfixed over replications, neglects a source of varibility of the bias-corrected LSDV estimator.

xtlsdvcsaves the following results ine():Scalars

e(N)Number of observationse(Tbar)Average number of time periodse(sigma)Estimate of s_e through the within residuals from the first stage regressione(N_g)Number of groupsMacros

e(cmd)xtlsdvce(depvar)Name of dependent variablee(ivar)Panel variablee(predict)Program used to implement predictMatrices

e(b)Coefficient vectore(V)Variance-covariance matrix of the estimatorse(b_lsdv)Coefficient vector of the uncorrected LSDVe(V_lsdv)Variance-covariance matrix of the uncorrected LSDVFunctions

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)

ReferencesBruno, G.S.F. 2005a. Approximating the bias of the LSDV estimator for dynamic unbalanced panel data models.

Economics Letters,87, 361-366.Bruno, G.S.F. 2005b. Estimation and inference in dynamic unbalanced panel data models with a small number of individuals.

CESPRI WPn.165, Università Bocconi-CESPRI, Milan.Bun, M.J.G., Kiviet, J.F., 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.Kiviet, J.F., 1999. Expectation of Expansions for Estimators in a Dynamic Panel Data Model; Some Results for Weakly Exogenous Regressors. In: Hsiao, C., Lahiri, K., Lee, L.-F., Pesaran, M.H. (Eds.),

Analysis ofPanel Data and Limited Dependent Variables.Cambridge University Press, Cambridge.

AuthorGiovanni S.F. Bruno Istituto di Economia Politica, Università Bocconi Milan, Italy giovanni.bruno@unibocconi.it

Also seeManual:

[U] 23 Estimation and post-estimation commands,[U] 29 Overview of Stata estimation commands,[XT] xtabond[XT] xtivreg[R] ivregOnline: help for estcom, ivreg, postest, xtabond, xtdes, xtivreg, xtreg,