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help for xtlsdvc
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 Bias corrected LSDV dynamic panel data estimator

xtlsdvc depvar [varlist] [if exp] , initial(estimator) [level(#) bias(#) lsdv first vcov(#)]

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 help tsset. However, since xtlsdvc calls xtreg varlists may not contain time-series operators; see help xtreg.

xtlsdvc shares the features of all estimation commands; see help estcom.

The syntax of predict following xtlsdvc is

predict [type] newvarname [if exp] [in range] [, statistic ]

where y[i,t] = y[i,t-1]a + x[i,t]b + u[i] + e[i,t] and statistic is

xb y[i,t-1]a + x[i,t]b, fitted values; the default ue u[i] + e[i,t], the combined residual (*) xbu y[i,t-1]a + x[i,t]b + u[i], prediction including fixed effect (*) u u[i], the fixed effect (*) e e[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

xtlsdvc calculates 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 panels

y[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 xtlsdvc can 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)) matrix my, the i.th element of which serves as an initial value for the coefficient on the i.th variable in varlist, 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 than ah, ab or bb.

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).

first requests that the first-stage regression results be displayed.

lsdv requests 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 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[i] + e[i,t].

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

u calculates the prediction of u[i], 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 varibility of the bias-corrected LSDV estimator.

xtlsdvc saves the following results in e():

Scalars e(N) Number of observations e(Tbar) Average number of time periods e(sigma) Estimate of s_e through the within residuals from the first stage regression e(N_g) Number of groups

Macros e(cmd) xtlsdvc e(depvar) Name of dependent variable e(ivar) Panel variable e(predict) Program used to implement predict

Matrices e(b) Coefficient vector e(V) Variance-covariance matrix of the estimators e(b_lsdv) Coefficient vector of the uncorrected LSDV e(V_lsdv) Variance-covariance matrix of the uncorrected LSDV

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.

Bruno, G.S.F. 2005b. Estimation and inference in dynamic unbalanced panel data models with a small number of individuals. CESPRI WP n.165 , UniversitÓ 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 of Panel Data and Limited Dependent Variables. Cambridge University Press, Cambridge.

Author

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

Also see

Manual: [U] 23 Estimation and post-estimation commands, [U] 29 Overview of Stata estimation commands, [XT] xtabond [XT] xtivreg [R] ivreg

Online: help for estcom, ivreg, postest, xtabond, xtdes, xtivreg, xtreg,