Stata 15 help for xtregar

[XT] xtregar -- Fixed- and random-effects linear models with an AR(1) disturbance

Syntax

GLS random-effects (RE) model

xtregar depvar [indepvars] [if] [in] [, re options]

Fixed-effects (FE) model

xtregar depvar [indepvars] [if] [in] [weight] , fe [options]

options Description ------------------------------------------------------------------------- Model re use random-effects estimator; the default fe use fixed-effects estimator rhotype(rhomethod) specify method to compute autocorrelation; seldom used rhof(#) use # for p and do not estimate p twostep perform two-step estimate of correlation

Reporting level(#) set confidence level; default is level(95) lbi perform Baltagi-Wu LBI test display_options control columns and column formats, row spacing, line width, display of omitted variables and base and empty cells, and factor-variable labeling

coeflegend display legend instead of statistics ------------------------------------------------------------------------- A panel variable and a time variable must be specified; use xtset. indepvars may contain factor variables; see fvvarlist. depvar and indepvars may contain time-series operators; see tsvarlist. by and statsby are allowed; see prefix. fweights and aweights are allowed for the fixed-effects model with rhotype(regress) or rhotype(freg), or with a fixed rho; see weight. Weights must be constant within panel. coeflegend does not appear in the dialog box. See [XT] xtregar postestimation for features available after estimation.

Menu

Statistics > Longitudinal/panel data > Linear models > Linear regression with AR(1) disturbance (FE, RE)

Description

xtregar fits cross-sectional time-series regression models when the disturbance term is first-order autoregressive. xtregar offers a within estimator for fixed-effects models and a GLS estimator for random-effects models. xtregar can accommodate unbalanced panels whose observations are unequally spaced over time.

Options

re requests the GLS estimator of the random-effects model, which is the default.

fe requests the within estimator of the fixed-effects model.

rhotype(rhomethod) allows the user to specify any of the following estimators of rho:

dw rho_dw = 1 - d/2, where d is the Durbin-Watson d statistic regress rho_reg = B from the residual regression e_t = B*e_(t-1) freg rho_freg = B from the residual regression e_t = B*e_(t+1) tscorr rho_tscorr = e'e_(t-1)/e'e, where e is the vector of residuals and e_(t-1) is the vector of lagged residuals theil rho_theil = rho_tscorr * (N-k)/N nagar rho_nagar = (rho_dw * N*N+k*k)/(N*N-k*k) onestep rho_onestep = (n/m_c)*rho_tscorr, where n is the number of observations and m_c is the number of consecutive pairs of residuals

dw is the default method. Except for onestep, the details of these methods are given in [TS] prais. prais handles unequally spaced data. onestep is the one-step method proposed by Baltagi and Wu (1999). More details on this method are available in Methods and formulas of [XT] xtregar.

rhof(#) specifies that the given number be used for rho and that rho not be estimated.

twostep requests that a two-step implementation of the rhomethod estimator of rho be used. Unless a fixed value of rho is specified (with the rhof() option), rho is estimated by running prais on the de-meaned data. When twostep is specified, prais will stop on the first iteration after the equation is transformed by rho -- the two-step efficient estimator. Although it is customary to iterate these estimators to convergence, they are efficient at each step. When twostep is not specified, the FGLS process iterates to convergence as described in the Methods and formulas of [TS] prais.

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

level(#); see [R] estimation options.

lbi requests that the Baltagi-Wu (1999) locally best invariant (LBI) test statistic that rho = 0 and a modified version of the Bhargava, Franzini, and Narendranathan (1982) Durbin-Watson statistic be calculated and reported. The default is not to report them. p-values are not reported for either statistic. Although Bhargava, Franzini, and Narendranathan (1982) published critical values for their statistic, no tables are currently available for the Baltagi-Wu LBI. Baltagi and Wu (1999) derive a normalized version of their statistic, but this statistic cannot be computed for datasets of moderate size. You can also specify these options upon reply.

display_options: noci, nopvalues, noomitted, vsquish, noemptycells, baselevels, allbaselevels, nofvlabel, fvwrap(#), fvwrapon(style), cformat(%fmt), pformat(%fmt), sformat(%fmt), and nolstretch; see [R] estimation options.

The following option is available with xtregar but is not shown in the dialog box:

coeflegend; see [R] estimation options.

Examples

Setup . webuse grunfeld . xtset company time

Random-effects model . xtregar invest mvalue kstock

Fixed-effects model . xtregar invest mvalue kstock, fe

Random-effects model and report Baltagi-Wu LBI test . xtregar invest mvalue kstock, re lbi

Fixed-effects model and perform two-step estimate of correlation . xtregar invest mvalue kstock, fe twostep

Stored results

xtregar, re stores the following in e():

Scalars e(N) number of observations e(N_g) number of groups e(df_m) model degrees of freedom e(g_min) smallest group size e(g_avg) average group size e(g_max) largest group size e(d1) Bhargava et al. Durbin-Watson e(LBI) Baltagi-Wu LBI statistic e(N_LBI) number of obs used in e(LBI) e(Tcon) 1 if T is constant e(sigma_u) panel-level standard deviation e(sigma_e) standard deviation of z_it e(r2_w) R-squared within model e(r2_o) R-squared overall model e(r2_b) R-squared between model e(chi2) chi-squared e(rho_ar) autocorrelation coefficient e(rho_fov) u_i fraction of variance e(thta_min) minimum theta e(thta_5) theta, 5th percentile e(thta_50) theta, 50th percentile e(thta_95) theta, 95th percentile e(thta_max) maximum theta e(Tbar) harmonic mean of group sizes e(rank) rank of e(V)

Macros e(cmd) xtregar e(cmdline) command as typed e(depvar) name of dependent variable e(ivar) variable denoting groups e(tvar) variable denoting time within groups e(model) re e(rhotype) method of estimating rho_ar e(dw) lbi, if lbi specified e(chi2type) Wald; type of model chi-squared test e(properties) b V e(predict) program used to implement predict e(marginsok) predictions allowed by margins e(marginsnotok) predictions disallowed by margins e(asbalanced) factor variables fvset as asbalanced e(asobserved) factor variables fvset as asobserved

Matrices e(b) coefficient vector e(V) VCE for random-effects model

Functions e(sample) marks estimation sample

xtregar, fe stores the following in e():

Scalars e(N) number of observations e(N_g) number of groups e(df_m) model degrees of freedom e(mss) model sum of squares e(rss) residual sum of squares e(g_min) smallest group size e(g_avg) average group size e(g_max) largest group size e(d1) Bhargava et al. Durbin-Watson e(LBI) Baltagi-Wu LBI statistic e(N_LBI) number of obs used in e(LBI) e(Tcon) 1 if T is constant e(corr) corr(u_i, Xb) e(sigma_u) panel-level standard deviation e(sigma_e) standard deviation of epsilon_it e(r2_a) adjusted R-squared e(r2_w) R-squared within model e(r2_o) R-squared overall model e(r2_b) R-squared between model e(ll) log likelihood e(ll_0) log likelihood, constant-only model e(rho_ar) autocorrelation coefficient e(rho_fov) u_i fraction of variance e(F) F statistic e(F_f) F for u_i=0 e(df_r) residual degrees of freedom e(df_a) degrees of freedom for absorbed effect e(df_b) numerator degrees of freedom for F statistic e(rmse) root mean squared error e(Tbar) harmonic mean of group sizes e(rank) rank of e(V)

Macros e(cmd) xtregar e(cmdline) command as typed e(depvar) name of dependent variable e(ivar) variable denoting groups e(tvar) variable denoting time within groups e(wtype) weight type e(wexp) weight expression e(model) fe e(rhotype) method of estimating rho_ar e(dw) lbi, if lbi specified e(properties) b V e(predict) program used to implement predict e(marginsok) predictions allowed by margins e(marginsnotok) predictions disallowed by margins e(asbalanced) factor variables fvset as asbalanced e(asobserved) factor variables fvset as asobserved

Matrices e(b) coefficient vector e(V) variance-covariance matrix of the estimators

Functions e(sample) marks estimation sample

References

Baltagi, B. H., and P. X. Wu. 1999. Unequally spaced panel data regressions with AR(1) disturbances. Econometric Theory 15: 814-823.

Bhargava, A., L. Franzini, and W. Narendranathan. 1982. Serial correlation and the fixed effects model. Review of Economic Studies 49: 533-549.


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