[U] User's Guide

366 [ U ] 26 Overview of Stata estimation commandsStata provides estimators for regression models with autoregressive conditional heteroskedastic(ARCH) disturbancesy t = x t β + µ twhere µ t is distributed N(0, σ 2 t ) and σ 2 tis given by some function of the lagged disturbances.Stata’s arch command provides different parameterizations of the conditional heteroskedasticity,and it also allows ARMA disturbances and/or multiplicative heteroskedasticity.For multivariate data with autoregressive conditional heteroskedasticity, the dvech command fits thediagonal vech model, allowing for multivariate ARCH and GARCH relationships among the variables.Stata provides var and svar for fitting vector autoregressive (VAR) and structural vector autoregressive(SVAR) models. See [TS] var for information on Stata’s suite of commands for forecasting,specification testing, and inference on VAR and SVAR models. Stata also provides vec for fitting vectorerror-correction models; see [TS] vec. See [TS] irf for information on Stata’s suite of commandsfor estimating, analyzing, and presenting impulse–response functions and forecast error variancedecompositions. There is also a set of commands for performing Granger causality tests, lag-orderselection, and residual analysis.sspace estimates the parameters of multivariate state-space models using the Kalman filter. Thestate-space representation of time-series models is extremely flexible and can be used to estimatethe parameters of many different models, including vector autoregressive moving-average (VARMA)models, dynamic-factor (DF) models, and structural time-series (STS) models. It can also solve somestochastic dynamic-programming problems.dfactor estimates the parameters of dynamic-factor models. These flexible models for multivariatetime series provide for a vector-autoregressive structure in both observed outcomes and in unobservedfactors. They also allow exogenous covariates for observed outcomes or unobserved factors.26.15 Panel-data models26.15.1 Linear regression with panel dataThis section could just as well be called “linear regression with complex error structures”. Commandsin this class begin with the letters xt.xtreg fits models of the formy it = x it β + ν i + ɛ itxtreg can produce the between-regression estimator, the within-regression (fixed effects) estimator,or the GLS random-effects (matrix-weighted average of between and within results) estimator. It canalso produce the maximum-likelihood random-effects estimator.xtregar can produce the within estimator and a GLS random-effects estimator when the ɛ it areassumed to follow an AR(1) process.xtivreg contains the between-2SLS estimator, the within-2SLS estimator, the first-differenced-2SLSestimator, and two GLS random-effects-2SLS estimators to handle cases in which some of the covariatesare endogenous.xtmixed is a generalization of xtreg that allows for multiple levels of panels, random coefficients,and variance-component estimation in general. In the xtmixed framework, residuals (random effects)can occur anywhere and have any level of subscript.