Stata 15 help for vec

[TS] vec -- Vector error-correction models

Syntax

vec depvarlist [if] [in] [, options]

options Description ------------------------------------------------------------------------- Model rank(#) use # cointegrating equations; default is rank(1) lags(#) use # for the maximum lag in underlying VAR model trend(constant) include an unrestricted constant in model; the default trend(rconstant) include a restricted constant in model trend(trend) include a linear trend in the cointegrating equations and a quadratic trend in the undifferenced data trend(rtrend) include a restricted trend in model trend(none) do not include a trend or a constant bconstraints(constraints_bc) place constraints_bc on cointegrating vectors aconstraints(constraints_ac) place constraints_ac on adjustment parameters

Adv. model sindicators(varlist_si) include normalized seasonal indicator variables varlist_si noreduce do not perform checks and corrections for collinearity among lags of dependent variables

Reporting level(#) set confidence level; default is level(95) nobtable do not report parameters in the cointegrating equations noidtest do not report the likelihood-ratio test of overidentifying restrictions

alpha report adjustment parameters in separate table pi report parameters in Pi=(alpha)(beta)' noptable do not report elements of Pi matrix mai report parameters in the moving-average impact matrix noetable do not report adjustment and short-run parameters dforce force reporting of short-run, beta, and alpha parameters when the parameters in beta are not identified; advanced option nocnsreport do not display constraints display_options control columns and column formats, row spacing, and line width

Maximization maximize_options control the maximization process; seldom used

coeflegend display legend instead of statistics ------------------------------------------------------------------------- vec does not allow gaps in the data. You must tsset your data before using vec; see [TS] tsset. varlist must contain at least two variables and may contain time-series operators; see tsvarlist. by, fp, rolling, statsby, and xi are allowed; see prefix. coeflegend does not appear in the dialog box. See [TS] vec postestimation for features available after estimation.

Menu

Statistics > Multivariate time series > Vector error-correction model (VECM)

Description

vec fits a type of vector autoregression in which some of the variables are cointegrated by using Johansen's (1995) maximum likelihood method. Constraints may be placed on the parameters in the cointegrating equations or on the adjustment terms. See [TS] vec intro for a list of commands that are used in conjunction with vec.

Options

+-------+ ----+ Model +------------------------------------------------------------

rank(#) specifies the number of cointegrating equations; rank(1) is the default.

lags(#) specifies the maximum lag to be included in the underlying VAR model. The maximum lag in a VECM is one smaller than the maximum lag in the corresponding VAR in levels; the number of lags must be greater than zero but small enough so that the degrees of freedom used up by the model are fewer than the number of observations. The default is lags(2).

trend(trend_spec) specifies which of Johansen's five trend specifications to include in the model. These specifications are discussed in Specification of constants and trends of [TS] vec. The default is trend(constant).

bconstraints(constraints_bc) specifies the constraints to be placed on the parameters of the cointegrating equations. When no constraints are placed on the adjustment parameters -- that is, when the aconstraints() option is not specified -- the default is to place the constraints defined by Johansen's normalization on the parameters of the cointegrating equations. When constraints are placed on the adjustment parameters, the default is not to place constraints on the parameters in the cointegrating equations.

aconstraints(constraints_ac) specifies the constraints to be placed on the adjustment parameters. By default, no constraints are placed on the adjustment parameters.

+------------+ ----+ Adv. model +-------------------------------------------------------

sindicators(varlist_si) specifies the normalized seasonal indicator variables to include in the model. The indicator variables specified in this option must be normalized as discussed in Johansen (1995). If the indicators are not properly normalized, the estimator of the cointegrating vector does not converge to the asymptotic distribution derived by Johansen (1995). More details about how these variables are handled are provided in Methods and formulas of [TS] vec. sindicators() cannot be specified with trend(none) or with trend(rconstant).

noreduce causes vec to skip the checks and corrections for collinearity among the lags of the dependent variables. By default, vec checks to see whether the current lag specification causes some of the regressions performed by vec to contain perfectly collinear variables; if so, it reduces the maximum lag until the perfect collinearity is removed.

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

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

nobtable suppresses the estimation table for the parameters in the cointegrating equations. By default, vec displays the estimation table for the parameters in the cointegrating equations.

noidtest suppresses the likelihood-ratio test of the overidentifying restrictions, which is reported by default when the model is overidentified.

alpha displays a separate estimation table for the adjustment parameters, which is not displayed by default.

pi displays a separate estimation table for the parameters in Pi=(alpha)(beta)', which is not displayed by default.

noptable suppresses the estimation table for the elements of the Pi matrix, which is displayed by default when the parameters in the cointegrating equations are not identified.

mai displays a separate estimation table for the parameters in the moving-average impact matrix, which is not displayed by default.

noetable suppresses the main estimation table that contains information about the estimated adjustment parameters and the short-run parameters, which is displayed by default.

dforce displays the estimation tables for the short-run parameters and alpha and beta -- if the last two are requested -- when the parameters in beta are not identified. By default, when the specified constraints do not identify the parameters in the cointegrating equations, estimation tables are displayed only for Pi and the MAI.

nocnsreport; see [R] estimation options.

display_options: noci, nopvalues, vsquish, cformat(%fmt), pformat(%fmt), sformat(%fmt), and nolstretch; see [R] estimation options.

+--------------+ ----+ Maximization +-----------------------------------------------------

maximize_options: iterate(#), nolog, trace, toltrace, tolerance(#), ltolerance(#), afrom(matrix_a), and bfrom(matrix_b); see [R] maximize.

toltrace displays the relative differences for the log likelihood and the coefficient vector at every iteration. This option cannot be specified if no constraints are defined or if nolog is specified.

afrom(matrix_a) specifies a 1 x (K*r) row vector with starting values for the adjustment parameters, where K is the number of endogenous variables and r is the number of cointegrating equations specified in the rank() option. The starting values should be ordered as they are reported in e(alpha). This option cannot be specified if no constraints are defined.

bfrom(matrix_b) specifies a 1 x (m1*r) row vector with starting values for the parameters of the cointegrating equations, where m1 is the number of variables in the trend-augmented system and r is the number of cointegrating equations specified in the rank() option. (See Methods and formulas in [TS] vec for more details about m1.) The starting values should be ordered as they are reported in e(betavec). For some trend specifications, e(beta) contains parameter estimates that are not obtained directly from the optimization algorithm. bfrom() should specify only starting values for the parameters reported in e(betavec). This option cannot be specified if no constraints are defined.

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

coeflegend; see [R] estimation options.

Examples

--------------------------------------------------------------------------- Setup . webuse rdinc

Fit a vector error-correction model (VECM), assuming quadratic trends in variables and one trend-stationary cointegrating equation . vec ln_ne ln_se

Fit a VECM by using 3 lags . vec ln_ne ln_se, lags(3)

Fit a VECM, assuming all means and trends are zero . vec ln_ne ln_se, trend(none)

Fit a VECM and report adjustment parameters in separate table . vec ln_ne ln_se, alpha

--------------------------------------------------------------------------- Setup . webuse urates

Fit a VECM, including a restricted constant (no linear trends in the variables) in the model, including 2 cointegrating equations, and using 4 lags . vec missouri indiana kentucky illinois, trend(rconstant) rank(2) lags(4)

Replay results and do not report parameters in the cointegrating equations . vec, nobtable ---------------------------------------------------------------------------

Stored results

vec stores the following in e():

Scalars e(N) number of observations e(k_rank) number of unconstrained parameters e(k_eq) number of equations in e(b) e(k_dv) number of dependent variables e(k_ce) number of cointegrating equations e(n_lags) number of lags e(df_m) model degrees of freedom e(ll) log likelihood e(chi2_res) value of test of overidentifying restrictions e(df_lr) degrees of freedom of the test of overidentifying restrictions e(beta_iden) 1 if the parameters in beta are identified and 0 otherwise e(beta_icnt) number of independent restrictions placed on beta e(k_#) number of variables in equation # e(df_m#) model degrees of freedom in equation # e(r2_#) R-squared of equation # e(chi2_#) chi-squared statistic for equation # e(rmse_#) RMSE of equation # e(aic) value of AIC e(hqic) value of HQIC e(sbic) value of SBIC e(tmin) minimum time e(tmax) maximum time e(detsig_ml) determinant of the estimated covariance matrix e(rank) rank of e(V) e(converge) 1 if switching algorithm converged, 0 if it did not converge

Macros e(cmd) vec e(cmdline) command as typed e(trend) trend specified e(tsfmt) format of the time variable e(tvar) variable denoting time within groups e(endog) endogenous variables e(covariates) list of covariates e(eqnames) equation names e(cenames) names of cointegrating equations e(reduce_opt) noreduce, if noreduce is specified e(reduce_lags) list of maximum lags to which the model has been reduced e(title) title in estimation output e(aconstraints) constraints placed on alpha e(bconstraints) constraints placed on beta e(sindicators) seasonal indicator variables e(properties) b V e(predict) program used to implement predict e(marginsok) predictions allowed by margins e(marginsnotok) predictions disallowed by margins e(marginsdefault) default predict() specification for margins

Matrices e(b) estimates of short-run parameters e(V) VCE of short-run parameter estimates e(beta) estimates of beta e(V_beta) VCE of beta hat e(betavec) directly obtained estimates of beta e(pi) estimates of pi hat e(V_pi) VCE of pi hat e(alpha) estimates of alpha e(V_alpha) VCE of alpha hat e(omega) estimates of omega hat e(mai) estimates of mai e(V_mai) VCE of mai hat

Functions e(sample) marks estimation sample

Reference

Johansen, S. 1995. Likelihood-Based Inference in Cointegrated Vector Autoregressive Models. Oxford: Oxford University Press.


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