Stata 15 help for sureg

[R] sureg -- Zellner's seemingly unrelated regression


Basic syntax

sureg (depvar1 varlist1) (depvar2 varlist2) ... (depvarN varlistN) [ if] [in] [weight]

Full syntax

sureg ([eqname1:] depvar1a [depvar1b ... =] varlist1 [, noconstant]) ([eqname2:] depvar2a [depvar2b ... =] varlist2 [, noconstant]) ... ([eqnameN:] depvarNa [depvarNb ... =] varlistN [, noconstant]) [if] [in] [weight] [, options]

Explicit equation naming (eqname:) cannot be combined with multiple dependent variables in an equation specification.

options Description ------------------------------------------------------------------------- Model isure iterate until estimates converge constraints(constraints) apply specified linear constraints

df adj. small report small-sample statistics dfk use small-sample adjustment dfk2 use alternate adjustment

Reporting level(#) set confidence level; default is level(95) corr perform Breusch-Pagan test nocnsreport do not display constraints display_options control columns and column formats, row spacing, line width, display of omitted variables and base and empty cells, and factor-variable labeling

Optimization optimization_options control the optimization process; seldom used

noheader suppress header table from above coefficient table notable suppress coefficient table coeflegend display legend instead of statistics ------------------------------------------------------------------------- varlist1, ..., varlistN may contain factor variables; see fvvarlist. You must have the same levels of factor variables in all equations that have factor variables. depvar and the varlists may contain time-series operators; see tsvarlist. bootstrap, by, fp, jackknife, rolling, and statsby are allowed; see prefix. Weights are not allowed with the bootstrap prefix. aweights are not allowed with the jackknife prefix. aweights and fweights are allowed, see weight. noheader, notable, and coeflegend do not appear in the dialog box. See [R] sureg postestimation for features available after estimation.


Statistics > Linear models and related > Multiple-equation models > Seemingly unrelated regression


sureg fits seemingly unrelated regression models (Zellner 1962; Zellner and Huang 1962; Zellner 1963). The acronyms SURE and SUR are often used for the estimator.


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

isure specifies that sureg iterate over the estimated disturbance covariance matrix and parameter estimates until the parameter estimates converge. Under seemingly unrelated regression, this iteration converges to the maximum likelihood results. If this option is not specified, sureg produces two-step estimates.

constraints(constraints); see [R] estimation options.

+---------+ ----+ df adj. +----------------------------------------------------------

small specifies that small-sample statistics be computed. It shifts the test statistics from chi-squared and z statistics to F statistics and t statistics. Although the standard errors from each equation are computed using the degrees of freedom for the equation, the degrees of freedom for the t statistics are all taken to be those for the first equation.

dfk specifies the use of an alternative divisor in computing the covariance matrix for the equation residuals. As an asymptotically justified estimator, sureg by default uses the number of sample observations (n) as a divisor. When the dfk option is set, a small-sample adjustment is made and the divisor is taken to be sqrt((n - k_i) * (n - k_j)), where k_i and k_j are the number of parameters in equations i and j, respectively.

dfk2 specifies the use of an alternative divisor in computing the covariance matrix for the equation residuals. When the dfk2 option is set, the divisor is taken to be the mean of the residual degrees of freedom from the individual equations.

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

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

corr displays the correlation matrix of the residuals between equations and performs a Breusch-Pagan test for independent equations; that is, the disturbance covariance matrix is diagonal.

nocnsreport; see [R] estimation options.

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.

+--------------+ ----+ Optimization +-----------------------------------------------------

optimization_options control the iterative process that minimizes the sum of squared errors when isure is specified. These options are seldom used.

iterate(#) specifies the maximum number of iterations. When the number of iterations equals #, the optimizer stops and presents the current results, even if the convergence tolerance has not been reached. The default value of iterate(#) is the current value of set maxiter, which is iterate(16000) if maxiter has not been changed.

trace adds to the iteration log a display of the current parameter vector.

nolog suppresses the display of the iteration log.

tolerance(#) specifies the tolerance for the coefficient vector. When the relative change in the coefficient vector from one iteration to the next is less than or equal to #, the optimization process is stopped. tolerance(1e-6) is the default.

The following options are available with sureg but are not shown in the dialog box:

noheader suppresses display of the header reporting F statistics, R-squared, and root mean squared error above the coefficient table.

notable suppresses display of the coefficient table.

coeflegend; see [R] estimation options.


Setup . sysuse auto

Fit seemingly unrelated regression model . sureg (price foreign weight length) (mpg foreign weight) (displ foreign weight)

Using a shorthand syntax . sureg (price foreign weight length) (mpg displ = foreign weight)

Using global macros . global price (price foreign weight length) . global mpg (mpg foreign weight) . global displ (displ foreign weight) . sureg $price $mpg $displ

With constraints . constraint 1 [price]foreign = [mpg]foreign . constraint 2 [price]foreign = [displacement]foreign . sureg (price foreign length) (mpg displacement = foreign weight), const(1 2)

Stored results

sureg stores the following in e():

Scalars e(N) number of observations e(k) number of parameters e(k_eq) number of equations in e(b) e(mss_#) model sum of squares for equation # e(df_m#) model degrees of freedom for equation # e(rss_#) residual sum of squares for equation # e(df_r) residual degrees of freedom e(r2_#) R-squared for equation # e(F_#) F statistic for equation # (small only) e(rmse_#) root mean squared error for equation # e(dfk2_adj) divisor used with VCE when dfk2 specified e(ll) log likelihood e(chi2_#) chi-squared for equation # e(p_#) p-value for equation # e(cons_#) 1 if equation # has a constant, 0 otherwise e(chi2_bp) Breusch-Pagan chi-squared e(df_bp) degrees of freedom for Breusch-Pagan chi-squared test e(rank) rank of e(V) e(ic) number of iterations

Macros e(cmd) sureg e(cmdline) command as typed e(method) sure or isure e(depvar) names of dependent variables e(exog) names of exogenous variables e(eqnames) names of equations e(wtype) weight type e(wexp) weight expression e(corr) correlation structure e(small) small, if specified e(dfk) dfk or dfk2, if 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(marginsdefault) default predict() specification for margins e(asbalanced) factor variables fvset as asbalanced e(asobserved) factor variables fvset as asobserved

Matrices e(b) coefficient vector e(Cns) constraints matrix e(Sigma) Sigma hat, covariance matrix of residuals e(V) variance-covariance matrix of the estimators

Functions e(sample) marks estimation sample


Zellner, A. 1962. An efficient method of estimating seemingly unrelated regressions and tests for aggregation bias. Journal of the American Statistical Association 57: 348-368.

------. 1963. Estimators for seemingly unrelated regression equations: Some exact finite sample results. Journal of the American Statistical Association 58: 977-992.

Zellner, A., and D. S. Huang. 1962. Further properties of efficient estimators for seemingly unrelated regression equations. International Economic Review 3: 300-313.

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