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sysest.c

/* 
 *  gretl -- Gnu Regression, Econometrics and Time-series Library
 *  Copyright (C) 2001 Allin Cottrell and Riccardo "Jack" Lucchetti
 * 
 *  This program is free software: you can redistribute it and/or modify
 *  it under the terms of the GNU General Public License as published by
 *  the Free Software Foundation, either version 3 of the License, or
 *  (at your option) any later version.
 * 
 *  This program is distributed in the hope that it will be useful,
 *  but WITHOUT ANY WARRANTY; without even the implied warranty of
 *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 *  GNU General Public License for more details.
 * 
 *  You should have received a copy of the GNU General Public License
 *  along with this program.  If not, see <http://www.gnu.org/licenses/>.
 * 
 */

#include "libgretl.h"
#include "gretl_matrix.h"
#include "system.h"
#include "tsls.h"
#include "sysml.h"

#define SDEBUG 0
#define SYS_USE_SVD 0

#define sys_ols_ok(s) (s->method == SYS_METHOD_SUR || \
                       s->method == SYS_METHOD_OLS || \
                       s->method == SYS_METHOD_WLS)

/* insert the elements of sub-matrix @M, multiplied by @scale, in the
   appropriate position within the big matrix @X */

static void 
kronecker_place (gretl_matrix *X, const gretl_matrix *M,
             int startrow, int startcol, double scale)
{
    int i, j;
    int row, col;
    double x;
    
    for (i=0; i<M->rows; i++) {
      row = startrow + i;
      for (j=0; j<M->cols; j++) {
          col = startcol + j;
          x = gretl_matrix_get(M, i, j);
          gretl_matrix_set(X, row, col, x * scale);
      }
    }
}

/* Retrieve the data placed on @pmod in the course of 2sls estimation:
   for endogenous regressors these values are the first-stage fitted
   values, otherwise they're just the original data.  Note that @endog
   is a mask with nonzero values identifying the endogenous
   regressors, and the special array @X contains a column for each
   endogenous variable.
*/

double *model_get_Xi (const MODEL *pmod, DATASET *dset, int i)
{
    const char *endog = gretl_model_get_data(pmod, "endog");
    double **X;
    double *xi = NULL;

    if (endog == NULL || !endog[i]) {
      /* return the original data */
      return dset->Z[pmod->list[i+2]];
    }

    X = gretl_model_get_data(pmod, "tslsX");

    if (X != NULL) {
      /* find and return the correct column */
      int j, k = 0;

      for (j=0; j<i; j++) {
          if (endog[j]) k++;
      }
      xi = X[k];
    }

    return xi;
}

/* retrieve the special k-class data wanted for LIML estimation: these
   represent a further transformation of the data placed on the model
   via 2sls estimation.
*/

static int make_liml_X_block (gretl_matrix *X, const MODEL *pmod,
                        DATASET *dset, int t1)
{
    int i, t;
    const double *Xi;

    X->cols = pmod->ncoeff;

    for (i=0; i<X->cols; i++) {
      Xi = model_get_Xi(pmod, dset, i);
      if (Xi == NULL) {
          return 1;
      }
      for (t=0; t<X->rows; t++) {
          gretl_matrix_set(X, t, i, Xi[t+t1]);
      }
    }

    return 0;
}

/* construct the X data block pertaining to a specific equation, using
   either the original data or fitted values from regression on a set
   of instruments */

static int 
make_sys_X_block (gretl_matrix *X, const MODEL *pmod,
              DATASET *dset, int t1, int method)
{
    int i, t;
    const double *Xi;

    X->cols = pmod->ncoeff;

    for (i=0; i<X->cols; i++) {
      if (method == SYS_METHOD_3SLS || 
          method == SYS_METHOD_FIML || 
          method == SYS_METHOD_TSLS) {
          Xi = model_get_Xi(pmod, dset, i);
      } else {
          Xi = dset->Z[pmod->list[i+2]];
      }
      if (Xi == NULL) {
          return E_DATA;
      }
      for (t=0; t<X->rows; t++) {
          gretl_matrix_set(X, t, i, Xi[t+t1]);
      }
    }

    return 0;
}

/* populate the cross-equation covariance matrix based on the
   per-equation residuals */

static int
gls_sigma_from_uhat (equation_system *sys, gretl_matrix *sigma)
{
    const gretl_matrix *e = sys->E;
    int m = sys->neqns;
    int T = sys->T;
    int geomean = system_vcv_geomean(sys);
    int i, j, t;
    double xx;

    for (i=0; i<m; i++) {
      for (j=i; j<m; j++) {
          xx = 0.0;
          for (t=0; t<T; t++) {
            xx += gretl_matrix_get(e, t, i) * gretl_matrix_get(e, t, j);
          }
          if (geomean) {
            xx /= system_vcv_denom(sys, i, j);
          } else {
            xx /= T;
          }
          gretl_matrix_set(sigma, i, j, xx);
          if (j != i) {
            gretl_matrix_set(sigma, j, i, xx);
          }
      }
    }

    if (sys->method == SYS_METHOD_OLS && sys->diag == 0.0) {
      double sii, sij, sjj;

      for (i=1; i<m; i++) {
          sii = gretl_matrix_get(sigma, i, i);
          for (j=0; j<i; j++) {
            sij = gretl_matrix_get(sigma, i, j);
            sjj = gretl_matrix_get(sigma, j, j);
            sys->diag += (sij * sij) / (sii * sjj);
          }
      }
      sys->diag *= T;
    }

    return 0;
}

/* Note: this was changed in Revision 1.86 of Fri Apr 30 2010. Up till
   then we were reporting the regular R^2 for models estimated as part
   of a system, which seems wrong.
*/

#define SYS_CORR_RSQ 1

/* compute residuals, for all cases other than FIML */

static void 
sys_resids (equation_system *sys, int eq, const DATASET *dset)
{
    MODEL *pmod = sys->models[eq];
    int yno = pmod->list[1];
    double yh;
    int i, t;

    pmod->ess = 0.0;

    for (t=pmod->t1; t<=pmod->t2; t++) {
      yh = 0.0;
      for (i=0; i<pmod->ncoeff; i++) {
          yh += pmod->coeff[i] * dset->Z[pmod->list[i+2]][t];
      }
      pmod->yhat[t] = yh;
      pmod->uhat[t] = dset->Z[yno][t] - yh;
      /* for cross-equation vcv */
      gretl_matrix_set(sys->E, t - pmod->t1, pmod->ID, pmod->uhat[t]);
      pmod->ess += pmod->uhat[t] * pmod->uhat[t];
    }

    /* df correction? */
    if (system_want_df_corr(sys)) {
      pmod->sigma = sqrt(pmod->ess / pmod->dfd);
    } else {
      pmod->sigma = sqrt(pmod->ess / pmod->nobs);
    }

    if (pmod->ifc && pmod->tss > 0) {
      /* R-squared */
      double r;

#if SYS_CORR_RSQ
      pmod->rsq = gretl_corr_rsq(pmod->t1, pmod->t2, dset->Z[yno], 
                           pmod->yhat);
#else
      pmod->rsq = 1 - (pmod->ess / pmod->tss);
#endif
      r = 1 - pmod->rsq;
      pmod->adjrsq = 1.0 - (r * (pmod->nobs - 1) / pmod->dfd);
    } else {
      pmod->rsq = pmod->adjrsq = NADBL;
    }
}

static void
liml_scale_vcv (equation_system *sys, gretl_matrix *vcv)
{
    double s2, vij;
    int vmin = 0;
    int vi, vj;
    int i, j, k;

    for (i=0; i<sys->neqns; i++) {
      s2 = sys->models[i]->sigma * sys->models[i]->sigma;
      for (j=0; j<sys->models[i]->ncoeff; j++) {
          for (k=j; k<sys->models[i]->ncoeff; k++) {
            vi = j + vmin;
            vj = k + vmin;
            vij = gretl_matrix_get(vcv, vi, vj);
            vij *= s2;
            gretl_matrix_set(vcv, vi, vj, vij);
            gretl_matrix_set(vcv, vj, vi, vij);
          }
      }
      vmin += sys->models[i]->ncoeff;
    }       
}

/* use the per-equation residual standard deviations for scaling
   the covariance matrix, block by diagonal block
*/

static void 
single_eq_scale_vcv (equation_system *sys, gretl_matrix *vcv)
{
    MODEL *pmod;
    double s2, vij;
    int ioff = 0, joff = 0;
    int i, k, ii, jj;

    for (i=0; i<sys->neqns; i++) {
      pmod = sys->models[i];
      s2 = pmod->sigma * pmod->sigma;
      k = pmod->ncoeff;
      for (ii=0; ii<k; ii++) {
          for (jj=0; jj<k; jj++) {
            vij = gretl_matrix_get(vcv, ioff + ii, joff + jj);
            gretl_matrix_set(vcv, ioff + ii, joff + jj, vij * s2);
          }
      }
      ioff += k;
      joff += k;
    }    
}

/* compute SUR, 3SLS or LIML parameter estimates (or restricted OLS,
   TSLS, WLS) */

static int 
calculate_sys_coeffs (equation_system *sys,
                  const DATASET *dset,
                  gretl_matrix *X, gretl_matrix *y, 
                  int mk, int nr, int do_iteration)
{
    int do_bdiff = ((sys->method == SYS_METHOD_3SLS) && do_iteration);
    double bij, oldb, bnum = 0.0, bden = 0.0;
    gretl_matrix *vcv = NULL;
    gretl_matrix *b = NULL;
    int i, j, k, j0;
    int err = 0;

    vcv = gretl_matrix_copy(X);
    if (vcv == NULL) {
      return E_ALLOC;
    }

    err = gretl_LU_solve(X, y);
    if (err) {
      return err;
    }

#if SDEBUG > 1
    gretl_matrix_print(y, "in calc_coeffs, betahat");
#endif

#if SYS_USE_SVD
    /* memory-intensive for big matrices */
    err = gretl_SVD_invert_matrix(vcv);
#else    
    err = gretl_invert_general_matrix(vcv);
#endif

#if SDEBUG
    fprintf(stderr, "calculate_sys_coeffs: invert, err=%d\n", err);
#endif

    if (err) {
      return err;
    }

#if SDEBUG > 1
    gretl_matrix_print(vcv, "in calc_coeffs, vcv");
#endif

    j0 = 0;
    for (i=0; i<sys->neqns; i++) {
      for (j=0; j<sys->models[i]->ncoeff; j++) {
          k = j0 + j;
          bij = gretl_vector_get(y, k);
          if (do_bdiff) {
            oldb = sys->models[i]->coeff[j];
            bnum += (bij - oldb) * (bij - oldb);
            bden += oldb * oldb;
          }
          sys->models[i]->coeff[j] = bij;
      }
      sys_resids(sys, i, dset);
      j0 += sys->models[i]->ncoeff;
    }

    if (do_bdiff) {
      sys->bdiff = sqrt(bnum / bden);
    }

    if (sys->method == SYS_METHOD_OLS || 
      sys->method == SYS_METHOD_TSLS) {
      single_eq_scale_vcv(sys, vcv);
    } else if (sys->method == SYS_METHOD_LIML) {
      liml_scale_vcv(sys, vcv);
    }

    /* now set the model standard errors */
    j0 = 0;
    for (i=0; i<sys->neqns; i++) {
      for (j=0; j<sys->models[i]->ncoeff; j++) {
          k = j0 + j;
          sys->models[i]->sderr[j] = sqrt(gretl_matrix_get(vcv, k, k));
      }
      j0 += sys->models[i]->ncoeff;
    }

    /* save the coefficient vector and covariance matrix */
    b = gretl_matrix_copy(y);
    system_attach_coeffs(sys, b);
    system_attach_vcv(sys, vcv);

    return err;
}

static int *
system_model_list (equation_system *sys, int i, int *freeit)
{
    int *list = NULL;

    *freeit = 0;

    if (sys_ols_ok(sys)) {
      return system_get_list(sys, i);
    }

    if (sys->method != SYS_METHOD_FIML) {
      list = system_get_list(sys, i);
    }

    if (sys->method == SYS_METHOD_3SLS || 
      sys->method == SYS_METHOD_TSLS ||
      sys->method == SYS_METHOD_LIML) {
      /* Is the list already in ivreg form? 
         If not, ignore it. */
      if (list != NULL && !gretl_list_has_separator(list)) {
          list = NULL;
      }
    }

    if ((sys->method == SYS_METHOD_FIML || 
       sys->method == SYS_METHOD_LIML ||
       sys->method == SYS_METHOD_3SLS || 
       sys->method == SYS_METHOD_TSLS) 
      && list == NULL) {
      list = compose_ivreg_list(sys, i);
      *freeit = 1;
    }

    return list;
}

/* Hansen-Sargan overidentification test for the system as a whole, as
   in Davidson and MacKinnon, ETM: p. 511 and equation (12.25) for the
   case of SUR; p. 532 and equation (12.61) for the case of 3SLS.  See
   also D & M, Estimation and Inference in Econometrics, equation
   (18.60), for a more computation-friendly statement of the criterion
   function.
*/

static int hansen_sargan_test (equation_system *sys, 
                         const DATASET *dset)
{
    const int *exlist = system_get_instr_vars(sys);
    const double *Wi, *Wj;
    int nx = exlist[0];
    int m = sys->neqns;
    int T = sys->T;
    int df = system_get_overid_df(sys);
    gretl_matrix *WTW = NULL;
    gretl_matrix *eW = NULL;
    gretl_matrix *tmp = NULL;
    double x, X2;
    int i, j, t;
    int err = 0;

    if (df <= 0) return 1;

    WTW = gretl_matrix_alloc(nx, nx);
    eW = gretl_matrix_alloc(m, nx);
    tmp = gretl_matrix_alloc(m, nx);

    if (WTW == NULL || eW == NULL || tmp == NULL) {
      err = E_ALLOC;
      goto bailout;
    }

    /* construct W-transpose W */
    for (i=0; i<nx; i++) {
      Wi = dset->Z[exlist[i+1]] + sys->t1;
      for (j=i; j<nx; j++) {
          Wj = dset->Z[exlist[j+1]] + sys->t1;
          x = 0.0;
          for (t=0; t<sys->T; t++) {
            x += Wi[t] * Wj[t];
          }
          gretl_matrix_set(WTW, i, j, x);
          if (i != j) {
            gretl_matrix_set(WTW, j, i, x);
          }
      }
    }

    err = gretl_invert_symmetric_matrix(WTW);
#if SDEBUG
    fprintf(stderr, "hansen_sargan: on invert, err=%d\n", err);
#endif
    if (err) {
      sys->X2 = NADBL;
      goto bailout;
    }

    /* set up vectors of SUR or 3SLS residuals, transposed, times W:
       these are stacked in an m * nx matrix
    */
    for (i=0; i<m; i++) {
      for (j=0; j<nx; j++) {
          Wj = dset->Z[exlist[j+1]] + sys->t1;
          x = 0.0;
          for (t=0; t<T; t++) {
            x += gretl_matrix_get(sys->E, t, i) * Wj[t];
          }
          gretl_matrix_set(eW, i, j, x);
      }
    }

    /* multiply these vectors into (WTW)^{-1} */
    for (i=0; i<m; i++) {
      for (j=0; j<nx; j++) {
          x = 0.0;
          for (t=0; t<nx; t++) {
            x += gretl_matrix_get(eW, i, t) * 
                gretl_matrix_get(WTW, t, j);
          }
          gretl_matrix_set(tmp, i, j, x);
      }
    }   

    /* cumulate the Chi-square value */
    X2 = 0.0;
    for (i=0; i<m; i++) {
      for (j=0; j<m; j++) {
          x = 0.0;
          for (t=0; t<nx; t++) {
            x += gretl_matrix_get(tmp, i, t) * 
                gretl_matrix_get(eW, j, t); /* transposed */
          }
          X2 += gretl_matrix_get(sys->S, i, j) * x;
      }
    }

#if SDEBUG
    fprintf(stderr, "Hansen-Sargan: Chi-square(%d) = %g (p-value %g)\n", 
          df, X2, chisq_cdf_comp(df, X2));
#endif
    sys->X2 = X2;

 bailout:

    gretl_matrix_free(WTW);
    gretl_matrix_free(eW);
    gretl_matrix_free(tmp);

    return err;
}

static int basic_system_allocate (equation_system *sys,
                          int mk, int nr, 
                          gretl_matrix **X,
                          gretl_matrix **y)
{
    int m = sys->neqns;
    int T = sys->T;
    int ldx = mk + nr;

    /* allocate a model for each stochastic equation */
    sys->models = gretl_model_array_new(m);
    if (sys->models == NULL) {
      return E_ALLOC;
    }    

    sys->E = gretl_matrix_alloc(T, m);
    if (sys->E == NULL) {
      return E_ALLOC;
    }

    sys->S = gretl_matrix_alloc(m, m);
    if (sys->S == NULL) {
      return E_ALLOC;
    }

    *X = gretl_matrix_alloc(ldx, ldx);
    if (*X == NULL) {
      return E_ALLOC;
    }

    *y = gretl_column_vector_alloc(ldx);
    if (*y == NULL) {
      return E_ALLOC;
    }

    return 0;
}

/* compute log-likelihood for iterated SUR estimator */

double sur_ll (equation_system *sys)
{
    int m = sys->neqns;
    int T = sys->T;
    gretl_matrix *tmp;
    double ldet;

    tmp = gretl_matrix_alloc(m, m);
    if (tmp == NULL) {
      return NADBL;
    }

    gls_sigma_from_uhat(sys, tmp);
    ldet = gretl_vcv_log_determinant(tmp);

    if (na(ldet)) {
      sys->ll = NADBL;
    } else {
      sys->ll = -(m * T / 2.0) * (LN_2_PI + 1.0);
      sys->ll -= (T / 2.0) * ldet;
    }

    gretl_matrix_free(tmp);

    return sys->ll;
}

/* if we're estimating with a specified set of linear restrictions,
   Rb = q, augment the X matrix with R and R-transpose */

static int 
augment_X_with_restrictions (gretl_matrix *X, int mk, 
                       equation_system *sys)
{
    double rij;
    int nr, nc;
    int i, j;

    if (sys->R == NULL) return 1;

    nr = sys->R->rows;
    nc = sys->R->cols;

    /* place the R matrix */
    kronecker_place(X, sys->R, mk, 0, 1.0);

    /* place R-transpose */
    for (i=0; i<nr; i++) {
      for (j=0; j<nc; j++) {
          rij = gretl_matrix_get(sys->R, i, j);
          gretl_matrix_set(X, j, i + mk, rij);
      }
    }

    /* zero the bottom right-hand block */
    for (i=mk; i<mk+nr; i++) {
      for (j=mk; j<mk+nr; j++) {
          gretl_matrix_set(X, i, j, 0.0);
      }
    }

    return 0;
}

/* when estimating with a specified set of linear restrictions,
   Rb = q, augment the y matrix with q */

static int 
augment_y_with_restrictions (gretl_matrix *y, int mk, int nr,
                       equation_system *sys)
{
    int i;

    if (sys->q == NULL) {
      return 1;
    }

    for (i=0; i<nr; i++) {
      gretl_vector_set(y, mk + i, gretl_vector_get(sys->q, i));
    }

    return 0;
}

#define SYS_MAX_ITER 100
#define SYS_LL_TOL 1.0e-12
#define SYS_BDIFF_TOL 1.0e-9

/* check for convergence of iteration: we use the change in the
   log-likelihood when iterating SUR to the ML solution, or
   a measure of the change in the coefficients when iterating
   three-stage least squares
*/

static int sys_converged (equation_system *sys, 
                    double *llbak, int *err,
                    gretlopt opt, PRN *prn)
{
    double crit, tol = 0.0;
    int met = 0;

    if (sys->method == SYS_METHOD_SUR || 
      sys->method == SYS_METHOD_WLS) {
      double ll = sur_ll(sys);

      tol = SYS_LL_TOL;
      crit = ll - *llbak;

      if (opt & OPT_V) {
          pprintf(prn, "Iteration %3d, ll = %#.8g\n", sys->iters, ll);
      }
      if (crit <= tol) {
          met = 1;
      } else if (sys->iters < SYS_MAX_ITER) {
          *llbak = ll;
      } 
    } else if (sys->method == SYS_METHOD_3SLS) {
      tol = SYS_BDIFF_TOL;
      crit = sys->bdiff;
      if (opt & OPT_V) {
          pprintf(prn, "Iteration %3d, criterion = %g\n", sys->iters, crit);
      }
      if (crit <= tol) {
          met = 1;
      } 
    }

    if (met && tol > 0 && (opt & OPT_V)) {
      pprintf(prn, "Tolerance of %g is met\n", tol);
    }

    if (!met && sys->iters >= SYS_MAX_ITER) {
      pprintf(prn, "Reached %d iterations without meeting "
            "tolerance of %g\n", sys->iters, tol);
      *err = E_NOCONV;
    } 

    return met;
}

static void clean_up_models (equation_system *sys)
{
    int i;

    if (sys->models == NULL) {
      /* "can't happen" */
      return;
    }

    sys->ess = 0.0;

    for (i=0; i<sys->neqns; i++) {
      sys->ess += sys->models[i]->ess;
      if (sys->method == SYS_METHOD_3SLS || 
          sys->method == SYS_METHOD_FIML || 
          sys->method == SYS_METHOD_TSLS || 
          sys->method == SYS_METHOD_LIML) {
          tsls_free_data(sys->models[i]);
      }
      if (sys->neqns > 1) {
          gretl_model_free(sys->models[i]);
      }
    }

    if (sys->neqns == 1) {
      /* ivreg (LIML) */
      sys->models[0]->rho = sys->models[0]->dw = NADBL;
    } else {
      free(sys->models);
      sys->models = NULL;
    }
}

static int drop_redundant_instruments (equation_system *sys,
                               const int *droplist, int i)
{
    int j, k, pos, err = 0;

    for (j=1; j<=droplist[0]; j++) {
      pos = in_gretl_list(sys->ilist, droplist[j]);
      if (pos > 0) {
          gretl_list_delete_at_pos(sys->ilist, pos);
      } else {
          err = 1;
      }
    }

    pos = gretl_list_separator_position(sys->lists[i]);
    if (pos > 0) {
      for (j=1; j<=droplist[0]; j++) {
          for (k=pos+1; k<=sys->lists[i][0]; k++) {
            if (sys->lists[i][k] == droplist[j]) {
                gretl_list_delete_at_pos(sys->lists[i], k);
                break;
            }
          }
      }
    }

    return err;
}

/* options to be passed in running initial 2sls */

static gretlopt sys_tsls_opt (const equation_system *sys)
{
    gretlopt opt = (OPT_E | OPT_A);

    if (sys->method == SYS_METHOD_LIML) {
      opt |= OPT_N; /* ML: no df correction */
    }

    if (sys->flags & SYSTEM_SINGLE) {
      opt |= OPT_H; /* add "hatlist" of instrumented vars */
    }

    return opt;
}

/* general function that forms the basis for all specific system
   estimators */

int system_estimate (equation_system *sys, DATASET *dset, 
                 gretlopt opt, PRN *prn)
{
    int i, j, k, T, t;
    int v, l, mk, krow, nr;
    int orig_t1 = dset->t1;
    int orig_t2 = dset->t2;
    gretl_matrix *X = NULL;
    gretl_matrix *y = NULL;
    gretl_matrix *Xi = NULL;
    gretl_matrix *Xj = NULL;
    gretl_matrix *M = NULL;
    MODEL **models = NULL;
    int method = sys->method;
    double llbak = -1.0e9;
    int single_equation = 0;
    int do_iteration = 0;
    int rtsls = 0;
    int err = 0;

    sys->iters = 0;

    if (sys->flags & SYSTEM_ITERATE) {
      do_iteration = 1;
    }
    
    nr = system_n_restrictions(sys);

    if (method == SYS_METHOD_OLS || method == SYS_METHOD_TSLS || 
      method == SYS_METHOD_LIML || method == SYS_METHOD_WLS) {
      single_equation = 1;
    }

    if (nr > 0 && method == SYS_METHOD_3SLS) {
      /* doing 3SLS with restrictions: we want to obtain
         restricted TSLS estimates as a starting point */
      rtsls = 1;
    }

    /* get uniform sample starting and ending points and check for
       missing data */
    err = system_adjust_t1t2(sys, dset);
    if (err) {
      return err;
    } 

    /* set sample for auxiliary regressions */
    dset->t1 = sys->t1;
    dset->t2 = sys->t2;

    /* max indep vars per equation */
    k = system_max_indep_vars(sys);

    /* total indep vars, all equations */
    mk = system_n_indep_vars(sys);

    /* set sample for auxiliary regressions */
    dset->t1 = sys->t1;
    dset->t2 = sys->t2;

    /* number of observations per series */
    T = sys->T;

    /* allocate models etc */
    err = basic_system_allocate(sys, mk, nr, &X, &y);
    if (err) {
      goto cleanup;
    }

    /* convenience pointers */
    models = sys->models;
          
    if ((method == SYS_METHOD_FIML || 
       method == SYS_METHOD_LIML) && !(opt & OPT_Q)) {
      print_equation_system_info(sys, dset, OPT_H, prn);
    }

    /* First estimate the equations separately (either by OLS or
       TSLS), and put the single-equation residuals into the uhat
       matrix.  Note that at this stage we are not in a position to
       impose any cross-equation restrictions, since we're doing
       straight equation-by-equation estimation.
    */

    for (i=0; i<sys->neqns; i++) {
      int freeit = 0;
      int *list = system_model_list(sys, i, &freeit);
      const int *droplist = NULL;
      MODEL *pmod = models[i];

      if (list == NULL) {
          err = 1;
          break;
      }

      if (sys_ols_ok(sys)) {
          *pmod = lsq(list, dset, OLS, OPT_A);
      } else {
          *pmod = tsls(list, dset, sys_tsls_opt(sys));
      }

      if (freeit) {
          free(list);
      }

      if ((err = pmod->errcode)) {
          fprintf(stderr, "system_estimate: failed to estimate equation %d: "
                "err = %d\n", i+1, err);
          break;
      } 

      droplist = gretl_model_get_data(pmod, "inst_droplist");
      if (droplist != NULL) {
          drop_redundant_instruments(sys, droplist, i);
      }

      pmod->ID = i;
      pmod->aux = AUX_SYS;
      gretl_model_set_int(pmod, "method", method);

      /* save the sigma-squared for an LR test for a diagonal
         covariance matrix */
      if (method == SYS_METHOD_SUR && do_iteration && nr == 0) {
          gretl_model_set_double(pmod, "ols_sigma_squared",
                           pmod->ess / pmod->nobs);
      }

      for (t=0; t<T; t++) {
          gretl_matrix_set(sys->E, t, i, pmod->uhat[t + sys->t1]);
      }
    }

    if (err) {
      fprintf(stderr, "system_estimate: after single-equation "
            "estimation, err = %d\n", err);
      goto cleanup;
    }

    if (method == SYS_METHOD_LIML) {
      /* compute the minimum eigenvalues and generate the
         k-class data matrices */
      err = liml_driver(sys, dset, prn);
      if (err) goto cleanup;
    }

    /* marker for iterated versions of SUR, WLS, or 3SLS; also for
       loopback in case of restricted 3SLS, where we want to compute
       restricted TSLS estimates first
    */
 iteration_start:

    gls_sigma_from_uhat(sys, sys->S);

#if SDEBUG > 1
    gretl_matrix_print(sys->S, "gls_sigma_from_uhat");
#endif

    if (method == SYS_METHOD_WLS) {
      gretl_matrix_zero(X);
      err = gretl_invert_diagonal_matrix(sys->S);
    } else if (single_equation || rtsls) {
      gretl_matrix_zero(X);
    } else {
      err = gretl_invert_symmetric_matrix(sys->S);    
    }

#if SDEBUG
    fprintf(stderr, "system_estimate: on invert, err=%d\n", err);
#endif

    if (err) goto cleanup;

    /* the initial tests against NULL here allow for the possibility
       that we're iterating */

    if (Xi == NULL) {
      Xi = gretl_matrix_alloc(T, k);
    }
    if (Xj == NULL) {
      Xj = gretl_matrix_alloc(T, k);
    } 
    if (M == NULL) {
      M = gretl_matrix_alloc(k, k);
    }

    if (Xi == NULL || Xj == NULL || M == NULL) {
      err = E_ALLOC;
      goto cleanup;
    }

    /* form the big stacked X matrix: Xi = data matrix for equation i, 
       specified in lists[i] 
    */

    krow = 0;
    for (i=0; i<sys->neqns && !err; i++) {
      int kcol = 0;

      err = make_sys_X_block(Xi, models[i], dset, sys->t1, method);

      for (j=0; j<sys->neqns && !err; j++) { 
          const gretl_matrix *Xk;
          double sij;

          if (i != j) {
            if (single_equation || rtsls) {
                kcol += models[j]->ncoeff;
                continue;
            }
            err = make_sys_X_block(Xj, models[j], dset, sys->t1, method);
            Xk = Xj;
          } else if (method == SYS_METHOD_LIML) {
            err = make_liml_X_block(Xj, models[i], dset, sys->t1);
            Xk = Xj;
          } else {
            Xk = Xi;
          }

          M->rows = Xi->cols;
          M->cols = Xk->cols;

          err = gretl_matrix_multiply_mod(Xi, GRETL_MOD_TRANSPOSE,
                                  Xk, GRETL_MOD_NONE, 
                                  M, GRETL_MOD_NONE);

          if (rtsls || (single_equation && method != SYS_METHOD_WLS)) {
            sij = 1.0;
          } else {
            sij = gretl_matrix_get(sys->S, i, j);
          }

          kronecker_place(X, M, krow, kcol, sij);
          kcol += models[j]->ncoeff;
      }

      krow += models[i]->ncoeff;
    }

    if (err) {
      fprintf(stderr, "after trying to make X matrix: err = %d\n", err);
      goto cleanup;
    }

    if (nr > 0) {
      /* there are restrictions to be imposed */
      augment_X_with_restrictions(X, mk, sys);
    }

    if (!do_iteration && !rtsls) {
      /* we're not coming back this way, so free some storage */
      gretl_matrix_free(Xj);
      Xj = NULL;
      gretl_matrix_free(M);
      M = NULL;
    }

    /* form stacked Y column vector (m x k) */

    v = 0;
    for (i=0; i<sys->neqns; i++) { 

      /* loop over the m vertically-arranged blocks */

      make_sys_X_block(Xi, models[i], dset, sys->t1, method);

      for (j=0; j<models[i]->ncoeff; j++) { 
          /* loop over the rows within each of the m blocks */
          double yv = 0.0;
          int lmin = 0, lmax = sys->neqns;

          if (single_equation || rtsls) {
            /* no cross terms wanted */
            lmin = i;
            lmax = i + 1;
          }

          for (l=lmin; l<lmax; l++) { 
            /* loop over the components that must be
               added to form each element */
            const double *yl = NULL;
            double sil, xx = 0.0;

            if (method == SYS_METHOD_LIML) {
                yl = gretl_model_get_data(models[l], "liml_y");
            } else {
                yl = dset->Z[system_get_depvar(sys, l)];
            }

            /* multiply X'[l] into y */
            for (t=0; t<T; t++) {
                xx += gretl_matrix_get(Xi, t, j) * yl[t + sys->t1];
            }

            if (rtsls || (single_equation && method != SYS_METHOD_WLS)) {
                sil = 1.0;
            } else {
                sil = gretl_matrix_get(sys->S, i, l);
            }

            yv += xx * sil;
          }
          gretl_vector_set(y, v++, yv);
      }
    }

    if (nr > 0) {
      /* there are restrictions */
      augment_y_with_restrictions(y, mk, nr, sys);
    }

#if SDEBUG
    gretl_matrix_print(X, "sys X");
    gretl_matrix_print(y, "sys y");
#endif    

    /* The estimates calculated below will be SUR, 3SLS or LIML,
       depending on how the data matrices above were constructed --
       unless, that is, we're just doing restricted OLS, WLS or TSLS
       estimates.
    */
    err = calculate_sys_coeffs(sys, dset, X, y, mk, nr, 
                         do_iteration);
    if (err) {
      goto cleanup;
    }

    if (rtsls) {
      rtsls = 0;
      goto iteration_start;
    }

    if (do_iteration) {
      if (!sys_converged(sys, &llbak, &err, opt, prn)) {
          if (err) {
            goto cleanup;
          } else {
            sys->iters += 1;
            goto iteration_start;
          }
      }
    }

    if (nr == 0 && (method == SYS_METHOD_3SLS || method == SYS_METHOD_SUR)) {
      /* compute this test while we have sigma-inverse available */
      hansen_sargan_test(sys, dset);
    }

    /* refresh sigma (non-inverted) */
    gls_sigma_from_uhat(sys, sys->S);

    if (method == SYS_METHOD_FIML) {
      /* compute FIML estimates */
      err = fiml_driver(sys, dset, opt, prn);
    }

    if (!err && !(sys->flags & SYSTEM_SINGLE)) {
      err = system_save_and_print_results(sys, dset, opt, prn);
    }

 cleanup:

    gretl_matrix_free(Xi);
    gretl_matrix_free(Xj);
    gretl_matrix_free(M);
    gretl_matrix_free(X);
    gretl_matrix_free(y);

    clean_up_models(sys);

    dset->t1 = orig_t1;
    dset->t2 = orig_t2;

    return err;
}

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