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/*
* 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 "version.h"
#include <glib.h>
/* Levin, Lin and Chu (Journal of Econometrics, 2002), Table 2:
correction factors for mean (mu) and standard deviation (s)
in context of panel unit-root statistic.
T = sample size
k = 1: no constant
k = 2: constant included
k = 3: constant plus trend
*/
static int get_LLC_corrections (int T, int k, double *mu, double *sigma)
{
const double LLCfac[] = {
/* T mu1 s1 mu2 s2 mu3 s3 */
25, 0.004, 1.049, -0.554, 0.919, -0.703, 1.003,
30, 0.003, 1.035, -0.546, 0.889, -0.674, 0.949,
35, 0.002, 1.027, -0.541, 0.867, -0.653, 0.906,
40, 0.002, 1.021, -0.537, 0.850, -0.637, 0.871,
45, 0.001, 1.017, -0.533, 0.837, -0.624, 0.842,
50, 0.001, 1.014, -0.531, 0.826, -0.614, 0.818,
60, 0.001, 1.011, -0.527, 0.810, -0.598, 0.780,
70, 0.000, 1.008, -0.524, 0.798, -0.587, 0.751,
80, 0.000, 1.007, -0.521, 0.789, -0.578, 0.728,
90, 0.000, 1.006, -0.520, 0.782, -0.571, 0.710,
100, 0.000, 1.005, -0.518, 0.776, -0.566, 0.695,
250, 0.000, 1.001, -0.509, 0.742, -0.533, 0.603,
0, 0.000, 1.000, -0.500, 0.707, -0.500, 0.500 /* \infty */
};
int c = 0, err = 0;
if (k > 0 && k < 4) {
c = 2 * k - 1;
} else {
err = E_DATA;
}
if (!err) {
int i, r = 12;
for (i=0; i<12; i++) {
if (T <= LLCfac[7*i]) {
r = i;
break;
}
}
*mu = LLCfac[7*r+c];
*sigma = LLCfac[7*r+c+1];
}
return err;
}
/* detrend \delta y for Levin-Lin-Chu case 3 */
static int LLC_detrend (gretl_matrix *dy)
{
gretl_matrix *X, *b;
int t, T = dy->rows;
int err;
X = gretl_matrix_alloc(T, 2);
b = gretl_matrix_alloc(2, 1);
if (X == NULL || b == NULL) {
err = E_ALLOC;
} else {
for (t=0; t<T; t++) {
gretl_matrix_set(X, t, 0, 1.0);
gretl_matrix_set(X, t, 1, t+1);
}
err = gretl_matrix_ols(dy, X, b, NULL, NULL, NULL);
}
if (!err) {
for (t=0; t<T; t++) {
/* replace with detrended values */
dy->val[t] -= (b->val[0] + b->val[1] * (t+1));
}
}
gretl_matrix_free(X);
gretl_matrix_free(b);
return err;
}
/* We could use gretl_long_run_variance() here, except that it
would have to be generalized to cover the cases (m == 1),
where we're _not_ subtracting the mean (on the maintained
hypothesis that the mean = 0), and (m == 3), where we have to
subtract a linear trend before computing the variance.
*/
static double LLC_lrvar (gretl_matrix *vdy, int K, int m, int *err)
{
double w, s21 = 0, s22 = 0;
double *dy = vdy->val;
int T = vdy->rows;
int t, j;
if (m == 3) {
/* subtract linear trend */
*err = LLC_detrend(vdy);
if (*err) {
return NADBL;
}
} else if (m == 2) {
/* subtract the mean */
double dybar = 0;
for (t=0; t<T; t++) {
dybar += dy[t];
}
dybar /= T;
for (t=0; t<T; t++) {
dy[t] -= dybar;
}
}
for (t=0; t<T; t++) {
s21 += dy[t] * dy[t];
}
for (j=1; j<=K; j++) {
w = 1.0 - j /((double) K + 1);
for (t=j; t<T; t++) {
s22 += w * dy[t] * dy[t-j];
}
}
return (s21 + 2 * s22) / T;
}
/* In case we got a list of individual-specific ADF order terms,
check that it makes sense and do some basic accounting.
*/
static int LLC_check_plist (const int *list, int N, int *pmax, int *pmin,
double *pbar)
{
int err = 0;
if (list == NULL || list[0] == 0) {
err = E_DATA;
} else if (list[0] > 1 && list[0] != N) {
err = E_DATA;
} else {
int i;
*pmax = *pmin = *pbar = 0;
for (i=1; i<=list[0]; i++) {
if (list[i] < 0) {
err = E_DATA;
break;
}
if (list[i] > *pmax) {
*pmax = list[i];
}
if (i == 1 || list[i] < *pmin) {
*pmin = list[i];
}
*pbar += list[i];
}
if (list[0] > 1) {
*pbar /= N;
}
}
return err;
}
static int LLC_sample_check (int N, int t1, int t2, int m,
const int *plist, int *NT)
{
int i, p, minT, T;
int err = 0;
*NT = 0;
for (i=1; i<=plist[0] && !err; i++) {
p = plist[i];
minT = m + p + 1; /* ensure df > 0 */
if (minT < 4) {
minT = 4;
}
/* T_i denotes the regression-usable series length, after
accounting for required lags */
T = t2 - t1 + 1 - (1 + p);
if (T < minT) {
err = E_DATA;
} else if (plist[0] == 1) {
*NT = N * T;
} else {
*NT += T;
}
}
return err;
}
static const char *DF_test_spec (int m)
{
const char *tests[] = {
N_("test without constant"),
N_("test with constant"),
N_("with constant and trend"),
};
if (m > 0 && m < 4) {
return tests[m-1];
} else {
return "";
}
}
#define LLC_DEBUG 0
/* Levin-Lin-Chu panel unit-root test */
int real_levin_lin (int vnum, const int *plist, DATASET *dset,
gretlopt opt, PRN *prn)
{
int u0 = dset->t1 / dset->pd;
int uN = dset->t2 / dset->pd;
int N = uN - u0 + 1; /* units in sample range */
gretl_matrix_block *B;
gretl_matrix *y, *yavg, *b;
gretl_matrix *dy, *X, *ui;
gretl_matrix *e, *ei, *v, *vi;
gretl_matrix *eps;
double pbar, SN = 0;
int t, t1, t2, T, NT;
int s, pt1, pt2, dyT;
int i, j, k, K, m;
int p, pmax, pmin;
int bigrow, p_varies = 0;
int err;
err = LLC_check_plist(plist, N, &pmax, &pmin, &pbar);
if (err) {
return err;
}
/* the 'case' (1 = no const, 2 = const, 3 = const + trend */
m = 2; /* the default */
if (opt & OPT_N) {
/* --nc */
m = 1;
} else if (opt & OPT_T) {
/* --ct */
m = 3;
}
/* does p vary by individual? */
if (pmax > pmin) {
p_varies = 1;
}
p = pmax;
/* the max number of regressors */
k = m + pmax;
t1 = t2 = 0;
/* check that we have a useable common sample */
for (i=0; i<N && !err; i++) {
int pt1 = (i + u0) * dset->pd;
int t1i, t2i;
dset->t1 = pt1;
dset->t2 = dset->t1 + dset->pd - 1;
err = series_adjust_sample(dset->Z[vnum], &dset->t1, &dset->t2);
t1i = dset->t1 - pt1;
t2i = dset->t2 - pt1;
if (i == 0) {
t1 = t1i;
t2 = t2i;
} else if (t1i != t1 || t2i != t2) {
err = E_MISSDATA;
break;
}
}
if (!err) {
err = LLC_sample_check(N, t1, t2, m, plist, &NT);
}
if (!err) {
int Tbar = NT / N;
/* the biggest T we'll need for regressions */
T = t2 - t1 + 1 - (1 + pmin);
/* Bartlett lag truncation (Andrews, 1991) */
K = (int) floor(3.21 * pow(Tbar, 1.0/3));
if (K > Tbar - 3) {
K = Tbar - 3;
}
/* full length of dy vector */
dyT = t2 - t1;
B = gretl_matrix_block_new(&y, T, 1,
&yavg, T+1+p, 1,
&dy, dyT, 1,
&X, T, k,
&b, k, 1,
&ui, T, 1,
&ei, T, 1,
&vi, T, 1,
&e, NT, 1,
&v, NT, 1,
&eps, NT, 1,
NULL);
if (B == NULL) {
err = E_ALLOC;
}
}
if (err) {
return err;
}
if (m > 1) {
/* constant in first column, if wanted */
for (t=0; t<T; t++) {
gretl_matrix_set(X, t, 0, 1.0);
}
}
if (m == 3) {
/* trend in second column, if wanted */
for (t=0; t<T; t++) {
gretl_matrix_set(X, t, 1, t+1);
}
}
gretl_matrix_zero(yavg);
/* compute period sums of y for time-demeaning */
for (i=0; i<N; i++) {
pt1 = t1 + (i + u0) * dset->pd;
pt2 = t2 + (i + u0) * dset->pd;
s = 0;
for (t=pt1; t<=pt2; t++) {
yavg->val[s++] += dset->Z[vnum][t];
}
}
gretl_matrix_divide_by_scalar(yavg, N);
bigrow = 0;
for (i=0; i<N && !err; i++) {
double yti, yti_1;
int p_i, T_i, k_i;
int pt0, ss;
if (p_varies) {
p_i = plist[i+1];
T_i = t2 - t1 + 1 - (1 + p_i);
k_i = m + p_i;
gretl_matrix_reuse(y, T_i, 1);
gretl_matrix_reuse(X, T_i, k_i);
gretl_matrix_reuse(b, k_i, 1);
gretl_matrix_reuse(ei, T_i, 1);
gretl_matrix_reuse(vi, T_i, 1);
} else {
p_i = p;
T_i = T;
k_i = k;
}
/* indices into Z array */
pt1 = t1 + (i + u0) * dset->pd;
pt2 = t2 + (i + u0) * dset->pd;
pt0 = pt1 + 1 + p_i;
/* build (full length) \delta y_t in dy */
s = 0;
for (t=pt1+1; t<=pt2; t++) {
ss = t - pt1;
yti = dset->Z[vnum][t] - gretl_vector_get(yavg, ss);
yti_1 = dset->Z[vnum][t-1] - gretl_vector_get(yavg, ss-1);
gretl_vector_set(dy, s++, yti - yti_1);
}
/* build y_{t-1} in y */
s = 0;
for (t=pt0; t<=pt2; t++) {
yti_1 = dset->Z[vnum][t-1] - gretl_vector_get(yavg, t - pt1 - 1);
gretl_vector_set(y, s++, yti_1);
}
/* augmented case: write lags of dy into X */
for (j=1; j<=p_i; j++) {
int col = m + j - 2;
double dylag;
s = 0;
for (t=pt0; t<=pt2; t++) {
dylag = gretl_vector_get(dy, t - pt1 - 1 - j);
gretl_matrix_set(X, s++, col, dylag);
}
}
/* set lagged y as last regressor */
for (t=0; t<T_i; t++) {
gretl_matrix_set(X, t, k_i - 1, y->val[t]);
}
#if LLC_DEBUG > 1
gretl_matrix_print(dy, "dy");
gretl_matrix_print(y, "y1");
gretl_matrix_print(X, "X");
#endif
if (p_i > 0) {
/* "virtual trimming" of dy for regressions */
dy->val += p_i;
dy->rows -= p_i;
}
/* run (A)DF regression */
err = gretl_matrix_ols(dy, X, b, NULL, ui, NULL);
if (err) {
break;
}
if (k_i > 1) {
/* reduced regressor matrix for auxiliary regressions:
omit the last column containing the lagged level of y
*/
gretl_matrix_reuse(X, T_i, k_i - 1);
gretl_matrix_reuse(b, k_i - 1, 1);
err = gretl_matrix_ols(dy, X, b, NULL, ei, NULL);
if (!err) {
err = gretl_matrix_ols(y, X, b, NULL, vi, NULL);
}
gretl_matrix_reuse(X, T, k);
gretl_matrix_reuse(b, k, 1);
} else {
/* no auxiliary regressions required */
gretl_matrix_copy_values(ei, dy);
gretl_matrix_copy_values(vi, y);
}
if (p_i > 0) {
/* restore dy to full length */
dy->val -= p_i;
dy->rows += p_i;
}
if (!err) {
double sui, s2yi, s2ui = 0.0;
for (t=0; t<T_i; t++) {
s2ui += ui->val[t] * ui->val[t];
}
s2ui /= (T_i - 1);
sui = sqrt(s2ui);
/* write normalized per-unit ei and vi into big matrices */
gretl_matrix_divide_by_scalar(ei, sui);
gretl_matrix_divide_by_scalar(vi, sui);
gretl_matrix_inscribe_matrix(e, ei, bigrow, 0, GRETL_MOD_NONE);
gretl_matrix_inscribe_matrix(v, vi, bigrow, 0, GRETL_MOD_NONE);
bigrow += T_i;
s2yi = LLC_lrvar(dy, K, m, &err);
if (!err) {
/* cumulate ratio of LR std dev to innovation std dev */
SN += sqrt(s2yi) / sui;
}
#if LLC_DEBUG
pprintf(prn, "s2ui = %.8f, s2yi = %.8f\n", s2ui, s2yi);
#endif
}
if (p_varies) {
gretl_matrix_reuse(y, T, 1);
gretl_matrix_reuse(X, T, k);
gretl_matrix_reuse(b, k, 1);
gretl_matrix_reuse(ei, T, 1);
gretl_matrix_reuse(vi, T, 1);
}
}
if (!err) {
/* the final step: full-length regression of e on v */
double ee = 0, vv = 0;
double delta, s2e, STD, td;
double mstar, sstar;
gretl_matrix_reuse(b, 1, 1);
err = gretl_matrix_ols(e, v, b, NULL, eps, NULL);
if (!err) {
for (t=0; t<NT; t++) {
ee += eps->val[t] * eps->val[t];
vv += v->val[t] * v->val[t];
}
SN /= N;
delta = b->val[0];
s2e = ee / NT;
STD = sqrt(s2e) / sqrt(vv);
td = delta / STD;
/* fetch the Levin-Lin-Chu corrections factors */
err = get_LLC_corrections(T, m, &mstar, &sstar);
}
if (!err) {
double z = (td - NT * (SN / s2e) * STD * mstar) / sstar;
double pval = normal_cdf(z);
#if LLC_DEBUG
pprintf(prn, "mustar = %g, sigstar = %g\n", mstar, sstar);
pprintf(prn, "SN = %g, se = %g, STD = %g\n", SN, sqrt(s2e), STD);
#endif
if (!(opt & OPT_Q)) {
const char *heads[] = {
N_("coefficient"),
N_("t-ratio"),
N_("z-score")
};
const char *s = dset->varname[vnum];
char NTstr[32];
int sp[3] = {0, 3, 5};
int w[3] = {4, 6, 0};
pputc(prn, '\n');
pprintf(prn, _("Levin-Lin-Chu pooled ADF test for %s\n"), s);
pprintf(prn, "%s ", _(DF_test_spec(m)));
if (p_varies) {
pprintf(prn, _("including %.2f lags of (1-L)%s (average)"), pbar, s);
} else if (p == 1) {
pprintf(prn, _("including one lag of (1-L)%s"), s);
} else {
pprintf(prn, _("including %d lags of (1-L)%s"), p, s);
}
pputc(prn, '\n');
pprintf(prn, _("Bartlett truncation at %d lags\n"), K);
sprintf(NTstr, "N,T = (%d,%d)", N, dyT + 1);
pprintf(prn, _("%s, using %d observations"), NTstr, NT);
pputs(prn, "\n\n");
for (i=0; i<3; i++) {
pputs(prn, _(heads[i]));
bufspace(w[i], prn);
w[i] = sp[i] + g_utf8_strlen(_(heads[i]), -1);
}
pputc(prn, '\n');
pprintf(prn, "%*.5g %*.3f %*.6g [%.4f]\n\n",
w[0], delta, w[1], td, w[2], z, pval);
}
record_test_result(z, pval, "Levin-Lin-Chu");
}
}
gretl_matrix_block_destroy(B);
return err;
}
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