La relation inflation-chômage en zone CEMAC

Annexe 8 : Retard optimal

. pvarsoc chomage inflation pibreel investtotal txinteretreel, pvaro(instl(1/4)) Running panel VAR lag order selection on estimation sample ....

Selection order criteria

Sample: 1998 - 2021 No. of obs = 144

No. of panels = 6

Ave. no. of T = 24.000

lag	CD J J pvalue MBIC MAIC MQIC
1	.9999984 87.31236 .1565396 -285.4236 -62.68764 -153.195
2	.9999975 59.15865 .1759214 -189.332 -40.84135 -101.1796
3	.9999979 27.91347 .311852 -96.33186 -22.08653 -52.25564
4	.999988 . . . . .

Estimations :

Annexe 9 : Estimation du modele linéaire (ARDL) PMG :

. xtpmg d(chomage inflation pibreel investtotal txinteretreel txdechangereel), lr(l.chomage inflation pibreel

> investtotal txinteretreel txdechangereel)ec(ECT) replace pmg

Iteration 0: log likelihood = -6.304936 (not concave)

Iteration 1: log likelihood = 5.7469344 (not concave)

Iteration 2: log likelihood = 6.6469746 (not concave)

Iteration 3: log likelihood = 7.8909736 (not concave)

Iteration 4: log likelihood = 9.6600744

Iteration 5: log likelihood = 9.6616443

Iteration 6: log likelihood = 10.315615

Iteration 7: log likelihood = 10.337006

Iteration 8: log likelihood = 10.337042

Iteration 9: log likelihood = 10.337042

Pooled Mean Group Regression

(Estimate results saved as pmg)

Panel Variable (i): id Number of obs = 168

Time Variable (t): années Number of groups = 6 Obs per group: min = 28 avg = 28.0 max = 28

Log Likelihood = 10.33704

D.chomage	Coef. Std. Err. z P>|z| [95% Conf. Interval]
ECT inflation	.1811211 .1113045 1.63 0.104 -.0370318 .3992739
pibreel	-.3475589 .1209572 -2.87 0.004 -.5846305 -.1104872
investtotal	-.0408306 .0310848 -1.31 0.189 -.1017558 .0200945
txinteretreel	-.9794337 .1903848 -5.14 0.000 -1.352581 -.6062863
txdechangereel	-.0747582 .067806 -1.10 0.270 -.2076555 .0581391
SR ECT	-.0930544 .0458407 -2.03 0.042 -.1829006 -.0032083
inflation D1.	-.0124101 .0075312 -1.65 0.099 -.027171 .0023509
pibreel D1.	-.009297 .0079019 -1.18 0.239 -.0247844 .0061904
investtotal D1.	.0040269 .0049429 0.81 0.415 -.005661 .0137148
txinteretreel D1.	-.2584055 .1012771 -2.55 0.011 -.456905 -.0599059
txdechangereel D1.	.0021138 .0020191 1.05 0.295 -.0018436 .0060711
_cons	2.124976 1.240025 1.71 0.087 -.3054293 4.555381

MG :

. xtpmg d(chomage inflation pibreel investtotal txinteretreel txdechangereel), lr(l.chomage inflation pibreel

> investtotal txinteretreel txdechangereel)ec(ECT) replace mg

Mean Group Estimation: Error Correction Form

(Estimate results saved as mg)

D.chomage	Coef. Std. Err. z P>|z| [95% Conf. Interval]
ECT inflation	-.1776513 .2490983 -0.71 0.476 -.6658751 .3105725
pibreel	.2827836 .4475003 0.63 0.527 -.5943009 1.159868
investtotal	.4748828 .467392 1.02 0.310 -.4411886 1.390954
txinteretreel	.8572774 1.182418 0.73 0.468 -1.460219 3.174774
txdechangereel	-.0585267 .0384155 -1.52 0.128 -.1338198 .0167663
SR ECT	-.3117279 .0952867 -3.27 0.001 -.4984864 -.1249695
inflation D1.	-.0080757 .0033785 -2.39 0.017 -.0146975 -.0014538
pibreel D1.	.009411 .0069415 1.36 0.175 -.004194 .0230161
investtotal D1.	.009742 .0123089 0.79 0.429 -.014383 .033867
txinteretreel D1.	-.2812857 .1266987 -2.22 0.026 -.5296105 -.0329609
txdechangereel D1.	.0044252 .0020939 2.11 0.035 .0003212 .0085293
_cons	4.641298 2.172837 2.14 0.033 .3826158 8.899979

DFE :

. xtpmg d(chomage inflation pibreel investtotal txinteretreel txdechangereel), lr(l.chomage inflation pibreel

> investtotal txinteretreel txdechangereel)ec(ECT) replace dfe

Dynamic Fixed Effects Regression: Estimated Error Correction Form

(Estimate results saved as DFE)

	Coef. Std. Err. z P>|z| [95% Conf. Interval]
ECT inflation	-.0137253 .119145 -0.12 0.908 -.2472452 .2197947
pibreel	-.0606266 .0523745 -1.16 0.247 -.1632788 .0420256
investtotal	.0477423 .0346909 1.38 0.169 -.0202507 .1157352
txinteretreel	-.4821345 .258411 -1.87 0.062 -.9886108 .0243419
txdechangereel	-.0686283 .0838183 -0.82 0.413 -.2329091 .0956524
SR ECT	-.0903986 .0265186 -3.41 0.001 -.1423741 -.0384231
inflation D1.	-.0021574 .0050822 -0.42 0.671 -.0121183 .0078035
pibreel D1.	-.0004788 .003257 -0.15 0.883 -.0068623 .0059047
investtotal D1.	-.0058804 .0035631 -1.65 0.099 -.0128639 .0011032
txinteretreel D1.	-.1436705 .0754635 -1.90 0.057 -.2915761 .0042352
txdechangereel D1.	.0049131 .0038602 1.27 0.203 -.0026527 .012479
_cons	.9946397 .2858844 3.48 0.001 .4343167 1.554963

Annexe 10 : Test de Hausman MG vs PMG :

. hausman mg pmg, sigmamore

Coefficients

	(b) (B) (b-B) sqrt(diag(V_b-V_B)) mg pmg Difference S.E.
inflation	-.1776513 .1811211 -.3587724 .3420979
pibreel	.2827836 -.3475589 .6303424 .6348628
investtotal	.4748828 -.0408306 .5157134 .6742943
txinteretr~l	.8572774 -.9794337 1.836711 1.697009
txdechange~l	-.0585267 -.0747582 .0162315 .

b = consistent under Ho and Ha; obtained from xtpmg B = inconsistent under Ha, efficient under Ho; obtained from xtpmg Test: Ho: difference in coefficients not systematic

chi2(5) = (b-B)'[(V_b-V_B)^(-1)](b-B) = 9.55

Prob>chi2 = 0.0890

(V_b-V_B is not positive definite)

MG vs DFE :

. hausman mg dfe, sigmamore

Coefficients

	(b) (B) (b-B) sqrt(diag(V_b-V_B)) mg dfe Difference S.E.
inflation	-.1776513 -.0137253 -.163926 3.967301
pibreel	.2827836 -.0606266 .3434102 7.130199
investtotal	.4748828 .0477423 .4271405 7.447262
txinteretr~l	.8572774 -.4821345 1.339412 18.83867
txdechange~l	-.0585267 -.0686283 .0101016 .6063404

b = consistent under Ho and Ha; obtained from xtpmg B = inconsistent under Ha, efficient under Ho; obtained from xtpmg Test: Ho: difference in coefficients not systematic

chi2(5) = (b-B)'[(V_b-V_B)^(-1)](b-B)

= -2.50 chi2<0 ==> model fitted on these data fails to meet the asymptotic assumptions of the Hausman test; see suest for a generalized test

.

DFE vs PMG :

. hausman pmg dfe, sigmamore

Coefficients

	(b) (B) (b-B) sqrt(diag(V_b-V_B)) pmg dfe Difference S.E.
inflation	.1811211 -.0137253 .1948464 1.222221
pibreel	-.3475589 -.0606266 -.2869323 1.333484
investtotal	-.0408306 .0477423 -.0885729 .3411977
txinteretr~l	-.9794337 -.4821345 -.4972993 2.084546
txdechange~l	-.0747582 -.0686283 -.0061299 .7433882

b = consistent under Ho and Ha; obtained from xtpmg B = inconsistent under Ha, efficient under Ho; obtained from xtpmg Test: Ho: difference in coefficients not systematic

chi2(5) = (b-B)'[(V_b-V_B)^(-1)](b-B)

= 0.12

Prob>chi2 = 0.9997

Annexe 10 : Test de non linéarité des pays de l'echantillon.

. xthreg chomage pibreel investtotal txinteretreel txdechangereel, rx(inflation) qx(inflation) thnum (1) trim(0.1) bs(300 > ) noreg

Estimating the threshold parameters: 1st ...... Done

Boostrap for single threshold

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Threshold estimator (level = 95):

model	Threshold Lower Upper
Th-1	4.8576 4.3100 5.0000

Threshold effect test (bootstrap = 300):

Threshold	RSS MSE Fstat Prob Crit10 Crit5 Crit1
Single	177.8727 1.2267 8.41 0.0533 7.0092 8.4258 12.5828

Annexe 11 : Test de non linéarité des trois (3) pays de l'échantillon.

. xthreg chomage pibreel investtotal txinteretreel txdechangereel, rx(inflation) qx(inflation)

> thnum (1) trim(0.05) bs(300) noreg

Estimating the threshold parameters: 1st ...... Done

Boostrap for single threshold

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Threshold estimator (level = 95):

model	Threshold Lower Upper
Th-1	4.8000 4.7000 5.0000

Threshold effect test (bootstrap = 300):

Threshold	RSS MSE Fstat Prob Crit10 Crit5 Crit1
Single	155.0703 2.6736 7.58 0.0367 6.6630 6.6994 7.9623

Annexe 12 : Test du nombre de régime dans le modele non linéaire (Méthode séquentielle)

. xthreg chomage pibreel investtotal txinteretreel txdechangereel, rx(inflation) qx(inflation)

> thnum (3) trim(0.05 0.05 0.05) bs(0 300 300) noreg

Estimating the threshold parameters: 1st ...... 2nd ...... 3rd ...... Done Boostrap for double threshold model:

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Threshold estimator (level = 95):

model	Threshold Lower Upper
Th-1	4.8000 4.7000 5.0000
Th-21	4.6560 4.1000 4.7000
Th-22	2.6790 2.6500 2.7000
Th-3	1.7000 1.5000 1.8000

Threshold effect test (bootstrap = 0 300 300):

Threshold	RSS MSE Fstat Prob Crit10 Crit5 Crit1
Single	. . . . . . .
Double	146.9693 2.5340 3.20 0.7067 5.7866 6.7507 7.0224
Triple	138.6218 2.3900 3.49 0.7967 8.5798 10.5857 10.8448

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Annexe 13 : Estimation des effets de seuil dans le modele non linéaire (PTR)

. xthreg chomage pibreel investtotal txinteretreel txdechangereel, rx(inflation) qx(inflation)

> thnum (1) trim(0.05) bs(300)

Estimating the threshold parameters: 1st ...... Done

Boostrap for single threshold

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Threshold estimator (level = 95):

model	Threshold Lower Upper
Th-1	4.8000 4.7000 5.0000

Threshold effect test (bootstrap = 300):

Threshold	RSS MSE Fstat Prob Crit10 Crit5 Crit1
Single	155.0703 2.6736 7.58 0.0233 6.5104 6.6630 7.9623

Fixed-effects (within) regression Number of obs = 87

Group variable: id Number of groups = 3

R-sq: within = 0.1719 Obs per group: min = 29 between = 0.1733 avg = 29.0 overall = 0.0003 max = 29

F(6,78) = 2.70 corr(u_i, Xb) = -0.0723 Prob > F = 0.0197

chomage	Coef. Std. Err. t P>|t| [95% Conf. Interval]
pibreel	-.0560309 .0486998 -1.15 0.253 -.1529847 .040923
investtotal	-.0026942 .0181101 -0.15 0.882 -.0387486 .0333603
txinteretreel	.1104411 .0972001 1.14 0.259 -.0830695 .3039517
txdechangereel	-.0498258 .0229604 -2.17 0.033 -.0955364 -.0041152
_cat#c.inflation 0	.2654049 .1016058 2.61 0.011 .0631233 .4676865
1	-.0421471 .0314368 -1.34 0.184 -.1047329 .0204387
_cons	13.96681 .8437679 16.55 0.000 12.287 15.64662
sigma_u	8.4087306
sigma_e	1.4099933
rho	.97265168 (fraction of variance due to u_i)

F test that all u_i=0: F(2, 78) = 558.64 Prob > F = 0.0000

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Post-estimation :