Os modelos de Markov oferecem ferramentas estatísticas e econométricas convenientes para lidar com distintas fases de mudanças estruturais em economia. Dentre as suas vantagens podemos citar a possibilidade de criar mais de um processo gerador dos dados, a partir de estimação de regressões para cada regime. Empiricamente, há fortes evidências de que os modelos markovianos seriam mais robustos aos dados, com a construção de projeções mais consistentes para as series macroeconômicas.
Em linha com a teoria, o modelo sugere que há uma tendência de afrouxamento monetário em média para o horizonte de curto e de longo prazos no Brasil. Essa nova realidade é reflexo das melhorias dos indicadores macroeconômicos do Brasil identificadas por consultorias, por órgãos de pesquisa econômica e por instituição de rating internacional, a exemplo da Moody’s10.
Contudo, acreditamos que é importante darmos maior atenção para o controle da dívida pública. Conforme demonstrado pelo modelo MS-VAR, a dívida pública elevada foi um dos fatores que contribuiu para o aperto monetário observado no Brasil nos primeiros anos do Plano Real. Naquele período, houve crescimento da desconfiança dos agentes quanto à sustentabilidade fiscal do setor público em virtude de redução do superávit primário. Diante disso cenário, os agentes econômicos passaram a exigir um prêmio de risco mais elevado, ilustrado pela taxa de juros mais alta e pela demanda por títulos públicos com vencimento mais curto.
Atualmente, em que pese a atual arquitetura da política macroeconômica doméstica baseada no tripé meta de inflação, taxa de câmbio flutuante e disciplina fiscal, a questão relacionada à magnitude e à composição das despesas pública não pode ser menosprezada, dado os resultados do modelo.
De fato, parte significante incremento dos gastos, nos últimos anos, se deve basicamente a despesas de difícil reversão, ligadas basicamente a reajuste e as contratações de
servidores públicos. Essa tendência de aumento das despesas públicas pode ser sustentada no curto prazo pelo aumento da arrecadação tributária, em função das perspectivas crescimento econômico.
Todavia, no longo prazo, o aumento da carga tributária acaba penalizando o investimento produtivo e expulsando a iniciativa privada do mercado, em um efeito crownding-out. Esse fato poderá contribuir para reduzir o crescimento no longo prazo e comprometer a receita pública em um ambiente de gastos rígidos e crescentes. Com isso, poderemos testemunhar uma ampliação dívida pública com maiores obrigações no passivo total do Governo Federal e, conseqüente, um movimento de overshooting da taxa de juros, alimentado pela elevação do grau de aversão ao risco (dominância fiscal).
REVISÃO BIBLIOGRÁFICA
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APÊNDICE A – RESULTADOS DO MODELO MSH(2)VAR(3)
--- EM algorithm converged after 18 iterations ---
EQ( 1) MSH(2)-VARX(3) model of (SELIC,IPCA,DIVIDA_M1) Estimation sample: 1995 (11) - 2009 (7)
no. obs. per eq. : 165 in the system : 495 no. parameters : 53 linear system : 45 no. restrictions : 6
no. nuisance p. : 2
log-likelihood : 1187.3532 linear system : 1005.8968
AIC criterion : -13.7497 linear system : -11.6472 HQ criterion : -13.3447 linear system : -11.3034 SC criterion : -12.7521 linear system : -10.8002
LR linearity test: 362.9127 Chi(6) =[0.0000] ** Chi(8)=[0.0000] ** DAVIES=[0.0000] **
--- matrix of transition probabilities ---
Regime 1 Regime 2 Regime 1 0.9364 0.0636 Regime 2 0.1558 0.8442
--- regime properties ---
Regime 1 113.8 0.7102 15.73 Regime 2 51.2 0.2898 6.42
--- coefficients ---
SELIC IPCA DIVIDA_M1 Const -0.001891 -0.000107 0.000377 SELIC_1 0.520715 0.000164 -0.006124 SELIC_2 0.207322 0.004355 0.125706 SELIC_3 -0.082861 0.000906 -0.046998 IPCA_1 0.219644 0.600086 -0.375258 IPCA_2 0.896418 -0.110225 1.074705 IPCA_3 -0.478124 0.129409 0.038224 DIVIDA_M1_1 -0.014635 -0.008438 -0.082004 DIVIDA_M1_2 -0.024420 0.001125 -0.070771 DIVIDA_M1_3 -0.006188 0.003640 -0.054579 FED_1 -0.002568 0.001033 0.051469 FED_2 -0.013097 -0.003460 -0.007023 FED_3 0.046469 0.002004 -0.050914 SE (Reg.1) 0.012791 0.003286 0.063466 SE (Reg.2) 0.211974 0.006545 0.081558 --- contemporaneous correlation --- Regime 1
SELIC IPCA DIVIDA_M1 SELIC 1.0000 0.2230 0.1244 IPCA 0.2230 1.0000 0.1234 DIVIDA_M1 0.1244 0.1234 1.0000
Regime 2
SELIC 1.0000 0.0886 -0.1242 IPCA 0.0886 1.0000 -0.0621 DIVIDA_M1 -0.1242 -0.0621 1.0000
--- calculate covariance matrix ---
--- standard errors ---
SELIC IPCA DIVIDA_M1 Mean 0.0013788 0.00033562 0.0055530 SELIC_1 0.058088 0.0048373 0.064943 SELIC_2 0.061419 0.0046575 0.060798 SELIC_3 0.044373 0.0043080 0.058890 IPCA_1 0.40197 0.064888 1.1646 IPCA_2 0.33202 0.11233 1.3375 IPCA_3 0.28518 0.099691 1.1360 DIVIDA_M1_1 0.019467 0.0048217 0.079382 DIVIDA_M1_2 0.019367 0.0045501 0.078332 DIVIDA_M1_3 0.019135 0.0043769 0.076442 FED_1 0.010946 0.0027538 0.052140 FED_2 0.014847 0.0036087 0.066729 FED_3 0.012555 0.0029516 0.053883 --- t - values ---
SELIC IPCA DIVIDA_M1 const -1.3718 -0.3197 0.0678 SELIC_1 8.9643 0.0340 -0.0943 SELIC_2 3.3756 0.9351 2.0676 SELIC_3 -1.8674 0.2103 -0.7981 IPCA_1 0.5464 9.2481 -0.3222 IPCA_2 2.6999 -0.9812 0.8035
IPCA_3 -1.6765 1.2981 0.0336 DIVIDA_M1_1 -0.7518 -1.7500 -1.0330 DIVIDA_M1_2 -1.2609 0.2472 -0.9035 DIVIDA_M1_3 -0.3234 0.8315 -0.7140 FED_1 -0.2346 0.3750 0.9871 FED_2 -0.8821 -0.9586 -0.1052 FED_3 3.7014 0.6788 -0.9449 --- regime classification --- Regime 1 1998:4 - 1998:8 [0.9422] 1999:8 - 2000:6 [0.9790] 2000:10 - 2001:5 [0.9458] 2001:8 - 2002:9 [0.9944] 2002:12 - 2003:7 [0.9083] 2003:11 - 2009:4 [0.9976] 2009:6 - 2009:7 [0.9859] Regime 2 1995:11 - 1998:3 [0.9848] 1998:9 - 1999:7 [0.9717] 2000:7 - 2000:9 [0.6996] 2001:6 - 2001:7 [0.9900] 2002:10 - 2002:11 [0.9999] 2003:8 - 2003:10 [0.9866] 2009:5 - 2009:5 [0.9938]
Gráfico de probabilidade de mudança de regime Gráfico de resíduos 2000 2005 2010 0.0 0.5 MSH(2)-VARX(3), 1995 (11) - 2009 (7) SELIC DIVIDA_M1 IP CA 2000 2005 2010 0.5 1.0 Probabilities of Regime 1 filtered predicted smoothed 2000 2005 2010 0.5 1.0 Probabilities of Regime 2 filtered predicted smoothed 2000 2005 2010 -0.5 0.0 0.5
1.0 SELIC - ErrorsPrediction errors Smoothed errors
2000 2005 2010
-2.5 0.0 2.5
5.0 SELIC - Standard residsStandard resids
2000 2005 2010
-0.02 -0.01 0.00 0.01
0.02 IPCA - ErrorsPrediction errors Smoothed errors
2000 2005 2010
-2.5 0.0 2.5
IPCA - Standard resids
Standard resids 2000 2005 2010 -0.2 0.0 0.2 DIVIDA_M1 - Errors
Prediction errors Smoothed errors
2000 2005 2010
-2.5 0.0 2.5
DIVIDA_M1 - Standard resids
Gráfico de diagnósticos 1
Gráfico de diagnósticos 2
1 13 25
0
1 Correlogram: Standard resids ACF-SELIC PACF-SELIC
0.0 0.5 1.0
0.1 0.2
Spectral density: Standard resids
SELIC
-5.0 -2.5 0.0 2.5 5.0 0.25
0.50
Density: Standard resids
SELIC N(s=0.98)
-2 0 2
-2.5 0.0 2.5
5.0 QQ Plot: Standard resids SELIC × normal
1 13 25
0
1 Correlogram: Standard resids ACF-IPCA PACF-IPCA
0.0 0.5 1.0
0.1 0.2
0.3 Spectral density: Standard resids IPCA
-5.0 -2.5 0.0 2.5 5.0 0.2
0.4
Density: Standard resids
IPCA N(s=0.993)
-2 0 2
-2.5 0.0 2.5
QQ Plot: Standard resids
IPCA × normal
1 13 25
0
1 Correlogram: Standard resids
ACF-DIVIDA_M1 PACF-DIVIDA_M1
0.0 0.5 1.0
0.1 0.2
Spectral density: Standard resids
DIVIDA_M1
-5.0 -2.5 0.0 2.5 0.25
0.50
Density: Standard resids
DIVIDA_M1 N(s=1)
-2 0 2
-2.5 0.0 2.5
QQ Plot: Standard resids
DIVIDA_M1 × normal
1 13 25
0
1 Correlogram: Prediction errors ACF-SELIC PACF-SELIC
0.0 0.5 1.0
0.1 0.2 0.3
Spectral density: Prediction errors
SELIC
-0.5 0.0 0.5 1.0
5 10
15 Density: Prediction errors SELIC N(s=0.119)
-2 0 2
0 5
QQ Plot: Prediction errors
SELIC × normal
1 13 25
0
1 Correlogram: Prediction errors ACF-IPCA PACF-IPCA
0.0 0.5 1.0
0.1 0.2
0.3 Spectral density: Prediction errors IPCA
-0.02 0.00 0.02
50 100
Density: Prediction errors
IPCA N(s=0.00455)
-2 0 2
-2.5 0.0 2.5
5.0 QQ Plot: Prediction errorsIPCA × normal
1 13 25
0
1 Correlogram: Prediction errors ACF-DIVIDA_M1 PACF-DIVIDA_M1
0.0 0.5 1.0
0.1 0.2
Spectral density: Prediction errors
DIVIDA_M1
-0.25 0.00 0.25 2.5
5.0 7.5
10.0 Density: Prediction errors DIVIDA_M1 N(s=0.0696)
-2 0 2
-2.5 0.0 2.5
QQ Plot: Prediction errors
Gráfico dos valores atuais e filtrados
Gráfico de probabilidade predita
2000 2005 2010
0.0 0.5
SELIC in the MSH(2)-VARX(3) mean
fitted SELIC 1-step prediction
2000 2005 2010
-0.02 0.00 0.02
IPCA in the MSH(2)-VARX(3) mean
fitted IP CA 1-step prediction
2000 2005 2010
-0.2 0.0 0.2
DIVIDA_M1 in the MSH(2)-VARX(3) mean
fitted DIVIDA_M1 1-step prediction
0 25 50
0.5 1.0
Predicted h-step probabilities when st = 1
Reg ime 1 Regime 2
0 25 50
0.5
1.0Predicted h-step probabilities when st = 2
Regime 1 Regime 2 0 25 50 75 0.05 0.10 0.15 Probability of duration = h
Reg ime 1 Reg ime 2
0 25 50 75 0.5 1.0 Probability of duration ≤h Regime 1 Regime 2 0 25 50 75 0.5 1.0
Probability of staying in the same regime h periods ahead
APÊNDICE B – RESULTADOS DO MODELO MSH(3)VAR(2)
--- EM algorithm converged after 30 iterations ---
EQ( 1) MSH(3)-VARX(2) model of (SELIC,IPCA,DIVIDA_M1) Estimation sample: 1995 (10) - 2009 (7)
no. obs. per eq. : 166 in the system : 498 no. parameters : 51 linear system : 33 no. restrictions : 12
no. nuisance p. : 6
log-likelihood : 1221.5678 linear system : 1006.2592
AIC criterion : -14.1032 linear system : -11.7260 HQ criterion : -13.7151 linear system : -11.4749 SC criterion : -13.1471 linear system : -11.1074
LR linearity test: 430.6172 Chi(12) =[0.0000] ** Chi(18)=[0.0000] ** DAVIES=[0.0000] **
--- matrix of transition probabilities ---
Regime 1 Regime 2 Regime 3 Regime 1 0.9680 0.01813 0.01386 Regime 2 0.04662 0.9534 2.896e-010 Regime 3 0.02634 0.02407 0.9496
nObs Prob. Duration Regime 1 76.5 0.5537 31.26 Regime 2 50.1 0.2940 21.45 Regime 3 39.4 0.1523 19.84
--- coefficients ---
SELIC IPCA DIVIDA_M1 Const -0.002890 -0.000259 0.000735 SELIC_1 0.603576 -0.003123 -0.010748 SELIC_2 0.082153 0.003782 0.117236 IPCA_1 0.216792 0.600300 -0.279833 IPCA_2 1.188155 -0.060271 0.689368 DIVIDA_M1_1 -0.035242 -0.007170 -0.085270 DIVIDA_M1_2 -0.046277 -0.003645 -0.084178 FED_1 -0.013734 -0.000651 0.058817 FED_2 0.030169 -0.000326 -0.037425 SE (Reg.1) 0.012563 0.002344 0.054325 SE (Reg.2) 0.027930 0.006977 0.071295 SE (Reg.3) 0.243633 0.004336 0.092166 --- contemporaneous correlation --- Regime 1
SELIC IPCA DIVIDA_M1 SELIC 1.0000 0.3598 0.0041 IPCA 0.3598 1.0000 -0.1344 DIVIDA_M1 0.0041 -0.1344 1.0000
Regime 2
SELIC 1.0000 0.1745 -0.0018 IPCA 0.1745 1.0000 0.0710 DIVIDA_M1 -0.0018 0.0710 1.0000
Regime 3
SELIC IPCA DIVIDA_M1 SELIC 1.0000 0.0082 -0.1320 IPCA 0.0082 1.0000 0.0387 DIVIDA_M1 -0.1320 0.0387 1.0000
--- calculate covariance matrix ---
--- standard errors ---
SELIC IPCA DIVIDA_M1 Mean 0.0014885 0.00026372 0.0052496 SELIC_1 0.058804 0.0035481 0.071233 SELIC_2 0.056028 0.0031861 0.063715 IPCA_1 0.42499 0.077375 1.1843 IPCA_2 0.41549 0.079218 1.1901 DIVIDA_M1_1 0.023589 0.0040247 0.077585 DIVIDA_M1_2 0.023966 0.0040403 0.078102 FED_1 0.010121 0.0018851 0.042408 FED_2 0.010173 0.0018928 0.042675 --- t - values ---
SELIC IPCA DIVIDA_M1 const -1.9415 -0.9822 0.1400 SELIC_1 10.2642 -0.8802 -0.1509 SELIC_2 1.4663 1.1870 1.8400 IPCA_1 0.5101 7.7583 -0.2363
IPCA_2 2.8596 -0.7608 0.5792 DIVIDA_M1_1 -1.4940 -1.7814 -1.0991 DIVIDA_M1_2 -1.9309 -0.9021 -1.0778 FED_1 -1.3570 -0.3455 1.3869 FED_2 2.9657 -0.1723 -0.8770 --- regime classification --- Regime 1 1998:4 - 1998:8 [0.9678] 2001:9 - 2002:4 [0.8454] 2004:3 - 2009:7 [0.9798] Regime 2 1999:6 - 2001:8 [0.9539] 2002:5 - 2004:2 [0.9892] Regime 3 1995:10 - 1998:3 [0.9992] 1998:9 - 1999:5 [1.0000] --- asymmetry testing ---
NonSharpness test: Chi(3) = 0.3172 [0.9568] p_12 = p_32 test: Chi(1) = 0.0415 [0.8386] p_13 = p_31 test: Chi(1) = 0.2739 [0.6007] p_21 = p_23 test: Chi(1) = 0.0082 [0.9280]
Gráfico de resíduos Gráfico de diagnóstico 1 2000 2005 2010 -0.5 0.0 0.5
1.0 SELIC - ErrorsPrediction errors Smoothed errors
2000 2005 2010
-2.5 0.0 2.5
SELIC - Standard resids
Standard resids
2000 2005 2010
-0.02 0.00
0.02 IPCA - Errors
Prediction errors Smoothed errors
2000 2005 2010
-2.5 0.0 2.5
IPCA - Standard resids
Standard resids 2000 2005 2010 -0.2 0.0 0.2 DIVIDA_M1 - Errors
Prediction errors Smoothed errors
2000 2005 2010
-2.5 0.0
2.5 DIVIDA_M1 - Standard residsStandard resids
1 13 25 0
1 Correlogram: Standard resids ACF-SELIC PACF-SELIC
0.0 0.5 1.0 0.1
0.2
Spectral density: Standard resids
SELIC
-5.0 -2.5 0.0 2.5 5.0 0.2
0.4
Density: Standard resids
SELIC N(s=0.993)
-2 0 2 -2.5
0.0 2.5
QQ Plot: Standard resids
SELIC × normal
1 13 25 0
1 Correlogram: Standard resids ACF-IPCA PACF-IPCA
0.0 0.5 1.0 0.1
0.2
0.3 Spectral density: Standard resids IPCA
-5.0 -2.5 0.0 2.5 0.2
0.4
Density: Standard resids
IPCA N(s=0.991)
-2 0 2 -2.5
0.0 2.5
QQ Plot: Standard resids
IPCA × normal
1 13 25 0
1 Correlogram: Standard resids ACF-DIVIDA_M1 PACF-DIVIDA_M1
0.0 0.5 1.0 0.1
0.2
Spectral density: Standard resids
DIVIDA_M1
-5.0 -2.5 0.0 2.5 0.2
0.4
0.6 Density: Standard resids DIVIDA_M1 N(s=0.999)
-2 0 2 -2.5
0.0
Gráfico de diagnóstico 2
Gráfico dos valores atuais e filtrados
1 13 25 0
1 Correlogram: Prediction errors
ACF-SELIC PACF-SELIC
0.0 0.5 1.0 0.1
0.2 0.3
Spectral density: Prediction errors
SELIC
-0.5 0.0 0.5 1.0 5
10
15 Density: Prediction errors
SELIC N(s=0.12)
-2 0 2 -5
0 5
QQ Plot: Prediction errors
SELIC × normal
1 13 25 0
1 Correlogram: Prediction errors
ACF-IPCA PACF-IPCA
0.0 0.5 1.0 0.1
0.2 0.3
Spectral density: Prediction errors
IPCA
-0.02 0.00 0.02 50
100
150 Density: Prediction errors
IPCA N(s=0.00465)
-2 0 2 -2.5
0.0 2.5
5.0 QQ Plot: Prediction errors
IPCA × normal
1 13 25 0
1 Correlogram: Prediction errors ACF-DIVIDA_M1 PACF-DIVIDA_M1
0.0 0.5 1.0 0.1
0.2
Spectral density: Prediction errors
DIVIDA_M1
-0.25 0.00 0.25 5
10 Density: Prediction errors DIVIDA_M1 N(s=0.07)
-2 0 2 -2.5
0.0 2.5
QQ Plot: Prediction errors
DIVIDA_M1 × normal
2000 2005 2010
0.0 0.5
SELIC in the MSH(3)-VARX(2) mean
fitted SE L IC 1-step prediction
2000 2005 2010
-0.02 0.00 0.02
IPCA in the MSH(3)-VARX(2) mean
fitted IP CA 1-step prediction
2000 2005 2010
-0.2 0.0 0.2
DIVIDA_M1 in the MSH(3)-VARX(2) mean