Quantitative Easing and Economic Stability: Adaptive Strategies in Indonesia’s New Trinity Framework

Research Methodology – Full Modeling

A. Definisi Variabel dan Sistem Model

A. Variable Definition and Model System

🇮🇩 Bahasa Indonesia

Penelitian ini menggunakan sistem multivariat berbasis VAR dengan enam variabel makroekonomi dan keuangan yang merepresentasikan kebijakan moneter, stabilitas harga, aktivitas riil, nilai tukar, pasar keuangan, dan pasar obligasi.

Vektor variabel endogen didefinisikan sebagai: $\mathbf{y}_t= \begin{bmatrix} BI_t\\ INF_t\\ GDP_t\\ REER_t\\ IHSG_t\\ SUN_t \end{bmatrix}$

dengan:

$BI_t$ : suku bunga kebijakan Bank Indonesia
$INF_t$ : tingkat inflasi
$GDP_t$ : pertumbuhan PDB
$REER_t$ : nilai tukar efektif riil
$IHSG_t$ : indeks pasar saham
$SUN_t$ : indikator obligasi pemerintah

🇬🇧 English

This study employs a multivariate VAR-based framework incorporating six macroeconomic and financial variables representing monetary policy, price stability, real activity, exchange rate dynamics, financial markets, and government bond markets.

The endogenous variable vector is defined as: $\mathbf{y}_t= \begin{bmatrix} BI_t\\ INF_t\\ GDP_t\\ REER_t\\ IHSG_t\\ SUN_t \end{bmatrix}$

where:

$BI_t$ : policy interest rate
$INF_t$ : inflation rate
$GDP_t$ : GDP growth
$REER_t$ : real effective exchange rate
$IHSG_t$ : stock market index
$SUN_t$ : government bond indicator

B. Tahapan Pra-Estimasi

B. Pre-Estimation Procedures

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Analisis deskriptif untuk mengidentifikasi tren, volatilitas, dan potensi structural break.
Uji stasioneritas (ADF) untuk setiap variabel:

$\Delta x_t=\alpha+\beta t+\rho x_{t-1}+\sum_{i=1}^{m}\psi_i\Delta x_{t-i}+u_t$

Penentuan lag optimal menggunakan AIC, HQ, SC, dan FPE.
Uji diagnostik: autokorelasi residual dan stabilitas sistem.

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Descriptive analysis to identify trends, volatility, and structural breaks.
Stationarity testing (ADF) for each variable:

$\Delta x_t=\alpha+\beta t+\rho x_{t-1}+\sum_{i=1}^{m}\psi_i\Delta x_{t-i}+u_t$

Lag length selection based on AIC, HQ, SC, and FPE.
Diagnostic tests: residual autocorrelation and system stability.

C. Model TVAR (Threshold Vector Autoregression)

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Model TVAR digunakan untuk menangkap nonlinearitas dan perbedaan rezim ekonomi. Variabel threshold ditetapkan sebagai pertumbuhan PDB. $\mathbf{y}_t= \begin{cases} \mathbf{c}_1+\sum_{i=1}^{p}\mathbf{A}_{1,i}\mathbf{y}_{t-i}+\boldsymbol{\varepsilon}_{1,t}, & GDP_{t-d}\le\gamma\\ \mathbf{c}_2+\sum_{i=1}^{p}\mathbf{A}_{2,i}\mathbf{y}_{t-i}+\boldsymbol{\varepsilon}_{2,t}, & GDP_{t-d}>\gamma \end{cases}$

Nilai ambang $\gamma$ γ ditentukan melalui grid search dengan meminimalkan sum of squared residuals.

TVAR memungkinkan analisis:

perbedaan transmisi QE pada kondisi volatilitas rendah dan tinggi,
perbedaan IRF dan FEVD antar-rezim.

🇬🇧

The TVAR model captures nonlinear dynamics and regime-dependent behavior. GDP growth is selected as the threshold variable. $\mathbf{y}_t= \begin{cases} \mathbf{c}_1+\sum_{i=1}^{p}\mathbf{A}_{1,i}\mathbf{y}_{t-i}+\boldsymbol{\varepsilon}_{1,t}, & GDP_{t-d}\le\gamma\\ \mathbf{c}_2+\sum_{i=1}^{p}\mathbf{A}_{2,i}\mathbf{y}_{t-i}+\boldsymbol{\varepsilon}_{2,t}, & GDP_{t-d}>\gamma \end{cases}$

The threshold value $\gamma$ γ is obtained through grid search, minimizing the sum of squared residuals.

TVAR allows:

comparison of QE transmission across regimes,
regime-specific IRF and FEVD analysis.

D. Model BVAR (Bayesian Vector Autoregression)

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Model VAR dasar: $\mathbf{y}_t=\mathbf{c}+\sum_{i=1}^{p}\mathbf{A}_i\mathbf{y}_{t-i}+\boldsymbol{\varepsilon}_t$

Pendekatan Bayesian: $p(\theta|\mathbf{Y})\propto p(\mathbf{Y}|\theta)\,p(\theta)$

dengan prior Minnesota untuk membatasi overfitting dan meningkatkan stabilitas estimasi. BVAR digunakan sebagai validasi robust terhadap hasil TVAR.

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The baseline VAR model is specified as: $\mathbf{y}_t=\mathbf{c}+\sum_{i=1}^{p}\mathbf{A}_i\mathbf{y}_{t-i}+\boldsymbol{\varepsilon}_t$

Bayesian inference follows: $p(\theta|\mathbf{Y})\propto p(\mathbf{Y}|\theta)\,p(\theta)$

Minnesota priors are employed to shrink parameters and improve estimation robustness. BVAR serves as a robustness check for TVAR findings.

E. Model TVP-VAR (Time-Varying Parameter VAR)

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TVP-VAR memungkinkan koefisien berubah seiring waktu: $\mathbf{y}_t=\mathbf{X}_t\boldsymbol{\beta}_t+\boldsymbol{\varepsilon}_t$

dengan evolusi parameter: $\boldsymbol{\beta}_t=\boldsymbol{\beta}_{t-1}+\mathbf{u}_t$

Model ini sangat relevan untuk menganalisis perubahan efektivitas QE selama krisis, khususnya pandemi COVID-19.

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The TVP-VAR model allows coefficients to evolve over time: $\mathbf{y}_t=\mathbf{X}_t\boldsymbol{\beta}_t+\boldsymbol{\varepsilon}_t$

Parameter evolution follows: $\boldsymbol{\beta}_t=\boldsymbol{\beta}_{t-1}+\mathbf{u}_t$

This framework is crucial for examining time-varying QE effectiveness, particularly during crisis episodes.

F. Catatan Metodologis Utama

G. Key Methodological Remarks

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Pendekatan multi-model (TVAR–BVAR–TVP-VAR) memungkinkan analisis kebijakan QE secara nonlinear, robust, dan adaptif, sejalan dengan kompleksitas kebijakan moneter di negara berkembang.

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The multi-model approach (TVAR–BVAR–TVP-VAR) enables a nonlinear, robust, and adaptive assessment of QE, consistent with the complexity of monetary policy in emerging economies.