StatMastery OS — Laboratorium Terapan: Ekonometrika, Keuangan IDR, Audit & Hukum

Lab 1 • The Econometrics & Policy Lab

Panel Data Visual Matrix (FE/RE & Simpson's Paradox), 2SLS IV & Macro VAR IRF

A. Panel Data Visual Matrix (4 Provinsi × 10 Tahun)

Heterogenitas Karakteristik Tak Teramati Antar Provinsi (αᵢ) Tinggi (Simpson's Paradox!)

Slope Pooled OLS (β̂_Pool) -0.64 (Arah Terbalik!)

Slope Fixed Effects (β̂_FE) +0.75 (Kausal Sejati)

Uji Hausman (χ² & Keputusan) χ² = 24.8 (p < 0.001 ➔ Pilih FE)

B. Endogeneity 2SLS (IV) & Macro VAR Impulse Response (IRF)

Shock Suku Bunga / Kekuatan Instrumen Z +1.50 SD (F-First Stage = 28.4)

Persistensi Makro (ρ) / Endogenitas Cov(X,ε) 0.75

Parameter Sejati (β_True) +0.80

Estimasi OLS Bias (β̂_OLS) +1.42 (Bias Endogen!)

Estimasi 2SLS / IV (β̂_2SLS) +0.81 (Konsisten)

Lab 2 • Quantitative Finance & Portfolio Risk Lab (Satuan Rupiah / IDR)

Markowitz Efficient Frontier, CAPM Alpha-Beta & Monte Carlo VaR / CVaR (Rp 1 Miliar)

A. Markowitz Efficient Frontier & CAPM Regression

Bobot Saham Unggulan vs SBN/Emas 60% Saham / 40% SBN

Korelasi Antar Aset (ρ) -0.15

Ekspektasi Return Tahunan (IDR) +13.4% (Rp 134,0 Jt)

Sharpe Ratio Portofolio 0.78 (Optimal: 0.84)

CAPM Beta (β) & Jensen's α β = 1.12 | α = +2.4%/thn

B. Monte Carlo GBM (252 Hari), VaR & Expected Shortfall (CVaR)

Tingkat Kepercayaan VaR (1 - α) 95%

GARCH Volatility Shock / Fat-Tails 22% / tahun

Parametric VaR (Modal Rp 1 Miliar) -Rp 184,5 Juta (-18.5%)

Expected Shortfall (CVaR Ekor) -Rp 238,2 Juta (-23.8%)

Rata-rata Nilai Akhir (252 Hari) Rp 1.124,0 Juta

Lab 3 • Economic Policy, Inequality & Micro-Elasticity Lab

Kurva Lorenz, Gini Ratio & Double-Log Demand Elasticity Estimator

A. Kurva Lorenz, Koefisien Gini & Simulasi Pajak Progresif

Ketimpangan Struktural Awal (p) 2.60

Redistribusi Pajak & Subsidi Tunai 20%

Koefisien Gini (A / (A + B)) 0.382 (Moderat)

Indeks Entropi Theil (T) 0.246

Pangsa Top 20% Populasi 45.8% Pendapatan

B. Double-Log Demand: ln(Q) = α + β·ln(P) + γ·ln(I)

Elastisitas Harga (β = %ΔQ / %ΔP) -1.35 (Elastis)

Elastisitas Pendapatan (γ = %ΔQ / %ΔI) +0.85 (Barang Normal)

Bukti Kalkulus: ∂ln(Q)/∂ln(P) = (∂Q/Q) / (∂P/P) = β = -1.35 ➔ Jika harga naik 10%, kuantitas permintaan turun 13.5%.

Lab 4 • Forensic Accounting, Audit & Tax Evasion Lab

Benford's Law Fraud Detector & Monetary Unit Sampling (MUS) / Mixed Cost OLS

A. Benford's Law First-Digit Fraud & Tax Evasion Detector

Chi-Square (χ²_hitung vs 15.51) 4.12 (Patuh / Alami)

Mean Absolute Deviation (MAD) 0.0082 (Close Conformity)

Status Audit Forensik ✓ Wajar Tanpa Indikasi Fraud

B. Monetary Unit Sampling (MUS) & Cost Behavior (OLS vs High-Low)

Tolerable Misstatement Audit (Rp Juta) Rp 250 Juta

Outlier Biaya Produksi Bulan Puncak +Rp 180 Juta

Ukuran Sampel MUS (Pop Rp 10 Miliar) n = 120 Faktur (Interval Rp 83,3 Jt)

Estimasi Biaya OLS (Tahan Outlier) FC = Rp 195 Jt + Rp 4.2rb/unit

Metode High-Low (Terkecoh Outlier) FC = Rp 62 Jt + Rp 6.8rb/unit

Lab 5 • Jurimetrics Legal Analytics & Survival Analysis Lab

Bayesian Evidentiary Weight (Log-Odds Ladder) & Kaplan-Meier Litigation Survival

A. Bayesian Evidentiary Weight & Standar Pembuktian Hukum

Probabilitas Awal / Prior P(H) 10%

LR Bukti 1 (Audit Jejak Digital) 5.0×

LR Bukti 2 (Aliran Rekening Forensik) 8.0×

Posterior Akhir P(H | E₁, E₂) 81.63%

Standar Perdata / Pajak (>50%) ✓ Terbukti (Preponderance)

Standar Pidana (>95% Beyond Doubt) ⚠️ Belum Mencapai 95%

B. Kaplan-Meier Survival Curve: Ketahanan Kontrak & Sengketa

Tingkat Risiko Sengketa / Hazard Rate Moderat (0.12)

Proporsi Data Tersensor (+) 25%

Estimator Kaplan-Meier: Ŝ(t) = ∏_(tᵢ ≤ t) [ 1 - (dᵢ / nᵢ) ] • Tanda (+) menandai observasi tersensor kanan.