Pendahuluan

Data panel menggabungkan dimensi cross-section dan time series, memungkinkan kita mengontrol heterogenitas individu yang tidak terobservasi. Tutorial ini membahas estimasi model data panel di STATA secara lengkap.

Notasi Model

\[ y_{it} = \alpha_i + \mathbf{x}_{it}'\boldsymbol{\beta} + \varepsilon_{it} \]

• \(\alpha_i\): efek individu (fixed atau random)
• \(\mathbf{x}_{it}\): vektor variabel independen
• \(\varepsilon_{it}\): error term idiosinkratik

Setup Data

Kita gunakan dataset nlswork (National Longitudinal Survey) bawaan STATA.

* Load data
webuse nlswork, clear

* Lihat struktur
describe
summarize ln_wage age tenure hours

* Deklarasi data panel
xtset idcode year

* Ringkasan panel
xtdescribe
xtsum ln_wage age tenure hours

xtsum memberikan dekomposisi between vs within variation — penting untuk memahami sumber variasi data.

Estimasi Model

Pooled OLS (Baseline)

reg ln_wage age c.age#c.age tenure hours i.race, robust
estimates store pooled

Fixed Effects (FE)

xtreg ln_wage age c.age#c.age tenure hours, fe robust
estimates store fe

Catatan: Variabel time-invariant (seperti race) otomatis tereliminasi di FE.

Random Effects (RE)

xtreg ln_wage age c.age#c.age tenure hours i.race, re robust
estimates store re

Perbandingan Output

estimates table pooled fe re, star stats(N r2 r2_a r2_w r2_b r2_o)

Hausman Test: FE vs RE

Hipotesis: - \(H_0\): RE konsisten dan efisien (gunakan RE) - \(H_1\): RE tidak konsisten (gunakan FE)

* Estimasi ulang tanpa robust untuk Hausman test
quietly xtreg ln_wage age c.age#c.age tenure hours, fe
estimates store fe_haus

quietly xtreg ln_wage age c.age#c.age tenure hours, re
estimates store re_haus

hausman fe_haus re_haus

Jika \(p < 0.05\), tolak \(H_0\) → gunakan Fixed Effects.

Uji Asumsi

1. Heteroskedastisitas (Modified Wald Test)

* Setelah xtreg, fe
quietly xtreg ln_wage age c.age#c.age tenure hours, fe
xttest3

2. Autokorelasi (Wooldridge Test)

xtserial ln_wage age tenure hours

3. Cross-Sectional Dependence (Pesaran CD Test)

quietly xtreg ln_wage age c.age#c.age tenure hours, fe
xtcsd, pesaran abs

Solusi jika Asumsi Dilanggar

Masalah	Solusi
Heteroskedastisitas	robust atau vce(cluster idcode)
Autokorelasi	vce(cluster idcode)
Keduanya	Driscoll-Kraay: xtscc

* Cluster-robust standard errors (solusi umum)
xtreg ln_wage age c.age#c.age tenure hours, fe vce(cluster idcode)

Visualisasi

* Marginal effects of age (quadratic)
quietly xtreg ln_wage c.age##c.age tenure hours, fe robust
margins, at(age=(18(2)46)) vsquish
marginsplot, ///
    title("Predicted Log Wage by Age") ///
    ytitle("Predicted ln(wage)") ///
    xtitle("Age") ///
    scheme(s2color)

Ringkasan Perintah

Langkah	Perintah STATA	Keterangan
Setup panel	xtset id time	Deklarasi struktur panel
Deskriptif	xtsum, xtdescribe	Statistik between/within
Fixed Effects	xtreg y x, fe	Eliminasi efek individu
Random Effects	xtreg y x, re	Efek individu sebagai random
Hausman test	hausman fe re	Pilih FE vs RE
Heteroskedastisitas	xttest3	Modified Wald test
Autokorelasi	xtserial	Wooldridge test
Robust SE	vce(cluster id)	Cluster-robust

Referensi

• Baltagi, B. H. (2021). Econometric Analysis of Panel Data. 6th ed. Springer.
• Wooldridge, J. M. (2010). Econometric Analysis of Cross Section and Panel Data. 2nd ed. MIT Press.

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Tutorial selanjutnya: Dynamic Panel Data — GMM Estimation di STATA.