Serial Correlation and Heteroscedasticity Tests in Panel Data

 

 

In panel data econometrics, valid model estimation depends on key assumptions about the error term. Two major issues to test for are:

 1. Serial Correlation (Autocorrelation)

 What is it?

Serial correlation occurs when error terms are correlated over time within a panel unit (i.e., the error in year t is related to error in year t-1 for the same unit).

 Why it matters:

·         Violates Gauss-Markov assumptions

·         Makes standard errors unreliable

·         Affects inference (t- and F-tests)

 Popular Serial Correlation Tests

Test

Description

Suitable For

Null Hypothesis

Wooldridge Test

Most popular for panel data

Panel with fixed effects

No first-order autocorrelation

Baltagi-Wu LBI Test

Extension of Durbin-Watson

Unequal panel

No serial correlation

Bhargava et al. Durbin-Watson (BDW)

Non-parametric

Balanced panel

No serial correlation

 Wooldridge Test for Autocorrelation

Hypothesis:

·         H₀: No serial correlation

·         H₁: Serial correlation exists

 2. Heteroscedasticity in Panel Data

 What is it?

Heteroscedasticity refers to non-constant variance of the error terms across cross-sectional units (or over time).

Why it matters:

·         OLS estimators still unbiased, but not efficient

·         Standard errors and hypothesis tests are unreliable

 

 Popular Heteroscedasticity Tests

Test

Description

Null Hypothesis

Modified Wald Test

Tests groupwise heteroskedasticity

Homoskedasticity

Breusch-Pagan LM Test

Used in random effects model

Homoskedasticity

White Test (for pooled OLS)

General heteroscedasticity

Homoskedasticity

 Modified Wald Test for Groupwise Heteroscedasticity

Hypothesis:

·         H₀: Homoskedasticity (equal variance across units)

·         H₁: Groupwise heteroskedasticity exists

 What to Do If Issues Are Detected?

Problem

Solution

Serial Correlation

Use robust standard errors clustered by panel ID, or use FGLS or System GMM

Heteroskedasticity

Use robust or heteroscedasticity-consistent standard errors (e.g., robust, cluster)

Both

Use Driscoll-Kraay standard errors (if both CSD and serial correlation exist) or panel-corrected standard errors (PCSE)

 Summary Table

Test

Purpose

Software

Command

Wooldridge Test

Serial correlation

Stata

xtserial

Modified Wald Test

Heteroskedasticity

Stata

xttest3

Breusch-Pagan LM

Heteroskedasticity

Stata

xttest0

White Test

General hetero.

R, Stata

imtest, white or bptest()

 

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