Estimation and Inference in Large Heterogeneous Panels with a Multifactor Error Structure

Source: Pesaran, M. H. (2006) · Econometrica 74(4), 967–1012 · DOI: 10.1111/j.1468-0262.2006.00692.x

Problem it solves

In large panels (firms, countries, assets), the error term typically contains **unobserved common

factors with heterogeneous loadings** (an unobserved market or global cycle hitting each unit

differently). This cross-sectional dependence — especially when the factors are correlated with the

regressors — biases standard fixed-effects/pooled estimators. The paper provides consistent slope

estimation without having to estimate the factors.

Model each unit i as y_it = regressors·β_i + factor loadings·f_t + ε_it, with a multifactor error

structure and unit-specific, random slopes.

**Filter out the common factors by augmenting the regression with (weighted) cross-sectional

averages** of the dependent variable and the regressors; as N → ∞ these averages span the latent

factor space, eliminating the factors' differential effects.

The augmented regression is estimated by OLS, giving the Common Correlated Effects (CCE)

estimators:

- CCEMG (mean group): average of unit-specific CCE estimates — asymptotically unbiased and

normal, and invariant to the (unknown, fixed) number of unobserved factors as N, T → ∞.

- CCEP (pooled): for the mean of the random coefficients.

Asymptotic distributions are derived for T fixed (N → ∞) and for N, T → ∞ jointly, with **no

restriction on the relative rates of N and T**.

A finite number of strong common factors captured by the cross-sectional averages; reasonably

large N (and T for some results); factor loadings may be random and correlated with the regressors.

Inputs are just the panel of y and the regressors — no factor-extraction step is needed.

Run OLS of y_it on the regressors augmented by period-by-period cross-sectional means of y and the

regressors; pool (CCEP) or average across units (CCEMG) for the common slope. Monte Carlo experiments

in the paper confirm the asymptotics and show good small-sample behavior even for modest N and T.

Widely used in cross-country / cross-firm panels with co-movement.

Assumes the factor space is spanned by a finite number of strong factors; weak factors, or more

factors than (averaged) variables, undermine the approximation.

Requires reasonably large N; small-N inference and rank conditions on loadings need care.

Pesaran, M. H. (2006) — Estimation and Inference in Large Heterogeneous Panels with a Multifactor Error Structure — Econometrica

Bai, J. (2009) — Panel Data Models with Interactive Fixed Effects — Econometrica

Pesaran, M. H. (2007) — A Simple Panel Unit Root Test in the Presence of Cross-Section Dependence — Journal of Applied Econometrics

Provenance: verified/generated from the paper's full text.