Estimators · Panel · dynamic
Pooled Mean Group ARDL
Long-run homogeneity across panels with short-run heterogeneity. Appropriate when regressors are I(1) and cointegrated with the dependent variable.
Overview
The PMG estimator of Pesaran, Shin & Smith (1999) constrains long-run coefficients θ to be equal across panels, while permitting intercepts, short-run dynamics, and error variances to differ. It is consistent when the number of panels is large and cointegration holds. PMG sits between two extremes: the fully-pooled estimator (which forces short-run homogeneity, often too restrictive) and the mean-group estimator (which estimates each panel independently, often noisy).
Specification
Δyᵢₜ = φᵢ (yᵢ,ₜ₋₁ − θ′xᵢₜ) + Σⱼ γᵢⱼ Δxᵢ,ₜ₋ⱼ + αᵢ + εᵢₜ
where φᵢ is the error-correction speed, θ is the (pooled) long-run coefficient vector, and γᵢⱼ are short-run panel-specific coefficients.
Python API
import quantfit as qf
df = qf.load("gdp_panel.csv").panel("country", "year")
model = qf.pmg(
y="gdp_growth",
long_run=["inflation", "trade_open", "gov_spend"],
short_run=["Δinflation", "Δtrade_open"],
lags=2,
robust=True,
)
fit = model.fit()
fit.summary() # journal-style table
fit.export("table_1.tex", format="latex")
fit.replication("./replication.qfpack")Diagnostics
PMG is valid only if the underlying series are cointegrated. The output panel auto-runs Kao and Pedroni tests and reports their verdict; it also surfaces a Hausman test comparing PMG with the fully heterogeneous Mean Group estimator.
Residual and specification battery
| Test | Stat. | p | Interpretation |
|---|---|---|---|
| Hausman PMG vs MG | 3.41 | 0.182 | Pool the long-run. |
| Kao cointegration | −4.38 | 0.000 | Cointegrated. |
| Pesaran CD | 1.21 | 0.227 | No cross-section dependence. |
References
- Pesaran, M. H., Shin, Y., & Smith, R. P. (1999). Pooled Mean Group estimation of dynamic heterogeneous panels. JASA 94(446), 621–634.
- Pesaran, M. H. (2007). A simple panel unit root test in the presence of cross-section dependence. J. Appl. Econometrics 22, 265–312.
- Kao, C. (1999). Spurious regression and residual-based tests for cointegration in panel data. J. Econometrics 90, 1–44.