Cross-Sectional Distributed Lag
Also known as: Panel distributed lag model
CS-DL (Cross-Sectional Distributed Lag) is a simplified dynamic panel model regressing outcomes on current and lagged explanatory variables without explicit autoregressive terms, while accounting for cross-sectional dependence. Built on Pesaran et al. (2001) and extended by Chudik et al. (2014), it estimates dynamic effects more parsimoniously than ARDL when autocorrelated lags are less critical. This approach is valuable for short-horizon effects and policy impact analysis.
Key highlights
- Parsimonious model with fewer parameters than ARDL
- Clear interpretation of lag coefficients as dynamic policy responses
- Handles cross-sectional dependence via common correlated effects
- Efficient in finite samples compared to full ARDL
Intuition
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How it works
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When to use it
Use CS-DL when interested in how shocks propagate through time (impulse responses to policy changes) rather than long-run relationships. It is useful for policy evaluation, short-horizon forecasting, and when sample size constraints make ARDL less attractive. Particularly suitable when autoregressive dynamics are weak.
Strengths & limitations
- Parsimonious model with fewer parameters than ARDL
- Clear interpretation of lag coefficients as dynamic policy responses
- Handles cross-sectional dependence via common correlated effects
- Efficient in finite samples compared to full ARDL
- Does not estimate long-run equilibrium relationships or cointegration
- Cannot distinguish between short-run adjustment and long-run elasticity
- May be biased if true dynamics involve lagged-dependent-variable effects
- Lag-length selection is ad hoc; no formal cointegration guidance
Common pitfalls
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Applications
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Frequently asked
How many lags of X should I include?
Use AIC or BIC; theory suggests lags until cumulative effects stabilize. For quarterly data, 2-4 lags are typical; for annual, 1-2 lags. Test sensitivity to lag choice.
How do I calculate long-run effects from DL models?
Sum coefficients on all lags: LR effect = sum(beta[0] + beta[1] + ... + beta[p]). But DL models don't distinguish short-run adjustment from long-run equilibrium; ARDL is better for that.
What is the relationship between DL and ARDL?
ARDL includes lagged dependent variable; DL does not. ARDL is more flexible but requires more data. DL is simpler but may miss autoregressive dynamics. Use ARDL if outcome is persistent; use DL if mainly driven by external shocks.
How do I account for cross-sectional dependence?
Include cross-sectional averages of X and outcome as additional regressors (common correlated effects). This controls for latent common factors.
Sources
- 1.Pesaran, M. H., Shin, Y., & Smith, R. J. (2001). Bounds testing approaches to the analysis of level relationships and dynamics. Journal of Applied Econometrics, 16(3), 289-326.
- 2.Chudik, A., Kapetanios, G., & Pesaran, M. H. (2014). Common correlated effects estimation in large panels with cross-sectional dependence. Econometric Reviews, 34(6-10), 1078-1088.
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Cite this page
ScholarGate. (2026, June 3). CS-DL. ScholarGate. https://scholargate.app/econometrics/cs-dl