Local Projections
Also known as: LP-IR, Multi-horizon regression
Local Projections (LP) is a semi-parametric method for estimating impulse responses directly via multi-horizon regressions, bypassing VAR-model specification. Introduced by Jorda (2005), it projects outcomes h periods ahead onto current shocks and lags, producing impulse-response functions without assuming a particular lag structure or VAR order. This flexibility has made it the dominant approach in applied macroeconomics for measuring policy effects and shock transmission.
Key highlights
- Flexible; no reliance on VAR-lag specification or parametric model structure
- Impulse responses directly interpretable as h-period-ahead responses to shocks
- Easier to incorporate identifying restrictions (sign, zero, instrumental-variable)
- Robust to lag-order misspecification relative to VARs
Intuition
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How it works
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When to use it
Use local projections when estimating impulse responses to identified shocks (e.g., monetary policy surprises, fiscal shocks, oil-price shocks). It is particularly useful when VAR lag order is uncertain, when parametric VAR assumptions may be violated, or when you need transparency about identifying assumptions. Requires careful attention to standard error clustering.
Strengths & limitations
- Flexible; no reliance on VAR-lag specification or parametric model structure
- Impulse responses directly interpretable as h-period-ahead responses to shocks
- Easier to incorporate identifying restrictions (sign, zero, instrumental-variable)
- Robust to lag-order misspecification relative to VARs
- Standard errors can be inflated due to multicollinearity across horizons
- Requires careful clustering of standard errors (time-dimension clustering justified, cross-sectional clustering context-dependent)
- Impulse responses may be noisy at long horizons with small samples
- Does not enforce VAR consistency; responses may appear 'lumpy' across horizons
Common pitfalls
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Applications
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Frequently asked
How do I cluster standard errors in local projections?
Time-dimension clustering is standard (grouping observations by time period). Cross-sectional clustering (if multiple units per time) requires careful thought; include if shocks or errors are correlated within units. Use two-way clustering (time and unit) when both dimensions matter.
How many lags of controls should I include?
Start with the lag order from a preliminary VAR estimated on the full sample (e.g., via AIC/BIC). Then test sensitivity: repeat results with lag order plus/minus 1. If results are stable, your choice is robust.
Can I enforce that responses sum to the VAR-implied total effect?
Yes. Estimate a VAR as well and compare its cumulative impulse response (sum of h-period responses) to the local-projection sequence. If they diverge, investigate lag specification or identifying assumptions.
How do I identify shocks in local projections?
Use instrumental variables (regress shock on exogenous instrument), sign restrictions (restrict impulse-response signs), or zero restrictions. IV identification is most straightforward; it yields the effect of shocks uncorrelated with information in lags.
Sources
- 1.Jorda, O. (2005). Estimation and inference of impulse responses by local projections. American Economic Review, 95(1), 161-182.
- 2.Ramey, V. A., & Zubairy, S. (2018). Government spending multipliers in good times and in bad times. Journal of Political Economy, 126(2), 850-901.
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Cite this page
ScholarGate. (2026, June 3). Local Projections. ScholarGate. https://scholargate.app/econometrics/local-projections