Local projection-instrumental variable (LP-IV) methods can identify a rich variety of impulse responses, including dynamic causal effects of shocks on economic variables even when facing endogenous regressors and complex dynamic structures.
Short answer: LP-IV methods enable the identification of dynamic impulse responses to structural shocks that may be endogenous or correlated with omitted variables, capturing causal effects over multiple horizons without requiring strong assumptions about the underlying data-generating process.
Understanding Impulse Responses and Identification Challenges
Impulse responses trace how an economic variable evolves over time following a shock to another variable or policy intervention. Traditional methods, such as vector autoregressions (VARs), estimate these responses but often rely on strong assumptions like linearity, stationarity, and exogeneity of regressors. When explanatory variables are endogenous—meaning they are correlated with the error terms—identification of causal impulse responses becomes complicated.
The local projection (LP) approach, introduced by Jordà (2005), offers a flexible alternative by estimating impulse responses directly at each horizon via separate regressions. This circumvents the need to impose restrictions on the entire dynamic system. However, endogenous regressors still pose a challenge because they bias estimates. Incorporating instrumental variables (IV) into the local projection framework—thus LP-IV—allows researchers to use external variation that is correlated with the endogenous shock but uncorrelated with the error term, enabling consistent identification of causal impulse responses.
Types of Impulse Responses Identified by LP-IV
LP-IV methods can identify several types of impulse responses in macroeconomics and applied microeconomics:
1. **Dynamic Responses to Structural Shocks with Endogeneity** LP-IV is particularly powerful in settings where the shock variable is endogenous. For example, monetary policy shocks are often correlated with contemporaneous economic conditions, making standard OLS impulse responses biased. By using external instruments such as high-frequency policy surprises or narrative instruments, LP-IV recovers the dynamic causal effect of monetary policy shocks on output, inflation, and employment over multiple periods.
2. **Heterogeneous and Nonlinear Impulse Responses** Unlike VAR-based impulse responses that assume linearity and homogeneity, LP-IV can be extended to capture heterogeneous effects across units or nonlinear dynamics by modifying the projection regressions accordingly. This flexibility allows identification of impulse responses that differ by state variables such as financial conditions or firm size, which is critical in understanding nuanced economic mechanisms.
3. **Impulse Responses in Panel Data and Cross-Sectional Settings** LP-IV can be adapted to panel data where cross-sectional variation and instruments help to identify impulse responses in micro-level data, such as firm-level or regional responses to policy shocks. This is useful in studies of spatial misallocation or market power where endogenous shocks affect heterogeneous units differently.
4. **Impulse Responses Accounting for Distributional and Equilibrium Effects** In contexts like the NBER working paper on markups and inequality by Boar and Midrigan (2019), LP-IV methods can identify impulse responses that reflect general equilibrium adjustments and distributional consequences of shocks to market power or regulation. These impulse responses capture how shocks propagate through firm behavior, wages, and inequality dynamically.
Advantages Over Traditional Methods
LP-IV methods do not require specifying the full vector autoregressive system or assuming invertibility conditions that are often violated in practice. This makes them robust to model misspecification. Moreover, LP-IV can handle weak or imperfect instruments by employing robust inference techniques, improving reliability of identified impulse responses.
Applications and Empirical Examples
While the provided excerpts do not explicitly discuss LP-IV impulse responses, the methodological literature widely applies these techniques in macroeconomics and industrial organization. For instance, in spatial misallocation studies such as Hsieh and Moretti (2019) in the American Economic Journal: Macroeconomics, causal effects of housing supply shocks on labor allocation and productivity are studied, which could be identified via LP-IV methods to handle endogenous spatial constraints and policy responses.
Similarly, the NBER working paper on markups and inequality utilizes dynamic models where identification of causal effects of market power shocks on wages and inequality may rely on instrumental variables within a local projection framework to uncover impulse responses that reflect the dynamic interplay between firms and households.
Limitations and Challenges
Despite its flexibility, LP-IV requires valid instruments—variables strongly correlated with the shock but exogenous to the outcome—which can be hard to find. Weak instruments may lead to imprecise or biased impulse responses. Also, the method typically demands large sample sizes for reliable inference, especially when estimating responses at many horizons.
Moreover, LP-IV methods generally focus on linear or locally linear responses; capturing fully nonlinear dynamics or regime switches may require additional modeling complexity.
Conclusion
Local projection-instrumental variable methods identify dynamic causal impulse responses to endogenous shocks across various economic contexts. They provide a flexible, robust tool to uncover how economic variables respond over time to structural shocks when traditional assumptions fail. By leveraging external instruments, LP-IV can disentangle complex dynamic causal relationships relevant for policy evaluation, market analysis, and understanding economic fluctuations.
Takeaway: LP-IV methods open a window into the dynamic causal effects of shocks that would otherwise be obscured by endogeneity and model complexity, enabling economists to identify impulse responses reflecting both immediate and longer-run economic adjustments. This makes LP-IV a vital tool for empirical macroeconomics and microeconomics alike.
For further reading and technical details, consult these sources:
nber.org (working papers on dynamic causal models and instrumented projections) aeaweb.org (American Economic Journal: Macroeconomics articles on spatial misallocation and causal inference) econpapers.repec.org (research papers on local projections and IV methods) papers.ssrn.com (working papers on impulse response identification) jstor.org (journal articles on econometric methods for dynamic causal inference) voxeu.org (policy discussions on identification of shocks and impulse responses) researchgate.net (methodological papers on local projections and instrumental variables) sciencedirect.com (articles on econometrics and macroeconomic dynamics)
