Project CEMAPRE internal
| Title | Impulse Response Functions through Vector Autoregressions and Local Projections |
| Participants | Adriana Cornea-Madeira (Principal Investigator) |
| Summary | Impulse Response Functions IRFs are crucial for understanding the effects of monetary policy on the economy. Monetary policy significantly impacts macroeconomic variables (Bernanke & Blinder, 1992) and financial markets (Bernanke & Kuttner, 2005; Madeira & Madeira, 2019), making research in this area highly relevant for policy decisions. As Samuelson & Nordhaus (1985) highlight (in Economics—a leading textbook for decades), monetary policy is "the most powerful and useful tool that macroeconomic policymakers have." IRFs also help assess the effects of fiscal policy (Blanchard & Perotti, 2002). Two dominant empirical methods for estimating impulse responses have emerged: structural vector autoregressions (VARs), pioneered by Sims (1980), and local projections (LPs), introduced by Jordà (2005). Local projections consist of a series of regressions where the outcome variable, measured at progressively distant horizons, is regressed on the intervention of interest. These regressions condition on controls, including lags of both the outcome and intervention, as well as other exogenous or predetermined variables. In forecasting, LPs are often called direct multistep forecasting regressions. Both LPs and VARs capture the dynamic covariance structure of a system of variables. When data are generated by a VAR, the two methods yield asymptotically equivalent impulse responses, though they may differ in small samples (Jordà, 2005; Plagborg-Møller & Wolf, 2021). However, LPs have gained popularity over VARs (Jordà & Taylor, forthcoming). First, LPs are more flexible as they impose fewer parametric restrictions. VARs assume a fixed lag structure across all equations, while LPs estimate each horizon-specific response separately, making them robust to model misspecification (Montiel Olea, Plagborg-Møller, Qian & Wolf, 2024). This robustness is useful when the correct lag length or underlying economic dynamics are uncertain. Second, LPs accommodate nonlinearities, state dependence, or interactions with other variables more easily than VARs, which require complex modifications such as regime-switching models. Third, unlike VARs, which estimate impulse responses by iterating on estimated coefficients, LPs estimate each horizon separately. This direct estimation is beneficial when focusing on specific horizons without estimating a full dynamic system. |