Introduction

This tutorial presents a step-by-step implementation of the local projection method in Stata, following the empirical framework of Jordà (2005).

The objective is to estimate impulse response functions and compare results obtained from local projections with those derived from a standard vector autoregressive (VAR) model.

Local projections provide a flexible alternative to VAR models and have become widely used in applied macroeconomics due to their robustness to model misspecification and ease of implementation.

Local Projection Method in Stata: Overview

The local projection method, introduced by Jordà (2005), estimates impulse response functions by running a sequence of linear regressions, one for each forecast horizon.

For each horizon, the future value of a variable is regressed on:

• A structural shock

• Lagged dependent variables

• Additional control variables

This differs from VAR models, which estimate a full system of equations with fixed dynamics.

As a result, local projections:

• Impose fewer restrictions

• Are more robust to misspecification

• Allow straightforward extensions 

Local Projections and VAR Models

A comparison between local projections and VAR models is central in empirical work.

VAR models:

• Estimate a system of equations

• Require stronger assumptions

• Are efficient under correct specification

Local projections:

• Estimate responses horizon by horizon

• Are more flexible

• Are robust to incorrect dynamic assumptions

Both approaches are often used jointly in applied research.

Empirical Application: Jordà (2005)

This tutorial replicates the empirical strategy based on Evans and Marshall (1998), as implemented in Jordà (2005).

The analysis proceeds in four steps:

1. Estimation of a VAR model

2. Computation of impulse response functions

3. Identification of a structural monetary policy shock

4. Estimation using local projections

Step 1: VAR Estimation in Stata

We begin by estimating a VAR(12) model using macroeconomic variables, including employment, prices, commodity prices, and the federal funds rate.

Identification is achieved through Cholesky decomposition, with the federal funds rate appropriately ordered in the system.

Step 3: Structural Shock Identification

Local projections require an exogenous shock.

To construct it:

• Residuals are extracted from the VAR

• Contemporaneous effects are removed

• The remaining component is interpreted as the structural shock

The shock is normalized to one standard deviation.

The following references are central to this tutorial. Jordà (2005) introduces the local projection method. The Stata manual developed by Ugarte-Ruiz provides detailed guidance for local projections implementation. Evans and Marshall (1998) present the VAR(12) model used by Jordà as a benchmark to compare impulse response functions obtained from local projections and VAR models.

1. Jordà, Ò. (2005). Estimation and inference of impulse responses by local projections. American economic review, 95(1), 161-182. Download

2. Ugarte-Ruiz, A. (2025). Locproj & Lpgraph: Stata commands to estimate Local Projections. BBVA Research WP, 25-09. Download

3. Evans, C. L., & Marshall, D. A. (1998, December). Monetary policy and the term structure of nominal interest rates: evidence and theory. In Carnegie-Rochester Conference Series on Public Policy (Vol. 49, pp. 53-111).  North  Holland. Download

Identification of Monetary Shocks

1. Romer, C. D., & Romer, D. H. (2004). A new measure of monetary shocks: Derivation and implications. American economic review, 94(4), 1055-1084. Download 

State Dependent Effects

In many macroeconomic applications, the effects of shocks depend on the state of the economy. For example, fiscal multipliers are often larger during recessions than during expansions, as shown by Valerie A. Ramey and Sarah Zubairy (2018). Similarly, financial shocks tend to have stronger effects during periods of credit stress, as documented by Oscar Jordà, Moritz Schularick, and Alan M. Taylor (2013). These findings highlight the importance of allowing for nonlinear and state-dependent responses when estimating impulse response functions.

1. Ramey, V. A., & Zubairy, S. (2018). Government spending multipliers in good times and in bad: evidence from US historical data. Journal of political economy, 126(2), 850-901. Download                   

2. Jordà, Ò., Schularick, M., & Taylor, A. M. (2013). When credit bites back. Journal of money, credit and banking, 45(s2), 3-28. Download