Local Projections and VARs Estimate the Same Impulse Responses

We prove that local projections (LPs) and Vector Autoregressions (VARs) estimate the same impulse responses. This nonparametric result only requires unrestricted lag structures. We discuss several implications: (i) LP and VAR estimators are not conceptually separate procedures; instead, they are simply two dimension reduction techniques with common estimand but different finite‐sample properties. (ii) VAR‐based structural identification—including short‐run, long‐run, or sign restrictions—can equivalently be performed using LPs, and vice versa. (iii) Structural estimation with an instrument (proxy) can be carried out by ordering the instrument first in a recursive VAR, even under noninvertibility. (iv) Linear VARs are as robust to nonlinearities as linear LPs.

Download Full-text

Long-Run Effects in Dynamic Systems: New Tools for Cross-Lagged Panel Models

Organizational Research Methods ◽

10.1177/1094428121993228 ◽

2021 ◽

pp. 109442812199322

Author(s):

Ali Shamsollahi ◽

Michael J. Zyphur ◽

Ozlem Ozkok

Keyword(s):

Recent Work ◽

Dynamic Systems ◽

Quantitative Methods ◽

Simulated Dataset ◽

Impulse Responses ◽

Panel Models ◽

Long Run ◽

Short Run ◽

User Friendly ◽

Over Time

Cross-lagged panel models (CLPMs) are common, but their applications often focus on “short-run” effects among temporally proximal observations. This addresses questions about how dynamic systems may immediately respond to interventions, but fails to show how systems evolve over longer timeframes. We explore three types of “long-run” effects in dynamic systems that extend recent work on “impulse responses,” which reflect potential long-run effects of one-time interventions. Going beyond these, we first treat evaluations of system (in)stability by testing for “permanent effects,” which are important because in unstable systems even a one-time intervention may have enduring effects. Second, we explore classic econometric long-run effects that show how dynamic systems may respond to interventions that are sustained over time. Third, we treat “accumulated responses” to model how systems may respond to repeated interventions over time. We illustrate tests of each long-run effect in a simulated dataset and we provide all materials online including user-friendly R code that automates estimating, testing, reporting, and plotting all effects (see https://doi.org/10.26188/13506861 ). We conclude by emphasizing the value of aligning specific longitudinal hypotheses with quantitative methods.

Download Full-text

Estimation and Inference of Impulse Responses by Local Projections

The American Economic Review ◽

10.1257/0002828053828518 ◽

2005 ◽

Vol 95 (1) ◽

pp. 161-182 ◽

Cited By ~ 725

Author(s):

Òscar Jordà

Keyword(s):

New Keynesian ◽

Closed Economy ◽

Impulse Responses ◽

Vector Autoregressions ◽

Central Idea ◽

Keynesian Model ◽

Highly Nonlinear ◽

Regression Techniques ◽

Local Projections ◽

Simple Regression

This paper introduces methods to compute impulse responses without specification and estimation of the underlying multivariate dynamic system. The central idea consists in estimating local projections at each period of interest rather than extrapolating into increasingly distant horizons from a given model, as it is done with vector autoregressions (VAR). The advantages of local projections are numerous: (1) they can be estimated by simple regression techniques with standard regression packages; (2) they are more robust to misspecification; (3) joint or point-wise analytic inference is simple; and (4) they easily accommodate experimentation with highly nonlinear and flexible specifications that may be impractical in a multivariate context. Therefore, these methods are a natural alternative to estimating impulse responses from VARs. Monte Carlo evidence and an application to a simple, closed-economy, new-Keynesian model clarify these numerous advantages.

Download Full-text

Pricing Under Fairness Concerns

Journal of the European Economic Association ◽

10.1093/jeea/jvaa041 ◽

2020 ◽

Author(s):

Erik Eyster ◽

Kristóf Madarász ◽

Pascal Michaillat

Keyword(s):

Phillips Curve ◽

New Keynesian ◽

Technology Shocks ◽

Impulse Responses ◽

Price Increases ◽

Keynesian Model ◽

Long Run ◽

Short Run ◽

Fairness Concerns ◽

Perceived Unfairness

Abstract This paper proposes a theory of pricing premised upon the assumptions that customers dislike unfair prices—those marked up steeply over cost—and that firms take these concerns into account when setting prices. Because they do not observe firms’ costs, customers must extract costs from prices. The theory assumes that customers infer less than rationally: When a price rises due to a cost increase, customers partially misattribute the higher price to a higher markup—which they find unfair. Firms anticipate this response and trim their price increases, which drives the passthrough of costs into prices below one: Prices are somewhat rigid. Embedded in a New Keynesian model as a replacement for the usual pricing frictions, our theory produces monetary nonneutrality: When monetary policy loosens and inflation rises, customers misperceive markups as higher and feel unfairly treated; firms mitigate this perceived unfairness by reducing their markups; in general equilibrium, employment rises. The theory also features a hybrid short-run Phillips curve, realistic impulse responses of output and employment to monetary and technology shocks, and an upward-sloping long-run Phillips curve.

Download Full-text

Impulse Response Estimation by Smooth Local Projections

Review of Economics and Statistics ◽

10.1162/rest_a_00778 ◽

2019 ◽

Vol 101 (3) ◽

pp. 522-530 ◽

Cited By ~ 16

Author(s):

Regis Barnichon ◽

Christian Brownlees

Keyword(s):

Impulse Response ◽

Simulation Study ◽

Structural Identification ◽

Monetary Shocks ◽

Spline Smoothing ◽

Impulse Responses ◽

B Spline ◽

Efficiency Cost ◽

Local Projections

Local projections (LP) is a popular methodology for the estimation of impulse responses (IR). Compared to the traditional VAR approach, LP allow for more flexible IR estimation by imposing weaker assumptions on the dynamics of the data. The nonparametric nature of LP comes at an efficiency cost, and in practice, the LP estimator may suffer from excessive variability. In this work, we propose an IR estimation methodology based on B-spline smoothing called smooth local projections (SLP). The SLP approach preserves the flexibility of standard LP, can substantially increase precision, and is straightforward to implement. A simulation study shows that SLP can deliver substantial gains in IR estimation over LP. We illustrate our technique by studying the effects of monetary shocks where we highlight how SLP can easily incorporate commonly employed structural identification strategies.

Download Full-text

Finite-Sample Properties of Percentile and Percentile-t Bootstrap Confidence Intervals for Impulse Responses

Review of Economics and Statistics ◽

10.1162/003465399558517 ◽

1999 ◽

Vol 81 (4) ◽

pp. 652-660 ◽

Cited By ~ 62

Author(s):

Lutz Kilian

Keyword(s):

Confidence Intervals ◽

Finite Sample ◽

Impulse Responses ◽

Bootstrap Confidence Intervals ◽

Finite Sample Properties

Download Full-text

Characterizing growth instability: new evidence on unit roots and structural breaks in countries’ long run trajectories

Journal of Evolutionary Economics ◽

10.1007/s00191-021-00727-6 ◽

2021 ◽

Author(s):

Emanuele Russo ◽

Neil Foster-McGregor

Keyword(s):

Unit Root ◽

Structural Breaks ◽

Structural Changes ◽

Alternative Hypothesis ◽

Unit Root Test ◽

Unit Roots ◽

Finite Sample ◽

Aggregate Shocks ◽

Long Run ◽

Finite Sample Properties

AbstractIn this paper we investigate whether long run time series of income per capita are better described by a trend-stationary model with few structural changes or by unit root processes in which permanent stochastic shocks are responsible for the observed growth discontinuities. For a group of advanced and developing countries in the Maddison database, we employ a unit root test that allows for an unspecified number of breaks under the alternative hypothesis (up to some ex ante determined maximum). Monte Carlo simulations studying the finite sample properties of the test are reported and discussed. When compared with previous findings in the literature, our results show less evidence against the unit root hypothesis. We find even fewer rejections when relaxing the assumption of Gaussian shocks. Our results are broadly consistent with the implications of evolutionary macro models which posit frequent growth shifts and fat-tailed distribution of aggregate shocks.

Download Full-text

Finite Sample Performance of Likelihood Ratio Tests for Cointegrating Ranks in Vector Autoregressions

Econometric Theory ◽

10.1017/s0266466600009956 ◽

1995 ◽

Vol 11 (5) ◽

pp. 1015-1032 ◽

Cited By ~ 89

Author(s):

Hiro Y. Toda

Keyword(s):

Monte Carlo Simulation ◽

Monte Carlo ◽

Likelihood Ratio ◽

Test Performance ◽

Likelihood Ratio Tests ◽

Nuisance Parameters ◽

Test Statistics ◽

Finite Sample ◽

Vector Autoregressions ◽

Finite Sample Properties

This paper investigates through Monte Carlo simulation the finite sample properties of likelihood ratio tests for cointegrating ranks that were proposed by Johansen (1991, Econometrica 59, 1551–1580). We transform the model into a canonical form so that the experiment is well controlled without loss of generality and then conduct a comprehensive simulation study. As expected, the test performance is very sensitive to the value of the stationary root(s) of the process. We also find that the test performance depends crucially on the correlation between the innovations that drive the stationary and the nonstationary components of the process. We conclude that 100 observations are not sufficient to ensure reasonably good performance uniformly over the values of the nuisance parameters that affect the distributions of the test statistics.

Download Full-text

ROBUST INFERENCE IN STRUCTURAL VECTOR AUTOREGRESSIONS WITH LONG-RUN RESTRICTIONS

Econometric Theory ◽

10.1017/s0266466619000045 ◽

2019 ◽

Vol 36 (1) ◽

pp. 86-121

Author(s):

Guillaume Chevillon ◽

Sophocles Mavroeidis ◽

Zhaoguo Zhan

Keyword(s):

Unit Roots ◽

Confidence Bands ◽

Nuisance Parameters ◽

Robust Methods ◽

Impulse Responses ◽

Vector Autoregressions ◽

Weak Identification ◽

Popular Method ◽

Long Run ◽

Structural Vector

Long-run restrictions are a very popular method for identifying structural vector autoregressions, but they suffer from weak identification when the data is very persistent, i.e., when the highest autoregressive roots are near unity. Near unit roots introduce additional nuisance parameters and make standard weak-instrument-robust methods of inference inapplicable. We develop a method of inference that is robust to both weak identification and strong persistence. The method is based on a combination of the Anderson-Rubin test with instruments derived by filtering potentially nonstationary variables to make them near stationary using the IVX instrumentation method of Magdalinos and Phillips (2009). We apply our method to obtain robust confidence bands on impulse responses in two leading applications in the literature.

Download Full-text