A simple estimator for smooth local projections

ABSTRACT

In this paper, we propose a simple approach to estimate impulse response function through smoothed local projections, thereby utilizing the flexibility of local projections, while creating smooth and economically plausible impulse response functions as provided by VARs. The approach allows to determine the appropriate degree of smoothing endogenously through a standard information criterion. This also avoids oversmoothing and provides an estimator that is generally more efficient than standard local projections.

KEYWORDS:

• Local projections
• semi parametric estimation
• smoothing
• impulse response function

JEL CLASSIFICATION:

• C3
• C14

Disclosure statement

No potential conflict of interest was reported by the author.

Notes

¹ This adds one further restriction to LP. While rarely done, it is possible to use different explanatory variables in equations used to forecast over different horizons. Since we smooth by smoothing corresponding coefficients over different forecast horizons, our approach requires identical explanatory variables for all horizons.

² Note that our notation deviates from Breitung and Roling (2015) since – for our application – redefining Breitung’s $\lambda$ as ${\lambda }^2$ allows for a considerably easier notation in the latter part of our technical exposition.

³ By using this type of smoothing operator, we implicitly use information from higher forecast horizons, to estimate low forecast horizons. This could be avoided by using a backward-looking or one-sided filter instead, following the argument proposed by Stock and Watson (1999) concerning forecasts. However, this would no longer give us a one-step estimator with a clearly defined projection matrix, which we need to compute the implicit degrees of freedom that we need to choose the proper degree of smoothing as outlined in the following subsection.

⁴ To keep the standard comparability between AIC and BIC, we perform the same finite sample adjustment that is done for the Akaike criterion for the Bayesian criterion.