Financial Econometrics Econ 40357 Local Projections N.C. Mark - - PowerPoint PPT Presentation

Financial Econometrics Econ 40357 Local Projections

N.C. Mark

University of Notre Dame and NBER

September 10, 2020

1 / 5

Pitfalls of VARs

VAR is optimally designed for one-period ahead forecasting. An impulse response, is a function of forecasts at increasingly distant horizons. Therefore misspecification errors are compounded with the forecast horizon. It might be better to use a collection of projections local to each forecast horizon

• instead. This is called a local projection.

2 / 5

Local Projection

Illustrate with the VAR(1). The first equation is y1t+1 = a1y1t + b1y2t + ǫt+1,1 Run these regressions y1t+2 = a2y1t + b2y2t + ǫt+2,2 y1,t+3 = a3y1t + b3y2t + ǫt+3,3 . . . y1,t+k = aky1t + bky2t + ǫt+k,k The impulse response of y1 to a shock to iself is a1,a2, ..., ak. The impulse response of y1 to a shock to y2 is b1, b2, ..., bk. ` Oscar Jord` a worked out the math to prove, if the true DGP is the VAR, the impulse responses from Local Projections and the VAR are identical (asymptotically). Construct confidence bands with Newey-West standard errors (the estimate divided by the t-ratio).

3 / 5

Local Projection

Illustrate with VAR(2). The first equation is y1t+1 = a1y1t + c1y1t−1 + b1y2t + d1y2t−1 + ǫt+1,1 Run these regressions y1t+2 = a2y1t + c2y1t−1 + b2y2t + d2y2t−1 + ǫt+2,2 y1,t+3 = a3y1t + c3y1t−1 + b3y2t + d3y2t−1 + ǫt+3,3 . . . y1,t+k = aky1t + cky1t−1 + bky2t + dky2t−1 + ǫt+k,k The impulse response of y1 to a shock to iself is a1,a2, ..., ak. The impulse response of y1 to a shock to y2 is b1, b2, ..., bk. Construct confidence bands with Newey-West standard errors (the estimate divided by the t-ratio).

4 / 5

Revisit Climate Change and the Real Exchange Rate

5 / 5