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 y 1 t + 1 = a 1 y 1 t + b 1 y 2 t + ǫ t + 1 , 1 Run these regressions y 1 t + 2 a 2 y 1 t + b 2 y 2 t + ǫ t + 2 , 2 = y 1 , t + 3 a 3 y 1 t + b 3 y 2 t + ǫ t + 3 , 3 = . . . y 1 , t + k a k y 1 t + b k y 2 t + ǫ t + k , k = The impulse response of y 1 to a shock to iself is a 1 , a 2 , ..., a k . The impulse response of y 1 to a shock to y 2 is b 1 , b 2 , ..., b k . ` 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 y 1 t + 1 = a 1 y 1 t + c 1 y 1 t − 1 + b 1 y 2 t + d 1 y 2 t − 1 + ǫ t + 1 , 1 Run these regressions y 1 t + 2 a 2 y 1 t + c 2 y 1 t − 1 + b 2 y 2 t + d 2 y 2 t − 1 + ǫ t + 2 , 2 = y 1 , t + 3 a 3 y 1 t + c 3 y 1 t − 1 + b 3 y 2 t + d 3 y 2 t − 1 + ǫ t + 3 , 3 = . . . y 1 , t + k a k y 1 t + c k y 1 t − 1 + b k y 2 t + d k y 2 t − 1 + ǫ t + k , k = The impulse response of y 1 to a shock to iself is a 1 , a 2 , ..., a k . The impulse response of y 1 to a shock to y 2 is b 1 , b 2 , ..., b k . 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