TimeSeriesBook.pdf

22 percent its contribution diminishes with the

Info icon This preview shows pages 320–323. Sign up to view the full content.

View Full Document Right Arrow Icon
explains more than 50 percent whereas demand shocks account for only 42.22 percent. Its contribution diminishes with the increase of the forecast horizon giving room for price and wage shocks. The variance of the inflation rate is explained in the short-run almost exclusively by price shocks. However, as the the forecast horizon is increased supply and wage shocks become relatively important. The money growth rate does not interact much with the other variables. Its variation is almost exclusively explained by money shocks. 15.5 Identification via Long-Run Restrictions 15.5.1 A Prototypical Example Besides short-run restrictions, essentially zero restrictions on the coefficients of A and/or B , Blanchard and Quah (1989) proposed long-run restrictions as an alternative option. These long-run restrictions have to be seen as complementary to the short-run ones as they can be combined. Long-run restrictions constrain the long-run effect of structural shocks. This technique makes only sense if some integrated variables are involved, because in the stationary case the effects of all shocks vanish eventually. To explain this, we discuss the two-dimensional example given by Blanchard and Quah (1989). They analyze a two-variable system consisting of logged real GDP de- noted by { Y t } and the unemployment rate { U t } . Logged GDP is typically integrated of order one (see Section 7.3.4 for an analysis for Swiss GDP) whereas U t is considered to be stationary. Thus they apply the VAR ap- proach to the stationary process { X t } = { (∆ Y t , U t ) 0 } . Assuming that { X t } is already demeaned and follows a causal VAR process, we have the following representations: X t = Y t U t = Φ 1 X t - 1 + . . . + Φ p X t - p + Z t = Ψ(L) Z t = Z t + Ψ 1 Z t - 1 + Ψ 2 Z t - 2 + . . . . For simplicity, we assume that A = I 2 , so that Z t = BV t = 1 b 12 b 21 1 v dt v st where V t = ( v dt , v st ) 0 WN(0 , Ω) with Ω = diag( ω 2 d , ω 2 s ). Thereby { v dt } and { v st } denote demand and supply shocks, respectively. The causal represen- tation of { X t } implies that the effect of a demand shock in period t on GDP
Image of page 320

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
302 CHAPTER 15. INTERPRETATION OF VAR MODELS Table 15.1: Forecast error variance decomposition (FEVD) in terms of de- mand, supply, price, wage, and money shocks (percentages) growth rate of real GDP horizon demand supply price wage money 1 99 . 62 0 . 38 0 0 0 2 98 . 13 0 . 94 0 . 02 0 . 87 0 . 04 4 93 . 85 1 . 59 2 . 13 1 . 86 0 . 57 8 88 . 27 4 . 83 3 . 36 2 . 43 0 . 61 40 86 . 13 6 . 11 4 . 29 2 . 58 0 . 89 unemployment rate horizon demand supply price wage money 1 42 . 22 57 . 78 0 0 0 2 52 . 03 47 . 57 0 . 04 0 . 01 0 . 00 4 64 . 74 33 . 17 1 . 80 0 . 13 0 . 16 8 66 . 05 21 . 32 10 . 01 1 . 99 0 . 63 40 39 . 09 16 . 81 31 . 92 10 . 73 0 . 89 inflation rate horizon demand supply price wage money 1 0 . 86 4 . 18 89 . 80 5 . 15 0 2 0 . 63 13 . 12 77 . 24 8 . 56 0 . 45 4 0 . 72 16 . 79 68 . 15 13 . 36 0 . 97 8 1 . 79 19 . 34 60 . 69 16 . 07 2 . 11 40 2 . 83 20 . 48 55 . 84 17 . 12 3 . 74 growth rate of wages horizon demand supply price wage money 1 1 . 18 0 . 10 0 . 97 97 . 75 0 2 1 . 40 0 . 10 4 . 30 93 . 50 0 . 69 4 2 . 18 2 . 75 9 . 78 84 . 49 0 . 80 8 3 . 80 6 . 74 13 . 40 74 . 72 1 . 33 40 5 . 11 8 . 44 14 . 19 70 . 14 2 . 13 growth rate of money stock horizon demand supply price wage money 1 0 . 10 0 . 43 0 . 00 0 . 84 98 . 63 2 1 . 45 0 . 44 0 . 02 1 . 02 97 . 06 4 4 . 22 1 . 09 0 . 04 1 . 90 92 . 75 8 8 . 31 1 . 55 0 . 81 2 . 65 86 . 68 40 8 . 47 2 . 64 5 . 77 4 . 55 78 . 57
Image of page 321
15.5. IDENTIFICATION VIA LONG-RUN RESTRICTIONS 303 growth in period t + h is given by: Y t + h ∂v dt = [Ψ h B ] 11 where [Ψ h B ] 11 denotes the upper left hand element of the matrix Ψ h B .
Image of page 322

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 323
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern