Palgrave Handbook of Econometrics: Applied Econometrics

352 The Long Swings Puzzle length the specification of the deterministic components. Section 8.7 discusses an estimation procedu ...

Katarina Juselius 353 The hypothesis thatxtisI( 1 )is formulated as a reduced rank restriction on the matrix: =αβ′, whereα,βar ...

354 The Long Swings Puzzle on the pushing and pulling forces of the cointegrated VAR model. Comparing assumed with actual behavi ...

Katarina Juselius 355 1975 0.50 0.75 1.00 0.0 1.25 1975 1980 1985 1990 Log of US CPI Log of German CPI The Dmk–$ rate Relative p ...

356 The Long Swings Puzzle 0.6 A cross-plot between relative prices and the nominal exchange rate +++ +++++++ +++ ++++ ++++++ ++ ...

Katarina Juselius 357 This is a fairly pragmatic way of classifying data that allow a variable to be treated asI( 1 )in one samp ...

358 The Long Swings Puzzle Whenxt∼I( 2 ), bothxtandxt− 1 contain a commonI( 1 )trend, which there- fore cancels in the regress ...

Katarina Juselius 359 Thus, one can test a number of hypotheses based on theI( 1 )procedure even ifxt isI( 2 ), but the interpre ...

360 The Long Swings Puzzle D′p,t=[Dp80.7,Dp91.1,Dptax,Dp97.7] with DpXX.yt=1 in 19XX:y, zero otherwise. The tax dummy is needed ...

Katarina Juselius 361 Table 8.2 Determination of rank in theI(1) model rp−r τp−r 4 largest characteristic roots 0 3 80.06 [57.9] ...

362 The Long Swings Puzzle 4.5 5 Beta1’*R1(t) Beta1’*x(t) 4 3 2 1 0 –1 –2 –3 3.6 2.7 1.8 0.9 –0.0 –0.9 –1.8 –2.7 1975 1977 1979 ...

Katarina Juselius 363 Beta2’*x(t) Beta2’*R1(t) 1975 1977 1979 1981 1983 1985 1987 1989 1991 1993 1995 1997 1975 2.4 5 4 3 2 1 0 ...

364 The Long Swings Puzzle Table 8.3 The estimated short-run dynamic adjustment structure in theI( 1 )model ⎡ ⎢⎢ ⎢⎣ p 1 t p2,t ...

Katarina Juselius 365 8.6 Representing theI( 2 )model 8.6.1 The basic structure As discussed in section 8.2, formulation (8.3) i ...

366 The Long Swings Puzzle It is now easy to see that theC 2 matrix has a similar reduced rank representation toC 1 in theI( 1 ) ...

Katarina Juselius 367 to the other is difficult to know, but we need to pay sufficient attention to this question, as the choice ...

368 The Long Swings Puzzle The shift dummyμ 01 is similarly decomposed: μ 01 =αγ 01 +α⊥ 1 γ 11 +α⊥ 2 γ 21. To investigate the ef ...

Katarina Juselius 369 Thus, unless we restrictα⊥ 2 ρ 2 = 0 the model will allow for cubic trends in the data. TheI( 2 )procedure ...

370 The Long Swings Puzzle The full ML procedure exploits the fact that theI( 2 )model containsp−s 2 cointe- gration relations,τ ...

Katarina Juselius 371 of the unrestricted VAR model (8.3) can be decomposed as: xt− 1 +xt− 1 =(β)β′xt− 1 ︸ ︷︷ ︸ I( 0 ) +(αα ...