Macroeconomic theory postulates two alternative specifications to test
the validity of the purchasing power parity (PPP) hypothesis:
(1) et = Ξ²0 + Ξ²1pdt + ut
(2) Ξet = Ξ³1Ξpdt + vt
where, e = (log) nominal exchange rate, p = (log.) domestic price level, p* = (log.)
foreign price level, pd = p-p*, Ξet = et - et-1 and Ξpdt = pdt - pdt-1.
The βAbsolute PPPβ holds if Ξ²1 = 1 and ut is a white-noise process.
The βRelative PPPβ holds if Ξ³1 = 1 and vt is a white-noise process.
The following equations are estimated using 40 annual observations.
MODEL A et = 0.04 + 0.98pdt
(2.13) (2.50)
R2 = 0.60, DW = 3.40, LM(AR(1)) = 19.6,
LM(WHITE)) = 1.4, SSR = 100
MODEL B Ξet = 0.95Ξpdt
(2.05)
R2 = 0.30, DW = 1.9, LM(AR(1)) = 0.9
LM(WHITE) = 15.4, SSR = 1000
MODEL C et = 0.02 + 0.80pdt + 0.20et-1 + 0.40pdt-1
(2.10) (5.06) (3.20) (2.45)
R2 = 0.80, DW = 2.1, LM(AR(1)) = 0.5,
LM(WHITE) = 0.8, SSR = 20.
MODEL D (C-O): et = 0.05 + 0.94pdt
(2.40) (10.8)
R2 = 0.98, DW = 1.9, LM(AR(1)) = 0.5
SSR = 100 LM(WHITE) = 11.1
Model D is estimated by Cochrane-Orcutt (C-O) iterative procedure. The values in
parentheses are the t-ratios.
i) Β Test the validity of the absolute and relative PPP hypotheses.
ii) Β Explain why the researcher estimated Model B. Considering
Models A and C, state the maintained hypotheses for the estimation of
Model B. Are these hypotheses supported by the data?
iii) Β Explain why the researcher estimated Model D. What are the
maintained hypotheses for the estimation of this model? What did the
researcher hope to achieve? Did the researcher succeed?