Macroeconomic theory postulates two alternative specifications to test
the validity of the purchasing power parity (PPP) hypothesis:
(1) et = β0 + β1pdt + ut
(2) Δet = γ1Δpdt + vt
where, e = (log) nominal exchange rate, p = (log.) domestic price level, p* = (log.)
foreign price level, pd = p-p*, Δet = et - et-1 and Δpdt = pdt - pdt-1.
The “Absolute PPP” holds if β1 = 1 and ut is a white-noise process.
The “Relative PPP” holds if γ1 = 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 Δet = 0.95Δpdt
(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) Test the validity of the absolute and relative PPP hypotheses.
ii) 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) 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?