Gregory and Veall (1986). Consider the dynamic equation yt = yt1 + 1xt + 2xt1 + ut where || < 1, and ut NID(0,

Gregory and Veall (1986). Consider the dynamic equation yt = ρyt−1 + β1xt + β2xt−1 + ut where |ρ| < 1, and ut ∼ NID(0, σ2). Note that for this equation to be the Cochrane-Orcutt transformation yt − ρyt−1 = β1(xt − ρxt−1) + ut the following nonlinear restriction must be satisfied −β1ρ = β2 called the common factor restriction by Hendry and Mizon (1978). Now consider the following four formulations of this restriction HA; β1ρ + β2 = 0; HB; β1 + (β2/ρ) = 0; HC; ρ + (β2/β1) = 0 and HD; (β1ρ/β2) + 1 = 0.

(a) Using equation (7.51) derive the four Wald statistics corresponding to the four formulations of the null hypothesis.

(b) Apply these four Wald statistics to the equation relating real personal consumption expenditures to real disposable personal income in the U.S. over the post World War II period 1950-1993, see Table 5.1.