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SDP1p,t, and SDP-p,t, respectively, and if we add m lags in (1), we obtain the
following specification:
kk
PRt 5 b01 O Bm1 PPPt2m 1 Obm2NPPt2m 1«t (2)
m50 m50
PRt stands for the retail price change in the urban area. PPPt and NPPt are the
variables denoting the rising and falling phases of live hog farm gate prices
respectively and are computed via the Houck procedure. Following Bailey and
Brorsen (1989), two asymmetry hypotheses can be tested in (2). The first null
hypothesis is that the aggregate impact of live hog price increases and decreases
on pork retail price are equal:
kk
H0: Obm1 5 Obm2
m50 m50
The second null hypothesis is that the speed of adjustment is the same for both
price increases and decreases:
H0: b015 b02, b115 b12 ...,bm1 5 bm2
Rejecting the first hypothesis implies that the two price series would tend to drift
apart over time as a result of imperfect information, time lags in information flow,
market power, or constraints to arbitrage (Punyawadee, 1991). Rejecting the
second hypothesis indicates that the rate of adjustment differs for positive and
negative price changes, that is, price asymmetry.
When (2) is estimated without regard to the time series nature of the data used,
spurious correlations can arise if Pr,t and Pp,t are nonstationary. Nevertheless, the
two variables can be cointegrated, meaning that Pr,t 5 a0 1 a1Pp,t 1 ut with
ut being stationary (Engle and Granger, 1987). If so, Granger and Lee (1989)
propose a modification to (2) that makes it possible to test for asymmetry between
nonstationary but cointegrated variables:
DPr,t 5 b01 b1DPt21 1 b21ECTt121 1 b22ECTt221 1 b3~L!DPr,t21
1 b4~L!DPp,t21 1«t (3)
where ECT is the error correction term such as ECT 5 ECT1 1 ECT- and
ECTt21 5 ut21 5 Pr,t21 2 a0 2 a1Pp,t2 1, and b3(L) and b4(L) are lagged
polynomials. In (3), the null hypothesis of symmetry therefore becomes: