Two illustrating the methods of understanding how food prices change over time
(3) Ihle, von Cramon-Taubadel, and Zorya (2009), "Markov-Switching Estimation of Spatial Maize Price Transmission Processes Between Tanzania and Kenya," Nov AJAE, 1432-39.
They apply a Markov-switching vector autoregressive (MS-VAR) nonlinear time series model to corn price changes. The Markov-switching part means that we're looking at the probability of changing states rather than the direct probability of each state. The advantage of the VAR part is that it allows the price to be in a high or low regime depending on unobservable variables, while most threshold models focus only on observables. The unobservable they care about most is unpredictable policy changes or the threat of such changes. Tanzania's policies are described by Aliguma et al (2008, MSU working paper), Kenya's by Jayne, Meyer, and Nyoro (2008, Ag Econ). They do caution that we don't understand MS-VAR models very well yet, in particular how to avoid over-identifying the model, creating imaginary regimes that "explain" the data for no reason.
They find two distinct regimes when average price margins between Tanzania and Kenya are twice as high in the high regime as in the low regime. The probability of transitioning from high to low or vice versa is quite small: 8% chance of going down, 11% chance of going back up. Some of the high price margin episodes occurred without an explicit export ban, but every time there is an official export ban the price is high. They hypothesize this could be because of unofficial export restrictions or drought.
(4) Adachi and Liu (2009), "Estimating Long-Run Price Relationship with Structural Change of Unknown Timing: An Application to the Japanese Pork Market," Nov AJAE, 1440-47, ungated.
The model is linear, but allows there to be breaks in the data. The complexity is telling the difference between a change in parameters of the model and data non-stationarity. They examine Japanese retail pork and farm hog price data from 1967 to 2008.
If they don't consider the possibility of structural breaks, tests claim that the data is non-stationary. If they do allow them, however, nonstationarity is rejected at the 1% level. If they only allow for one structural break, they find it occurred (depending on specification) either in Feb 1974 or Feb 1975 for retail prices and for farm prices in Feb or Mar 1974. Given two breaks, retail prices change in early 1974 and late 1978, whiel farm prices change in mid 1978 and mid 2003. Each data series between break points is stationary.
A more general test lets them consider the possibility that there is "one more" break, and they come up 4 breaks altogether: Sept 1976, Oct 1982, Sept 1990, and January 1997, each with a confidence interval of no more than 12 months. They explain the breaks as: cheap feed imports from a strong yen that reduced farm prices but not retail; foot-and-mouth in Denmark; the beginning of Japan's lost decade; and shifting imports from Taiwan to the US and Canada for food safety concerns. The log of the retail pork price has been remarkably steady from 1984 to the present, particularly compared to the more volatile farm price.