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7.2. DEVIATIONS FROM THE LAW-OF-ONE PRICE 211Table 7.1: Slope coefficients in Isard’s regression of the US import toexport price ratio on nominal exchange rateImports from Germany Imports from JapanSoap Tires Wallpaper Soap Tires Wallpaper0.094 0.04 0.03 15.49 6.28 6.79(0.04) (0.02) (0.01) (13.8) (1.04) (1.28)Engel and Rogers on the BorderEngel and Rogers [46] ask what determines the volatility of the percentagechange in the price of 14 categories of consumer prices sampledin various US and Canadian cities from Sept. 1978 through Dec. 1994. 2Let p ijt be the price of good i in city j at time t, measuredinUSdollars.Let σ ijk be the volatility of the percentage change in the relativeprice of good i in cities j and k. Thatis,σ ijk is the time-series samplestandard deviation of ∆ ln(p ijt /p ikt ). In addition, deÞne D jk as the logarithmof the distance between cities j and k. The idea of the distancevariable is to capture potential effects of transportation costs that maycause violations of the law-of-one price between two locations. Let B jkbe a dummy variable that is 1 if cities j and k are separated by theUS-Canadian border and 0 otherwise, and let X 0 i be a vector of controlvariables, such as a separate dummy variable for each good i and/or foreach city in the sample. Engel and Rogers run restricted cross-sectionregressionsσ ijk = αD jk + βB jk + X 0 i γ i + u ijk,and obtain ˆβ = 10.6 × 10 −4 (s.e.=3.25 × 10 −4 ), ˆα = 11.9 × 10 −3(s.e.=0.42 × 10 −3 ), ¯R2 =0.77. The regression estimates imply thatthe border adds 11.9 × 10 −3 to the average volatility (standard deviation)of prices between two pairs of cities. Based on the estimate of2 The cities are Baltimore, Boston, Chicago, Dallas, Detroit, Houston, Los Angeles,Miami, New York, Philadelphia, Pittsburgh, San Francisco, St. Louis, WashingtonD.C., Calgary, Edmonton, Montreal, Ottawa, Quebec, Regina, Toronto, Vancouver,and Winnipeg.