Econometrica: Oct, 1955, Volume 23, Issue 4

Correlation and Regression Estimates when the Data are Ratios

https://doi.org/0012-9682(195510)23:4<400:CAREWT>2.0.CO;2-0
p. 400-416

Edwin Kuh, John R. Meyer

This paper examines the influence of ratio transformations on correlation and regression estimates. After a discussion of the "spurious" ratio correlation problem necessary and sufficient conditions are adduced for the correlation between two series with a common denominator to equal the partial correlation between numerator series with the deflating variable's influence held constant. So far as regression coefficients are concerned, it is shown what conditions must be fulfilled to obtain best linear unbiased least squares estimates when the data are in ratio form. These conditions will be more frequently fulfilled with cross-section than with time series data. Some empirical properties of Chenery's test of the capacity principle are then re-evaluated in light of these technical conditions. Chenery's work illustrates the point that ratio transformations on time series usually require circumspection when the data are cross-sectional.