The Efficiency of Taking First Differences in Regression Analysis: A Note

IN a recent article, Geary [1972] discussed the merit of taking first differences to deal with the problems that trends in data present in regression analysis. Geary gave examples of situations where this procedure leads to highly inefficient estimates of the regression coefficients. The first difference transforma­ tion has also been suggested as an appropriate way of dealing with multicollinearity among the independent variables, for example Kane [1968, p, 280]. This note generalises Geary's results and shows that transforming the data by taking first differences for such a purpose cannot improve the efficiency of the regression estimates but will in general cause a reduction in efficiency. Although the usual least squares formula is not appropriate for calculating the variance of regression estimates obtained from the transformed data, they are often used for this purpose. Their relation to the variance of the regression estimates obtained from the untransformed data is examined. For completeness this note concludes with a brief discussion of first differencing to deal with serially correlated disturbances in the regression model.