Statistical Inference in Incremental and Difference Equation Formulations

Autoregressive linear equations are being used with increasing frequency in modeling political phenomena. Two forms of the autoregressive equation, the incremental equation and the equation are algebraically equivalent, as are their estimated regression coefficients. However, the squared (multiple) correlation coefficient, R2, will take on different values because of the difference in variance of the dependent variable. Furthermore, the R2 in autoregressive equations responds differently to increases in error variance than it does in nonautoregressive equations. The conditions under which these various results obtain are derived and we discuss some of the implications of these results for the study of autoregressive systems.