On Comparing Regression Models in Levels and First Differences
提出基于最大对数似然函数的准则，用于比较水平值和一阶差分回归模型的拟合优度，帮助研究者避免虚假回归问题。
It has long been recognized that regressions involving economic variables in levels can be misleading. A high value of R2 is often obtained even when there is no underlying causal relationship between the dependent and explanatory variables. This has been stressed again recently by Granger and Newbold [1974]. Spurious correlations are less likely to occur with variables in first differences, and this has led some researchers to adopt first difference formulations automatically.2 However, if the choice is between an equation in levels and a corresponding equation with the same variables in first differneces, the relative merits of the two formulations should, in the absence of any a priori guidelines, be assessed on statistical grounds. The situation envisaged is therefore one in which models involving dependent variables in both levels and differences have been fitted, and it is desired to discriminate between them on the basis of goodness of fit. The proposed criteria are based on the maximized log-likelihood function, log L. This is a natural measure of goodness of fit; see Sargan [1964]. However, when competing models contain different numbers of parameters some adjustment is necessary. The Akaike Information Criterion (AIC) makes an allowance for the number of parameters estimated, v, by adopting a decision rule to select the model for which