Log Income vs. Linear Income: An Application of the Encompassing Principle

An open question in empirical economics is whether models should be estimated by using the actual, or linear, values of economic variables or their logarithms. This paper applies the principle of encompassing to suggest specification and mis-specification tests of log vs. linear individual equations fitted to I(1) data, and illustrates the analysis for US quarterly disposable income. The finite-sample properties of the encompassing tests are examined in a Monte Carlo experiment Customized to the parameter values round in the empirical analysis.