Estimating and testing the compensated double-log demand model

In spite of the proliferation of flexible functional forms for consumer demand systems, the double-log demand model continues to be popular, especially in applied work calling for single-equation models. It is usually estimated in uncompensated form. It can also be estimated in compensated form, by deflating the income variable alone using Stone's price index. The compensated form has the same right-hand side as a single-equation version of the popular linear approximation to the Almost Ideal demand model, facilitating the construction of a test for choosing between the two alternatives. This paper demonstrates these results, develops the specification test, and illustrates its application using US meat consumption data. Simulations suggest that the test is well-behaved with good power in typical applications.