Now allow RFPEQ to fail so that the relative wage of quality adjusted non-production workers is 50% higher in region r (y _ 1.5) and to simplify the argument let a non-production worker in region r be equal to one third of a non-production worker in region s. From equation 11, we can see that observed relative non-production wages will be 50% lower in region r even though it is a region with high true relative non-production wages. From equation 10, we can see that the relative quantity of non-production to production workers will in fact be higher in region r than in region s. From these two facts we would be likely to conclude mistakenly that region r had relatively cheap non-production workers and thus employed relatively more of them. The actual ratio of the relative wage bills depends on whether y ^ 1 and whether p > 0, p < 0, or p _ 0.
Rejecting (yff)P/(P 1) _ 1 is necessary but not sufficient to reject relative factor price equality. To see why, note that there are two ways for (yNP)р/(р 1) to equal unity. First, if RFPEQ holds, y _ 1, then (Yff)р/(р 1) _ 1 no matter what value p takes. However, if p is close to zero (i.e. if production is close to Cobb-Douglas), (Yff)P/(P 1) may equal unity even if y does not. On the other hand, (yff)P/(P 1) _ 1 can only be due to the failure of relative factor price equality, y _ 1. In addition, even if p _ 0 and we reject (Yff)P/(P 1) _ 1, we will not be able to determine which region has the higher relative wages without making an assumption on the elasticity of substitution, 1/ (1 — p).
To reject RFPEQ we need only to reject (7^ = 1 for one pair of factors f and g because RFPEQ implies that all relative factor rewards are equal. That is, even if the non-production to production wages are equal in regions r and s, it still may be the case that the wage-rental ratios are not equal. One can use either of the remaining two relationships to examine the variation, if any, in wage-rental ratios,
Before developing our empirical framework, we explore the additional implications of factor price equality.