Non-constant returns to scale and competitive factor markets
Frankel examines the use of the Cobb-Douglas formulation in aggregate data, where as a matter of macroeconomic(and essentially logical) identity output is exhausted in paying the factors of production.

So the macroeconomic identity states, for any aggregate production function

$$Q=F(K,L) \equiv rK + wL$$

where $r,w$ are ex post average unit rewards for the factors of production (hence the identity character).

The only way to equate $r$ and $w$ with marginal product is to have a function homogeneous of degree one ("constant returns to scale") because it is only then that we have

$$F(K,L) = F_K\cdot K + F_L\cdot L$$

and we can map $r=F_K,\; w=F_L$.

If the function is homogeneous but not of degree one but of a degree $k\neq 1$, then we have 

$$F(K,L) = \frac 1k(F_K\cdot K + F_L\cdot L)$$

which leads to $r=(1/k)F_K,\;\; w=(1/k)F_L$

If $k&gt;1$ we have Increasing returns to scale and factors are paid less than their marginal product (again, on average and on aggregate), while if $k&lt;1$ we have Decreasing returns to scale and factors are paid more than their marginal product.

We then run into trouble regarding the behavior and structure assumptions at the micro level that lead to such a result at the macro-level.