Problems with regional production functions and estimates of agglomeration economies: A caveat emptor for regional scientists

Over the last 20 years or so, mainstream economists have become more interested in spatial economics and have introduced largely neoclassical economic concepts and tools to explain phenomena that were previously the preserve of economic geographers. One of these concepts is the aggregate production function, which is also central to much of regional growth theory. However, as Franklin Fisher, inter alios, has shown, the conditions necessary to aggregate microproduction functions into an aggregate production function are so stringent that in all probability the aggregate production function does not exist. This paper shows that the good statistical fits commonly found empirically are solely due to the use of value data and an underlying accounting identity. The result is that the estimates obtained cannot be regarded as providing evidence of the underlying technological structure of the spatial economy, including the aggregate elasticity of substitution, the degree of returns to scale, and the rate of technical progress.