I haven’t finished reading “Cleaning Up the Kitchen Sink” (pdf) by Francisco Rodriguez, but the first nine pages are compelling enough for me to pass it along anyway.
Rodriguez goes into the archives to revisit Mankiw-Romer-Weil and the models from which linear regression specifications are derived in growth theory. When authors toss in a vector of variables of interest in addition to the standard measures of initial GDP, human capital, etc, they almost always assume that the variables of interest (malaria, institutions, etc) are linearly related to growth. Of course, that doesn’t jive very well with good economic theory (for example, binding constrants and the theory of the second best). Rodriguez argues that the ad hoc introduction of quadratic terms and interaction variables is not a sufficient remedy.
What if the non-linearity is more complex than what can be captured by a set of simple quadratic and linear interaction terms? As I discuss below, if this is the case then most of the regressions currently estimated suffer from misspecification bias, making the type of inferences commonly drawn from their estimation invalid. Furthermore, the data requirements of estimating truly non-linear functions can be quite demanding and far outstrip the availability of data in currently existing data sets.
This problem is more than a theoretical curiosum. A systematic exploration of the theoretical foundations of the linear growth specification reveals that the set of assumptions necessary to justify fitting a linear function to the data is so restrictive as to practically make the linear specification the true theoretical curiosum. I suggest that the starting framework for an exploration of the growth evidence should be a specification that allows for a general set of interactions between the set of potential production function shifters.
[Hat tip: AdamSmithee]