Dhananjay Ghei and Nikita Singh on Ajay Shah’s Blog show the predicament for any researcher. Which estimation model should one use which represents the analysis in best way?
They look at the recent debate between two economists on impact of doing business rankings:
Can a country achieve growth by implementing large pro-business reforms? If yes, then how much growth is really possible from such reforms? In a recent WSJ op-ed, Cochrane takes a stab at this question for the United States. Using data from the World Bank’s ease of doing business index, Cochrane claims there is a log-linear relationship between GDP per person and business climate. By extrapolating this relationship out of sample, he predicts that the US would register a 209% improvement in per capita income (or, 6% additional annual growth if the required reforms are implemented over the next 20 years) by achieving the ease of doing business index value of 100.
Brad Delong disagrees. He fits a fourth-degree polynomial on the same data. He justifies this on the grounds that the third degree coefficient is negative and statistically significant. His forecast shows that an increase in the index value beyond 90 would actually lead to a lowerGDP per person. Figure 1 juxtaposes the log-linear and polynomial regression fit, and we can see how the two views are sharply different. The straight line yields higher and higher GDP as you go to 100; the polynomial droops off at the end.
There are problems with both and they suggest an alternative approach…
We use a second order Gaussian kernel and fit a local linear estimator to identify the functional form in sample. Business climate is significant at 1% level in the local linear non-parametric model. Moreover, based on a lower cross validation score, the non-parametric regression is favoured. In addition, we do a bunch of robustness tests by changing the type of kernel and regression. The results do not change much in either of the cases. These calculations were done in R using the np package.
The results, shown above, show that there is nonlinearity in the data. The linear model used by Cochrane is not appropriate. But we’re better off as compared with using a polynomial regression; the confidence interval is tighter at the edges.
Figure 4 superposes the three models. The coloured dots show the predicted value of GDP per person using the three different specifications when the doing business index takes the value of 100.
Our nonparametric estimate shows that gains from achieving a score beyond 90 are increasing and somewhere in between Cochrane and DeLong’s numbers. Cochrane predicts that the US would achieve 6% additional annual growth for 20 years by moving to a score of 100. If we go out of sample to estimate using the nonparametric fit, this shows an annual growth of 2.22% for the next 20 years. This is not something to laugh at, but it’s a smaller, and we think a more plausible estimate.
A kind of post only for the strong hearts…