Identifying reduced-form relations with panel data

The literature that tests for U-shaped relationships using panel data, such as those between pollution and income or inequality and growth, reports widely divergent (parametric and non-parametric) empirical findings. We explain why lack of identification lies at the root of these differences. To deal with this lack of identification, we propose an identification strategy that explicitly distinguishes between what can be identified on the basis of the data and what is a consequence of subjective choices due to a lack of identification. We apply our methodology to the pollution-income relationship of both CO2- and SO2-emissions. Interestingly, our approach yields estimates of both income (scale) and time (composition and/or technology) effects for these reduced-form relationships that are insensitive to the required subjective choices and consistent with theoretical predictions.