# Efficient Estimation by Fully Modified GLS with an Application to the Environmental Kuznets Curve

## TL;DR

This paper introduces a Fully Modified GLS estimator for multivariate cointegrating regressions, improving inference and bias correction, with applications to environmental economics and tests for cointegration.

## Contribution

It develops the asymptotic theory for a new Fully Modified GLS estimator that handles complex cointegrating relations with deterministic and stochastic trends.

## Key findings

- The FM-GLS estimator shows good performance in simulations.
- The tests for cointegration are effective and reliable.
- Application to EKC hypothesis provides new insights.

## Abstract

This paper develops the asymptotic theory of a Fully Modified Generalized Least Squares estimator for multivariate cointegrating polynomial regressions. Such regressions allow for deterministic trends, stochastic trends and integer powers of stochastic trends to enter the cointegrating relations. Our fully modified estimator incorporates: (1) the direct estimation of the inverse autocovariance matrix of the multidimensional errors, and (2) second order bias corrections. The resulting estimator has the intuitive interpretation of applying a weighted least squares objective function to filtered data series. Moreover, the required second order bias corrections are convenient byproducts of our approach and lead to standard asymptotic inference. We also study several multivariate KPSS-type of tests for the null of cointegration. A comprehensive simulation study shows good performance of the FM-GLS estimator and the related tests. As a practical illustration, we reinvestigate the Environmental Kuznets Curve (EKC) hypothesis for six early industrialized countries as in Wagner et al. (2020).