Original Results on the Relationship between Unemployment and Emissions of CO2: A Reconsideration of the Environmental Phillips Curve from the Statistical-Mathematical Point of View

The nexus between the emissions of Carbon Dioxide (CO2) and unemployment represents an important research interest, because of the social cost of combating air pollution. One of the most useful and flexible tools for analyzing the relationship between air pollution and unemployment is the Environmental Phillips curve. Until today, the existing economic literature has proposed estimates of the Environmental Phillips curve assuming that the relationship between the emissions of CO2 and the unemployment rate is properly fitted by a linear regression model that, based on the evidence about variables’ stationarity and cointegration, can be estimated by Ordinary Least Squares, Autoregressive Distributed Lag, Vector Autoregression, and Vector Error Correction. In this manuscript, the authors perform an original analysis aiming at providing new insights about the optimal specification of the curve, the economic meaning of its coefficients, and the identification issues needing to be addressed when estimating it. In particular, they elaborate a theoretical model of imperfect competition and, using the predictions of such a 46 framework, demonstrate that the Environmental Phillips curve admits two alternative specifications: one including the first differences of the variables of interest (difference version) and another comprising the deviations of the same variables from their respective equilibrium values (gap version). The predictions of the theoretical model are validated by using U.S. time-series ranging between 1971 and 2022. The authors choose the United States of America as a case study because, according to the data released by the European Commission in 2022 and the World Bank in 2023, this is the most polluting country (namely, that with the largest emissions of CO2 per capita) after China, as well as the largest economy in the world. Nevertheless, as documented in the paper through an appropriate descriptive analysis, the cross-correlation between Gross Domestic Product, unemployment rate, and emissions of CO2 is spurious, calling for a rigorous theoretical and empirical investigation. The results obtained by the authors indicate that the gap version outperforms its difference counterpart, and its optimal estimator is given by the Restricted Error Correction representation of the Autoregressive Distributed Lag model. The procedure proposed by the authors to estimate the Environmental Phillips curve is not limited to the U.S. context only, but it is of general interest as it can be exploited to assess the relationship between unemployment and air pollution in any single country.