Purpose The purpose of this study aims to analyze the dynamic behavior of the relationship between atmospheric carbon emissions and the Organisation for Economic Co-operation and Development (OECD) industrial production index (IPI) in the short and long term by applying multifractal techniques. Design/methodology/approach Multifractal de-trended cross-correlation technique is used for this analysis based on the relevant literature. In addition, it is the most widely used approach to estimate multifractality because it generates robust empirical results against non-stationarities in the time series. Findings It is revealed that industrial production causes long and short term environmental costs. The OECD IPI and atmospheric carbon emissions were found to have a strong correlation between the time domain. However, this relationship does not mostly take into account the frequency-based correlations with the tail effects caused by shocks that are effective on the economy. In this study, the long-term dependence of the relationship between the OECD IPI and atmospheric carbon emissions differs from the correlation obtained by linear methods, as the analysis is based on the frequency. The major finding is that the Hurst coefficient is in the range 0.40-0.75 indicating. Research limitations/implications In this study, the local singular behavior of the time-series is analyzed to test for the multifractality characteristics of the series. In this context, the scaling exponents and the singularity spectrum are obtained to determine the origins of this multifractality. The multifractal time series are defined as the set of points with a given singularity exponent a where this exponent a is illustrated as a fractal with fractal dimension f(α). Therefore, the multifractality term indicates the existence of fluctuations, which are non-uniform and more importantly, their relative frequencies are also scale-dependent. Practical implications The results provide information based on the fluctuation in IPI, which determines the main conjuncture of the economy. An optimal strategy for shaping the consequences of climate change resulting from industrial production activities will not only need to be quite comprehensive and global in scale but also policies will need to be applicable to the national and local conditions of the given nation and adaptable to the needs of the country. Social implications The results provide information for the analysis of the environmental cost of climate change depending on the magnitude of the impact on the total supply. In addition to environmental problems, climate change leads to economic problems, and hence, policy instruments are introduced to fight against the adverse effects of it. Originality/value This study may be of practical and technical importance in regional climate change forecasting, extreme carbon emission regulations and industrial production resource management in the world economy. Hence, the major contribution of this study is to introduce an approach to sustainability for the analysis of the environmental cost of growth in the supply side economy.