Abstract This paper first introduces the algorithmic steps of the ARDL model, explores the long-run relationship of variables using the cointegration test and estimates the long-run relationship, and then builds an error correction model to explore the short-run relationship in the model to estimate the model coefficients. Finally, we analyze the changes in carbon emissions and the relationship between carbon emissions and economic growth in China in time and space, respectively, and use the ARDL model to empirically test the correlation between fiscal decentralization and carbon tax Between 1978 and 2004, the growth rate of the economy remained above 10%, and the growth rate of carbon emissions also increased rapidly at this time, and carbon emissions were positively correlated with economic growth, and the growth rate of economic growth was positively correlated with the growth rate of carbon emissions. The growth rate of carbon emissions is positively correlated with economic growth, and the trend of the growth rate of economic growth and carbon emissions is roughly the same. The coefficient of fiscal decentralization degree on carbon tax expenditure is inhibited at a 1% significant level. The coefficient of the industrial structure plays a catalytic role in carbon tax expenditure at a 1% significant level, and for every 1% unit decrease in the proportion of secondary industry to GDP, carbon tax expenditure decreases by 2.473%. The implementation of a carbon tax can achieve the goal of energy saving and emission reduction, but we should also pay attention to the possible counter-effects of a carbon tax on economic development and reasonably levy carbon tax to make the economy and environment reach a balanced state.