Since the beginning of carbon allowance trading, the connection between carbon price and emission demand has become a research focus as the supply of allowances is controlled by the government and is relatively stable (Koch et al., 2014). The theoretical connection suggests that if the demand for carbon emission allowances exceeds the available supply, then the prices of carbon allowance increase (Quemin, 2020). However, the results of empirical investigations vary regarding carbon prices and carbon emissions. For example, Venmans (2012) reported that carbon emissions and carbon prices were positively connected between 2005 and 2012. O’Gorman and Jotzo (2014) argued that higher carbon prices led to a significant reduction in carbon emissions, as observed in the electricity industry. Lin and Jia (2019) applied a dynamic recursive computable general equilibrium model, reporting that higher ETS prices resulted in higher carbon emission reduction. Zakeri et al. (2015) observed a non-linear connection between carbon emission reduction and carbon prices. Laing et al. (2014) reported that rising carbon prices in the EU ETS reduced carbon dioxide emissions by an average of 40–80 million tons annually.

Previous studies were mainly conducted based on the ETS in developed countries or areas, i.e., the EU, US, and Australia. However, few such studies have been conducted in developing countries, i.e., the Chinese ETS.

Research on inflation has mainly focused on the New Keynesian Phillips curve (NKPC). However, the theoretical connections and empirical results vary. Numerous studies have reported evidence to challenge this theory. For example, Bardsen et al. (2004) showed that economists do not accept the NKPC; thus, Nason and Smith (2008) questioned the credibility of estimating the political implications of NKPC. The authors provided evidence that it did not also match the NKPC. Galí and Gertler (2005) proposed a hybrid variant of the NKPC to associate inflation with marginal cost. Nason and Smith (2008) outlined single-equation econometric methods for studying NKPC. The two studies reported no close association between inflation and marginal costs. Recently, Mavroeidis et al. (2014) evaluated current research on the NKPC, identified the limitations of current studies, and suggested the need for new approaches and data for further NKPC progress. While new estimations and forms of the NKPC are better, they are still weak indicators of inflation dynamics (Rudd and Whelan, 2005; Abbas et al., 2016).

Although some research on the topic challenges the NKPC, circumstances vary in different situations, and empirical evidence still suggests the existence of a curve; for example, Brissimis and Magginas (2006) reported that real-time data on lagged inflation provide strong evidence in favor of the NKPC. Zobl and Ertl (2021) identified new empirical evidence proving the existence of the original NKPC in emerging, small, and open economies in Central and Eastern Europe.

Current investigations on the environment and economic growth mainly revolve around the EKC model. However, the results are contradictory. Several studies argue that the relationships between environmental indicators and economic growth do not fit the EKC model (Grossman and Krueger, 1994; Dasgupta et al., 2002). Other research provides empirical evidence showing that the EKC model exists in cross-country contexts. For example, Lieb (2003) showed that the EKC exists for certain pollutants and under certain policy measures. Chow and Li (2014) demonstrated the presence of the EKC between carbon dioxide emissions and GDP per capita. Nasreen et al. (2017) provided evidence to support the EKC hypothesis and argued that economic development and financial stability damage and improve the environment, respectively. Shahbaz and Sinha (2019) provided empirical evidence for NKC from both national and international perspectives. Mazzanti et al. (2007), Shahbaz et al. (2010), Adebayo (2020), and Gao et al. (2019) provided abundant evidence to support the EKC in Indonesia, the Mediterranean region, Portugal, and Italy, respectively.

The results of the literature review indicate a close correlation between carbon prices and carbon emissions as well as a tight proportional relationship between inflation and economic growth. This allows carbon price and inflation to be substituted as variables in the EKC as carbon emissions and economic growth, thus creating a potential for the EKC to exist between these two variables. Grossman and Krueger (1994) argued that as the economy develops, there is an initial deterioration stage, which will change when the per capita income reaches $8,000. Currently, the per capita income in China is >$10,000; however, there is limited evidence in China about a potential EKC; thus, research on this topic is needed. Unfortunately, as the literature review indicates, extensive research in China about the EKC is lacking.

This study investigated the possible EKC relationship between carbon prices and inflation in China. Regarding carbon price data, we evaluated all eight pilots in China and finally selected three (Xu and Salem, 2021), namely, Shenzhen (SZ), Guangdong (GD), and Hubei (HB). We selected these pilots due to their higher frequency of trading carbon allowances and their representativeness among Chinese carbon pilots. Data on carbon allowance transaction prices are accessible from the regional carbon emission exchange websites of Shenzhen, Guangdong, and Hubei, respectively. We collected data on trading prices in August 2013. Data pre-processing showed that after April 2004, all the pilots had frequent transactions and could be used for empirical investigations.

We obtained CPI data from the Chinese National Bureau of Statistics (http://www.stats.gov.cn/) to represent inflation in China. The calculated returns of carbon prices and CPI and some basic descriptive statistics of the selected data are shown in Table 1.

As shown in Table 1, the mean values varied in the three carbon pilots. The mean value of carbon price for Shenzhen was significantly larger than those in Guangdong and Hubei. The Shenzhen carbon pilot had the largest maximum carbon price compared to the other two pilots. While the difference between maximized and minimized values for the Shenzhen pilot is the largest, the standard deviation is also the largest. These two aspects indicate that the carbon prices were more volatile in Shenzhen. The results of the Jarque–Bera tests suggest that the carbon prices in Guangdong and Shenzhen were not normally distributed. The values for skewness and kurtosis as well as the ADF test suggest that the original series is similar to the common financial series. As shown in Table 1, the mean value of CPI is 100.005 and the standard deviation and difference between the maximized and minimized CPI are small. These three aspects suggest that the CPI levels were stable from 2013 to 2022. Furthermore, the CPI does not follow a standard normal distribution and the series for CPI is stationary. Table 1 also shows that Hubei has the highest carbon return, followed by Guangdong and Shenzhen. The absolute values for the maximized and minimized returns are quite large, possibly due to inactive trading in the Chinese carbon trading pilots. The Jarque–Bera and ADF test results showed that the carbon return series have the same characteristics as the common financial time series. The mean value, the difference between maximized and minimized values, and the standard deviation further show that the CPI was stable during our sample period. The negative median growth rate of the CPI indicated negative growth in CPI for more than half of the sample collected.

To allow a more intuitive overlook of the selected data, we visualize the trends of the variables in the following Figures 1, 2. Specifically, Figure 1 shows the behavior of the CPI and carbon prices from 2013 to 2022 and Figure 2 shows the trends in inflation and carbon return. The Shenzhen pilot was the first among the three pilots to begin trading carbon allowances. The carbon prices increased sharply to about 90 yuan per ton and then showed a downward trend until the first half of 2020. Then, the prices increase to more than 40 yuan per ton and fell below 20 yuan. The carbon prices in Guangdong and Hubei showed similar trends except for the sharp increase when Guangdong started carbon trading. The prices showed a downward trend and then showed an upward trend until now. Compared to the fluctuations in Guangdong, Hubei was more stable. The CPI fluctuated from 2013 to 2022. Combining all four series, the behaviors of carbon prices in the Shenzhen pilot were more similar to the CPI trends. In contrast, the Guangdong and Hubei pilots showed their own trends, which may indicate that the prices in the two pilots were not directly associated with the changes in CPI (Figure 1).

Figure 2 shows the behavior of inflation and carbon returns from 2013 to 2022. In the Guangdong pilot, the carbon returns fluctuated widely during 2014–2017 and then remained at a positive level after 2017, contrary to the fluctuations in inflation. The Hubei pilot showed regular changes in carbon returns; however, the return rate was notably lower than inflation. The Shenzhen pilot showed trends similar to those in the Guangdong pilot. In general, apart from occasional spikes in inflation, the carbon return levels were consistent with the inflation rates from 2013 to 2022 in the Shenzhen pilot (details on the comparisons are shown in Figure 2).

In this section, we estimate Eq. 5 to test the connections between inflation and the carbon market. The detailed regression results are shown in Table 2. Table 2 lists the estimation results of the multiple linear regression model. In the three pilots, inflation did not significantly affect the growth rate of carbon prices, indicating no significant linear relationship between the inflation rate and carbon return in general.

We set the monthly inflation rate and the price logarithm of carbon markets as the threshold variables to assess the relationship between inflation and the carbon price growth rate. Under different inflation or carbon price levels, the direction and magnitude of the impact of inflation on the growth rate of carbon prices differ. The related estimation results for Eq. 8 are shown in Table 3.

While Section 5.1 briefly explored the relationship between inflation and carbon return for linear connection, Zhang et al. (2022) showed that one variable may show a non-linear impact on another variable. Thus, according to Zhang et al. (2022), we constructed Eq. 6. The estimation results are shown in Table 4.

As shown in Table 4, the impacts of inflation on carbon price growth are insignificant in the three markets, consistent with the estimation results for Eq. 5. Moreover, all the squared terms are insignificant, indicating that there may not exist a U-shaped or inverted U-shaped connection between inflation and carbon return in general. Similar to Section 5.1, we implement threshold regression for Eq. 9, the estimation results of which are shown in Table 5.

Volatility is also an important factor to one asset for its importance in portfolio management and risk mitigation. This increases our interest in exploring the roles of inflation on carbon volatility. Thus, we calculated a squared term of carbon return to represent the volatility of the carbon market and re-implemented the OLS regression between carbon volatility and inflation. The related estimation results are shown in Table 6. While inflation showed negative impacts on carbon volatility in all three carbon pilots, the impacts were not significant as all the coefficients for inflation are insignificant.

Similar to previous subsections, the threshold regression of Eq. 10 was also implemented. The results are shown in Table 7. The empirical estimations in Sections 5.1, 5.2, and 5.3 suggest that inflation shows both linear and non-linear effects on carbon return; however, whether there exists a U-shaped or inverted U-shaped connection is uncertain. Moreover, inflation is a crucial factor in understanding the carbon volatility in the Chinese carbon market.

Table 3 reveals several interesting findings regarding the relationship between inflation and carbon return. First, when the indicator of CPI is lower than the threshold, inflation shows a positive impact on the carbon return, as all three coefficients for π t are significant. Specifically, a 1% increase in inflation increases the carbon return by 34.16%, 8.58%, and 4.113% in the three selected carbon pilots, respectively. This phenomenon may be explained by the following reasons. First, in this case, all the thresholds are negative; in actual economic operation, this indicates deflation in general. Then, when inflation increases, it indicates that the economy is beginning to recover. Production may show a sharp increase, resulting in increased demand for carbon emission. Finally, the carbon return increases. The differences in the three coefficients may be due to different carbon emission demands caused by different industrial structures in the three regions.

Second, when the indicator of CPI is greater than the threshold, inflation does not affect the carbon return, as none of the coefficients are significant, contrary to the theoretical connection. These interesting findings may be explained by the following reasons. A CPI greater than the threshold, despite increased inflation, may indicate increased production and that the allowances allocated to emitters in China are too much in general. Combined with the fact that the carbon trading in the Chinese carbon pilot is not active enough, the carbon return may not reflect changes due to inflation. Moreover, as shown by the descriptive statistic of standard deviation in Table 1, the carbon pilots are violently fluctuating, which may result from an ignorance of inflation-related factors in the carbon market. The two aspects may account for the insignificance of inflation in the carbon market when the CPI is greater than the threshold.

Third, when the carbon return is equal to or smaller than the threshold, the signal is negative in all three pilots; however, the significance levels in the three markets vary. When the value of carbon return is smaller than the threshold, considering the rapid development of the Chinese economy, increased inflation implies that investment will bring more profits. In this case, more capital will exit the carbon pilot to other financial activities, causing a decreased carbon return. Thus, the signal between inflation and carbon return is negative. Generally, Shenzhen seems to be the region with more profit opportunities compared to the other two areas. Thus, the capital exit is more significant, causing a significant coefficient of inflation. Although the coefficients for Guangdong and Hubei are insignificant at the 10% level, the absolute value of the t-value of the coefficient in Guangdong is greater than that in Hubei due to the different economic statuses of the two regions.

Fourth, when the carbon return is equal to or greater than the threshold, the signal is positive in all three pilots, possibly due to increased production expansion caused by inflation. However, the significance levels in the three markets vary. Compared with Guangdong and Hubei, heavy industry is not a focus in Shenzhen; thus, increased inflation may not significantly affect the carbon return. However, as the Guangdong pilot covers the large emitters across Guangdong Province, increased inflation may indicate more production, causing more carbon emission demand to increase the carbon return.

As shown in Table 5, when implementing the threshold regression, the estimation results vary and are controversial compared with the results in Table 3. For example, when the CPI is selected as the threshold variable and the value is smaller than the threshold, after adding the squared term, the signal of π t in Shenzhen turns from significantly positive to significantly negative. Moreover, the squared term is also significant, indicating that inflation shows both linear and non-linear impacts on carbon returns in Shenzhen. When the CPI is selected as the threshold variable and the value is greater than the threshold, the coefficient of π t in Guangdong becomes significantly positive and the non-linear term is also significant, indicating that inflation in Guangdong shows both linear and non-linear impacts on carbon return. When the carbon return is equal to or is larger than the threshold, the coefficient of π t in Hubei changes from significant to insignificant. Thus, inflation also shows a non-linear impact on carbon return. Interestingly, inflation shows significant negative impacts on carbon return in coastal areas, i.e., Shenzhen and Guangdong, but positive impacts on the inland area, i.e., Hubei. The reasons may be as follows: when inflation occurs, the profitability of certain companies may change. Considering the over-allocation of allowances, the actual economic structure in these regions, and the decreasing marginal effect, increased inflation will show non-linear impacts on carbon return.

Four findings are indicated by the estimation results in Table 7. First, when the CPI is traded as the threshold variable and the values are smaller than the threshold, inflation shows a significant positive impact on carbon volatility in all three carbon pilots. Combined with the results in Table 3, inflation shows a great impact on carbon return, causing the carbon price to increase sharply. The results support our insights that when the economy is recovering from a recession, production expansion requires huge amounts of carbon allowances, which results in sharp increases in carbon prices. Thus, the coefficients for inflation in the estimation results are all significantly positive.

Second, when the CPI is used as the threshold variable and its values are smaller than the threshold, inflation has no impact on carbon return as all coefficients for inflation are insignificant, consistent with the estimation results in Table 3. This phenomenon may also be explained by the fact that when the economy is recovering to its normal status, the market shows relatively abundant carbon permits. In this case, the willingness of emitters to continuously purchase carbon permits is not strong enough; thus, neither the carbon return nor carbon volatility is significantly affected.

Third, as shown in Table 7,when the carbon return is selected as the threshold variable and the value is smaller than the threshold, the signals of the coefficients for inflation are negative in all three pilots. Furthermore, the impact is significant in Shenzhen, consistent with the results in Table 3. Combined with the results in Tables 3, 7, increased inflation may indicate decreased carbon return; however, due to the limited capital and inactive trading in the carbon market of Shenzhen, the fluctuations of carbon return simultaneously decrease.

Fourth, when the carbon return is selected as the threshold variable and the value is greater than the threshold, the coefficient for inflation turns from significant to insignificant. Moreover, the coefficient is significantly negative in Hubei. These results suggest that when inflation increases, the carbon price in Guangdong is smoothly increasing with a certain trend, while the carbon return in Hubei is gradually converging.

Numerous studies have assessed the EKC model. Recent studies have explored the issue of inflation and carbon emissions; for example, Andersson (2018) estimates the effects of inflation on carbon prices. The author reported the smaller impact of inflation on carbon prices in developed countries and the large impact in developing countries. Pardo (2021) empirically investigated the connection between inflation and carbon price, showing that inflation negatively affected carbon prices in Germany and the United Kingdom. Moessner (2022) reported that inflation and carbon emissions tend to be positively connected. The connection between inflation and carbon emission was controversial in previous investigations. Compared with international evidence on carbon emission and inflation, our results add additional empirical evidence on the connection between inflation and carbon emissions, although the results in the present study showed that inflation exerted positive or negative impacts on carbon prices. Domestic researchers in China also explored fitness in the EKC model. Zhang et al. (2009) and Peng and Bao (2006) investigated the EKC from the aspects of different pollutants, while Qu et al. (2022) and Feng et al. (2022) explored the EKC model in different industries. The results showed U-shaped or inverted U-shaped connections between the environment and economic development. However, to our knowledge, current investigations on the EKC model in China did not consider the connection between carbon emission and inflation. Thus, our results may provide a new insight for researchers in China to comprehensively explore the EKC theory.

The results of this paper demonstrating that inflation is an important factor when the market is pricing Chinese carbon allowances may show certain theoretical and practical implications, as well as policy recommendations. Theoretically, our results further extend the EKC theory by testing the connections between carbon markets and inflation in China. The results showed U-shaped or inverted U-shaped curves from inflation to the carbon market, which is uncertain, and may warrant further investigation in future research on the EKC model. Practically, the results of traditional investigations suggest that investors considering variations in carbon prices focus on the energy markets as these markets are closely connected. The results of this study provide a novel insight into understanding carbon prices. Specifically, the results remind investors to understand that the carbon market forms macro-inflation. The Chinese government is trying to balance economic growth and carbon emission; thus, our results are useful from the perspective of policy. For example, our results demonstrated that different industrial infrastructures or whether it is a coastal area affects the impacts of inflation on carbon markets. Thus, when authorities try to implement monetary policies, it is better to distinguish target areas to avoid large fluctuations in the carbon market that may be unfavorable for achieving the “carbon peak.”