Explore Associations between Subjective Well-Being and Eco-Logical Footprints with Fixed Effects Panel Regressions

: As environmental degradations constantly and directly threaten human well-being, it is imperative to explore the environmental impacts on people’s happy life. This research investigates the association between subjective well-being (SWB) and ecological footprints (EF) through space-time ﬁxed effects panel regressions. EF, as a vital indicator of environmentally sustainable development, plays a vital role in ecological balance. SWB determines the subjective quality of life for humanity. EF-related factors and socio-economic indexes referring to GDP, urbanization rate, income, education, health, political stability, and political voice accountability in 101 countries were captured. Compared with ordinary least square (OLS), stepwise regression (SR) and ﬁxed effects panel regression models (FEPR) exhibited good ﬁtness regardless of the cross-section or longitudinal models due to R2 beyond 0.9. The ﬁnding also discloses that EF and health were positively signiﬁcant to SWB, while income was negatively signiﬁcant to SWB. EF was an invert u-shaped link to SWB, which met the assumption of EKC. This research provided a model-driven quantitative method to address environmental impacts on people’s quality life of happiness, and opened shared doors for further research of carbon balance and circular economy.


Introduction
Environmental degradations constantly threaten human well-being. According to the Intergovernmental Panel on Climate Change (IPCC)'s data (see: https://www.ipcc.ch/ accessed on 31 August 2021), diverse environmental metrics are dramatically tended to negative impacts with different levels [1,2], not to mention COVID-19, as a global social, environmental, and economic comprehensive crisis, intangibly deprived human life, public health [3]. The research of environmental deterioration in the world triggering problematical environmental health has far-reaching effects, not only facilitating both countries environment and health head for the right direction but also finding out the best way to realize the goal of higher well-being with lower consumption. Therefore, exploring spatio-temporal associations between ecological footprint and subjective well-being (SWB) in the world is significant and worthy for understanding gaps in environment mitigations and adaptions.
Subjective well-being (SWB), a longstanding concern in the west, is a synonym of the term "happiness" by a single score representing an aggregate of a person/country's satisfaction. SWB is an interdisciplinary perspective, which refers to ethical, theological, political, economic, and psychological terms [4]. In a nutshell, it is used as an approach of the subjective quality of life to widen the measures of the objective living criteria that have dominated welfare research in social science for a long time. Life satisfaction (LS) is defined as the degree of that individual estimates their life-as-a-whole quality, involving an affective aspect and cognitive contentment [5]. The happiness survey in the U.S had ical footprint changes with spatio-temporal dimensions affecting well-being, preventing bias, or interval estimation.
Spatio-temporal semantic explanation of environmental impacts on subjective wellbeing is better to understand the trajectory of happiness and environment irreversible process [37,38]. Panel regression models can be measured with serial correlation or spatial dependence so that the model control for spatio-temporal dependence and heterogeneity can be determined [39]. We set forth the use of time differencing and spatial differencing transformations to handle space-time non-stationarity in estimation in this research. In order to eliminate endogenous or exogenous problems, we investigated panel data regression models based on previous research of partial correlations [8].

Data
In the previous research, The World Bank, the World Value Survey, the global footprint network, and the Gallup World Poll were used to explore the association between SWB and EF with partial correlation analysis. Via partial correlation, EF impacts on SWB were examined and separated in synergistic coupling between EF and other social-economic indexes [8]. The same datasets are used in this research. To find out the fixed effects panel regression model of correlation between SWB and EF on 101 countries data (2006)(2007)(2008)(2009)(2010)(2011)(2012)(2013)(2014)(2015)(2016), representation of SWB changes with the components of EF is employed by a panel data. SWB is a dependent variable, GDP per capita, urbanization rate, literacy rate, youth life expectancy, wage and salaried workers, political stability, voice accountability are control variables. Bio-capacity, carbon footprint, cropland footprint, fishing land footprint, built-up land footprint, forestland footprint, grazing-land footprint, EF consumption per capital are independent variables. The EF dataset has been extracted from the global footprint network dataset. Control variables are extracted from the World Bank and World Value Survey. LS is an alternative to SWB, collected from the Gallup World Poll. More details were listed in Supplementary Materials Table S1: Variable abbreviation list.

Study Framework
In order to figure out the association between SWB and EF-related factors to substitute traditional SWB survey, through data observation, a unit root test was initially conducted to make sure variables pass the test, then a simple OLS regression model and detect t-test were conducted. Multicollinearity and endogeneity were found out as the reasons without passing the t-test. Facing multicollinearity, stepwise regression was set forth, and the results showed biased R-square. Facing endogeneity, a fixed-effects panel regression model in cross-section and time-series was elucidated, respectively. The modeling framework in Figure 1 is as follows.

Panel Unit Root Test
Panel unit root test is the common feature of panel data analysis. The early panel unit root test meant Dickey-Fuller (ADF) tests, the Phillips-Perron tests, and the Iwiatkowski et al. (1992) tests [40]. The first-generation panel unit root test is called the Levin-Lin-Chu (LLC) [41]. Im-Pesaran-Shin [42] and the Hadri [43] are the second-generation panel unit root tests. They minimized the size distortions and increased the power. A theoretical description of these tests is presented as follows: The data-producing process of the series y, in its different form, be: where i = 1, 2, 3, · · · , N representing cross-sections and t = 1, 2, 3, · · · , T meaning period observations, X_it are the exogenous variables such as individual effects and linear trends, α = (ρ − 1) and ρ_i are the autoregressive coefficients. The LLC assumes that the autoregressive coefficients in (2) are identical across the panel (common unit root process), while in the IPS test, they are different. In the LLC test, the null hypothesis is the presence of a unit root for all i, and the alternative hypothesis requires that the individual process is stationary for all i, and when the null hypothesis is the same, the alternative in the IPS test is illustrated to include a non-zero fraction of individual process as stationary. IPS statistic equation as: In Equation (2), according to the simple Lindberg-Levy theory, the test statistic is asymptotically distributed as N (0,1) as the number of observations is extremely large. Im et al. (2003) exhibited values of the mean and variance for standardizing the test statistic [44].

Panel Unit Root Test
Panel unit root test is the common feature of panel data analysis. The early panel unit root test meant Dickey-Fuller (ADF) tests, the Phillips-Perron tests, and the Iwiatkowski et al. (1992) tests [40]. The first-generation panel unit root test is called the Levin-Lin-Chu (LLC) [41]. Im-Pesaran-Shin [42] and the Hadri [43] are the second-generation panel unit root tests. They minimized the size distortions and increased the power. A theoretical description of these tests is presented as follows: The data-producing process of the series y, in its different form, be: where = 1, 2, 3, ⋯ , representing cross-sections and = 1, 2, 3, ⋯ , meaning period observations, _ are the exogenous variables such as individual effects and linear trends, = ( − 1) and _ are the autoregressive coefficients. The LLC assumes that the autoregressive coefficients in (2) are identical across the panel (common unit root process), while in the IPS test, they are different. In the LLC test, the null hypothesis is the presence of a unit root for all , and the alternative hypothesis requires that the individual process is stationary for all , and when the null hypothesis is the same, the alternative in the IPS test is illustrated to include a non-zero fraction of individual process as stationary. IPS statistic equation as:

Stepwise Regression (SR)
SR is an automatic variable selection procedure that selects from a couple of candidates the explanatory variables, which are the most related. We used the unidirectional forward methods. Forward selection begins with no variables in the model, examining each variable with a chosen model-fit criterion until none of the remaining variables improves the model to a statistically significant extent [45].

Fixed Effect Panel Model
In order to eliminate the endogenous or exogenous problems, we investigated panel data regression models based on previous research of partial correlations [8]. Panel data typically mean "data containing time series observations of a number of individuals" [46]. They contain independently pooled panels, random-effects models, and fixed effects models. Fixed effects panel regression models (FEPR) have two-dimensional data, referring to cross-sectional fixed effects models and longitudinal fixed-effects models. It is a widespread regression model in macros spectrum analysis due to the impact disparity of spatio-temporal heterogeneity. Panel data have many strengths in either cross-sectional or time-series data, including: (1) more accurate model parameters; (2) more widely available in the international spectrum; (3) more intensive capacity for collecting the complication of human behavior than a single angle; (4) more simplified computation and statistical inference (Hsiao, 2007); (5) minimize the effects of aggregation bias, from aggregating firms into large scale; (6) better measure the impacts that can be detected in neither cross-section nor time-series data; (7) more reliable estimates and test more sophisticated behavioral models with less restrictive assumptions; (8) control for individual heterogeneity [47,48].
The below equation is used to model SWB on various dimensions of EF.
where the dependent variable SWB is the subjective well-being level for country i in year t. The explanatory variables EF si are a set of environmental indices, which measure the different types of resources consumption including EF, BC, CBF, CLF, FIF, BLF, GLF, and FLF. Controls i are variables that may relatively affect SWB including GDP, URB, WSW, LR, YLE, PS, and VA. u it is the disturbance term.

Panel Unit Root Tests
To keep stability-based time-series data and avoid pseudo regression models, unit root tests were emphasized to examine the association between variables. Panel unit root test is a conventional method to examine variable rationality in panel data analysis. The result of panel unit root with SWB variable is shown in Table 1. p-value is 0, qualified cross-section records are 99, observation records are 826 cases. The result of panel unit root of TEF variable of p-value is 0, qualified cross-section records are 99, observation records are 826 cases. The result of panel unit root with TBC variable of p-value is 0.0001, qualified cross-section records are 99, observation records are 826 cases. The result of panel unit root of SWB with control variable of P-value is 0, qualified cross-section records are 4, and observation records are 4655 cases. All variables passed unit root tests owing to p-value less than 0.05.

Regression Analysis
By 965 observation records over a decade, we performed four regression models in Table 2 such as ordinary least square (OLS), stepwise regressions, cross-sectional fixed effects regressions, and time-series fixed effects regressions. In the OLS, we partitioned SWB-control variables OLS (model 1), SWB-EF OLS without control variables (model 2), and SWB-EF OLS with control variables (model 3). The 0.77 R 2 of model 3 is higher than others, implying multicollinearity might cause pseudo regressions. The stepwise regression aimed to eliminate multicollinearity negative inventions. Without doubt, EF coefficients were reduced in the step-wise model while the coefficients of control variables were the same as the model 3, including the coefficient of TEF was reduced from −16.17 to −0.026, the coefficient of BLF was reduced from 1.252 to 17.4, the coefficient of CLF was reduced from 0.185 to 16.33, the coefficient of FIF was reduced from −0.22 to 15.93, the coefficient of FLF was reduced from −0.055 to 16.09, the coefficient of GLF was reduced from 0.204 to 16.35. In the cross-section fixed effects panel regression (model 5) of Table 2, the result shows that BC is negatively related to SWB, based on the coefficient of −0.001, meaning natural supply over time did not impact SWB due to its stationary characteristic, but EF is positive related to SWB due to the coefficient of 0.048, indicating human consumption positively impacts SWB change with time. In particular, the coefficient of BLF was 2.48, the highest value beyond the impacts of control variables and the other explanatory variables, portraying a rise of built-up land consumption in a decade dramatically increased life satisfaction. GLF was positively related to SWB owing to the coefficient of 0.231, depicting grazing-land consumption enhancing people's happy feelings. Among the control variables, the coefficients of Health, GDP, stability, and education are positive, meaning they have positive impacts on happiness. In other words, an increase in health, GDP, PS, and LR will facilitate more people's pleasure. In contrast, WSW, VA, and URB have negative coefficients, which means an increase in these coefficients caused losses of people's safety and indirectly caused SWB shrinking.  Table 2 is considered spatial disparity without time differencing. The results show that BC is positively related to SWB, based on the coefficient of 0.022, meaning bio-capacity on geographical differences positively increased happiness recognition, but EF is negatively related to SWB due to the coefficient of −0.022, indicating human consumption with spatial heterogeneity inhibits happiness identity. Only interpretation can we imagine that geographical disparity is dominated by culture and religions in a region, and over-sufficient material hedonism induced spirit vacuity. Fixed effect parameters are influenced on discrepancy of geographical location, as shown in Table 3. The coefficients of BLF and GDP (1.611 and 1.56) were the number one and two impacts on SWB spatial dependence, demonstrating that personal spatio-occupation and individual income directly support happiness growth. GLF was positively related to SWB owing to the coefficient of 0.212, which means individual grazing-land consumption can improve people's happy feelings. Despite the coefficients of WSW and PS are negative, GDP, VA, URB, and LR are positive, meaning their increases will promote more people's pleasure.
From the time-series fixed effects regression model to the cross-sectional fixed effects regression model, the reliability of the model increased due to an increase in the R-squared value from 0.77 to 0.92. The results also indicated that the stepwise regression model could eliminate multicollinearity. Similarly, Table 2 shows that impacts of cross-section differences in SWB are more striking than time series in several dimensions, including: (1) the effect degree of longitudinal fixed-effects panel regression is in a small range from −0.12 to 0.14, while the effect degree of cross-sectional fixed effects is in a large range from −2.09 to 1.75. According to the spatial distribution impacts map of the cross-section fixed effects model, fixed effects in each country are generated in Table 3. We also established a crosssection fixed effects map whose impacts are categorized into five classes with different colors in Figure 2. Green color represents negatively high effects, the values range from −2.09 to −0.98, those countries are distributed in the second-most-populous continent. In these areas, most countries are mainly poor countries with poor health care such as Congo, Niger, and Afghanistan. Tender green colors represent negatively low effects, the values are in the range from −0.98 to −0.03, those countries are distributed in the most populous continent such as Asia. In these areas, most countries are mainly developing countries with fair health care such as China, India, and Mali. The yellow color represents mediate effects. The values are the range from −0.03 to 0.73, those countries are distributed in Europe. In these areas, most countries belong to developed countries with good health care such as France, Germany, and Italy. The red color represents the highest positive effects. The values are in the range from 0.73 to 1.75, those countries are in North America, Europe, and South America. In these areas, most countries belong to the most developed countries with very good health care such as U.S., Denmark, and Sweden. The blue color represents no data.

Discussion
According to fixed effects panel regression analysis, the results portrayed that the cross-sectional model was more remarkable than the time-series model. However, in reality, the time-series model is more available than the cross-sectional model in the association between SWB and EF-related factors. First, R-squared values could not determine whether the model is good or not. R-square (R 2 ) is a statistical measure of model fit that indicates how much variation of a dependent variable is explained by the independent variable(s) in a regression model. Indeed, high R-square does not mean good models. In other words, R-square could neither convey the reliability of the model, nor whether the right regression had been chosen. R-square is not a unique standard to examine the reliability of the model. A good model might have a low R-square, a poorly fitted model might have a high R-square, and vice versa. Second, effects values' range could not determine whether the model is good or not. In the context of the fixed effect models, effects values are constants, which are less important than variables, just like residuals. They just influence the model's movements but could not change the tendency or directions of the models. Hence, the value of the effects is not a key point when good models or bad models were estimated. Third, correlation coefficients are not reliable in the cross-sectional fixed effects panel regression model. Gehlke and Biehl (1934) argued that correlation coefficients go up with the level of geographic aggregation by census data [49]. In 1950, Robinson found out that the correlation between race and illiteracy increased with the level of geographic aggregation [50]. In other words, what is significant at one spatial scale may not be significant at another. The reason is heteroscedasticity, which is common in spatial regression analysis. Accordingly, correlation coefficients in the cross-sectional fixed effects panel regression model are not available in this research. Last but most importantly, the time-series fixed effects panel regression model supported PC analysis, i.e., SWB is significantly positively related to TBC. In the cross-sectional fixed effects panel regression model (Table 4), SWB has no significant impacts on TBC due to p-value (0.337) beyond

Discussion
According to fixed effects panel regression analysis, the results portrayed that the cross-sectional model was more remarkable than the time-series model. However, in reality, the time-series model is more available than the cross-sectional model in the association between SWB and EF-related factors. First, R-squared values could not determine whether the model is good or not. R-square (R 2 ) is a statistical measure of model fit that indicates how much variation of a dependent variable is explained by the independent variable(s) in a regression model. Indeed, high R-square does not mean good models. In other words, R-square could neither convey the reliability of the model, nor whether the right regression had been chosen. R-square is not a unique standard to examine the reliability of the model. A good model might have a low R-square, a poorly fitted model might have a high R-square, and vice versa. Second, effects values' range could not determine whether the model is good or not. In the context of the fixed effect models, effects values are constants, which are less important than variables, just like residuals. They just influence the model's movements but could not change the tendency or directions of the models. Hence, the value of the effects is not a key point when good models or bad models were estimated. Third, correlation coefficients are not reliable in the cross-sectional fixed effects panel regression model. Gehlke and Biehl (1934) argued that correlation coefficients go up with the level of geographic aggregation by census data [49]. In 1950, Robinson found out that the correlation between race and illiteracy increased with the level of geographic aggregation [50]. In other words, what is significant at one spatial scale may not be significant at another. The reason is heteroscedasticity, which is common in spatial regression analysis. Accordingly, correlation coefficients in the cross-sectional fixed effects panel regression model are not available in this research. Last but most importantly, the time-series fixed effects panel regression model supported PC analysis, i.e., SWB is significantly positively related to TBC. In the cross-sectional fixed effects panel regression model (Table 4), SWB has no significant impacts on TBC due to p-value (0.337) beyond 0.05, but SWB has significantly positive impacts on TEF in that coefficient is 0.059 and p-value (0.006) is less than 0.05. On the contrary, in the time-series fixed effects panel regression model, SWB is significantly positively related to TBC for the reason that coefficient is 0.022 and p-value is 0.002, but not significantly related to TEF since coefficient is −0.023 and p-value is 0.143. Hence, it is evident that the time-series fixed effects panel regression model reveals the same result as previous PC analysis. With respect to the map shown in Figure 2, big disparity of SWB between developed countries and developing countries can be seen. EF has a statistically insignificant impact on the SWB gap, but the economic and demographic structure and GDP growth contribute to the underlying SWB growth. Therefore, environmental improvement is not a determinant of SWB development. However, their correlations might be two folds.
On the one hand, EF is related to individual SWB improvement. For example, we chose 12 countries to represent debtor countries and creditor countries, respectively. In the ranking table of between total EF and EF per capital (Table 5), EF in developed countries is higher than that in developing countries. Resources consumption per person is highly related to the degree of own property. The increasing of the population is the main reason for environmental degradation in developing countries, which leads to low EF producing bad feeling of happiness. In other words, EF might indirectly generate causality with SWB. It probably gets the consequence that individual about environmental improvement benefits individual happiness in a certain time by hedonic treadmill [51], instead, SWB of each country is restricted by multiple factors such as economic and demographic structure, and GDP per capita growth.
On the other hand, even though EF has not had a causality with SWB, EF is an inverted u-shaped link to SWB in correlation analysis using the Weka machine learning in Figure 3. That is in accord with a Kuznets curve, which means environmental improvement has increased from the beginning of SWB growth to a turning point [52,53]. After that, the SWB development benefits environmental degradation with excessive carbon emission, taking up over 60% of TEF [50]. As far as environmental quality increasing, the low-carbon circular economy model might be an underlying, sustainable development trend in future. On the other hand, even though EF has not had a causality with SWB, EF is an inverted u-shaped link to SWB in correlation analysis using the Weka machine learning in Figure 3. That is in accord with a Kuznets curve, which means environmental improvement has increased from the beginning of SWB growth to a turning point [52,53]. After that, the SWB development benefits environmental degradation with excessive carbon emission, taking up over 60% of TEF [50]. As far as environmental quality increasing, the low-carbon circular economy model might be an underlying, sustainable development trend in future.

Conclusions
Within the continuous improvement of the human development index and the popularity of the concept of environmental protection, the low-carbon circular economy model will be an underlying, sustainable development trend to mitigate environment pressure and improve happiness satisfaction from being enforced by the government to people's subjective consciousness. Space-time fixed effects regression model based on a panel data analysis provided an effective way to study those imbalanced problems.

Conclusions
Within the continuous improvement of the human development index and the popularity of the concept of environmental protection, the low-carbon circular economy model will be an underlying, sustainable development trend to mitigate environment pressure and improve happiness satisfaction from being enforced by the government to people's subjective consciousness. Space-time fixed effects regression model based on a panel data analysis provided an effective way to study those imbalanced problems.

Implication
This research provided an underlying quantitative method to measure SWB using socio-economic and environmental impact factors. It not only compensates weakness of qualitative SWB research but also sets forth the feasibility of model-dominated SWB calculation. Because the shortcoming of SWB calculation endows weights to partition ranks from 1 to 10 [54], the fixed-effect model is a supplement through regression analysis, especially missing data in qualitative research. Besides, with increasing environmental awareness and government emission policies, shrinking EF targets carbon emission reduction and end-of-life products supply [55]. This research provides public and transparent platform for exploring carbon-footprint tracking and carbon balance [56]. Resource scarcity is a common tendency around the globe so that circular economy [57] and zero-waste policy is not a surprise for environmental austerity consideration at the local government level. Lastly, a circular economy is just as important for a healthy environment as the balance of natural supply and demand. Nevertheless, the traditional linear model that resources are extracted from the nature and eventually discarded as waste to landfill, caused resource overconsumption and hampered environmental sustainability [58]. A circular economy aims to move away from the model in the context of stretching the life of material resources while minimizing pressures to ensure environmental benefits [59]. This research gave data-driven support in favor of circular economy.

Limitation
This paper just addressed the model-based interpretation of environmental, political, social-economic impacts on SWB, and there are still unperfect considerations to be improved. First, some essential culture-related factors should be encompassed in the model, such as religion, social media, the tradition of wisdom, and tourism [60][61][62][63][64][65]. Sometimes those entities predominate developed countries or undeveloped countries in intangible or tangible stimulations of human life. Second, the model presents different ways without fixed equations and coefficients, showing that the model has more potential requirements to be improved in the future. EF concept himself should offer detailed components in terms of structures. For example, carbon footprint takes up beyond 70% of total footprints, which disguise the influence of other footprints, especially built-up land sprawls due to global urbanization overwhelming. Lastly, environmental impacts on SWB need an unfolded process, thus, it is important to draw attention to individual EF in our daily lifestyle. Future research of calculating individual EF impacts should focus on the ecological research agenda.
Supplementary Materials: The following are available online at https://www.mdpi.com/article/ 10.3390/land10090931/s1, Table S1: Variable abbreviation list. Data Availability Statement: All data, models, and code generated or used during the study appear in the submitted article.