### The sample

Mainland China has 31 provincial-level districts. Since some data of Tibet are missing, the rest provinces are chosen as the sample. In this paper we analyze a perfectly balanced dataset that consists of annual observations from 2005 to 2010 for the sample of 30 provinces. This results in a sample of 180 total observations. All data used in this paper are from officially published statistics in China, including China Statistical Yearbook and China Energy Statistical Yearbook, where the missing data about average life expectancy at birth are obtained by linear interpolation method.

### Measure of CIWB

The ecological intensity of human well-being is a ratio between a measure of environmental stress and that of human well-being. Recent analyses use the ecological footprint or greenhouse gas emissions to measure environmental stress, and average life expectancy at birth to measure human well-being (Dietz et al. 2012; Jorgenson and Dietz 2015; Jorgenson 2014). In this paper, we employ the method introduced by Jorgenson (2014): carbon dioxide emissions per capita divided by average life expectancy at birth. Following his method, we constrain the coefficient of variation (standard deviation/mean) of the numerator and the denominator to be equal by adding a constant to the numerator, which shifts the mean without changing the variance. Thus, the measure of CIWB we employ is as follows.

$$\begin{aligned} CIWB=[(\text{CO}_{2}\text{PC}+33.5)/LE]\times 100 \end{aligned}$$

(1)

where \(\text{CO}_{2}\text{PC}\) is the carbon dioxide emissions per capita in metric tons; *LE* is the average life expectancy at birth in years; the number 33.5 is calculated from the data we employed to make the coefficient of variation of the carbon dioxide emissions per capita and the average life expectancy at birth be equal; the number 100 is the scale of the ratio. In this paper, we adopt the guidelines of IPCC (2006) to calculate carbon dioxide emissions.

According to IPCC (2006), carbon dioxide emission in this paper is calculated via the following equation.

$$\begin{aligned} CI_{it}=\sum \limits _{r=1}^{m}E_{itr}\times \lambda _{r}\times O_{r}\times \frac{44}{12} \end{aligned}$$

(2)

where \(CI_{it}\) is the carbon dioxide emission of province *i* in year *t*, and \(E_{itr}\) is the consumption of fossil energy *r* of province *i* in year *t*. \(\lambda _{r}\) [unit: kgc/kg (km\(^{3}\))] is the carbon emission coefficient of fossil energy *r*, and is calculated as the product of the default carbon content and the average net calorific value, where the data are from IPCC (2006) and the China Energy Statistical Yearbook. \(O_{r}\) is the carbon oxidation rate of fossil energy *r*, and is set at the default value of 1. In this paper we consider 8 kinds of fossil energy (m = 8), namely, raw coal, coke, crude oil, gasoline, kerosene, diesel oil, fuel oil and natural gas, with the unit of the first 7 kinds of fossil energy being KJ/kg and the unit of the last one being kg/m\(^{3}\).

### Measures of technology innovation and spillovers

On the one hand, technical change plays a significantly important role in improving environmental performance (Jaffe et al. 2003), which can be achieved through R&D activity and interregional knowledge spillovers. For example, Fisher-Vanden et al. (2004) find R&D expenditure to be one of the principal drivers of China’s declining energy intensity; some studies find that the interregional knowledge spillovers can boost local innovation (e.g., Bottazzi and Peri 2003; Moreno et al. 2005). On the other hand, it is also beneficial to human well-being (Kavetsos and Koutroumpis 2011; Graham and Nikolova 2013). Therefore, it is important to address the advantages of technical change to society.

Technology innovation and spillovers are recognized as the main determinants of technology progress (Coe and Helpman 1995; Keller 2004). Analyzing determinants of technology innovation has developed inside the knowledge production function framework (Griliches 1979). Audretsch and Feldman (2004) demonstrate that the relationship between innovative outputs and innovative inputs (R&D inputs) is stronger. In addition, geographic proximity to innovation producers can favor knowledge spillovers within the region, proximity to other innovative regions can boost local innovation (Cabrer-Borras and Serrano-Domingo 2007). Therefore, in this paper we choose technology innovation and spillovers as independent variables, and analyze their effects on CIWB.

Similar to Yang et al. (2014), in this paper we adopt R&D intensity to measure technological innovation. Some studies on technological change support the idea that the interregional knowledge spillovers can boost local innovation (e.g., Bottazzi and Peri 2003; Moreno et al. 2005). And R&D spillovers are one of the main forms of interregional knowledge spillovers (Yang et al. 2014). Therefore, in this paper we use interregional R&D spillovers to measure technology spillovers.

Following Coe and Helpman (1995) and Yang et al. (2014), we use weighted average of R&D intensity of neighboring regions to reflect interregional R&D spillovers. Thus, the following formula is derived.

$$\begin{aligned} TS_{it}=\sum \limits _{j=1}^{k}w_{ij}\times RD_{jt} \end{aligned}$$

(3)

where *TS* denotes technology spillover; \(w_{ij}\) is the spatial weight to reflect the relationship between province *i* and province *j*. If province *i* and province *j* are neighbors, \(w_{ij}=1\); otherwise \(w_{ij}=0\). RD is the R&D intensity, which is computed as R&D stock divided by GDP. The unit of measurement for GDP is million yuan RMB, and is in current price. The R&D stock \(K_{it}\) can be calculated as the accumulation of R&D expenditures minus depreciation (Coe and Helpman 1995).

$$\begin{aligned} K_{it}=(1-\delta )K_{i,t-1}+I_{it} \end{aligned}$$

(4)

where \(\delta\) is the depreciation rate and is set at 15 %; \(I_{it}\) is the R&D investment of province *i* in year *t*. The base year (2005) can be calculated through the following formula.

$$\begin{aligned} K_{i,2005}=\frac{I_{i,2006}}{r_{2005-2010}+\delta } \end{aligned}$$

(5)

where \(r_{2005-2010}\) is the average growth rate of R&D expenditures from 2005 to 2010.

### Model specification

In this paper, two variables are chosen as control variables, namely GDP per capita and manufacturing. Previous work on CIWB, particularly Jorgenson (2014), finds economic development affects CIWB. Therefore GDP per capita is chosen as one control variable. On the one hand, it is often found that relative levels of manufacturing increase energy consumption (Clark et al. 2010), which increase carbon dioxide emissions. On the other hand, the impacts of manufacturing on life expectancy or other aspects of human well-being remain understudied and under-theorized in macro-comparative contexts (Jorgenson et al. 2014). Hence, manufacturing is chosen as the other control variable, which is measured as the ratio of manufacturing output to GDP in this paper.

In order to investigate the effect of technology innovation and spillovers on CIWB, based on the above analysis, the following double log model is derived.

$$\begin{aligned} lnCIWB_{it}=\phi _{i}+\varphi _{t}+\alpha _{1}lnTI_{it}+\alpha _{2}lnTS_{it}+\alpha _{3}lnGDPPC_{it}+\alpha _{4}lnM_{it}+\varepsilon _{it} \end{aligned}$$

(6)

where subscript *i* denotes province *i* and subscript *t* denotes year *t*. \(CIWB_{it}\) indicates the carbon intensity of human well-being of province *i* in year *t*. \(\phi _{i}\) and \(\varphi _{t}\) are the regional effect and the year effect respectively. \(\varepsilon\) is error term; *TI* is technology innovation; *TS* is technology spillover; *GDPPC* is GDP per capita; and *M* is manufacturing.