Human Capital, Innovation, and Climate Policy: an Integrated Assessment

Abstract

This paper looks at the interplay between human capital and innovation when climate and educational policies are implemented. Following recent empirical studies, human capital and general purpose research and development (R&D) are introduced in an integrated assessment model used to study the dynamics of climate change mitigation. Our results suggest that climate policy stimulates general purpose as well as clean R&D but reduces the incentive to invest in human capital formation. Both innovation and human capital have a scale effect, which increases pollution, as well as a technique effect, which saves emissions for each unit of output produced. While the energy-saving effect prevails when innovation increases, human capital is pollution-using, also because of the gross complementarity between the labor and energy input. When the role of human capital is the key input in the production of general purpose and energy knowledge is accounted for, the crowding-out of education induced by climate policy is mitigated, though not completely offset. By contrast, a policy mix that combines educational as well as climate objectives offsets the human capital crowding-out, at moderate and short-term costs. Over the long run, the policy mix leads to global welfare gains.

Appendix: Equations and Variables

WITCH is a dynamic optimal growth model (top–down) with a detailed representation of the energy sector. It can be classified as a hybrid model. The geographical coverage is global and world regions are grouped into twelve macro-regions sharing economic, geographic, and energy similarities. These regions are USA (USA), WEURO (Western Europe), EEURO (Eastern Europe), KOSAU (Korea, South Africa, Australia), CAJANZ (Canada, Japan, New Zealand), TE (Transition Economies), MENA (Middle East and North Africa), SSA (Sub-Saharan Africa), SASIA (South Asia), CHINA (China and Taiwan), EASIA (South East Asia), LACA ( Latin America, Mexico and Caribbean).

The WITCH model includes a range of technology options that describe the use of energy and power generation. Different fuels can be used for electricity generation and final consumption: coal, oil, gas, uranium, and biofuels. Electricity can be generated using either traditional fossil-fuel-based technologies or carbon-free options. Fossil-fuel-based technologies include natural gas combined cycle, oil, and pulverized coal power plants. Coal-based electricity can also be generated using integrated gasification combined cycle production with carbon capture and sequestration. Carbon free technologies include hydroelectric and nuclear power, wind turbines and photovoltaic panels (wind and solar), and a backstop technology. A second backstop option represents an alternative to oil in transportation, such as hydrogen or second-generation biofuels. The model features endogenous technical change in the energy sector in the form of both learning-by-researching and learning-by-doing.

The model features a game-theoretic setup that makes it possible to capture the non-cooperative nature of international relationships. Climate change is the major global externality, but other economic externalities induce free-riding behaviors and strategic interactions. The model can produce two different solutions. The cooperative solution is globally optimal, because it maximizes global social welfare and internalizes environmental and economic externalities. It represents a first-best optimum. The decentralized, or noncooperative solution is strategically optimal for each given region (Nash equilibrium), but it does not internalize externalities. It represents a second-best optimum. An intermediate solution that internalizes only the environmental externality can also be computed. The Nash equilibrium is computed as an open-loop Nash equilibrium. It is the outcome of a non-cooperative, simultaneous, open membership game with full information. This remaining part of the Appendix describes the main equations of the economic module of the model. The complete description of all model equations can be found in Bosetti et al. [42, 43].

In each region, indexed by n, a social planner maximizes the following welfare function:

$$ W(n)={\displaystyle \sum_tL\left(n,t\right)}\left\{ \log \left[c\left(n,t\right)\right]\right\}R(t) $$

(4)

where t are 5-year time steps and the discount factor is given by:

$$ R(t)={\displaystyle \prod_{v=0}^t{\left[\;1+\rho (v)\right]}^{-5}} $$

(5)

where ρ(ν)is the pure rate of time preference and $c=\frac{C}{L}$ is per capita consumption. The budget constraint defines consumption as output minus investments and operation and maintenance costs in different energy technologies i, (I _i ) and (O&M _i ) investments in final good (I _c ), education expenditure (I _EDU), investments in general purpose R&D (I _R&_D) and energy R&D (I _ER&_{D, j} ) in energy efficiency (j = EFF) and backstop technologies (j = BACK):

$$ C\left(n,t\right)=\begin{array}{c}\hfill Y\left(n,t\right)-{\displaystyle \sum_i{I}_i}\left(n,t\right)-{\displaystyle \sum_iO\&{M}_i\left(n,t\right)-{I}_C\left(n,t\right)-{I}_{EDU}\left(n,t\right)}\hfill \\ {}\hfill -{I}_{R\&D}\left(n,t\right)-{\displaystyle \sum_{j= EFF, BACK}{I}_{ER\&D,j}\left(n,t\right)}\hfill \end{array} $$

(6)

Output is produced via a nested CES function that combines capital (K), labor (L), and energy services (EN):

$$ Y\left(n,t\right)=H\left(n,t\right)\varOmega {\left({A}_K\left(n,t\right)K{\left(n,t\right)}^{\rho Y}+{A}_L\left(n,t\right)L{\left(n,t\right)}^{\rho Y}+{A}_{EN}\left(n,t\right)\mathrm{EN}{\left(n,t\right)}^{\rho Y}\right)}^{\frac{1}{\rho Y}} $$

(7)

Neutral technical change (H) evolves exogenously with time. Factor productivity is endogenous and depends on the stock of general-purpose knowledge (R&D), or human capital (HK). Energy productivity is also affected by a dedicated stock of energy knowledge (R&D _{E, EFF}):

$$ \begin{array}{l}{A}_K\left(n,t\right)={A}_{K0}\left(n,t\right){\left(\frac{\mathrm{R}\&\mathrm{D}\left(n,t\right)}{\mathrm{R}\&\mathrm{D}\left(n,0\right)}\right)}^{\chi_K}\\ {}{A}_{\mathrm{EN}}\left(n,t\right)={A}_{E0N}\left(n,t\right){\left(\frac{\mathrm{R}\&\mathrm{D}\left(n,t\right)+{\mathrm{R}\&\mathrm{D}}_{E,\mathrm{EFF}}\left(n,t\right)}{\mathrm{R}\&\mathrm{D}\left(n,0\right)+{\mathrm{R}\&\mathrm{D}}_{E,\mathrm{EFF}}\Big(n,0}\right)}^{\chi_E}\\ {}{A}_L\left(n,t\right)={A}_{L0}\left(n,t\right){\left(\frac{\mathrm{HK}\left(n,t\right)}{\mathrm{HK}\left(n,0\right)}\right)}^{\chi_L}\end{array} $$

(8)

The production of both human capital and knowledge is characterized by intertemporal spillovers, as the stock available in the economy at each point in time contributes to the creation of the future stock. The new addition to human capital (Z _EDU) is produced using a Cobb–Douglas combination of the existing stock of human capital (HK) and the current expenditure in education (I _EDU). In a similar way, the available knowledge stock (R&D) and current R&D investments (I _R&_D) are combined to produce the new knowledge capital (Z _R&_D). The sum of the exponents is less than one to account for diminishing returns on education and R&D:

$$ \begin{array}{l}{Z}_{\mathrm{E}}{}_{\mathrm{DU}}\left(n,t\right)={\alpha}_{\mathrm{E}\mathrm{DU}}{I}_{\mathrm{E}\mathrm{DU}}{\left(n,t\right)}^{\beta_{\mathrm{E}\mathrm{DU}}}\mathrm{HK}\left(n,t\right){}^{\phi_{\mathrm{E}\mathrm{DU}}}\\ {}{Z}_{\mathrm{R}\&\mathrm{D}}\left(n,t\right)={\alpha}_{\mathrm{R}\&\mathrm{D}}{I}_{\mathrm{R}\&\mathrm{D}}{\left(n,t\right)}^{\beta_{R\&D}}\mathrm{R}\&\mathrm{D}\left(n,t\right){}^{\phi_{\mathrm{R}\&\mathrm{D}}}\\ {}\mathrm{where}\\ {}{\beta}_{\mathrm{E}\mathrm{DU}}+{\phi}_{\mathrm{E}\mathrm{DU}}<1\\ {}{\beta}_{\mathrm{R}\&\mathrm{D}}+{\phi}_{\mathrm{R}\&\mathrm{D}}<1\end{array} $$

(9)

The stock of both knowledge and human capital depreciate over time. Following Jorgenson and Fraumeni [65], the depreciation rate of human capital (δ _EDU ) is lower than the depreciation rate of knowledge (δ _R&_D; 2 and 5 %/year, respectively). The final laws of accumulation read as follows:

$$ \begin{array}{l}\mathrm{HK}\left(n,t+1\right)=\mathrm{HK}\left(n,t\right)\left(1-{\delta}_{\mathrm{EDU}}\right)+{Z}_{\mathrm{EDU}}\left(n,t\right)\\ {}\\ {}\mathrm{R}\&\mathrm{D}\left(n,t+1\right)=\mathrm{R}\&\mathrm{D}\left(n,t\right)\left(1-{\delta}_{\mathrm{R}\&\mathrm{D}}\right)+{Z}_{\mathrm{R}\&\mathrm{D}}\left(n,t\right)\end{array} $$

(10)

Investments in R&D that build up the stock in Eq. (9) represent the total innovative activity of the economy. Therefore, we also refer to it as general-purpose innovation. Investments in clean energy R&D (I _ER&_{D, j} ) are combined with the existing stock of knowledge (R&D _{E, j} ) and the knowledge of other countries (SPILL _{E, j} ) to produce new dedicated energy knowledge (Z _{E, j} ). The model specifies three different energy knowledge stocks, energy efficiency (j = EFF), and two stocks of breakthrough knowledge, (j = BACK):

$$ \begin{array}{l}{Z}_{E,j}\left(n,t\right)={\alpha}_{E,j}{I}_{E\mathrm{R}\&\mathrm{D},j}{\left(n,t\right)}^{\beta_{E,j}}{\mathrm{R}\&\mathrm{D}}_{E,j}{\left(n,t\right)}^{\phi_{E,j}}{\mathrm{SPILL}}_{E,j}{\left(n,t\right)}^d\\ {}\mathrm{where}\\ {}{\beta}_{E,j}+{\phi}_{E,j}+d<1\end{array} $$

(11)

with the standard accumulation equation:

$$ {\mathrm{R}\&\mathrm{D}}_{E,j}\left(n,t+1\right)={\mathrm{R}\&\mathrm{D}}_{E,j}\left(n,t\right)\left(1-{\delta}_{E,j}\right)+{Z}_{{}_{E,j}}\left(n,t\right) $$

(12)

The contribution of foreign knowledge (SPILL) is not immediate, but depends on the interaction between two terms [59]: the first describes the absorptive capacity, whereas the second captures the distance from the technology frontier, which is represented by the stock of knowledge in high-income countries, denoted with the index HI. They include USA, WEURO, EEURO, CAJANZ, and KOSAU). Domestic investments are required to benefit from the international pool of knowledge.

$$ {\mathrm{SPILL}}_{E,j}\left(n,t\right)=\frac{{\mathrm{R}\&\mathrm{D}}_{E,j}\left(n,t\right)}{{\displaystyle \sum_{\mathrm{HI}}{\mathrm{R}\&\mathrm{D}}_{E,j}\left(n,t\right)}}\left({\displaystyle \sum_{\mathrm{HI}}{\mathrm{R}\&\mathrm{D}}_{E,j}\left(n,t\right)}-{\mathrm{R}\&\mathrm{D}}_{E,j}\left(n,t\right)\right) $$

(13)

The WITCH model includes two backstop technologies. These are innovative, zero-carbon technologies currently not commercialized, because they are very expensive. They necessitate dedicated R&D investments to become economically competitive and deployment to become available on large scale. The costs of these technologies are modeled with a two-factor learning curve. The unit cost of each backstop technology (P _BACK) evolves over time with technology deployment (CC _BACK) and the accumulation of a dedicated knowledge stock (R&D _{E, BACK}):

$$ \frac{P_{\mathrm{BACK}}\left(n,t\right)}{P_{\mathrm{BACK}}\left(n,0\right)}={\left(\frac{{\mathrm{R}\&\mathrm{D}}_{E,\mathrm{BACK}}\left(n,t-2\right)}{{\mathrm{R}\&\mathrm{D}}_{E,\mathrm{BACK}}\left(n,0\right)}\right)}^{-c}{\left(\frac{{\mathrm{CC}}_{\mathrm{BACK}}\left(n,t\right)}{{\mathrm{CC}}_{\mathrm{BACK}}\left(n,0\right)}\right)}^{-b} $$

(14)

R&D stock accumulates with the perpetual rule and with the contribution of international knowledge spillovers as in Eqs. (11) and (12). Equations (4)–(14) describe the basic formulation of the model. Starting from this version, we considered two possible variations. First (model 2, Section 3.2), human capital has an indirect effect on technological absorption and it contributes to increasing the absorptive capacity in the energy sector:

$$ {\mathrm{SPILL}}_{E,j}\left(n,t\right)=\frac{\left({\mathrm{R}\&\mathrm{D}}_{E,j}\left(n,t\right)+\mathrm{HK}\left(n,t\right)\right)}{{\displaystyle \sum_{\mathrm{HI}}{\mathrm{R}\&\mathrm{D}}_{E,j}\left(n,t\right)}}\left({\displaystyle \sum_{\mathrm{HI}}{\mathrm{R}\&\mathrm{D}}_{E,j}\left(n,t\right)}-{\mathrm{R}\&\mathrm{D}}_{E,j}\left(n,t\right)\right) $$

(15)

Second (model 3, Section 3.3), human capital is an input in the creation of both stocks of generic and energy knowledge (for energy efficiency and backstop technologies). Therefore, Eqs. (9), and (11) are modified as follows

$$ \begin{array}{l}{Z}_{\mathrm{R}\&\mathrm{D}}\left(n,t\right)={\overline{\alpha}}_{\mathrm{R}\&\mathrm{D}}{I}_{\mathrm{R}\&\mathrm{D}}{\left(n,t\right)}^{\beta_{\mathrm{R}\&\mathrm{D}}}\mathrm{R}\&\mathrm{D}{\left(n,t\right)}^{{\overline{\varphi}}_{\mathrm{R}\&\mathrm{D}}}\mathrm{HK}{\left(n,t\right)}^{\gamma_{\mathrm{EDU}}}\\ {}\\ {}{Z}_{E,j}\left(n,t\right)={\overline{\alpha}}_{e,j}{I}_{E\mathrm{R}\&\mathrm{D},j}{\left(n,t\right)}^{\beta_{{}_{e,j}}}{\mathrm{R}\&\mathrm{D}}_{E,j}{\left(n,t\right)}^{{\overline{\varphi}}_{e,j}}{\mathrm{SPILL}}_{E,j}{\left(n,t\right)}^d\mathrm{HK}{\left(n,t\right)}^{\gamma_{\mathrm{EDU}}}\end{array} $$

(16)

When human capital is introduced in the production function of new ideas, the parameters α and φ are recalibrated so that the dynamics of knowledge and education investments replicate those in the model version 1, $\overline{\alpha}<\alpha$ and $\overline{\varphi}<\varphi$.