Skip to main content

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


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.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4


  1. 1.

    The choice of a non-nested CES as opposed to a nested CES between a capital labor bundle and energy is not relevant for the results discussed in the paper. What ultimately drives the results is that non-energy inputs, capital, and labor, are gross complements to energy.

  2. 2.

    A thorough description and a list of related papers and applications are available at

  3. 3.

    Although it would be natural to characterize spillovers in the general purpose R&D sector, we refrain from doing so, mostly because of consistency with the empirical study that is used to calibrate our model, which did not account for spillovers. In addition, previous studies (see [59]) show that the contribution of knowledge spillovers is limited.

  4. 4.

    It is reasonable to expect the education effect on knowledge to be lower than the effect of both R&D investments and capital stock. The size of this parameter is also constrained by the value of the other parameters and the restriction that the sum cannot exceed 1. Parameters in the innovation production frontier have been recalibrated so as to yield the same baseline as in the basic model.

  5. 5.

    It should be stressed that the chosen climate policy scenario is only illustrative. The goal of this paper is to understand the basic mechanisms behind induced innovation when there is also human capital. We therefore abstract from second-best considerations and from the analysis of more realistic policy scenarios.

  6. 6.

    Permits are allocated on an equal per capita basis. This allocation schemes tend to favor developing countries. However, the goal is not to provide a comprehensive evaluation of different policy architectures, but rather to emphasize the trade-off and/or the synergies between different policy goals at the global level.

  7. 7.

    High-income countries in the WITCH model are the USA, Western Europe, Eastern Europe, South Korea, Australia, Canada, Japan, and New Zealand.

  8. 8.

    It is reasonable to expect the education effect on knowledge to be lower than the effect of both R&D investments and capital stock. The size of this parameter is also constrained by the value of the other parameters and the restriction that the sum cannot exceed 1. Parameters in the innovation production frontier have been recalibrated so as to yield the same baseline as in the basic model.

  9. 9.

    Countries or population are classified on-track in achieving universal primary education if continuing on linear trends between 1990 and 2002 will result in a completion rate above 95 % by 2015. Off-track means that the completion rate is projected to be below 50 % in 2015 (seriously off-track) or below 95 % (moderately off-track).

  10. 10.

    The implicit assumption is that average spending and the percentage of population off-track remains constant between 2000 and 2015.

  11. 11.

    After 2015 SSA and SASIA continue to spend at least the average amount required to have all population on-track.


  1. 1.

    Grubler, A., Nakicenovic, N., & Nordhaus, W. D. (Eds.). (2002). Technological change and the environment. Washington: Resources for the Future.

    Google Scholar 

  2. 2.

    van der Zwaan, B. C. C., Gerlagh, R., Klaassen, G., & Schrattenholzer, L. (2002). Endogenous technological change in climate change modelling. Energy Economics, 24, 1.

    Article  Google Scholar 

  3. 3.

    Carraro, C., De Cian, E., Nicita, L., Massetti, E., & Verdolini, E. (2010). Environmental policy and technical change: a survey. International Review of Environmental and Resource Economics, 4(2), 163–219. doi:10.1561/101.00000033.

    Article  Google Scholar 

  4. 4.

    Nordhaus William, D. (2002). Modeling induced innovation in climate change policy. In A. Grubler, N. Nakicenovic, & W. D. Nordhaus (Eds.), Modeling induced innovation in climate change policy. Washington: Resources for the Future Press.

    Google Scholar 

  5. 5.

    Popp, D. (2002). Induced innovation and energy prices. American Economic Reviews, 1, 160–180.

    Article  Google Scholar 

  6. 6.

    Bosetti, V., Carraro, C., Galeotti, M., Massetti, E., Tavoni, M. (2006). WITCH: A World Induced Technical Change Hybrid Model. The Energy J., Special Issue Hybrid Modelling of Energy Environment Policies: Reconciling Bottom-up and Top-down, pp. 13–38.

  7. 7.

    Managi, S., & Kumar, S. (2009). Trade-induced technological change: analyzing economic and environmental outcomes. Economic Modeling, 26(3), 721–732.

    Article  Google Scholar 

  8. 8.

    Carraro, C., De Cian, E. (2012). Factor-Augmenting Technical Change: An Empirical Assessment. Environmental Modelling and Assessment, DOI: 10.1007/s10666-012-9319-1.

  9. 9.

    Goulder, L. H., & Schneider, S. (1999). Induced technological change and the attractiveness of CO2 abatement policies. Resources and Energy Economics, 21, 211–253.

    Article  Google Scholar 

  10. 10.

    Otto, V. M., Löschel, A., & Dellink, R. (2007). Energy biased technical change: a CGE analysis. Resource and Energy Economics, 29, 137–158.

    Article  Google Scholar 

  11. 11.

    Gerlagh, R. (2008). A climate-change policy induced shift from innovations in carbon-energy production to carbon-energy saving. Energy Economics, 30, 425–448.

    Article  Google Scholar 

  12. 12.

    Carraro, C., Massetti, E., & Nicita, L. (2009). How does climate policy affect technical change? An analysis of the direction and pace of technical progress in a climate-economy model. The Energy Journal, 30, 7–38.

    Article  Google Scholar 

  13. 13.

    Massetti, E., Nicita, L. (2010). Optimal R&D Investments and the Cost of GHG Stabilization when Knowledge Spills across Sectors. CESifo Working Papers No. 2988.

  14. 14.

    Acemoglu, D. (2002). Directed technical change. Review of Economic Studies, 69, 781–809.

    Article  Google Scholar 

  15. 15.

    Lanjouw, J. O., & Mody, A. (1996). Innovation and the international diffusion of environmentally responsive technology. Research Policy, 25, 549–571.

    Article  Google Scholar 

  16. 16.

    Jaffe, A. B., & Palmer, K. (1997). Environmental regulation and innovation: a panel data study. Review Economic and Statistics, 79, 610–619.

    Article  Google Scholar 

  17. 17.

    Newell, R. G., Jaffe, A. B., & Stavins, R. N. (1999). The induced innovation hypothesis and energy-saving technological change. Quarterly Journal Economics, 114, 941–975.

    Article  Google Scholar 

  18. 18.

    Arrow, K. J. (1962). The economic implications of learning by doing. Reviews on Economic Studies, 29(3), 155–173.

    Article  Google Scholar 

  19. 19.

    Romer, P. M. (1986). Increasing returns and long-run growth. Journal of Political Economy, 94(5), 1002–1037.

    Article  Google Scholar 

  20. 20.

    Grossman, G. M., & Helpman, E. (1991). Trade, knowledge spillovers, and growth. European Economic Review, 35, 517–526.

    Article  Google Scholar 

  21. 21.

    Aghion, P., & Howitt, P. (1992). A model of growth through creative destruction. Econometrica, 60, 323–352.

    Article  Google Scholar 

  22. 22.

    Acemoglu, D., Aghion, P., Bursztyn, L., & Hemous, D. (2012). The environment and directed technical change. American Economic Review, 102(1), 131–166.

    Article  Google Scholar 

  23. 23.

    Lucas, R. E. (1988). On the mechanics of economic development. Journal of Monetary Economics, 22, 3–42.

    Article  Google Scholar 

  24. 24.

    Blankenau, W., & Simpson, N. (2004). Public education expenditure and growth. Journal of Development Economics, 73, 583–605.

    Article  Google Scholar 

  25. 25.

    Cameron, G., Proudman, J., & Redding, S. (2005). Technological convergence, R&D, trade and productivity growth. European Economic Review, 49(3), 775–807.

    Article  Google Scholar 

  26. 26.

    Sianesi, B., & van Reenen, J. (2003). The returns to education: macroeconomics. Journal of Economic Surveys, 17, 157–200.

    Article  Google Scholar 

  27. 27.

    Cohen, D., & Soto, M. (2007). Growth and human capital: good data, good results. Journal of Economic Growth, 12, 51–76.

    Article  Google Scholar 

  28. 28.

    Lutz, W., Cuaresma, J. C., & Sanderson, W. (2008). The demography of educational attainment and economic growth. Science, 319, 1047.

    CAS  Article  Google Scholar 

  29. 29.

    Barro, R.J., Lee, W. (2010). A new data set of educational attainment in the world, 1950–2010. NBER Working Paper No. 15902.

  30. 30.

    Yohe, G. (2001). Mitigative capacity: the mirror image of adaptive capacity on the emissions side. Climatic Change, 49, 247–262.

    Article  Google Scholar 

  31. 31.

    Griffith, R., Redding, S., & van Reenen, J. (2004). Mapping the two faces of R&D: productivity growth in a panel of OECD industries. The Review of Economics and Statistics, 86, 883–895.

    Article  Google Scholar 

  32. 32.

    Teixeira, A. A. C., & Fortuna, N. (2004). Human capital, innovation capability and economic growth in Portugal, 1960–2001. Portuguese Economics Journal, 3, 205–225.

    Article  Google Scholar 

  33. 33.

    Zografakis, N., Menegaki, A. N., & Tsagarakis, K. P. (2008). Effective education for energy efficiency. Energy Policy, 36, 3226–3232.

    Article  Google Scholar 

  34. 34.

    Kahn, M. E., & Matsusaka, J. (1997). Environmental demand: evidence from California voting initiatives. Journal of Law and Economics, 40(1997), 137–173.

    Article  Google Scholar 

  35. 35.

    Nelson, R., & Phelps, E. (1966). Investment in humans, technological diffusion and economic growth. American Economic Reviews, 56, 69–75.

    Google Scholar 

  36. 36.

    Cohen, W., & Levinthal, D. (1990). Absorptive capacity: a new perspective on learning and innovation. Administrative Science Q, 35, 128–152.

    Article  Google Scholar 

  37. 37.

    Benhabib, J., & Spiegel, M. (1994). The role of human capital in economic development: evidence from aggregate cross-country data. Journal of Monetary Economics, 34, 143–173.

    Article  Google Scholar 

  38. 38.

    Grimaud, A., & Tournemaine, F. (2007). Why can environmental policy tax promote growth through the channel of education? Ecological Economics, 62, 27–36.

    Article  Google Scholar 

  39. 39.

    Gradus, R., & Smulders, S. (1993). The trade-off between environmental care and long-term growth-pollution in three prototype growth models. Journal of Economics, 58, 25–51.

    Article  Google Scholar 

  40. 40.

    Hettich, F. (1998). Growth effects of a revenue-neutral environmental tax reform. Journal of Economics, 67, 287–316.

    Article  Google Scholar 

  41. 41.

    Pautrel, X. (2008). Environmental policy, education and growth: A reappraisal when lifetime is finite. Fondazione ENI Enrico Mattei, Nota di Lavoro 57-2008, Milan.

  42. 42.

    Bosetti, V., Massetti, E., Tavoni, M. (2007). The WITCH Model. Structure, Baseline, Solutions. Fondazione ENI Enrico Mattei, Nota di Lavoro 10-2007, Milan.

  43. 43.

    Bosetti V., De Cian, E., Sgobbi, A., Tavoni, M. (2009). The 2008 WITCH Model: New Model Features and Baseline. Fondazione ENI Enrico Mattei, Nota di Lavoro 85-2009, Milan.

  44. 44.

    Hourcade, J.C., Pottier, A., Espagne, E. (2011). The Environment and Directed Technical Change. A comment. FEEM Working Paper No. 95.2011.

  45. 45.

    Pottier, A., Hourcade, JC., Espagne, E. (2013). Modelling the redirection of technical change: the pitfalls of incorporeal visions of the economy. Forthcoming in Energy Economics.

  46. 46.

    Coe, D., Helpman, E., & Hoffmaister, W. (1997). North-South R&D Spillovers. The Economic Journal, 07, 134–149.

    Article  Google Scholar 

  47. 47.

    Madsen, J. B. (2007). Technology spillovers through trade and TFP convergence: 135 years of evidence for the OECD countries. Journal of International Economics, 72, 464–480.

    Article  Google Scholar 

  48. 48.

    Badinger, H., Breuss, F. (2008). Trade and productivity: an industry perspective. Empirica. Berlin: Springer, vol. 35(2), pp 213–231.

  49. 49.

    Franco, C., Montresor, S., & Marzetti, G. V. (2010). On indirect trade-related R&D spillovers: the average propagation length of foreign R&D. Structural Change Economic Dynamics. doi:10.1016/j.strueco.2011.04.003.

    Google Scholar 

  50. 50.

    Seck, A. (2011). International technology diffusion and economic growth: explaining the spillovers benefits to developing countries. Structural Change Economic Dynamics. doi:10.1016/j.strueco.2011.01.003.

    Google Scholar 

  51. 51.

    Coe, D., & Helpman, E. (1995). International R&D spillovers. European Economic Review, 39, 859–887.

    Article  Google Scholar 

  52. 52.

    Bernstein, J. I., & Mohnen, P. (1998). International R&D spillovers between U.S. and Japanese R&D intensive sectors. Journal of International Economics, 44, 315–338.

    Article  Google Scholar 

  53. 53.

    Eaton, J., & Kortum, S. (1996). Trade in ideas: patenting & productivity in the OECD. Journal of International Economics, 40(3–4), 251–278.

    Article  Google Scholar 

  54. 54.

    Nadiri, W. (1998). Are International R&D spillovers trade-related? Analyzing spillovers among randomly matched trade partners. European Economic Reviews, 42(8), 1469–1481.

    Article  Google Scholar 

  55. 55.

    López-Pueyo, C., Barcenilla-Visús, S., & Sanaú, J. (2008). International R&D spillovers and manufacturing productivity: a panel data analysis. Structural Change Economics Dynamics, 19, 152–172.

    Article  Google Scholar 

  56. 56.

    Romer, P. M. (1990). Endogenous technological change. Journal of Political Economy, 98, 71–102.

    Article  Google Scholar 

  57. 57.

    Jones, C. I. (1995). R&D-based models of economic growth. Journal of Political Economy, 103, 759–784.

    Article  Google Scholar 

  58. 58.

    Glomm, G., & Ravikumar, B. (1992). Public versus private investment in human capital: endogenous growth and income inequality. Journal of Polish Economy, 100, 818–834.

    Article  Google Scholar 

  59. 59.

    Bosetti, V., Carraro, C., Massetti, E., & Tavoni, M. (2008). International energy R&D spillovers and the economics of greenhouse gas atmospheric stabilization. Energy Economics, 30, 2912–2929.

    Article  Google Scholar 

  60. 60.

    Pessoa, S., de Abreu, S., Pessoa, M., Rob, R. (2005). Elasticity of Substitution Between Capital and labour and its Applications to growth and Development. PIER Working Paper 05-012, University of Pennsylvania.

  61. 61.

    Popp, D., Newell, R.G. (2009). Where does energy R&D come from? Examining Crowding Out from Environmentally-Friendly R&D. NBER Working Paper 15423.

  62. 62.

    IPCC. (2007). Climate change 2007: mitigation. In B. Metz, O. R. Davidson, P. R. Bosch, R. Dave, & L. A. Meyer (Eds.), Contribution of Working Group III to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change. Cambridge, UK: Cambridge University Press.

    Google Scholar 

  63. 63.

    Glewwe, P., Zhao, M., Binder, M. (2006). Achieving Universal Basic and Secondary Education: How Much Will It Cost? Cambridge, MA: American Academy of Arts and Sciences.

  64. 64.

    Hourcade, J. C., & Ghersi, F. (2008). Interpreting environmental policy cost measures. In V. Bosetti, R. Gerlagh, & S. Schleicher (Eds.), Modeling transitions to sustainable development. London: Edwar Elgar Publishing.

    Google Scholar 

  65. 65.

    Jorgenson, D., & Fraumeni, B. (1992). Investment in education and U.S. economic growth. Scandinavian Journal of Economics, 94, S51–S70.

    Article  Google Scholar 

Download references

Author information



Corresponding author

Correspondence to Enrica De Cian.

Appendix: Equations and Variables

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:

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

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

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

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):

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

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

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

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):

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

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:

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

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:

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

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):

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

with the standard accumulation equation:

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

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.

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

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):

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

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:

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

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

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

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 \( \overline{\varphi}<\varphi \).

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Carraro, C., De Cian, E. & Tavoni, M. Human Capital, Innovation, and Climate Policy: an Integrated Assessment. Environ Model Assess 19, 85–98 (2014).

Download citation


  • Climate policy
  • Innovation
  • Human capital

JEL Classification

  • O33
  • O41
  • Q43