Technology innovation and diffusion in “less than ideal” climate policies: An assessment with the WITCH model

Abstract

This paper examines the dynamics of innovation in low-carbon energy technologies distinguishing between research and development and technology diffusion as a response to alternative climate policies. We assess the implications of second-best policies that depart from the assumption of immediate and global participation and of full technology availability. The analysis highlights the heterogeneous effects of climate policy on different energy R&D programs and discusses the contribution of important determinants such as carbon price and policy stringency, policy credibility, policy and technological spillovers and absorptive capacity.

Appendix I. WITCH: A model of endogenous technology and knowledge innovation and diffusion

The WITCH model describes technological advances that can occur in the energy sector of the economy, distinguishing between invention/innovation and diffusion/deployment. Innovation can either improve energy efficiency or increase competitiveness of advanced, not yet available, zero carbon technologies (breakthrough technologies). In both cases, the process of innovation follows similar dynamics. Knowledge creation is characterised by an innovation possibility frontier that exhibits both intertemporal and international spillovers of knowledge. The flow of new ideas (Z _J ) adds to the exiting stock of knowledge (HE _J ), depreciated by factor δ, and generates the new stock of knowledge available to each region, indexed by n, at each point in time, t:

$$ \begin{gathered} H{E_j}\left( {n,t + 1} \right) = {Z_j}\left( {n,t} \right) + H{E_j}\left( {n,t} \right)\left( {1 - {\delta_{{R\& D}}}} \right) \hfill \\ {\text{j}} = {\text{EE; breakthrough, power sector; breakthrough, final sector;}} \hfill \\ \end{gathered} $$

(A1)

Innovation can have three different applications, indexed by j, namely to improve energy efficiency (EE) and to reduce the cost of the two carbon-free technologies (breakthrough, power sector and breakthrough, final sector) and is meant to emphasise that each form of innovation requires specific, dedicated investments, I _j .

At each point in time, new ideas (Z _J ) are produced using a Cobb-Douglas combination between dedicated domestic investments (I _j,R&D ), a domestic stock of knowledge (HE _J ) and a foreign stock of knowledge (SPILL _J ):

$$ \begin{gathered} {Z_j}\left( {n,t} \right) = a\,{I_{{j,R\& D}}}{\left( {n,t} \right)^b}H{E_j}{\left( {n,t} \right)^c}SPIL{L_j}{\left( {n,t} \right)^d} \hfill \\ {\text{j}} = {\text{EE; breakthrough, power sector; breakthrough, final sector;}} \hfill \\ \end{gathered} $$

(A2)

The contribution of foreign knowledge, SPILL _j , is not immediate, but depends on the interaction between two components shown in Eq. A3. The first term describes the countries’ absorptive capacity whereas the second one captures the distance of each region from the technology frontier. The technology frontier is represented by the sum of the stock of knowledge across high-income countries HI ⁶:

$$ \begin{gathered} SPIL{L_j}\left( {n,t} \right) = \frac{{H{E_j}\left( {n,t} \right)}}{{\sum\limits_{{n \in HI}} {H{E_j}\left( {n,t} \right)} }}\left[ {\sum\limits_{{n \in HI}} {H{E_j}\left( {n,t} \right)} - H{E_j}\left( {n,t} \right)} \right] \hfill \\ {\text{j}} = {\text{EE; breakthrough, power sector; breakthrough, final sector;}} \hfill \\ \end{gathered} $$

(A3)

Figure 8 depicts the innovation possibility frontier for each country relative to the USA which has been normalised to one. Because rich countries are closer to the frontier, the potential inflow of knowledge is smaller compared to poor countries, despite the higher absorptive capacity (see also Table 1). Over time, developing countries progressively increase their knowledge stock and absorptive capacity but at the same time the potential inflow of knowledge is reduced as they converge to the frontier. Overall, spillovers are relatively higher in developing countries, as it can be seen from Fig. 9, which shows the ratio of international spillovers to the domestic R&D knowledge stock.

Fig. 8

Innovation possibility frontier normalised with respect to USA

Fig. 9

International spillovers. Ratio to the domestic R&D knowledge stock

The empirical evidence that could guide the parameter value selection is almost nonexistent (see Bosetti et al. 2008 for a discussion on this issue). They have been chosen so as to assign the largest contribution to the knowledge stock (on average 0.4, close to what assumed in Popp 2004). Domestic R&D investments contribute to the creation of new ideas with a share of 0.18 whereas international spillovers have a slightly lower contribution of 0.15 (e.g. a 1% increase in international spillovers increases the output of domestic ideas by 0.15%).

R&D itself has an opportunity cost. Since we do not model non-energy R&D, exogenous crowding-out is assumed. Within each given region, domestic externalities are fully internalised and we consider the social return of investment four times larger than the private one. In addition, each dollar spent on energy R&D crowds out half as much investments in other R&D (Popp 2004). In Eq. A4 we set $\psi = 0.{5}$:

$$ COS{T_{{R\& D}}}\left( {n,t} \right) = I\left( {n,t} \right) + 4\psi I\left( {n,t} \right) $$

(A4)

Each stock of energy knowledge can have an alternative application.

The energy efficiency stock of knowledge augments the quantity of final energy services (ES) that can be provided per unit of physical energy (EN) according to a Constant Elasticity formulation:

$$ ES\left( {n,t} \right) = {\left( {{\alpha_H}H{E_{{en}}}{{\left( {n,t} \right)}^{{{\rho_{{EN}}}}}} + {\alpha_{{en}}}EN{{\left( {n,t} \right)}^{{{\rho_{{en}}}}}}} \right)^{{\frac{1}{{^{{\rho en}}}}}}} $$

(A5)

This is a formulation that can be used to describe energy efficiency improvements (see also Popp 2004) because an increase in the stock of knowledge substitutes for the physical input of energy, reducing emissions per unit of energy services provided.

The stock of energy knowledge can also reduce the unit cost of breakthrough technologies. The cost of each technology is described by a two-factor learning curve which also considers the role of diffusion (Kouvaritakis et al. 2000). The unit cost of technology, ${P_{{tec}}}\left( {n,t} \right)$, at time t is a function of global deployment, $\sum\limits_n {{K_{{tec}}}} \left( {n,t} \right)$, which accrues with technology investments or deployment in the case of the final sector breakthrough and a dedicated energy knowledge stock, $H{E_{{tec}}}\left( {n,t} \right)$. To roughly capture the lag exiting between research and commercialisation, innovation has an impact on costs with a delay of two periods which in the model correspond to 10 years:

$$ \begin{gathered} \frac{{{P_{{tec}}}\left( {n,t} \right)}}{{{P_{{tec}}}\left( {n,0} \right)}} = {\left( {\frac{{H{E_{{tec}}}\left( {n,t - 2} \right)}}{{H{E_{{tec}}}\left( {n,0} \right)}}} \right)^{{ - c}}}*{\left( {\frac{{\sum\limits_n {{K_{{tec}}}} \left( {n,t} \right)}}{{\sum\limits_n {{K_{{tec}}}} \left( {n,0} \right)}}} \right)^{{ - b}}} \hfill \\ {\text{tec}} = {\text{breakthrough, power sector; breakthrough, final sector;}} \hfill \\ \end{gathered} $$

(A6)

The R&D stock accumulates with the perpetual rule and with the contribution of international knowledge spillovers, as in Eq. A1. The R&D expenditure devoted to breakthrough technologies prior 2005 has been very small. As a consequence, we omit the contribution of the knowledge stock which however is negligible. To give a term of comparison, the total stock of energy knowledge computed using International Energy Agency statistics amounts at 120 2005US$ billion in 2005. Only 4 billion can be attributed to a technology that could represent a breakthrough, namely concentrated solar power.

The two exponents are the Learning-by-Doing index (−b) and the Learning-by-Researching index (−c). They define the speed of learning due to diffusion and deployment (Learning-by-Doing) and to innovation (Learning-by-Researching). They are derived from a learning ratio which is the rate at which the generating cost declines each time the cumulative capacity or the knowledge stock doubles.

This formulation has received significant attention from the empirical and modelling literature in the most recent past (Criqui et al. 2000; Barreto and Kypreos 2004; Klassen et al. 2005; Kypreos 2007; Jamasab 2007; Söderholm and Klassens 2007). Table 2 summarises some estimates of parameters controlling the learning processes mostly for technologies used in the power sector and it shows a large variability. Based on those estimates, we assumed values in the lower range which are reported in the last row of the table. Note that the value chosen for the Learning-by-Doing parameter is lower than those normally estimated in single factor experience curves since part of the technology advancement is now led by specific investments.

Table 2 Learning ratios for diffusion (LbD) and innovation (LbR) processes

Finally, it must be highlighted that modelling of long-term and uncertain phenomena such as technological evolution calls for caution in the interpretation of exact quantitative figures and for accurate sensitivity analysis. The model parsimony allows for tractable sensitivity studies as stressed above. One should nonetheless keep in mind that the economic implications of climate policies as well as carbon price signals are influenced by innovative technologies availability only after 2030.

Once competitive, the uptake of the two breakthrough technologies is not immediate and complete but there is a transition/adjustment period. These penetration limits reflect the inertia of current energy and transport systems. The upper limit on penetration is set equal to 5% of electricity generation from other technologies in the case of the electric backstop and to 5% of consumption of other energy carriers in the case of non-electric backstop.

Initial prices are about ten times the 2005 price of commercial equivalents (16,000 US$/kW for electric, and 550 US$/bbl for non-electric). The cumulative deployment is initiated at 1,000 TWH and 1,000 EJ, for the electric and non-electric backstop, respectively, an arbitrarily low value (Kypreos 2007). The backstop technologies are assumed to be renewable in the sense that the fuel cost component is negligible; for power generation, it is assumed to operate at load factors comparable with those of base load power generation.

Once competitive, deployment and technology diffusion contribute to further reduce the costs of backstop technologies. This is the second component of Eq. A5. International spillovers characterise also the diffusion phase and thus technology costs depend on the capacity installed globally. Differently from knowledge spillovers occurring during the innovation phase, experience spillovers that are embodied in the use of the technology are free and immediate within the period time step of the model which is 5 years.

Learning-by-doing also affects the cost of wind and solar photovoltaic power. In this case, most cost reduction comes from increased deployment and the cost, $SC\left( {n,t + 1} \right)$, follows a one-factor learning curve and declines with the world installed capacity, $\sum\nolimits_n {K\left( {n,t} \right)}$:

$$ SC\left( {n,t + 1} \right) = B(n) \cdot \sum\nolimits_n {K{{\left( {n,t} \right)}^{{ - {{\log }_2}PR}}}} $$

(A7)

The progress ratio, PR, defines the speed of learning. Although the econometric approach used to estimate learning curves and ratios has recently been criticised by Nordhaus (2009), there is evidence for a negative relationship between capacity and costs. For example, the annual world market for wind turbines has increased to tens of billions of dollars over the last two decades and the price of turbines has been reduced by a factor of four (Nemet 2010).

Without any policy, investment costs decline from the initial level 1,906US$/kW in 2005 to 1,010 in 2050 and 649 in 2100 with an overall reduction of about 66%. With a stabilisation policy (550 ppm CO₂-eq), investment costs can be lowered to reach the floor price of US$ 500.