Silviase/jgov_v1.4_full_ann huggingface dataset:
Is there any long-term bias of technical progress and is climate policy likely to reverse or exacerbate it? This is one of the questions addressed in this report. In particular, by explicitly modeling endogenous and directed technical change, we can investigate the possibility that additional R&D investments for reducing carbon emissions come, at least in part, at the expense of other forms of R&D spending, thus partially offsetting the gains from the innovative effort induced by climate policy.

The idea that traditional R&D efforts are crowded out by climate-related R&D investments is often cited in the modeling literature and originates from the hypothesis that the supply of R&D inputs is inelastic: an increase in the demand of scientists (or laboratories) is assumed to increase the rental costs of these factors, while leaving the overall amount of research largely unaffected.

Unfortunately, the majority of models used for climate policy analysis has only one R&D stock and imposes ad hoc assumptions to take into account the alternative and competitive uses of R&D funds. For example, Nordhaus (2002) and Popp (2004) explicitly consider the opportunity cost of R&D when they measure the overall impact of modeling endogenous technical change on stabilization costs. However, R&D expenditure not directly related to de-carbonizing the economy is not explicitly modeled, but rather included in the economy-wide investment variable.

Even without modeling how non-climate-policy-induced R&D investments react to a GHG stabilization policy, Nordhaus believes that neglecting the competition between different forms of R&D would overestimate the benefit of endogenizing technical change and thus assumes an exogenous “crowding out” effect. In his view, the overall amount of R&D investment is fixed, both in the short and in the long run, and thus any increase of carbon-related R&D completely crowds out other forms of R&D. As pointed out by Gillingham, Newell and Pizer (2007), it is mainly because of this hypothesis that Nordhaus (2002) finds that knowledge accumulation has a limited effect on the optimal timing of mitigation efforts and on total mitigation costs.

Popp (2004) introduces ENTICE, a modified version of the DICE model, where energy efficiency increases when investing in R&D. Popp rejects the complete “crowding out” hypothesis of Nordhaus (2002), but not the idea that different forms of R&D necessarily compete against each other for the allocation of investment resources. Accordingly, in the base version of the ENTICE model, each dollar spent on energy R&D crowds out half as much investment in other forms of R&D. Since only energy R&D is explicitly modeled, Popp mimics the “crowding out” effect by subtracting the eroded
R&D resources from the amount of investments in the overall R&D stock. $ ^{1} $ With this assumption, Popp finds that when endogenous technical change is neglected there is a limited overestimation of stabilization costs of about 10 percent and that crowding out effects work against additional welfare gains. $ ^{2} $

However, in the long-run time horizon usually assumed to study climate policy, the allocation of total R&D investments across different sectors should not be constrained, because a strong stabilization policy may induce higher expenditure in R&D to de-carbonize the economy, while maintaining the same level of investment in other forms of R&D. At the same time, it is not possible to rule out that forces other than the pure “crowding out” effects will turn a de-carbonized economy into a less technologically advanced economy. Goulder (2004) correctly points out that the increase of R&D in carbon-free energy and high efficiency equipment might be associated with lower investment in other sectors, with adverse effects on aggregate knowledge and productivity. For the fossil fuels extraction industry, it is reasonable to expect this contraction to be induced by both price and income effects, if stabilization costs reduce demand for goods in other knowledge-intensive industries. It is thus the “net” equilibrium R&D effect that determines the actual role of climate policy-induced technical change.

Goulder and Schneider (1999), Sue Wing (2003) and Gerlagh (2008) consider the effect of climate policy on total R&D investments rather than simply studying the re-allocation of R&D across sectors. They all find that induced technical change makes the economy more flexible to adjust to climate policy. Nevertheless, while Gerlagh (2008) finds that aggregate R&D investments increase substantially, Goulder and Schneider (1999) and Sue Wing (2003) find that they tend to decrease.

Goulder and Schneider (1999) first noted that climate policy affects the equilibrium amount of R&D and the rate of knowledge accumulation not only in the energy sector, but in all the other sectors where knowledge is used. With a dynamic general equilibrium model where knowledge is sector-specific and input-neutral – and where abatement policies affect the R&D investments of private firms and thus change the incentive to knowledge accumulation as well as input requirements across different sectors – they find that policy-induced technical change generally increases the equilibrium abatement effort. Nevertheless, gross abatement costs, in terms of GDP losses, increase with respect to a baseline in which induced technical change is not modeled. This result is explained by a positive and increasing opportunity cost of R&D: a carbon tax policy determines a re-allocation of R&D
across sectors, and a fall in the aggregate level of R&D due to a slower growth of output, especially in the conventional energy fuel sector.

Building on the work of Goulder and Schneider (1999), Sue Wing (2003) develops a multi-sector general equilibrium model to study how knowledge is optimally reallocated in response to a carbon tax. However, choices are limited in his model because total R&D investment is assumed to be a fixed proportion of savings and the propensity to consume of the economy is given as in a Solow model. With this framework, Sue Wing finds that a carbon tax induces an inter-sectoral and intrasectoral re-allocation of knowledge services and reduces the rate of knowledge accumulation, thus causing a decline of output.

Gerlagh (2008) develops an endogenous growth model where the level of output of the final good is a nested function of a generic intermediate good and of carbon-energy. The model allows for three different stocks of knowledge: one affecting the productivity of carbon-energy in the outer nest, one increasing the productivity of a capital-labor composite for the production of the intermediate good, and another increasing the productivity of a capital-labor composite for the production of carbon energy input. With this model structure, Gerlagh finds that induced technical change substantially increases the elasticity of emissions to a carbon tax and decreases the costs of emission reductions, especially when all knowledge stocks are free to respond to the policy stimulus. This result is explained by a reallocation of knowledge accumulation within the energy nest: energy-saving knowledge increases and energy-augmenting knowledge decreases.

This brief summary of the literature can help to understand the original features of our work. We study the effects of climate policy on both the direction and the aggregate level of knowledge accumulation as in Goulder and Schneider (1999), Sue Wing (2003), and Gerlagh (2008), but we adopt a different set-up. First, we use WITCH, a Ramsey-type neoclassical optimal growth model in which investment decisions in a variety of energy and non-energy technologies are fully endogenous and 12 regions interact in a strategic setting (for a full description of the WITCH model see Bosetti, Carraro et al., 2006; Bosetti, Massetti and Tavoni, 2007). We introduce in WITCH a new module to endogenize directed technical change in order to highlight in a simple but coherent framework the dynamics of R&D investments induced by climate policy. R&D expenditures, and therefore knowledge accumulation, are factor-specific and can be directed towards increasing energy efficiency or towards rising productivity of non-energy inputs, namely capital and labor. By explicitly modeling two R&D capital stocks, we avoid exogenous assumptions on energy R&D crowding out, and we can then study how mitigation policies change the direction and the magnitude of technical
change. Also, our detailed description of the energy sector allows us to study how the re-allocation of investments towards low-emitting, or carbon-free, electricity generation technologies might affect investments in other sectors.

Our findings are different from those in Goulder and Schneider (1999) and Sue Wing (2003). While these authors find that a carbon tax moves knowledge accumulation away from carbon-intensive sectors, and towards low-emitting sectors, we find that a mitigation policy not only re-allocates investments towards low-emitting or carbon-free technologies, but it also changes the direction of technical change. While under a Business as Usual (BaU) scenario technical change is directed towards capital and labor, the introduction of a climate policy readdresses technical change towards the energy sector. In addition, enhanced investments in energy R&D and in the energy sector are found not to “crowd-out” investments in non-energy R&D.

We also find that endogenizing technical change, no matter the sector in which it is introduced, has important consequences on GHG stabilization costs. We thus depart from Gerlagh (2008), in which endogenous technical change was found to affect the cost of climate policy only if modeled in the energy sector. More specifically, we find that omitting the effect of induced technical change in the non-energy sector underestimates the cost of the climate policy.

The rest of the report is organized as follows: Section 2 describes the model and in particular how technical change has been endogenized. Section 3 explains the calibration procedure and, to this purpose, also reviews the main studies that estimate the elasticity of substitution between capital, labor and energy. Section 4 describes the basic features of our BaU scenario and introduces some historical evidence on R&D patterns. Section 5 introduces and discusses the stabilization policy scenario. Some sensitivity analysis has been carried out and is presented in Section 6. A concluding session summarizes our main findings.

### 2. DIRECTED TECHNICAL CHANGE IN THE WITCH MODEL

#### 2.1. Short Model Description

WITCH - World Induced Technical Change Hybrid - is a regional integrated assessment model designed to provide information on the optimal responses of world economies to climate damages and related policy measures. WITCH is a hybrid model because it combines features of both top-down and bottom-up modeling: the top-down component consists of an inter-temporal optimal growth model in which the energy input of the aggregate production function has been expanded to
yield a bottom-up like description of the energy sector. World countries are grouped in 12 regions whose strategic interactions are modeled using a game-theoretic approach. A climate module and a damage function provide the feedback on the economy of carbon dioxide emissions into the atmosphere.

WITCH's top-down framework guarantees a coherent, fully intertemporal allocation of investments that have an impact on the level of mitigation – R&D effort, investment in energy technologies, fossil fuel expenditures. The regional specification of the model and the presence of strategic interactions among regions – through GHG emissions, exhaustible natural resources, technological spillovers – allows us to account for the incentives to free-ride. Investment strategies are indeed determined by taking into account both economic and environmental externalities. In WITCH, the energy sector is described with a sufficient degree of detail and a reasonable characterization of future energy and technological scenarios. By endogenously modeling fuel (oil, coal, natural gas, uranium) prices, and the cost of storing the captured $ CO_{2} $ , the model can be used to evaluate the main impacts of mitigation policies on the energy system, in all its components. In the following section and in Appendix A, we selectively present some features and equations of the model that are functional to our analysis of technological change. For a thorough description of the model see Bosetti, Carraro et al. (2006) and for calibration details and a discussion of the baseline see Bosetti, Massetti and Tavoni (2007).

#### 2.2. Directed Technical Change in the WITCH model

In previous versions of the WITCH model, only energy-related technological progress was endogenous. In this report, we describe and use a more general version of the model in which two types of R&D – Non-Energy and Energy R&D – are introduced to study the direction of technical change and to better describe long-term productivity dynamics.

In the model, gross output, $ GY(n,t) $ , in country n at time t is produced by combining energy services, $ ES(n,t) $ , and capital-labor services $ KLS(n,t) $ in a CES nest: $ ^{3} $

$$ G Y\big(n,t\big)=T F P\big(n,t\big)\Big[\alpha_{Y}\left(n\right)\cdot K L S^{\rho_{Y}}+(1-\alpha_{Y}\left(n\right))\cdot E S\big(n,t\big)^{\rho_{Y}}\Big]^{1/\rho_{Y}} $$

Net output, $ Y(n,t) $ , is obtained after accounting for the effects of climate change on production and for the expenditure for fuels and carbon capture and sequestration, as shown in detail in Appendix A. Energy services and capital-labor services are obtained by aggregating raw inputs to knowledge,
which raises their productivity. We use, as a proxy of knowledge, the cumulated stocks of R&D in the Non-Energy and Energy sectors, $ HKL(n,t) $ and $ HE(n,t) $ , respectively. As in Popp (2004), the aggregation between raw inputs and knowledge is assumed to follow a standard CES function:

$$ E S\big(n,t\big)=\left[\alpha_{E S}\big(n\big)H E(n,t)^{\rho_{E S}}+\big(1-\alpha_{E S}\big(n\big)\big)E N(n,t)^{\rho_{E S}}\right]^{1/\rho_{E S}} $$

$$ KLS(n,t)=\left[\alpha_{KLS}(n)HKL(n,t)^{\rho_{KLS}}+\left(1-\alpha_{KLS}(n)\right)KL(n,t)^{\rho_{KLS}}\right]^{1/\rho_{KLS}} $$

Calibration details are discussed in Section 3. The energy input $ EN\left(n,t\right) $ is produced in the Energy sector of the economy and is described in detail in Bosetti, Massetti and Tavoni (2007). It basically consists of a series of nested CES functions that describe energy supply and demand at different levels of aggregation. Capital and labor are aggregated in a CES nest to produce the capital-labor raw input KL as follows:

$$ KL\big(n,t\big)=\Big[\alpha_{KL}\big(n\big)K_{C}(n,t)^{\rho_{KL}}+\big(1-\alpha_{KL}\big(n\big)\big)L(n,t)^{\rho_{KL}}\Big]^{1/\rho_{KL}} $$

This is supported to some degree by the empirical literature that finds a higher elasticity of substitution between capital and labor than between any of the two inputs and energy (see van der Werf, 2007; Kemfert, 1998; Chang, 1994). As in previous versions of WITCH, the hybrid nature of the model allows us to portray endogenous technological change also from a bottom-up perspective, by letting Learning-by-Doing reduce the cost of power generation plants (see Appendix A for a more detailed presentation of the main equations of the WITCH model).

#### 2.3. The R&D Sectors

Knowledge is produced standing on the shoulders of one nation's giants: investment in R&D is combined with the stock of ideas already discovered and produces new knowledge which will be the base for new discoveries in the following years. In the seminal paper by Romer (1990), the research sector productivity increases proportionally with the stock of knowledge cumulated in the past, giving rise to endogenous growth. Strong intertemporal spillovers for the economy as a whole are questioned by, among others, Jones (1995), and, in the specific narrower scope of our analysis, by Popp (2002), who finds that the energy R&D sector exhibits diminishing returns. Therefore, the production of new ideas, $ Z(n,t) $ , in the Energy and Non-Energy sectors is modeled as follows:
$$ Z_{H E}\left(n,t\right)=a\;I_{H E}(n,t)^{b}H E(n,t)^{c}, $$

$$ Z_{H K L}\big(n,t\big)=f I_{H K L}(n,t)^{g}H K L(n,t)^{h}. $$

where $ b + c < 1 $ and $ g + h < 1 $ . We assume that obsolescence makes a fraction $ \delta $ of past ideas not fruitful for the purpose of current innovation activity. As a consequence, the stocks of knowledge evolve according to the following law of motion:

$$ H E(n,t+1)\;=\;H E(n,t)(1-\delta)+Z_{H E}\left(n,t\right) $$

$$ H K L(n,t+1)~=~H K L(n,t)(1-\delta)+Z_{H K L}\left(n,t\right) $$

The decision variables of the model are investments in physical capital (for all different technologies in the energy sector and for the domestic capital stock), the two types of R&D investments and fuel expenditures for non-electric energy. As a consequence the decision to invest in Energy R&D and Non-Energy R&D, and therefore total R&D, is endogenous and determined in each country/region by solving a dynamic open-loop game. Therefore, crowding out effects are also endogenous. We will indeed be able to compute the reaction of both types of R&D investments to the introduction of climate policy and to compute the resulting crowding-out effect.

### 3. CALIBRATION

With respect to the standard version of the model, we use here an elasticity of substitution lower than unity for the final nest, in which KLS and ES are aggregated to produce final output. There is still substantial uncertainty on the best nesting structure and the most appropriate elasticity of substitution to describe the relationship between capital, labor and energy demand. However, there seems to be evidence in favor of a capital-labor nest that is subsequently aggregated to energy, with an elasticity of substitution lower than one. Let us provide an overview of the empirical evidence to shed some light on these issues.

As to the nesting structure, both van der Werf (2007) and Kemfert and Welsch (2000) estimate alternative nesting structure to select the most appropriate one. van der Werf (2007) estimates a two-level CES production function for three combinations of capital (K), labor (L) and energy (E), for 12 OECD countries and 7 industries. He finds that the structure in which capital and labor are nested together and then combined to energy fits the data better than the nesting structure in which capital
and energy are nested together and then combined to labor. Nevertheless, van der Werf (2007) finds that the null-hypothesis of a non-nested structure cannot be rejected. Kemfert and Welsch (2000) estimate a two-level CES function for Germany and get mixed results: at national level the KE-L structure fits data best, while at industry level and for 5 industries out of 7 the KL-E structure fits data best.

Several studies focus on the estimation of the elasticities of substitution between energy, capital and labor at industry level (Prywes, 1986; Manne and Richels, 1992; Chang, 1994; Kemfert, 1998; Kemfert and Welsch, 2000; Okagawa and Ban, 2008), or both at national and industry level (van der Werf, 2007). These studies use the definition of “full elasticity” derived by Morishima, with the exception of Prywes (1986), Chang (1994) and van der Werf (2007) that estimate the Allen partial elasticities. The two measures differ and, as emphasized by Markandya and Pedroso-Galinato (2007), the former is generally lower than the latter. The different estimates are shown in Table 1.

Table 1. Elasticities of Substitution in the Empirical Literature (Adapted from Markandya and Pedroso Galinato, 2007)

K/L	L/E
0.88A	Prywes (1986)	0.88A	Prywes (1986)
0.82M	Kemfert (1998)	0.35A	Chang (1994)
0.793M	Kemfert and Welsch (2000)	0.42M	Kemfert (1998)
0.224 to 0.616A	van der Werf (2007)	0.167M	Kemfert and Welsch (2000)
0.07 to 0.33	Okagawa and Ban (2008)	0.517 to 0.863A	van der Werf (2007)
K/E	KL/E
0.87M	Chang (1994)	0.4	Manne and Richelss (1992)
0.65M	Kemfert (1998)	0.42A	Chang (1994)
0.871M	Kemfert and Welsch (2000)	0.5	Kemfert (1998)
0.804 to 1.000A	van der Werf (2007)	0.698	Kemfert and Welsch (2000)
0.04 to 0.45	Okagawa and Ban (2008)	0.147 to 0.622A	van der Werf (2007)
0.00 to 0.64	Okagawa and Ban (2008)
KE/L
0.681 to 1.169A	van der Werf (2007)
0.00 to 0.94	Okagawa and Ban (2008)

A and M superscripts denote Allen and Morishima elasticities of substitutions, respectively.

As for technological change, van der Werf (2007) shows that the rates of factor-specific technological change differ significantly across factors, thus supporting our choice to introduce directed technical change in WITCH.
In the version of WITCH proposed in this report, the elasticity between energy and capital-labor services, $ \sigma_{Y} $ , is set equal to 0.5. This choice is in line with models that aggregate capital, labor and energy analogously (see Table 1 and Manne et al., 1990; Whalley and Wigle, 1990). We adopt an elasticity of substitution between labor and capital, $ \sigma_{KL} $ , equal to 0.8 for all regions but China and South Asia, for which we allow for a greater elasticity of substitution ( $ \sigma_{KL} $ equal to 0.85). In previous versions of the WITCH model, a unit elasticity had been assumed. The value chosen here fits better with the empirical estimates found in the literature (see Table 1).

We calibrate energy R&D as in Popp (2004). Parameters of the CES function between energy and knowledge and of the innovation possibility frontier are chosen to be consistent with historical levels, to reproduce the elasticity of Energy R&D to energy prices and to achieve a return four times the one of physical capital, thus taking into account the positive externality of knowledge creation. The elasticity of substitution between energy and energy knowledge, $ \sigma_{ES} $ , is accordingly set equal to 1.67 and the same is assumed for the elasticity between capital-labor and non-energy knowledge, $ \sigma_{KLS} $ . R&D investments in the non-energy sector are also assumed to yield a return four times higher than the interest rate. The initial stock of Non-Energy knowledge is calibrated to obtain R&D investments in the initial time period which are about 2% of GDP, a figure very close to the historical one (see Figure 1).

The calibration of the Non-Energy R&D innovation possibility frontier and the elasticity of substitution between the Non-Energy knowledge stock and the capital-labor aggregate is based on the model performance in terms of output elasticity to R&D investments (as detailed in Table 2), for which a sufficient empirical evidence is available.

Table 2. Elasticity of Output with respect to Non-Energy R&D

2002	2022	2042	2062	2082	2102
USA	0.09	0.09	0.09	0.10	0.10	0.10
OLDEURO	0.07	0.07	0.07	0.07	0.07	0.08
NEWEURO	0.03	0.03	0.04	0.04	0.05	0.05
KOSAU	0.07	0.07	0.07	0.08	0.08	0.09
CAJAZ	0.09	0.09	0.09	0.10	0.10	0.10
TE	0.04	0.04	0.05	0.05	0.06	0.06
MENA	0.03	0.03	0.03	0.04	0.04	0.04
SSA	0.00	0.00	0.00	0.00	0.00	0.00
SASIA	0.03	0.03	0.04	0.04	0.04	0.05
CHINA	0.04	0.04	0.05	0.05	0.06	0.06
EASIA	0.02	0.02	0.02	0.02	0.03	0.03
LACA	0.02	0.03	0.03	0.03	0.03	0.03