Silviase/jgov_v1.4_full_ann huggingface dataset:
Cross-section econometric studies that use firm- or industry- level data to estimate the elasticity of specific industries' output with respect to private R&D, find a range of values between 0.05 and 0.60, with a central tendency around 0.10 and 0.20. Estimates from studies that use economy-wide data to measure GDP elasticity with respect to private R&D are not many and find elasticities from 0 to 0.60, with a central tendency around 0.10. Coe and Helpman (1995) find a value of 0.23 for G7 countries and a value of 0.08 for non-G7 OECD countries. Lichtenberg (1992) finds the elasticity to be equal to 0.07 when poorer economies are included in the sample. Table 2 displays the elasticity of gross output with respect to R&D in the Non-Energy sector for all WITCH countries/regions, at different time intervals. Base-year values are generally consistent with the central tendencies of the empirical literature briefly summarized above. $ ^{4} $ Most interestingly, we are able to replicate the difference of elasticities between high- and low-income countries/regions and the model endogenously displays a (mild) degree of convergence of elasticities across time, in line with output per capita convergence rates.

### 4. BASELINE SCENARIO

From the baseline scenario – which corresponds to the non-cooperative Nash equilibrium of the WITCH model under the assumption of no mitigation policy – we obtain the equilibrium investment trajectories, together with the equilibrium R&D investments, GWP and consumption path. Table 3 summarizes baseline trends of major variables and indicators of interest. GWP increases over the whole century, starting from 34 trillions in 2002 to 246 trillions in 2102. Population grows at a declining rate and eventually stabilizes at about 9.5 billions at the end of the century. Income per capita expands five-fold. Interestingly, while the energy intensity of the world economy decreases, coherently with historical observations, the carbon intensity of energy slightly increases, showing a preference for cheap coal based electricity generation in the BaU. The gains in energy efficiency explain the reduction of emissions per unit of output, which is another desirable property of our BaU; however, the strong expansion of output offsets all efficiency gains and overall carbon emissions increase throughout the century, leading to a doubling of $ CO_{2} $ concentrations in the atmosphere.

While investments in final good capital and in the energy sector decline as a share of GWP, the model yields a rather constant path of R&D expenditure as share of GWP. As a result, the fraction of investment devoted to knowledge creation is increasing. The model yields a slightly declining path of
Energy R&D as share of GWP, a first increasing and then declining path of Non-Energy R&D as share of GWP, and a declining rate of Energy to Non-Energy R&D investments.

Table 3. Baseline Trend of Major Variables

2002	2022	2042	2062	2082	2102
GWP (Trillions, 1995 USD)	34	64	106	153	200	246
World Population (billions)	6.2	7.6	8.5	9.0	9.3	9.5
GWP Growth Rate (20 years average)	3.2%	2.5%	1.8%	1.4%	1.1%	--
Population Growth Rate (20 years average)	1.0%	0.6%	0.3%	0.2%	0.1%	--
Carbon Intensity of Energy (Ton C/Toe)	0.691	0.710	0.728	0.737	0.733	0.716
Energy Intensity (Toe/USD)	0.287	0.239	0.198	0.164	0.139	0.121
Carbon Intensity of Output (Ton C/USD)	0.198	0.170	0.144	0.121	0.102	0.087
CO2 concentrations in the atmosphere (ppm)	369	421	511	593	673	749
Investment in final good capital (Trillions, 1995 USD)	7.6	13.0	19.6	26.5	33.3	39.9
Investment in R&D (Trillions, 1995 USD)	0.84	1.70	2.89	4.26	5.51	6.14
Investment in Energy Sector (Trillions, 1995 USD)	0.36	0.59	0.78	0.95	1.11	1.27
Investment in Final Good Capital (% GWP)	22.29%	20.25%	18.50%	17.36%	16.68%	16.19%
Investment in Energy Sector (% GWP)	1.07%	0.91%	0.74%	0.62%	0.55%	0.52%
R&D expenditure (% GWP)	2.476%	2.656%	2.730%	2.790%	2.761%	2.492%
Non-Energy R&D (% GWP)	2.454%	2.636%	2.711%	2.772%	2.742%	2.475%
Energy R&D (% GWP)	0.022%	0.019%	0.019%	0.019%	0.019%	0.017%
Energy R&D (% Total investment in R&D)	0.884%	0.734%	0.684%	0.671%	0.670%	0.679%
Non-Energy R&D knowledge stock per worker (index)	1.00	0.89	1.03	1.37	1.83	2.35
Energy R&D knowledge stock per worker (index)	1.00	1.00	1.16	1.41	1.70	1.97

Table 4 and 5 show output-growth accounting for three representative countries/regions: the high income USA, the fast growing CHINA and the least advanced Sub-Saharan Africa (SSA). Table 4 shows how raw inputs, labor, capital and Non-Energy R&D contribute to the growth rate of the “capital-labor services” aggregate (KLS). Table 5 displays the same exercise for the aggregate “energy services” (ES). In italics, for each country/region, we report the growth rate of KLS and EN; immediately below the average yearly contribution of each input to the growth rate of the sectoral output is computed. Averages are calculated over twenty-year time periods.
Table 4. Contribution of Raw Inputs to the Growth Rate of Capital-Labor Services (Average Annual Growth Rates)

2002-2021	2022-2041	2042-2061	2062-2081	2082-2102
USA
capital-labor services	1.14%	0.68%	0.42%	0.29%	0.22%
labor	0.39%	0.20%	0.06%	0.01%	0.00%
capital for final good production	0.73%	0.39%	0.26%	0.18%	0.13%
non-energy R&D knowledge stock	0.02%	0.09%	0.11%	0.11%	0.08%
CHINA
capital-labor services	2.20%	1.47%	0.73%	0.43%	0.29%
labor	0.40%	0.08%	-0.08%	-0.09%	-0.04%
capital for final good production	1.68%	1.18%	0.60%	0.34%	0.21%
non-energy R&D knowledge stock	0.12%	0.21%	0.21%	0.17%	0.13%
Sub Saharan Africa (SSA)
capital-labor services	3.51%	2.47%	1.67%	1.17%	0.90%
labor	1.42%	1.01%	0.64%	0.40%	0.28%
capital for final good production	2.07%	1.44%	1.01%	0.76%	0.60%
non-energy R&D knowledge stock	0.02%	0.02%	0.01%	0.01%	0.01%

Table 5. Contribution of Raw Inputs to the Growth Rate of Energy Services (Average Annual Growth Rates)

2002-2021	2022-2041	2042-2061	2062-2081	2082-2102
USA
energy services	1.50%	0.63%	0.22%	0.10%	0.06%
energy	1.51%	0.62%	0.21%	0.08%	0.04%
energy R&D knowledge stock	0.00%	0.01%	0.01%	0.01%	0.01%
CHINA
energy services	3.88%	2.30%	1.00%	0.47%	0.24%
energy	3.83%	2.27%	0.98%	0.45%	0.22%
energy R&D knowledge stock	0.05%	0.03%	0.02%	0.02%	0.01%
Sub Saharan Africa (SSA)
energy services	4.10%	2.62%	1.81%	1.45%	1.29%
energy	4.07%	2.60%	1.80%	1.44%	1.29%
energy R&D knowledge stock	0.04%	0.02%	0.01%	0.01%	0.01%

As displayed in the table, in both USA and CHINA growth becomes more and more (Non-Energy) R&D driven. $ ^{5} $ Population growth and capital investments remain instead a major source of growth of the capital-labor services aggregate in Sub-Saharan Africa, while R&D plays only a minor role in
explaining growth throughout the century in this less advanced economy. Table 5 shows that, in the BaU, Energy R&D knowledge plays only a minor role in explaining growth of energy services in all three countries/regions. Increasing energy-demand is mainly satisfied by increases in the energy input. WITCH's equilibrium R&D investment trajectories are in line with historical trends of both aggregate R&D and Energy R&D expenditures, as shown in Figure 1 and Figure 2. Figure 1 shows both the historical levels of total R&D over GDP for the OECD countries and the equilibrium values of the same ratio as determined in the baseline scenario. Historical data show a slightly increasing trend over the past 25 years, starting from 1.9% in 1981 and reaching 2.25% in 2005. The same trend is predicted in the baseline scenario, with total R&D over GDP increasing from 2.55% in 2007 to almost 2.8% after 70 years, and then decreasing to 2.5% at the end of the century.

Figure 1. R&D as Percentage of GDP

Figure 2 shows the historical values of energy R&D over total R&D for OECD countries. The trend is decreasing, starting from 1.7% in 1992 and dropping to 1.1% in 2005. A decreasing trend is also derived under our baseline scenario as shown in the same figure 2. Energy R&D as percentage of total R&D slowly decreases across the century from about 0.9% to 0.7% in 2102. Technical change is therefore mainly capital-labor augmenting and this trend is even reinforced across the century because wages, endogenously determined, increase faster than equilibrium fuel prices.
Figure 2. Energy R&D as Percentage of Total R&D

Most interestingly, capital-labor augmenting technical change is energy-biased in our model. This means that R&D investments are mainly directed towards the capital-labor aggregate, but they increase the productivity of the energy input relative to the productivity of the capital-labor aggregate. This emerges clearly from the analysis of equation (9), in which we derive the ratio of the marginal products of energy (EN) and capital-labor (KL):

$$ \frac{MP_{EN}}{MP_{KL}}=\frac{\left(1-\alpha_{Y}(n)\right)\left(1-\alpha_{ES}(n)\right)\left[\alpha_{ES}(n)HE(n,t)^{\rho_{ES}}+\left(1-\alpha_{ES}(n)\right)EN(n,t)^{\rho_{ES}}\right]^{\frac{\rho_{Y}}{\rho_{ES}}-1}EN(n,t)^{\rho_{ES}-1}}{\alpha_{Y}(n)\left(1-\alpha_{KLS}(n)\right)\left[\alpha_{KLS}(n)HKI(n,t)^{\rho_{KLS}}+\left(1-\alpha_{KLS}(n)\right)KL(n,t)^{\rho_{KLS}}\right]^{\frac{\rho_{Y}}{\rho_{KLS}}-1}KL(n,t)^{\rho_{KLS}-1}} $$

As discussed above, the elasticity of substitution between KLS and ES is lower than the elasticity of substitution between KL and HKL in the model, i.e. $ \rho_{Y} < \rho_{KLS} $ . For this reason capital-labor augmenting technical change increases the relative marginal product of EN. Thus, KL-augmenting technical change is energy-biased. In other words, KL-augmenting technical change is pollution-biased and knowledge advancements per se are not necessarily good for the environment. This result derives from the assumption of complementarity between the KLS nest and ES intermediate inputs in the final output nest and the high elasticity of the Non-energy knowledge stock with respect to capital-labor input: any increase in the productivity of KL increases the demand of EN more than the demand for KL.
### 5. STABILIZATION POLICY

### 5.1 Gross World Product, Consumption and Total Investments

We use the WITCH model to study how an ambitious climate policy might affect the direction and pace of technical change. Let us assume that world countries agree to stabilize $ CO_{2} $ concentrations at 450 ppm. $ ^{6} $ Let us also assume that they agree to introduce a global cap and trade scheme as main climate policy tool. Initial allocations are grandfathered according to an equal per capita allocation rule. This is a simplified policy scheme, but useful to analyze the optimal reactions in terms of R&D investments and thus the direction and pace of technical change.

For an easy comparison between the stabilization and baseline scenarios, Tables 6, 7 and 8 display the same variables and indicators already portrayed in Tables 3, 4 and 5. According to WITCH, the $ CO_{2} $ stabilization policy just briefly described reduces Gross World Product (GWP) over the whole optimization interval 2002-2102. Discounted costs, measured as reductions of net GDPs and aggregated over regions, are 3.9% of baseline discounted GWP. Investments in capital, with respect to the baseline scenario, decline in absolute terms and as share of GWP; investments in the energy sector absorb instead a higher share of GWP.

Table 6. Stabilization Trends of Major Variables

2002	2022	2042	2062	2082	2102
GWP (Trillions, 1995 USD)	34	63	103	143	183	225
World Population (billions)	6.2	7.6	8.5	9.0	9.3	9.5
GWP Growth Rate (20 years average)	3.2%	2.5%	1.7%	1.2%	1.0%	--
Population Growth Rate (20 years average)	1.0%	0.6%	0.3%	0.2%	0.1%	--
Carbon Intensity of Energy (Ton C/ Toe)	0.690	0.550	0.419	0.306	0.246	0.173
Energy Intensity (Toe / USD)	0.286	0.178	0.118	0.085	0.073	0.082
Carbon Intensity of Output (Ton C/ USD)	0.197	0.098	0.049	0.026	0.018	0.014
CO2 concentrations in the atmosphere (ppm)	369	408	431	441	444	447
Investment in final good capital (Trillions, 1995 USD)	7.5	12.5	18.2	23.1	28.3	34.2
Investment in R&D (Trillions, 1995 USD)	0.84	1.65	2.68	3.69	4.58	5.07
Investment in Energy Sector (Trillions, 1995 USD)	0.32	0.59	0.82	1.10	1.45	1.85
Investment in Final Good Capital (% GWP)	22.18%	19.78%	17.67%	16.16%	15.46%	15.21%
Investment in Energy Sector (% GWP)	0.94%	0.93%	0.79%	0.77%	0.79%	0.83%
R&D expenditure (% GWP)	2.47%	2.60%	2.60%	2.58%	2.50%	2.26%
Non-Energy R&D (% GWP)	2.43%	2.55%	2.53%	2.49%	2.41%	2.18%
Energy R&D (% GWP)	0.04%	0.05%	0.07%	0.09%	0.09%	0.08%
Energy R&D (% Total investment in R&D)	1.43%	1.85%	2.66%	3.46%	3.77%	3.64%
Non-Energy R&D knowledge stock per worker (index)	1.0	0.9	1.0	1.3	1.6	2.0
Energy R&D knowledge stock per worker (index)	100.00%	111.38%	148.34%	206.27%	272.33%	332.02%
Table 7. Contribution of Raw Inputs to the Growth Rate of Capital-Labor Services (Average Annual Growth Rates)

2002-2021	2022-2041	2042-2061	2062-2081	2082-2102
USA
capital-labor services	1.12%	0.64%	0.34%	0.19%	0.15%
labor	0.39%	0.20%	0.06%	0.01%	0.00%
capital for final good production	0.71%	0.36%	0.19%	0.11%	0.10%
non-energy R&D knowledge stock	0.02%	0.08%	0.09%	0.08%	0.06%
CHINA
capital-labor services	2.11%	1.43%	0.66%	0.35%	0.25%
labor	0.40%	0.08%	-0.08%	-0.09%	-0.04%
capital for final good production	1.59%	1.14%	0.54%	0.28%	0.18%
non-energy R&D knowledge stock	0.11%	0.20%	0.19%	0.15%	0.11%
Sub Saharan Africa (SSA)
capital-labor services	3.18%	2.48%	1.65%	1.26%	1.00%
labor	1.41%	1.00%	0.63%	0.40%	0.28%
capital for final good production	1.76%	1.46%	1.01%	0.85%	0.71%
non-energy R&D knowledge stock	0.01%	0.01%	0.01%	0.01%	0.01%

Table 8. Contribution of Raw Inputs to the Growth Rate of Energy Services (Average Annual Growth Rates)

2002-2021	2022-2041	2042-2061	2062-2081	2082-2102
USA
energy services	0.40%	-0.79%	-1.65%	-0.84%	-0.23%
energy	0.38%	-0.82%	-1.70%	-0.89%	-0.27%
energy R&D knowledge stock	0.02%	0.03%	0.05%	0.05%	0.04%
CHINA
energy services	2.18%	0.87%	-0.83%	-0.42%	-0.02%
energy	2.13%	0.82%	-0.88%	-0.46%	-0.05%
energy R&D knowledge stock	0.06%	0.05%	0.05%	0.04%	0.03%
Sub Saharan Africa (SSA)
energy services	2.23%	0.97%	-0.16%	0.75%	1.27%
energy	2.18%	0.94%	-0.18%	0.73%	1.25%
energy R&D knowledge stock	0.04%	0.03%	0.03%	0.02%	0.02%

Energy R&D investments increase substantially to improve energy efficiency. However, equilibrium Non-Energy R&D investments are found to be lower than in the baseline scenario. The contraction of knowledge generation in the Non-Energy sector offsets increased knowledge creation in the Energy
sector. As a total R&D investments are lower and the pace of knowledge accumulation is slowed down as displayed in Table 6. This determines a lower contribution of R&D investments to capital-labor services growth with respect to the baseline scenario, as Table 7 clearly shows. The contribution of the Energy knowledge stock to Energy services growth increases instead, as shown in Table 8. Let us now examine the R&D equilibrium paths in both the baseline and stabilization scenarios in greater detail.

### 5.2 Energy and Non-Energy Investments

As specified above (Equation 1), gross output is obtained from a combination of energy services produced by the Energy Sector and capital-labor services produced in the Non-Energy sector. Investments in the Energy Sector include all investments in electricity generation technologies, operation and maintenance expenditures for power plants (as well as nuclear waste management and transportation costs for captured carbon emissions), and investments in Energy R&D. Investments in the Non-Energy sector are allocated between Non-Energy R&D and the overall economy capital stock, which is combined with labor.

The ratio of Energy to Non-Energy investments declines in the Baseline scenario, while it increases when a stabilization policy is implemented (see Figure 3). The reason is that resources devoted to investment are diverted towards the energy sector to build capital-intensive and O&M demanding carbon-free electricity generation capacity, and to increase energy efficiency by augmenting the energy R&D capital stock.

Figure 3. Energy to Non-Energy Investment Ratio
In the Non-Energy Sector, we can distinguish between investments to increase the stock of Non-Energy R&D and general capital investments. In the BaU scenario, the ratio between the two increases substantially and the economy becomes more and more knowledge-intensive. Under a stringent stabilization policy, we find that the equilibrium ratio between Non-Energy R&D investments and general investments in the capital stock is increasing as well, but the time path is lower with respect to an economy without a carbon constraint (see Figure 4.). This result is explained by the exogenous population dynamics, which keep labor force unchanged under the stabilization scenario, and a weak substitutability between capital and labor. $ ^{7} $ Climate policy induces a contraction of economic activity and exerts a pressure to reduce investments in the Non-Energy sector. However, labor force cannot adjust and cannot be easily substituted by capital. As a result the downward pressure in the Non-Energy sector is accommodated by a proportionally greater reduction of Non-Energy knowledge, and thus by a contraction of Non-Energy R&D investments.

Figure 4. Ratio between Non-Energy R&D Investment and Capital Investments

### 5.3 Energy R&D and Non-Energy R&D Investments

Energy R&D investments increase substantially under the $ CO_{2} $ stabilization policy, as shown in Figure 5. The need to increase energy efficiency modifies the equilibrium ratio of Energy R&D to Non-Energy R&D investments from a declining path, over the century, to a rising one. Contrary to what found by Goulder and Schneider (1999) and Sue Wing (2003), we find that climate policy strongly re-directs investments to Energy R&D and to the energy sector in general. Therefore, in an
unconstrained economy (without a stabilization target and the related climate policy), R&D is directed to augment the productivity of the capital-labor aggregate, which becomes relatively scarcer with respect to energy, as population growth slows down worldwide. In a carbon constrained economy, instead, the price of the energy input grows faster than the price of the Non-Energy input, and thus R&D resources are directed to increase energy efficiency.

Nonetheless, the drop in Non-Energy R&D is larger than the sharp increase in Energy R&D. As a consequence, at the equilibrium, overall expenditure in R&D decreases, as illustrated in Figure 6. This result confirms what found by Goulder and Schneider (1999) and Sue Wing (2003).

Figure 5. Energy R&D Investments

There are two driving forces behind this result. First, as emphasized above, the level of economic activity is lower when a carbon constraint is introduced and Non-Energy R&D is therefore accordingly reduced. Second, as shown in Figure 4, the equilibrium ratio of Non-Energy R&D investments to capital investments is lower in the presence of a stabilization target than without climate policy.
Figure 6. Total Investments in R&D

A wide concern has been expressed in the literature that the increase in Energy R&D induced by climate policy might come at the expenses – i.e. “crowd out” – of other types of knowledge investments (Nordhaus, 2002; Popp, 2004). As a consequence, the benefits of induced technical change should be evaluated net of the costs arising from a lower knowledge accumulation in other sectors of the economy. By modeling two R&D sectors we are now in a good stance to explore this issue with greater transparency than in previous analyses.

We define the Energy R&D crowding-out effect on Non-Energy R&D as the reduction in investments in the latter, directly or indirectly caused by an increase of investments in the former. Our definition is straightforwardly borrowed from macroeconomic theory, where the crowding out effect of government expenditure on private investments is a well-established result (see, for example, Mankiw 2003). Following closely the macroeconomic approach to the crowding out issue, we say that Energy R&D crowds-out Non-Energy R&D if the higher expenditure for increasing energy efficiency, ceteris paribus, has the effect to increase the opportunity cost of capital and thus to reduce investments in Non-energy R&D (as well as all other types of investment). $ ^{8} $
In our set-up, we investigate R&D investments assuming that economies are free to optimally allocate resources among sectors. Sector-specific knowledge stocks are not interchangeable, but R&D investments are. It is thus possible, in principle, to expand Energy R&D investments without reducing Non Energy R&D expenditures, until the long term equilibrium ratio between the two knowledge stocks is reached.

However, we find that mitigation policy reduces the growth rate of Non-Energy R&D investments, as pictured in Figure 7. What are the economic forces behind this result? Does this contraction result from a crowding out effect of increased investment in Energy R&D?

Figure 7. Growth Rate of Investments in Non-Energy R&D

Let us start exploring this issue from a theoretical perspective. To this purpose, we built a simplified version of the model (described in Appendix B in detail), from which we can derive the following Proposition 1:

Proposition 1 At each time t, the conditions characterizing the equilibrium trade-off between knowledge accumulation in the energy sector and consumption, and knowledge accumulation in the capital-labor sector and consumption are:

$$ \frac{\partial Y\left(t\right)}{\partial HE\left(t\right)}\frac{\partial HE\left(t\right)}{\partial I_{_{HE}}\left(t-1\right)}+\frac{I_{_{HE}}\left(t\right)}{I_{_{HE}}\left(t-1\right)}=\beta\frac{c\left(t\right)}{c\left(t-1\right)} $$