3.2.2. Technology Progress

(1) Progress and Diffusion of Traditional Technology

There are four stylized facts of the technological progress in China's fuel ethanol industry. First, traditional production technology is relatively mature, so technological progress is mostly reflected in the continuous improvement of the original technology. However, there are a few major technological innovations. In other words, with an increase in the degree of technological progress, the occurrence probability of technological progress rapidly decreases. Second, R&D investment will improve the probability of technological progress. Third, the higher the original level of technology, the lower the probability of major innovation. Finally, due to technology diffusion, the technological progress of a specific firm is positively correlated with the most advanced technology level in the industry.

In this study, it is assumed that there is the highest level of technical efficiency boundary, denoted as *e*0. Let Δ*ei*,*<sup>t</sup>* be the change of the firm's technical level; then, the technology change will not exceed the difference between the firm's technical level and the highest level (*<sup>e</sup>*0 − *ei*,*<sup>t</sup>*). Therefore, the firm's technology change is

$$
\Delta \varepsilon\_{\rm i,t+1} = \Theta\_{\rm i,t+1} \cdot (\varepsilon \eta - \varepsilon\_{\rm i,t}) \tag{3}
$$

where θ*i*,*t*+<sup>1</sup> is the random variable of the interval [0,1], in order to reflect the first stylized fact of technological progress, that is, the larger the degree of technological progress, the smaller the occurrence probability.

We construct variables *k* = 100 · θ*i*,*t*+<sup>1</sup> and assume Poisson distribution with parameters *k* and λ. Then, there is

$$
\lambda = \lambda\_0 \cdot R\_{i,t}^{\lambda\_1} \cdot (e\_0 - e\_{i,t})^{\lambda\_2} \cdot (\max\_i \{ e\_{i,t} \} / e\_{i,t})^{\lambda\_3} \tag{4}
$$

where λ is the mean value of the random variable *k*. The larger the value, the higher the probability that the technical efficiency will be greatly improved. The technology R&D investment, *Ri*,*t*, is positively correlated with λ, which reflects the second stylized fact of the above mentioned technological progress. The gap between the firm's technical level and the highest technical level, *e*0 − *ei*,*t*, is positively related to λ, which reflects the third stylized fact. max*i* {*ei*,*<sup>t</sup>*}/*ei*,*<sup>t</sup>* reflects the gap between the technological level of the firm and the highest technological level in the industry. This value is positively correlated with λ, which reflects the fourth stylized fact of technological progress—the diffusion of advanced technologies in the industry. λ0,λ1,λ2, and λ3 are nonnegative constants.

Finally, when the technical level of the firm reaches its highest boundary value, the firm will stop its R&D investment.

(2) Entry, Progress, and Exit of New Technology

Due to the insufficient supply of feedstock, another stylized fact of China's fuel ethanol firms is that firms need to constantly explore new feedstock and corresponding production technologies. Due to the diversity of fuel ethanol feedstock, the corresponding production technology also shows diverse characteristics. The adoption, progress, diffusion, and withdrawal of different production technologies lead to the change of technological diversity in the industrial technology system, thus promoting the evolution of the technology system.

*The entry rules of new technology:* This research focuses on the evolution of production technology, which is closely related to industry evolution. Therefore, we use the innovative activities of an R&D firm to describe the evolution of new technology. An R&D firm is a corporation whose output is new technology while the R&D expenditure is its input. We assume that when the industry profit of using traditional technology is negative, new R&D firms start to enter the industry, and the number of entries is random. Among them, the number of R&D firms created by the incumbent firm γ1 and the number of completely new R&D firms γ2 is both randomly selected from 0,1......, *nt*. Upon entry, all newly created R&D firms are faced with the same initial technical efficiency level, and if an R&D firm already exists in the technology system, the newly created R&D firms will search for the maximum technical

efficiency in the existing R&D firms as its initial technical e fficiency. The change in the technical efficiency of R&D firms is expressed as follows:

$$
\Delta e\_{i,t+1} = \varepsilon\_{i,t} \cdot R\_{i,t} \tag{5}
$$

In this model, the entry of R&D firms is used to reflect the evolution characteristics of new technologies in the industry. There are two forms of entry for R&D firms: one type of firm is newly created by incumbent firms, and the other is a random start-up. The R&D output of these two kinds of R&D firms is mainly determined by the e fficiency of technical output and the amount of R&D input. If the newly established R&D firms have the same total amount of R&D capital, *B*, and take a fixed proportion of the R&D capital as the R&D investment in each period, the di fferences between the two kinds of newly established R&D firms include two elements. First, since newly established R&D firms are usually more flexible than incumbent firms, and the flexibility of the system is more conducive to the formation of new technologies, newly established firms will have higher R&D productivity than incumbent firms, which is mainly reflected in the di fference between the two types of firms in terms of value ς*i*,*<sup>t</sup>* [43]. Second, as mentioned above, new technology may replace old technology, which will lead to a sunk cost loss for the incumbent firm. Therefore, the incumbent firm will reduce the proportion of R&D investment, which is negatively correlated with the residual fixed assets of the original firm. Its R&D investment is

$$R\_{i,t} = t \cdot d \cdot \delta \cdot B \tag{6}$$

and the newly established firms take a fixed amount as the R&D investment:

$$R\_{i,t} = \delta \cdot B \tag{7}$$

where δ is a constant. Equations (6) and (7) mean that before the depreciation of fixed assets is completed, the R&D input of the incumbent firm will be less than the R&D input of the new firm.

*New technology adoption rules:* Firms will only adopt new technology when the average cost of production using that new technology is lower than the average level of traditional technology. This means that, before a firm is able to enter the market, it must go through a long R&D period. During this period, it is di fficult for the firm to generate profits and maintain survival. Therefore, in the start-up stage of the new R&D firm, that firm must rely on external capital which is reflected as the initial capital stock of the new R&D firm in this model.

*Rules for R&D firms to withdraw from R&D activities:* When the initial capital stock is all used for R&D expenditures, and the production costs of new technology still do not reach the average levels of those of traditional technology, the R&D firms will choose to withdraw, which means the withdrawal of new technology.
