4.1.1. Baseline Scenario

The aim of the history replicating runs is to find a set of parameters values, based on which the simulation results can reflect the historical stylized facts of the fuel ethanol industry in China [56]. This kind of replicated history is also called the baseline scenario which could be used as a starting point for further policy assessment [57]. Therefore, it is important to select the historical stylized facts that the simulation results intend to capture. Given that the ultimate purpose of our paper is to understand how the fuel ethanol industry has grown, we mainly focused on the following stylized facts about the number of firms and the output of the fuel ethanol industry in China, which are derived from a detailed analysis of the industrial history and from the existing appreciative literature on the fuel ethanol industry in China [58,59].


In order to find the set of parameters values which can 'reproduce' the above-mentioned stylized facts, the following steps used in most of the relevant literature were employed in this paper [46,51,60,61]. Firstly, we set the initial values of the variables in the system based on the historical data of the fuel ethanol industry in China. These initial values are shown in Table A1 in Appendix A. Then, we divided the parameters into two groups when setting the values of the parameters. The first group includes the parameters (e.g., the rate of depreciation) which can be set based on the industry history. In these cases, it is possible to fix the parameter to one value. The second group includes other parameters (e.g., the degree of firm rationality) which could not be set to a fixed value for the lack of enough data to estimate its exact value. Thirdly, for the second group of parameters, we did not attempt detailed quantitative matching to historical data, reflecting our ignorance about their 'true' values. Alternatively, we chose values randomly in the predetermined ranges of the parameters and then adjusted the values until the simulation results could qualitatively capture the stylized facts. To adjust the values of the parameters more e fficiently, we assessed each parameter's impact on the simulation results, respectively, through keeping all parameters but one constant and then gave preference to adjusting the parameters which had greater impacts. Once the simulation results about the output and the number of firms could qualitatively reflect all the above eight stylized facts, we stopped the adjustment and chose this set of values as the parameters' values under the baseline scenario. Although 'qualitatively reflect' means that there may be many sets of parameters values satisfying the above condition, we did not need to judge which was the best one to reflect these stylized facts because the aim of the history-friendly model was to explore the causal relationships rather than the magnitude of the e ffects between variables. The final values of parameters are shown in Table A2 in the Appendix A. An additional constraint orienting the choice of parameter values was provided by the time structure of the model, because the definition of what 'one period' means in real-time (half a year in this model) is crucial for establishing which actions take place at any one period. The simulation is implemented using Mathematica software package. The results under the baseline scenario are shown in Figures 1–4.

Figure 1 shows the change in the number of firms in the fuel ethanol industry under the baseline scenario, which can be divided into four stages. There were only traditional technology firms in the first stage, and the number of firms kept increasing. The second stage starts after the 17th period, during which the number of traditional technology firms was no longer increasing. At the same time, R&D firms with new technology appeared, and their numbers increased gradually. However, after the 22nd period, the number of R&D firms began to decline. On the one hand, some R&D firms transformed into production firms and began to produce fuel ethanol. On the other hand, some R&D firms failed to survive because they did not meet the expected innovation goals. The third stage starts in the 26th period. New technology firms began to produce at this stage, and their number increased gradually due to the establishment of the new technology firms and the transformation of R&D firms

to new technology firms. According to the simulation results, all production firms transformed from R&D firms are originated from the newly established R&D firms, while the R&D firms created by traditional technology firms failed to transform into production firms, which is consistent with the evolutionary history of the fuel ethanol industry in China. The fourth stage starts from the 31st period. Due to the limitation of market capacity, the number of new technology firms is no longer increasing, and the number of firms in the market remains stable.

**Figure 1.** Change in the number of firms.

**Figure 2.** Change in the output of the fuel ethanol industry.

**Figure 3.** Change of a firm's average technical efficiency.

**Figure 4.** Transformation of the firm's production technology.

Figure 2 shows the change in the output of the fuel ethanol industry under the baseline scenario, which is divided into four stages. In the first stage, the total output of the industry increased continuously. The total output curve coincides with the output of traditional technology firms since there are only traditional technology firms in the industry. The second stage starts from the 17th period when the number of traditional technology firms was not increasing. Although the total output was still increasing, the growth rate of the total output decreased significantly. The increase in output mainly comes from the increase in the output of incumbent firms. The 25th period indicates the third stage: with the entry of new technology firms, the total output began to increase rapidly until the 31st phase. Due to the limitation of market capacity in this period, the number of new technology firms did not increase. The output growth of new technology firms significantly dropped again and then entered the fourth stage. The total output growth is relatively low since there is no entry of new firms. The increase of output in this stage mainly depends on the expansion of the production scale of existing firms.

Figure 3 shows the change of the average technical efficiency of traditional technology firms, R&D firms, and new technology firms under the baseline scenario. The average technical efficiency of all three kinds of firms is increasing. However, the extent of this increase varies from firm to firm. The average technical efficiency of traditional technology firms changes relatively slowly, while the average technical efficiency of R&D firms improves relatively quickly. The average technical efficiency of new technology firms improves rapidly in the initial stage of production but tends to be flat in later stages. The main reason for the above difference is that the technological progress of R&D firms is significantly faster than that of existing production firms. The average technical efficiency of all R&D firms improves relatively quickly because the technical progress among R&D firms is cumulative, and new R&D firms will absorb the experience of existing R&D firms. In the initial stages of production, new technology firms usually adopt the most advanced technology, which significantly improves the average technical efficiency of the whole industry. When the entry of new technology firms stagnates, the improvement of average technical efficiency only depends on the technological progress of incumbent firms. As a result, the rate of technological progress becomes relatively slow.

Figure 4 describes the technology transformation in the fuel ethanol industry under a baseline scenario. Technology transformation refers to the transformation of the industry from traditional production techniques to new production technology. The proportion of the output of new technology firms to the total output of the industry is used to measure technology transformation. According to Figure 4, the value of the technology transformation has rapidly increased since the 25th period and reached about 32% in the 31st period. However, the growth rate of technology transformation has declined rapidly because new technology firms have closed entry to the industry. This means that technology transformation mainly depends on the continuous entry of new technology firms. When there is no continuous entry of new technology firms, the competitive advantage of traditional technology firms in incumbent firms is comparable to that of new technology firms, so, the market share of traditional technology firms will not significantly decrease.
