3. Model Specification

2022-09-08 -

3.1 Basic Model Framework

Based on the framework of technology gap convergence, this paper creates an endogenous technology progress model for late-moving large countries to simulate how market size influences the shift of technology progress path and technology catch-up under various innovation strategies. It is assumed that the preferences of the representative household in a late-moving economy satisfy the CRRA utility function for a continuous period of time.

Where, ρ is the discount rate, θ is the risk aversion coefficient, and C(t) is total consumption at t. To maximize utility, the representative household’s consumption decision satisfies Euler equation: / C=(r− ρ)/θ.

The late-moving country is a closed economy, which employs labor in its production process. Let total labor input be a constant L, and labor supply is inelastic. Thus, the economy is faced with the following resource constraint at time point :

Where, Z(t) is the economy’s total R&D spending at time, and Y(t) is total output.

The late-moving country’s final product Y(t) is manufactured with a continuous intermediate product yi(t). The intermediate product category is standardized as 1, and the form of production function is specified as the C-D production function:

Final product Y(t) is specified as the value standard, and pi(t) is the price of intermediate product yi(t). In a final product market of perfect competition, the demand function for the intermediate product may be obtained according to equation (1):

Technology of intermediate product yi(t) manufacturer i is specified as follows:

Where, qi(t) is the most advanced technology on the production line of the product, i.e. the highest level of productivity, and 1i( t) is the labor input employed by the enterprise i, which pays a wage compensation of w(t). Aggregate labor input of the late-moving economy satisfies 1nL=∫1n1i( t)di.

Based on equation (2), the marginal cost of the intermediate product is:

Technology progress is manifested in the improvement of the most advanced technology qi(t) for the intermediate product, whose manufacturers are engaged in the R&D of new technologies. Once an R&D program succeeds, the most advanced technology qi(t) for the intermediate product will increase to (1+ λ)

qi(t) . On this production line, an enterprise with the latest technology qi(t) competes with the incumbent enterprise qi(t) /(1+ λ) with originally the most advanced technology. Under the Bertrand competition, the enterprise with the latest technology will set the price of the intermediate product according to the marginal cost of the incumbent enterprise:

If the actual price is higher than the above price, the incumbent enterprise remains profitable, and the intermediate product market will be occupied by the incumbent enterprise; if the actual price is below the above price, although the incumbent enterprise still finds it hard to profit, there is still room for the enterprise with the latest technology to increase its profitability.

Based on equations (2)-(4), the profit function of the intermediate product manufacturer can be obtained as follows:

While market size is determined by such factors as household income and population, total output (income) Y( t) denotes the total purchasing power of households in the country and may represent the market size of a country (Alesina et al., 2000; Acemoglu and Linn, 2004; Aghion and Howitt, 2008). As can be learned from the above equation, market size has a positive effect on the profitability of intermediate input manufacturers, i.e. larger market size means greater profit from innovation and more incentives for enterprises to innovate. This virtuous cycle also reflects the scale advantage of innovation.

Of course, R&D and innovation are risky. If an enterprise succeeds in its R&D program, it will acquire a more advanced patent technology and employ the new technology for the manufacturing of intermediate product to earn more profits; if it fails in its R&D program, it will not be able to upgrade technology, leaving the manufacturing of the intermediate product to any incumbent enterprise (Aghion and Howitt, 2008).

It is assumed that the manufacturer of the intermediate product may improve technology for the intermediate product in category i through innovation and imitation. It is specified that after the manufacturer succeeds in innovation and imitation at time point t, it may upgrade the level of technology in phase t+ 1 to the following, respectively:

Where, λD and λF are the levels of technology improvement for innovation and imitation, and

a(t)=A(t)/ A(t) is the relative level of technology or technology gaps of a late-moving country, i.e. the ratio between the late-moving country A(t)’ s level of technology and the level of global frontier technology A(t). Higher value of a(t) means that the country is closer to the global technology frontier and has smaller technology gaps with developed countries (Acemoglu et al., 2006). Obviously, the level of technology improvement achieved by late-moving large countries with imitation λF / a(t) is subject to technology gaps since greater technology gaps suggest a broader space for late-moving countries to import foreign technology and benefit from the spillover effects (Keller and Yeaple, 2009). As latemoving countries approach the global technology frontier, there are fewer technologies to imitate, and remaining advanced technologies are highly sophisticated with diminishing spillover effects. At this moment, technology importation and imitation play a limited role in their technological advancement. Meanwhile, the progress rate of global frontier technology is g, i.e. A(t)= A( 0) ·egt.

Given the high-risk characteristic of firm innovation, we introduce the innovation success rate to measure R&D risk, i.e. higher success rate means a smaller R&D risk, and vice versa. The success rates of innovation and imitation are specified as the increasing functions of their respective R&D input:

Where, ζD and ζF respectively denote the cost parameters of innovation and imitation. Since innovation is costlier than imitation, we specify ζF ≤ ζD ≤ Y. A reasonable hypothesis is that the marginal effect of R&D input on the success rate of innovation decreases with the increase of R&D input, i.e. R&D cost increases with R&D spending. When R&D inputs zDi( t) and zFi( t) remain constant, the success rate of innovation is also subject to the goal of R&D, i.e. the degrees of improvement in new technology λD and λF / a(t) after successful innovation. Greater improvement in new technology suggests a smaller possibility for such technological breakthrough to be achieved through R&D innovation. Function φ reflects the increase of R&D cost with the increasing degrees of technology improvement λD and λF / a(t), as well as the increasing R&D inputs zDi( t) and zFi( t).

In order for the model to have an explicit solution without losing generality, we assume the function form of φ to be:

R&D inputs for innovation and imitation ZD( t) and ZF( t) at time point t, together with aggregate R&D input Z( t), are:

3.2 Technology Progress Path under the Constraint of Innovation Strategy

In this section, we further analyze the technology progress path for late-moving countries under the constraint of different innovation strategies. As for the manifestations of various innovation strategies, Acemoglu et al. (2006) believed that heterogeneous innovation strategies were reflected in the differences of productivity under various decisions. In contrast, Huang and Song (2017) defined technology progress based on technology gaps and technology spillover effects as catch-up oriented and technology progress driven by competitive innovation as competition-oriented.

Hence, this paper defines different innovation strategies by the respective goals of the two patterns of innovation, i.e. the relative degrees of technology improvement λD and λF / a(t): When λD> λF / a(t), the results of innovation may cover and substitute those of imitation, allowing the late-moving large country to pursue innovation in lieu of imitation. When λD ≤ λF / a( t), however, innovation and imitation are complementary with each other, prompting the late-moving large country to combine innovation with imitation.

Classification of the two innovation strategies responds to the controversy over the complementarity and substitution between innovation and imitation at the theoretical level (Zhang, 2020). Moreover, it also reflects the evolving trajectory of China’s innovation-driven development strategy in various stages. While China vowed to develop into an “innovative country” in 2006, for instance, it also encouraged enterprises to import advanced technology, which is in effect a strategy of combining innovation with imitation (“Imitation Plus Innovation Strategy” for short); the 18th CPC National Congress called for pursuing innovation with Chinese characteristics and implementing an innovation-driven development strategy, which is consistent with the strategy of replacing imitation with innovation (“Innovation Instead of Imitation Strategy” for short).

Under different innovation strategies, the degrees to which the two types of innovation contribute to technology improvement remain constant, and the technology progress rate of the economy is correlated with the success rate of technology innovation. As such, the R&D inputs ZD( t) and ZF( t) for innovation and imitation should be determined at first. Manufacturer i of the intermediate product will determine the R&D inputs zDi( t) and zFi( t) for innovation and imitation according to the following expected profit Eπi(t +1):

Where, EπDi(t +1) and EπFi(t +1) are the expected profits from successful innovation and imitation, respectively, and the enterprise forecasts its profit in the next phase according to market performance in the current phase. From equation (5), we have: EπFi(t+ 1)=( λF / a(t)) Y(t)/( 1+ λF / a(t)) and EπDi(t+ 1)= λDY(t)/ (1+ λD). As can be learned from the above equations, expected profit from technology innovation by the manufacturer of the intermediate input is jointly influenced by market size, the degrees of technology improvement from innovation and imitation, and their respective success rates of innovation.

As can be learned from equations (7) and (10), enterprises commit a limited amount of R&D input under the high-risk and high-cost constraints of new technology development. When an economy boasts a large market, however, R&D risk in the innovation success rate is offset by the market size implicit in the profit function, i.e. the high R&D input of innovation is spread by a large market. The absorption and

scattering of firm innovation risk by market heft reflect the scale advantage of market heft for R&D.

(1) When a late-moving large country pursues the Innovation Instead of Imitation Strategy (the strategy of replacing imitation with innovation), i.e. λD> λF / a(t), if its enterprise succeeds in innovation but fails in imitation, the level of new technology in phase t +1 will increase to (1+ λD) ·qi( t ), and there is a probability of pDi(t) ·(1− pFi(t)) for the enterprise to earn an expected profit EπDi(t +1); if the enterprise fails in its innovation, but manages to improve the level of its new technology to (1+ λF / a(t)) ·qi( t ) by means of imitation, there is a probability of pFi(t) ·(1− pDi(t)) for the enterprise to earn an expected profit

of EπFi ( t +1); if the enterprise successfully achieves technological breakthroughs in both innovation and imitation at the same time, since innovation contributes more to technology improvement than does imitation, the results of innovation will cover and substitute those of imitation, the level of new technology will still increase to (1+ λD) ·qi( t ), and there is a probability of pDi(t) ·pFi( t) for the enterprise to earn an expected profit of EπDi ( t +1); however, if the enterprise fails to achieve any technological breakthrough in neither innovation nor imitation, there is a probability of (1− pFi(t)) ·(1− pDi(t)) for the enterprise to end up with zero profit.

According to the first-order condition of equation (10), the enterprise’s R&D inputs for innovation and imitation can be determined in relation to equations (5)-(7):

Obviously, the expansion of market size Y( t) helps raise profit for the manufacturer of the intermediate product, and R&D inputs will increase for both innovation and imitation under the profit incentive. Since R&D input is subject to the level of technology improvement λD, the enterprise will increase its the level of R& D input for innovation and imitation when the level of its technology improvement increases. The distribution of R&D resources for innovation and imitation within the enterprise is subject to innovation cost coefficients ζD and ζF, and the two types of R&D input will increase with cost.

As can be learned from equations (9) and (11), the society-wide aggregate R&D input is as follows:

As can be learned from the above equation, corporate R&D input can be spread over a large market Y(t), so that market expansion helps increase overall R&D input, which reflects the scale advantage of late-moving countries for innovation. Furthermore, there is a preference for R&D investment to be made in new technical field with great growth potentials, and the enterprise will focus on major technological breakthroughs that can be achieved with innovation, i.e. the level of technology improvement λD, and thus determine the amount of R&D input. A higher level of technology improvement will encourage the enterprise to invest more in R&D.

In relation to equations (7), (8) and (11), the success rates of innovation and imitation can be calculated as follows:

Success rates of both types of innovation are subject to the innovation cost parameter, the level of technology improvement, market size, among other factors. By heightening innovation risk, an increase in the innovation cost parameter will make the enterprise more scrupulous and cut back on R&D spending, dimming the prospect of successful innovation. A large domestic market, however, will reinforce the motivation of enterprises to innovate, invest more in R&D, spread the exorbitant innovation cost, and thus reduce the risk of R&D innovation and increase the success rates of innovation and imitation by giving play to the economies of scale advantage. Moreover, the success rate of imitation is

also correlated with the degree of technology improvement and the relative level of technology. A higher success rate of imitation is associated with a smaller technology improvement achieved with imitation and a higher relative level of technology of the late-moving country.

In relation to equation (13), the enterprise may raise the level of production technology for the intermediate product i at time point t +1 by means of innovation and imitation:

Based on equation ( 1), the aggregate level of technology is defined as the aggregation of the highest levels of production technologies possessed by all enterprises, i.e. 1nA( t)=∫

0 11nqi( t)di. On such a basis, we may obtain the technology progress rate of the late-moving large country at time point t by aggregating all enterprises after taking logarithm of equation (14):

As can be learned from equation (15), the late-moving large country achieves technology progress by means of innovation and imitation. First, the technology progress rate g(t) is subject to the level of technology improvement and the country’s relative level of technology. The more the country achieves technology improvement λD and λF by means of innovation and imitation, the faster it will make technology progress.

For the late-moving country and the early-moving country, their relative levels of technology in the previous phase have both positive and negative inter-temporal effects on technology progress in the current phase: On one hand, the relative level of technology in the previous phase a(t− 1) has a negative effect on technology progress rate in the current phase g(t) as technology spillover effects diminish with narrowing technology gaps, and technology improvement that can be achieved through imitation also starts to decrease, causing technology progress to slow. On the other, the relative level of technology a(t− 1) has a positive effect on the technology progress rate. As technology gaps narrow, barriers to technology assimilation start to wane, making imitation more likely to succeed. As such, how the relative level of technology influences technology progress rate is subject to the relative magnitude of those two effects: As can be learned from the above equation, as the late- moving large country approaches the global technology frontier, the positive effect of increasing success rate of imitation is insufficient as to offset the negative effect of decreasing technology improvement, and the technology progress rate will decrease with the increasing relative level of technology.

On such a basis, the relative contributions of innovation and imitation to technology progress rate g(t) is examined in relation to equation (15). Thus, the evolving trajectory of technology progress path is examined from the perspective of innovation output: If ∂( gD(t)/gF(t))> 0, innovation will lead to a faster pace of technology progress compared with imitation, so that a shift of technology progress path towards innovation is consistent with the expected strategic goal; if ∂( gD(t)/gF(t))< 0, imitation will lead to a faster pace of technology progress compared with innovation, which means that the technology progress path is skewed towards imitation, and the Innovation Instead of Imitation Strategy has failed to achieve the expected effect.

As can be learned from equations (16), ∂( gD(t)/gF(t))/∂a(t− 1)> 0, i.e. the growth rate of imitation gF( t) slows amid narrowing technology gaps, and innovation plays a more prominent role. Then, technology progress naturally leans towards innovation.

Lastly, in observing the degrees to which technology improvement λD and λF can be achieved by means of innovation and imitation may influence technology progress path, we find that ∂( gD(t)/ gF(t))/∂λD> 0, and ∂( gD(t)/gF(t))/∂λF < 0, i.e. λD has a positive effect on the growth rate of innovation gD(t),

shifting the technology progress path towards innovation; λF has a positive effect on imitation gF(t), causing the technology progress path to be more dependent on imitation.

(2) If the late-moving large country pursues an Imitation Plus Innovation Strategy (strategy of combining innovation with imitation), we have λD ≤ λF / a(t). The success rates of innovation and imitation are derived according to the first-order condition of equation (10), with which the technology progress rate and path of the late-moving large country can be obtained:

As can be learned from equations (17)-(18), first, when the late-moving country approaches to the global technology frontier, i.e. technology gaps narrow and the technology progress rate g(t) and the innovation and imitation rates gD(t) and gF(t) will decrease. Since imitation slows more substantially than innovation, technology progress will shift towards innovation.

Second, the greater degrees of technology improvement λD and λF achieved by means of innovation and imitation, the faster the pace of technology progress.

Third, the degree of technology improvement λD achieved by means of innovation is positively correlated with the innovation rate gD(t), causing technology progress to move towards innovation; the degree of technology improvement λF achieved by means of imitation has positive effects on both innovation and imitation, but the effect on imitation is stronger, causing technology progress to move towards imitation. Obviously, there is a non-uniformity in their effects on the growth rates of innovation gD(t) and imitation gF(t).

3.3 Market Size, Innovation Strategy and Technology Progress Path

Massive and expanding domestic market is a prominent strength of late-moving large countries. In this section, we will further reveal the heterogeneous effects of market size on innovation and imitation under different innovation strategies, as well as effects on the transition of technology progress path and technology catch-up:

(1) When the late-moving country pursues the Innovation Instead of Imitation Strategy, i.e. λD >λF ⁄a(t), based on equation (15), the effects of market size on the growth rates of innovation and imitation are shown as follows:

On one hand, ∂gD(t)/∂Y(t− 1)> 0, indicating that growth in market size helps increase the growth rate of innovation gD(t). The reason is that a large market may spread R&D cost and scatter the risk of innovation. On the other hand, the effect of market size on imitation is subject to the threshold effect. Although market size may increase the success rates of innovation and imitation at the same time, innovation has a substitutive effect on imitation, and whether technology improvement can be achieved by means of imitation is subject to the results of innovation. As such, the effect of market size on the growth rate of imitation is subject to the magnitude of its effect on the success rates of innovation and

imitation.

Let Y1 = 2ζD be the threshold, when the large country’s market size is smaller than the threshold, i.e. Y(t− 1)≤ Y1, ∂gF(t)/∂Y(t− 1)> 0, and an increase in market size will speed up imitation, i.e. market size contributes to the success rate of imitation more than it defuses the risk of innovation; when market size crosses the threshold Y(t− 1)> Y1, ∂gF(t)/∂Y(t− 1)< 0, and market expansion will inhibit the growth of imitation, i.e. market size has a greater effect of defusing the risk of innovation.

The effect of market size on technology progress pathway is also subject to the threshold effect.

( )

Let Y2 = ζD(ζD− ζF) + ζD be the threshold, and when Y(t− 1)≤ Y2, and we have ∂(gD(t)/ gF(t))/∂Y(t− 1)< 0, i.e. market size will speed up imitation, shifting technology progress towards imitation. In this case, the limited market size may not scatter the huge risk of innovation and spread the cost of independent R&D. When Y(t− 1)> Y2, the market size is large enough to spread the cost of innovation and defuse the risk of independent R&D, ∂(gD(t)/ gF(t))/∂Y(t− 1) > 0. In this case, market expansion will speed up innovation, shifting technology progress towards innovation.

On the whole, when market size Y(t− 1)≤ Y2, market expansion is conducive to the growth rates of both innovation and imitation, and the growth of imitation is faster and causes technology progress to be more dependent on imitation, deviating from the strategic goal of replacing imitation with innovation; when market size Y2< Y(t− 1) ≤ Y1, market expansion has positive effects on the growth rates of both innovation and imitation, but the growth of innovation is faster, causing the technology progress to shift towards innovation; when market size Y(t− 1)> Y1, further market expansion will restrain the growth of imitation, prompting innovation to speed up and replace imitation, hence accelerating the transition of the technology progress path towards innovation.

Then, we proceed to analyze the effects of market size on the technology catch-up of late-moving countries under the Innovation Instead of Imitation Strategy. The evolving path of the economy’s technology gap a(t) satisfies: a(t)/a(t)= g(t)− g. In relation to equation (15), it can be learned that if g(t)> g, technology progress in the late-moving large country will outpace the progress of the global frontier technology, raising the country’s relative level of technology, but its technology progress rate will decrease, i.e. g(t)< 0; if g(t)< g, technology progress in the late-moving large country is below the global technology frontier, and when the country’s relative level of technology declines, the technology progress rate will increase, i.e. g(t)> 0, and its technology progress rate will gradually converge to the global frontier technology progress rate g. When g(t)=g, the late-moving country maintains the same growth rate as the global frontier technology, and its relative level of technology converges at a*: Where, Γ( g)=( exp( g)− 1)(1+ λD 1)−( 1+ λD ). As can be learned from equations (19), the late-moving

− large country’s technology gap a* along the equilibrium growth path is directly subject to market size, the degrees of technology improvement by means of innovation and imitation, as well as innovation cost. The effect of the late-moving large country’s market size on the equilibrium technology gap is

( ), also subject to the threshold effect2: The threshold is defined as Y4 = ζD+ ζD(ζD+ζF( 1+ λD)Γ( g)− 1) when market size has yet to reach the threshold, i.e. Y(t− 1) ≤ Y4, ∂ a*/∂Y(t− 1)< 0, and the domestic market size will restrain the improvement of the equilibrium technology level. On one hand, if the market size is limited, it is difficult to spread the cost of innovation and scatter the risk of independent R&D, and the enterprise will hesitate to spend on R&D. On the other hand, imitation has a limited effect on technology improvement, and whether technology improvement can be achieved still depends on the success of innovation. Market expansion cannot effectively give play to the advantage of economies of

scale for R&D. When the market size of the late-moving large country crosses the threshold of scale, i.e. Y(t− 1) >Y4, we have ∂ a*/∂Y(t− 1) > 0, and the late-moving large country will develop a unique large market advantage, which is conducive to narrowing the technology gap.

(2) Under the Imitation Plus Innovation Strategy, i.e. λD ≤ λF / a(t), the market size of the late-moving large country also has an asymmetric effect on innovation and imitation, thus influencing the technology progress path. In relation to equations (17)-(18), the effects of market size on innovation and imitation are expressed in the following equations: First, ∂gF(t)/∂Y(t− 1)> 0, indicating that market expansion is always conducive to raising the growth rate of imitation gF(t). Second, the effect of market size on the growth rate of innovation gD(t) is subject to the threshold effect. Under the Imitation Plus Innovation Strategy, although market heft makes it more likely for both innovation and imitation to succeed, innovation will complement imitation and will contribute to technological advancement only when imitation fails. While market expansion makes it more likely for innovation to pull off, it may also reduce the risk of imitation. The net effect of market expansion on innovation is subject to its relative effects on innovation and imitation.

Let Y3 = 2ζF denote the threshold, and when the market size of the late- moving large country Y(t− 1) ≤ Y3, ∂gD(t) /∂ Y(t− 1) > 0, and the positive effect of domestic market expansion on the success rate of innovation exceeds its risk scattering effect for imitation, which helps accelerate innovation; when the market size of the late- moving large country Y( t− 1) > Y3, ∂ gD( t) /∂ Y( t− 1) < 0, and further market expansion plays a stronger role in mitigating the risk of imitation, thus inhibiting the growth of innovation.

On such a basis, we will analyze the effect of market size on the technology progress pathway, ∂( gD( t) / gF( t) )/∂ Y(t− 1)< 0, i.e. market expansion will cause technology progress to deepen its path dependence on imitation. 3

On the whole, when market size Y(t− 1) ≤ Y3, market expansion has positive effects on the growth rates of both innovation and imitation, but imitation grows at a faster pace, causing the technology progress path to shift towards imitation; when market size Y(t− 1)> Y3, further market expansion will inhibit the growth of innovation and speed up imitation, causing technology progress to deepen its path dependence on imitation and thus deviate from the original intention for the strategy for innovation and imitation to develop in lockstep.

Then, we proceed to analyze the effect of the late-moving country’s market size on its technology catch-up under the Imitation Plus Innovation Strategy. If denotes the equilibrium technology gap of the late-moving country under such an innovation strategy, the equilibrium technology gap of the late-moving country ∂ /∂ Y(t− 1) < 0 suggests that when the late-moving large country implements an Imitation Plus Innovation Strategy, market expansion will trap the country into a low-level equilibrium trap. 4

Proposition 1: Under different innovation strategies, market size has heterogeneous effects on the shift of the late-moving large country’s technology progress path: Before market size reaches the threshold Y(t− 1) ≤ Y2, whichever innovation strategy is implemented, market expansion will deepen the reliance of technology progress path on imitation; after market size crosses the threshold Y(t− 1) >Y2, if the Imitation Plus Innovation Strategy is followed, technology progress will become more dependent ( ). 3 Let ∂(gD(t)/ gF(t))/∂Y(t− 1)= 0, and we may have a quadratic equation with one unknown with respect to Y(t), whose root is Y = ζF ± ζF (− ζF ζD) When ζF < ζD, the equation has no real root, and ∂(gD(t)/ gF(t))/∂Y(t− 1)< 0.

4 Let ∂ /∂ Y= 0, and we may solve the equation root as Y =2ζF (1+ λD)/( λD−λF). Under the Indigenous Plus Imitation Strategy λD ≤ λF / a(t), the equation root is negative, i.e. ∂ /∂ Y(t− 1) < 0.

on imitation, thus deviating from the strategic goal; if the Innovation Instead of Imitation Strategy is followed, market expansion may cause the technology progress pathway to shift towards innovation. Following the technology progress pathway as the standard, the large country should promptly adjust its innovation strategy when its market size crosses the threshold Y2.

Proposition 2: Under different innovation strategies, market size has heterogeneous effects on the technology catch-up of late-moving countries: Before market size crosses the threshold Y(t− 1) ≤ Y4,

whichever innovation strategy is adopted, market expansion will restrain the narrowing of the equilibrium technology gap; when market size crosses the threshold Y(t− 1) >Y4, if the Imitation Plus Innovation Strategy is adopted, market expansion will restrain the improvement of the country’s equilibrium level of technology; if the Innovation Instead of Imitation Strategy is followed, market expansion will be conducive to the country’s convergence to the global technology frontier. With technology catch-up as the standard, the threshold of market size for adjusting the innovation strategy is Y4.

Propositions 1 and 2 reveal how a late-moving large country should identify its changing market size and promptly adjust its innovation strategy to shift its technology progress path and advance technological catch-up. The problem is that when the shift of technology progress path and technology catch-up are set as the goals, there is a non-uniformity in the threshold of market size for adjusting the innovation-driven development strategy. Table 1 lists the heterogeneous effects of market expansion on the shift of technology progress path and technology catch-up when a late-moving large country implements different innovation-driven development strategies at different levels of market size. Based on those effects, the country may enact an innovation strategy compatible with its market size: (1) When the market size of the late-moving large country increases from large to super-large but has yet to become a super-large market, whichever strategy is followed, market size has negative effects on both the shift of technology progress pathway and technological catch-up. In this case, the Imitation Plus Innovation Strategy helps achieve a higher technology progress rate, and the economy’s technological advancement is primarily dependent on its late-mover advantage and competitive advantage. (2) When the late-moving large country has yet to develop into a super-strong economy, whichever strategy is adopted, market size has a negative effect on the shift of its technology progress path, but under the Innovation Instead of Imitation Strategy, market size helps the economy converge to the global technology frontier. Under the Imitation Plus Innovation Strategy, however, market expansion will restrain the improvement of the equilibrium level of technology. At this moment, although the large country still relies on its late-mover advantage for technology progress, it should shift to the Innovation Instead of Imitation Strategy to avoid the trap of low-level equilibrium. (3) After the late-moving large country completes its transition from a super-large to a super-strong economy, under the Innovation Instead of Imitation Strategy, market expansion will not only increase the equilibrium level of technology, but shift the technology progress path towards innovation.

On the whole, the effects of market expansion on the shift of technology progress path and technology catch- up are subject to dual thresholds, which correspond to market size Y2 and Y4.

The threshold of market size for the shift of technology progress path lags behind the threshold for technology gap convergence, i.e. Y2 > Y4. The underlying reason is that a large market may scatter the risks of both types of technological innovation. When the market is large enough, it mitigates the risk of innovation more than it does the risk of imitation, prompting technology progress path to shift towards innovation.

The mathematical model provides theoretical basis for formulating an innovation strategy compatible with changing market size and conducive to the shift of technology progress path and technology catch-up for late-moving large countries. However, the stylized facts and policy practices of the shift of China’s technology progress path are far more complicated than mathematical simulations.

The question is whether those stylized facts and policy practices are consistent with the evolving pattern of market size and logically coherent at the theoretical level? In retrospect, China vowed to enhance innovation in 2006 under the strategy of building an innovative country while encouraging enterprises to import advanced foreign technology. The 18th CPC National Congress has reaffirmed the commitment to embarking on a path of innovation with Chinese characteristics and implementing an innovation-driven development strategy. The 19th CPC National Congress further identified innovation as the primary force of economic development and a strategic pillar of building a modern economic system. Adjustment of the innovation strategy also reflects a structural change of China’s R&D input. In fact, China’s strategic adjustment of replacing imitation with innovation predates the adoption of the “innovation-driven development strategy.” In 2010, China increased its spending on both the importation and assimilation of foreign technology, which marks the beginning of change in China’s innovation strategy (Fang and Xing, 2017). 5

However, the adjustment of innovation strategy and reallocation of R&D resources seem to have not delivered expected results. While imitation and technology spillover effects may increase total factor productivity (TFP) contribution to economic growth, scientific research and innovation did little to raise TFP in the short run (Ye and Liu, 2018). We may wonder whether the underlying reason is the failure to shift to a suitable innovation strategy according to market size at the time. With a middle-income group of some 400 million people and a land area of close to 10 million km², China registered a GDP aggregate of 13.6 trillion US dollars and a total retail volume of social consumer goods worth 5.8 trillion US dollars. With a large population, broad land area, market heft and market integration, China’s economy is super-large, but has yet to become super-strong (Research Group of the State Council Development Research Center, 2020). According to our analysis of Table 1, China should implement an Innovation Instead of Imitation Strategy to give full play to its super-large market advantage. The Innovation Instead of Imitation Strategy is consistent with the evolving trends of China’s market size. It is a realistic choice based on the goal of technology catch-up and helps avoid the premature adjustment of innovation strategy that may cause China’s technology progress path to deviate from its strategic goal. Under this innovation strategy, there is a lag in the effect of market expansion on the shift of technology progress pathway, and the U-shaped trend of the contribution of innovation is also consistent with theoretical expectations. With the transition of China’s economy from a super-large to a super-strong economy, market expansion will further shift China’s technology progress path towards innovation.

The “turning point” mentioned by Fang and Xing (2017) in their paper is the turning point for China’s technology progress mode from the perspective of R&D input, and is unlike the transition of technology progress path analyzed in this paper from the perspective of innovation output. The shift of technology progress mode in their paper is more similar to the adjustment of innovation strategy in this paper because strategic adjustment drives change in the structure of R&D input. In addition, Yu and Zhang (2015) believed that this transition could have occurred in 2002, when China’s R&D input started to exceed its spending on technology importationand the gap between the two kept widening over the years.

4. Numerical Simulation

In relation to the theoretical model, this section will employ the numerical simulation method to simulate the evolving trends of the dynamic transition and technology catch-up of the late-moving large country’s technology progress path amid market expansion and analyze the effects of parametric change.

4.1 Parametric Calibration

Referencing existing literature, this paper calibrates model parameters based on China’s empirical data to align model specification with China’s reality. Our simulation employs empirical data from the China Statistical Yearbook, the China Statistical Yearbook of Science and Technology, and the Penn World Table 10, and all indicators are actual values after deflating price volatility.

First, market size Y is measured by China’s actual GDP referencing Alesina et al. (2000). Second, the reverse indicator of technology gap, i.e. relative technology Level a, indicates China’s gap with the global technology frontier. In the iterature, this indicator is measured on such dimensions as the ratio between the capital stock per capita of Chinese and foreign-funded enterprises, technology density, as well as the total factor productivity (TFP), labor productivity and R&D spending as a share of GDP and GDP per capita of China and the US. Referencing Huang and Song (2017), this paper employs the TFP ratio between China and the United States to measure the relative level of technology. Third, the global technology frontier, i.e. the technology progress rate of early-moving countries g, is specified as 0.02 following the general practice of literature (Barro and Sala-i-Martin, 2003; Acemoglu and Cao, 2015). Lastly, the degrees of technology improvement λD and λF achieved by means of innovation and imitation under different innovation strategies. The cost parameters ζD and ζF for the two types of innovation are the key to parametric calibration in this paper. Referencing Acemoglu and Cao (2015), assuming that the degree of technology improvement achieved by means of innovation is large enough to replace the results of imitation, this paper specifies technology improvement by means of innovation as 10 times that achieved by means of imitation, i.e. λD / λF =10 under the Innovation Instead of Imitation Strategy, and λF / λD =10 under the Imitation Plus Innovation Strategy.

On such a basis, referencing Fu and Wu (2013), the degrees of technology improvement by means of innovation and imitation and cost parameters are calibrated in relation to R&D input and equations (11)(12) and (A1)-(A2) under different innovation strategies6 using the actual data of China’s technology progress rate, the relative level of technology, market size and R&D input, as well as the relative degrees of technology improvement achieved by means of the two innovation modes. With respect to the R&D input data for innovation and imitation, referencing Liu (2011), we denote the input of innovation zD( t) by R&D spending, and the input of imitation zF( t) by the sum of spending on foreign technology importation and domestic technology acquisition.

Meanwhile, the implementation status of the two innovation strategies also needs to be defined to utilize the actual data of various stages to calibrate the parametric levels of the two innovation strategies. Referencing Fang and Xing (2017), we define 2010 as the turning point of China’s innovation development strategy and employ the data of 1991-2010 to calibrate the parameters for the Imitation Plus Innovation Strategy, so as to determine λD= 0.00175, λF= 0.0175, ζD= 5455.69, and ζF =2693.78; data of 2011-2019 are for calibrating the parameters for the Innovation Instead of Imitation Strategy to be λD= 0.0322, λF =0.0032, ζD= 105879.93 and ζF= 58599.28.

To test the validity of the theoretical model, this paper performs a numerical simulation of the above theoretical model based on empirical data calibration parameters for a comparative analysis of the simulated technology progress rate and the actual technology progress rate. The mean values and

variation trends of the simulated and estimated values of the technology progress rate are generally

7 consistent, thus verifying the validity of the mathematical model.

4.2 Different Types of Innovation Strategy

This paper specifies 2019 as the base period to simulate the dynamic evolving trends of the technology progress path gD(t)/ gF(t) and relative technology Level a(t) amid market expansion under the two types of innovation strategies after multiple iterations, as shown in Figure 1 and Figure 2. Figure 1 is the dynamic shift of the technology progress path under different innovation strategies, which shows that under the Imitation Plus Innovation Strategy, innovation contributes a diminishing share to imitation amid the large country’s continuous market expansion. As a result, the late-moving large country’s technology progress path becomes increasingly dependent on imitation, deviating from the strategic goal of combining innovation with imitation. Under the Innovation Instead of Imitation Strategy, market expansion will give rise to a dynamic U-shaped trend of innovation relative to imitation.

From Phase 1 to Phase 11, innovation continuously slows relative to imitation, and with the turning point of Phase 12, the technology progress path starts to shift towards innovation. This shift stems from the positive effect of the late-moving country’s market expansion on the growth rate of innovation. Despite slowing innovation, the effect on the growth rate of imitation demonstrates an inverted U-shaped threshold. This result also implies that when the strategy of imitation is replaced with innovation at the macro level, the continuous shift of R&D resources towards innovation is not accompanied by equal changes in the relative contribution rates of the two types of innovation at the level of R&D output. Indeed, there is a certain lag in the effect of market expansion on the shift of the technology progress path. The market size threshold for the transition of technology progress path is 18,795.79 billion yuan, i.e. after China’s actual GDP exceeds this level, market expansion may induce a transition of the technology progress path towards innovation.

Figure 2 shows the dynamic evolving trends of technology catch-up for the late-moving country.

Data suggest that whichever innovation strategy is adopted by the late- moving large country, its technology gap with early- moving countries will narrow amid its domestic market expansion. In comparison of the dynamic evolving trajectories of technology catch-up for the late-moving country under the two innovation strategies, if the Imitation Plus Innovation Strategy is adopted, the late-moving country’s relative level of technology will increase logarithmically, and while the economy’s relative level of technology increases fast in the early stage, its domestic market expansion will cause its growth to slow; if the Innovation Instead of Imitation Strategy is adopted, however, the country’s relative level of technology will increase exponentially, and while its relative level of technology increases slowly in the initial stage, the growth of local market demand in the late stage may bring about exponential economies of scale, causing the relative level of technology to improve at a faster pace.

Throughout Phases 1-70, technology catch-up under the Innovation Instead of Imitation Strategy lags behind that under the Imitation Plus Innovation Strategy, but since Phase 71, the catch-up trend starts to reverse, i.e. under the Innovation Instead of Imitation Strategy, the relative level of technology starts to catch up and overtake that under the other strategy. In the long run, if the Innovation Instead of Imitation Strategy is followed, market expansion will increase the relative equilibrium level of technology; if the Imitation Plus Innovation Strategy is followed, market expansion will inhibit improvement in the relative equilibrium level of technology.

Based on China’s large and expanding market and in relation to the numerical simulation results of Figure 1 and Figure 2, we find that China’s economy is transitioning from super-large to super-strong. To avoid the low-level equilibrium trap, the Innovation Instead of Imitation Strategy with the goal of technology catch-up may raise the relative equilibrium level of technology. In this sense, China’s innovation-driven development strategy is compatible with its current domestic market size. In terms of the shift of technology progress path, since China’s economy has yet to reach a super-strong level, market expansion will reduce the contribution of innovation to technology progress in the short term. As China completes its transition from a super-large to a super-strong economy in the long run, however, market expansion will not only increase the equilibrium level of technology, but will scatter the risks of innovation and the cost of independent R&D to support the transition of technology innovation mode and shift its technology progress path towards innovation.

4.3 Adjustment in the Intensity of Innovation Strategies

On such a basis, this paper further analyzes the effect of adjustment in the intensity of innovation strategy on the shift of technology progress path and technology catch-up for the late-moving large country, i.e. the degree of technology improvement achieved by means of innovation and imitation to move λD and λF upwards and downwards by 20%, respectively, to denote the adjustment in the intensity of the two innovation strategies and the intensity of inclination towards innovation or imitation, as shown in Figure 3:

Under the Innovation Plus Imitation Strategy (see Figure 3a), the degree of technology improvement is more significant by adjusting imitation while the effect of innovation is insignificant. Under this innovation strategy, the late-moving large country may raise its relative level of technology by means of imitation. Meanwhile, the shift of the innovation strategy to imitation will cause the technology progress path to be more dependent on imitation, deviating from the strategic goal of reinforcing innovation through imitation.

Under the Innovation Instead of Imitation Strategy ( see Figure 3b), compared with imitation, technological improvement by means of innovation has a more significant effect, indicating that a further shift towards innovation under this strategy allows market expansion to better serve the late-moving large country’s shift of technology progress path and technological catch-up. Increasing intensity in the Innovation Instead of Imitation Strategy will enhance the positive effect of a large market on the shift of technology progress path, allowing the turning point for the late-moving large country’s technology

progress path to shift from imitation to innovation, so as to raise the country’s relative equilibrium level

8 of technology and give play to the scale advantage of market heft at the level of innovation.

4.4 Dynamic Adjustment of Innovation Strategy

The above section has verified the exponential effect of the increase in the intensity of innovation strategy. Considering that the late-moving large country’s innovation strategy is not constant and keeps deepening, this paper further evaluates the evolving trends of the late-moving large country’s technology progress path and technology catch- up amid market expansion when the time- varying innovation strategy is adopted, as shown in Figure 4. To reflect the dynamic adjustment of innovation strategy, it is assumed that technology improvement under the two modes of innovation will change with time, i. e. λD(t+ 1)= λD(t) ×(1+ gλD), λF(t+ 1)= λF(t) ×(1+ gλF), and gλD and gλF are specified as 2%, -2% and 0, respectively.

Under the Innovation Plus Imitation Strategy (see Figure 4a), the benchmark scenario is specified as: gλD = gλF = 0. First, the benchmark scenario gλD =0 is replaced with gλD= 2% or gλD=- 2%, which has a

minimal effect on the late-moving large country’s technology progress path and technological catch

up, indicating that the adjustment of λD to weaken (deepen) the innovation strategy has a limited impact on the strategy’s policy effect. But if the innovation strategy is increasingly deepened by adjusting λF to shift the innovation strategy towards imitation, i.e. when gλF =0 is replaced with gλF =2%, the technology progress path will increasingly shift towards imitation amid rapid market expansion, the technology gap will converge at a faster pace in sync, and its evolving trend will lead the benchmark by an increasing margin; if specified as gλF =- 2%, the imitation strategy will become less intense, and the evolving trends of the late-moving country’s technology progress path and technology catch-up will lag behind in comparison.

Under the Innovation Instead of Imitation Strategy (see Figure 4b), the benchmark status is specified as gλD = gλF = 0, and if the innovation strategy is gradually shifted in favor of innovation by adjusting λD, i.e. when gλD =0 is replaced with gλD =2%, there will be earlier changes in the evolving trajectories of the large country’s technology progress path and relative level of technology compared with the benchmark status. Specifically, continuous market expansion will be accompanied by a shift of technology progress path towards innovation and a faster increase in the country’s relative level of technology; if technology improvement by means of imitation is adjusted to reduce the intensity of innovation strategy, i.e. when gλD =0 is replaced with gλD =-2%, the evolving trends of the late-moving large country’s technology

progress path and technology catch- up will lag behind the benchmark status with widening gaps. Under the condition of continuous market expansion, if the shift of technology progress path towards innovation weakens, the convergence of technology gaps will slow. If the benchmark status gλF = 0 is

replaced with gλF =2% or gλF =-2%, the effect on the late-moving large country’s technology progress path and technology catch-up is insignificant, indicating the ineffectiveness of strategic adjustment by weakening or deepening the innovation strategy through the dynamic change of λF. On the whole, there is a certain lag effect in the continuous adjustment of the innovation strategy’s intensity compared with the direct adjustment of the innovation strategies intensity, but it may still further unleash the exponential effect of the large market advantage.

4.5 Robustness Test

In calibrating parameters, this paper specifies the relative magnitudes of technological improvement by means of innovation and imitation based on Acemoglu and Cao (2015). Yet literature based on the empirical facts of developed countries is inconsistent with the reality of China’s technological catchup. For this reason, this paper has adjusted the ratio between technology improvements by means of innovation and imitation to examine whether changes in the relative magnitudes of technological improvement have an effect on the path of technology progress and technology catch-up to test the robustness of simulated -the results, as shown in Figure 5.

Under the Innovation Plus Imitation Strategy ( see Figure 5a), the ratio between technology improvements under the two modes of innovation is adjusted under different scenarios. The benchmark scenario is λD= 0.00175, λF =0.0175, and λF /λD= 10. Scenario 1 maintains the same degree of technological improvement λD= 0.00175 by means of innovation, specifies λF= 0.00875, and adjusts λF /λD from 10 to 5. With the increasing market size, the late-moving large country’s path of technology progress becomes less dependent on imitation, but its relative level of technology also decreases.

Scenario 2 considers λF =0.0175 to be constant, and adjusts the level of technological improvement by means of innovation λD to 0.0035, making λF /λD= 5, and the late-moving large country’s technology progress path and technology catch-up barely change. Compared with Scenario 2, parametric adjustment in Scenario 1 has a more significant impact on the simulated results, but further research is needed to unravel whether such an impact stems from technological improvement by means of innovation or the adjustment of ratio between technological improvements under the two types of innovation. Hence, both Scenario 3 and Scenario 4 specify λF /λD= 10, but the former specifies λF =0.00875, which is consistent with Scenario 1, and the latter specifies λD= 0.0035, which is consistent with Scenario 2.

Under Scenario 1 and Scenario 3, technology improvement by means of imitation are the same,. technological improvement by means of innovation and the ratio of technological improvements under the two types of innovation are different. Results suggest that the path of technology progress and the trend of technology catch-up are almost identical. Meanwhile, innovation leads to the same degree of technology improvement under both Scenario 2 and Scenario 4. Although the ratio of technology improvement by means of imitation and the ratio of technological improvements under the two types of innovation are different,, there is no change in the path of technology progress and the trend of technological catch-up.

As can be learned from a comparative analysis of the above four scenarios against the benchmark scenario, under Innovation Plus Imitation Strategy, the degree of technology improvement achieved by means of imitation - rather than the ratio of technology improvements achieved by means of the two innovation modes - has a key impact on the late-moving large country’s technology progress path and technology catch-up trend. Under the Innovation Instead of Imitation Strategy (see Figure 5b), the result of adjusting parameters is similar, i.e. the degree of technology improvement achieved by means of innovation - rather than the ratio of technology improvements achieved under the two innovation modes - holds the key to the late-moving large country’s technology progress path and technology catch-up

trend. This result is consistent with that for the intensity of the innovation strategy in the above section. Under the Imitation Plus Innovation Strategy, adjustment in the technology improvement achieved by means of imitation has a major impact on the late-moving large country’s technology progress path and technology catch-up trend; under the Innovation Instead of Imitation Strategy, technology improvement achieved by means of innovation has a major effect, and the degree of technology improvement by means of both types of innovation are calibrated using China’s actual data. Specification of the technology improvement ratio for the two types of innovation referencing the literature does not affect the technology progress path and the technology catch- up trend, thus verifying the robustness of simulated results.

5. Conclusions and Policy Recommendations

This paper creates an endogenous technology progress model for late-moving large countries to simulate the heterogeneous effects of market size on indigenous and imitation under various innovation strategies, as well as the mechanism of its effects on the shift of technology progress path and technology catch- up. Based on China’s empirical data, a numerical simulation is performed for the evolving trajectories of shifting technology progress path and technology catch-up under various types and intensities of innovation strategies amid domestic market expansion. Our research suggests that first, the

scale advantage for R&D innovation is reflected in the large market being able to motivate enterprises to innovate, spread the high innovation cost, reduce R&D risk, and increase the success rate of innovation Second, under the Imitation Plus Innovation Strategy, market expansion will inhibit the convergence of the economy to the technology frontier, making its technology progress more dependent on imitation. Under the Innovation Instead of Imitation Strategy, the effects of market size on the technology progress path and technology catch-up are subject to a non-uniform U-shaped threshold effect, and the threshold of market size for the shift of technology progress path lags behind that for technology catch-up. The reason is that a large market may mitigate the risks of both indigenous and imitation, and that market size should be large enough to defuse the risk of innovation more than it does the risk of imitation to induce the transition of technology progress to innovation. Third, China should pursue a benchmark goal of technology catch-up, and advance and reinforce the strategy of replacing imitation with innovation to avoid the low-level convergence trap and further unleash the exponential effect of large market advantage. Lastly, China’s innovation-driven development strategy is a realistic choice for its current market size. However, since China’s economy remains in the stage of transition from a super-large to a super-strong economy, market expansion will cause the contribution of innovation to technology progress to decrease at first before increasing. The seemingly ineffective adjustment of innovation strategy stems from the choice of different strategic goals and the lagged policy effect. Of course, realworld innovation strategies are far more complex than theoretical simulations, and Chinese enterprises remain weak and inefficient when it comes to innovation.

In creating a new development pattern of domestic and international circulations, China should not only use its large market to induce endogenous firm innovation, but implement an innovation strategy at the national level to wean its dependence on critical foreign technologies. Based on the conclusions, we put forth the following policy recommendations:

First, we should further explore and give play to our super- large market advantage based on domestic demand. We should break through market segmentation and increase market integration by enhancing transportation, telecom, policy and institutional assurances and form a unified domestic large market by consolidating commodity market demand, deepening factor market reforms, removing barriers to factor flow and reallocation, and improving the factor demand system Various measures should be taken to improve inequalities in primary income distribution and redistribution to broaden domestic demand, smoothen domestic economic circulation, and derive profits from the super-large market to incentivize firms to innovate.

Second, we should create demand with high-quality supply for domestic demand to drive innovation and create a virtuous cycle between innovation and market demand. Institutional market environment should be improved to strengthen the agglomeration effect of the super-large market and foster a strong domestic market. In this manner, China should transition from a super-large economy to a super-strong one and scatter the risk in corporate R&D innovation with its huge market demand and ramp up the input of innovation resources. Efforts should be made to increase market competition, encourage R&D entities to learn from consumers, and improve the trial and error mechanism for innovation to bear fruit. Technology innovation driven by domestic demand should shift from imitative to innovation. On one hand, new demand for high-quality supply should be created to improve supply quality amid demand growth, create a dynamic demand-supply equilibrium, and smoothen domestic economic circulation by matching supply with demand on a dynamic basis. On the other, the shift from imitation to innovation has also become a new strength for China to take part in international technology cooperation, reshape the international innovation alliance, and form the basis for participation in the international circulation.

Lastly, the innovation-driven development strategy should be followed to remove institutional barriers preventing the large market demand from inducing innovation. The large domestic market should be leveraged to induce critical technologies. Under the dual circulations, we should rely on our domestic market demand as a driver of original firm innovation but not technology progress in early

moving countries and international market demand. In this process, we should also give play to the institutional strengths of Chinese socialism and government top-down design, identify changing market size, promptly shift our innovation strategy, and adjust the intensity of innovation strategy for specific industries. After the adjustment of innovation strategy, market expansion will induce the contribution of innovation to decrease before increasing. To reduce the gap between the dual thresholds for the shift of technology progress path and technology catch-up and reduce the downward cycle of contribution from innovation, it is necessary to break through institutional barriers to the transition of innovation modes by means of institutional innovation, and improve the property system conducive to the protection of innovation results and the performance management and profit-sharing systems for R&D personnel to spur the innovation dynamism and potentials of R&D entities.

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1 In the interest of length, we have omitted the illustrated international comparisons of R&D personnel per million population and R&D spending as a share of GDP, which will be provided upon request.