2. Related literature

Our study contributes to the literature on innovation-based growth (Romer (Reference Romer1990), Grossman and Helpman (Reference Grossman and Helpman1991), Aghion and Howitt (Reference Aghion and Howitt1992)). While, as we first mentioned, the importance of culture as an essential source of growth is widely perceived in economics, few studies explore the role of cultural aspects of people’s preferences in innovation-based growth. Chu (Reference Chu2007), for example, notably argues that entrepreneurial overconfidence can cause different economic growth rates across countries, using a standard innovation-based growth model.Footnote ⁶ More recently, Pan et al. (Reference Pan, Zhang and Zou2018), Hof and Prettner (Reference Hof and Prettner2019), and Chu et al. (Reference Chu, Cozzi, Pan and Zhang2020) have examined status-seeking preferences in the innovation-based growth model. Our study contributes to this literature by examining the role of consumer love of novelty as a cultural source of innovation-based growth.

Broadly interpreting the meaning of culture or cultural preferences, our study also relates to Galor and Michalopoulos (Reference Galor and Michalopoulos2012) and Doepke and Zilibotti (Reference Doepke and Zilibotti2014). They identify the critical role of entrepreneurial traits in innovation and economic growth by considering the endogenous evolution of a fraction of people who exhibit entrepreneurial spirit (in terms of risk tolerance). Given that entrepreneurial traits should be partially attributable to culture, their studies and ours contribute to the literature on culture, innovation, and growth by examining different cultural factors.Footnote ⁷

More broadly, several studies examine the role of culture in other classes of the endogenous growth model. For example, Cozzi (Reference Cozzi1998) considers a cultural asset unproductive at the individual level, traded between different generations, yet has positive external effects on productivity growth. He further shows that culture can be a bubble that causes dynamic indeterminacy and self-fulfilling stagnation. Thus, the role of culture in his model is ambiguous in that it can encourage or discourage economic growth. Galor and Moav (Reference Galor and Moav2002) show that individual preferences for offspring quality contribute to population growth and human capital formation. Subsequent studies by Ashraf and Galor (Reference Ashraf and Galor2007, Reference Ashraf and Galor2013a, Reference Ashraf and Galor2013b, Reference Ashraf and Galor2018) explore cultural/genetic diversity and regional development at different stages and places.Footnote ⁸ Several studies in this line of research have identified the ambiguous role of some cultural factors, as in our study. For example, Ashraf and Galor (Reference Ashraf and Galor2013a) show an inverted U-shaped relationship between genetic diversity within a country and regional economic development.

We also contribute to the theoretical literature on innovation cycles by identifying the love of novelty as a novel factor for cyclical innovation (Judd (Reference Judd1985), Shleifer (Reference Shleifer1986), Deneckere and Judd (Reference Deneckere, Judd, Deneckere and Judd1992), Gale (Reference Gale1996), Francois and Shi (Reference Francois and Shi1999), Matsuyama (Reference Matsuyama1999, Reference Matsuyama2001), Furukawa (Reference Furukawa2015), Sunaga (Reference Sunaga2017), and Yano and Furukawa (Reference Yano and Furukawa2023)). In the main analysis, following this theoretical literature, we assume that the innovator can enjoy only a single-period monopoly, and we demonstrate that when the love of novelty is moderate, innovation is cyclical on an equilibrium path. On this cyclical path, the two types of innovations, new and existing product development, perpetually alternate on an equilibrium path. As explained above, it is reasonably justifiable because the duration of patent protection, or, more generally, monopoly power, can persist for only a finite period in reality. Allowing for a multiperiod monopoly, from a more general perspective, Iwaisako and Futagami (Reference Iwaisako and Futagami2007) identify an essential role of the temporary nature of monopoly in growth cycles in an innovation-based growth model with a finite patent length.Footnote ⁹ Our study extends these by developing a new model of innovation and growth cycles and characterizing the role of consumer love of novelty as a source of innovation cycles.

Lastly, our study is related to the literature on two-stage innovation models. Most models in this literature have distinguished basic and applied research (see, e.g., Aghion and Howitt (Reference Aghion and Howitt1996), Michelacci (Reference Michelacci2003), Akiyama(Reference Akiyama2009), Cozzi and Galli (Reference Cozzi and Galli2009, Reference Cozzi and Galli2013, Reference Cozzi and Galli2014), Acs and Sanders (Reference Acs and Sanders2012), Chu et al. (Reference Chu, Cozzi and Galli2012), Chu and Furukawa (Reference Chu and Furukawa2013), Konishi (Reference Konishi2018)). We consider two separate activities of applied innovation; thus, firms earn profits in both stages of innovation. This differs from existing models, in which there is no profit in the early, basic research stages of innovation. Therefore, our study complements the literature by first considering two commercial stages of innovation and further characterizing the role of consumer love of novelty on aggregate innovation and growth.

3. Innovation-based growth model with love of novelty

This section presents our basic innovation-based growth model, following Matsuyama (Reference Matsuyama1999, Reference Matsuyama2001). As in his models, innovation occurs endogenously as a product of the firms’ profit-seeking R&D investment, and the variety of products increases over time (Romer (Reference Romer1990)) with the assumption that firms can only enjoy temporary (one period) monopoly power. This assumption is used because new and old products play separate but essential roles in equilibrium, facilitating the modeling of people’s love of novelty—as will be apparent later.

Our model demonstrates two new assumptions to investigate the role of love of novelty of optimizing agents. First, we assume that the representative agent is endowed with the standard love-of-product variety and love of novelty; therefore, they would have some extra weight on new products compared with old products.Footnote ¹⁰ Second, we think of two types of innovation: one is to invent new products, and the other is to ensure invented products have a long life in the market. We refer to these two types of innovation as new and existing product development, which both require R&D investment by profit-seeking firms.

3.1 Consumption and love of novelty

An infinitely lived representative agent inelastically supplies $L$ units of labor during each period. The representative agent solves the standard dynamic optimization of consumption and saving over an infinite horizon:

(1) \begin{equation} \max U=\sum _{t=0}^{\infty }\beta ^{t}\ln{u{(t),}} \end{equation}

where $\beta \in (0,1)$ is the time preference rate, and $u(t)$ is an index of consumption in period $t$ . We assume that periodic utility $u$ is defined over differentiated consumption goods, and each is indexed by $j$ .Footnote ¹¹ Namely, the agent is endowed with so-called love-of-variety preferences. As is standard, we consider a constant elasticity of substitution utility function:

(2) \begin{equation} u(t)=\left ( \int _{j\in A(t)\cup N(t)}(\varepsilon (j,t)\ {x(j,t))^{\frac{\sigma -1}{\sigma }}dj}\right ) ^{\frac{\sigma }{\sigma -1}}\text{, } \end{equation}

where $x(j,t)$ represents the consumption of good $j$ in period $t,$ $\sigma \geq 1$ represents the elasticity of substitution between any two consumption goods, and $\varepsilon (j,t)$ is a variable determining the consumer’s preference for each good, $j$ . Here, the consumption goods are categorized into two types: new goods and old goods. Let $N(t)$ be the set of new goods invented in period $t$ and $A(t)$ be the set of old goods invented prior to period $t.$ To simplify the description, let $A(t)$ and $N(t)$ also denote the number (measure) of goods.

When considering the innate love of novelty, we assume that the representative agent is endowed with love-of-novelty preferences, in addition to the standard love-of-variety preferences.

First, we attempt to observe a benchmark wherein the consumer prefers new goods and old goods equally; there is no particular love of novelty. In this case, all goods should have identical $\varepsilon (j,t)$ for all $j\in A(t)\cup N(t)$ . Normalizing this parameter to 1, the consumer’s utility function can be written as

(3) \begin{equation} u(t)=\left ( \int _{j\in A(t)}{x(j,t)^{\frac{\sigma -1}{\sigma }}dj+}\int _{j\in N(t)}{x(j,t)^{\frac{\sigma -1}{\sigma }}dj}\right ) ^{\frac{\sigma }{\sigma -1}}. \end{equation}

Now, suppose that the consumer has some extra preference, ${\varepsilon },$ for novelty that he/she considers in terms of a good being new or a condition in which a good is new:

(4) \begin{equation} \varepsilon (j,t)=\left \{ \begin{array} [c]{ll}1 & \text{if }j\in A(t)\ \text{(old goods)}\\{\varepsilon } & \text{if }j\in N(t)\ \text{(new goods)}\end{array} \right. . \end{equation}

Applying (4) to (2) yields

(5) \begin{equation} u(t)=\left ( \int _{j\in A(t)}{x(j,t)^{\frac{\sigma -1}{\sigma }}dj+}\int _{j\in N(t)}{({\varepsilon } \, x(j,t))^{\frac{\sigma -1}{\sigma }}dj}\right ) ^{\frac{\sigma }{\sigma -1}}. \end{equation}

When ${\varepsilon }=1,$ first, the consumer has no preference for novelty and prefers all goods equally, as in (3). This provides the benchmark, which has been intensively investigated in the literature. When $\varepsilon \gt 1,$ the consumer has a love of novelty and prefers new goods to old goods. The higher ${\varepsilon },$ the stronger the love of novelty. To retain generality, we also allow for $\varepsilon \lt 1.$ When $\varepsilon \lt 1,$ the consumer’s love of novelty is very weak, or we can say that the consumer has a so-called “fear of novelty” (Barber (Reference Barber1961)), preferring old goods to new goods. This sort of negative preference for novelty can also be observed in reality and develops from people’s innate “mental resistance to new ideas” (Beveridge (Reference Beveridge1959)). For simplicity, we refer to $\varepsilon$ as the consumer’s love of novelty for all $\varepsilon \gt 0.$ Footnote ¹²

The infinitely lived consumer solves the static optimization in (1); as is well known, we have the demand functions:

(6) \begin{equation} x(j,t)=\varepsilon (j,t)^{\sigma -1}\frac{E(t)p(j,t)^{-\sigma }}{P(t)^{1-\sigma }}\text{,} \end{equation}

where the consumer’s spending on differentiated goods is

(7) \begin{equation} E(t)\equiv \int _{j\in A(t)\cup N(t)}p(j,t)x(j,t)dj, \end{equation}

$P(t)$ is the usual price index, defined as

(8) \begin{equation} P(t)\equiv \left ( \int _{j\in A(t)\cup N(t)}(p(j,t)/\varepsilon (j,t))^{1-\sigma }dj\right ) ^{\frac{1}{1-\sigma }}, \end{equation}

and $p(j,t)$ is the price of good $j$ in period $t$ . By solving the dynamic optimization, we also obtain the Euler equation:Footnote ¹³

(9) \begin{equation} \frac{E(t+1)}{E(t)}=\beta (1+r(t))\text{,} \end{equation}

where $r(t)$ denotes the interest rate.

3.2 Production

A continuum of firms produces consumption goods $j\in A(t)\cup N(t)$ . Each good $j,$ a new or old good, is dominated by a monopolistic producer. We consider a one-for-one technology in goods production. Namely, any producer, $j\in A(t)$ or $N(t),$ hires $x(j,t)$ units of labor to produce $x(j,t)$ units of good $j$ , and monopolistically sells them to the consumer. The marginal cost is, therefore, equal to the wage rate, $w(t).$

As shown in (6), the consumption good producers, $j\in A(t)\cup N(t),$ face a constant price elasticity of market demand, equal to $\sigma \geq 1.$ The unconstrained mark-up for a monopolistic producer is $\sigma/(\sigma -1)\gt 1.$ Thus, the mark-up goes to infinity in a Cobb–Douglas case of $\sigma =1.$ Nevertheless, to observe the role of substitutability between goods, captured by $\sigma$ , we allow for the case of $\sigma =1,$ Footnote ¹⁴ by introducing an upper bound of the mark-up, say, $\mu \gt 1$ . This upper bound $\mu$ has often been referred to as a patent breadth.Footnote ¹⁵ Following the literature, we assume $\mu \leq \sigma/(\sigma -1).$ Footnote ¹⁶ Notably, this introduction of a mark-up upper bound, $\mu,$ is only for clarifying what occurs in the Cobb–Douglas case ( $\sigma =1$ ). Therefore, the main results do not alter qualitatively at all without the upper bound $\mu .$

Accordingly, each firm sets a monopolistic price at:

(10) \begin{equation} p(j,t)=\mu w(t) \end{equation}

for all $j.$ Using (4), (6), and (10), the output and monopolistic profit for a new good are given by

(11) \begin{equation} x(j,t)=\frac{\varepsilon ^{\sigma -1}E(t)}{P(t)^{1-\sigma }}\left ( \mu w(t)\right ) ^{-\sigma }\equiv x^{n}(t)\ \text{for }j\in N(t) \end{equation}

and

(12) \begin{equation} \pi (j,t)=\varepsilon ^{\sigma -1}\frac{\mu -1}{\mu ^{\sigma }}E(t)\left ( \frac{w(t)}{P(t)}\right ) ^{1-\sigma }\equiv \pi ^{n}(t)\ \text{for }j\in N(t). \end{equation}

Equation (12) shows that when $\sigma \gt 1$ , the profit for a new good, $\pi ^{n}(t),$ increases with the love of novelty $\varepsilon$ and the total expenditure, $E(t)$ , and decreases with the real wage, $w(t)/P(t)$ . When $\sigma =1$ (the Cobb–Douglas case with no substitutability between goods), it becomes independent of the love of novelty $\varepsilon,$ and the real wage, $w(t)/P(t)$ .

We can also derive the output and monopolistic profit for an old good, from (4), (6), and (10):

(13) \begin{equation} x(j,t)=\frac{E(t)}{P(t)^{1-\sigma }}\left ( \mu w(t)\right ) ^{-\sigma }\equiv x^{a}(t)\ \text{for }j\in A(t) \end{equation}

and

(14) \begin{equation} \pi (j,t)=\frac{\mu -1}{\mu ^{\sigma }}E(t)\left ( \frac{w(t)}{P(t)}\right ) ^{1-\sigma }\equiv \pi ^{a}(t)\ \text{for }j\in A(t). \end{equation}

The profit $\pi ^{a}(t)$ associated with an old good is always free from the love of novelty $\varepsilon .$

3.3 Innovation

In this section, we present two types of innovation. One is to invent new goods, and the other is to ensure that invented goods have a long life in the market; we label these two types of innovation new product development and existing product development, respectively. First, R&D firms invent new consumption goods. We suppose new goods will become obsolete without further investments. Firms would further invest in existing product development. If investments succeed, new goods would be transformed and developed into new “old” goods.Footnote ¹⁷

3.3.1 New product development

There is a potentially infinite number of R&D firms. A firm can invent a new good in period $t$ by making an investment of $1/A(t-1)$ units of labor in period $t-1$ . We follow Romer (Reference Romer1990) to consider “external effects arising from knowledge spillovers” of the stock of existing technologies, represented by $A(t-1)$ . There is no spillover from newly invented goods as they are so new that their information would not be diffused appropriately. Nevertheless, even if we allow for new goods in the stock of existing technologies, the main results will not change qualitatively. Firms that invent new goods earn a monopolistic profit in period $t,$ $\pi ^{n}(t).$

As aforementioned, in the baseline model, we assume that the monopolistic firm can enjoy only a temporary (one-period) monopoly, following Matsuyama (Reference Matsuyama1999, Reference Matsuyama2001). The free entry condition for new product development can be written as:

(15) \begin{equation} W^{n}(t-1)\equiv \frac{\pi ^{n}(t)}{1+r(t-1)}-\frac{w(t-1)}{A(t-1)}\leq 0\ \text{for }t\geq 1, \end{equation}

where $W^{n}(t-1)$ denotes the discounted present value of inventing a new good. $R^{N}(t-1)$ denotes the units of labor devoted to new product development in period $t-1.$ Then, we have

(16) \begin{equation} N(t)=A(t-1)R^{N}(t-1). \end{equation}

3.3.2 Existing product development

Owing to the one-period nature of monopoly power, the new goods, $N(t),$ invented in period $t$ can potentially be manufactured by any firm in the subsequent period, $t+1.$ At this point, the goods are no longer new but “old.” We assume that each new good becomes obsolete before becoming an old good unless additional investments are made and succeed; however, one can utilize new goods as seeds and develop them into new “old goods.” We refer to this type of activity for developing old goods as existing product development.

As a first step, an R&D firm engaging in existing product development invests one unit of labor in period $t$ and searches through the set of new goods, $N(t)$ . From among $N(t),$ the firm meets only a fraction, $\phi \in (0,1)$ , of the new goods as seeds for old goods. The new goods each firm meets are randomly chosen from $N(t)$ . The firm then makes $\chi (t)$ units of old products from the new goods of $\phi N(t)$ by coming up with different combinations of those new goods. It is worth mentioning that the number of differentiated old goods that can potentially emerge from $N(t)$ is not bounded. This is because the number of possible combinations of $\phi N(t)$ new goods is not bounded due to continuity.

After existing product development, the firm enjoys a one-period monopoly for those $\chi (t)$ old goods to earn the profits of $\chi (t)\pi ^{a}(t+1)$ . The free entry condition for existing product development can be given as

(17) \begin{equation} W^{a}(t)\equiv \frac{\chi (t)\pi ^{a}(t+1)}{1+r(t)}-w(t)\leq 0\ \text{for }t\geq 0, \end{equation}

in which $W^{a}(t)$ denotes the discounted present value for existing product development. Concerning $\chi (t)$ , we consider a simple technology, $\chi (t)\equiv \lambda (\phi N(t))$ , where $\lambda \gt 0$ is a productivity parameter.Footnote ¹⁸ For descriptive purposes, we define a composite parameter, $\kappa \equiv \lambda \phi \gt 0$ . Then we have $\chi (t) = \kappa N(t)$ .

Through this process, the new goods of $N(t)$ are partially converted into the old goods, whose number is expressed as $A(t+1)-A(t)$ . Denote $R^{A}(t)$ as the units of labor devoted to existing product development in period $t.$ Further we obtain

(18) \begin{equation} A(t+1)-A(t)=\chi (t)R^{A}(t). \end{equation}

For simplicity, we assume that none of the old goods becomes obsolete. However, it is easy to allow for some depreciation for $A(t)$ without rendering any essential change to the result. For descriptive purposes, we define $\rho (t)$ as a macroeconomic rate of existing product development at which old goods are made from new goods:

(19) \begin{equation} \rho (t+1)\equiv \chi (t)R^{A}(t)/N(t). \end{equation}

In the subsequent period, $t+2,$ owing to the temporary monopoly again, the new “old” goods, $A(t+1)-A(t),$ could potentially be produced by any firm. We follow Acemoglu et al. (Reference Acemoglu, Aghion, Bursztyn and Hemous2012) by assuming that monopoly rights will be allocated randomly to a firm from the pool of potential firms whose ownership belongs to the representative agent. Thus, the monopoly profits for these “new” old goods will be transferred to new monopolistic firms owned by the representative agent.Footnote ¹⁹ Consequently, in our model, all goods are monopolistically competitively produced in equilibrium, and their profits are allocated to the representative agent as dividends.

Alternatively, we could also adopt another standard setting that old goods are sold at a perfectly competitive price (e.g., Matsuyama (Reference Matsuyama1999, Reference Matsuyama2001)). However, we understand that this option would complicate the analysis without changing the results qualitatively. In addition, while the interaction between monopolistic and competitive sectors is known as a source of perpetual cycles in the literature, our analysis shows that without this source, cycles can persist on an equilibrium path owing to a novel mechanism depending on the strength of consumer love of novelty. Therefore, in this study, we ensure that the analysis is as simple as possible to highlight the insight derived from our new framework.

3.4 Labor market

As shown in (12) and (14), the real wage $w(t)/P(t)$ is a critical component of the profits. Thus, having the following is beneficial:

(20) \begin{equation} \frac{w(t)}{P(t)}=\frac{1}{\mu }\left [ A(t)+\varepsilon ^{\sigma -1}N(t)\right ] ^{\frac{1}{\sigma -1}}, \end{equation}

which uses $p(j,t)=\mu w(t)$ for any $j\in A(t)\cup N(t)$ with (8). The labor market clearing condition is

(21) \begin{equation} L=\int _{j\in A(t)\cup N(t)}x(j,t)dj+R^{N}(t)+R^{A}(t). \end{equation}

The left side in (21) denotes the labor supply, and the right side denotes the labor demand for production, new product development $R^{N}(t)$ , and existing product development $R^{A}(t)$ in each period $t.$ It is useful to derive the labor demand from the production sector as

(22) \begin{equation} \int _{j\in A(t)\cup N(t)}x(j,t)dj=\frac{1}{\mu }\frac{E(t)}{w(t)}, \end{equation}

which uses (11), (13), (20), and (21).

4. Equilibrium dynamics

In order to derive the dynamical system that characterizes the law of motion for the equilibrium trajectory of the economy, it is beneficial to define $n(t)\equiv N(t)/A(t),$ which is the ratio of new to old goods. By using the free entry conditions in (15) and (17), along with (12) and (14), we derive the following lemma.

Proof. Suppose that firms invest in new product development in equilibrium. Then, the free entry condition (15) must hold with equality (giving firms a zero net payoff). With (12), (14), (17), and (20), this equality implies $n(t)\leq \varepsilon ^{\sigma -1}/\kappa .$ Where $n(t)\lt \varepsilon ^{\sigma -1}/\kappa,$ that is, (17) holds with inequality, there is no investment in existing product development in equilibrium. Using this information, we can easily prove the first half of the lemma. An analogous proof can be applied to the second half.

Figure 2 presents the result of Lemma 1. The cutoff level of $n(t),$ $\varepsilon ^{\sigma -1}/\kappa,$ generates two regimes in the economy. The first regime corresponds to $n(t)\in (0,\varepsilon ^{\sigma -1}/\kappa ),$ which we refer to as a new product development regime. The second regime corresponds to $n(t)\in (\varepsilon ^{\sigma -1}/\kappa,\infty ),$ which we refer to as an existing product development regime. At the cutoff point, the economy includes both activities; however, we can ignore it because the point has zero measure.

Figure 2. Illustration of Lemma 1.

As shown in Lemma 1, a type of specialization occurs in this model. In reality, any economy appears to be engaged in both new and existing product development, more or less, at any point in time. We can easily eliminate this unrealistic aspect concerning specialization from the model by allowing the innovator a long-lived monopoly or simply introducing an exogenous growth factor. Either change to the baseline model could provide another interesting analysis, but the tractability of our model would cease to exist.Footnote ²⁰ Thus, we adopt the present setting for simplicity.

In each period, $t$ , the value of $n(t)$ should be given, because it is a predetermined (stock) variable. In a hypothetical situation in which $n(t)$ is taken as given, Lemma 1 implies that, for a given $n(t),$ an economy is more likely to engage in new product development if (and only if) the love of novelty, $\varepsilon,$ is stronger and/or the productivity for existing product development, $\kappa,$ is lower. This is because there is a higher relative profit for the invention of a new good, compared to the investment in existing product development, when the consumer prefers new goods to old goods more strongly (owing to larger $\varepsilon$ ) and/or the cost for investments in existing product development is higher (owing to lower $\kappa$ ). The development of technologies that earn a higher profit is encouraged in market equilibrium. For the analogous reason, an economy is more likely to engage in existing product development when $\varepsilon ^{\sigma -1}/\kappa$ is smaller, in which case there is a higher relative profit for investments in existing product development.

4.1 New product development regime

With $n(t)\lt \varepsilon ^{\sigma -1}/\kappa,$ by Lemma 1, the economy falls into the new product development regime. With (9), (15), (12), and (20), the free entry condition for invention, $W^{n}(t)=0,$ becomes:

(23) \begin{equation} N(t+1)=\frac{A(t)}{\varepsilon ^{\sigma -1}}\left [ \frac{\beta \varepsilon ^{\sigma -1}}{\mu/(\mu -1)}\frac{E(t)}{w(t)}-1\right ], \end{equation}

which uses $A(t+1)=A(t)$ (or $\rho (t+1)=0$ ). Given $A(t),$ this describes a profit-motive aspect of the inventive activity: the larger the discounted profit from selling new goods ( $(\beta \varepsilon ^{\sigma -1}(\mu -1)/\mu )E(t)/w(t)$ ), the greater the incentives for firms to invent a new good. The profit for a new good increases as the wage-adjusted expenditure $E(t)/w(t)$ increases and as the consumer’s love of novelty $\varepsilon$ increases. Additionally, when $n(t)\lt \varepsilon ^{\sigma -1}/\kappa,$ no firm has an incentive to invest in existing product development; in such a case, $R^{A}(t)=0.$ The labor market condition (21), therefore, becomes:

(24) \begin{equation} N(t+1)=A(t)\left [ L-\frac{1}{\mu }\frac{E(t)}{w(t)}\right ], \end{equation}

which uses (16) and (22). Given $A(t)$ , the greater the wage-adjusted expenditure $E(t)/w(t),$ the more resources will be devoted to production, leaving fewer resources for innovation, resulting in a smaller $N(t+1)$ .

Figure 3 depicts (23) and (24) and is labeled with $FE$ and $LE$ , respectively, which determine the equilibrium number of new goods, $N(t+1),$ and the wage-adjusted expenditure, $E(t)/w(t)$ , as a unique intersection. Given the predetermined variable, $A(t),$ new goods, $N(t+1),$ are increasing in the time preference rate $\beta,$ the labor force $L,$ and the patent breadth $\mu$ , all of which are natural effects.

Figure 3. New product development regime.

The effect of the elasticity of substitution between goods, $\sigma \geq 1,$ is more complex, and it becomes positive if the consumer has a love of novelty, that is, if $\varepsilon \gt 1.$ Because $\sigma$ determines the level of goods substitutability, a higher $\sigma$ generally results in a larger demand for a preferable good (relative to a less preferred good). Thus, with the consumer’s love of novelty ( $\varepsilon \gt 1$ ), the elasticity of substitution $\sigma$ positively affects $N(t+1)$ through an upward shift of the $FE$ curve in Figure 3, by increasing the expenditure share for a new good and thereby its profit. However, in the benchmark case of $\varepsilon =1,$ comprising neither a love or fear of novelty, the elasticity of substitution $\sigma$ has no role because all new and old goods are equally desirable for the consumer; thus, their demands/profits are also equal. When the consumer has a fear of novelty, that is, $\varepsilon \lt 1,$ the effect of $\sigma$ on $N(t+1)$ is negative because old goods are now preferable. Again, a higher substitutability $\sigma$ leads to a larger demand for a preferable good, generally. Therefore, in this fear-of-novelty case, higher $\sigma$ generates a downward shift of the $FE$ curve, by decreasing the profits for new goods (and increasing the profits for old goods).

Regarding the love of novelty $\varepsilon$ , a higher $\varepsilon$ causes an upward shift in the $FE$ curve in the standard case of $\sigma \gt 1,$ where goods are substitutes. This result is simply because the demand for a new good becomes larger if the consumer prefers new goods to old goods more strongly (higher $\varepsilon$ ). Further, the equilibrium profit for new goods, $(\beta \varepsilon ^{\sigma -1}(\mu -1)/\mu )E(t)/w(t),$ is also larger.Footnote ²¹ The upward shift of the $FE$ curve results in an increase in $N(t+1)$ in equilibrium. In the special case of $\sigma =1$ (where goods are independent goods), the love of novelty $\varepsilon$ has no role because the expenditure share for any independent good, new or old, is constant, and free from $\varepsilon .$

We can formally confirm this effect of $\varepsilon$ by solving (23) and (24):

(25) \begin{equation} N(t+1)=\Theta A(t), \end{equation}

where

(26) \begin{equation} \Theta \equiv \frac{\varepsilon ^{\sigma -1}(\mu -1)L-1/\beta }{\varepsilon ^{\sigma -1}\left ( \left ( \mu -1\right ) +1/\beta \right ) }. \end{equation}

Equation (25) determines the equilibrium amount of new goods in the new product development regime. The coefficient $\Theta$ is increasing in the love of novelty $\varepsilon $ and the standard parameters $\beta,$ $L,$ and $\mu .$ We can interpret the parameter composite $\Theta$ as the potential demand for new goods. Assuming $\Theta \gt 0,$ we exclude a trivial case where there is no invention of new goods in any situation, by imposing $\varepsilon ^{\sigma -1}\beta (\mu -1)L\gt 1,$ which provides a lower bound of $\varepsilon$ as $[1/(\beta (\mu -1)L)]^{1/(\sigma -1)}\equiv \varepsilon _{0}$ . Additionally, because $R^{A}(t)=0$ and then $\rho (t+1)=0$ in the present regime, from (18), the old goods do not increase; $A(t+1)=A(t).$ Therefore, we easily verify that if $\Theta \gt \varepsilon ^{\sigma -1}/\kappa$ holds, then $N(t+1)/A(t+1)\equiv n(t+1)\gt \varepsilon ^{\sigma -1}/\kappa$ holds, whereby the economy moves to the existing product development regime in period $t+1.$ Conversely, if $\Theta \lt \varepsilon ^{\sigma -1}/\kappa,$ $n(t+1)\lt \varepsilon ^{\sigma -1}/\kappa .$ Then, the economy is trapped in the new product development regime. In this situation, $N(t)$ and $A(t)$ are constant over time, resulting in less innovation in the sense that there is only one type of innovation—new product development, $N(t).$ Consequently, there is no long-run growth because the variety of goods, $N(t)+A(t),$ is constant over time.

Lemma 2. The economy is trapped in the new product development regime if and only if $\Theta \lt \varepsilon ^{\sigma -1}/\kappa .$

4.2 Existing product development regime

With $n(t)\gt \varepsilon ^{\sigma -1}/\kappa,$ by Lemma 1, the economy is in the existing product development regime in period $t;$ $R^{A}(t)\geq 0,$ and $R^{N}(t)=0.$ Rearranging the labor market condition (21), with (22), yields the rate of existing product development for new goods as

(27) \begin{equation} \rho (t+1)=\kappa R^{A}(t)=\kappa \left ( L-\frac{1}{\mu }\frac{E(t)}{w(t)}\right ). \end{equation}

Analogous to (24), (27) captures the trade-off on resources between the production of goods and the investment in existing product development. With (9), (14), and (17), the free entry condition $W^{a}(t)=0$ becomes

(28) \begin{equation} \rho (t+1)=\frac{\kappa \beta }{\mu/(\mu -1)}\frac{E(t)}{w(t)}-\frac{A(t)}{N(t)}, \end{equation}

which uses $N(t+1)=R^{N}(t)=0$ from (16) and $A(t+1)=A(t)+\chi (t)R^{A}(t)=A(t)+\chi (t)\rho (t+1)/\kappa$ from (18). Naturally, the rate of existing product development $\rho (t+1)$ increases with the discounted profit from producing the old good $(\beta (\mu -1)/\mu )E(t)/w(t)$ and also increases with the number of new goods $N(t)$ because R&D firms can find more inventions (i.e., opportunities for improvement). Figure 4 illustrates how $\rho (t+1)$ is determined by (27) and (28). Solving (27) and (28), we obtain:Footnote ²²

(29) \begin{equation} \rho (t+1)= \frac{1}{1+\beta \left ( \mu -1\right ) }\left ( \kappa \beta \left ( \mu -1\right ) L-\frac{A(t)}{N(t)}\right ). \end{equation}

Using (29), with (18), the growth of old goods is as follows:

Figure 4. Existing product development regime.

(30) \begin{equation} A(t+1)=\frac{\beta \left ( \mu -1\right ) }{1+\beta \left ( \mu -1\right ) }\left ( 1+\kappa L\frac{N(t)}{A(t)}\right ) A(t). \end{equation}

Lemma 3. The existing product development regime is always unstable; thus, the economy necessarily shifts to the new product development regime.

5. Role of love of novelty in innovation and long-run growth

In this section, we examine the effects of consumers’ love of novelty on innovation and growth in the long run. We follow the standard literature to assume $\sigma \gt 1$ .Footnote ²³ Lemma 2 shows that in the case with $\Theta \lt \varepsilon ^{\sigma -1}/\kappa,$ the economy is fatally caught in the trap without existing product development, in which no long-run growth is possible because new goods $N(t)\ $ and old goods $A(t)$ are constant. In such a trapped economy, the inventive potential $\Theta$ is relatively low, and the consumer’s love of novelty, $\varepsilon,$ is relatively strong. On the one hand, the new product development regime is larger owing to a high $\varepsilon$ . On the other hand, the invention flow $N(t)$ within the regime tends to be low, owing to a low $\Theta .$ These two effects are negative on innovation; therefore, the economy with $\Theta \lt \varepsilon ^{\sigma -1}/\kappa$ is trapped. To avoid traps, $\Theta \gt \varepsilon ^{\sigma -1}/\kappa$ must hold as shown in Lemma 3. As is common in the standard R&D-based growth model, traps can be avoided only if labor is sufficiently abundant.Footnote ²⁴ Specifically, we assume the following condition:

(31) \begin{equation} L\gt 2\sqrt{\frac{1}{\kappa }\left ( 1+\frac{1}{\beta \left ( \mu -1\right ) }\right ) \frac{1}{\beta \left ( \mu -1\right ) }}\equiv L_{0}. \end{equation}

Lemma 4. Under ( 31 ), there exist threshold values $\varepsilon _{+} \gt \varepsilon _{- } \gt \varepsilon _{0}$ for which

\begin{align*} \Theta \gt \varepsilon ^{\sigma - 1}/ \kappa \ \Longleftrightarrow \ \varepsilon \in (\varepsilon _{-}, \varepsilon _{+}). \end{align*}

Proof. From (26), we can show that $\Theta \gt \varepsilon ^{\sigma -1}/\kappa$ if and only if

(32) \begin{equation} F\left(\varepsilon ^{\sigma -1}\right)\equiv \frac{1}{\kappa }\left ( 1+\frac{1}{\beta \left ( \mu -1\right ) }\right ) \left ( \varepsilon ^{\sigma -1}\right ) ^{2}-L\varepsilon ^{\sigma -1}+\frac{1}{\beta \left ( \mu -1\right ) }\lt 0. \end{equation}

Because $F$ is quadratic and convex in $\varepsilon ^{\sigma -1}$ , (32) is possible only when $F(x)=0$ has two distinct real roots. The positiveness of the discriminant ensures this,

(33) \begin{equation} D\equiv L^{2}-\frac{4}{\kappa }\left ( 1+\frac{1}{\beta \left ( \mu -1\right ) }\right ) \frac{1}{\beta \left ( \mu -1\right ) }\gt 0, \end{equation}

which is equivalent to (31). Suppose that (31) holds and let the solutions to $F(x)=0$ be $\varepsilon _{-}^{\sigma -1}\lt \varepsilon _{+}^{\sigma -1}$ .Footnote ²⁵ As is easily verified, $\varepsilon _{+}^{\sigma -1}\gt 0$ holds. Because $F(0)\gt 0$ , $\varepsilon _{-}^{\sigma -1}\gt 0$ also holds. To prove that $\varepsilon _{0}^{\sigma -1}=1/(\beta (\mu -1)L)\lt \varepsilon _{-}^{\sigma -1}$ , it suffices to show that $F\left(\varepsilon _{0}^{\sigma -1}\right)\gt 0$ and $F^{\prime }\left(\varepsilon _{0}^{\sigma -1}\right)\lt 0$ . In fact,

\begin{align*} F\left(\varepsilon _{0}^{\sigma -1}\right) & =\frac{1}{\kappa }\left ( 1+\frac{1}{\beta (\mu -1)}\right ) \left ( \varepsilon _{0}^{\sigma -1}\right ) ^{2}\gt 0,\\ F^{\prime }\left(\varepsilon _{0}^{\sigma -1}\right) & =\frac{2}{\kappa }\left ( 1+\frac{1}{\beta \left ( \mu -1\right ) }\right ) \frac{1}{\beta L\left ( \mu -1\right ) }-L=\frac{1}{2L}(L_{0}^{2}-L^{2})\lt 0. \end{align*}

Because the solution set to $F(x)\lt 0$ is $(\varepsilon _{-}^{\sigma -1},\varepsilon _{+}^{\sigma -1})$ , with $\varepsilon _{0}\lt \varepsilon _{-}$ , any $\varepsilon \in (\varepsilon _{-},\varepsilon _{+})$ satisfies both $\varepsilon \gt \varepsilon _{0}$ and the no-trap condition. Conversely, any $\varepsilon \gt \varepsilon _{0}$ outside of this interval violates the no-trap condition.

Condition (31) is indispensable for our analysis. Notably, there exists an $\varepsilon \gt \varepsilon _{0}$ that satisfies the no-trap condition, $\Theta \gt \varepsilon ^{\sigma -1}/\kappa$ , if and only if (31) holds.Footnote ²⁶ Thus, in the following analysis, we assume (31) to avoid the trivial case of any economies trapped in the no-innovation situation.

Lemma 4 characterizes the parameter range in which the economy has the potential to innovate and grow in the long run. Lemma 4 also states that the role of love of novelty $\varepsilon$ in achieving $\Theta \gt \varepsilon ^{\sigma -1}/\kappa$ is ambiguous because $\Theta$ is increasing in $\varepsilon,$ which generates two opposite effects of $\varepsilon .$ On the one hand, (a) a higher $\varepsilon$ makes the invention of new goods profitable relative to the investment in existing product development. As a result of this relative profitability effect, the new product development regime $(0,\varepsilon ^{\sigma -1}/\kappa )$ will become large, whereby the economy is more likely to become trapped in the new product development regime. However, (b) a higher $\varepsilon$ also results in a larger potential demand $\Theta$ , and there are more new goods $N(t)$ to be created in the new product development regime. This leaves more incentives for firms to engage in existing product development, noting that new goods are the essential source of existing product development. With this positive indirect effect of $\varepsilon$ , the economy is more likely to jump out of the new product development region. These two opposite effects interact to create an equilibrium role for $\varepsilon .$ The following two propositions show that the role of the love of novelty $\varepsilon$ in innovation is also ambiguous.

Proof. For $\varepsilon \in (\varepsilon _{-},\varepsilon _{+}),$ because of Lemmas 2 and 4, $\Theta \gt \varepsilon ^{\sigma -1}/\kappa$ holds and the new product development regime is always explosive. Thus, any path starting from initial values lower than $\varepsilon ^{\sigma -1}/\kappa$ eventually moves toward the existing product development regime. Furthermore, because of Lemma 3, the economy will necessarily go back to some point within the new product development regime. Therefore, if $\varepsilon$ is moderate, the economy perpetually fluctuates, moving back and forth between the two regimes. In this case, innovation occurs perpetually and cyclically because both $N_{t}$ and $A_{t}$ permanently grow over time, but alternately.

Proposition 1 suggests that the love of novelty $\varepsilon$ can be a source of innovation-driven growth in the long run, because there are permanently expanding goods spaces, $N(t)$ and $A(t)$ . Innovation-driven growth occurs here because the aforementioned two opposite effects of $\varepsilon$ can be balanced well in a moderate range of $\varepsilon .$ However, if the level is extreme, the love of novelty $\varepsilon$ can be a cause of underdevelopment traps rather than the source of growth, by depressing innovation.

Proof. For $\varepsilon \notin (\varepsilon _{-},\varepsilon _{+}),$ because of Lemmas 2 and 4, $\Theta \leq \varepsilon ^{\sigma -1}/\kappa$ holds and the new product development regime is a trap. Because of Lemma 3, the existing product development regime is always explosive, and any path starting from any point in either regime is eventually trapped in the new product development regime.

Proposition 2 implies that the “fear of novelty” (Beveridge (Reference Beveridge1959), Barber (Reference Barber1961)) and “love of novelty” may both cause an economy to fall into an underdevelopment trap. It is straightforward to understand that the consumer’s fear of novelty negatively affects innovation. Intuitively, with a smaller $\varepsilon,$ the consumer has a smaller demand for new products $N(t)$ , implying smaller $N(t).$ Because new goods are the input for existing product development, a smaller $N(t)$ discourages existing product development by lowering its net benefit, which results from the aforementioned effect (b). Consequently, with a strong fear of novelty, or a very low $\varepsilon,$ the economy is more likely to be caught in the trap, in which investments in new product development occur and investments in existing product development do not occur. Because both types of innovative investments are essential, the numbers of new goods and old goods, $N(t)$ and $A(t),$ are constant over time. Thus, a very weak of love of novelty, or a strong fear of novelty, can cause the underdevelopment trap of no long-run growth. This result is consistent with the historical view in Mokyr (Reference Mokyr2000), who considers that the lack of “receptivity of a society to new technological ideas” is “an integral part of underdevelopment.” The innate fear of novelty for consumers should be an important source of the absence of receptivity.

Significantly, Proposition 2 also identifies the negative role of a too strong love of novelty. This role may seem counter-intuitive, but the mechanism is natural. Owing to effect (b), a high $\varepsilon$ encourages new product development, providing more new goods $N(t).$ It further encourages existing product development because existing product development uses new goods as input. However, owing to effect (a), $\varepsilon$ increases the relative profitability of new product development to existing product development. When $\varepsilon$ is very high, this relative profitability effect dominates the positive one to take away/remove any incentives from firms for existing product development. In this case, only new product development occurs in equilibrium. The economy is trapped again, in which $N(t)$ and $A(t)$ are constant over time. Thus, no long-run growth is observed in an economy with a too strong love of novelty.

Those two propositions identify the ambiguous role of the consumer’s love of novelty in innovation and innovation-based growth. The following theorem provides a summary:

Proof. Proven in the text by using Propositions 1 and 2.

In Theorem 1, we identify an ambiguous role of the public’s love of novelty in innovation and innovation-based economic growth. Intuitively, the love of novelty encourages the invention of new goods, but each innovation also involves investments for existing product development. Thus, innovation at the aggregate level can be maximized with a good balance between new and existing product development. This is why the role of love of novelty is ambiguous; a too weak and a too strong love of novelty depresses innovation, whereby the economy can be caught in underdevelopment traps with no long-run growth. We conclude that the love of novelty is a source of innovation-based growth but can become a cause of underdevelopment traps when it is too strong.

It is worth repeating that the key assumption generating the ambiguous role of love of novelty is the structure of an innovation market: innovation covers various activities including the creation of new goods but also the development of existing (relatively old) goods. Too strong love for new goods, as well as the same for old goods, can be harmful for innovation-driven growth because long-run innovation essentially depends on a good balance between two separate but sequential innovation activities, new and existing good development.

In summary, the theoretical analysis in this section suggests that, empirically, we should expect an inverted-U relationship between love of novelty and innovations. Besides, assuming new product development generates more original innovations than existing product development, we should also expect a positive relationship between love of novelty and original innovations. The scatter plots in Figure 1 are consistent with these predictions. Additional regression results are shown in the Appendix.

6. Quantitative analysis

In this section, we calibrate the model to aggregate US data to perform quantitative exercises. We aim to quantify the love of novelty and then simulate the transition dynamics of the economy switching between the two innovation processes, which also gives an idea concerning values of the upper/lower bounds of love of novelty, $\varepsilon .$ In calibrating the model, we normalize the labor size $L$ to be unity as is standard in the endogenous growth literature.

Now, the model features the following parameters: $\left \{ \beta,\sigma,\kappa,\mu,\varepsilon \right \}$ . We set the discount rate $\beta$ to $0.95,$ which falls in the range of conventional values.Footnote ²⁷ Then, we consider a range of values for the markup ratio $\mu \in \left \{ 1.1,1.2,1.3,\sigma/(\sigma -1) \right \}$ , which roughly cover the empirically plausible range, $1.05-1.4$ , of markups suggested in Jones and Williams (Reference Jones and Williams2000). Note that $\sigma/(\sigma -1)$ gives a theoretical upper bound of $\mu$ . Further, we set the elasticity of substitution between differentiated goods $\sigma$ to $4$ , which is the mean of estimates of substitution elasticity at the three-digit level in Broda and Weinstein (Reference Broda and Weinstein2006). Accordingly, the upper bound of $\mu$ becomes $ \sigma/(\sigma -1) = 1.33\cdots$ , which is also within the empirically plausible range. Since this value of $\sigma =4$ is calculated using data during the period from 1990 to 2001, for the rest of the parameters $\left \{ \kappa, \varepsilon \right \},$ we calibrate the model using an average of aggregate data during the same period. For each value of $\mu$ , we calibrate the values of R&D productivity $\kappa$ and love of novelty $\varepsilon$ targeting a GDP growth rate of $3.09\%$ and an R&D share in GDP of $2.54\%$ .Footnote ²⁸ We report the calibrated parameter values in Table 1.

Table 1. Calibrated parameters

Under these calibrated parameter values, for all values of markup $\mu$ , the calibrated love-of-novelty parameter, $\varepsilon,$ is larger than unity, that is, a love of novelty, not a fear of novelty. Note, however, that for the lowest markup $\mu = 1.1$ , the growth condition, $\varepsilon \in (\varepsilon _-, \varepsilon _+)$ , does not hold because (31) is violated. This indicates that the economy with lower markups tends to be trapped in underdevelopment, consistent with the usual intuition. Thus, depending on the markup, our quantitative exercise may suggest the U.S. economy in the 1990s had a love of novelty.

We also demonstrate the transitional dynamics of the economy switching between the two innovation processes, that is, new and existing product development. Figure 5 illustrates an equilibrium path of (the logarithm of) the total output (in real terms), that is, $Y^i (t) \equiv E(t)/P(t)+w (t) R^{i}(t)/ P(t) \ $ with $i=\left \{ N,A\right \} .$ Without any loss of generality, we may suppose that the initial period, $t=0,$ is a period where new product development occurs and normalize $A(0)$ to be $1$ .Footnote ²⁹

Figure 5. The dynamics of total output.

Figure 5 (a) illustrates four equilibrium paths of the total output, $Y^i (t)$ , with different levels of the love of novelty $\varepsilon$ . As shown in the figure, with either level of $\varepsilon$ , the total output fluctuates along an equilibrium path, and the growth rate trend is higher with higher $\varepsilon$ . It also suggests that the growth path becomes first less volatile and then more volatile as the love $\varepsilon$ of novelty becomes stronger, implying a nonmonotonic effect of $\varepsilon$ on volatility.

To formally identify the relationship between the love of novelty $\varepsilon$ and growth volatility, in the lower half of Figure 5(b), we illustrate the relationship between $\varepsilon$ and the three growth rates: one in the new product development (NPD) regime (the blue line, labeled as “NPD”), another in the existing product development (EPD) regime (the orange line, labeled as “EPD”), and an arithmetic mean of these two (the green line, labeled as (NPD + EPD)/2).Footnote ³⁰ As shown, as $\varepsilon$ increases, the growth rate with NPD increases; then, the growth rate with EPD first increases and then decreases, showing an inverted U-shaped relationship. Notably, these two growth rates are equated at two points, where the total output grows at a constant rate without any fluctuations (i.e., balanced growth). This further implies that the volatility is minimized at these two points; as shown in the upper half of Figure 5(b), a very strong love of novelty, $\varepsilon$ , causes higher volatility as well as higher trend growth. In summary, our numerical exercise indicates that (a) a stronger love of novelty increases the trend growth rate, but (b) a substantial increase from the benchmark level may tend to increase volatility.

To end up this section, we elaborate on an intuition behind the relationship between the love of novelty $\varepsilon$ and the growth rates. Potentially, there are four effects of a stronger love of novelty (i.e., higher $\varepsilon$ ) on growth. Higher $\varepsilon$ , at first, encourages NPD. The increased NPD investment results in two effects. On the one hand, (i) it leaves fewer labor resources for production in the NPD regime, decreasing $Y^N$ . On the other hand, (ii) it also brings about more new products in the EPD regime, which encourages production in the EPD regime and increases the output $Y^A$ . Since more new products also imply more “seeds” for EPD, (iii) it increases the EPD investment, which leaves fewer resources for production in the EPD regime and decreases $Y^A$ . Finally, (iv) the increased EPD investment leads the old goods $A(t)$ to grow faster from the EPD to NPD regime, and the NPD regime has more old goods, which encourages production in the NPD regime and increases $Y^N$ . Given that the growth rate in the NPD (EPD) regime is defined as $g^N \equiv Y^A/ Y^N -1$ ( $g^A \equiv Y^N/ Y^A -1$ ), effects (i) and (ii) affect $g^N (t)$ positively and $g^A (t)$ negatively; effects (iii) and (iv) do the opposite. Therefore, the total effects are potentially ambiguous. With our calibrated parameters, as shown in Figure 5(b), the positive effect on $g^N$ dominates; the opposite effects on $g^A$ interact with each other to create an inverted-U relationship between $\varepsilon$ and $g^A$ .

Acknowledgements

The authors thank the Co-editor (Oded Galor), an anonymous referee, Kenzo Abe, Taro Akiyama, Tomohiro Ara, Martine Carré-Tallon, Nicola Coniglio, Mario Curucini, Erkan Gören, Gene Grossman, Makoto Hanazono, Tomoya Hanibuchi, Keisaku Higashida, Takeo Hori, Mitsuhide Hoshino, Kenta Ikeuchi, Jun-ichi Itaya, Arata Ito, Takashi Kamihigashi, Yoshimasa Komoriya, Keisuke Kondo, Sung-Ho Lee, Ryo Makioka, Junya Masuda, Kiyoshi Matsubara, Koyo Miyoshi, Akira Momota, Masayuki Morikawa, Hiroshi Mukunoki, Takumi Naito, Kenta Nakamura, Masao Oda, Ryoji Ohdoi, Yuka Ohno, Masayuki Okawa, Rui Ota, Pascalis Raimondos, Yoko Sakamoto, Yoichi Sugita, Takaji Suzuki, Yasuhiro Takarada, Yasuo Takatsuki, Yoshihiro Tomaru, Yoshiaki Usui, Annalisa Vinella, Akihiko Yanase, Makoto Yano, and the conference/seminar/meeting participants at Economic Theory and Policy Workshop, Fukushima Economics Workshop 2018, Chonnam National University, Copenhagen Business School, Dosisha University (Goshokita Seminar), 2015/2017 IEFS JapanAnnual Meeting, IESEG School of Management, JapanPatent Office, Paris-Dauphine University, RIETI (Discussion Paper Seminar), Sophia University, University of Bari, University of Porto, and Yokohama National University for their helpful comments and support. Yuichi Furukawa acknowledges the partial financial support from a Research Grant Program of the Toyota Foundation as well as JSPS Grant-in-Aids for Scientific Research (#18K01522, #22K01405, #16H03612, and #20H01492). Kenji Sato acknowledges the partial financial support from JSPS (a Grant-in-Aid for JSPS Research Fellow and Grant-in-Aids #16K03552 and #19K13650).