In this section, we develop a theoretical framework on firms’ intangible investment and derive the hypotheses to be tested with firm-level data in the next section. Assume that a firm produces goods and services according to the following production function:
Y = A(IC, H, θ)F(L, K)
where Y is value added produced by the firm; H is human capital; L is labour; K is physical capital; A is total factor productivity; IC is intangible capital; and 𝜃 represents other factors determining total factor productivity. F is a continuous function of L and K with F′> 0 and F′′< 0, which reflects diminishing marginal returns of labour and capital input. Total factor productivity A is an increasing function of intangible capital, human capital and other factors, which reflects the fact that intangible capital and human capital improve the efficiency and total factor productivity of a firm. The productivity boost from intangible capital and human capital follows diminishing marginal return. That is,
∂A ∂IC > 0, ∂2A ∂2IC< 0, ∂A ∂H> 0, ∂2A ∂2H< 0 and ∂A ∂IC ∂H= ∂A ∂H ∂IC> 0.
The quality of the human resources employed by firms is a key condition both for the generation of new intangible assets and the exploitation of existing intangible assets (Abramovitz and David, 2000; Galor and Moav, 2004). Given the fact that the production of intangible capital such as R&D and organization capital requires high-
skilled workers, increases in human capital lowers the costs of investing in new intangible capital as well as the cost of using existing intangible capital.
If a firm has sufficient funds, whether it invests in intangible capital or not depends on the relative marginal return of intangible capital compared with that of tangible capital4. The marginal return from investing in intangible capital is
∂Y
∂IC= F(L, K)
∂A(IC, H, θ) ∂IC The marginal return from investing in tangible capital is
∂Y
∂K= A(IC, H, θ)F𝐾(L, K)
Then the difference in marginal return between intangible and tangible capital (DMR) is
DMR = F(L, K)∂A(IC,H,θ)
∂IC − A(IC, H, θ)FK(L, K) (1)
Higher DMR indicates that a firm is more likely to invest in intangible capital instead of tangible capital.
From equation (1), we obtain ∂DMR
∂K = FK(L, K)
∂A(IC, H, θ)
∂IC − A(IC, H, θ)FKK(L, K) > 05
Intuitively, as the tangible capital of a firm increases, the marginal return of tangible capital falls. Meanwhile, as intangible capital improves productivity, that is ∂A(IC,H,θ)
∂IC > 0, return of an additional unit of intangible capital increases as the amount of tangible capital increases. Both of these two effects cause increased DMR as tangible capital grows. As a result, higher tangible capital leads to an increase in DMR, making it more likely that the firm invests in intangibles.
4 Tangible capital is also called physical capital. 5 Noting that F
KK(L, K) <0 and A(IC, H, θ) > 0 and therefore FK(L, K)
∂A(IC,H,θ) ∂IC and
This mechanism is summarized as Hypothesis 1 below:
Hypothesis 1. A larger firm is more likely to invest in intangible capital, with firm size measured by the fixed assets (tangible capital) of the firm.
Besides firm size, human capital might also influence firms’ decisions about intangible investment. Higher human capital lowers the costs of producing new intangible capital and improves the efficiency of using existing intangible capital and therefore raises the probability of investing in intangible capital. One example that reflects such
complementarities between human capital and intangible capital is the large amount of human resources employed in direct R&D activities (Liu et al., 2000). More examples include the use of advanced software and the introduction of new management
practices, which all need to be carried out by people with high levels of education. With F(L, K) > F𝐾(L, K)6 and ∂A ∂IC ∂H> ∂A ∂H 7, we obtain ∂DMR ∂H = ∂A ∂IC ∂HF(L, K) − ∂A ∂HF𝐾(L, K) > 0
which is summarized as Hypothesis 2 below:
Hypothesis 2. A firm with more human capital is more likely to invest in intangible capital.
Institutional quality is another important factor influencing the investment in intangible
6 This is often true in this context. Use the Cobb-Douglas form production function as an example: F(L, K) = L𝛼𝐾𝛽 and F
𝐾(L, K) = βL𝛼𝐾𝛽−1. Noting that β < 1 and K > 1, so we have F(L, K) >
F𝐾(L, K).
7 This is likely to be true because this study focuses on whether a firm invests in intangible capital or not.
For those that have not invested in intangible capital yet, IC = 0 and thus ∂A
∂IC ∂H is likely to be
sufficiently large to ensure ∂A
∂IC ∂H> ∂A ∂H.
capital. The features of innovation activities as a form of risky investment make them particularly sensitive to institutional quality (Jorde and Teece, 1990). Zhou (2014) finds that low institutional quality is harmful to R&D investment, using data from Chinese firms: in an area where intellectual property is not properly protected, a firm has a higher probability of losing some of the intangible capital it produces because its designs, R&D and business secrets are more likely to be stolen, which in turn deters R&D investment. Mathematically, we add the institutional component into equation (1) by modelling it as a rate of survival, and then we have
DMR = 𝐼𝑄 × F(L, K)∂A
∂IC− A(𝐼𝐶, 𝐻, 𝜃)F𝐾(L, K)
where 𝐼𝑄 is the institutional quality, which indicates the survival rate of intangible capital vulnerable to thefts or knockoffs and enters the equation as a probability and hence a multiplicative term. Therefore, 𝐼𝑄 × F(L, K)∂A
∂IC is the expected marginal return
of intangible investment. Then we obtain
∂DMR
∂IQ = F(L, K)
∂A
∂IC > 0
which forms the basis for Hypothesis 3:
Hypothesis 3. Lower institutional quality reduces the probability of a firm investing in intangible capital vulnerable to thefts or knockoffs.
Another factor to be considered is market competition. The impact of competition on firms’ effort to innovate is not yet conclusive in the literature. Some studies have found that market competition exerts a negative effect on firms’ incentives to increase their R&D efforts (Loury, 1979; Martin, 1993), while others find that only firms with low R&D productivity tend to exhibit a lower level of R&D efforts when facing increased
market competition (Lee, 2009). A non-linear relationship (inverted U-shape relationship) is also proposed by a previous study based on UK data (Aghion et al., 2005) but a later study (Hashmi, 2013) finds the non-linear relationship non-exists in US data. While the theories of Aghion et al. (2005) and Hashmi (2013) both agree that firms are less likely to engage in innovation activities when facing a competitive market, their main difference is whether the relationship between competition and innovation within moderate to medium competition is negative or not, which needs further evidence from other economies. In China, firms facing a competitive market are likely to earn a low markup from innovating and often earn zero economic profit and hence are not able to fund investment in intangibles. In contrast, firms facing an
oligopoly market are likely to earn a high markup from innovation, and thus more likely to invest in intangibles. Firms facing a market between oligopoly and competitive might demonstrate a medium propensity to invest in intangibles. This mechanism is
summarized in Hypothesis 4.
Hypothesis 4. Firms facing a competitive market are less likely to invest in intangible capital while firms facing an oligopoly market are more likely to invest in intangible capital, compared with firms facing a market between competitive and oligopoly.