Competition, R&D and innovation: testing the inverted-U in a simultaneous system

Abstract

To address the relationship between innovation and competition we jointly estimate the opportunity, production, and impact functions of innovation in a simultaneous system. Based on Swiss micro-data, we apply a 3-SLS system estimation. The findings confirm a robust inverted-U relationship, in which a rise in the number of competitors at low levels of initial competition increases the firm’s research effort, but at a diminishing rate, and the research effort ultimately decreases at high levels of competition. When we split the sample by firm types, the inverted-U shape is steeper for creative firms than for adaptive ones. The numerical solution indicates three particular configurations of interest: (i) an uncontested monopoly with low innovation; (ii) low competition with high innovation; and (iii) a ‘no innovation trap’ at very high levels of competition. The distinction between solution (i) and (ii) corresponds to Arrow’s positive effect of competition on innovation, whereas the difference between outcomes (ii) and (iii) captures Schumpeter’s positive effect of market power on innovation. Simulating changes of the exogenous variables, technology potential, demand growth, firm size and exports have a positive impact on innovation, while foreign ownership has a negative effect, and higher appropriability has a positive impact on the number of competitors.

Appendices

Annex 1: Reduced form solution

We can also solve the system of Eqs. 1 to 3 in reduced form. For the sake of simplicity, we omit the subscripts for firms i when substituting Eq. 1 in Eq. 2:

$$I=\alpha_2 +\beta_2 \left( {\alpha_1 +\beta_1 C+\theta C^2+\gamma_1 X+\delta_1 O_j} \right)+\gamma_2 X+\delta_2 M_j $$

By substitution in Eq. 3, we get the following reduced form for the number of competitors:

$$\begin{array}{rll} C&=&\alpha_3 +\beta_3 \left[ {\alpha_2 +\beta_2 \left( {\alpha_1 +\beta _1 C+\theta C^2+\gamma_1 X+\delta_1 O_j} \right)+\gamma_2 X+\delta_2 M_j} \right]\\ &&+\gamma_3 X+\delta_3 A_j \end{array} $$

Multiplication of terms yields:

$$\begin{array}{rll} C&=&\alpha_3 +\alpha_2 \beta_3 +\alpha_1 \beta_2 \beta_3 +\beta_1\beta_2 \beta_3 C+\beta_2 \beta_3 \theta C^2+\beta_2 \beta_3 \gamma_1 X \\ &&+\beta_2 \beta_3 \delta_1 O_j +\beta_3 \gamma_2 X+\beta_3 \delta_2 M_j +\gamma_3 X+\delta_3 A_j \end{array} $$

Some rearrangement leads to the following expression of a quadratic function:

$$\begin{array}{l} \beta_2 \beta_3 \theta C^2+\left( {\beta_1 \beta_2 \beta_3 -1} \right)C+\beta_2 \beta_3 \gamma_1 X+\beta_3 \gamma_2 X+\gamma_3 X+\beta_2 \beta_3 \delta_1 O_j \\ \quad +\beta_3 \delta_2 M_j +\delta_3 A_j+\alpha_1 \beta_2 \beta_3 +\alpha _2 \beta_3 +\alpha_3 =0 \end{array} $$

We thus have a quadratic system $\alpha C^{2} + bC + c = 0$, which can be solved by

$$C_{1,2} =\frac{-b\pm \sqrt {b^2-4\alpha c}} {2\alpha} $$

for $a =\beta _{2}\beta _{3}\theta , b = (\beta _{1}\beta _{2}\beta _{3}-1)$, and $c=\alpha _1 \beta _2 \beta _3 +\alpha _2 \beta _3 +\alpha _3 +\beta _2 \beta _3 \gamma _1 X+\beta _3 \gamma _2 X+\gamma _3 X+\beta _2 \beta _3 \delta _1 O_j +\beta _3 \delta _2 M_j +\delta _3 A_j$, and provided $b^{2}-4\alpha c\ge 0$.

Substituting Eq. 2 directly into Eq. 3, we get the following expression relating research effort E to the number of competitors C:

$$\begin{array}{rll} C&=&\alpha_3 +\beta_3 \left( {\alpha_2 +\beta_2 E+\gamma_2 X+\delta_2 M_j} \right)+\gamma_3 X+\delta_3 A_j \\ C&=&\beta_2 \beta_3 E+\alpha_3 +\alpha_2 \beta_3 +\beta_3 \gamma_2 X+\gamma_3 X+\beta_3 \delta_2 M_j +\delta_3 A_j \\ \beta_2 \beta_3 E&=&C-\left( {\alpha_3 +\alpha_2 \beta_3 +\beta _3 \gamma_2 X+\gamma_3 X+\beta_3 \delta_2 M_j +\delta_3 A_j}\right)=C-Intercept\\ E&=&\frac{C-Intercept}{\beta_2 \beta_3} \end{array} $$

Annex 2: Supplementary tables

Tables 8, 9, 10 and 11

Table 8 Number of firms by industry and year

Table 9 3 SLS estimations with time-varying instruments (standard errors in brackets)

Table 10 3 SLS estimations with $\mathbf {C_i^{squared}}$ also instrumented (standard errors in brackets)

Table 11 Reduced form $\mathbf {C_i^{squared}}$ (standard errors in brackets)