Explaining the Current Innovative R&D Outsourcing to Developing Countries

Abstract

While multinational firms from developed countries have used researchers from emerging areas to assist in the adaption of an existing product, few multinational firms have carried out innovative R&D, or R&D for the creation of a new product, in these areas. Using the threat of imitation and wage differences of researchers across regions, this study proposes a partial equilibrium model to explain the lack of innovative R&D in developing countries. I build a North-South model examining a single firm’s choice of research locations. The model predicts that weak IPR-protection in developing countries does not necessarily explain the lack of Southern research. In some situations, reduced IPR-protection can even increase Southern research. Harsh competition resulting from information leaks coupled with weak IPR-protection can explain much of the lack of innovative research investment in the developing world. My model also predicts that firms with low research needs, or firms in low-tech industries, locate their R&D in the North. Firms with medium research need locate in both countries while the firms with the largest research needs, or firms in high-tech industries, locate research in just the South.

Appendices

Appendix A: Proof of Propositions and Results

1.1 A.1 Proof of Proposition 1

The second derivative of profit function (7) is equal to:

$$ \frac{\partial^{2} \pi}{\partial {R^{N}}^{2}}=\frac{-(1-\zeta) \zeta \overline{R} [\overline{\pi}-\underline{\pi}] }{(R^{N}(1-\zeta)+\zeta\overline{R})^{3}} <0 $$

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Since 1 > ζ > 0, $[\overline {\pi }-\underline {\pi }]$, and R^N > 0, it must be the case that $\frac {\partial ^{2} \pi }{\partial {R^{N}}^{2}}<0$. Therefore, the profit function (7) is concave.

1.2 A.2 Proof of Result 1

Result 1 presents the assumption values for Cases 1, 2, and 3. In Case 1, the Northern firm locates entirely in the North. Using Eq. 8, the Northern firm sets $R^{N}=\overline {R}$ when ${R^{N}}^{*} \geq \overline {R}$:

$$\begin{array}{@{}rcl@{}} \left( \frac{1}{1-\zeta}\right)\left( \frac{[\overline{\pi}-\underline{\pi}]\zeta\overline{R}}{w^{N}-w^{S}}\right)^{\frac{1}{2}}-\left( \frac{\zeta}{1-\zeta}\right)\overline{R} & \geq& \overline{R} \\ \left( \frac{1}{1-\zeta}\right)\left( \frac{[\overline{\pi}-\underline{\pi}]\zeta\overline{R}}{w^{N}-w^{S}}\right)^{\frac{1}{2}} &\geq& \overline{R}+ \left( \frac{\zeta}{1-\zeta}\right)\overline{R} \\ \left( \frac{1}{1-\zeta}\right)\left( \frac{[\overline{\pi}-\underline{\pi}]\zeta\overline{R}}{w^{N}-w^{S}}\right)^{\frac{1}{2}} &\geq& \left( \frac{1}{1-\zeta}\right)\overline{R} \\ \left( \frac{[\overline{\pi}-\underline{\pi}]\zeta}{w^{N}-w^{S}}\right) &\geq& \overline{R} \\ \end{array} $$

Thus, in Case 1, $\left (\frac {[\overline {\pi }-\underline {\pi }]\zeta }{w^{N}-w^{S}}\right ) \geq \overline {R}$ must be true. For Case 2, the Northern firm is at an interior condition. Using Eq. 8, the Northern firm sets R^N = R^N∗ when $0 < {R^{N}}^{*} < \overline {R}$:

$$\begin{array}{@{}rcl@{}} 0&<& \left( \frac{1}{1-\zeta}\right)\left( \frac{[\overline{\pi}-\underline{\pi}]\zeta\overline{R}}{w^{N}-w^{S}}\right)^{\frac{1}{2}}-\left( \frac{\zeta}{1-\zeta}\right)\overline{R} < \overline{R} \\ \left( \frac{\zeta}{1-\zeta}\right)\overline{R} &<& \left( \frac{1}{1-\zeta}\right)\left( \frac{[\overline{\pi}-\underline{\pi}]\zeta\overline{R}}{w^{N}-w^{S}}\right)^{\frac{1}{2}} < \overline{R}+ \left( \frac{\zeta}{1-\zeta}\right)\overline{R} \\ \left( \frac{\zeta}{1-\zeta}\right)\overline{R} &<& \left( \frac{1}{1-\zeta}\right)\left( \frac{[\overline{\pi}-\underline{\pi}]\zeta\overline{R}}{w^{N}-w^{S}}\right)^{\frac{1}{2}} < \left( \frac{1}{1-\zeta}\right)\overline{R}\\ \zeta &<& \left( \frac{[\overline{\pi}-\underline{\pi}]\zeta}{(w^{N}-w^{S})\overline{R} }\right)^{\frac{1}{2}} < 1\\ \end{array} $$

$$\begin{array}{@{}rcl@{}} \zeta^{\frac{1}{2}} &<& \left( \frac{[\overline{\pi}-\underline{\pi}]}{(w^{N}-w^{S})\overline{R} }\right)^{\frac{1}{2}} < \zeta^{\frac{-1}{2}} \\ \zeta^{\frac{1}{2}} \left( \frac{[\overline{\pi}-\underline{\pi}]}{(w^{N}-w^{S}) }\right)^{\frac{-1}{2}} < (\overline{R} )^{\frac{-1}{2}} &<& \zeta^{\frac{-1}{2}} \left( \frac{[\overline{\pi}-\underline{\pi}]}{(w^{N}-w^{S}) }\right)^{\frac{-1}{2}} \\ \frac{\zeta [\overline{\pi}-\underline{\pi}]}{(w^{N}-w^{S})}&<&\overline{R}<\frac{[\overline{\pi}-\underline{\pi}]}{\zeta (w^{N}-w^{S})} \end{array} $$

Therefore, the condition needed for an interior solution is, or for a Northern firm in Case 2:

$$ \frac{\zeta [\overline{\pi}-\underline{\pi}]}{(w^{N}-w^{S})}<\overline{R}<\frac{[\overline{\pi}-\underline{\pi}]}{\zeta (w^{N}-w^{S})} $$

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Using Eq. 8, the Northern firm sets R^N = 0 when R^N∗≤ 0:

$$\begin{array}{@{}rcl@{}} 0 &\leq& \left( \frac{1}{1-\zeta}\right)\left( \frac{[\overline{\pi}-\underline{\pi}]\zeta\overline{R}}{w^{N}-w^{S}}\right)^{\frac{1}{2}}-\left( \frac{\zeta}{1-\zeta}\right)\overline{R} \\ \left( \frac{\zeta}{1-\zeta}\right)\overline{R} &\leq& \left( \frac{1}{1-\zeta}\right)\left( \frac{[\overline{\pi}-\underline{\pi}]\zeta\overline{R}}{w^{N}-w^{S}}\right)^{\frac{1}{2}}\\ (\zeta \overline{R})^{\frac{1}{2}} &\leq& \left( \frac{[\overline{\pi}-\underline{\pi} ] }{w^{N}-w^{S}}\right)^{\frac{1}{2}}\\ \overline{R} &\leq& \left( \frac{[\overline{\pi}-\underline{\pi} ] }{\zeta(w^{N}-w^{S})}\right)^{\frac{1}{2}}\\ \end{array} $$

Thus, in Case 3, $\overline {R} \leq \left (\frac {[\overline {\pi }-\underline {\pi } ] }{\zeta (w^{N}-w^{S})}\right )^{\frac {1}{2}}$ must be true.

1.3 A.3 Proof of Result 2

The Northern firm in Case 2 is the only type of firm to be affected by IPR changes. Taking the derivative of Eq. 8 wrt ζ for a Northern firm in Case 2 yields:

$$\begin{array}{@{}rcl@{}} {} \frac{\partial R^{N}}{\partial \zeta}&=&\left( \frac{[\overline{\pi}-\underline{\pi}]}{\overline{R}(w^{N}-w^{S})} \right)^{\frac{1}{2}} \left( \frac{1}{1-\zeta} \right) \left( \frac{\zeta^{\frac{1}{2}}}{1-\zeta} + \frac{1}{2\zeta^{\frac{1}{2}}} \right) - \left( \frac{1}{1-\zeta} \right) \left( 1+\frac{\zeta}{1-\zeta} \right) \\ && \frac{\partial R^{N}}{\partial \zeta}=\left( \frac{[\overline{\pi}-\underline{\pi}]}{\overline{R}(w^{N}-w^{S})} \right)^{\frac{1}{2}} \left( \frac{1+\zeta} {(1-\zeta)2\zeta^{\frac{1}{2}}} \right) - \left( \frac{1}{1-\zeta} \right) \end{array} $$

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For the Northern firm to increase Northern research in the face of weaker IPR-protection, or $\frac {\partial R^{N}}{\partial \zeta }>0$, the following must be true:

$$\begin{array}{@{}rcl@{}} {}\frac{\partial R^{N}}{\partial \zeta}>0 \ \ \ \ \\ \left( \frac{[\overline{\pi}-\underline{\pi}]}{\overline{R}(w^{N}-w^{S})} \right)^{\frac{1}{2}} \left( \frac{1+\zeta} {(1-\zeta)2\zeta^{\frac{1}{2}}} \right)&>\left( \frac{1}{1-\zeta} \right) \\ \left( \frac{[\overline{\pi}-\underline{\pi}]}{\overline{R}(w^{N}-w^{S})} \right)^{\frac{1}{2}} >&\frac{2}{1+\zeta} \\ \left( \frac{[\overline{\pi}-\underline{\pi}]}{\zeta(w^{N}-w^{S})} \right) \left( \frac{1+\zeta}{2}\right)^{2} >& \overline{R} \end{array} $$

So, for a firm with a value of total research that is smaller than $\frac {[\overline {\pi }-\underline {\pi }]}{\zeta (w^{N}-w^{S})}\left (\frac {1+\zeta }{2}\right )^{2}$, weakening of IPR-protection results in more northern research. Since ζ is less than one, it is not difficult to see that:

$$\begin{array}{@{}rcl@{}} {} \frac{\zeta[\overline{\pi}-\underline{\pi}]}{(w^{N}-w^{S})}<\frac{[\overline{\pi}-\underline{\pi}]}{\zeta(w^{N}-w^{S})} \left( \frac{1+\zeta}{2}\right)^{2} <\frac{[\overline{\pi}-\underline{\pi}]}{\zeta(w^{N}-w^{S})} \end{array} $$

Therefore, when the Northern firm locates in both countries, its reaction to IPR reform will be ambiguous. Low-tech firms in Case 2 will increase the amount of Northern research when IPR-protection weakens, while the high-tech firms will react by lowering the amount of Northern researchers.

1.4 A.4 Proof of Result 3

Taking the derivative of Eq. 8 wrt $[\overline {\pi }-\underline {\pi }]$ for a Northern firm in Case 2 yields:

$$ \frac{\partial R^{N}}{\partial [\overline{\pi}-\underline{\pi}] }=\left( \frac{1}{2} \right) \left( \frac{1}{1-\zeta} \right) \left( \frac{\overline{R} \zeta }{ [\overline{\pi}-\underline{\pi}] (w^{N}-w^{S})} \right)^{\frac{1}{2}} >0 $$

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So, the amount of Northern researchers employed by the Northern firm in Case 1 and 3, the Northern firm’s choice in Northern researchers does not change as the penalty of imitation changes.

1.5 A.5 Proof of Result 4

Taking the derivative of Eq. 8 wrt (w^N − w^S) for a Northern firm in Case 2 yields:

$$ \frac{\partial R^{N}}{\partial (w^{N}-w^{S})}=\left( \frac{-1}{2} \right) \left( \frac{1}{1-\zeta} \right) \left( \frac{\overline{R} [\overline{\pi}-\underline{\pi}] \zeta }{ (w^{N}-w^{S})^{2}} \right)^{\frac{1}{2}} <0 $$

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In Case 1 and 3, the Northern firm’s choice in Northern researchers does not change as the difference in wages changes while holding the penalty of imitation constant.

Appendix B: Additions to the Model

2.1 B.1 Including 𝜃 as an IPR-Protection Parameter

Let 0 < 𝜃 < 1. This yields a new expected profit function:

$$\begin{array}{@{}rcl@{}} {} E(\pi)&=&\frac{R^{N}+\zeta R^{S}(1-\theta)}{R^{N}+\zeta R^{S}} \overline{\pi}- \frac{\zeta\theta R^{S}}{R^{N}+\zeta R^{S}} \underline{\pi}-w^{N}(R^{N})-w^{S}(R^{S}) \\ &=&\left( \frac{R^{N}+\zeta R^{S}(1-\theta)}{R^{N}+\zeta R^{S}} \right)[\overline{\pi}-\underline{\pi}]+\underline{\pi}-w^{N}(R^{N})-w^{S}(\overline{R}-R^{N}) \end{array} $$

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Maximizing equation (18) by choosing R^N yields:

$$ R^{N}=\left( \frac{1}{1-\zeta}\right)\left( \frac{\theta[\overline{\pi}-\underline{\pi}]\zeta\overline{R}}{w^{N}-w^{S}}\right)^{\frac{1}{2}}-\left( \frac{\zeta}{1-\zeta}\right)\overline{R} $$

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While 𝜃 does decrease the value R^N at any given $\overline {R}$, the inclusion of the IPR-protection parameter does not affect the directional response of R^N to any other given parameter; however, with 0 < 𝜃 < 1, the magnitude of any comparative statics will change. Since 𝜃 enters equation (19) in only one place, the parameter can be absorbed into the penalty of imitation variable. So, the inclusion of the variable will be akin to lowering the penalty of imitation. Results 3 and 4 remain unchanged then. This can be seen by reworking Appendix A using Eq. 19. Result 1 slightly changes; however, the general result does not change. That is, Northern firms with small research needs still locate research in the North while Northern firms with large research needs locate all research in the North. Firms with medium research needs locate in both countries. Result 1 can then be rewritten:

Result 1

Low values of total research, $\overline {R}\leq \frac {\zeta \theta [\overline {\pi }-\underline {\pi }]}{(w^{N}-w^{S})}$ , induce the Northern firm to locate all research in the North (Case 1). Large values of total research, specifically $\overline {R}\geq \frac { \theta [\overline {\pi }-\underline {\pi }]}{\zeta (w^{N}-w^{S})}$ , induce the Northern firm to locate research only in the South (Case 3). The Northern firm locates in both countries (Case 2) for medium values of research, $\frac {\zeta \theta [\overline {\pi }-\underline {\pi }]}{ (w^{N}-w^{S})}<\overline {R}<\frac { \theta [\overline {\pi }-\underline {\pi }]}{\zeta (w^{N}-w^{S})}$ .

Result 2 also changes in specific values; however, the general result does not change. Reworking Appendix A.3 yields:

Result 2

Weakening Southern IPR-protection has an ambiguous effect on R ^N and R ^S . Specifically, a weakening of Southern IPR-protection, or increasing ζ , decreases R ^N iff $\left (\frac {1+\zeta }{2}\right )^{2}\frac {\theta [\overline {\pi }-\underline {\pi }]}{\zeta (w^{N}-w^{S})}<\overline {R}<\frac { \theta [\overline {\pi }-\underline {\pi }]}{\zeta (w^{N}-w^{S})}$ . Otherwise, $\frac {\partial R^{N}}{\partial \zeta }\geq 0$ and $\frac {\partial R^{S}}{\partial \zeta }\leq 0$ .

2.2 B.2 Including a Probability of Failure to Create the New Product

First, I assume that the innovation may not succeed even after the total amount of research requirement has been met. That is, the creating of one new unit of knowledge, or Y = 1, yields a successful innovation at a probability 1 − y₀. The new expected profit function can be determined:

$$ E(\pi)=y_{0} \left[ (1-\phi)\overline{\pi}+\phi\underline{\pi}\right]-f_{e} $$

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where y₀ is less than 1. Expected profit function (7) can then be rewritten as:

$$\begin{array}{@{}rcl@{}} {} E(\pi)&=&y_{0}\frac{R^{N}}{R^{N}+\zeta R^{S}} \overline{\pi}- y_{0}\frac{\zeta R^{S}}{R^{N}+\zeta R^{S}} \underline{\pi}-w^{N}(R^{N})-w^{S}(R^{S}) \\ &=&y_{0}\left( \frac{R^{N}+\zeta }{R^{N}+\zeta R^{S}} \right)[\overline{\pi}-\underline{\pi}]+y_{0}\underline{\pi}-w^{N}(R^{N})-w^{S}(\overline{R}-R^{N}) \end{array} $$

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Maximizing Eq. 21 by choosing R^N yields:

$$ R^{N}=\left( \frac{1}{1-\zeta}\right)\left( \frac{y_{0}[\overline{\pi}-\underline{\pi}]\zeta\overline{R}}{w^{N}-w^{S}}\right)^{\frac{1}{2}}-\left( \frac{\zeta}{1-\zeta}\right)\overline{R} $$

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Again, y₀ does decrease the value R^N at any given $\overline {R}$, but the overall results are not affected greatly. In fact, the inclusion of y₀ changes the model in the exact way that inclusion of 𝜃 in the previous subsection. Since y₀ enters Eq. 22 in only one place, the parameter can be absorbed into the penalty of imitation variable. So, the inclusion of the variable will be akin to lowering the penalty of imitation. Results 3 and 4 remain unchanged then. Result 1 changes:

Result 1

Low values of total research, $\overline {R}\leq \frac {\zeta y_{0}[\overline {\pi }-\underline {\pi }]}{(w^{N}-w^{S})}$ , induce the Northern firm to locate all research in the North (Case 1). Large values of total research, specifically $\overline {R}\geq \frac { y_{0} [\overline {\pi }-\underline {\pi }]}{\zeta (w^{N}-w^{S})}$ , induce the Northern firm to locate research only in the South (Case 3). The Northern firm locates in both countries (Case 2) for medium values of research, $\frac {\zeta y_{0} [\overline {\pi }-\underline {\pi }]}{ (w^{N}-w^{S})}<\overline {R}<\frac { y_{0} [\overline {\pi }-\underline {\pi }]}{\zeta (w^{N}-w^{S})}$ .

Result 2 also changes in specific values; however, the general result does not change.

Result 2

Weakening Southern IPR-protection has an ambiguous effect on R ^N and R ^S . Specifically, a weakening of Southern IPR-protection, or increasing ζ , decreases R ^N iff $\left (\frac {1+\zeta }{2}\right )^{2}\frac {y_{0} [\overline {\pi }-\underline {\pi }]}{\zeta (w^{N}-w^{S})}<\overline {R}<\frac { y_{0} [\overline {\pi }-\underline {\pi }]}{\zeta (w^{N}-w^{S})}$ . Otherwise, $\frac {\partial R^{N}}{\partial \zeta }\geq 0$ and $\frac {\partial R^{S}}{\partial \zeta }\leq 0$ .

2.3 B.3 Including Productivity Differences as an IPR-Protection Parameter

Suppose that Northern researchers are more effective than Southern researchers. So, $\overline {R}=R^{N}+dR^{S}$, where 1 > d > 0. The profit function (7) can then be written as:

$$\begin{array}{@{}rcl@{}} {} E(\pi)&=&\frac{R^{N}}{R^{N}+\zeta R^{S}}\overline{\pi}-\frac{\zeta R^{S}}{R^{N}+\zeta R^{S}}\underline{\pi}-w^{N}R^{N}-w^{S}R^{S} \\ &=&\left( \frac{R^{N}}{R^{N}(1-\frac{\zeta}{d} )+\frac{\zeta}{d} \overline{R}}\right)[\overline{\pi}-\underline{\pi}]+\underline{\pi}-w^{N}R^{N}-\frac{w^{S}}{d}*(\overline{R}-R^{N}) \end{array} $$

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Taking the new FOC yields:

$$ {R^{N}}^{*}=\left( \frac{1}{1-\frac{\zeta}{d} }\right)\left( \frac{ [\overline{\pi}-\underline{\pi}]\frac{\zeta}{d} \overline{R}}{w^{N}-\frac{w^{S}}{d} }\right)^{\frac{1}{2}}-\left( \frac{\frac{\zeta}{d} }{1-\frac{\zeta}{d} }\right)\overline{R} $$

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The inclusion of the d scales both the IPR-protection parameter ζ and the Southern wage. This does not affect the directional response of R^N to any other given parameter. Reworking Appendix A using Eq. 24 shows that Results 3 and 4 are unchanged by allowing the productivities of Northern and Southern workers to differ. Result 1 slightly changes; however, the general result does not change. Result 1 can then be rewritten:

Result 1

Low values of total research, $\overline {R}\leq \frac {\frac {\zeta }{d} [\overline {\pi }-\underline {\pi }]}{(w^{N}-\frac {w^{S}}{d})}$ , induce the Northern firm to locate all research in the North (Case 1). Large values of total research, specifically $\overline {R}\geq \frac { [\overline {\pi }-\underline {\pi }]}{\frac {\zeta }{d} (w^{N}-\frac {w^{S}}{d})}$ , induce the Northern firm to locate research only in the South (Case 3). The Northern firm locates in both countries (Case 2) for medium values of research, $\frac {\frac {\zeta }{d} [\overline {\pi }-\underline {\pi }]}{ (w^{N}-\frac {w^{S}}{d})}<\overline {R}<\frac { [\overline {\pi }-\underline {\pi }]}{\frac {\zeta }{d}(w^{N}-\frac {w^{S}}{d})}$ .

Result 2 also changes in specific values; however, the general result does not change. Reworking Appendix A.3 yields:

Result 2

Weakening Southern IPR-protection has an ambiguous effect on R ^N and R ^S . Specifically, a weakening of Southern IPR-protection, or increasing ζ , decreases R ^N iff $\left (\frac {1+\frac {\zeta }{d}}{2}\right )^{2}\frac { d[\overline {\pi }-\underline {\pi }]}{\zeta (w^{N}-\frac {w^{S}}{d})}<\overline {R}<\frac { [\overline {\pi }-\underline {\pi }]}{\frac {\zeta }{d}(w^{N}-\frac {w^{S}}{d})}$ . Otherwise, $\frac {\partial R^{N}}{\partial \zeta }\geq 0$ and $\frac {\partial R^{S}}{\partial \zeta }\leq 0$ .