Subsidizing Away Exports? A Note on R&D-policy Towards Multinational Firms

Abstract

In this paper, I investigate whether instead of strengthening home-based production, government R&D-subsidies can induce R&D-intensive firms to locate production abroad. Investigating firm-level data on Swedish MNEs, however, I find no evidence of such relocation. R&D subsidies rather tend to encourage export production at the expense of foreign production. The theory presented suggests that this is consistent with technology transfer costs, which outweigh trade costs for physical goods.

Appendix

First, the statements in Lemmas 1 and 2 are proved, then Table 3 is derived. A simulation of the model is also provided. Finally, second-order conditions are shown.

A.1 Proof of Lemmas 1 and 2

In Table 7, I provide most expressions needed for this appendix. These can be derived noting that Π _h from Table 2 can be written as follows:

$$ \Pi _{E}=\frac{1}{2s}\frac{\left( s\left( A-t\right) +\sigma \frac{\eta }{ \theta }\right) ^{2}}{2-\eta }+\frac{\sigma ^{2}}{2\gamma },\ \text{\ \ \ \ \ \ }\Pi _{A}=\frac{1}{2s}\frac{\left( sA+\sigma \frac{\eta }{\tau \theta } \right) ^{2}}{2-\frac{\eta }{\tau }}-G+\frac{\sigma ^{2}}{2\gamma \tau }. $$

(17)

The first entries in the first row in Table 7 proves Lemma 1. To prove Lemma 2, define the difference in variable profits as $\triangle \Pi =\Pi _{E}-\Pi _{A}$. It is easily seen that τ = ∞ (infinite transfer costs) implies $\tfrac{\partial \triangle \Pi }{\partial \eta }>0$, whereas τ = 1 (no transfer costs) implies $\tfrac{\partial \triangle \Pi }{\partial \eta }<0.$ It follows that $\tfrac{\partial \triangle \Pi }{\partial \eta }$ must be monotonically increasing in τ. Then, define τ ^∗ such that $\tfrac{\partial \triangle \Pi ((\tau ^{\ast },\mathbf{z})}{ \partial \eta }=0$. Hence, if there is a η = η ^∗ such that $\triangle \Pi (\eta ^{\ast },\mathbf{z})=0\Leftrightarrow \Pi _{E}\left( \eta ^{\ast },\mathbf{z}\right) =\Pi _{A}\left( \eta ^{\ast },\mathbf{z} \right) ,$ where z is the vector of exogenous variables, it follows that Π _E  < Π _A for η > η ^∗ and τ < τ ^∗, whereas Π _E  > Π _A for η > η ^∗ and τ > τ ^∗.

Table 7 Comparative statics

A.2 Proof of Proposition 3

I show only the proof for a small subsidy. Below, I provide a simulation illustrating that results also extend beyond infinitesimal subsidies.

Using the equality $\Pi _{E}\left( \eta ^{\ast },\mathbf{z}\right) =\Pi _{A}\left( \eta ^{\ast },\mathbf{z}\right)$, implicit differentiation yields:

$$ \frac{d\eta ^{\ast }}{dz}=-\frac{\frac{\partial \left( \Pi _{E}-\Pi _{A}\right) }{\partial z}}{\frac{\partial \left( \Pi _{E}-\Pi _{A}\right) }{ \partial \eta }}=-\frac{\frac{\partial \Delta \Pi }{\partial z}}{\frac{ \partial \Delta \Pi }{\partial \eta }}, $$

(18)

where Eq. 18 is used to determine the signs in Table 3. Inserting the appropriate expressions from Table 7 in Eq. 18 yields these signs. Inspecting Table 7, it can be shown that there exists a $\hat{\tau}$, such that $\tau > \hat{\tau}$ implies $\tfrac{\partial \left( \Pi _{E}-\Pi _{A}\right) }{ \partial \sigma }>0$, a $\tilde{\tau}$ such that $\tau >\tilde{\tau}$ implies $\tfrac{\partial \left( \Pi _{E}-\Pi _{A}\right) }{\partial \eta }>0$ and that $\hat{\tau}>\tilde{\tau}>0$ holds. Setting $\tau ^{\ast }=\hat{\tau}$ completes the proof of Proposition 3.

A.2.1 A simulation with non-infinitesimal R&D-subsidies

Here, I present a simulation showing that the results also extend into subsidies which are not infinitesimal. Figure 1 shows how large the trade cost must be for the firm to be indifferent between affiliate- and export production. More formally, I define this critical trade cost, t ^∗, where $\Pi _{E}\left( t^{\ast },\mathbf{z}\right) =\Pi _{A}\left( t^{\ast },\mathbf{z}\right)$. In Fig. 1, t ^∗, is plotted against the transfer cost, τ, and the return to R&D, η. Other parameter values are A = s = 5, σ = 0.5, θ = 0.2 and G = 1. Figure 1 is easily interpreted: If trade costs are above the surface t ^∗, “tariff-jumping” occurs and the firm chooses FDI. Conversely, if trade cost are below t ^∗, export production takes place. Note that when transfer costs τ are high (low) and the return to R&D η is high, exports (FDI) are chosen, as predicted by the theory in Section 2.

Fig. 1

Trade costs t ^∗ at which the firm is indifferent between affiliate- and export production. A = s = 5, σ = 0.5, θ = 0.2 and G = 1

In Fig. 2, I make the following experiment. Suppose that the R&D subsidy is originally set at σ = 0.5, generating the critical trade cost $\left. t^{\ast }(\tau ,\eta )\right\vert _{\sigma ={\kern.8pt} 0.5}$ shown in Fig. 1, where once more t ^∗ is level of the trade cost such that the firm is indifferent between the two location strategies. Figure 2 then shows the effect on the location decision of an increase in the R&D subsidy from σ = 0.5 to σ = 3. Calculating $\left. t^{\ast }(\tau ,\eta )\right\vert _{\sigma =3}$, it follows that the firm chooses affiliate production whenever $\left. t^{\ast }(\tau ,\eta )\right\vert _{\sigma =3}<\left. t^{\ast }(\tau ,\eta )\right\vert _{\sigma =0.5}$ and export production, whenever the opposite holds. As predicted from the theory, it can be seen that when transfer costs are absent or low, FDI is chosen. However, once the return to R&D η is sufficiently increased for positive transfer costs, exports are preferred. This is also the case for higher transfer costs, irrespective of the return to R&D.

Fig. 2

The effect on the firm’s location decision of an increase in the subsidy from σ = 0.5 to σ = 3. Other parameters at A = s = 5, θ = 0.2 and G = 1

A.3 Appendix: second-order conditions

In this appendix, we check the firm’s second-order conditions for the maximization of Π _h . For having a well-posed maximization problem, the Hessian, defined in (19), must be negative definite:

$$ Q_{h}=\left[ \begin{array}{ll} \Pi _{h,q_{h},q_{h}} & \Pi _{h,q_{h},x_{h}} \\ \Pi _{h,x_{h},q_{h}} & \Pi _{h,x_{h},x_{h}} \end{array} \right] , \label{A3} $$

(19)

where, for example, $\Pi _{h,q_{h},x_{h}}=\frac{\partial ^{2}\Pi _{h}}{ \partial q_{h}\partial x_{h}}$. This, in turn, requires that $\left\vert Q_{h}\right\vert >0,\Pi _{h,q_{h},q_{h}}<0$ and $\Pi _{h,x_{h},x_{h}}<0$. I can show that this will hold if $\frac{\eta }{\tau }<2$, since:

$$ \begin{array}{rcl} \left| Q_{E}\right| &=&\frac{\gamma }{s}(2-\eta ), \Pi_{E,q_{E},q_{E}}=- \frac{2}{s}<0, \Pi _{E,x_{E},x_{E}}=-\gamma <0\\ \left\vert Q_{A}\right\vert &=&\frac{\gamma }{s}(2\tau -\eta ), \Pi _{A,q_{A},q_{A}}=-\frac{2}{s}<0, \Pi _{A,x_{A},x_{A}}=-\frac{\gamma }{\tau }<0. \end{array} $$